SPA for quantitative analysis: Lecture 6 Modelling Biological Processes
|
|
- Dina Bryant
- 5 years ago
- Views:
Transcription
1 1/ 223 SPA for quantitative analysis: Lecture 6 Modelling Biological Processes Jane Hillston LFCS, School of Informatics The University of Edinburgh Scotland 7th March 2013
2 Outline 2/ Introduction Some Biological Background 2 Process Calculi for Systems Biology 3 Bio-PEPA: Syntax 4 Formal Semantics 5 Bio-PEPA Analysis 6 Formal Mappings 7 Example
3 Introduction 3/ 223 Outline 1 Introduction Some Biological Background 2 Process Calculi for Systems Biology 3 Bio-PEPA: Syntax 4 Formal Semantics 5 Bio-PEPA Analysis 6 Formal Mappings 7 Example
4 Introduction 4/ 223 Systems Biology Biological advances mean that much more is now known about the components of cells and the interactions between them. Systems biology aims to develop a better understanding of the processes involved. Formalisms from theoretical computer science have found a new role in developing models for systems biology, allowing biologists to test hypotheses and prioritise experiments.
5 Introduction 5/ 223 Systems Biology Biological advances mean that much more is now known about the components of cells and the interactions between them. Systems biology aims to develop a better understanding of the processes involved. Formalisms from theoretical computer science have found a new role in developing models for systems biology, allowing biologists to test hypotheses and prioritise experiments.
6 Introduction 6/ 223 Systems Biology Biological advances mean that much more is now known about the components of cells and the interactions between them. Systems biology aims to develop a better understanding of the processes involved. Formalisms from theoretical computer science have found a new role in developing models for systems biology, allowing biologists to test hypotheses and prioritise experiments.
7 Introduction 7/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
8 Introduction 8/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
9 Introduction 9/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
10 Introduction 10/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
11 Introduction 11/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
12 Introduction 12/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
13 Introduction 13/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
14 Introduction 14/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
15 Introduction 15/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
16 Introduction 16/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
17 Introduction 17/ 223 Systems Biology Methodology Natural System Measurement Observation Biological Phenomena Explanation Interpretation Induction Modelling Systems Analysis Deduction Inference Formal System
18 Introduction Some Biological Background 18/ 223 Networks in cells We can distinguish three distinct types of links or networks in cells Gene networks: Genes control the production of proteins but are themselves regulated by the same or different proteins. Signal transduction networks: External stimuli initiate messages that are carried through a cell via a cascade of biochemical reactions. Metabolic pathways: The survival of the cell depends on its ability to transform nutrients into energy.
19 Introduction Some Biological Background 19/ 223 Networks in cells We can distinguish three distinct types of links or networks in cells Gene networks: Genes control the production of proteins but are themselves regulated by the same or different proteins. Signal transduction networks: External stimuli initiate messages that are carried through a cell via a cascade of biochemical reactions. Metabolic pathways: The survival of the cell depends on its ability to transform nutrients into energy.
20 Introduction Some Biological Background 20/ 223 Networks in cells We can distinguish three distinct types of links or networks in cells Gene networks: Genes control the production of proteins but are themselves regulated by the same or different proteins. Signal transduction networks: External stimuli initiate messages that are carried through a cell via a cascade of biochemical reactions. Metabolic pathways: The survival of the cell depends on its ability to transform nutrients into energy.
21 Introduction Some Biological Background 21/ 223 Networks in cells We can distinguish three distinct types of links or networks in cells Gene networks: Genes control the production of proteins but are themselves regulated by the same or different proteins. Signal transduction networks: External stimuli initiate messages that are carried through a cell via a cascade of biochemical reactions. Metabolic pathways: The survival of the cell depends on its ability to transform nutrients into energy.
22 Introduction Some Biological Background 22/ 223 Extracellular signalling Extracellular signalling communication between cells. Signalling molecules released by one cell migrate to another; These molecules enter the cell and instigate a pathway, or series of reactions, which carries the information from the membrane to the nucleus; For example, the Ras/Raf-1/MEK/ERK pathway conveys differentiation signals to the nucleus of a cell. Signal Raf MEK ERK Activated ERK enters nucleus Specific gene activation cellular response to signal
23 Introduction Some Biological Background 23/ 223 Cell signalling All signalling is biochemical: Increasing protein concentration broadcasts the information about an event; for example, that a gene promoter is on. The message is received by a concentration dependent response at the protein signal s site of action. This stimulates a response at the signalling protein s site of action. Signals propagate through a series of protein accumulations.
24 Introduction Some Biological Background 24/ 223 Cell signalling All signalling is biochemical: Increasing protein concentration broadcasts the information about an event; for example, that a gene promoter is on. The message is received by a concentration dependent response at the protein signal s site of action. This stimulates a response at the signalling protein s site of action. Signals propagate through a series of protein accumulations.
25 Introduction Some Biological Background 25/ 223 Cell signalling All signalling is biochemical: Increasing protein concentration broadcasts the information about an event; for example, that a gene promoter is on. The message is received by a concentration dependent response at the protein signal s site of action. This stimulates a response at the signalling protein s site of action. Signals propagate through a series of protein accumulations.
26 Introduction Some Biological Background 26/ 223 Cell signalling All signalling is biochemical: Increasing protein concentration broadcasts the information about an event; for example, that a gene promoter is on. The message is received by a concentration dependent response at the protein signal s site of action. This stimulates a response at the signalling protein s site of action. Signals propagate through a series of protein accumulations.
27 Introduction Some Biological Background 27/ 223 Cell signalling All signalling is biochemical: Increasing protein concentration broadcasts the information about an event; for example, that a gene promoter is on. The message is received by a concentration dependent response at the protein signal s site of action. This stimulates a response at the signalling protein s site of action. Signals propagate through a series of protein accumulations.
28 Introduction Some Biological Background 28/ 223 Signal transduction pathways A series of biochemical reactions serve to pass a message from the cell membrane to the nucleus.
29 Introduction Some Biological Background 29/ 223 Gene expression pathways Genetic activity is controlled by molecular signals that determine when and how often a given gene is transcribed. The product encoded by one gene often regulates the expression of other genes. For appropriate combinations of input signals transcription is initiated and protein product accumulates when production exceeds degradation. Links are established between genes when the product of one regulates the expression of another. Thus networks of interaction can be deduced and these may be quite complex.
30 Introduction Some Biological Background 30/ 223 Gene expression pathways Genetic activity is controlled by molecular signals that determine when and how often a given gene is transcribed. The product encoded by one gene often regulates the expression of other genes. For appropriate combinations of input signals transcription is initiated and protein product accumulates when production exceeds degradation. Links are established between genes when the product of one regulates the expression of another. Thus networks of interaction can be deduced and these may be quite complex.
31 Introduction Some Biological Background 31/ 223 Gene expression pathways Genetic activity is controlled by molecular signals that determine when and how often a given gene is transcribed. The product encoded by one gene often regulates the expression of other genes. For appropriate combinations of input signals transcription is initiated and protein product accumulates when production exceeds degradation. Links are established between genes when the product of one regulates the expression of another. Thus networks of interaction can be deduced and these may be quite complex.
32 Introduction Some Biological Background 32/ 223 Gene expression pathways Genetic activity is controlled by molecular signals that determine when and how often a given gene is transcribed. The product encoded by one gene often regulates the expression of other genes. For appropriate combinations of input signals transcription is initiated and protein product accumulates when production exceeds degradation. Links are established between genes when the product of one regulates the expression of another. Thus networks of interaction can be deduced and these may be quite complex.
33 Introduction Some Biological Background 33/ 223 Gene expression pathways Genetic activity is controlled by molecular signals that determine when and how often a given gene is transcribed. The product encoded by one gene often regulates the expression of other genes. For appropriate combinations of input signals transcription is initiated and protein product accumulates when production exceeds degradation. Links are established between genes when the product of one regulates the expression of another. Thus networks of interaction can be deduced and these may be quite complex.
34 Introduction Some Biological Background 34/ 223 Dynamic issues In biochemical regulatory networks, the delay between events are determined by the delay while signal molecule concentrations accumulate or decline sufficiently. All reactions rely on the random process of molecules colliding with the cell. Thus the accumulation of protein is a stochastic process affected by several factors in the cell (temperature, ph, etc.). Thus the reaction time is a distribution rather than a deterministic time, and this can be shown to be an exponential distribution for basis molecular reactions.
35 Introduction Some Biological Background 35/ 223 Dynamic issues In biochemical regulatory networks, the delay between events are determined by the delay while signal molecule concentrations accumulate or decline sufficiently. All reactions rely on the random process of molecules colliding with the cell. Thus the accumulation of protein is a stochastic process affected by several factors in the cell (temperature, ph, etc.). Thus the reaction time is a distribution rather than a deterministic time, and this can be shown to be an exponential distribution for basis molecular reactions.
36 Introduction Some Biological Background 36/ 223 Dynamic issues In biochemical regulatory networks, the delay between events are determined by the delay while signal molecule concentrations accumulate or decline sufficiently. All reactions rely on the random process of molecules colliding with the cell. Thus the accumulation of protein is a stochastic process affected by several factors in the cell (temperature, ph, etc.). Thus the reaction time is a distribution rather than a deterministic time, and this can be shown to be an exponential distribution for basis molecular reactions.
37 Introduction Some Biological Background 37/ 223 Dynamic issues In biochemical regulatory networks, the delay between events are determined by the delay while signal molecule concentrations accumulate or decline sufficiently. All reactions rely on the random process of molecules colliding with the cell. Thus the accumulation of protein is a stochastic process affected by several factors in the cell (temperature, ph, etc.). Thus the reaction time is a distribution rather than a deterministic time, and this can be shown to be an exponential distribution for basis molecular reactions.
38 Introduction Some Biological Background 38/ 223 Stochastic behaviour The stochastic reaction rate of a chemical reaction is a function of only those molecular species involved as reactants or catalysts, and a stochastic rate constant c. The stochastic rate constant takes into account volume, temperature, ph and other environmental factors. The stoichiometry of the reaction how many molecules of each reactant species are required also has an impact. Commonly the law of mass action is used to determine the effective rate of a reaction: this is the product of the stochastic rate constant and the amount of each of the reactants.
39 Introduction Some Biological Background 39/ 223 Using Stochastic Process Algebras Process algebras have several attractive features which can be useful for modelling and understanding biological systems: Process algebraic formulations are compositional and make interactions/constraints explicit. Structure can also be apparent. Equivalence relations allow formal comparison of high-level descriptions. There are well-established techniques for reasoning about the behaviours and properties of models, supported by software. These include qualitative and quantitative analysis, and model checking.
40 Introduction Some Biological Background 40/ 223 Using Stochastic Process Algebras Process algebras have several attractive features which can be useful for modelling and understanding biological systems: Process algebraic formulations are compositional and make interactions/constraints explicit. Structure can also be apparent. Equivalence relations allow formal comparison of high-level descriptions. There are well-established techniques for reasoning about the behaviours and properties of models, supported by software. These include qualitative and quantitative analysis, and model checking.
41 Introduction Some Biological Background 41/ 223 Using Stochastic Process Algebras Process algebras have several attractive features which can be useful for modelling and understanding biological systems: Process algebraic formulations are compositional and make interactions/constraints explicit. Structure can also be apparent. Equivalence relations allow formal comparison of high-level descriptions. There are well-established techniques for reasoning about the behaviours and properties of models, supported by software. These include qualitative and quantitative analysis, and model checking.
42 Introduction Some Biological Background 42/ 223 Using Stochastic Process Algebras Process algebras have several attractive features which can be useful for modelling and understanding biological systems: Process algebraic formulations are compositional and make interactions/constraints explicit. Structure can also be apparent. Equivalence relations allow formal comparison of high-level descriptions. There are well-established techniques for reasoning about the behaviours and properties of models, supported by software. These include qualitative and quantitative analysis, and model checking.
43 Introduction Some Biological Background 43/ 223 Using Stochastic Process Algebras Process algebras have several attractive features which can be useful for modelling and understanding biological systems: Process algebraic formulations are compositional and make interactions/constraints explicit. Structure can also be apparent. Equivalence relations allow formal comparison of high-level descriptions. There are well-established techniques for reasoning about the behaviours and properties of models, supported by software. These include qualitative and quantitative analysis, and model checking.
44 Introduction Some Biological Background 44/ 223 Molecular processes as concurrent computations A correspondence between cellular processes and process alebras was first highlighted by Regev and her co-authors in the early 2000s. Concurrency Concurrent computational processes Molecular Biology Molecules Synchronous communication Molecular interaction Transition or mobility Biochemical modification or relocation Metabolism Enzymes and metabolites Binding and catalysis Metabolite synthesis Signal Transduction Interacting proteins Binding and catalysis Protein binding, modification or sequestration [Regev et al 2000]
45 Introduction Some Biological Background 45/ 223 Molecular processes as concurrent computations A correspondence between cellular processes and process alebras was first highlighted by Regev and her co-authors in the early 2000s. Concurrency Concurrent computational processes Molecular Biology Molecules Synchronous communication Molecular interaction Transition or mobility Biochemical modification or relocation Metabolism Enzymes and metabolites Binding and catalysis Metabolite synthesis Signal Transduction Interacting proteins Binding and catalysis Protein binding, modification or sequestration [Regev et al 2000]
46 Introduction Some Biological Background 46/ 223 Calculi for Systems Biology Several different process caluli have been developed or adapted for application in systems biology. Each of them has different properties able to render different aspects of biological phenomena. They may be divided into two main categories: Calculi defined originally in computer science and then applied in biology, such as the biochemical stochastic π-calculus, SCCP, CCS-R and PEPA; Calculi defined specifically by observing biological structures and phenomena, such as BioAmbients, Brane Calculi, Beta-binders, BlenX and Bio-PEPA.
