Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal Metropolis–Hastings Method

Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods.

Binding free energies for the SAMPL8 CB8 “Drugs of Abuse” challenge from umbrella sampling combined with Hamiltonian replica exchange

Umbrella sampling along a one-dimensional order parameter in combination with Hamiltonian replica exchange was employed to calculate the binding free energy of five guest molecules with known affinity to cucurbit[8]uril. A simple empirical approach correcting for the overestimation of the affinity by the GAFF force field was proposed and subsequently applied to the seven guest molecules of the “Drugs of Abuse” SAMPL8 challenge. Compared to the uncorrected binding free energies, the systematic error decreased but quantitative agreement with experiment was only reached for a few compounds. From a retrospective analysis a weak point of the correction term was identified.

Исследование влияния слабых магнитных полей на термодинамические свойства модели Поттса с числом состояний спина q=4 на гексагональной решетке

The replica exchange algorithm of the Monte Carlo method was used to study phase transitions and thermodynamic properties of the two-dimensional Potts model with the number of spin states q = 4 on a hexagonal lattice in weak magnetic fields. The studies were carried out for the interval of the magnetic field value 0.0 ≤ Н ≤ 3.0 with a step of 1.0. It is found that a first-order phase transition is observed in the considered range of field values.

Enhanced Conformational Sampling of Nanobody CDR H3 Loop by Generalized Replica-Exchange with Solute Tempering

The variable domains of heavy-chain antibodies, known as nanobodies, are potential substitutes for IgG antibodies. They have similar affinities to antigens as antibodies, but are more heat resistant. Their small size allows us to exploit computational approaches for structural modeling or design. Here, we investigate the applicability of an enhanced sampling method, a generalized replica-exchange with solute tempering (gREST) for sampling CDR-H3 loop structures of nanobodies. In the conventional replica-exchange methods, temperatures of only a whole system or scaling parameters of a solute molecule are selected for temperature or parameter exchange. In gREST, we can flexibly select a part of a solute molecule and a part of the potential energy terms as a parameter exchange region. We selected the CDR-H3 loop and investigated which potential energy term should be selected for the efficient sampling of the loop structures. We found that the gREST with dihedral terms can explore a global conformational space, but the relaxation to the global equilibrium is slow. On the other hand, gREST with all the potential energy terms can sample the equilibrium distribution, but the structural exploration is slower than with dihedral terms. The lessons learned from this study can be applied to future studies of loop modeling.

Induced fit with replica exchange improves protein complex structure prediction

Despite the progress in prediction of protein complexes over the last decade, recent blind protein complex structure prediction challenges revealed limited success rates (less than 20% models with DockQ score > 0.4) on targets that exhibit significant conformational change upon binding. To overcome limitations in capturing backbone motions, we developed a new, aggressive sampling method that incorporates temperature replica exchange Monte Carlo (T-REMC) and conformational sampling techniques within docking protocols in Rosetta. Our method, ReplicaDock 2.0, mimics induced-fit mechanism of protein binding to sample backbone motions across putative interface residues on-the-fly, thereby recapitulating binding-partner induced conformational changes. Furthermore, ReplicaDock 2.0 clocks in at 150-500 CPU hours per target (protein-size dependent); a runtime that is significantly faster than Molecular Dynamics based approaches. For a benchmark set of 88 proteins with moderate to high flexibility (unbound-to-bound iRMSD over 1.2 Angstroms), ReplicaDock 2.0 successfully docks 61% of moderately flexible complexes and 35% of highly flexible complexes. Additionally, we demonstrate that by biasing backbone sampling particularly towards residues comprising flexible loops or hinge domains, highly flexible targets can be predicted to under 2 angstrom accuracy. This indicates that additional gains are possible when mobile protein segments are known.

Replica exchange molecular dynamics simulations reveal self-association sites in M-crystallin caused by mutations provide insights of cataract

Crystallins are ubiquitous, however, prevalence is seen in eye lens. Eye lens crystallins are long-lived and structural intactness is required for maintaining lens transparency and protein solubility. Mutations in crystallins often lead to cataract. In this study, we performed mutations at specific sites of M-crystallin, a close homologue of eye lens crystallin and studied by using replica exchange molecular dynamics simulation with generalized Born implicit solvent model. Mutations were made on the Ca2+ binding residues (K34D and S77D) and in the hydrophobic core (W45R) which is known to cause congenital cataract in homologous γD-crystallin. The chosen mutations caused large motion of the N-terminal Greek key, concomitantly broke the interlocking Greek keys interactions and perturbed the compact core resulting in several folded and partially unfolded states. Partially unfolded states exposed large hydrophobic patches that could act as precursors for self-aggregation. Accumulation of such aggregates is the potential cause of cataract in homologous eye lens crystallins.