Adaptive Landscape Flattening Accelerates Sampling of Alchemical Space in Multisite λ Dynamics

Abstract

Multisite λ dynamics (MSλD) is a powerful emerging method in free energy calculation that allows prediction of relative free energies for a large set of compounds from very few simulations. Calculating free energy differences between substituents that constitute large volume or flexibility jumps in chemical space is difficult for free energy methods in general, and for MSλD in particular, due to large free energy barriers in alchemical space. This study demonstrates that a simple biasing potential can flatten these barriers and introduces an algorithm that determines system specific biasing potential coefficients. Two sources of error, deep traps at the endpoints and solvent disruption by hard-core potentials, are identified. Both scale with the size of the perturbed substituent and are removed by sharp biasing potentials and a new soft-core implementation, respectively. MSλD with landscape flattening is demonstrated on two sets of molecules: derivatives of the heat shock protein 90 inhibitor geldanamycin and derivatives of benzoquinone. In the benzoquinone system, landscape flattening leads to two orders of magnitude improvement in transition rates between substituents and robust solvation free energies. Landscape flattening opens up new applications for MSλD by enabling larger chemical perturbations to be sampled with improved precision and accuracy.

Approaching protein design with multisite λ dynamics: Accurate and scalable mutational folding free energies in T4 lysozyme

“…Recently, landscape flattening and soft‐core interactions have been shown to give marked improvements in MS λ D predictions of ΔΔ G . Those methods are used here with several important updates, including a new biasing potential that better flattens soft‐core landscapes and a more general flattening algorithm.…”

“…Scalability to combinatorial sequence spaces allows MS λ D to mitigate the high cost of MD simulations by searching much larger swaths of sequence space than FEP or Rosetta during each in silico evolutionary step. λ dynamics is over two decades old, but has matured substantially in recent years via generalization to multiple sites, the use of implicit constraints to focus sampling on physical endpoint states, enhanced sampling with biasing potential replica exchange (BP‐REX), adaptive landscape flattening (ALF) to remove alchemical barriers, and the use of soft‐core interactions …”

Gibbs Sampler-Based λ-Dynamics and Rao–Blackwell Estimator for Alchemical Free Energy Calculation

“…If the linear biasing potential energy cannot make the biased free energy landscape over the λ space flat enough, a quadratic form of biasing potential can be utilized as in Hayes et al’s flattening method. 19 The biasing potential $G_1^b$ is determined automatically using the following Wang-Landau like algorithm: Set the initial biasing potential $G_1^b=0\text{kcal}/\text{mol}$, the decay parameter α such that 0 < α < 1 ( α = 0.998 in this study), the biasing potential increment Δ in each step (Δ = 2.0 kcal/mol in this study) and the number of steps R ( R = 3000 in this study). Initialize the starting state (λ 0 , ${\{x_i^0\}}_{i=0}^1$, X 0 ).…”

“…If the linear biasing potential energy cannot make the biased free energy landscape over the λ space flat enough, a quadratic form of biasing potential can be utilized as in Hayes et al’s flattening method. 19 The biasing potential $G_1^b$ is determined automatically using the following Wang-Landau like algorithm:…”

“…The biasing potential $G_1^b$ is determined iteratively by running multiple short simulations. 14,15,18,19 The dynamics of the system (λ, ${\{x_i\}}_{i=0}^1$, X ) is generated from the extended Hamiltonian: $$H(\lambda ,{\{x_i\}}_{i=0}^1,X)=T_{x,X}+T_{\lambda }+V(\lambda ,{\{x_i\}}_{i=0}^1,X)$$ where T x, X and T λ are the kinetic energy associated with coordinates ( ${\{x\}}_{i=0}^1$, X ) and λ, respectively. The free energy difference between ligand L 0 and L 1 , with the biasing potential $G_1^b$, is…”