47 Introduction Some Biological Background 47/ 223 Calculi for Systems Biology Several different process caluli have been developed or adapted for application in systems biology. Each of them has different properties able to render different aspects of biological phenomena. They may be divided into two main categories: Calculi defined originally in computer science and then applied in biology, such as the biochemical stochastic π-calculus, SCCP, CCS-R and PEPA; Calculi defined specifically by observing biological structures and phenomena, such as BioAmbients, Brane Calculi, Beta-binders, BlenX and Bio-PEPA.
48 Introduction Some Biological Background 48/ 223 Calculi for Systems Biology Several different process caluli have been developed or adapted for application in systems biology. Each of them has different properties able to render different aspects of biological phenomena. They may be divided into two main categories: Calculi defined originally in computer science and then applied in biology, such as the biochemical stochastic π-calculus, SCCP, CCS-R and PEPA; Calculi defined specifically by observing biological structures and phenomena, such as BioAmbients, Brane Calculi, Beta-binders, BlenX and Bio-PEPA.
49 Introduction Some Biological Background 49/ 223 Calculi for Systems Biology Several different process caluli have been developed or adapted for application in systems biology. Each of them has different properties able to render different aspects of biological phenomena. They may be divided into two main categories: Calculi defined originally in computer science and then applied in biology, such as the biochemical stochastic π-calculus, SCCP, CCS-R and PEPA; Calculi defined specifically by observing biological structures and phenomena, such as BioAmbients, Brane Calculi, Beta-binders, BlenX and Bio-PEPA.
50 Introduction Some Biological Background 50/ 223 Stochastic π-calculus The stochastic π-calculus has been used to model and analyse a wide variety of biological systems. Examples include metabolic pathways, gene transcription and signal transduction. Analysis is mainly based on stochastic simulation (Gillespie s algorithm). Two tools: BioSPI and SPIM which implement slightly different versions of the language. There has also been some work on a graphical notation associated with the SPIM tool.
51 Introduction Some Biological Background 51/ 223 Stochastic π-calculus The stochastic π-calculus has been used to model and analyse a wide variety of biological systems. Examples include metabolic pathways, gene transcription and signal transduction. Analysis is mainly based on stochastic simulation (Gillespie s algorithm). Two tools: BioSPI and SPIM which implement slightly different versions of the language. There has also been some work on a graphical notation associated with the SPIM tool.
52 Introduction Some Biological Background 52/ 223 Stochastic π-calculus The stochastic π-calculus has been used to model and analyse a wide variety of biological systems. Examples include metabolic pathways, gene transcription and signal transduction. Analysis is mainly based on stochastic simulation (Gillespie s algorithm). Two tools: BioSPI and SPIM which implement slightly different versions of the language. There has also been some work on a graphical notation associated with the SPIM tool.
53 Introduction Some Biological Background 53/ 223 Stochastic π-calculus The stochastic π-calculus has been used to model and analyse a wide variety of biological systems. Examples include metabolic pathways, gene transcription and signal transduction. Analysis is mainly based on stochastic simulation (Gillespie s algorithm). Two tools: BioSPI and SPIM which implement slightly different versions of the language. There has also been some work on a graphical notation associated with the SPIM tool.
54 Introduction Some Biological Background 54/ 223 Stochastic π-calculus The stochastic π-calculus has been used to model and analyse a wide variety of biological systems. Examples include metabolic pathways, gene transcription and signal transduction. Analysis is mainly based on stochastic simulation (Gillespie s algorithm). Two tools: BioSPI and SPIM which implement slightly different versions of the language. There has also been some work on a graphical notation associated with the SPIM tool.
55 Introduction Some Biological Background 55/ 223 Stochastic π-calculus Stochastic π-calculus [Priami, 1995] extends the π-calculus with exponentially-distributed rates.
56 Introduction Some Biological Background 56/ 223 Stochastic π-calculus Stochastic π-calculus [Priami, 1995] extends the π-calculus with exponentially-distributed rates. 0 Nil
57 Introduction Some Biological Background 57/ 223 Stochastic π-calculus Stochastic π-calculus [Priami, 1995] extends the π-calculus with exponentially-distributed rates. 0 Nil (π, r).p Prefix
58 Introduction Some Biological Background 58/ 223 Stochastic π-calculus Stochastic π-calculus [Priami, 1995] extends the π-calculus with exponentially-distributed rates. 0 Nil (π, r).p Prefix (νn)p New
59 Introduction Some Biological Background 59/ 223 Stochastic π-calculus Stochastic π-calculus [Priami, 1995] extends the π-calculus with exponentially-distributed rates. 0 Nil (π, r).p Prefix (νn)p New [x = y]p Matching
60 Introduction Some Biological Background 60/ 223 Stochastic π-calculus Stochastic π-calculus [Priami, 1995] extends the π-calculus with exponentially-distributed rates. 0 Nil (π, r).p Prefix (νn)p New [x = y]p Matching P 1 P 2 Parallel
61 Introduction Some Biological Background 61/ 223 Stochastic π-calculus Stochastic π-calculus [Priami, 1995] extends the π-calculus with exponentially-distributed rates. 0 Nil (π, r).p Prefix (νn)p New [x = y]p Matching P 1 P 2 Parallel P 1 + P 2 Choice
62 Introduction Some Biological Background 62/ 223 Stochastic π-calculus Stochastic π-calculus [Priami, 1995] extends the π-calculus with exponentially-distributed rates. 0 Nil (π, r).p Prefix (νn)p New [x = y]p Matching P 1 P 2 Parallel P 1 + P 2 Choice!P Replication
63 Introduction Some Biological Background 63/ 223 Stochastic π-calculus Stochastic π-calculus [Priami, 1995] extends the π-calculus with exponentially-distributed rates. 0 Nil (π, r).p Prefix (νn)p New [x = y]p Matching P 1 P 2 Parallel P 1 + P 2 Choice!P Replication where π is either x(y) (input), xy (output ) or τ (silent).
64 Introduction Some Biological Background 64/ 223 Example: The VICE project The aim was to construct a minimal cell in silico in order to track the dynamics of a complete metabolome. Thus a VIrtual CEll was defined as a stochastic π-calculus model, which seems to behave as a simplified prokaryote. Started from a published minimal gene set which eliminated duplicated genes and other redundancies from the smallest known bacterial genomes. This was further reduced to 180 different genes. Experimental results were in accordance with those available from in vivo experiments. Some extensions to the stochastic π-calculus were needed.
65 Introduction Some Biological Background 65/ 223 Example: The VICE project The aim was to construct a minimal cell in silico in order to track the dynamics of a complete metabolome. Thus a VIrtual CEll was defined as a stochastic π-calculus model, which seems to behave as a simplified prokaryote. Started from a published minimal gene set which eliminated duplicated genes and other redundancies from the smallest known bacterial genomes. This was further reduced to 180 different genes. Experimental results were in accordance with those available from in vivo experiments. Some extensions to the stochastic π-calculus were needed.
66 Introduction Some Biological Background 66/ 223 Example: The VICE project The aim was to construct a minimal cell in silico in order to track the dynamics of a complete metabolome. Thus a VIrtual CEll was defined as a stochastic π-calculus model, which seems to behave as a simplified prokaryote. Started from a published minimal gene set which eliminated duplicated genes and other redundancies from the smallest known bacterial genomes. This was further reduced to 180 different genes. Experimental results were in accordance with those available from in vivo experiments. Some extensions to the stochastic π-calculus were needed.
67 Introduction Some Biological Background 67/ 223 Example: The VICE project The aim was to construct a minimal cell in silico in order to track the dynamics of a complete metabolome. Thus a VIrtual CEll was defined as a stochastic π-calculus model, which seems to behave as a simplified prokaryote. Started from a published minimal gene set which eliminated duplicated genes and other redundancies from the smallest known bacterial genomes. This was further reduced to 180 different genes. Experimental results were in accordance with those available from in vivo experiments. Some extensions to the stochastic π-calculus were needed.
68 Introduction Some Biological Background 68/ 223 Example: The VICE project The aim was to construct a minimal cell in silico in order to track the dynamics of a complete metabolome. Thus a VIrtual CEll was defined as a stochastic π-calculus model, which seems to behave as a simplified prokaryote. Started from a published minimal gene set which eliminated duplicated genes and other redundancies from the smallest known bacterial genomes. This was further reduced to 180 different genes. Experimental results were in accordance with those available from in vivo experiments. Some extensions to the stochastic π-calculus were needed.
69 Process Calculi for Systems Biology 69/ 223 Outline 1 Introduction Some Biological Background 2 Process Calculi for Systems Biology 3 Bio-PEPA: Syntax 4 Formal Semantics 5 Bio-PEPA Analysis 6 Formal Mappings 7 Example
70 Process Calculi for Systems Biology 70/ 223 Process Algebras for Systems Biology The process algebra of choice for Regev and her co-workers was the stochastic π-calculus. This work was hugely influential and many people followed their lead in applying the stochastic π-calculus to model intracellular processes. However the style of modelling in the π-calculus is not always ideal for representing biochemical processes. Nevertheless a certain flavour of the π-calculus still predominately influences many of the process algebras for systems biology.
71 Process Calculi for Systems Biology 71/ 223 Process Algebras for Systems Biology The process algebra of choice for Regev and her co-workers was the stochastic π-calculus. This work was hugely influential and many people followed their lead in applying the stochastic π-calculus to model intracellular processes. However the style of modelling in the π-calculus is not always ideal for representing biochemical processes. Nevertheless a certain flavour of the π-calculus still predominately influences many of the process algebras for systems biology.
72 Process Calculi for Systems Biology 72/ 223 Process Algebras for Systems Biology The process algebra of choice for Regev and her co-workers was the stochastic π-calculus. This work was hugely influential and many people followed their lead in applying the stochastic π-calculus to model intracellular processes. However the style of modelling in the π-calculus is not always ideal for representing biochemical processes. Nevertheless a certain flavour of the π-calculus still predominately influences many of the process algebras for systems biology.
73 Process Calculi for Systems Biology 73/ 223 Process Algebras for Systems Biology The process algebra of choice for Regev and her co-workers was the stochastic π-calculus. This work was hugely influential and many people followed their lead in applying the stochastic π-calculus to model intracellular processes. However the style of modelling in the π-calculus is not always ideal for representing biochemical processes. Nevertheless a certain flavour of the π-calculus still predominately influences many of the process algebras for systems biology.
74 Process Calculi for Systems Biology 74/ 223 Issues with the π-calculus The restriction to always consider actions as occurring in conjugate pairs does not always match well with biochemical reactions where you might want more than two molecules to be involved. The molecule-as-processes abstraction can lead to problems pragmatically. By focussing on the individual molecules the calculus forces the modeller into an individuals-based interpretation of the model. This means that simulation is often the only feasible interpretation.
75 Process Calculi for Systems Biology 75/ 223 Issues with the π-calculus The restriction to always consider actions as occurring in conjugate pairs does not always match well with biochemical reactions where you might want more than two molecules to be involved. The molecule-as-processes abstraction can lead to problems pragmatically. By focussing on the individual molecules the calculus forces the modeller into an individuals-based interpretation of the model. This means that simulation is often the only feasible interpretation.
76 Process Calculi for Systems Biology 76/ 223 Bio-PEPA: motivations With Bio-PEPA we have been experimented with the more abstract mapping between elements of signalling pathways and process algebra constructs: species as processes. We also wanted to be able to capture more of the biological features expressed in the models such as those found in the BioModels database.
77 Process Calculi for Systems Biology 77/ 223 Bio-PEPA: motivations With Bio-PEPA we have been experimented with the more abstract mapping between elements of signalling pathways and process algebra constructs: species as processes. We also wanted to be able to capture more of the biological features expressed in the models such as those found in the BioModels database.
78 Process Calculi for Systems Biology 78/ 223 Motivations for Abstraction Our motivations for seeking more abstraction: Process algebra-based analyses such as comparing models (e.g. for equivalence or simulation) and model checking are only possible if the state space is not prohibitively large. The data that we have available to parameterise models is sometimes speculative rather than precise.
79 Process Calculi for Systems Biology 79/ 223 Motivations for Abstraction Our motivations for seeking more abstraction: Process algebra-based analyses such as comparing models (e.g. for equivalence or simulation) and model checking are only possible if the state space is not prohibitively large. The data that we have available to parameterise models is sometimes speculative rather than precise.
80 Process Calculi for Systems Biology 80/ 223 Motivations for Abstraction Our motivations for seeking more abstraction: Process algebra-based analyses such as comparing models (e.g. for equivalence or simulation) and model checking are only possible if the state space is not prohibitively large. The data that we have available to parameterise models is sometimes speculative rather than precise.
81 Process Calculi for Systems Biology 81/ 223 Motivations for Abstraction Our motivations for seeking more abstraction: Process algebra-based analyses such as comparing models (e.g. for equivalence or simulation) and model checking are only possible if the state space is not prohibitively large. The data that we have available to parameterise models is sometimes speculative rather than precise. This suggests that it can be useful to use semi-quantitative models rather than quantitative ones.
