c15_disc_dyn_mod

# c15_disc_dyn_mod - Discrete dynamic modeling of biological...

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Discrete dynamic modeling of biological systems The functional form of regulatory relationships and kinetic parameters are often unknown Increasing evidence for robustness to changes in kinetic parameters. bistability (two steady states) Hypothesis: the kinetic details of individual interactions are less portant than the organization of the regulatory network important than the organization of the regulatory network Discrete dynamic models assume that nodes can be characterized by only a few (minimum two) discrete states. Discrete models can handle larger networks than continuous models.

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Boolean modeling of biological systems Main assumption: components have two main states : Expressed or not expressed , active or inactive, open or closed (ion p p , , p ( channel), high or low level . Denote these states by ON (1) or OFF (0) he changes in state are given by discrete (logical) rules The changes in state are given by discrete (logical) rules. The future state of a regulated node (the output) depends on the current state of its regulators (inputs), which may or may not include its own current state. e.g. If transcription factor is active, gene will be transcribed, gene will be expressed in the next time step. Boole logic: based on the operators NOT, AND, OR an be defined based on set intersection and union or input- utput relations Can be defined based on set intersection and union, or input output relations (gates, truth tables)
Truth tables for Boolean operators OT ND R In1 In2 Out In1 In2 Out NOT AND OR In Out 00 0 0 0 1 10 0 1 0 0 0 1 1 1 1 1 1 1 1 1 Out= NOT In ut= In1 AND In2 ut= In1 OR In2 Out= In1 AND In2 Out= In1 OR In2

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In Out 01 In1 In2 Out 000 In1 In2 Out 10 010 100 011 101 ut= NOT In 1 1 1 1 1 1 Ou O Out= In1 AND In2 Out= In1 OR In2 x 1 Give examples for the realization of these Boolean rules in a gene regulatory Ex. 1 Give examples for the realization of these Boolean rules in a gene regulatory network. Ex. 2 Consider a transcription event activated by a transcription factor. Compare the continuous and Boolean description of this process.
From dose-response curves to oolean switches Boolean switches X – mRNA Y – transcriptional activator If ν is large, the dose-response curve becomes a switch Y>K X/dt>0 If Y>K Y dX/dt>0 If Y<K Y dX/dt<0 The activation threshold is K Y activation is weak mRNA Hill function If activation is weak, mRNA can decay.

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c15_disc_dyn_mod - Discrete dynamic modeling of biological...

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