This paper investigates the use of a high-speed computer to simulate the unwinding of DNA. A Langevin equation of motion for the well-known bead-spring statistical macromolecule is written in difference form. An appropriate set of boundary conditions is developed to simulate a helical molecule and the resulting set of rules for the motion of the chain elements is used to produce the strand unwinding. The unwinding appears to proceed via initial end-unwinding followed by progressive unwinding inward. The latter process appears to occur by diffusion of twist outward from the central portion of the macromolecule. A computer simulation, using the Langevin equation, of linear tensile relaxation is compared with the appropriate analytical solution via the Rouse treatment of polymer dynamics, good agreement being obtained. The helical results are compared both with tensile relaxation and with Crothers' (1964) analytical treatment of the unwinding problem, which is analogous to the well-known temperature diffusion problem. The tensile results and Crothers' results are identical in form, and agree quantitatively remarkably closely with the computer-simulated helical unwinding, although the helical unwinding is somewhat slower.
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Financial support for E.M.S. from the National Institutes of Health is acknowledged. We are also indebted to the National Institutes of Health for grant GM-11916, which supported the cost of the calculations.
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Simon, E.M., Zimm, B.H. A computer simulation of the unwinding of a DNA-like helix. J Stat Phys 1, 41–55 (1969). https://doi.org/10.1007/BF01007240
- helical molecule
- computer simulation
- Langevin equation
- bead-spring macromolecule
- polymer dynamics
- unwinding of DNA
- tensile relaxation
- Rouse-Bueche model