Stochastic Molecular Dynamics Research Articles

Single-Molecule Bioelectronic Sensors with AI-Aided Data Analysis: Convergence and Challenges.

Single-molecule bioelectronic sensing, a groundbreaking domain in biological research, has revolutionized our understanding of molecules by revealing deep insights into fundamental biological processes. The advent of emergent technologies, such as nanogapped electrodes and nanopores, has greatly enhanced this field, providing exceptional sensitivity, resolution, and integration capabilities. However, challenges persist, such as complex data sets with high noise levels and stochastic molecular dynamics. Artificial intelligence (AI) has stepped in to address these issues with its powerful data processing capabilities. AI algorithms effectively extract meaningful features, detect subtle changes, improve signal-to-noise ratios, and uncover hidden patterns in massive data. This review explores the synergy between AI and single-molecule bioelectronic sensing, focusing on how AI enhances signal processing and data analysis to boost accuracy and reliability. We also discuss current limitations and future directions for integrating AI, highlighting its potential to advance biological research and technological innovation.

Design single-stranded DNA aptamer of cluster of differentiation 47 protein by stochastic tunnelling-basin hopping-discrete molecular dynamics method

The formation of the Cluster of Differentiation 47 (CD47, PDB code: 2JJT)/signal regulatory protein α (SIRPα) complex is very important as it protects healthy cells from immune clearance while promoting macrophage phagocytosis for tumour elimination. Although several antibodies have been developed for cancer therapy, new function-blocking aptamers are still under development. This study aims to design the aptamer AptCD47, which can block the formation of the CD47/SIRPα complex. This study employs the MARTINI coarse-grained (CG) force field and the stochastic tunnelling-basin hopping-discrete molecular dynamics (STUN-BH-DMD) method to identify the most stable AptCD47/CD47 complexes. Coarse-grained molecular dynamics (CGMD) simulations were used to obtain root-mean-square deviation (RMSD) and root-mean-square fluctuation (RMSF) analyses. The results demonstrate that the formation of AptCD47/CD47 complexes renders the CD47 structure more stable than the single CD47 molecule in a water environment. The minimum energy pathway (MEP) obtained by the nudged elastic band (NEB) method indicates that the binding processes of 5′-ATTCAATTCC-3′ and 5′-AGTGCAATCT-3′ to CD47 are barrierless, which is much lower than the binding barrier of SIRPα to CD47 of about 14.23 kcal/mol. Therefore, these two AptCD47/CD47 complexes can create a high spatial binding barrier for SIRPα, preventing the formation of a stable CD47/SIRPα complex. The proposed numerical process with the MARTINI CG force field can be used to design CD47 aptamers that efficiently block SIRPα from binding to CD47. Communicated by Ramaswamy H. Sarma

H-Bonds in Crambin: Coherence in an α-Helix.

We applied coherence analysis-used by engineers to identify linear interactions in stochastic systems-to molecular dynamics simulations of crambin, a thionin storage protein found in Abyssinian cabbage. A key advantage of coherence over other analyses is that it is robust, independent of the properties, or even the existence of probability distributions often relied on in statistical mechanics. For frequencies between 0.391 and 5.08 GHz (corresponding reciprocally to times of 2.56 and 0.197 ns), the displacements of oxygen and nitrogen atoms across α-helix H-bonds are strongly correlated, with a coherence greater than 0.9; the secondary structure causes the H-bonds to effectively act as a spring. Similar coherence behavior is observed for covalent bonds and other noncovalent interactions including H-bonds in β-sheets and salt bridges. In contrast, arbitrary pairs of atoms that are physically distant have uncorrelated motions and negligible coherence. These results suggest that coherence may be used to objectively identify atomic interactions without subjective thresholds such as H-bond lengths angles and angles. Strong coherence is also observed between the average position of adjacent leaves (groups of atoms) in an α-helix, suggesting that the harmonic analysis of classical molecular dynamics can successfully describe the propagation of allosteric interactions through the structure.