82 Process Calculi for Systems Biology 82/ 223 Alternative Representations ODEs Abstract SPA model Stochastic Simulation
83 Process Calculi for Systems Biology 83/ 223 Alternative Representations ODEs population view Abstract SPA model Stochastic Simulation individual view
84 Process Calculi for Systems Biology 84/ 223 Discretising the population view We can discretise the continuous range of possible concentration values into a number of distinct states. These form the possible states of the component representing the reagent.
85 Process Calculi for Systems Biology 85/ 223 Alternative Representations Abstract SPA model ODEs CTMC with M levels Stochastic Simulation
86 Process Calculi for Systems Biology 86/ 223 Alternative Representations Abstract SPA model ODEs population view CTMC with M levels abstract view Stochastic Simulation individual view
87 Process Calculi for Systems Biology 87/ 223 Alternative models The ODE model can be regarded as an approximation of a CTMC in which the number of molecules is large enough that the randomness averages out and the system is essentially deterministic. The full molecular view can be used for detailed study of the stochastic behaviour, usually via stochastic simulation In models with levels, each level of granularity gives rise to a CTMC, and the behaviour of this sequence of Markov processes converges to the behaviour of the system of ODEs. Some analyses which can be carried out via numerical solution of the CTMC are not readily available from ODEs or stochastic simulation.
88 Process Calculi for Systems Biology 88/ 223 Alternative models The ODE model can be regarded as an approximation of a CTMC in which the number of molecules is large enough that the randomness averages out and the system is essentially deterministic. The full molecular view can be used for detailed study of the stochastic behaviour, usually via stochastic simulation In models with levels, each level of granularity gives rise to a CTMC, and the behaviour of this sequence of Markov processes converges to the behaviour of the system of ODEs. Some analyses which can be carried out via numerical solution of the CTMC are not readily available from ODEs or stochastic simulation.
89 Process Calculi for Systems Biology 89/ 223 Alternative models The ODE model can be regarded as an approximation of a CTMC in which the number of molecules is large enough that the randomness averages out and the system is essentially deterministic. The full molecular view can be used for detailed study of the stochastic behaviour, usually via stochastic simulation In models with levels, each level of granularity gives rise to a CTMC, and the behaviour of this sequence of Markov processes converges to the behaviour of the system of ODEs. Some analyses which can be carried out via numerical solution of the CTMC are not readily available from ODEs or stochastic simulation.
90 Process Calculi for Systems Biology 90/ 223 Alternative models The ODE model can be regarded as an approximation of a CTMC in which the number of molecules is large enough that the randomness averages out and the system is essentially deterministic. The full molecular view can be used for detailed study of the stochastic behaviour, usually via stochastic simulation In models with levels, each level of granularity gives rise to a CTMC, and the behaviour of this sequence of Markov processes converges to the behaviour of the system of ODEs. Some analyses which can be carried out via numerical solution of the CTMC are not readily available from ODEs or stochastic simulation.
91 Process Calculi for Systems Biology 91/ 223 Modelling biological features There are some features of biochemical reaction systems which are not readily captured by π-calculus-based stochastic process algebras. Particular problems are encountered with: stoichiometry the multiplicity in which an entity participates in a reaction; general kinetic laws although mass action is widely used other kinetics are also commonly employed. multiway reactions although thermodynamic arguments can be made that there are never more than two reagents involved in a reaction, in practice it is often useful to model at a more abstract level.
92 Process Calculi for Systems Biology 92/ 223 Modelling biological features There are some features of biochemical reaction systems which are not readily captured by π-calculus-based stochastic process algebras. Particular problems are encountered with: stoichiometry the multiplicity in which an entity participates in a reaction; general kinetic laws although mass action is widely used other kinetics are also commonly employed. multiway reactions although thermodynamic arguments can be made that there are never more than two reagents involved in a reaction, in practice it is often useful to model at a more abstract level.
93 Process Calculi for Systems Biology 93/ 223 Modelling biological features There are some features of biochemical reaction systems which are not readily captured by π-calculus-based stochastic process algebras. Particular problems are encountered with: stoichiometry the multiplicity in which an entity participates in a reaction; general kinetic laws although mass action is widely used other kinetics are also commonly employed. multiway reactions although thermodynamic arguments can be made that there are never more than two reagents involved in a reaction, in practice it is often useful to model at a more abstract level.
94 Process Calculi for Systems Biology 94/ 223 Modelling biological features There are some features of biochemical reaction systems which are not readily captured by π-calculus-based stochastic process algebras. Particular problems are encountered with: stoichiometry the multiplicity in which an entity participates in a reaction; general kinetic laws although mass action is widely used other kinetics are also commonly employed. multiway reactions although thermodynamic arguments can be made that there are never more than two reagents involved in a reaction, in practice it is often useful to model at a more abstract level.
95 Process Calculi for Systems Biology 95/ 223 Modelling biological features There are some features of biochemical reaction systems which are not readily captured by π-calculus-based stochastic process algebras. Particular problems are encountered with: stoichiometry the multiplicity in which an entity participates in a reaction; general kinetic laws although mass action is widely used other kinetics are also commonly employed. multiway reactions although thermodynamic arguments can be made that there are never more than two reagents involved in a reaction, in practice it is often useful to model at a more abstract level.
96 Process Calculi for Systems Biology 96/ 223 Illustration Consider a conversion of a substrate S, with stoichiometry 2, to a product P, under the influence of an enzyme E, i.e. 2 S E P In the stochastic π-calculus (for example) this must modelled as a sequence of unary and binary reactions: S + S 2S 2S + E 2S :E 2S :E P :E P :E P + E
97 Process Calculi for Systems Biology 97/ 223 Illustration Consider a conversion of a substrate S, with stoichiometry 2, to a product P, under the influence of an enzyme E, i.e. 2 S E P In the stochastic π-calculus (for example) this must modelled as a sequence of unary and binary reactions: S + S 2S 2S + E 2S :E 2S :E P :E P :E P + E
98 Process Calculi for Systems Biology 98/ 223 Illustration cont. The problems with this are various: Rates must be found for all the intermediate steps. Alternate intermediate states are possible and it may not be known which is the appropriate one. The number of states of the system is significantly increased which has implications for computational efficiency/tractability. The use of multiway synchronisation, and the reagent-centric style of modelling, avoids these problems
99 Process Calculi for Systems Biology 99/ 223 Illustration cont. The problems with this are various: Rates must be found for all the intermediate steps. Alternate intermediate states are possible and it may not be known which is the appropriate one. The number of states of the system is significantly increased which has implications for computational efficiency/tractability. The use of multiway synchronisation, and the reagent-centric style of modelling, avoids these problems
100 Process Calculi for Systems Biology 100/ 223 Illustration cont. The problems with this are various: Rates must be found for all the intermediate steps. Alternate intermediate states are possible and it may not be known which is the appropriate one. The number of states of the system is significantly increased which has implications for computational efficiency/tractability. The use of multiway synchronisation, and the reagent-centric style of modelling, avoids these problems
101 Process Calculi for Systems Biology 101/ 223 Illustration cont. The problems with this are various: Rates must be found for all the intermediate steps. Alternate intermediate states are possible and it may not be known which is the appropriate one. The number of states of the system is significantly increased which has implications for computational efficiency/tractability. The use of multiway synchronisation, and the reagent-centric style of modelling, avoids these problems
102 Process Calculi for Systems Biology 102/ 223 Illustration cont. The problems with this are various: Rates must be found for all the intermediate steps. Alternate intermediate states are possible and it may not be known which is the appropriate one. The number of states of the system is significantly increased which has implications for computational efficiency/tractability. The use of multiway synchronisation, and the reagent-centric style of modelling, avoids these problems
103 Process Calculi for Systems Biology 103/ 223 Illustration cont. The reaction 2S E P represents the enzymatic reaction from the substrate S, with stoichiometry 2, to the product P with enzyme E. In Bio-PEPA this is described as: S E P def = (α, 2) S def = (α, 1) E def = (α, 1) P (S(l S0 ) {α} E(l E0)) {α} P(l P0) The dynamics is described by the law f α = v E S2 (K+S 2 ).
104 Process Calculi for Systems Biology 104/ 223 Illustration cont. The reaction 2S E P represents the enzymatic reaction from the substrate S, with stoichiometry 2, to the product P with enzyme E. In Bio-PEPA this is described as: S E P def = (α, 2) S def = (α, 1) E def = (α, 1) P (S(l S0 ) {α} E(l E0)) {α} P(l P0) The dynamics is described by the law f α = v E S2 (K+S 2 ).
105 Process Calculi for Systems Biology 105/ 223 Illustration cont. The reaction 2S E P represents the enzymatic reaction from the substrate S, with stoichiometry 2, to the product P with enzyme E. In Bio-PEPA this is described as: S E P def = (α, 2) S def = (α, 1) E def = (α, 1) P (S(l S0 ) {α} E(l E0)) {α} P(l P0) The dynamics is described by the law f α = v E S2 (K+S 2 ).
106 Process Calculi for Systems Biology 106/ 223 Bio-PEPA In Bio-PEPA: Unique rates are associated with each reaction (action) type, separately from the specification of the logical behaviour. These rates may be specified by functions. The representation of an action within a component (species) records the stoichiometry of that entity with respect to that reaction. The role of the entity is also distinguished. The local states of components are quantitative rather than functional, i.e. distinct states of the species are represented as distinct components, not derivatives of a single component.
107 Process Calculi for Systems Biology 107/ 223 Bio-PEPA In Bio-PEPA: Unique rates are associated with each reaction (action) type, separately from the specification of the logical behaviour. These rates may be specified by functions. The representation of an action within a component (species) records the stoichiometry of that entity with respect to that reaction. The role of the entity is also distinguished. The local states of components are quantitative rather than functional, i.e. distinct states of the species are represented as distinct components, not derivatives of a single component.
108 Process Calculi for Systems Biology 108/ 223 Bio-PEPA In Bio-PEPA: Unique rates are associated with each reaction (action) type, separately from the specification of the logical behaviour. These rates may be specified by functions. The representation of an action within a component (species) records the stoichiometry of that entity with respect to that reaction. The role of the entity is also distinguished. The local states of components are quantitative rather than functional, i.e. distinct states of the species are represented as distinct components, not derivatives of a single component.
109 Process Calculi for Systems Biology 109/ 223 Bio-PEPA In Bio-PEPA: Unique rates are associated with each reaction (action) type, separately from the specification of the logical behaviour. These rates may be specified by functions. The representation of an action within a component (species) records the stoichiometry of that entity with respect to that reaction. The role of the entity is also distinguished. The local states of components are quantitative rather than functional, i.e. distinct states of the species are represented as distinct components, not derivatives of a single component.
110 Process Calculi for Systems Biology 110/ 223 Bio-PEPA reagent-centric example A c_a b_a ab_c C B c_b A B C def = (ab c, 1) A + (b a, 1) A + (c a, 1) A def = (ab c, 1) B + (b a, 1) B + (c b, 1) B def = (c a, 1) C + (c b, 1) C + (ab c, 1) C ( ) A(l A0 ) B(l B0) {ab c,b a} {ab c,c a,c b} C(l C0)
111 Process Calculi for Systems Biology 111/ 223 Reagent-centric view Role Impact on reaction rate Impact on reagent Reactant positive impact, decreases level e.g. proportional to current concentration Product no impact, increases level except at saturation Enzyme positive impact, level unchanged e.g. proportional to current concentration Inhibitor negative impact, e.g. inversely proportional to current concentration level unchanged
112 Bio-PEPA: Syntax 112/ 223 Outline 1 Introduction Some Biological Background 2 Process Calculi for Systems Biology 3 Bio-PEPA: Syntax 4 Formal Semantics 5 Bio-PEPA Analysis 6 Formal Mappings 7 Example
113 Bio-PEPA: Syntax 113/ 223 The syntax Sequential component (species component) S ::= (α, κ) op S S + S C where op = Model component P ::= P P S(l) L The parameter l is abstract, recording quantitative information about the species. Depending on the interpretation, this quantity may be: number of molecules (SSA), concentration (ODE) or a level within a semi-quantitative model (CTMC).
114 Bio-PEPA: Syntax 114/ 223 The syntax Sequential component (species component) S ::= (α, κ) op S S + S C where op = Model component P ::= P P S(l) L The parameter l is abstract, recording quantitative information about the species. Depending on the interpretation, this quantity may be: number of molecules (SSA), concentration (ODE) or a level within a semi-quantitative model (CTMC).
115 Bio-PEPA: Syntax 115/ 223 The syntax Sequential component (species component) S ::= (α, κ) op S S + S C where op = Model component P ::= P P S(l) L The parameter l is abstract, recording quantitative information about the species. Depending on the interpretation, this quantity may be: number of molecules (SSA), concentration (ODE) or a level within a semi-quantitative model (CTMC).
116 Bio-PEPA: Syntax 116/ 223 The syntax Sequential component (species component) S ::= (α, κ) op S S + S C where op = Model component P ::= P P S(l) L The parameter l is abstract, recording quantitative information about the species. Depending on the interpretation, this quantity may be: number of molecules (SSA), concentration (ODE) or a level within a semi-quantitative model (CTMC).
117 Bio-PEPA: Syntax 117/ 223 The syntax Sequential component (species component) S ::= (α, κ) op S S + S C where op = Model component P ::= P P S(l) L The parameter l is abstract, recording quantitative information about the species. Depending on the interpretation, this quantity may be: number of molecules (SSA), concentration (ODE) or a level within a semi-quantitative model (CTMC).
