In the basin-hopping approach the original potential energy surface (solid) is transformed into a set of plateaux (dashed). The local minima are not changed, but the transition state regions are removed.
The basin-hopping algorithm is defined by a few parameters that make it readily transferable between different systems.
Variation of the energy of the current minimum as a function of for minima encountered in the Markov chain during a basin-hopping run using a Gō model. Steps that increase the energy are sometimes allowed by the Monte Carlo criterion, which employed a temperature of .
Energy as a function of for local minima of 434 repressor encountered during 100 independent basin-hopping optimizations (top) and 20 annealing simulations (bottom).
The lowest energy structures of the training set protein, 434 repressor (top), and the blind prediction proteins, HDEA (bottom) identified from 100 independent basin-hopping simulations. Each minimum has values for energy, illustrated by dots, and structural overlap with the native state , represented by the continuous line. These minima are ordered with respect to their structural overlap with the native state (index). The data show correlations between the energy and , while the number of high quality structures is superior for the training protein.
Energy as a function of for the 434 repressor and cytochrome c proteins obtained in basin-hopping calculations with the structure prediction Hamiltonian. These runs employed an additional umbrella potential that constrains the simulation to different values of . The results for the 434 repressor are similar to the unconstrained basin-hopping results, but the structures for cytochrome c are lower in energy than those found in unconstrained basin-hopping runs.
Energies of local minima obtained using basin-hopping with the original and a sequence-averaged Hamiltonian for two training proteins. Importantly for both the top graph (434 repressor) and the bottom graph (uteroglobin), fewer non-native states are seen with the sequence-averaged (red) Hamiltonian when compared to standard Hamiltonian (black).
Results of 100 independent basin-hopping runs for the 434 repressor using the set of backbone parameters that was optimized for molecular dynamics. Structures were saved every 20 basin-hopping steps. The ratio of contacts to native state contacts shows that most of the structures are more compact than the native state.
A Gō potential simulation for the 434 repressor shows a modest amount of overcollapse during a basin-hopping simulation, which is resolved as the structure approaches a value of 1.0.
Results of 100 independent basin-hopping runs for the 434 repressor using the set of backbone parameters that was optimized for molecular dynamics. Structures were saved every 20 basin-hopping steps. An altered set of backbone parameters produces structures that have similar collapse behavior when compared to the native state.
Minima located by molecular dynamics/annealing (MD) and basin-hopping (BH); the first three proteins are in the training set of the Hamiltonian, while the results for the second three proteins are predictions.
Contribution of different energy terms in local minima obtained using molecular dynamics/annealing (MD) and basin-hopping (BH).
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