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Thermodynamic Models of Gene Regulation

Thermodynamic Models of Gene Regulation. Xin He CS598SS 04/30/2009. A. Thermodynamic Background: Micro-states. Micro-states: a bio-molecular system can exist in a number of different “states”. Protein:. Folded state. Unfolded state. DNA:. Unbound state. Bound state. Boltzmann constant.

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Thermodynamic Models of Gene Regulation

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  1. Thermodynamic Models of Gene Regulation Xin He CS598SS 04/30/2009

  2. A Thermodynamic Background: Micro-states Micro-states: a bio-molecular system can exist in a number of different “states”. Protein: Folded state Unfolded state DNA: Unbound state Bound state

  3. Boltzmann constant Probability of state s Temperature Energy of state s Boltzmann weight Partition function Thermodynamic background: Boltzmann Distribution Intuition: if a state has lower energy, the additional energy (because the total energyis conserved) is used to increase the entropy of the environment, thus it is more likely.

  4. Chemical potential Number of molecules in state s Concentration Chemical potential at the standard condition Standard condition: e.g. 1mol/l Thermodynamic Background: Gibbs Distribution Suppose the system exchanges, not just energy, but also molecules, with its environment, the probability of a state will also depend on the number of molecules in the state.

  5. Chemical potential Concentration B A A Free energy Number of bound molecules [Shea & Ackers, JMB, 1985] Application of Gibbs Distribution to Protein-DNA Interaction A promoter/enhancer sequence can bind multiple protein molecules. Suppose in one state s, two types of molecules A and B are bound, the probability of the state is given by: ΔGs usually consists of two parts: protein-DNA interaction energy; and protein-protein interaction energy

  6. A Transcription Factor-DNA Binding Question: what is the probability that a site is bound by its corresponding TF? Boltzmann weight of the bound state Equilibrium binding constant of the consensus site Mismatch energy Log-likelihood ratio score Site occupancy

  7. Gene Expression and Promoter Occupation mRNA level: mRNA degradation rate Probability of promoter occupation by RNAP At steady state: Transcription factors activate or repress gene expression level by modifying the promoter occupancy by RNAP.

  8. Transcriptional Activation by Recruitment Strength of interaction between A and RNAP, in the range of 20~100 Promoter occupancy:

  9. Transcriptional Repression by Exclusion Promoter and OR cannot be simultaneously occupied

  10. Combinatorial Transcriptional Control (I) Indicator variable of the i-th site Weight of a state TF-TF, TF-RNAP interactions TF-DNA, RNAP-DNA interactions

  11. Combinatorial Transcriptional Control (II) Total weight of all states where the promoter is occupied by RNAP: Total weight of all states where the promoter is not occupied by RNAP: Probability that the promoter is occupied by RNAP:

  12. Synergistic Activation Assumption: RNAP can simultaneously contact two TFs, A and B.

  13. Competitive Activation Assumption: binding of A or B excludes the other factor.

  14. Computing Partition Functions Problem: the number of states is exponential to the number of sites. To compute the partition function, one needs to sum over all states. Assumption: each bound TF interacts only with its neighboring TF Define σ[i] as a state where the last bound site is i, and W(.) be the weight of a state: For a state σ[i], suppose the nearest bound site of i is j, then: Interaction of TF with site i Interaction between TFs bound at site i and j Sum over all possible values of j, and all states:

  15. Transcriptional Activation in Eukaryotic Cells • Transcription involves assembly of many more proteins (GTFs, co-factors) • Enhancer sequences are often located far from the transcription start site • DNA looping for distant activators to interact with proteins in the transcriptional machinery

  16. Transcriptional Repression in Eukaryotic Cells (I) • Competitive DNA binding • Masking the activation surface • Direct interaction with the general transcription factors

  17. Transcriptional Repression in Eukaryotic Cells (I) • Recruitment of repressive chromatin remodeling complexes • Recruitment of histone deacetylases

  18. References • Terrence Hwa’s course of quantitative molecular biology http://matisse.ucsd.edu/~hwa/class/w07/ • Biological background Alberts et al, Molecular Biology of the Cell • Physical background Nelson, Biological Physics: Energy, Information, Life • Thermodynamic Modeling of transcriptional regulation Buchler et al, On schemes of combinatorial transcription logic, PNAS, 2003 Berg and von Hippel, Selection of DNA binding sites by regulatory proteins, Trends Biochem Sci, 1998

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