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Register a new userPrecise binding free energy calculations for multiple molecules using an optimal measurement network of pairwise differences
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Alchemical binding free energy (BFE) calculations offer an efficient and thermodynamically rigorous approach to in silico binding affinity predictions. As a result of decades of methodological improvements and recent advances in computer technology, alchemical BFE calculations are now widely used in drug discovery research. They help guide the prioritization of candidate drug molecules by predicting their binding affinities for a biomolecular target of interest (and potentially selectivity against undesirable anti-targets). Statistical variance associated with such calculations, however, may undermine the reliability of their predictions, introducing uncertainty both in ranking candidate molecules and in benchmarking their predictive accuracy. Here, we present a computational method that substantially improves the statistical precision in BFE calculations for a set of ligands binding to a common receptor by dynamically allocating computational resources to different BFE calculations according to an optimality objective established in a previous work from our group and extended in this work. Our method, termed Network Binding Free Energy (NetBFE), performs adaptive binding free energy calculations in iterations, re-optimizing the allocations in each iteration based on the statistical variances estimated from previous iterations. Using examples of NetBFE calculations for protein-binding of congeneric ligand series, we demonstrate that NetBFE approaches the optimal allocation in a small number (<= 5) of iterations and that NetBFE reduces the statistical variance in the binding free energy estimates by approximately a factor of two when compared to a previously published and widely used allocation method at the same total computational cost.
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When both the difference between two quantities and their individual values can be measured or computational predicted, multiple quantities can be determined from the measurements or predictions of select individual quantities and select pairwise differences. These measurements and predictions form a network connecting the quantities through their differences. Here, I analyze the optimization of such networks, where the trace ($A$-optimal), the largest eigenvalue ($E$-optimal), or the determinant ($D$-optimal) of the covariance matrix associated with the estimated quantities are minimized with respect to the allocation of the measurement (or computational) cost to different measurements (or predictions). My statistical analysis of the performance of such optimal measurement networks -- based on large sets of simulated data -- suggests that they substantially accelerate the determination of the quantities, and that they may be useful in applications such as the computational prediction of binding free energies of candidate drug molecules.
In this paper we first analyzed the inductive bias underlying the data scattered across complex free energy landscapes (FEL), and exploited it to train deep neural networks which yield reduced and clustered representation for the FEL. Our parametric method, called Information Distilling of Metastability (IDM), is end-to-end differentiable thus scalable to ultra-large dataset. IDM is also a clustering algorithm and is able to cluster the samples in the meantime of reducing the dimensions. Besides, as an unsupervised learning method, IDM differs from many existing dimensionality reduction and clustering methods in that it neither requires a cherry-picked distance metric nor the ground-true number of clusters, and that it can be used to unroll and zoom-in the hierarchical FEL with respect to different timescales. Through multiple experiments, we show that IDM can achieve physically meaningful representations which partition the FEL into well-defined metastable states hence are amenable for downstream tasks such as mechanism analysis and kinetic modeling.
We report the binding energy of $^{87}$Rb$^{133}$Cs molecules in their rovibrational ground state measured using an offset-free optical frequency comb based on difference frequency generation technology. We create molecules in the absolute ground state using stimulated Raman adiabatic passage (STIRAP) with a transfer efficiency of 88%. By measuring the absolute frequencies of our STIRAP lasers, we find the energy-level difference from an initial weakly-bound Feshbach state to the rovibrational ground state with a resolution of 5 kHz over an energy-level difference of more than 114 THz; this lets us discern the hyperfine splitting of the ground state. Combined with theoretical models of the Feshbach state binding energies and ground-state hyperfine structure, we determine a zero-field binding energy of $htimes114,268,135,237(5)(50)$ kHz. To our knowledge, this is the most accurate determination to date of the dissociation energy of a molecule.
Extensions of statistical mechanics are routinely being used to infer free energies from the work performed over single-molecule nonequilibrium trajectories. A key element of this approach is the ubiquitous expression dW/dt=partial H(x,t)/ partial t which connects the microscopic work W performed by a time-dependent force on the coordinate x with the corresponding Hamiltonian H(x,t) at time t. Here we show that this connection, as pivotal as it is, cannot be used to estimate free energy changes. We discuss the implications of this result for single-molecule experiments and atomistic molecular simulations and point out possible avenues to overcome these limitations.
A Monte Carlo simulation is performed on a billiard-type model system, which contains a locally nonchaotic energy barrier. Without extensive particle collision across the energy barrier, the system steady state is nonequilibrium; that is, the particles follow a non-Boltzmann distribution. Remarkably, as the energy barrier varies in an isothermal cycle, the total produced work is greater than the total consumed work, because of the asymmetry in the cross-influence of the thermally correlated thermodynamic driving forces. Such a phenomenon cannot be explained by the second law of thermodynamics. Similar anomalous effects may be achieved if the barrier is switchable or asymmetric. In essence, the energy barrier is a spontaneously nonequilibrium dimension. It is fundamentally different from Maxwells demon, unrelated to the physical nature of information.
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