Design the RNA aptamer of PCA3 long non-coding ribonucleic acid by the coarse-grained molecular mechanics

The stochastic tunneling-basin hopping-discrete molecular dynamics (STUN-BH-DMD) method was applied to predict the tertiary structure of the prostate cancer marker PCA3 using two respective secondary structures predicted by the Vienna RNA package and Mathews lab package. The RNA CG force field with the geometrical restraints for maintaining PCA3 secondary structures is used. For each secondary structure, 5000 PCA3 structures were predicted by using 5000 independent initial structures. These structures were then evaluated by a scoring function, considering the contributions from the radius of gyration, contact energy, and surface fraction of complementary nucleotides to ASO683 and ASO735 used in the related experiment. For each secondary structure, the PCA3 structures with the highest three scores were selected for aptamer design and further adsorption simulation. The ASOs complementary to PCA3 surface segments possessing relatively higher RMSF values are selected to be the potential PCA3 aptamers. After the adsorption simulation, the adsorption energies of ASO961, ASO3181, ASO3533, and ASO3595 are higher than or comparable to those of ASO683 and ASO735 used in the experiment. The NEB method was used to obtain MEPs for the adsorption process of all predicted ASOs onto PCA3. The adsorption barriers range between 29 ∼ 39 kcal/mol, while the desorption barriers range between 112 ∼ 352 kcal/mol, indicating these aptamer/PCA3 complexes are very stable. Using PCA3 surface segments with relatively higher RMSF values, longer ASOs can be also obtained and most longer ASOs possess lower binding energy, ranging between −486.1 and −618.2 kcal/mol. Communicated by Ramaswamy H. Sarma

Exploring the most stable aptamer/target molecule complex by the stochastic tunnelling-basin hopping-discrete molecular dynamics method

The stochastic tunnelling-basin hopping-discrete molecular dynamics (STUN-BH-DMD) method was applied to the search for the most stable biomolecular complexes in water by using the MARTINI coarse-grained (CG) model. The epithelial cell adhesion molecule (EpCAM, PDB code: 4MZV) was used as an EpCAM adaptor for an EpA (AptEpA) benchmark target molecule. The effects of two adsorption positions on the EpCAM were analysed, and it is found that the AptEpA adsorption configuration located within the EpCAM pocket-like structure is more stable and the energy barrier is lower due to the interaction with water. By the root mean square deviation (RMSD), the configuration of EpCAM in water is more conservative when the AptEpA binds to EpCAM by attaching to the pocket space of the EpCAM dimer. For AptEpA, the root mean square fluctuation (RMSF) analysis result indicates Nucleobase 1 and Nucleobase 2 display higher flexibility during the CGMD simulation. Finally, from the binding energy contour maps and histogram plots of EpCAM and each AptEpA nucleobase, it is clear that the binding energy adsorbed to the pocket-like structure is more continuous than that energy not adsorbed to the pocket-like structure. This study has proposed a new numerical process for applying the STUN-BH-DMD with the CG model, which can reduce computational details and directly find a more stable AptEpA/EpCAM complex in water.

Stochastic simulation of nonequilibrium heat conduction in extended molecular junctions.

Understanding phononic heat transport processes in molecular junctions is a central issue in the developing field of nanoscale heat conduction. Here, we present a Langevin dynamics simulation framework to investigate heat transport processes in molecular junctions at and beyond the linear response regime and apply it to saturated and unsaturated linear hydrocarbon chains connecting two gold substrates. Thermal boundary conditions represented by Markovian noise and damping are filtered through several (up to four) gold layers to provide a realistic and controllable bath spectral density. Classical simulations using the full universal force field are compared with quantum calculations that use only the harmonic part of this field. The close agreement found at about room temperature between these very different calculations suggests that heat transport at such temperatures is dominated by lower frequency vibrations whose dynamics is described well by classical mechanics. The results obtained for alkanedithiol molecules connecting gold substrates agree with previous quantum calculations based on the Landauer formula and match recent experimental measurements [e.g., thermal conductance around 20 pW/K for alkanedithiols in single-molecule junctions (SMJs)]. Heat conductance simulations on polyynes of different lengths illuminate the effects of molecular conjugation on thermal transport. The difference between alkanes and polyynes is not large but correlates with the larger rigidity and stronger mode localization that characterize the polyyne structure. This computational approach has been recently used [R. Chen, I. Sharony, and A. Nitzan, J. Phys. Chem. Lett. 11, 4261-4268 (2020)] to unveil local atomic heat currents and phononic interference effect in aromatic-ring based SMJs.

