EE 5393
UMN
Circuits, Computation, and Biology
Winter 2013
⊕
⊕
Homework # 2
Due March 29, 2013 [in class]
1.
Analyzing Stochasticity in Molecular Reactions
Randomness is inherent to all forms of biochemical computation: at any given
instant, the choice of which reaction fires next is a matter of chance. Certain
biochemical systems appear to exploit this randomness for evolutionary advan
tage, choosing between different outcomes with a probability distribution – in
effect, hedging their bets with a portfolio of responses that is carefully tuned to
the environmental conditions.
For instance, the
lambda
bacteriophage, a virus that infects the
E. coli
bacteria,
chooses one of two survival strategies: either it integrates its genetic material
with that of its host and then replicates when the bacterium divides (call this
“stealth” mode); or else it manipulates the molecular machinery of its host to
make many copies of itself, killing the bacterium in the process, and thereby
releasing its progeny into the environment (call this the “hijack” strategy).
The choice of which strategy to pursue, while based on environmental inputs,
is probabilistic:
in some cases, the virus chooses the first strategy, say with
probability
p
and the second with probability 1

p
. Clearly the virus is hedging
its bets, an approach that provides significant advantages in an evolutionary
context.
A model for the biochemistry of
lambda
is at:
A set of initial values for the molecular types is at:
With this model, we can assume that
lambda
has entered “stealth” mode when
cI
2
>
145; it has entered “hijack” mode when
Cro
2
>
55.
EE 5393, Winter ’13
2
For the reactions and initial values given, compute the probability that
lambda
has entered “stealth” mode vs.
“hijack” mode for a range of values of the
molecular type
MOI
= 1
. . .
10.
For this problem, you can either use your own code for simulating chemical
reactions from Homework 1 or use my code:
.
2.
Computing with Molecular Reactions
For this problem, use Phil Senum’s compiler:
(a)
Euclid’s Algorithm
Euclid’s algorithm is an efficient method for computing the greatest com
mon divisor (GCD) of two integers, also known as the greatest common
factor (GCF) or highest common factor (HCF). It is named after the Greek
mathematician Euclid, who described it in Books VII and X of his Ele
ments.
In its simplest form, Euclid’s algorithm starts with a pair of positive
integers and forms a new pair that consists of the smaller number and the
difference between the larger and smaller numbers.
The process repeats
until the numbers are equal. That number then is the greatest common
divisor of the original pair.
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 Spring '14
 Riedel,Marc
 Boolean Algebra, Boolean function, Logical connective, Winter ’13, Molecular Reactions