118 Bio-PEPA: Syntax 118/ 223 The syntax Sequential component (species component) S ::= (α, κ) op S S + S C where op = Model component P ::= P P S(l) L The parameter l is abstract, recording quantitative information about the species. Depending on the interpretation, this quantity may be: number of molecules (SSA), concentration (ODE) or a level within a semi-quantitative model (CTMC).
119 Bio-PEPA: Syntax 119/ 223 The syntax Sequential component (species component) S ::= (α, κ) op S S + S C where op = Model component P ::= P P S(l) L The parameter l is abstract, recording quantitative information about the species. Depending on the interpretation, this quantity may be: number of molecules (SSA), concentration (ODE) or a level within a semi-quantitative model (CTMC).
120 Bio-PEPA: Syntax 120/ 223 The syntax Sequential component (species component) S ::= (α, κ) op S S + S C where op = Model component P ::= P P S(l) L The parameter l is abstract, recording quantitative information about the species. Depending on the interpretation, this quantity may be: number of molecules (SSA), concentration (ODE) or a level within a semi-quantitative model (CTMC).
121 Bio-PEPA: Syntax 121/ 223 The syntax Sequential component (species component) S ::= (α, κ) op S S + S C where op = Model component P ::= P P S(l) L The parameter l is abstract, recording quantitative information about the species. Depending on the interpretation, this quantity may be: number of molecules (SSA), concentration (ODE) or a level within a semi-quantitative model (CTMC).
122 Bio-PEPA: Syntax 122/ 223 The syntax Sequential component (species component) S ::= (α, κ) op S S + S C where op = Model component P ::= P P S(l) L The parameter l is abstract, recording quantitative information about the species. Depending on the interpretation, this quantity may be: number of molecules (SSA), concentration (ODE) or a level within a semi-quantitative model (CTMC).
123 Bio-PEPA: Syntax 123/ 223 The Bio-PEPA system A Bio-PEPA system P is a 6-tuple V, N, K, F R, Comp, P, where: V is the set of compartments; N is the set of quantities describing each species (step size, number of levels, location,...); K is the set of parameter definitions; F R is the set of functional rate definitions; Comp is the set of definitions of sequential components; P is the model component describing the system.
124 Formal Semantics 124/ 223 Outline 1 Introduction Some Biological Background 2 Process Calculi for Systems Biology 3 Bio-PEPA: Syntax 4 Formal Semantics 5 Bio-PEPA Analysis 6 Formal Mappings 7 Example
125 Formal Semantics 125/ 223 Semantics The semantics of Bio-PEPA is given as a small-step operational semantics, intended for deriving the CTMC with levels. We define two relations over the processes: 1 capability relation, that supports the derivation of quantitative information; 2 stochastic relation, that gives the rates associated with each action.
126 Formal Semantics 126/ 223 Semantics The semantics of Bio-PEPA is given as a small-step operational semantics, intended for deriving the CTMC with levels. We define two relations over the processes: 1 capability relation, that supports the derivation of quantitative information; 2 stochastic relation, that gives the rates associated with each action.
127 Formal Semantics 127/ 223 Semantics The semantics of Bio-PEPA is given as a small-step operational semantics, intended for deriving the CTMC with levels. We define two relations over the processes: 1 capability relation, that supports the derivation of quantitative information; 2 stochastic relation, that gives the rates associated with each action.
128 Formal Semantics 128/ 223 Semantics: prefix rules prefixreac ((α, κ) S)(l) (α,[s: (l,κ)]) c S(l κ) κ l N prefixprod prefixmod ((α, κ) S)(l) (α,[s: (l,κ)]) c S(l + κ) 0 l (N κ) ((α, κ) op S)(l) (α,[s:op(l,κ)]) c S(l) 0 < l N
129 Formal Semantics 129/ 223 Semantics: prefix rules prefixreac ((α, κ) S)(l) (α,[s: (l,κ)]) c S(l κ) κ l N prefixprod prefixmod ((α, κ) S)(l) (α,[s: (l,κ)]) c S(l + κ) 0 l (N κ) ((α, κ) op S)(l) (α,[s:op(l,κ)]) c S(l) 0 < l N
130 Formal Semantics 130/ 223 Semantics: prefix rules prefixreac ((α, κ) S)(l) (α,[s: (l,κ)]) c S(l κ) κ l N prefixprod prefixmod ((α, κ) S)(l) (α,[s: (l,κ)]) c S(l + κ) 0 l (N κ) ((α, κ) op S)(l) (α,[s:op(l,κ)]) c S(l) 0 < l N with op =,, or
131 Formal Semantics 131/ 223 Semantics: constant and choice rules Choice1 S 1 (l) (α,v) c S 1(l ) (S 1 + S 2 )(l) (α,v) c S 1(l ) Choice2 Constant S 2 (l) (α,v) c S 2(l ) (S 1 + S 2 )(l) (α,v) c S 2(l ) S(l) (α,s:[op(l,κ))] c S (l ) C(l) (α,c:[op(l,κ))] c S (l ) with C def = S
132 Formal Semantics 132/ 223 Semantics: constant and choice rules Choice1 S 1 (l) (α,v) c S 1(l ) (S 1 + S 2 )(l) (α,v) c S 1(l ) Choice2 Constant S 2 (l) (α,v) c S 2(l ) (S 1 + S 2 )(l) (α,v) c S 2(l ) S(l) (α,s:[op(l,κ))] c S (l ) C(l) (α,c:[op(l,κ))] c S (l ) with C def = S
133 Formal Semantics 133/ 223 Semantics: constant and choice rules Choice1 S 1 (l) (α,v) c S 1(l ) (S 1 + S 2 )(l) (α,v) c S 1(l ) Choice2 Constant S 2 (l) (α,v) c S 2(l ) (S 1 + S 2 )(l) (α,v) c S 2(l ) S(l) (α,s:[op(l,κ))] c S (l ) C(l) (α,c:[op(l,κ))] c S (l ) with C def = S
134 Formal Semantics 134/ 223 Semantics: cooperation rules coop1 coop2 P 1 P 1 P 1 (α,v) c P 1 P (α,v) 2 L c P 1 L P 2 P 2 (α,v) c P 2 P (α,v) 2 L c P 1 L P 2 with α / L with α / L coopfinal P 1 (α,v 1 ) c P 1 P 2 (α,v 2 ) c P 2 P 1 P (α,v 1 ::v 2 ) 2 L c P 1 L P 2 with α L
135 Formal Semantics 135/ 223 Semantics: cooperation rules coop1 coop2 P 1 P 1 P 1 (α,v) c P 1 P (α,v) 2 L c P 1 L P 2 P 2 (α,v) c P 2 P (α,v) 2 L c P 1 L P 2 with α / L with α / L coopfinal P 1 (α,v 1 ) c P 1 P 2 (α,v 2 ) c P 2 P 1 P (α,v 1 ::v 2 ) 2 L c P 1 L P 2 with α L
136 Formal Semantics 136/ 223 Semantics: cooperation rules coop1 coop2 P 1 P 1 P 1 (α,v) c P 1 P (α,v) 2 L c P 1 L P 2 P 2 (α,v) c P 2 P (α,v) 2 L c P 1 L P 2 with α / L with α / L coopfinal P 1 (α,v 1 ) c P 1 P 2 (α,v 2 ) c P 2 P 1 P (α,v 1 ::v 2 ) 2 L c P 1 L P 2 with α L
137 Formal Semantics 137/ 223 Semantics: rates and transition system In order to derive the rates we consider the stochastic relation s P Γ P, with γ Γ := (α, r) and r R +. The relation is defined in terms of the previous one: P (α j,v) c P V, N, K, F R, Comp, P (α j,r αj ) s V, N, K, F R, Comp, P r αj represents the parameter of an exponential distribution and the dynamic behaviour is determined by a race condition. The rate r αj is defined as f αj (V, N, K)/h.
138 Formal Semantics 138/ 223 Semantics: rates and transition system In order to derive the rates we consider the stochastic relation s P Γ P, with γ Γ := (α, r) and r R +. The relation is defined in terms of the previous one: P (α j,v) c P V, N, K, F R, Comp, P (α j,r αj ) s V, N, K, F R, Comp, P r αj represents the parameter of an exponential distribution and the dynamic behaviour is determined by a race condition. The rate r αj is defined as f αj (V, N, K)/h.
139 Formal Semantics 139/ 223 Semantics: rates and transition system In order to derive the rates we consider the stochastic relation s P Γ P, with γ Γ := (α, r) and r R +. The relation is defined in terms of the previous one: P (α j,v) c P V, N, K, F R, Comp, P (α j,r αj ) s V, N, K, F R, Comp, P r αj represents the parameter of an exponential distribution and the dynamic behaviour is determined by a race condition. The rate r αj is defined as f αj (V, N, K)/h.
140 Formal Semantics 140/ 223 Semantics: rates and transition system In order to derive the rates we consider the stochastic relation s P Γ P, with γ Γ := (α, r) and r R +. The relation is defined in terms of the previous one: P (α j,v) c P V, N, K, F R, Comp, P (α j,r αj ) s V, N, K, F R, Comp, P r αj represents the parameter of an exponential distribution and the dynamic behaviour is determined by a race condition. The rate r αj is defined as f αj (V, N, K)/h.
141 Formal Semantics 141/ 223 Semantics: rates and transition system In order to derive the rates we consider the stochastic relation s P Γ P, with γ Γ := (α, r) and r R +. The relation is defined in terms of the previous one: P (α j,v) c P V, N, K, F R, Comp, P (α j,r αj ) s V, N, K, F R, Comp, P r αj represents the parameter of an exponential distribution and the dynamic behaviour is determined by a race condition. The rate r αj is defined as f αj (V, N, K)/h.
142 Formal Semantics 142/ 223 Example: Michaelis-Menten The reaction S E P represents the enzymatic reaction from the substrate S to the product P with enzyme E. The dynamics is described by the law v E S (K+S). S E P def = (α, 1) S def = (α, 1) E def = (α, 1) P (S(l S0 ) {α} E(l E0 )) {α} P(l P0)
143 Formal Semantics 143/ 223 Example: Michaelis-Menten The reaction S E P represents the enzymatic reaction from the substrate S to the product P with enzyme E. The dynamics is described by the law v E S (K+S). S E P def = (α, 1) S def = (α, 1) E def = (α, 1) P (S(l S0 ) {α} E(l E0 )) {α} P(l P0)
144 Formal Semantics 144/ 223 Example: Michaelis-Menten The reaction S E P represents the enzymatic reaction from the substrate S to the product P with enzyme E. The dynamics is described by the law v E S (K+S). S E P def = (α, 1) S def = (α, 1) E def = (α, 1) P (S(l S0 ) {α} E(l E0 )) {α} P(l P0)
145 Bio-PEPA Analysis 145/ 223 Outline 1 Introduction Some Biological Background 2 Process Calculi for Systems Biology 3 Bio-PEPA: Syntax 4 Formal Semantics 5 Bio-PEPA Analysis 6 Formal Mappings 7 Example
146 Bio-PEPA Analysis 146/ 223 Analysis A Bio-PEPA system is a formal, intermediate and compositional representation of the system. From it we can obtain a CTMC (with levels) a ODE system for simulation and other kinds of analysis a Gillespie model for stochastic simulation a PRISM model for model checking Each of these kinds of analysis can be of help for studying different aspects of the biological model. Moreover they can be used in conjunction.
147 Bio-PEPA Analysis 147/ 223 Analysis A Bio-PEPA system is a formal, intermediate and compositional representation of the system. From it we can obtain a CTMC (with levels) a ODE system for simulation and other kinds of analysis a Gillespie model for stochastic simulation a PRISM model for model checking Each of these kinds of analysis can be of help for studying different aspects of the biological model. Moreover they can be used in conjunction.
148 Bio-PEPA Analysis 148/ 223 Analysis A Bio-PEPA system is a formal, intermediate and compositional representation of the system. From it we can obtain a CTMC (with levels) a ODE system for simulation and other kinds of analysis a Gillespie model for stochastic simulation a PRISM model for model checking Each of these kinds of analysis can be of help for studying different aspects of the biological model. Moreover they can be used in conjunction.
149 Bio-PEPA Analysis 149/ 223 Analysis A Bio-PEPA system is a formal, intermediate and compositional representation of the system. From it we can obtain a CTMC (with levels) a ODE system for simulation and other kinds of analysis a Gillespie model for stochastic simulation a PRISM model for model checking Each of these kinds of analysis can be of help for studying different aspects of the biological model. Moreover they can be used in conjunction.
150 Bio-PEPA Analysis 150/ 223 Analysis A Bio-PEPA system is a formal, intermediate and compositional representation of the system. From it we can obtain a CTMC (with levels) a ODE system for simulation and other kinds of analysis a Gillespie model for stochastic simulation a PRISM model for model checking Each of these kinds of analysis can be of help for studying different aspects of the biological model. Moreover they can be used in conjunction.
151 Bio-PEPA Analysis 151/ 223 Analysis A Bio-PEPA system is a formal, intermediate and compositional representation of the system. From it we can obtain a CTMC (with levels) a ODE system for simulation and other kinds of analysis a Gillespie model for stochastic simulation a PRISM model for model checking Each of these kinds of analysis can be of help for studying different aspects of the biological model. Moreover they can be used in conjunction.
152 Bio-PEPA Analysis 152/ 223 The abstraction When modelling in Bio-PEPA we use the following abstraction: Each species i is described by a Bio-PEPA component C i. Each reaction j is associated with an action type α j and its dynamics is described by a specific function f αj. Given a reaction j, all the species/components cooperate on the action type α j and consequently, reactants decrease their levels, while products increase them. The species components are then composed together to describe the behaviour of the system.
