Implementation of adaptive integration method for free energy calculations in molecular systems

Abstract

Estimating free energy differences by computer simulation is useful for a wide variety of applications such as virtual screening for drug design and for understanding how amino acid mutations modify protein interactions. However, calculating free energy differences remains challenging and often requires extensive trial and error and very long simulation times in order to achieve converged results. Here, we present an implementation of the adaptive integration method (AIM). We tested our implementation on two molecular systems and compared results from AIM to those from a suite of other methods. The model systems tested here include calculating the solvation free energy of methane, and the free energy of mutating the peptide GAG to GVG. We show that AIM is more efficient than other tested methods for these systems, that is, AIM results converge to a higher level of accuracy and precision for a given simulation time.

Keywords: Adaptive integration; Biomolecule; Computational Biology; Free energy; Monte Carlo; Protein; Scientific Computing and Simulation; Solvation.

Figure 1. Different λ densities for methane solvation free energy calculations.

Eight trial simulations of 100 ps per λ for 11, 21 and 31 λ values. This shows how the number of λ values were chosen to effectively compare AIM to fixed λ simulations. The circles indicate the region where the λ density needed to be increased.

Figure 2. Violin plot showing methane solvation results for 31 λ values averaged over eight trials.

A violin plot combines a box plot and a density plot to visualize the distribution and probability density. The graphic shows all methods have similarly converged at 1 ns per λ. AIM and AIM-CUBIC converge earlier than other methods at 750 ps per λ.

Figure 3. Different simulation times for alanine to valine mutation free energy calculations.

Eight trial simulations of 41 λ values at 1 ps, 100 ps and 1 ns per λ. Note the smoothness of AIM versus fixed λ simulations. AIM requires less samples than fixed λ simulations to smooth the free energy function.

Figure 4. Violin plot showing alanine to valine mutation results for 41 λ values averaged over eight trials.

The graphic shows all methods have similarly converged at 1 ns per λ. AIM and AIM-CUBIC converge more rapidly than other methods and are mostly converged at 100 ps per λ.