This is an new subject for me, studying the motion of biopolymers via simulation. I represent the biopolymer as a sequence of balls that are `tethered together.' The tethering is achieved by using a nonlinear spring potential that holds the balls at roughly the same distance (in my units this distance is 1). To get the polymer balls to attract each other, I have added a Lennard-Jones potential with a minimum at $r=1$, for all balls that are not nearest neighbors. The minimum energy is -1.

Finally, to represent the steric interactions of the polymer, I invoke a new description of the polymer backbone as a flexible tube. This description was developed by Jayanth Banavar and his collaborators. The variable that measures how tightly at tube is bent, is given by taking three points on the polymer and computing the radius R of the circle that passes through them. When this variable is small, the polymer is either tightly bent, or parts of the polymer that are far away are in close contact. When this happens I have a large repulsive potential that depends on R. From the pont of view of molecular dynamics, this three body potential is quite a task to evaluate, since I must sum over all possible triples of particles.. I have developed a relatively efficient method for doing this. The movie I have shows at 43 atom chain that is initially straight and at a temperature of 1 (total energy of +0.42) it is then cooled by removing some kinetic energy every so often.

4.1 MB MPG Movie of a 43 atom polymer folding up as its energy is reduced. Occasionally portions of the polymer are chopped off by the program that produced the figures. The energy per particle is noted in the upper right hand corner. The repulsive tube potential has a range of 0.9, the spacing of the balls is 1, and the van der Waals attraction has a minimum at 1.16. Total wall time for this simulation (106 steps) is 2 minutes on a 450 MHz Pentium III.