Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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