Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy, Precision and Reproducibility

The binding free energy between a ligand and its target protein is an essential quantity to know at all stages of the drug discovery pipeline. Assessing this value computationally can offer insight into where efforts should be focused in the pursuit of effective therapeutics to treat myriad diseases. In this work we examine the computation of alchemical relative binding free energies with an eye to assessing reproducibility across popular molecular dynamics packages and free energy estimators. The focus of this work is on 54 ligand transformations from a diverse set of protein targets: MCL1, PTP1B, TYK2, CDK2 and thrombin. These targets are studied with three popular molecular dynamics packages: OpenMM, NAMD2 and NAMD3. Trajectories collected with these packages are used to compare relative binding free energies calculated with thermodynamic integration and free energy perturbation methods. The resulting binding free energies show good agreement between molecular dynamics packages with an average mean unsigned error between packages of 0.5 $kcal/mol$ The correlation between packages is very good with the lowest Spearman's, Pearson's and Kendall's tau correlation coefficient between two packages being 0.91, 0.89 and 0.74 respectively. Agreement between thermodynamic integration and free energy perturbation is shown to be very good when using ensemble averaging.

Tissue-Nonspecific Alkaline Phosphatase (TNAP) as the Enzyme Involved in the Degradation of Nucleotide Analogues in the Ligand Docking and Molecular Dynamics Approaches

Tissue-nonspecific alkaline phosphatase (TNAP) is known to be involved in the degradation of extracellular ATP via the hydrolysis of pyrophosphate (PPi). We investigated, using three different computational methods, namely molecular docking, thermodynamic integration (TI) and conventional molecular dynamics (MD), whether TNAP may also be involved in the utilization of β,γ-modified ATP analogues. For that, we analyzed the interaction of bisphosphonates with this enzyme and evaluated the obtained structures using in silico studies. Complexes formed between pyrophosphate, hypophosphate, imidodiphosphate, methylenediphosphonic acid monothiopyrophosphate, alendronate, pamidronate and zoledronate with TNAP were generated and analyzed based on ligand docking, molecular dynamics and thermodynamic integration. The obtained results indicate that all selected ligands show high affinity toward this enzyme. The forming complexes are stabilized through hydrogen bonds, electrostatic interactions and van der Waals forces. Short- and middle-term molecular dynamics simulations yielded very similar affinity results and confirmed the stability of the protein and its complexes. The results suggest that certain effectors may have a significant impact on the enzyme, changing its properties.

An introduction to thermodynamic integration and application to dynamic causal models

In generative modeling of neuroimaging data, such as dynamic causal modeling (DCM), one typically considers several alternative models, either to determine the most plausible explanation for observed data (Bayesian model selection) or to account for model uncertainty (Bayesian model averaging). Both procedures rest on estimates of the model evidence, a principled trade-off between model accuracy and complexity. In the context of DCM, the log evidence is usually approximated using variational Bayes. Although this approach is highly efficient, it makes distributional assumptions and is vulnerable to local extrema. This paper introduces the use of thermodynamic integration (TI) for Bayesian model selection and averaging in the context of DCM. TI is based on Markov chain Monte Carlo sampling which is asymptotically exact but orders of magnitude slower than variational Bayes. In this paper, we explain the theoretical foundations of TI, covering key concepts such as the free energy and its origins in statistical physics. Our aim is to convey an in-depth understanding of the method starting from its historical origin in statistical physics. In addition, we demonstrate the practical application of TI via a series of examples which serve to guide the user in applying this method. Furthermore, these examples demonstrate that, given an efficient implementation and hardware capable of parallel processing, the challenge of high computational demand can be overcome successfully. The TI implementation presented in this paper is freely available as part of the open source software TAPAS.

Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson’s theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs–Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born–Oppenheimer molecular dynamics performed at a single temperature. This advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.