TY - JOUR KW - Protein Folding KW - graph KW - cut-based free energy profile KW - ultrametric distance KW - markov state models KW - ford-fulkerson theorem KW - Kramers theory KW - separation of time scales AU - R. Scalco AU - A. Caflisch AB -

The free energy of the transition state (TS) between two nodes of an ergodic Markov state model (MSM) can be obtained from the minimum cut, which is the set of edges that has the smallest sum of the flow capacities among all the possible cuts separating the two nodes. Here, we first show that the free energy of the TS is an ultrametric distance. The ultrametric property offers a way to simplify the MSM in a small number of states and, as a consequence, meaningful rate constants (free energy barriers) for the simplified MSM can be defined. We also present a new definition of the cut-based free energy profile (cbFEP), which is useful to check for the existence of a state for which the equilibration is much faster than the time to escape from it. From our analysis, a parallelism emerges between the minimum cut (maximum flow), and transition state theory (TST) or Kramers’ theory.

BT - Journal of Chemical Theory and Computation C1 - 0156 DA - May 8 2012 DO - 10.1021/ct3000052 IS - 5 J2 - J. Chem. Theory Comput. LA - eng M1 - 5 M3 - Research Article N2 -

The free energy of the transition state (TS) between two nodes of an ergodic Markov state model (MSM) can be obtained from the minimum cut, which is the set of edges that has the smallest sum of the flow capacities among all the possible cuts separating the two nodes. Here, we first show that the free energy of the TS is an ultrametric distance. The ultrametric property offers a way to simplify the MSM in a small number of states and, as a consequence, meaningful rate constants (free energy barriers) for the simplified MSM can be defined. We also present a new definition of the cut-based free energy profile (cbFEP), which is useful to check for the existence of a state for which the equilibration is much faster than the time to escape from it. From our analysis, a parallelism emerges between the minimum cut (maximum flow), and transition state theory (TST) or Kramers’ theory.

PY - 2012 SP - 1580 EP - 1588 T2 - Journal of Chemical Theory and Computation TI - Ultrametricity in protein folding dynamics UR - http://dx.doi.org/10.1021/ct3000052 VL - 8 ER -