Here’s a very deep and very interesting paper: the origin and consequences of noise in biochemical systems, by Prof. Alexander Van Oudenaarden and Mukund Thattai.
The paper is about probabilistic reaction kinetics and stochastic simulation of chemical reactions (among other stuff), thus encompassing Stochastic Processes, Theoretical and Computational Chemistry and Systems Biology. Fascinating stuff.
An excerpt:
Surprising things happen when we take the discreteness of molecule number seriously, abandoning the notion that chemical concentrations may be treated as continuous variables. Here we will show how ideas of discreteness force us into dealing with issues of noise and randomness. We will arrive at a probabilistic description of reaction kinetics which, in the limit of large numbers, will reproduce the familiar reaction-rate description. We will show how probabilistic systems may be treated numerically using Monte Carlo simulations, and use such simulations to investigate how frequently large random fluctuations can change the state of a bistable system. This will help us understand the stability and spontaneous switching rates of actual biological switches such as those which underlie cell fate determination during development, or long-term potentiation in neurons.
I found this while surfing around the MIT OCW course on Systems Biology.
Tags: Biochemistry, Biomathematics, Reaction Kinetics, Scientific Papers, Stochastic Processes, Systems Biology, Theoretical Chemistry
March 3, 2008 at 12:55 am |
This reminds me that I once attended a talk given by Prof. John Doyle on the “robust yet fragile” nature of complex systems such as the internet, engineering systems, or biological cells.
After Doyle’s presentation, I talked to him a bit about what mathematical tools were being used to model the complex mechanisms within living cells. Among many things, he told me that models based on Markov chains were used when there are “few” molecules reacting (thus forcing one to consider the “discreteness” of molecule number), while models based on differential equations are used when there are “many” molecules.
Interestingly enough, I had “discovered” this when working in optics and trying to model nonlinear interactions of just a “few” photons.