Biol 591 
Introduction to Bioinformatics
Problem Set 4
Fall 2002 

PS4.1. The liver enzyme cytochrome P450 is involved in the metabolism a large number of compounds, particularly those of foreign origin, like acetomeniphen, caffeine, codeine, and AZT. Since and the effect of a drug is closely related to its lifetime in the body, understanding of the action of cytochrome P450 on a particular drug is often critical for predicting the drug's efficacy. You want to model the reaction below, catalyzed by cytochrome P450. Determine whether each of the proposed rate equations that follow is correct. If it isn't, make it correct.

                                                         kf ==>                     kc ==>
Reaction:  Pg  + NADPH + O2 + E <=====>  E-complex  =====> 6-beta-OH-Pg + NADP+ + E
                                                    <== kr

(Pg = progesterone, 6-beta-OH-Pg = 6-beta-hydroxy-progesterone, and E = cytochrome P450)

a. d[6-beta-OH-Pg]/dt  = [E-complex] kc  -  [6-beta-OH-Pg] [NADP] [E] kc
b. d[E]/dt = [Pg] [NADPH] [O2] [E] kf
c. d[E-complex]/dt = - [Pg] [NADPH] [O2] [E] + [E-complex] kc

PS4.2. Alter the program glycolysis.pl in the following ways:
a. Get rid of the irritating lines of values printed on the monitor.
b. Have the program print instead the current time step each iteration through the loop, so you can tell where it is.
c. Have the program print instead every 100th time step (to cut down on printing), so you can tell about where it is.
Hint: Use the Perl function int( ) (which gives you the greatest integer less than a given number) in conjunction with division. Only every 100th time step $time_step/100 will be equal to int($time_step/100). If you aren't sure how int( ) works, try writing a one-line program to test it's function.
PS4.3. The given version of glycolysis.pl has (line 159):
$dGlcx_dt  = -$v_Rxn1
a. What is the physical significance of this equation?

b. It seems pretty absurd to think that a trypanosome can suck up a significant amount of blood glucose. Change the statement to model the alternative view that glycolysis in Trypanosomes has no effect on the level of blood glucose. Use this version of the program in all subsequent work.

PS4.4. Alter the program glycolysis.pl so as to test what effect inhibiting hexokinase will have on the level of metabolites. (note that Eisenthal and Cornish-Bowden (1998) have already done the enzymological derivation for you)

PS4.5. The conentrations of the metabolites in glycolysis.pl are given using units of mM. Suppose that's all right with you, but in the end you want to print the results in units of M. Add one line to the program and modify another to accomplish this task.

PS4.6. What happens when you decrease the time interval used in stepping through glycolysis.pl? What happens when you increase the time interval? Be sure you try enough values to get a picture of the general trend.

PS4.7. Write a rate equation to describe the number of bacteria in a culture where the bacteria doubles every 20 minutes. Presume that there is no limitation by food or other resources.

PS4.8. Consider the growth of a virus on a population of bacterial cells.

a. Write an equation to describe the interaction between a virus and a bacterium, capturing the idea that one virus attacks one bacteria and the result 90 minutes later is a dead bacterium and 40 progeny viruses.

b. Write rate equations that describe the change in the population of viruses and the change in the population of bacteria.

c. Write a program that simulates the growth of virus on bacteria and display the growth curve in Excel. Assume a bacterial generation time of 20 minutes. [Of course, steal 90% of the program from the most convenient source, probably ADP-As.pl]

PS4.9. You'd like to develop a model that predicts the acquisition of drug resistance by HIV over the course of many viral generations... but let's stick with more familiar territory (but an analogous problem). Mutation of a specific nucleotide occurs in bacterial viruses at a rate of about 1 mutation every 109 generations (or every 109 viruses). Suppose that the virus considered in PS4.7 takes on special properties when a certain nucleotide is mutated from A to G (maybe the virus becomes resistant to a particular defense against it). Find by modeling the time course with which that mutant virus will appear in the population. Note that a virus may come to possess the key mutation in one of two ways: (1) by a new mutation (rarely), or (2) by inheritance (100% if parent is mutant, 0% if not).
(If you manage to complete this problem, your program will be an example of numerical integration, i.e. integrating a function by computer even when you don't know how to integrate the function by means of calculus)