153 Bio-PEPA Analysis 153/ 223 The abstraction When modelling in Bio-PEPA we use the following abstraction: Each species i is described by a Bio-PEPA component C i. Each reaction j is associated with an action type α j and its dynamics is described by a specific function f αj. Given a reaction j, all the species/components cooperate on the action type α j and consequently, reactants decrease their levels, while products increase them. The species components are then composed together to describe the behaviour of the system.
154 Bio-PEPA Analysis 154/ 223 The abstraction When modelling in Bio-PEPA we use the following abstraction: Each species i is described by a Bio-PEPA component C i. Each reaction j is associated with an action type α j and its dynamics is described by a specific function f αj. Given a reaction j, all the species/components cooperate on the action type α j and consequently, reactants decrease their levels, while products increase them. The species components are then composed together to describe the behaviour of the system.
155 Bio-PEPA Analysis 155/ 223 The abstraction When modelling in Bio-PEPA we use the following abstraction: Each species i is described by a Bio-PEPA component C i. Each reaction j is associated with an action type α j and its dynamics is described by a specific function f αj. Given a reaction j, all the species/components cooperate on the action type α j and consequently, reactants decrease their levels, while products increase them. The species components are then composed together to describe the behaviour of the system.
156 Bio-PEPA Analysis 156/ 223 State representation The state of the system at any time consists of the local states of each of its sequential/species components. The local states of components are quantitative rather than functional, i.e. distinct states of the species are represented as distinct components, not derivatives of a single component. A component varying its state corresponds to it varying its quantity or level. This is captured by an integer parameter associated with the species and the effect of a reaction is to vary that parameter by a number of levels corresponding to the stoichiometry of this species in the reaction as we saw in the formal semantics.
157 Bio-PEPA Analysis 157/ 223 State representation The state of the system at any time consists of the local states of each of its sequential/species components. The local states of components are quantitative rather than functional, i.e. distinct states of the species are represented as distinct components, not derivatives of a single component. A component varying its state corresponds to it varying its quantity or level. This is captured by an integer parameter associated with the species and the effect of a reaction is to vary that parameter by a number of levels corresponding to the stoichiometry of this species in the reaction as we saw in the formal semantics.
158 Bio-PEPA Analysis 158/ 223 State representation The state of the system at any time consists of the local states of each of its sequential/species components. The local states of components are quantitative rather than functional, i.e. distinct states of the species are represented as distinct components, not derivatives of a single component. A component varying its state corresponds to it varying its quantity or level. This is captured by an integer parameter associated with the species and the effect of a reaction is to vary that parameter by a number of levels corresponding to the stoichiometry of this species in the reaction as we saw in the formal semantics.
159 Bio-PEPA Analysis 159/ 223 State representation The state of the system at any time consists of the local states of each of its sequential/species components. The local states of components are quantitative rather than functional, i.e. distinct states of the species are represented as distinct components, not derivatives of a single component. A component varying its state corresponds to it varying its quantity or level. This is captured by an integer parameter associated with the species and the effect of a reaction is to vary that parameter by a number of levels corresponding to the stoichiometry of this species in the reaction as we saw in the formal semantics.
160 Bio-PEPA Analysis 160/ 223 Analysis with Bio-PEPA Bio-PEPA SSA CTMCs ODEs StochKit Dizzy PRISM CVODES Matlab
161 Formal Mappings 161/ 223 Outline 1 Introduction Some Biological Background 2 Process Calculi for Systems Biology 3 Bio-PEPA: Syntax 4 Formal Semantics 5 Bio-PEPA Analysis 6 Formal Mappings 7 Example
162 Formal Mappings 162/ 223 CTMC Analysis of the Markov process can yield quite detailed information about the dynamic behaviour of the model. A steady state analysis provides statistics for average behaviour over a long run of the system. A transient analysis provides statistics relating to the evolution of the model over a fixed period. This will be dependent on the starting state. In the biological context transient analysis is appropriate much more frequently than steady state analysis. If molecule counts are kept in states then either analysis rapidly becomes infeasible. Bio-PEPA models can also be simulated using the Gillespie Stochastic Simulation Algorithm for CTMCs that we considered for PEPA.
163 Formal Mappings 163/ 223 CTMC Analysis of the Markov process can yield quite detailed information about the dynamic behaviour of the model. A steady state analysis provides statistics for average behaviour over a long run of the system. A transient analysis provides statistics relating to the evolution of the model over a fixed period. This will be dependent on the starting state. In the biological context transient analysis is appropriate much more frequently than steady state analysis. If molecule counts are kept in states then either analysis rapidly becomes infeasible. Bio-PEPA models can also be simulated using the Gillespie Stochastic Simulation Algorithm for CTMCs that we considered for PEPA.
164 Formal Mappings 164/ 223 CTMC Analysis of the Markov process can yield quite detailed information about the dynamic behaviour of the model. A steady state analysis provides statistics for average behaviour over a long run of the system. A transient analysis provides statistics relating to the evolution of the model over a fixed period. This will be dependent on the starting state. In the biological context transient analysis is appropriate much more frequently than steady state analysis. If molecule counts are kept in states then either analysis rapidly becomes infeasible. Bio-PEPA models can also be simulated using the Gillespie Stochastic Simulation Algorithm for CTMCs that we considered for PEPA.
165 Formal Mappings 165/ 223 CTMC Analysis of the Markov process can yield quite detailed information about the dynamic behaviour of the model. A steady state analysis provides statistics for average behaviour over a long run of the system. A transient analysis provides statistics relating to the evolution of the model over a fixed period. This will be dependent on the starting state. In the biological context transient analysis is appropriate much more frequently than steady state analysis. If molecule counts are kept in states then either analysis rapidly becomes infeasible. Bio-PEPA models can also be simulated using the Gillespie Stochastic Simulation Algorithm for CTMCs that we considered for PEPA.
166 Formal Mappings 166/ 223 CTMC Analysis of the Markov process can yield quite detailed information about the dynamic behaviour of the model. A steady state analysis provides statistics for average behaviour over a long run of the system. A transient analysis provides statistics relating to the evolution of the model over a fixed period. This will be dependent on the starting state. In the biological context transient analysis is appropriate much more frequently than steady state analysis. If molecule counts are kept in states then either analysis rapidly becomes infeasible. Bio-PEPA models can also be simulated using the Gillespie Stochastic Simulation Algorithm for CTMCs that we considered for PEPA.
167 Formal Mappings 167/ 223 CTMC Analysis of the Markov process can yield quite detailed information about the dynamic behaviour of the model. A steady state analysis provides statistics for average behaviour over a long run of the system. A transient analysis provides statistics relating to the evolution of the model over a fixed period. This will be dependent on the starting state. In the biological context transient analysis is appropriate much more frequently than steady state analysis. If molecule counts are kept in states then either analysis rapidly becomes infeasible. Bio-PEPA models can also be simulated using the Gillespie Stochastic Simulation Algorithm for CTMCs that we considered for PEPA.
168 Formal Mappings 168/ 223 CTMC with levels Models are based on discrete levels of concentration within a species. The granularity of the system is defined in terms of the step size h of the concentration intervals. We define the same step size h for all the species. This follows from the law of conservation of mass. If l i is the concentration level for the species i, the concentration is taken to be x i = l i h.
169 Formal Mappings 169/ 223 CTMC with levels Models are based on discrete levels of concentration within a species. The granularity of the system is defined in terms of the step size h of the concentration intervals. We define the same step size h for all the species. This follows from the law of conservation of mass. If l i is the concentration level for the species i, the concentration is taken to be x i = l i h.
170 Formal Mappings 170/ 223 CTMC with levels Models are based on discrete levels of concentration within a species. The granularity of the system is defined in terms of the step size h of the concentration intervals. We define the same step size h for all the species. This follows from the law of conservation of mass. If l i is the concentration level for the species i, the concentration is taken to be x i = l i h.
171 Formal Mappings 171/ 223 CTMC with levels Models are based on discrete levels of concentration within a species. The granularity of the system is defined in terms of the step size h of the concentration intervals. We define the same step size h for all the species. This follows from the law of conservation of mass. If l i is the concentration level for the species i, the concentration is taken to be x i = l i h.
172 Formal Mappings 172/ 223 CTMC with levels The rate of a transition is set to be consistent with the granularity. The granularity must be specified by the modeller as the expected range of concentration values and the number of levels considered. The structure of the CTMC derived from Bio-PEPA, which we term the CTMC with levels, will depend on the granularity of the model. As the granularity tends to zero the behaviour of this CTMC with levels tends to the behaviour of the ODEs [CDHC FBTC08].
173 Formal Mappings 173/ 223 CTMC with levels The rate of a transition is set to be consistent with the granularity. The granularity must be specified by the modeller as the expected range of concentration values and the number of levels considered. The structure of the CTMC derived from Bio-PEPA, which we term the CTMC with levels, will depend on the granularity of the model. As the granularity tends to zero the behaviour of this CTMC with levels tends to the behaviour of the ODEs [CDHC FBTC08].
174 Formal Mappings 174/ 223 CTMC with levels The rate of a transition is set to be consistent with the granularity. The granularity must be specified by the modeller as the expected range of concentration values and the number of levels considered. The structure of the CTMC derived from Bio-PEPA, which we term the CTMC with levels, will depend on the granularity of the model. As the granularity tends to zero the behaviour of this CTMC with levels tends to the behaviour of the ODEs [CDHC FBTC08].
175 Formal Mappings 175/ 223 CTMC with levels The rate of a transition is set to be consistent with the granularity. The granularity must be specified by the modeller as the expected range of concentration values and the number of levels considered. The structure of the CTMC derived from Bio-PEPA, which we term the CTMC with levels, will depend on the granularity of the model. As the granularity tends to zero the behaviour of this CTMC with levels tends to the behaviour of the ODEs [CDHC FBTC08].
176 Formal Mappings 176/ 223 ODE system The derivation of the ODEs from the Bio-PEPA is straightforward, based on the definitions of the species components. 1 definition of the (N M) stoichiometry matrix D, where N is the number of species and M is the number of reactions; 2 definition of the kinetic law vector v KL containing the kinetic law of each reaction; 3 association of the variable x i with each component C i and definition of the vector x. The ODE system is then obtained as dx dt = D v KL
177 Formal Mappings 177/ 223 ODE system The derivation of the ODEs from the Bio-PEPA is straightforward, based on the definitions of the species components. 1 definition of the (N M) stoichiometry matrix D, where N is the number of species and M is the number of reactions; 2 definition of the kinetic law vector v KL containing the kinetic law of each reaction; 3 association of the variable x i with each component C i and definition of the vector x. The ODE system is then obtained as dx dt = D v KL
178 Formal Mappings 178/ 223 ODE system The derivation of the ODEs from the Bio-PEPA is straightforward, based on the definitions of the species components. 1 definition of the (N M) stoichiometry matrix D, where N is the number of species and M is the number of reactions; 2 definition of the kinetic law vector v KL containing the kinetic law of each reaction; 3 association of the variable x i with each component C i and definition of the vector x. The ODE system is then obtained as dx dt = D v KL
179 Formal Mappings 179/ 223 ODE system The derivation of the ODEs from the Bio-PEPA is straightforward, based on the definitions of the species components. 1 definition of the (N M) stoichiometry matrix D, where N is the number of species and M is the number of reactions; 2 definition of the kinetic law vector v KL containing the kinetic law of each reaction; 3 association of the variable x i with each component C i and definition of the vector x. The ODE system is then obtained as dx dt = D v KL
180 Formal Mappings 180/ 223 ODE system There are advantages to be gained by using a process algebra model as an intermediary to the derivation of the ODEs. The ODEs can be automatically generated from the descriptive process algebra model, thus reducing human error. The process algebra model allow us to derive properties of the model, such as freedom from deadlock, before numerical analysis is carried out. The algebraic formulation of the model emphasises interactions between the biochemical entities.
181 Formal Mappings 181/ 223 ODE system There are advantages to be gained by using a process algebra model as an intermediary to the derivation of the ODEs. The ODEs can be automatically generated from the descriptive process algebra model, thus reducing human error. The process algebra model allow us to derive properties of the model, such as freedom from deadlock, before numerical analysis is carried out. The algebraic formulation of the model emphasises interactions between the biochemical entities.
182 Formal Mappings 182/ 223 ODE system There are advantages to be gained by using a process algebra model as an intermediary to the derivation of the ODEs. The ODEs can be automatically generated from the descriptive process algebra model, thus reducing human error. The process algebra model allow us to derive properties of the model, such as freedom from deadlock, before numerical analysis is carried out. The algebraic formulation of the model emphasises interactions between the biochemical entities.
183 Formal Mappings 183/ 223 ODE system There are advantages to be gained by using a process algebra model as an intermediary to the derivation of the ODEs. The ODEs can be automatically generated from the descriptive process algebra model, thus reducing human error. The process algebra model allow us to derive properties of the model, such as freedom from deadlock, before numerical analysis is carried out. The algebraic formulation of the model emphasises interactions between the biochemical entities.
184 Formal Mappings 184/ 223 PRISM model and model checking Analysing models of biological processes via stochastic model-checking has considerable appeal. As with stochastic simulation the answers which are returned from model-checking give a thorough stochastic treatment to the small-scale phenomena. However, in contrast to a simulation run which generates just one trajectory, probabilistic model-checking gives a definitive answer so it is not necessary to re-run the analysis repeatedly and compute ensemble averages of the results. Building a reward structure over the model it is possible to express complex analysis questions.
