A discrete-to-continuous mathematical model for ensemble distributions of a ligand-interacting macromolecular species across milieux-dependent conformational states may offer insights into the genesis and progression of cooperative binding
Small molecule modifiers whence bound, allosterically, will alter the binding of a macromolecule to one- or more-cognate substrates/partners via conformational and non-conformational changes. Although allostery is inferred directly from empirical data, the mathematical basis of these models, constraints deployed and choice of parameter(s) are not clear. Here, we present and characterize a discrete-to-continuous mathematical model for ensemble distributions of a ligand-interacting macromolecular species across milieux-dependent conformational states and examine its’ role in the genesis and progression of cooperative binding. The premise, of our model, is a set of occupancy matrices (sparse, binary, strictly delocalized) which can be partitioned by a probability-based hyperparameter into mutually exclusive proper subsets of occupancy matrices with identical multinomial probabilities. Since each subset is canonical with a constituent occupancy matrix, it is characterized by a unique multinomial probability. The inner product of combinatorial pairs of all mutually exclusive subsets of occupancy matrices, with an expression for the summed transitional probabilities (finite differences between unique multinomial probabilities), is the differentiable matrix of strictly positive real-valued numbers for the system of ensemble distributions. Whilst the harmonic mean is presented as a generic solution for a system of ensemble distributions, the row-wise definite integral for each column is the finite union of open intervals (contiguous, strictly monotone) which in tandem with a set of interval-specific and bounded transitional probabilities constitutes a piecewise smooth curve (path-connected-, closed- and compact-set). Our discrete-to-continuous model is phenomenological and able to recapitulate the basic tenets of cooperative binding whilst offering insights into the genesis and progression of the same.
PHASE (Protein Hamiltonians for Sampling of Ensembles), a system-specific framework that converts atomistic conformational ensembles into an explicit and interpretable statistical model, is introduced.
Daniele Angioletti, Marco S. Nobile, Matteo Carli et al.· 0 citations
We present a statistical-mechanics framework for computing equilibrium binding constants $K$ in the dilute limit. From first principles, we derive a general expression relating $K$ to the relative populations of the bound and unbound states. Its transparency has twofold advantage: it makes the origin of the unbound-state volumetric term explicit, and it allows one to track exactly how an imposed volume restraint propagates through the expression. This makes $K$ directly computable, as restrained simulations can account for the volumetric contribution exactly, under the physically mild assumption of a homogeneous unbound state. The resulting estimators are computable from histograms of any suitably defined reaction coordinate, and determine unambiguously how the boundaries of the thermodynamic states of interest must be defined. We apply our framework to the cucurbit[7]uril/1-adamantanol host--guest complex and the galactonate--DgoT ligand--protein complex. Our results show that commonly used single-bin estimators depart from the theoretically correct one by $\approx 1$~kcal/mol in both systems. This shift originates in the definition of the bound state: by anchoring that definition to what state-of-the-art experiments resolve, the theory turns it from a hidden assumption into a controlled input, and provides a principled route to absolute binding affinities from molecular simulations.
Davide Mandelli, E. Ippoliti, C. Plate· 0 citations
RNA molecules explore heterogeneous conformational ensembles that are essential for their biological function and molecular recognition, yet this intrinsic flexibility poses a major challenge for structure-based drug discovery. In particular, the absence of well-defined binding pockets in static structures limits the identification of ligandable sites. Here, we present an integrative ensemble-based approach that combines enhanced-sampling molecular dynamics simulations with Nuclear Magnetic Resonance data to characterize the conformational landscape of the HIV-1 TAR RNA at atomic resolution. Starting from extensive sampling, we refined the resulting conformational distribution through maximum-entropy reweighting to achieve quantitative agreement with experimental data. Analysis of the reweighted ensemble reveals a diverse set of conformational substates, including compact arrangements that exhibit pocket features compatible with ligand recognition and overlap with known ligand-bound structures. At the same time, highly ligandable conformations, which are only marginally populated, might nonetheless be critical for RNA recognition. Our results demonstrate that integrative ensemble modeling can reveal pharmacologically relevant RNA conformations that are not apparent from experimental static structures, providing a framework for ensemble-based strategies in RNA-targeted drug discovery.