Stochastic Constrained Extended System Dynamics for Solving Charge Equilibration Models.

We present a new stochastic extended Lagrangian molecular dynamics solution to charge equilibration that eliminates self-consistent field (SCF) calculations, thus eliminating the computational bottleneck in solving the charge distribution with standard SCF solvers. By formulating both charges and chemical potential as latent variables and introducing a holonomic constraint that satisfies charge conservation, the SC-XLMD method accurately reproduces thermodynamic, dynamic, and structural properties within the framework of ReaxFF for a bulk water system and highly reactive RDX molecules simulated at high temperature. The SC-XLMD method shows excellent computational performance and is available in the publicly available LAMMPS package.

Effect of Fluorine Patterns on Electronic Transport in Fluorinated Graphene

AbstractWithin the framework of stochastic reactive molecular dynamics simulations a statistical method for generating fluorinated graphene structures with desirable fluorine distribution is developed. Electronic transport properties of fluorinated graphene in a wide range of functionalization degrees and system ordering are investigated. A strong correlation between irregularities in fluorine distribution and electronic properties is found. In particular, proposed consideration allows for the reproduction of both the experimentally observed electron–hole asymmetry in transport properties of fluorinated graphene and a recently revealed conductivity peak at 10% fluoride content.

Моделирование неравновесных процессов методом стохастической молекулярной динамики: столкновения

Моделирование неравновесных процессов методом стохастической молекулярной динамики: столкновения

Stochastic Model of Pore Nucleation when the Sample is Irradiates with Inert Gas Ions

Abstract—Non-point vacancy-gas defects (VGD) (pores, blisters) in the crystal lattice arise as a result of its irradiation with an inert gas Xe++, the process is considered as the formation of first-order phase transition nuclei by means of computational mathematics, kinetic theory, and the theory of stochastic dynamic variables and Wiener random processes. The characteristics of disordered porosity in samples consisting of layers (“dielectric/metal”) at various layer thicknesses are calculated. The formation of spherical shape defects in materials at times of the order of 10–4 s, when the porosity of the material nucleates, is preceded or accompanied by the appearance of microcracks. Irradiation of surfaces with an inert gas with ion energies of 5–10 keV refers to low-temperature blistering; in the model, the constancy of the influence of radiation fluxes stimulating a phase transition creates the condition of an “open” physical system in which it is possible to combine lattice defects into structures that cause local stresses, and the constancy of the temperature of the sample, the pressure of the implantable “monomers” of the gas, and supersaturation (similar to the parameters of vapor condensation) are characteristic of the fluctuation unstable stage of the phase transition move. Partial kinetic equations with nonlinear coefficients (Kolmogorov–Feller and Einstein–Smoluchowski) are solved by the method of stochastic molecular dynamics, which establishes a connection between the solution of Ito stochastic equations in the sense of Stratonovich and kinetic equations; stable numerical methods are used. The conditions for the formation of VGD are determined taking into account the influence of the elastic properties of the lattice, and the porosity and local stresses in thin layers of irradiated materials are calculated.

The Impact of Rate Formulations on Stochastic Molecular Motor Dynamics

Cells are complex structures which require considerable amounts of organization via transport of large intracellular cargo. While passive diffusion is often sufficiently fast for the transport of smaller cargo, active transport is necessary to organize large structures on the short timescales necessary for biological function. The main mechanism of this transport is by cargo attachment to motors which walk in a directed fashion along intracellular filaments. There are a number of models which seek to describe the motion of motors with attached cargo, from detailed microscopic to coarse phenomenological descriptions. We focus on the intermediate-detailed discrete stochastic hopping models, and explore how cargo transport changes depending on the number of motors, motor interaction, system constraints and rate formulations, which are derived from common thermodynamic assumptions. We find that, despite obeying the same detailed balance constraint, the choice of rate formulation considerably affects the characteristics of the overall motion of the system, with one rate formulation exhibiting novel behavior of loaded motor groups moving faster than a single unloaded motor.