185 Formal Mappings 185/ 223 PRISM model and model checking Analysing models of biological processes via stochastic model-checking has considerable appeal. As with stochastic simulation the answers which are returned from model-checking give a thorough stochastic treatment to the small-scale phenomena. However, in contrast to a simulation run which generates just one trajectory, probabilistic model-checking gives a definitive answer so it is not necessary to re-run the analysis repeatedly and compute ensemble averages of the results. Building a reward structure over the model it is possible to express complex analysis questions.
186 Formal Mappings 186/ 223 PRISM model and model checking Analysing models of biological processes via stochastic model-checking has considerable appeal. As with stochastic simulation the answers which are returned from model-checking give a thorough stochastic treatment to the small-scale phenomena. However, in contrast to a simulation run which generates just one trajectory, probabilistic model-checking gives a definitive answer so it is not necessary to re-run the analysis repeatedly and compute ensemble averages of the results. Building a reward structure over the model it is possible to express complex analysis questions.
187 Formal Mappings 187/ 223 PRISM model and model checking Analysing models of biological processes via stochastic model-checking has considerable appeal. As with stochastic simulation the answers which are returned from model-checking give a thorough stochastic treatment to the small-scale phenomena. However, in contrast to a simulation run which generates just one trajectory, probabilistic model-checking gives a definitive answer so it is not necessary to re-run the analysis repeatedly and compute ensemble averages of the results. Building a reward structure over the model it is possible to express complex analysis questions.
188 Formal Mappings 188/ 223 PRISM model and model checking Stochastic model checking in PRISM is based on a CTMC and the logic CSL. Formally the mapping from Bio-PEPA is based on the structured operational semantics, generating the underlying CTMC in the usual way. In practice, it is more straightforward to directly map to the input language of the tool, the language of interacting, reactive modules. From a Bio-PEPA description one module is generated for each species component with an additional module to capture the functional rate information.
189 Formal Mappings 189/ 223 PRISM model and model checking Stochastic model checking in PRISM is based on a CTMC and the logic CSL. Formally the mapping from Bio-PEPA is based on the structured operational semantics, generating the underlying CTMC in the usual way. In practice, it is more straightforward to directly map to the input language of the tool, the language of interacting, reactive modules. From a Bio-PEPA description one module is generated for each species component with an additional module to capture the functional rate information.
190 Formal Mappings 190/ 223 PRISM model and model checking Stochastic model checking in PRISM is based on a CTMC and the logic CSL. Formally the mapping from Bio-PEPA is based on the structured operational semantics, generating the underlying CTMC in the usual way. In practice, it is more straightforward to directly map to the input language of the tool, the language of interacting, reactive modules. From a Bio-PEPA description one module is generated for each species component with an additional module to capture the functional rate information.
191 Formal Mappings 191/ 223 PRISM model and model checking Stochastic model checking in PRISM is based on a CTMC and the logic CSL. Formally the mapping from Bio-PEPA is based on the structured operational semantics, generating the underlying CTMC in the usual way. In practice, it is more straightforward to directly map to the input language of the tool, the language of interacting, reactive modules. From a Bio-PEPA description one module is generated for each species component with an additional module to capture the functional rate information.
192 Example 192/ 223 Outline 1 Introduction Some Biological Background 2 Process Calculi for Systems Biology 3 Bio-PEPA: Syntax 4 Formal Semantics 5 Bio-PEPA Analysis 6 Formal Mappings 7 Example
193 Example 193/ 223 Goldbeter s model [Goldbeter 91] Goldbeter s model describes the activity of the cyclin in the cell cycle. The cyclin promotes the activation of a cdk (cdc2) which in turn activates a cyclin protease. This protease promotes cyclin degradation. This leads to a negative feedback loop. In the model most of the kinetic laws are of kind Michaelis-Menten and this can be reflected in the Bio-PEPA model
194 Example 194/ 223 Goldbeter s model [Goldbeter 91] Goldbeter s model describes the activity of the cyclin in the cell cycle. The cyclin promotes the activation of a cdk (cdc2) which in turn activates a cyclin protease. This protease promotes cyclin degradation. This leads to a negative feedback loop. In the model most of the kinetic laws are of kind Michaelis-Menten and this can be reflected in the Bio-PEPA model
195 Example 195/ 223 Goldbeter s model [Goldbeter 91] Goldbeter s model describes the activity of the cyclin in the cell cycle. The cyclin promotes the activation of a cdk (cdc2) which in turn activates a cyclin protease. This protease promotes cyclin degradation. This leads to a negative feedback loop. In the model most of the kinetic laws are of kind Michaelis-Menten and this can be reflected in the Bio-PEPA model
196 Example 196/ 223 Goldbeter s model [Goldbeter 91] Goldbeter s model describes the activity of the cyclin in the cell cycle. The cyclin promotes the activation of a cdk (cdc2) which in turn activates a cyclin protease. This protease promotes cyclin degradation. This leads to a negative feedback loop. In the model most of the kinetic laws are of kind Michaelis-Menten and this can be reflected in the Bio-PEPA model
197 Example 197/ 223 Goldbeter s model [Goldbeter 91] Goldbeter s model describes the activity of the cyclin in the cell cycle. The cyclin promotes the activation of a cdk (cdc2) which in turn activates a cyclin protease. This protease promotes cyclin degradation. This leads to a negative feedback loop. In the model most of the kinetic laws are of kind Michaelis-Menten and this can be reflected in the Bio-PEPA model
198 Example 198/ 223 The biological model R1 CYCLIN (C) R2 cdc2 inactive (M ) R3 cdc2 active (M) R7 R4 Protease inactive (X ) R5 Protease active (X) R6
199 Example 199/ 223 The biological model (2) There are three different biological species involved: cyclin, the protein protagonist of the cycle, represented as C; cdc2 kinase, in both active and inactive form. The variables used to represent them are M and M, respectively; cyclin protease, in both active and inactive form. The variable are X and X.
200 Example 200/ 223 The biological model (2) There are three different biological species involved: cyclin, the protein protagonist of the cycle, represented as C; cdc2 kinase, in both active and inactive form. The variables used to represent them are M and M, respectively; cyclin protease, in both active and inactive form. The variable are X and X.
201 Example 201/ 223 The biological model (2) There are three different biological species involved: cyclin, the protein protagonist of the cycle, represented as C; cdc2 kinase, in both active and inactive form. The variables used to represent them are M and M, respectively; cyclin protease, in both active and inactive form. The variable are X and X.
202 Example 202/ 223 The biological model (2) There are three different biological species involved: cyclin, the protein protagonist of the cycle, represented as C; cdc2 kinase, in both active and inactive form. The variables used to represent them are M and M, respectively; cyclin protease, in both active and inactive form. The variable are X and X.
203 Example 203/ 223 Reactions id reaction react. prod. mod. kinetic laws α 1 creation of cyclin - C - v i α 2 degradation of cyclin C - - kd C activation of M M C C V M1 M α 3 α 4 α 5 α 6 α 7 cdc2 kinase deactivation of cdc2 kinase activation of cyclin protease deactivation of cyclin protease X triggered degradation of cyclin M M - X X M X X - C - X (K c +C) (K 1+M ) M V 2 (K 2+M) X M V M3 (K 3+X ) X V 4 K 4+X C v d X C+K d α 1, α 2 have mass-action kinetics; others are Michaelis-Menten.
204 Example 204/ 223 Translation into Bio-PEPA Definition of the set N : N = [C : h C, N c ; M : h M, N M ; M : h M, N M ; Definition of functional rates (F): X : h X, N X, ; X : h X, N X ] f α1 = fma(v i ); f α2 = fma(k d ); f α4 = fmm(v 2, K 2 ); f α5 = fmm(v 3, K 3 ); f α6 = fmm(v 4, K 4 ); f α7 = fmm(v d, K d ); f α3 = v 1 C M K c + C K1 + M
205 Example 205/ 223 Translation into Bio-PEPA Definition of the set N : N = [C : h C, N c ; M : h M, N M ; M : h M, N M ; Definition of functional rates (F): X : h X, N X, ; X : h X, N X ] f α1 = fma(v i ); f α2 = fma(k d ); f α4 = fmm(v 2, K 2 ); f α5 = fmm(v 3, K 3 ); f α6 = fmm(v 4, K 4 ); f α7 = fmm(v d, K d ); f α3 = v 1 C M K c + C K1 + M
206 Example 206/ 223 The Bio-PEPA model Definition of species components (Comp): C M M X X def = (α 1, 1) C + (α 2, 1) C + (α 7, 1) C + (α 3, 1) C def = (α 4, 1) M + (α 3, 1) M def = (α 3, 1) M + (α 4, 1) M + (α 5, 1) M def = (α 6, 1) X + (α 5, 1) X def = (α 5, 1) X + (α 6, 1) X + (α 7, 1) X Definition of the model component (P): C(l 0C ) {α 3 } M(l 0M) {α 3,α 4 } M (l 0M ) {α 5,α 7 } X (l 0X ) {α 5,α 6 } X (l 0X )
207 Example 207/ 223 The Bio-PEPA model Definition of species components (Comp): C M M X X def = (α 1, 1) C + (α 2, 1) C + (α 7, 1) C + (α 3, 1) C def = (α 4, 1) M + (α 3, 1) M def = (α 3, 1) M + (α 4, 1) M + (α 5, 1) M def = (α 6, 1) X + (α 5, 1) X def = (α 5, 1) X + (α 6, 1) X + (α 7, 1) X Definition of the model component (P): C(l 0C ) {α 3 } M(l 0M) {α 3,α 4 } M (l 0M ) {α 5,α 7 } X (l 0X ) {α 5,α 6 } X (l 0X )
208 Example 208/ 223 ODEs The stoichiometry matrix D: α 1 α 2 α 3 α 4 α 5 α 6 α 7 C x C M x M M x M X x X X x X The vector that contains the kinetic laws is: w = ( v i 1, k d x C, V M1 x C K c + x C x M (K 1 + x M ), V 2 x M (K 2 + x M ), V M3 x M x X V 4 x X, (K 3 + x X ) (K 4 + x X ), v d x C x X (K d + x C ) )
209 Example 209/ 223 ODEs The stoichiometry matrix D: α 1 α 2 α 3 α 4 α 5 α 6 α 7 C x C M x M M x M X x X X x X The vector that contains the kinetic laws is: w = ( v i 1, k d x C, V M1 x C K c + x C x M (K 1 + x M ), V 2 x M (K 2 + x M ), V M3 x M x X V 4 x X, (K 3 + x X ) (K 4 + x X ), v d x C x X (K d + x C ) )
210 Example 210/ 223 ODEs (2) The system of ODEs is obtained as d x dt = D w, where x T =: (x C, x M, x M, x X, x X ) is the vector of the species variables: dx C dt dx M dt dx M dt dx X dt dx X dt = v i 1 k d x C v d x C x X (K d + x C ) = V M1 x C K c + x C x M (K 1 + x M ) + V 2 x M (K 2 + x M ) = + V M1 x C K c + x C x M (K 1 + x M ) V 2 x M (K 2 + x M ) = V M3 x M x X (K 3 + x X ) = V M3 x M x X (K 3 + x X ) + V 4 x X (K 4 + x X ) V 4 x X (K 4 + x X )
211 Example 211/ 223 ODE results K 1 = K 2 = K 3 = K 4 = 0.02µM
212 Example 212/ 223 ODE results K 1 = K 2 = K 3 = K 4 = 40µM
Modelling Biochemical Pathways with Stochastic Process Algebra
Modelling Biochemical Pathways with Stochastic Process Algebra Jane Hillston. LFCS, University of Edinburgh 13th April 2007 The PEPA project The PEPA project started in Edinburgh in 1991. The PEPA project
More informationModels and Languages for Computational Systems Biology Lecture 1
Models and Languages for Computational Systems Biology Lecture 1 Jane Hillston. LFCS and CSBE, University of Edinburgh 13th January 2011 Outline Introduction Motivation Measurement, Observation and Induction
More informationSome investigations concerning the CTMC and the ODE model derived from Bio-PEPA
FBTC 2008 Some investigations concerning the CTMC and the ODE model derived from Bio-PEPA Federica Ciocchetta 1,a, Andrea Degasperi 2,b, Jane Hillston 3,a and Muffy Calder 4,b a Laboratory for Foundations
More informationModeling biological systems with delays in Bio-PEPA
Modeling biological systems with delays in Bio-PEPA Giulio Caravagna Dipartimento di Informatica, Università di Pisa, argo Pontecorvo 3, 56127 Pisa, Italy. caravagn@di.unipi.it Jane Hillston aboratory
More informationModelling Biological Compartments in Bio-PEPA
Electronic Notes in Theoretical Computer Science 227 (2009) 77 95 www.elsevier.com/locate/entcs Modelling Biological Compartments in Bio-PEPA Federica Ciocchetta 1 and Maria Luisa Guerriero 2 Laboratory
More informationModelling biological compartments in Bio-PEPA
MeCBIC 2008 Modelling biological compartments in Bio-PEPA Federica Ciocchetta 1 and Maria Luisa Guerriero 2 Laboratory for Foundations of Computer Science, The University of Edinburgh, Edinburgh EH8 9AB,
More informationBiological Pathways Representation by Petri Nets and extension
Biological Pathways Representation by and extensions December 6, 2006 Biological Pathways Representation by and extension 1 The cell Pathways 2 Definitions 3 4 Biological Pathways Representation by and
More informationCells in silico: a Holistic Approach
Cells in silico: a Holistic Approach Pierpaolo Degano Dipartimento di Informatica, Università di Pisa, Italia joint work with a lot of nice BISCA people :-) Bertinoro, 7th June 2007 SFM 2008 Bertinoro
More informationUNIVERSITÀ DEGLI STUDI DI TRENTO
UNIVERSITÀ DEGLI STUDI DI TRENTO Facoltà di Scienze Matematiche, Fisiche e Naturali Corso di Laurea Specialistica in Informatica Within European Masters in Informatics Tesi di Laurea An Automatic Mapping
More informationModelling protein trafficking: progress and challenges
Modelling protein trafficking: progress and challenges Laboratory for Foundations of Computer Science School of Informatics University of Edinburgh 21 May 2012 Outline Protein Trafficking Modelling Biology
More informationVarieties of Stochastic Calculi
Research is what I'm doing when I don't know what I'm doing. Wernher Von Braun. Artificial Biochemistry Varieties of Stochastic Calculi Microsoft Research Trento, 26-5-22..26 www.luca.demon.co.uk/artificialbiochemistry.htm
More information86 Part 4 SUMMARY INTRODUCTION
86 Part 4 Chapter # AN INTEGRATION OF THE DESCRIPTIONS OF GENE NETWORKS AND THEIR MODELS PRESENTED IN SIGMOID (CELLERATOR) AND GENENET Podkolodny N.L. *1, 2, Podkolodnaya N.N. 1, Miginsky D.S. 1, Poplavsky
More informationPopulation models from PEPA descriptions
Population models from PEPA descriptions Jane Hillston LFCS, The University of Edinburgh, Edinburgh EH9 3JZ, Scotland. Email: jeh@inf.ed.ac.uk 1 Introduction Stochastic process algebras (e.g. PEPA [10],
More information38050 Povo Trento (Italy), Via Sommarive 14 CAUSAL P-CALCULUS FOR BIOCHEMICAL MODELLING
UNIVERSITY OF TRENTO DEPARTMENT OF INFORMATION AND COMMUNICATION TECHNOLOGY 38050 Povo Trento (Italy), Via Sommarive 14 http://www.dit.unitn.it CAUSAL P-CALCULUS FOR BIOCHEMICAL MODELLING M. Curti, P.
