c15_disc_dyn_mod_handout - Discrete dynamic modeling of...

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1 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 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. Boolean modeling of biological systems Main assumption: components have two main states : Expressed or not expressed , active or inactive, open or closed (ion channel), high or low level . Denote these states by ON (1) or OFF (0) 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 Can be defined based on set intersection and union, or input-output relations (gates, truth tables) Truth tables for Boolean operators In Out In1 In2 Out 0 0 0 In1 In2 Out 000 NOT AND OR 01 10 010 100 111 011 101 Out= NOT In Out= In1 AND In2 Out= In1 OR In2 In Out In1 In2 Out In1 In2 Out Out= NOT In Out In1 AND In2 Out In1 OR In2 Out= In1 AND In2 Out= In1 OR In2 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.
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2 From dose-response curves to Boolean switches X – mRNA Y – transcriptional activator If ν is large, the dose-response curve becomes a switch If Y>K Y dX/dt>0 If Y<K Y dX/dt<0 Hill function The activation threshold is K Y If activation is weak, mRNA can decay. Boolean simplification: X* = Y Activation: If Y=ON X*=ON Decay: If Y= OFF X*=OFF Hybrid models: Boolean regulation combined with continuous decay Each node is characterized by both a continuous and a Boolean variable.
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c15_disc_dyn_mod_handout - Discrete dynamic modeling of...

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