Multisite λ Dynamics for Simulated Structure–Activity Relationship Studies

Abstract

Multi-Site λ-dynamics (MSλD) is a new free energy simulation method that is based on λ-dynamics. It has been developed to enable multiple substituents at multiple sites on a common ligand core to be modeled simultaneously and their free energies assessed. The efficacy of MSλD for estimating relative hydration free energies and relative binding affinties is demonstrated using three test systems. Model compounds representing multiple identical benzene, dihydroxybenzene and dimethoxybenzene molecules show total combined MSλD trajectory lengths of ~1.5 ns are sufficient to reliably achieve relative hydration free energy estimates within 0.2 kcal/mol and are less sensitive to the number of trajectories that are used to generate these estimates for hybrid ligands that contain up to ten substituents modeled at a single site or five substituents modeled at each of two sites. Relative hydration free energies among six benzene derivatives calculated from MSλD simulations are in very good agreement with those from alchemical free energy simulations (with average unsigned differences of 0.23 kcal/mol and R2=0.991) and experiment (with average unsigned errors of 1.8 kcal/mol and R2=0.959). Estimates of the relative binding affinities among 14 inhibitors of HIV-1 reverse transcriptase obtained from MSλD simulations are in reasonable agreement with those from traditional free energy simulations and experiment (average unsigned errors of 0.9 kcal/mol and R2=0.402). For the same level of accuracy and precision MSλD simulations are achieved ~20–50 times faster than traditional free energy simulations and thus with reliable force field parameters can be used effectively to screen tens to hundreds of compounds in structure-based drug design applications.

Communication: Estimating the initial biasing potential for λ-local-elevation umbrella-sampling (λ-LEUS) simulations via slow growth

“…The introduction of a coordinate transformation [12][13][14][15][16][17] λ(θ ), where θ is the actual dynamical variable, determina) Electronic mail: phil@igc.phys.chem.ethz.ch ing indirectly the value of the coupling parameter λ. This leads to the extended Hamiltonian (omitting r and p for the simplicity of the notation)…”

Predicting Thermodynamic Properties over Combinatorially Large Chemical Spaces

“…However, how would we transform between all the different amino acids in a single simulation? A few researchers have designed thermodynamic paths connecting multiple molecules through multidimensional paths [51,52], shared volume methods [49,50], and iteratively updating the thermodynamic path [91,103,104]. The researchers implementing these methods have been able to generate free energy differences for 2 to 10 3 structurally similar molecules, with more theoretically possible [50].…”

“…We propose moves through λ-dynamics [51,52,202] where both Cartesian coordinates, and chemical coordinates are updated at the same time. Each λ variable is assigned a fictitious mass and is subject to a Hamiltonian of…”

“…Computational methods can only help reduce the number of molecules that need to be synthesized, and will never replace the need for a laboratory. Free energy differences are a particularly helpful property to compute as they provide This work specifically combines our basis function method with λ-dynamics [51,52] and Hybrid MC [193,194] to preserve the correct thermodynamic ensemble, run stable simulations, and explore a multidimensional chemical space. In this implementation,…”

“…They unfortunately require substantial reference data and are very prone to over fitting as small changes in molecular structure can result in large changes to thermodynamic properties, even for approaches which couple data mining with experimentation to fill in the gaps [48]. Within drug design, the methods of simultaneously estimating properties in chemical spaces are limited to either compounds which roughly share the same volume [49,50], or can only scale to a few molecular structure changes before computational time becomes a limiting factor [51,52]. There is substantial room for improvement in developing new methods for estimating properties across large chemical spaces.…”