Download CS 626 project III (folding of hetero

CS 626 project III (folding of hetero-polymers), due Thursday May 9.
We consider a two dimensional hetero-polymer on a cubic lattice. There are four types of
monomers H, P, + and -. The chain is self-avoiding (the chain cannot step on itself). The
lattice spacing is a . The energy is evaluated as the sum of all contact energies. A contact
is defined between monomers that are separated by at least two bonds along the chain and
their spatial distance is either a or 2a . A contact energy is defined between two
monomers that are in contact and depends on the types of the two monomers according to
the table below
Contact types
Contact energies
(H,H)
-1
(+,-) (P,H/+/-)
0
(H,+/-) (+,+) (-,-)
2
Our task is to find the correct two-dimensional structure of the polymer
HPH+P+-+PPHHPP
Starting from an extended chain configuration we shall use Metropolis Monte Carlo
simulations to determine the structure of the global energy minimum.
The following functions are required:
1. A function to compute a step (a step is a rotation of a bond by 90 degrees)
2. A function to evaluate if the step is acceptable according to Metropolis criterion:
acceptance probability  min 1, exp  E / T   , E is the energy difference of
the configurations before and after the attempted step.
3. A function that samples configurations of the above polymers at a specific
temperature.
4. A function that evaluates the heat capacity at a specific temperature
5. A function that performs a complete simulated annealing run
To simulate the folding of the polymer start at a high temperature of and decrease the
temperature (while computing the heat capacity for each temperature). You will need to
run 10 million steps at every temperature window to converge the averages. Use the
following formula for the heat capacity:
1
2
C  2 E2  E
T
Note that at the lowest temperatures the simulations are difficult to converge and the
results are therefore unreliable at that range.


Identify the heat capacity peak and re-run simulated annealing of folding at a more
relevant temperature range.
In your final report include the above codes, a plot of the heat capacity as a function of
temperature, the final configuration and its energy