8.592JHST.452J: Statistical Physics in Biology
Assignment # 3
Extreme Values
1. Optimized Gaussians: Let x = maxcfw_r1 , r2 , , rN be the largest of N independent,
identically distributed Gaussian variables. Specically, each r is distributed according to
8.592JHST.452J: Statistical Physics in Biology
Assignment # 2
Fixation & Sequence Alignment
1. Multiallele model: Consider a locus occurring in one of s + 1 states (A1 , A2 , As , As+1 )
with frequencies x1 , x2 , , xs , xs+1 = 1 s=1 xi in a (haploid) pop
8.592JHST.452J: Statistical Physics in Biology
Assignment # 1
Probability
1. Open Reading Frames: Assume that the nucleotides A, G, T, C occur with equal proba
bility (and independently) along a segment of DNA.
(a) From the genetic code calculate the prob
8.592JHST.452J: Statistical Physics in Biology
Assignment # 4
Coulomb Interactions
1. Flory Theory: The Coulomb energy of a ball of charge Q and dimension R in d spacial
dimensions scales as
Q2
Ec d2 .
R
The proportionality coecient depends on the exact s
8.592JHST.452J: Statistical Physics in Biology
Assignment # 5
Protein Folding
1. Designed Random Energy Model (REM): Consider a protein model in which for a given
sequence and structure, the energy is randomly taken from the Gaussian probability density
1
8.592JHST.452J: Statistical Physics in Biology
Assignment # 6
Force-Extension Curves
1. Linear polymers: Using optical tweezers, it is now possible to pull on the two ends of a
single molecule. (Actually the tweezers pull on latex balls that are attached
8.592JHST.452J: Statistical Physics in Biology
Assignment # 7
ProteinDNA Interactions
1. Weight matrices: You are given a set of binding sites for the E. Coli purine repressor,
P urR (see le purR sites.txt on the assignment page).
(a) Build a weight matri
8.592JHST.452J: Statistical Physics in Biology
Assignment # 8
Drift, Diusion, and Dynamic Instability
1. Treadmilling Actin: Actin laments are long, asymmetric, polymers involved in a variety
of cellular functions. In some cases the laments are in a dynam