Lambda-ABF: Simplified, Portable, Accurate and Cost-effective Alchemical Free Energy Computations (2307.08006v2)

Abstract: We introduce an efficient and robust method to compute alchemical free energy differences, resulting from the application of multiple walker Adaptive Biasing Force (ABF) in conjunction with strongly damped Langevin $\lambda$-dynamics. Unbiased alchemical free energy surfaces are naturally recovered by Thermodynamic Integration (TI). No manual optimization of the $\lambda$ schedule is required as the sampling of the $\lambda$ variable is continuous and converges towards a uniform distribution. Free diffusion of $\lambda$ improves orthogonal relaxation compared to fixed $\lambda$ methods such as standard TI or Free Energy Perturbation (FEP). Furthermore, the multiple walker strategy provides coverage of orthogonal space in a generic way with minimal user input and negligible computational overhead. Of practical importance, no adiabatic decoupling between the alchemical and Cartesian degrees of freedom is assumed, ensuring unbiased estimates for a wide envelope of numerical parameters. We present two high-performance implementations of the method in production molecular dynamics engines, namely NAMD and Tinker-HP, through coupling with the Colvars open source library. These interfaces enable the combination of the rich feature sets of those packages. We demonstrate the correctness and efficiency of the approach on several real-world cases: from solvation free energies up to ligand-receptor binding (using a recently proposed binding restraint scheme) with both fixed-charge and polarizable models. We find that, for a chosen accuracy, the computational cost is strongly reduced compared to state-of-the-art fixed-lambda methods and that results within 1~kcal/mol of experimental value are recovered for the most complex system. The implementation is publicly available and readily usable by practitioners of current alchemical methods.

• The paper introduces Lambda-ABF, a novel method that combines multiple-walker Adaptive Biasing Force with λ-dynamics to eliminate post-processing in free energy computations.
• It demonstrates enhanced sampling efficiency and significantly reduced convergence variance in benchmarks ranging from hydration energies to protein-ligand interactions.
• The methodology offers a portable, user-friendly framework integrated with NAMD and Tinker-HP, simplifying workflows for complex biomolecular simulations.

Lambda-ABF: Advancements in Alchemical Free Energy Computation

Lambda-ABF introduces an innovative method for alchemical free energy calculations designed to optimize the computation process by achieving a balance between accuracy and computational efficiency. This method is built on the foundation of integrating multiple-walker Adaptive Biasing Force (mwABF) with $\lambda$-dynamics, offering continuous sampling of the alchemical variable while negating the need for manual optimization of the $\lambda$ schedule. This paper not only proposes a novel methodological framework but also discusses its practical implications and demonstrates its effectiveness across various biomolecular systems.

Core Methodological Advancements

The central advancement presented in this paper is the Lambda-ABF method which effectively eliminates the need for post-processing steps typically necessary in conventional approaches. This is achieved by immediately providing alchemical free energy estimates as the simulations proceed. The method leverages the concept of free diffusion of $\lambda$, which facilitates improved orthogonal relaxation as opposed to fixed-$\lambda$ Thermodynamic Integration (TI) or Free Energy Perturbation (FEP).

Significantly, the employment of multiple walkers enables comprehensive exploration of orthogonal space with minimal computational overhead, enhancing the method's efficiency. The implementations coupling the Colvars library with NAMD and Tinker-HP allow Lambda-ABF to handle complex real-world scenarios such as ligand-receptor binding in both fixed-charge and polarizable models, surpassing the sampling richness of traditional fixed-$\lambda$ methods.

Numerical Results and Comparisons

The Lambda-ABF method demonstrates strong numerical results in various test cases ranging from hydration free energies of simple ions and molecules to more complex systems like protein-ligand interactions. Notably, in the case of hydration free energies, the method aligns well with results obtained from fixed-$\lambda$ methods, validating its robustness and lack of bias.

For more intricate systems, such as the Cucurbit[8]uril host-guest complex and the lysozyme-phenol interaction, Lambda-ABF not only yields comparable binding free energies but also exhibits reduced variance in convergence compared to fixed-$\lambda$ approaches. This reduction in variance indicates more consistent sampling per simulation, reinforcing the method's efficiency.

Practical and Theoretical Implications

Lambda-ABF's ability to provide immediate free energy estimates without post-processing simplifies the workflow for practitioners and enhances the accessibility of alchemical simulations. This method's adaptability to varying backend programs and unified user interface, courtesy of the portable Colvars library, significantly reduces learning curves and operational complexities.

Theoretically, the Lambda-ABF framework expands the repertoire of free energy calculation techniques by incorporating adaptive biasing in $\lambda$-space and enabling dynamic $\lambda$ transitions through multiple-walker strategies. This methodology successfully combines the precision of ABF-based thermodynamic integration with the exploration capacity of $\lambda$-dynamics, setting a new standard for alchemical free energy computations.

Speculation on Future Developments

While Lambda-ABF presents significant advancements, future research may focus on enhancing its scalability across different hardware architectures and integrating more sophisticated biasing techniques to further streamline sampling efficiency. Additionally, its application to larger biomolecular systems and drug discovery contexts could reveal potential areas for refinement and adaptation.

In conclusion, Lambda-ABF offers a promising and methodologically sound advancement in alchemical free energy computations. By streamlining processes and incorporating adaptive, dynamic elements, it holds significant potential to influence practical applications and future theoretical developments in computational chemistry and molecular simulation.