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drenm_lec3

# drenm_lec3 - MIT 20.181 Module 3 Class 3 notes(DRAFT 27...

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MIT 20.181 Module 3 Class 3 notes (DRAFT)� 27 November 2006 Exact Methods for Computing Biological System Dynamics Drew Endy ( http://mit.edu/endy/ ) Goals Covered Last Time 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? Goals for Today E. Review how the physics model leads to computational method F. What is the complete computational method? G. What is the difference between a reaction rate and a reaction propensity? 46. Review. From physics model to computational method 47. Givens: i. A self-mixing volume, V. ii. V contains a system of N chemical species, S 1 -> S N iii. Each species, S i , is present at some number of molecules, X i iv. Species, S i , participate in M chemical reactions, R 1 -> R M v. Each time a reaction event occurs substrate molecules are converted into product molecules in accordance with the stoichiometry of that particular reac- tion. 48. What can we compute (from previous lecture)? i. a i is the probability that reaction i will occur in the next time interval. � a i = c u x h u . ii. c u is the average probability that a particular combination of R u reactant mole- cules will react. Computed via hard-sphere, will mixed, Arrhenius model. iii. h u is the number of unique reactant (i.e., substrate) combinations.for reaction R u at time, t. Computed via combinations.

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drenm_lec3 - MIT 20.181 Module 3 Class 3 notes(DRAFT 27...

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