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# The Conveyor Belt Umbrella Sampling (CBUS) Scheme: Principle and Application to the Calculation of the Absolute Binding Free Energies of Alkali Cations to Crown Ethers

journal contribution

posted on 2020-03-25, 15:39 authored by David
F. Hahn, Rhiannon A. Zarotiadis, Philippe H. HünenbergerWe recently introduced a method called
conveyor belt (CB) thermodynamic
integration (TI) for the calculation of alchemical free-energy differences
based on molecular dynamics simulations. In the present work, the
CBTI approach is generalized to conformational free-energy changes,
i.e., to the determination of the potential of mean force (PMF) along
a conformational coordinate ξ of interest. The proposed conveyor
belt umbrella sampling (CBUS) scheme relies on the parallel simulation
of

*K*replicas*k*= 0,1, ...,*K*– 1 of the system, with*K*even. For each replica*k*, the instantaneous value of ξ is restrained to an anchor value*λ*_{k}. The latter anchor points are equally spaced along a forward-turn-backward-turn path (i.e., a CB) between two extreme values defining the ξ-range of interest. The rotation of the CB is controlled by a variable Λ (range from 0 to 2π) which evolves dynamically along the simulation. The evolution of Λ results from the forces exerted by the restraining potentials on the anchor points, taken equal and opposite to those they exert on the replicas. Because these forces tend to cancel out along the CB, the dynamics of Λ is essentially diffusive, and the continuous distribution of ξ-values sampled by the replica system is automatically close to homogeneous. The latter feature represents an advantage over direct counting (DCNT) and traditional umbrella sampling (TRUS), shared to some extent with replica-exchange umbrella sampling (REUS). In this work, the CBUS scheme is introduced and compared to the three latter schemes in the calculation of 45 standard absolute binding free energies. These correspond to the binding of five alkali cations to three crown ethers in three solvents. Different free-energy estimators are considered for the PMF calculation, and the calculated values are also compared to those of a previous study relying on an alchemical path, as well as to experimental data.## History

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## Keywords

replica systemreplica-exchange umbrella samplinglatter anchor pointsTRUSalkali cationsξ- rangealchemical pathumbrella samplingcrown ethersPMF calculationanchor value λ kConveyor Belt Umbrella SamplingREUSlatter featureconveyor belt umbrella samplingξ- valuesCBUS schemealchemical free-energy differencesDifferent free-energy estimatorsi.eAlkali Cationsforward-turn-backward-turn pathanchor pointsDCNTAbsolute Binding Free Energiesbindingconveyor beltK replicas kreplica kΛ resultsCBTI approachfree-energy changesdynamics simulationslatter schemesCrown Ethers

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