|| (<-) || [Chap10] || ComputationalModelingOfGeneticAndBioChemicalNetworks ||

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

||<<TableOfContents>>||

== 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.