Implementation of an adaptive umbrella sampling method for the calculation of multidimensional potential of mean force of chemical reactions in solution

Abstract

We describe the implementation of an adaptive umbrella sampling method, making use of the weighted histogram analysis method, for computing multidimensional potential of mean force for chemical reaction in solution. The approach is illustrated by investigating the effect of aqueous solution on the free energy surface for the proton transfer reaction of [H(3)N-H-NH(3)](+) using a combined quantum mechanical and molecular mechanical AM1/TIP3P potential.

Prediction of Molecular Interaction between Platelet Glycoprotein Ibα and von Willebrand Factor using Molecular Dynamics Simulations

“…In order to calculate the free energy profiles for the process of A1 domain of VWF binding with GPIb , Potential of Mean Force (PMF) calculations were conducted using umbrella sampling method 26) . Each windows were separated by 0.5 Å, covering the reaction coordinate, which represent the distance between the center of mass of A1 domain of VWF and GPIb N-terminal domain, from 20 to 78 Å.…”

FEARCF a multidimensional free energy method for investigating conformational landscapes and chemical reaction mechanisms

“…We coupled the Ferrenberg-Swendsen Multiple Histogram weighting scheme [12] to the method to calculate the free energy profile for a one dimensional W(  ) torsion [13] and two-dimensional torsion [14]. Shortly thereafter we showed that the approach can be used in conjunction with hybrid quantum classical (QM/MM) methods to simulate chemical reactions free energy surfaces [15]. Recently the method was generalized to calculate multidimensional free energy volumes and identified it as the FEARCF (Scheme 1) [16,17].…”

“…Recent modifications allow the calculation of a variety of reaction coordinate types besides the distances I have used here in this application [17]. Although an early version of the procedure [15] has been shown to be useful in applications to enzymatic reactions involving complex reaction mechanisms that require the distinction between concerted and step-wise processes [49][50][51].…”

Introducing sampling entropy in repository based adaptive umbrella sampling

“…Unfortunately, such information is exactly what we try to obtain from simulations and is not known in the first place. In past years, many adaptive sampling approaches 3,8,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] have been proposed to overcome this inherent challenge. Among them, very recently we have introduced the repository based adaptive umbrella sampling ͑RBAUS͒ method, 27 in which a sampling repository is periodically updated based on the latest simulation data, and the accumulated knowledge and sampling history are then employed to determine whether and how to update the biasing umbrella potential to achieve more uniform sampling for subsequent simulations.…”

“…Among them, very recently we have introduced the repository based adaptive umbrella sampling ͑RBAUS͒ method, 27 in which a sampling repository is periodically updated based on the latest simulation data, and the accumulated knowledge and sampling history are then employed to determine whether and how to update the biasing umbrella potential to achieve more uniform sampling for subsequent simulations. In comparison with other adaptive sampling methods, such as adaptive umbrella sampling, 3,[11][12][13][14] the Wang-Landau approach, 15,16 the adaptive biasing force, 17,18,28 nonequilibrium metadynamics, 8,19,20 and self-healing umbrella sampling, 24 a unique and attractive feature of the RBAUS method is that the frequency for updating the biasing potential is not predetermined but depends on the sampling history and is adaptively determined on the fly, which smoothly bridges nonequilibrium and equilibrium simulations. Such an adaptive updating is achieved by employing the following general principle: If the subsequent simulations still explore a previously oversampled region more than a previously undervisited one, the biasing potential needs to be updated, otherwise, no updating.…”