(<-)

[Chap10]

ComputationalModelingOfGeneticAndBioChemicalNetworks

Chap.11 Simplifying and Reducing Complex Models (in [Sefiroth/2004-02-05])

Summary

11.1 Introduction

  • experimental biology 의 발전 -> challenge to create a mathematical model or simulation of a given system

  • At what point does the model cease to have explanatory value?
  • dozens of parameters / complexity of the model -> stochastic system 인 경우는 더욱 심함

  • large simulations -> a tremendous amount of output -> useless

  • simplified models
  • focus on some particular level, often using heuristic approximations fo the finer details
  • principle of reductionism
  • microscopic <-> macroscopic level

  • modelling a biological system
  • the choice of parameters : an average of similar systems -> simplifed models

  • Is it possible to construct simplified models that are quatitative rather than just qualitative?
  • In this chapter we describe some methods that allow one to derive quantitatively correct models from more complex systems.

11.1.1 Averaging

  • fast quantity <-> slow quantity

  • spatial averaging : mean-field approximation

11.2 Master Equations

  • many biological problems : continuous time jump processes in which a system switches from one state to the next
  • e.g. random opening and closing of a channel, growth of an actin polymer, chemical reactions
  • Markov process : figure11.1
  • master equation

11.2.1 Application to a Model fo Fibroblast Orientation

  • effect of density on the behavior of fibroblasts in culture
  • fibroblasts will align with each other with a probability that depends on their relative angles of motion

11.2.2 Mean-Field Reduction of a Neural System

  • The master equation essentially averages over many sample paths in a system and leads to a set of equations for the probability of any given state of the system.
  • Another way to average a systme that haas intrinsic randomness is the so-called mean-field approximation.
  • the effect that cortical processing has on thalamic input in the somatosensory whisker barrel area of the rat

11.3 Deterministic Systems

  • There are many ways to reduce the dimension and complexity of deterministic systems.
  • Here we will concentrate on techniques for reduction by exploiting time scales.

11.3.1 Reduction of Dimension by Using the Pseudo-Steady State

11.3.2 Averaged Equations

  • A related way to reduce complexity is to again exploit time scales and average, keeping only the slow variables.
  • Hebbian Learning
  • Neural Network from Biophysics
  • Weakly Coupled Oscillators

11.4 Discussion and Caveats

  • Averaging is an intuitively appealing method for reducing the complexity of biological systems that operate on many different time and space scales.
  • When are important details being neglected? -> This is a very difficult question to answer.

  • How can you know when important details are missing? -> The only way to know is to do simulations.

web biohackers.net