BME 5742 Biosystems Modeling and Control
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1 BME 5742 Biosystems Modeling and Control Lecture 24 Unregulated Gene Expression Model Dr. Zvi Roth (FAU) 1
2 The genetic material inside a cell, encoded in its DNA, governs the response of a cell to various conditions. DNA is organized into collections of genes, with each gene encoding a corresponding protein that performs a set of functions in the cell. DNA and Genes Dr. Zvi Roth (FAU) 2
3 Introductory Comments about Gene Expression All cellular functions are driven by proteins Protein production occurs through Gene Expression Gene expression is a two-step process that involves at the start the reading of information encoded in the DNA and at the end a synthesis of a protein molecule The production rate of each protein is controlled by proteins called Transcription Factors Dr. Zvi Roth (FAU) 3
4 The Central Dogma of Biology Dr. Zvi Roth (FAU) 4
5 Transcription Definition The process by which the coding region of a gene is rewritten in the form of a complementary RNA strand called messenger RNA (mrna) Dr. Zvi Roth (FAU) 5
6 Translation Definition The process by which the mrna binds to a ribosome which reads the nucleotide sequence and produces a corresponding polypeptide chain That chain, when done, spontaneously folds to create the protein Dr. Zvi Roth (FAU) 6
7 Gene Regions Any DNA segment that encodes some protein production must include specific regions: Promoter, Regulation, Coding and Termination Dr. Zvi Roth (FAU) 7
8 The Transcription Process RNA Polymerase enzyme first binds to the promoter part of the gene. Once bound it splits open the DNA strands. Then the enzyme moves along the coding part of the gene to create an mrna sequence Once the enzyme finds the termination sequence it detaches from the DNA and the transcription ends Dr. Zvi Roth (FAU) 8
9 Cell and mrna Typical Timing Figures Production rate of mrna = base pairs per second Half life of mrna is around 100 seconds Cell division time is around 3000 seconds Dr. Zvi Roth (FAU) 9
10 From Transcription to Translation DNA strands re-attach, become ready for more copies of the same mrna or other ones. RNA goes through some pre-processing steps, and is eventually transported out of the nucleus and into the cytoplasm RNA then encounters the ribosomes Dr. Zvi Roth (FAU) 10
11 From Transcription to Translation in Prokaryotic and Eukaryotic Cells No nucleus in prokaryotic cells mrna as it is produced encounters the ribosomes Translation starts Dr. Zvi Roth (FAU) 11
12 From Transcription to Translation in Prokaryotic and Eukaryotic Cells In eukaryotic cells mrna needs to be transported from the nucleus to the cytoplasm Some pre-processing of the mrna is needed Dr. Zvi Roth (FAU) 12
13 From Transcription to Translation in Prokaryotic and Eukaryotic Cells In eukaryotic cells In pre-mrna needs to excise of introns, splice of exons, attach an ending segment (polyadenylation) Mature mrna Transport out of the nucleus Dr. Zvi Roth (FAU) 13
14 Ribosomes Dr. Zvi Roth (FAU) 14
15 What are Ribosomes? The ribosome is a large and complex molecular machine, found within all living cells, that serves as the primary site of biological protein synthesis (translation). Ribosomes link amino acids together in the order specified by messenger RNA (mrna) molecules. Dr. Zvi Roth (FAU) 15
16 Ribosomes Major Subunits Ribosomes consist of two major subunits the small ribosomal subunit reads the mrna, while the large subunit joins amino acids to form a polypeptide chain. Each subunit is composed of one or more ribosomal RNA (rrna) molecules and a variety of proteins. Dr. Zvi Roth (FAU) 16
17 The Translation Process Dr. Zvi Roth (FAU) 17
18 Translation: the role of trna The mrna goes through the ribosome. Each mrna codon is translated by trna as to what would be the next protein link to be assembled (selecting one of 20 possible amino acids) Dr. Zvi Roth (FAU) 18
19 Ribosomes, mrna, trna and Translation The cell must have sufficient number of types of trna molecules (between 31 and 61) The assembled protein folds on itself to create its functional 3D shape. Dr. Zvi Roth (FAU) 19
20 Protein typical timing figures Protein production time is around amino acids per second Protein half life is around 50,000 seconds (much larger than the cell s division time). Dr. Zvi Roth (FAU) 20
21 Transcriptional Regulation DNA transcription may be regulated by Repressors and Activators Transcription factors (such as proteins that bind the DNA near its promoter region operator region) may turn the gene off. Activators enhance the binding of RNA Polymerase to the promoter. Dr. Zvi Roth (FAU) 21
22 Simplified Mathematical Model of Unregulated Gene Expression dm( = k0 δ mm( dp( = k1m( δ p p( A highly approximated prokaryotic gene expression Concentration of mrna molecules = m( Concentration of gene s protein product = p( Dr. Zvi Roth (FAU) 22
23 Simplified Mathematical Model of Unregulated Gene Expression dm( = k0 δ mm( dp( = k1m( δ p p( Average transcription rate = k 0 The rate k 0 depends on the number of gene copies, the abundance of RNA polymerase, the affinity of gene s promoter to the transcription factor and the availability of nucleotide building blocks Dr. Zvi Roth (FAU) 23
24 Simplified Mathematical Model of Unregulated Gene Expression dm( = k0 δ mm( dp( = k1m( δ p p( Per-mRNA translation rate = k 1 The rate k 1 depends on availability of ribosomes, affinity of the mrna to the ribosome binding site, availability of trna and free amino acids. Dr. Zvi Roth (FAU) 24
25 Simplified Mathematical Model of Unregulated Gene Expression dm( = k0 δ mm( dp( = k1m( δ p p( Transcription and translation are balanced by the decay of the mrna and protein pools, characterized by the δ rates. There are enzymes that their role is to decimate the mrna and specific protein molecues. Dr. Zvi Roth (FAU) 25
26 Simplified Mathematical Model of Unregulated Gene Expression dm( = k0 δ mm( dp( = k1m( δ p p( The δ rates also include the dilution effect due to the increase of cell volume to accommodate the constructed new protein molecules. Dr. Zvi Roth (FAU) 26
27 Simplified Mathematical Model of Unregulated Gene Expression dm( = k0 δ mm( dp( = k1m( δ p p( dm( = 0 m dp( = 0 pe e k0 = δ k1 = δ p m m e = k1 δ p k0 δ m So, this simplified unregulated gene expression model is linear Equilibrium point is shown above. Typically, m( reaches equilibrium much faster than p( Dr. Zvi Roth (FAU) 27
28 More Simplified Mathematical Model of Unregulated Gene Expression dm( = k0 δ mm( dp( = k1m( δ p p( dm( dp( Typically, m( reaches equilibrium in minutes which is much faster than p( that reaches equilibrium in hours. Simplified model for dp( k1k0 protein synthesis, where δ p p( δ k m 1 k 0 /δ m is the expression rate = = 0 0 m p Dr. Zvi Roth (FAU) 28 e e k0 = δ k1 = δ p m m e k1 = δ p k0 δ m
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