From populations to absolute binding affinities in molecular simulations: exact volumetric terms and practical estimators

Charged Systems in Absolute Binding Free Energy Calculations: An Analytical Electrostatic Approach.

Alchemical free energy perturbation (FEP) is one of the most rigorous methods for predicting protein-ligand binding affinities, yet charged-ligand calculations suffer from finite-size electrostatic artifacts introduced by periodic boundary conditions, which can bias results by several kcal·mol-1. Existing approaches each have limitations: finite-size correction methods rely on approximate dielectric models and Poisson-Boltzmann (PB) calculations, while alchemical co-ion methods introduce alchemically transformed particles, causing spurious interactions and sampling difficulties. Here we present Electrostatic Interaction Decoupling (EID), a postprocessing approach that combines an exact algebraic isolation of the ligand-environment linear electrostatic interaction under the neutral-environment condition with an analytical correction for the residual periodic-boundary offset. By separating the physical ligand-environment interaction from artifact-contaminated terms, EID corrects charge-changing FEP results without PB/continuum-electrostatics calculations or alchemically transformed particles. In benchmarks across four charged protein-ligand systems, EID achieved improved predictive accuracy and more consistent cross-system performance than both comparison methods. Because EID operates as a postprocessing step requiring no additional simulations or PB calculations, it provides a rigorous, immediately deployable solution for charge-changing free energy calculations.

Thermodynamic Binding Networks Capture Equilibrium Monomer-Polymer Thermodynamics

Integrated Alchemical and Conformational Enhanced Sampling for Solvation Free Energy Calculations

Accurate solvation free energies from molecular dynamics simulations require efficient sampling of coupled slow variables, including solvent coordinates, solute conformational modes, and the alchemical coordinate $\lambda$. Here, we develop a $\lambda$-dynamics framework that combines mass scaling, on-the-fly probability enhanced sampling (OPES), and driven adiabatic free energy dynamics (d-AFED) to address these sampling challenges within a unified protocol. For rigid organic solutes, Hamiltonian replica exchange with mass scaling is first used to quantify the effect of octanol solvent relaxation. Reducing all octanol atomic masses by a factor of ten accelerates convergence by more than fivefold while preserving equilibrium solvation free energies. These calculations then provide reference benchmarks for $\lambda$-OPES, a dual-bias $\lambda$-dynamics strategy that combines the"standard"and"explore"variants of OPES to promote transitions along the alchemical coordinate. This approach reaches convergence on timescales comparable to replica exchange, but without predefined $\lambda$ windows or multiple parallel simulations. For flexible $N$-acetyl amino-acid amide solutes, $\lambda$-OPES is coupled with d-AFED on selected backbone and side-chain dihedrals to enable simultaneous alchemical and conformational enhanced sampling. This combined strategy improves agreement with experimental octanol-water partition coefficients and reduces the mean absolute error from 0.75 log units with $\lambda$-OPES alone to 0.30 log units with $\lambda$-OPES-d-AFED. Overall, this work establishes an integrated enhanced sampling protocol for solvation free energy calculations across rigid organic solutes and flexible peptide-like solutes, and provides a foundation for the application of alchemical free energy methods to larger and more conformationally complex systems.

Dual-Coordinate Relative Free Energy Simulations Using Machine-Learned Interatomic Potentials

This work employs a dual-coordinate approach where both solutes are explicitly present but do not interact with one another, and utilizes a harmonic ″anchor″ restraint to a central atom on each molecule to enforce spatial overlap without modifying the internal intramolecular dynamics of either solute.

A concentration-independent paradigm rendering weak interactions inherently quantifiable

A vast class of weak, millimolar-affinity molecular interactions governs cellular function, yet their quantitative characterization has remained largely beyond conventional methods. For over a century, biochemistry has worked within a concentration-based framework where molarity scales with molecular number per volume (N/V), and experiments have usually, often implicitly, changed concentration by moving N while holding V fixed. The weak-interaction measurement bottleneck arises from this paradigm: reading weak binding through bulk concentration requires concentrations beyond practical limits, a framework constraint rather than one of instrumental sensitivity. Here we show that shifting experimental control from N to accessible volume V overcomes this bottleneck and opens previously intractable affinity ranges through nanoscale spatial confinement. Controlling V means controlling what biochemists have called"local concentration"and"proximity effects,"recasting these long-ambiguous notions as quantitative variables grounded in first principles. Implemented in DNA nanocavities, the approach showed that geometric arrangement alone can override solution-phase binding hierarchies. The same spatial control quantified a protein-peptide interaction of order 10 mM from femtomoles per well, totalling under a picomole per titration. Even so, a standard plate reader gave a signal-to-noise ratio near 10^3, leaving headroom for still weaker interactions. The affinity-and-geometry readout also enabled rational screening for protein-protein-interaction modulators, identifying compounds that enhance weak associations by reweighting local encounters rather than binding tightly on their own or forming a stable ternary complex. Together, this volume-based paradigm and its implementation provide a general strategy for probing and modulating previously inaccessible biochemical phenomena.

Experimental access to molarity's blind spot in macroscopic assays

Chemical kinetics has long inferred local molecular behaviour through the flask-and-molarity pairing, where well-mixed concentrations serve as the experimental readout. Yet many biological reactions occur in structured environments. Researchers have long recognized that concentration may not carry the same operational meaning in such environments, but even local concepts such as effective molarity usually translate local effects back into a single value with units of concentration. What has been missing is the complementary path: a bench-compatible way to make local structure an experimental variable, rather than only a correction to molarity. Here we show a chemistry-geometry crossover that the flask-and-molarity interface could not make visible. In the micromolar-or-weaker affinity regime, inhibition can switch sharply out of the familiar concentration-and-affinity mode: chemical binding strength no longer determines the response, and the shape of the target's local space does. A bench-compatible interface made this switch measurable by separating bulk dose from local geometry. This blind spot arose from the hidden premise that macroscopic pooling makes a structured local state readable as a single local concentration. The chemistry-geometry crossover breaks that premise: in a structured target environment, a macroscopic assay can remain sensitive to the probability distribution of local states, so collapsing that distribution to one concentration-valued number removes the geometric control axis from the readout. By preserving that axis in the experiment, the interface bypasses molarity's hidden bottleneck and provides a routine experimental route to remeasure and reinterpret molecular interactions in structured space.