Frustration in Condensed Matter and Protein Folding

By means of computer modeling, we are studying frustration in condensed matter and protein folding. Frustration is due to random and/or competing interactions between characters. One definition of frustration is the sum of squares of the differences between actual and expected distances between characters. If this sum is non-zero then the system is said to have frustration. A computer simulation ``Frustration'' is used to track the movement of characters to lower their frustration. Our research is conducted on frustration as a function of temperature using a logarithmic scale. At absolute zero, the relaxation for frustration is mostly a power function for randomly assigned patterns or an exponential function for regular patterns like Thomson figures. Thomson shapes are formed and the temperature-dependent frustration shows exponential behavior. At later times a linear trend sets in, close to zero or finite frustration. These findings have implications for protein folding; we attempt to apply our frustration modeling to protein folding and dynamics. We use coding in Python to simulate different ways a protein can fold. An algorithm is being developed to find the lowest frustration (and thus energy) states possible.