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Protein-mRNA network Parameter Optimization

This projects fits the parameters of a regulatory network

Background Data

  • mRNA levels can be measured in a variety of ways.
  • The same methods can be applied to all sequences.
  • Protein levels are much harder to measure
  • Mutants give information
  • It is possible to determine where on the DNA a transcription factor binds. Likewise to determine if two proteins interact, etc.
  • Mutations are useful to: reveal components involved in a system, indicate causality, hint at how things are regulated.

System Description

  • A/B/C form a loop.
  • A activates transcription of B.
  • B activates transcription of C.
  • A represses B’s activation of C.
  • C represses transcription of A.
  • C increases degradation of B (which is otherwise slow).
  • Other components are degraded by dx/dt = -kx.
  • D is regulated by A, B and/or C but the relationship is unknown
  • Hill coefficients in the system are small integers (1 or 2)

The network showed in the next figure

system

The equation system proposed is:

equations

To solve it simmulated annealing and genetic algorithms were applied. An example of genetic algorithms can be found here.

Data

The Experimental data that needs to be fit is shown in the figures bellow:

Experimental_1

When mD is not considered

Experimental_2

When mD is considered

Experimental_3

Overexpression mutants, transcription.

Results

Using simulated annealing the results obtained are as follows:

Comparison_1

Comparison_2

Comparison_3