Frustration in Condensed Matter and Protein Folding

Using computer modeling [1-3] we study frustration in condensed matter and protein folding. Frustration is due to random and/or competing interactions. One definition of frustration is the sum of squares of the differences between actual and expected distances between characters. [3] If this sum is non-zero, then the system is said to have frustration. A simulation tracks 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 a power function for randomly assigned patterns or an exponential function for regular patterns like Thomson figures. These findings have implications for protein folding; we attempt to apply our frustration modeling to protein folding and dynamics. [4,5] 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. [6,7] Research supported by SJSU {\&} AFC. [1] AK Dewdney, \textit{Scientific American } (1987) 112. [2] C Boekema \textit{et al,} \textit{Hpf Interact 26 }(1990) 345. [3] I M Suarez \textit{et al,} Conf Proc 2nd Woodward Conference, Springer Verlag NY 1990; Am Phys Soc Bull 35 (1990) 548. [4] J Claycomb {\&} JQP Tran, \textit{Introductory Biophysics }(2010). [5] LN Mazzoni {\&} L Casetti, \textit{Phys Rev Lett} (2006) [6] JL Van Hemmen, \textit{Phys Rev Lett }49 (1982) 4109. [7] M Mezard \textit{et al}, Spin Glass Theory and Beyond\textit{. World Scientific }(1987).