Advanced Algorithms and Models for Computational Biology

Transcription

1 Advanced Algorithms and Models for Computational Biology Introduction to cell biology genomics development and probability Eric ing Lecture January Reading: Chap. DTM book Introduction to cell biology functional genomics development etc.

2 Model Organisms Bacterial hage: T4

3 Bacteria: E. Coli The Budding Yeast: Saccharomyces cerevisiae 3

4 The Fission Yeast: Schizosaccharomyces pombe The Nematode: Caenorhabditis elegans SMALL: ~ 50 µm TRANSARENT 959 CELLS 300 NEURONS SHORT GENERATION TIME SIMLE GROWTH MEDIUM SELF- FERTILIZING HERMAHRODITE RAID ISOLATION AND CLONING OF MULTILE TYES OF MUTANT ORGANISMS 4

5 The Fruit Fly: Drosophila Melanogaster The Mouse transgenic for human growth hormone 5

6 rokaryotic and Eukaryotic Cells A Close Look of a Eukaryotic Cell The structure: The information flow: 6

7 Cell Cycle Signal Transduction A variety of plasma membrane receptor proteins bind extracellular signaling molecules and transmit signals across the membrane to the cell interior 7

8 Signal Transduction athway Functional Genomics and -omics 8

9 A Multi-resolution View of the Chromosome DNA Content of Representative Types of Cells Organism ROKARYOTIC Mycoplasma genitalum Bacterium Helicobacter pylori Bacterium Haemophilus influenza Bacterium EUKARYOTIC Number of base pairs millions Number of encoded proteins Number of chromosomes Saccharomyces cerevisiae yeast Drosophila melanogaster insect Caenorhabditis elegans worm Homo sapiens human TO Arabidopsis thaliana plant

10 Functional Genomics The various genome projects have yielded the complete DNA sequences of many organisms. E.g. human mouse yeast fruitfly etc. Human: 3 billion base-pairs thousand genes. Challenge: go from sequence to function i.e. define the role of each gene and understand how the genome functions as a whole. Regulatory Machinery of Gene Expression motif 0

11 Classical Analysis of Transcription Regulation Interactions Gel shift : electorphoretic mobility shift assay EMSA for DNA-binding proteins * rotein-dna complex * Free DNA probe Advantage: sensitive Disadvantage: requires stable complex; little structural information about which protein is binding Modern Analysis of Transcription Regulation Interactions Genome-wide Location Analysis ChI-chip Advantage: High throughput Disadvantage: Inaccurate

12 Gene Regulatory Network Biological Networks and Systems Biology rotein-protein Interaction networks Regulatory networks Gene Expression networks Systems Biology: understanding cellular event under a systemlevel context Metabolic networks Genome + proteome + lipome +

13 Gene Regulatory Functions in Development Temporal-spatial Gene Regulation and Regulatory Artifacts A normal fly Hopeful monster? 3

14 Gene Regulation and Carcinogenesis oncogenetic stimuli ie. Ras p4 time required for DNA repaircell damage severe DNA damage M G 0 or G G p53 p53 Cancer! p6 S p5 p extracellular stimuli TGF-β activates Inhibits activates activates transcriptional activation Cdk + EF - hosphorylation of Rb Cycli CNA n DNA repair Rb Gadd45 + E A B G CNA not cycle specific romotes Apoptosis Fas TNF TGF-β... The athogenesis of Cancer Normal BCH DYS CIS SCC 4

15 Genetic Engineering: Manipulating the Genome Restriction Enzymes naturally occurring in bacteria that cut DNA at very specific places. Recombinant DNA 5

16 Transformation Formation of Cell Colony 6

17 How was Dolly cloned? Dolly is an exact genetic replica of another sheep. Definitions Recombinant DNA: Two or more segments of DNA that have been combined by humans into a sequence that does not exist in nature. Cloning: Making an exact genetic copy. A clone is one of the exact genetic copies. Cloning vector: Self-replicating agents that serve as vehicles to transfer and replicate genetic material. 7

18 Software and Databases NCBI/NLM Databases Genbank ubmed DB DNA rotein rotein 3D Literature Introduction to robability fx µ x 8

