Easy Removal of Steric Clashes and Entanglements in Macromolecular Systems by Temporary Addition of a Fourth Spatial Dimension

When models of complicated macromolecular systems are constructed, it is common to inadvertently include either gross steric clashes or entanglements of extended loop regions. Removing these problems with conventional energy minimization or dynamics algorithms can often be difficult. Here I show that one easy alternative is to temporarily add an extra spatial dimension and to displace atoms or molecules along this fourth dimension such that the distances between atoms, when measured in 4D, are no longer considered clashing. Adding in half-harmonic potential functions to mimic walls in this 4th dimension, and then moving these walls toward each other, has the effect of decreasing the space available in the 4th dimension and drives atoms to avoid each other in 3D. I illustrate the method with three examples: two showing how interlocked ring polymers can be easily disentangled from each other in both 2D and 3D, and one showing how ten identical coarse-grained protein models, all placed at the same point in 3D space, can be separated from each other, without distorting their structures, during the course of a single energy minimization. A sample program implementing the method is available that can be easily adapted to other situations.