Linear Basis Function Approach to Efficient Alchemical Free Energy Calculations. 1. Removal of Uncharged Atomic Sites

Abstract

We present a general approach to transform between molecular potential functions during free energy calculations using a variance minimized linear basis functional form. This approach splits the potential energy function into a sum of pairs of basis functions, which depend on coordinates, and 'alchemical' switches, which depend only on the coupling variable. The power of this approach is that, first, the calculation of the coupling parameter dependent terms is removed from inner loop force calculation routines, second, the flexibility in specifying basis functions and alchemical switches allows users to choose transformation pathways that maximize statistical efficiency, and third, it is possible to predict entirely in postprocessing, without any additional energy evaluations, the thermodynamic properties along any alchemical path with moderate overlap from an initial simulation that uses the same basis functions. This allows construction of optimized, minimum variance alchemical switches from a single simulation with fixed basis functions and trial alchemical switching functions. We describe how to construct these linear basis potentials for real molecular systems of different sizes and shapes, considering particularly the problems of eliminating singularities and minimizing variance of particle removal in dense fluids. The statistical error in free energy calculations using the optimized basis functions is lower than standard soft core models, and approach the minimum variance possible over all pair potentials. We recommend an optimized set of basis functions and alchemical switches for standard molecular free energy calculations.

Predicting Thermodynamic Properties over Combinatorially Large Chemical Spaces

“…Researchers in molecular simulation have designed many thermodynamic paths between molecules or for inserting molecules into dense fluids [14,57,[81][82][83][84][85][86][87][88][89], each with their own strengths and weaknesses [90][91][92]. There has also been limited effort in designing paths to directly maximize phase space overlap [54,55,84,[93][94][95][96][97]. Estimating the free energy from these paths is also done with any number of methods [81,93,[98][99][100][101], where each method also has its own strengths and weaknesses [60,102].…”

“…[105] Minimizing the statistical uncertainty of calculations performed along an alchemical path is equivalent to minimizing the thermodynamic length of the path. [54,84,93,94,96,97] The path which minimizes the total uncertainty for the transformation is one which has an equal contribution to the uncertainty across every point along the path. However, the minimum not necessarily achievable via pairwise potentials [97].…”

“…When comparing pathways, the most statistically efficient path is roughly independent of the method performing the analysis such as TI, BAR, or MBAR [54,97] Since the variance of the mean in ∂u/∂λ at any simulated state will be proportional to the number of samples at that state, the overall variance of the entire process will also be proportional to the number of samples used for the entire process at all states, assuming fixed proportion of samples per state and samples that are statistically decorrelated. We can thus normalize this variance in the calculation by the total number of decorrelated samples used in the calculation to obtain a measure of the statistical efficiency of the pathway that is independent of the length of the simulations.…”

“…[58, 84-88, 95, 96] and an efficient formalism has been developed for calculating minimal variance paths within a given function space. [54,84,97] The functional form of the soft core potentials adds significant complexity when implementing free energy methods on new, highly parallelized architectures such as GPU's or Many Integrated Core (MIC) platforms. As described in Chapter 2 and our previous study, [54] soft core methods require writing special code to handle the alchemical modifications to atoms and implementing these modifications on new platforms have lagged behind the implementation of other molecular mechanics methods.…”

“…Chapters 2-4 are my current publications modified slightly to fit in as a chapter [54][55][56]. Chapter 5 applies the basis function method to the solvation properties of multiple molecules built combinatorially from a common structure.…”