Free energy landscapes of model peptides and proteins

Abstract

A parallel searching algorithm based on eigenvector-following is used to generate databases of minima and transition states for an all-atom model of the peptide Ac(ala) 3 NHMe and for a simplified bead model of a protein. We analyze the energy landscapes of both systems using disconnectivity graphs based upon both potential energy and free energy. This approach highlights the role of vibrational entropy in determining the relative free energy of local minima. Thermodynamic properties for Ac(ala) 3 NHMe calculated using the superposition approach are in reasonable agreement with parallel-tempering Monte Carlo simulations.

Exploring Energy Landscapes: Metrics, Pathways, and Normal-Mode Analysis for Rigid-Body Molecules

“…The free energy of a transition state can be defined in a similar way, except that the negative eigenvalue in the normal mode frequency calculation is excluded (κ − 1 vibrational modes). 22 …”

“…20 These frequencies are needed to calculate thermodynamic properties within the harmonic superposition approximation. [21][22][23] To provide proof of principle, we apply the angleaxis framework to characterize the potential and free energy landscape of a water cluster containing eight molecules, described by the TIP4P potential. 1 To map the energy landscape, we first employ basin-hopping global optimization 24 to find the global minimum and construct a database of low energy minima.…”

“…This procedure provides a global survey of the potential energy landscape, which we visualize using disconnectivity graphs. 27,28 Finally, we compute the free energy of the minima and transition states using the harmonic superposition approach, 21,23 and construct the free energy disconnectivity graphs 22,29 at several representative temperatures.…”

Decoding the energy landscape: extracting structure, dynamics and thermodynamics

“…For example, figure 3 illustrates a free energy disconnectivity graph [19,20] for a peptide containing 16 amino acids, which forms Free energy (kcal mol −1 ) disconnectivity graph calculated at 298 K for the GB1 peptide using an implicit solvent and a barrier threshold of 5 kcal mol −1 for regrouping [89]. Structures corresponding to one member of the denatured set and five members of the expanded group of folded states are superimposed on the graph.…”

“…An alternative approach, which does preserve the lowest potential or free energy barriers between local minima, can be realized using disconnectivity graphs [17][18][19][20]. This framework is described in §3.…”