Stefano Bosio, Vincent Schnapka, Mattia Bernetti et al.· bioRxiv· 0 citations
The aim of this paper is to test whether biological macromolecules carry information through two distinct, separable channels. The conformational channel (C-channel), governed by three-dimensional structure and the Coulomb potential, sets binding geometry, catalysis, and stability. The spectral channel (S-channel), the one-dimensional electron-ion interaction potential (EIIP) profile and its characteristic frequency fRRM, is proposed to mediate resonant molecular recognition. In quantum information biology, recognition - a protein selecting a partner among thousands of candidates - is modelled as a decision following quantum-probabilistic laws despite macroscopic physics. This requires the channels to form a bipartite system whose state space factorises as a tensor product HC⊗HS of separable degrees of freedom. Whether the channels are coupled, independent, or complementary is the empirical prerequisite tested here. We analyse 87,389 single-nucleotide missense substitutions across 222 non-redundant, full-length proteins (51-4684 residues, <40% pairwise identity, >40 functional families), classifying each as fRRM-silent or fRRM-disruptive over seven physicochemical metrics, with within-protein clustering handled explicitly (intraclass correlation, design effect, and a protein-level cluster bootstrap). We report two principal findings. First, across the full sample fRRM is essentially uncorrelated with every conformational determinant, namely Grant ham distance, hydropathy, molecular weight, and helix and sheet propensity (all |ρ|<0.1), establishing channel independence. Second, the silent-versus-disruptive contrast reproduces: disruptive substitutions are marginally more conformationally conservative on every metric, yet each difference, though statistically significant, is negligible in magnitude (|d|<0.2), a consistent but negligible-magnitude anti-correlated tendency, not a substantive coupling. The sequence-level state is therefore separable, a product state in HC⊗HS rather than an entanglement-like or complementary one, and this holds residue by residue (aspartate is the principal spectral hotspot, tryptophan is conserved structurally yet remains spectrally neutral). We interpret these results within the quantum-like framework: the protein is a dual-channel processor whose spectral "software" (frequency-domain recognition) can be updated independently of its conformational "hardware" (spatial binding), providing the separable substrate that quantum-like molecular decision-making requires.
A category-stratified, statistically powered benchmark comparing pose prediction from receptor conformational ensembles against AlphaFold2, used as a matched static-structure baseline, across 29 protein–ligand systems spanning cryptic-pocket, induced-fit, water-mediated, and autoimmune-indication target classes is presented.
Ryan Varghese, Pooja Tiwary, Krishil Oswal· bioRxiv· 0 citations
We present a kinetic Monte Carlo (KMC) modeling approach to describe the stochastic dynamics of a peptide molecule spanning nanosecond to second timescales. The dynamics of protein conformational changes is interpreted at a local level in terms of dihedral transitions. Taking Trp-cage miniprotein as an example, the KMC model"learns"about the transitions from multiple MD trajectories. Training is based on local divide-and-conquer strategy that identifies the discretized backbone dihedral states as building blocks for the conformational space, along with associated transition rates of dihedral flips to describe the conformational state-to-state dynamics. A key feature in our approach is the incorporation of backbone correlations, such that rates are conditioned on the local environment and steric coupling. We show that with the correlations built-in, the KMC model closely matches MD. Such an approach is shown to reach second timescales in a few CPU hours on a standard desktop computer, and can easily yield multiple stochastic realizations of the conformational dynamics. Our KMC model construction scheme should be generally applicable to a wide range of proteins, and can be used for bridging local flexibility to protein-wide dynamics.
A. Chatterjee, Rishav Deb, Gauri Thapa et al.· 0 citations