More informationA compartmental model of the camp/pka/mapk pathway in Bio-PEPA
A compartmental model of the camp/pka/mapk pathway in Bio-PEPA Federica Ciocchetta The Microsoft Research - University of Trento Centre for Computational and Systems Biology, Trento, Italy ciocchetta@cosbi.eu
More informationQualitative and Quantitative Analysis of a Bio-PEPA Model of the Gp130/JAK/STAT Signalling Pathway
Qualitative and Quantitative Analysis of a Bio-PEPA Model of the Gp13/JAK/STAT Signalling Pathway Maria Luisa Guerriero Laboratory for Foundations of Computer Science, The University of Edinburgh, UK Abstract.
More informationTowards a framework for multi-level modelling in Computational Biology
Towards a framework for multi-level modelling in Computational Biology Sara Montagna sara.montagna@unibo.it Alma Mater Studiorum Università di Bologna PhD in Electronics, Computer Science and Telecommunications
More informationCellular Systems Biology or Biological Network Analysis
Cellular Systems Biology or Biological Network Analysis Joel S. Bader Department of Biomedical Engineering Johns Hopkins University (c) 2012 December 4, 2012 1 Preface Cells are systems. Standard engineering
More informationFormal Methods and Systems Biology: The Calculus of Looping Sequences
Formal Methods and Systems Biology: The Calculus of Looping Sequences Paolo Milazzo Dipartimento di Informatica, Università di Pisa, Italy Verona January 22, 2008 Paolo Milazzo (Università di Pisa) Formal
More informationRegulation and signaling. Overview. Control of gene expression. Cells need to regulate the amounts of different proteins they express, depending on
Regulation and signaling Overview Cells need to regulate the amounts of different proteins they express, depending on cell development (skin vs liver cell) cell stage environmental conditions (food, temperature,
More informationSimulation of Chemical Reactions
Simulation of Chemical Reactions Cameron Finucane & Alejandro Ribeiro Dept. of Electrical and Systems Engineering University of Pennsylvania aribeiro@seas.upenn.edu http://www.seas.upenn.edu/users/~aribeiro/
More informationThis article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution
More informationChapter 6- An Introduction to Metabolism*
Chapter 6- An Introduction to Metabolism* *Lecture notes are to be used as a study guide only and do not represent the comprehensive information you will need to know for the exams. The Energy of Life
More informationIntroduction Probabilistic Programming ProPPA Inference Results Conclusions. Embedding Machine Learning in Stochastic Process Algebra.
Embedding Machine Learning in Stochastic Process Algebra Jane Hillston Joint work with Anastasis Georgoulas and Guido Sanguinetti, School of Informatics, University of Edinburgh 16th August 2017 quan col....
More informationStochastic Simulation of Biochemical Reactions
1 / 75 Stochastic Simulation of Biochemical Reactions Jorge Júlvez University of Zaragoza 2 / 75 Outline 1 Biochemical Kinetics 2 Reaction Rate Equation 3 Chemical Master Equation 4 Stochastic Simulation
More informationWhere Membrane Meet Complexes
Where Membrane Meet Complexes Luca Cardelli Microsoft Research Sylvain Pradalier ENS Cachan 2005-08-27 Bioconcur Complexes In biochemistry proteins and other molecules have two fundamental ways of interacting,
More informationCourse plan Academic Year Qualification MSc on Bioinformatics for Health Sciences. Subject name: Computational Systems Biology Code: 30180
Course plan 201-201 Academic Year Qualification MSc on Bioinformatics for Health Sciences 1. Description of the subject Subject name: Code: 30180 Total credits: 5 Workload: 125 hours Year: 1st Term: 3
More informationDeducing Interactions in Partially Unspecified Biological Systems
Deducing Interactions in Partially Unspecified Biological Systems P. Baldan 1 A. Bracciali 2 L. Brodo 3 R. Bruni 2 1 Università di Padova 2 Università di Pisa 3 Università di Sassari Algebraic Biology
More informationStochastic Process Algebra models of a Circadian Clock
Stochastic Process Algebra models of a Circadian Clock Jeremy T. Bradley Thomas Thorne Department of Computing, Imperial College London 180 Queen s Gate, London SW7 2BZ, United Kingdom Email: jb@doc.ic.ac.uk
More informationInvestigating modularity in the analysis of process algebra models of biochemical systems
Investigating modularity in the analysis of process algebra models of biochemical systems Federica Ciocchetta 1 Maria Luisa Guerriero 2 Jane Hillston 2,3 1 The Microsoft Research - University of Trento
More informationLectures on Medical Biophysics Department of Biophysics, Medical Faculty, Masaryk University in Brno. Biocybernetics
Lectures on Medical Biophysics Department of Biophysics, Medical Faculty, Masaryk University in Brno Norbert Wiener 26.11.1894-18.03.1964 Biocybernetics Lecture outline Cybernetics Cybernetic systems Feedback
More informationChapter 15 Active Reading Guide Regulation of Gene Expression
Name: AP Biology Mr. Croft Chapter 15 Active Reading Guide Regulation of Gene Expression The overview for Chapter 15 introduces the idea that while all cells of an organism have all genes in the genome,
More informationCompare and contrast the cellular structures and degrees of complexity of prokaryotic and eukaryotic organisms.
Subject Area - 3: Science and Technology and Engineering Education Standard Area - 3.1: Biological Sciences Organizing Category - 3.1.A: Organisms and Cells Course - 3.1.B.A: BIOLOGY Standard - 3.1.B.A1:
More informationFrom cell biology to Petri nets. Rainer Breitling, Groningen, NL David Gilbert, London, UK Monika Heiner, Cottbus, DE
From cell biology to Petri nets Rainer Breitling, Groningen, NL David Gilbert, London, UK Monika Heiner, Cottbus, DE Biology = Concentrations Breitling / 2 The simplest chemical reaction A B irreversible,
More informationUnravelling the biochemical reaction kinetics from time-series data
Unravelling the biochemical reaction kinetics from time-series data Santiago Schnell Indiana University School of Informatics and Biocomplexity Institute Email: schnell@indiana.edu WWW: http://www.informatics.indiana.edu/schnell
More informationAn Introduction to Metabolism
LECTURE PRESENTATIONS For CAMPBELL BIOLOGY, NINTH EDITION Jane B. Reece, Lisa A. Urry, Michael L. Cain, Steven A. Wasserman, Peter V. Minorsky, Robert B. Jackson Chapter 8 An Introduction to Metabolism
More informationIntroduction to Bioinformatics
Systems biology Introduction to Bioinformatics Systems biology: modeling biological p Study of whole biological systems p Wholeness : Organization of dynamic interactions Different behaviour of the individual
More informationFUNDAMENTALS of SYSTEMS BIOLOGY From Synthetic Circuits to Whole-cell Models
FUNDAMENTALS of SYSTEMS BIOLOGY From Synthetic Circuits to Whole-cell Models Markus W. Covert Stanford University 0 CRC Press Taylor & Francis Group Boca Raton London New York Contents /... Preface, xi
More informationProgram for the rest of the course
Program for the rest of the course 16.4 Enzyme kinetics 17.4 Metabolic Control Analysis 19.4. Exercise session 5 23.4. Metabolic Control Analysis, cont. 24.4 Recap 27.4 Exercise session 6 etabolic Modelling
More informationWritten Exam 15 December Course name: Introduction to Systems Biology Course no
Technical University of Denmark Written Exam 15 December 2008 Course name: Introduction to Systems Biology Course no. 27041 Aids allowed: Open book exam Provide your answers and calculations on separate
More informationProkaryotic Gene Expression (Learning Objectives)
Prokaryotic Gene Expression (Learning Objectives) 1. Learn how bacteria respond to changes of metabolites in their environment: short-term and longer-term. 2. Compare and contrast transcriptional control
More informationMultiple Choice Review- Eukaryotic Gene Expression
Multiple Choice Review- Eukaryotic Gene Expression 1. Which of the following is the Central Dogma of cell biology? a. DNA Nucleic Acid Protein Amino Acid b. Prokaryote Bacteria - Eukaryote c. Atom Molecule
More informationLecture 8: Temporal programs and the global structure of transcription networks. Chap 5 of Alon. 5.1 Introduction
Lecture 8: Temporal programs and the global structure of transcription networks Chap 5 of Alon 5. Introduction We will see in this chapter that sensory transcription networks are largely made of just four
More informationAn introduction to SYSTEMS BIOLOGY
An introduction to SYSTEMS BIOLOGY Paolo Tieri CNR Consiglio Nazionale delle Ricerche, Rome, Italy 10 February 2015 Universidade Federal de Minas Gerais, Belo Horizonte, Brasil Course outline Day 1: intro
More informationProcess Calculi for Biological Processes
a joint work with A. Bernini, P. Degano, D. Hermith, M. Falaschi to appear in Natural Computing, Springer-Verlag, 2018 Siena, May 2018 Outline 1 Specification languages: Process Algebras 2 Biology 3 Modelling
More informationBasic Synthetic Biology circuits
Basic Synthetic Biology circuits Note: these practices were obtained from the Computer Modelling Practicals lecture by Vincent Rouilly and Geoff Baldwin at Imperial College s course of Introduction to
More informationUnit 3: Control and regulation Higher Biology
Unit 3: Control and regulation Higher Biology To study the roles that genes play in the control of growth and development of organisms To be able to Give some examples of features which are controlled
More informationBasic modeling approaches for biological systems. Mahesh Bule
Basic modeling approaches for biological systems Mahesh Bule The hierarchy of life from atoms to living organisms Modeling biological processes often requires accounting for action and feedback involving
More informationRegulation of metabolism
Regulation of metabolism So far in this course we have assumed that the metabolic system is in steady state For the rest of the course, we will abandon this assumption, and look at techniques for analyzing
More informationV19 Metabolic Networks - Overview
V19 Metabolic Networks - Overview There exist different levels of computational methods for describing metabolic networks: - stoichiometry/kinetics of classical biochemical pathways (glycolysis, TCA cycle,...
