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Unformatted text preview: MIT 20.181 Module 3 Class 2 notes (DRAFT) 22 November 2006 Exact Methods for Computing Biological System Dynamics Drew Endy ( http://mit.edu/endy/ ) Goals Covered Last Time A. When to use computational methods? B. When to use exact methods? Goals for Today C. What is the underlying physics models used by exact methods? D. How can we use this model to compute when a reaction will take place? 25. Question C. To develop an exact discrete reaction even t method we need to con- sider the underlying physics model that might be used to represent individual reactions events inside cells . [ T he method we ' ll consider was developed by Daniel T. Gillespie and published in Journal of Computational Physics v22 p403-434 in 1976 . Y ou can find a one hour video of Dan talking about his work online ; the structure of this lecture is based directly on his presentation. Here s the URL: http://streaming1.osu.edu/ramgen/media/mbi/mbi302.rm ] 26. What sort of system are we talking about? Let s define a volume (V) containing N different types of molecules S (aka, species), with X number of molecules for each spe- cies. 27. How does the system change over time? They change via elementary chemical re- actions. What is an elementary chemical reaction? An elementary chemical reaction is a single instantaneous physical event. Only three such events are really likely. (i) from nothing comes a molecule (i.e., spontaneous generation), (ii) one molecule changes into another molecule(s), and (iii) two molecule collide and react to produce something (or nothing). 28. How could we determine what reactions occur when? Well, we can consider all sorts of information. For example, consider the 3D position and velocity of all the molecules. This might lead us to use molecular dynamics : follow ing every molecule in the system of interest as it moves about, bumping into other molecules, changing course, reacting every now and then. This would be great-- except that it s computational ly impractical for most systems of interest. One reason for this is that most molecule-molecule collision events are non- reactive....
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This note was uploaded on 11/11/2011 for the course BIO 20.010j taught by Professor Lindagriffith during the Spring '06 term at MIT.
- Spring '06