19 Basic robability Theory Concepts A sample space S is the set of all possible outcomes of a conceptual or physical repeatable experiment. S can be finite or infinite. E.g. S may be the set of all possible nucleotides of a DNA site: S { AT CG} A random variable is a function that associates a unique numerical value a token with every outcome of an experiment. The value of the r.v. will vary from trial to trial as the experiment is repeated ω S E.g. seeing an "A" at a site = o/w =0. This describes the true or false outcome a random event. Can we describe richer outcomes in the same way? i.e. = 3 4 for being A C G T --- think about what would happen if we take expectation of. Unit-Base Random vector i =[ ia it ig ic ] T i =[000] T seeing a "G" at site i ω Basic rob. Theory Concepts ctd In the discrete case a probability distribution on S and hence on the domain of is an assignment of a non-negative real number s to each s S or each valid value of x such that Σ s S s=. 0 s intuitively s corresponds to the frequency or the likelihood of getting s in the experiments if repeated many times call θ s = s the parameters in a discrete probability distribution A probability distribution on a sample space is sometimes called a probability model in particular if several different distributions are under consideration write models as M M probabilities as M M e.g. M may be the appropriate prob. dist. if is from "splice site" M is for the "background". M is usually a two-tuple of {dist. family dist. parameters} 9

20 Discrete Distributions Bernoulli distribution: Berp p for x = 0 x = p for x = x x Multinomial distribution: Multθ A Multinomial indicator variable: C = G T p x j = Multinomial distribution: Multnθ where = [ 0 ] j and = w.p. θ { j = where j index the observed nucleotide} xa xc xg xt xk x j = θa θc θg θt = θ k θ = θ = x Count variable: = M where x j = n j x K x x x θ θ LθK =! LxK! x! x k x = p p n! n! K p x = θ x! x! Lx! K j x j j j [ACGT] j j [ACGT] = θ =. Basic rob. Theory Concepts ctd A continuous random variable can assume any value in an interval on the real line or in a region in a high dimensional space usually corresponds to a real-valued measurements of some property e.g. length position It is not possible to talk about the probability of the random variable assuming a particular value --- x = 0 Instead we talk about the probability of the random variable assuming a value within a given interval or half interval [ x x ] < x = [ x ] The probability of the random variable assuming a value within some given interval from x to x is defined to be the area under the graph of the probability density function between x and x. x robability mass: [ x x] = p x dx note that Cumulative distribution function CDF: robability density function DF: x p x = x = d dx x < x = x + p x dx =. p x ' dx ' 0

21 Continuous Distributions Uniform robability Density Function p x = / b a for a x b = 0 elsewhere Normal robability Density Function p x = x µ / σ e πσ The distribution is symmetric and is often illustrated x µ as a bell-shaped curve. Two parameters µ mean and σ standard deviation determine the location and shape of the distribution. The highest point on the normal curve is at the mean which is also the median and mode. fx The mean can be any numerical value: negative zero or positive. Exponential robability Distribution x / µ density : p x = x / µ e o CDF : x x = e µ fx x < = area =.4866 x Time Between Successive Arrivals mins. Statistical Characterizations Expectation: the center of mass mean value first moment: Sample mean: E = i i S x p x i xp x dx discrete continuous Variance: the spreadness second moment: Var = x S [ x E ] p x i [ x E ] p x dx i discrete continuous Sample variance

22 Basic rob. Theory Concepts ctd Joint probability: For events E i.e. =x and H say Y=y the probability of both events are true: E and H := xy Conditional probability The probability of E is true given outcome of H E and H := x y Marginal probability The probability of E is true regardless of the outcome of H E := x=σ x xy utting everything together: x y = xy/y Independence and Conditional Independence Recall that for events E i.e. =x and H say Y=y the conditional probability of E given H written as E H is E and H/H = the probability of both E and H are true given H is true E and H are statistically independent if E = E H i.e. prob. E is true doesn't depend on whether H is true; or equivalently E and H=EH. E and F are conditionally independent given H if E HF = E H or equivalently EF H = E HF H

23 3 = = = i i p 6 5 p p 5 4 p 4 p p = Representing multivariate dist. Joint probability dist. on multiple variables: If i 's are independent: i = i If i 's are conditionally independent the joint can be factored to simpler products e.g. The Graphical Model representation The Bayesian Theory The Bayesian Theory: e.g. for date D and model M M D = D MM/D the posterior equals to the likelihood times the prior up to a constant. This allows us to capture uncertainty about the model in a principled way