Evolutionary Switches Structural Transitions via Coarse-Grained Models.

Transitions between different conformational states are ubiquitous in proteins. A vast class of conformation-changing proteins includes evolutionary switches, which vary their conformation as an effect of few mutations or weak environmental variations. However, modeling those processes is extremely difficult due to the need of efficiently exploring a vast conformational space to look for the actual transition path. In this study, we report a strategy that simplifies this task attacking the complexity on several sides. We first apply a minimalist coarse-grained model to the protein, based on an empirical force field with a partial structural bias toward one or both the reference structures. We then explore the transition paths by means of stochastic molecular dynamics and select representative structures by means of a principal path-based clustering algorithm. We finally compare this trajectory with that produced by independent methods adopting a morphing-oriented approach. Our analysis indicates that the minimalist model returns trajectories capable of exploring intermediate states with physical meaning, retaining a very low computational cost, which can allow systematic and extensive exploration of the multistable proteins transition pathways.

A pH Replica Exchange Scheme in the Stochastic Titration Constant-pH MD Method.

Solution pH is a physicochemical property that has a key role in cellular regulation, and its impact at the molecular level is often difficult to study by experimental methods. In this context, several theoretical methods were developed to study pH effects in macromolecules. The stochastic titration constant-pH molecular dynamics method (CpHMD) was developed by coupling molecular sampling methods, which are appropriate to study the conformational ensemble of biomolecules, with continuum electrostatics approaches, which properly describe pH-dependent protonation states. However, in difficult cases, the protonation sampling can be too slow for the commonly accessible computational times. In this work, we combined a pH replica exchange scheme with this CpHMD method and explored several optimization strategies and possible limitations.

Refinement of thermostated molecular dynamics using backward error analysis.

Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integration may lead to deviations from equipartition. Fortunately, backward error analysis allows us to obtain a higher-order estimate of the quantity that is actually subject to equipartition. This is related to a shadow Hamiltonian, which converges to the specified Hamiltonian only when the time-step size approaches zero. This paper deals with discretization effects in a straightforward way. With a small computational overhead, we obtain refined versions of the kinetic and potential energies, whose sum is a suitable estimator of the shadow Hamiltonian. Then, we tune the thermostatting procedure by employing the refined kinetic energy instead of the conventional one. This procedure is shown to reproduce a canonical ensemble compatible with the refined system, as opposed to the original one, but canonical averages regarding the latter can easily be recovered by reweighting. Water, modeled as a rigid body, is an excellent test case for our proposal because its numerical stability extends up to time steps large enough to yield pronounced discretization errors in Verlet-type integrators. By applying our new approach, we were able to mitigate discretization effects in equilibrium properties of liquid water for time-step sizes up to 5 fs.

Structural effects and competition mechanisms targeting the interactions between p53 and MDM2 for cancer therapy

Approximately half of all human cancers show normal TP53 gene expression but aberrant overexpression of MDM2 and/or MDMX. This fact suggests a promising cancer therapeutic strategy in targeting the interactions between p53 and MDM2/MDMX. To help realize the goal of developing effective inhibitors to disrupt the p53–MDM2/MDMX interaction, we systematically investigated the structural and interaction characteristics of p53 with inhibitors of its interactions with MDM2 and MDMX from an atomistic perspective using stochastic molecular dynamics simulations. We found that some specific α helices in the structures of MDM2 and MDMX play key roles in their binding to inhibitors, and that the hydrogen bond formed by the Trp23 residue of p53 with its counterpart in MDM2 or MDMX determines the dynamic competition processes of the disruption of the MDM2–p53 interaction and replacement of p53 from the MDM2–p53 complex in vivo. The results reported in this paper are expected to provide basic information for designing functional inhibitors and realizing new strategies of cancer gene therapy.

