Thermodynamic Models of Gene Regulation

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Thermodynamic Models of Gene Regulation

• Xin He
• CS598SS
• 04/30/2009

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(No Transcript)
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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
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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.
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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.
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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
?Gs usually consists of two parts protein-DNA
interaction energy and protein-protein
interaction energy
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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
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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.
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Transcriptional Activation by Recruitment
Strength of interaction between A and RNAP, in
the range of 20100
Promoter occupancy
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Transcriptional Repression by Exclusion
Promoter and OR cannot be simultaneously occupied
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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
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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
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Synergistic Activation
Assumption RNAP can simultaneously contact two
TFs, A and B.
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Competitive Activation
Assumption binding of A or B excludes the other
factor.
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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 si as a state where the last bound site
is i, and W(.) be the weight of a state
For a state si, 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
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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

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Transcriptional Repression in Eukaryotic Cells (I)

1. Competitive DNA binding
2. Masking the activation surface
3. Direct interaction with the general transcription
   factors

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Transcriptional Repression in Eukaryotic Cells (I)

1. Recruitment of repressive chromatin remodeling
   complexes
2. Recruitment of histone deacetylases

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References

• Terrence Hwas 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