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 selfmixing 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 hardsphere, 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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 Spring '06
 LindaGriffith
 Chemistry, Reaction, Probability theory, Chemical reaction, Rate equation

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