More informationL3.1: Circuits: Introduction to Transcription Networks. Cellular Design Principles Prof. Jenna Rickus
L3.1: Circuits: Introduction to Transcription Networks Cellular Design Principles Prof. Jenna Rickus In this lecture Cognitive problem of the Cell Introduce transcription networks Key processing network
More informationCHAPTER : Prokaryotic Genetics
CHAPTER 13.3 13.5: Prokaryotic Genetics 1. Most bacteria are not pathogenic. Identify several important roles they play in the ecosystem and human culture. 2. How do variations arise in bacteria considering
More informationTopic 4 - #14 The Lactose Operon
Topic 4 - #14 The Lactose Operon The Lactose Operon The lactose operon is an operon which is responsible for the transport and metabolism of the sugar lactose in E. coli. - Lactose is one of many organic
More informationName: SBI 4U. Gene Expression Quiz. Overall Expectation:
Gene Expression Quiz Overall Expectation: - Demonstrate an understanding of concepts related to molecular genetics, and how genetic modification is applied in industry and agriculture Specific Expectation(s):
More informationGrundlagen der Systembiologie und der Modellierung epigenetischer Prozesse
Grundlagen der Systembiologie und der Modellierung epigenetischer Prozesse Sonja J. Prohaska Bioinformatics Group Institute of Computer Science University of Leipzig October 25, 2010 Genome-scale in silico
More informationLecture: Computational Systems Biology Universität des Saarlandes, SS Introduction. Dr. Jürgen Pahle
Lecture: Computational Systems Biology Universität des Saarlandes, SS 2012 01 Introduction Dr. Jürgen Pahle 24.4.2012 Who am I? Dr. Jürgen Pahle 2009-2012 Manchester Interdisciplinary Biocentre, The University
More informationPetri net models. tokens placed on places define the state of the Petri net
Petri nets Petri net models Named after Carl Adam Petri who, in the early sixties, proposed a graphical and mathematical formalism suitable for the modeling and analysis of concurrent, asynchronous distributed
More informationFROM ODES TO LANGUAGE-BASED, EXECUTABLE MODELS OF BIOLOGICAL SYSTEMS
FROM ODES TO LANGUAGE-BASED, EXECUTABLE MODELS OF BIOLOGICAL SYSTEMS A. PALMISANO, I. MURA AND C. PRIAMI CoSBi, Trento, Italy E-mail: {palmisano, mura, priami}@cosbi.eu Modeling in biology is mainly grounded
More informationA Structured Approach Part IV. Model Checking in Systems and Synthetic Biology
A Structured Approach Part IV Model Checking in Systems and Synthetic Biology Robin Donaldson Bioinformatics Research Centre University of Glasgow, Glasgow, UK Model Checking - ISMB08 1 Outline Introduction
More informationIntroduction to Bioinformatics
CSCI8980: Applied Machine Learning in Computational Biology Introduction to Bioinformatics Rui Kuang Department of Computer Science and Engineering University of Minnesota kuang@cs.umn.edu History of Bioinformatics
More informationnatural development from this collection of knowledge: it is more reliable to predict the property
1 Chapter 1 Introduction As the basis of all life phenomena, the interaction of biomolecules has been under the scrutiny of scientists and cataloged meticulously [2]. The recent advent of systems biology
More informationRESEARCH PROPOSAL MODELING A CELLULAR TRANSMEMBRANE SIGNALING SYSTEM THROUGH INTERACTION WITH G-PROTEINS BY USING CONCURRENT
RESEARCH PROPOSAL MODELING A CELLULAR TRANSMEMBRANE SIGNALING SYSTEM THROUGH INTERACTION WITH G-PROTEINS BY USING CONCURRENT CONSTRAINT PROCESS CALCULI BY DIANA-PATRICIA HERMITH-RAMIREZ, B.S. ADVISOR:
More informationSemantics and Verification
Semantics and Verification Lecture 2 informal introduction to CCS syntax of CCS semantics of CCS 1 / 12 Sequential Fragment Parallelism and Renaming CCS Basics (Sequential Fragment) Nil (or 0) process
More informationActivation of a receptor. Assembly of the complex
Activation of a receptor ligand inactive, monomeric active, dimeric When activated by growth factor binding, the growth factor receptor tyrosine kinase phosphorylates the neighboring receptor. Assembly
More informationV14 extreme pathways
V14 extreme pathways A torch is directed at an open door and shines into a dark room... What area is lighted? Instead of marking all lighted points individually, it would be sufficient to characterize
More informationIntroduction. Gene expression is the combined process of :
1 To know and explain: Regulation of Bacterial Gene Expression Constitutive ( house keeping) vs. Controllable genes OPERON structure and its role in gene regulation Regulation of Eukaryotic Gene Expression
More informationModeling Biological Systems in Stochastic Concurrent Constraint Programming
Modeling Biological Systems in Stochastic Concurrent Constraint Programming Luca Bortolussi Alberto Policriti Abstract We present an application of stochastic Concurrent Constraint Programming (sccp) for
More informationModeling Biological Systems in Stochastic Concurrent Constraint Programming
Modeling Biological Systems in Stochastic Concurrent Constraint Programming Luca Bortolussi 1 Alberto Policriti 1 1 Department of Mathematics and Computer Science University of Udine, Italy. Workshop on
More informationGene Network Science Diagrammatic Cell Language and Visual Cell
Gene Network Science Diagrammatic Cell Language and Visual Cell Mr. Tan Chee Meng Scientific Programmer, System Biology Group, Bioinformatics Institute Overview Introduction Why? Challenges Diagrammatic
More informationHybrid Model of gene regulatory networks, the case of the lac-operon
Hybrid Model of gene regulatory networks, the case of the lac-operon Laurent Tournier and Etienne Farcot LMC-IMAG, 51 rue des Mathématiques, 38041 Grenoble Cedex 9, France Laurent.Tournier@imag.fr, Etienne.Farcot@imag.fr
More informationComputational Modelling in Systems and Synthetic Biology
Computational Modelling in Systems and Synthetic Biology Fran Romero Dpt Computer Science and Artificial Intelligence University of Seville fran@us.es www.cs.us.es/~fran Models are Formal Statements of
More informationSimulation of Kohn s Molecular Interaction Maps Through Translation into Stochastic CLS+
Simulation of Kohn s Molecular Interaction Maps Through Translation into Stochastic CLS+ Roberto Barbuti 1, Daniela Lepri 2, Andrea Maggiolo-Schettini 1, Paolo Milazzo 1, Giovanni Pardini 1, and Aureliano
More informationName Period The Control of Gene Expression in Prokaryotes Notes
Bacterial DNA contains genes that encode for many different proteins (enzymes) so that many processes have the ability to occur -not all processes are carried out at any one time -what allows expression
More informationFormal Modeling of Biological Systems with Delays
Universita degli Studi di Pisa Dipartimento di Informatica Dottorato di Ricerca in Informatica Ph.D. Thesis Proposal Formal Modeling of Biological Systems with Delays Giulio Caravagna caravagn@di.unipi.it
More informationPlant Molecular and Cellular Biology Lecture 8: Mechanisms of Cell Cycle Control and DNA Synthesis Gary Peter
Plant Molecular and Cellular Biology Lecture 8: Mechanisms of Cell Cycle Control and DNA Synthesis Gary Peter 9/10/2008 1 Learning Objectives Explain why a cell cycle was selected for during evolution
More informationMap of AP-Aligned Bio-Rad Kits with Learning Objectives
Map of AP-Aligned Bio-Rad Kits with Learning Objectives Cover more than one AP Biology Big Idea with these AP-aligned Bio-Rad kits. Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 ThINQ! pglo Transformation
More informationFrom Petri Nets to Differential Equations An Integrative Approach for Biochemical Network Analysis
From Petri Nets to Differential Equations An Integrative Approach for Biochemical Network Analysis David Gilbert drg@brc.dcs.gla.ac.uk Bioinformatics Research Centre, University of Glasgow and Monika Heiner
More informationBig Idea 3: Living systems store, retrieve, transmit and respond to information essential to life processes. Tuesday, December 27, 16
Big Idea 3: Living systems store, retrieve, transmit and respond to information essential to life processes. Enduring understanding 3.B: Expression of genetic information involves cellular and molecular
More informationBIOLOGY 10/11/2014. An Introduction to Metabolism. Outline. Overview: The Energy of Life
8 An Introduction to Metabolism CAMPBELL BIOLOGY TENTH EDITION Reece Urry Cain Wasserman Minorsky Jackson Outline I. Forms of Energy II. Laws of Thermodynamics III. Energy and metabolism IV. ATP V. Enzymes
More informationBiology Assessment. Eligible Texas Essential Knowledge and Skills
Biology Assessment Eligible Texas Essential Knowledge and Skills STAAR Biology Assessment Reporting Category 1: Cell Structure and Function The student will demonstrate an understanding of biomolecules
More informationSTAAR Biology Assessment
STAAR Biology Assessment Reporting Category 1: Cell Structure and Function The student will demonstrate an understanding of biomolecules as building blocks of cells, and that cells are the basic unit of
More informationSig2GRN: A Software Tool Linking Signaling Pathway with Gene Regulatory Network for Dynamic Simulation
Sig2GRN: A Software Tool Linking Signaling Pathway with Gene Regulatory Network for Dynamic Simulation Authors: Fan Zhang, Runsheng Liu and Jie Zheng Presented by: Fan Wu School of Computer Science and
More informationREGULATION OF GENE EXPRESSION. Bacterial Genetics Lac and Trp Operon
REGULATION OF GENE EXPRESSION Bacterial Genetics Lac and Trp Operon Levels of Metabolic Control The amount of cellular products can be controlled by regulating: Enzyme activity: alters protein function
More informationCOMPUTER SIMULATION OF DIFFERENTIAL KINETICS OF MAPK ACTIVATION UPON EGF RECEPTOR OVEREXPRESSION
COMPUTER SIMULATION OF DIFFERENTIAL KINETICS OF MAPK ACTIVATION UPON EGF RECEPTOR OVEREXPRESSION I. Aksan 1, M. Sen 2, M. K. Araz 3, and M. L. Kurnaz 3 1 School of Biological Sciences, University of Manchester,
More informationModelling in Systems Biology
Modelling in Systems Biology Maria Grazia Vigliotti thanks to my students Anton Stefanek, Ahmed Guecioueur Imperial College Formal representation of chemical reactions precise qualitative and quantitative
More informationStochastic Simulation of Biological Systems with Dynamical Compartments
Frontmatter Stochastic Simulation of Biological Systems with Dynamical Compartments Cristian Versari versari(at)cs.unibo.it Department of Computer Science University of Bologna Workshop on Computational
More informationDeducing Interactions in Partially Unspecified Biological Systems
Deducing Interactions in Partially Unspecified Biological Systems P. Baldan 1 A. Bracciali 2 L. Brodo 3 R. Bruni 2 1 Università di Padova 2 Università di Pisa 3 Università di Sassari Algebraic Biology
More informationLecture 4: Transcription networks basic concepts
Lecture 4: Transcription networks basic concepts - Activators and repressors - Input functions; Logic input functions; Multidimensional input functions - Dynamics and response time 2.1 Introduction The
More informationEnzyme Enzymes are proteins that act as biological catalysts. Enzymes accelerate, or catalyze, chemical reactions. The molecules at the beginning of
Enzyme Enzyme Enzymes are proteins that act as biological catalysts. Enzymes accelerate, or catalyze, chemical reactions. The molecules at the beginning of the process are called substrates and the enzyme
More informationBoolean models of gene regulatory networks. Matthew Macauley Math 4500: Mathematical Modeling Clemson University Spring 2016
Boolean models of gene regulatory networks Matthew Macauley Math 4500: Mathematical Modeling Clemson University Spring 2016 Gene expression Gene expression is a process that takes gene info and creates
More informationBioControl - Week 6, Lecture 1
BioControl - Week 6, Lecture 1 Goals of this lecture Large metabolic networks organization Design principles for small genetic modules - Rules based on gene demand - Rules based on error minimization Suggested
More information2. The study of is the study of behavior (capture, storage, usage) of energy in living systems.
Cell Metabolism 1. Each of the significant properties of a cell, its growth, reproduction, and responsiveness to its environment requires. 2. The study of is the study of behavior (capture, storage, usage)
More informationDISI - University of Trento Optimizing the Execution of Biological Models
PhD Dissertation International Doctorate School in Information and Communication Technologies DISI - University of Trento Optimizing the Execution of Biological Models Roberto Larcher Advisor: Prof. Corrado
More informationbiological networks Claudine Chaouiya SBML Extention L3F meeting August
Campus de Luminy - Marseille - France Petri nets and qualitative modelling of biological networks Claudine Chaouiya chaouiya@igc.gulbenkian.pt chaouiya@tagc.univ-mrs.fr SML Extention L3F meeting 1-13 ugust
More information9/25/2011. Outline. Overview: The Energy of Life. I. Forms of Energy II. Laws of Thermodynamics III. Energy and metabolism IV. ATP V.
Chapter 8 Introduction to Metabolism Outline I. Forms of Energy II. Laws of Thermodynamics III. Energy and metabolism IV. ATP V. Enzymes Overview: The Energy of Life Figure 8.1 The living cell is a miniature
More informationOrganization of Genes Differs in Prokaryotic and Eukaryotic DNA Chapter 10 p
Organization of Genes Differs in Prokaryotic and Eukaryotic DNA Chapter 10 p.110-114 Arrangement of information in DNA----- requirements for RNA Common arrangement of protein-coding genes in prokaryotes=
More informationStochastic Simulation.
Stochastic Simulation. (and Gillespie s algorithm) Alberto Policriti Dipartimento di Matematica e Informatica Istituto di Genomica Applicata A. Policriti Stochastic Simulation 1/20 Quote of the day D.T.
More informationMITOCW enzyme_kinetics
MITOCW enzyme_kinetics In beer and wine production, enzymes in yeast aid the conversion of sugar into ethanol. Enzymes are used in cheese-making to degrade proteins in milk, changing their solubility,
More informationThe Calculus of Looping Sequences
The Calculus of Looping Sequences Roberto Barbuti, Giulio Caravagna, Andrea MaggioloSchettini, Paolo Milazzo, Giovanni Pardini Dipartimento di Informatica, Università di Pisa, Italy Bertinoro June 7, 2008
More informationUnderstanding Science Through the Lens of Computation. Richard M. Karp Nov. 3, 2007
Understanding Science Through the Lens of Computation Richard M. Karp Nov. 3, 2007 The Computational Lens Exposes the computational nature of natural processes and provides a language for their description.
More information