Math 193 - 0680
Molecular Reactions – MSI Project
Project due : Wednesday, 12/5/2007 (100 points)
To complete this project, please refer to your notes from our visit at the Molecular
Sciences Institute last week. The slides of the presentations by the researchers at MSI
have been uploaded on the DVC website at
http://voyager.dvc.edu/calculusfieldtrips/MSI/Presentation%20Slides.htm
1. What is systems biology?
2. The mole (mol) is a unit that measures the amount of a substance. Describe in your
own words what amount is 1 mole of a certain substance.
3. The molarity (M) is a unit of concentration. Describe in your own words what is a
solution of molarity 1M
In what follows, A and B are molecule types that react with certain probability to form
molecule AB, while the reverse reaction, with molecule AB breaking back up into its
components A and B may also occur.
4. In his presentation Dr. Lok explained how a chemical reaction where molecule A and
molecule B react to form molecule AB can be predicted assuming Markov’s principle
by using the probability density function f (t )  0.5e 0.5t . Under that model, what is
the probability that such a reaction will take place between 0 and 1 seconds?
5. (a) Denote the probability that the next reaction event will happen between time a and
time b, a  b, by Pab . In problem 4, you calculated P01 . Calculate P56 in the same
way.
(b) Calculate P5  lim b P5b This is the probability that the next reaction event will
happen after time 5 seconds.
(c) What is P0  lim b P0b ?
P56
P01
P56
(d) Note that    . The ratio  is the probability that the next reaction event
P5
P0
P5
will happen before time 6, given that (or assuming that) it does
P a 1 P 6
P1
not happen before time 5. Can you see that a   5  0 for all a, a  0? This
Pa
P5
P0
means that if the reaction event has not happened before any chosen time a, then the
probability that it will happen within 1 sec. after a does not depend on a.
6. In Dr. Addy’s presentation, the following mass action equations where given:
dforward
dreverse
 0.005M 1 s 1 [ A][ B] and
 0.001s 1 [ AB]
dt
dt
Explain what these equations mean.
7. Consider the differential equations
dAB
= rate in which AB is produced- rate in which AB is broken up (1)
dt
dA
= rate in which A is produced- rate in which A is used up (2)
dt
dB
= rate in which B is produced- rate in which B is used up (3)
dt
Assume at the beginning of the chemical reaction (time t = 0), the concentrations of A, B
and AB were given by
[A] =1M
[B] = 1M
[AB] = 0M
dAB dA
dB
,
and
at time 0. Follow
dt
dt
dt
Euler’s method to calculate [A], [B], and [AB] at time t = 0.2, 0.4, 0.6 0.8 and 1 sec.
Use equations (1) , (2) and (3) above to evaluate
8. In about 30-50 words, please describe how and whether the field trip has helped
your learning.