Pore translocation of knotted DNA rings

We use an accurate coarse-grained model for DNA and stochastic molecular dynamics simulations to study the pore translocation of 10-kbp-long DNA rings that are knotted. By monitoring various topological and physical observables we find that there is not one, as previously assumed, but rather two qualitatively different modes of knot translocation. For both modes the pore obstruction caused by knot passage has a brief duration and typically occurs at a late translocation stage. Both effects are well in agreement with experiments and can be rationalized with a transparent model based on the concurrent tensioning and sliding of the translocating knotted chains. We also observed that the duration of the pore obstruction event is more controlled by the knot translocation velocity than the knot size. These features should advance the interpretation and design of future experiments aimed at probing the spontaneous knotting of biopolymers.

A hybrid molecular dynamics study on the non-Newtonian rheological behaviors of shear thickening fluid.

To investigate the microstructural evolution dependency on the apparent viscosity in shear-thickening fluids (STFs), a hybrid mesoscale model combined with stochastic rotation dynamics (SRD) and molecular dynamics (MD) is used. Muller-Plathe reverse perturbation method is adopted to analyze the viscosities of STFs in a two-dimensional model. The characteristic of microstructural evolution of the colloidal suspensions under different shear rate is studied. The effect of diameter of colloidal particles and the phase volume fraction on the shear thickening behavior is investigated. Under low shear rate, the two-atom structure is formed, because of the strong particle attractions in adjacent layers. At higher shear rate, the synergetic pair structure extends to layered structure along flow direction because of the increasing hydrodynamics action. As the shear rate rises continuously, the layered structure rotates and collides with other particles, then turned to be individual particles under extension or curve string structure under compression. Finally, at the highest shear rate, the strings curve more severely and get into two-dimensional cluster. The apparent viscosity of the system changes from shear-thinning behavior to the shear-thickening behavior. This work presents valuable information for further understanding the shear thickening mechanism.

On the numerical approximation of the Perron-Frobenius and Koopman operator

Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review different methods that have been developed over the last decades to compute finite-dimensional approximations of these infinite-dimensional operators - e.g. Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and differences between these approaches. The results will be illustrated using simple stochastic differential equations and molecular dynamics examples.

Kinetics of the formation of pores and a change in the properties of materials in numerical models

Vacancy-gas defects (VGDs) in thin layers of silicon carbide and a metal (SiC/Me) are formed upon 1–10-keV Xe++ ion implantation as the result of a first-order phase transition. The nonequilibrium stage of this transition is modeled by stochastic processes of point-defect clustering and the Brownian motion of cluster centers of mass under the action of potentials of their indirect elastic interaction in the crystal lattices of materials. A numerical experiment for studying pore formation during ion implantation is constructed on the basis of kinetic theory. Stochastic molecular dynamics makes it possible to analyze the formation of pores depending on functions of the nonequilibrium distribution of VGD nucleus clusters over sizes and coordinates of the layer volume. An example of calculation for conditions of phase-transition fluctuation instability is given.

Constant-pH MD Simulations Portray the Protonation and Structural Behavior of Four Decapeptides Designed to Coordinate Cu(2+).

The cyclic decapeptide C-Asp, containing one Asp residue and three His residues, was designed by Fragoso et al. (Chem. Eur. J. 2013, 19, 2076) to bind Cu(2+) exclusively through the side chain groups and mimic copper coordination in metalloproteins. A variant of the cyclodecapeptide where Asp is substituted by Asn (C-Asn) has also been synthesized in addition to the linear ("open") counterparts of both forms (O-Asp and O-Asn), testing the importance of cyclization and the presence of Asp in Cu(2+) coordination (Chem. Eur. J. 2013, 19, 2076; Dalton Trans. 2013, 42, 6182). All peptides formed a major species at neutral pH that was able to coordinate Cu(2+) exclusively through the neutral imidazole groups and the Asp side chain, when present, with C-Asp being the most effective. A detailed description of the protonation behavior of each histidine could help understanding the coordination species being formed in the pH range and eventually further optimizing the peptide's design. However, the standard current methods (NMR titrations) are not very suited for proximal groups titrating in the same pH range. In this work, we used the stochastic titration constant-pH molecular dynamics method to calculate the protonation curves and pKa of each titrable residue in the four decapeptides, in the absence of Cu(2+) ions. The global protonation curves obtained in our simulations are in very good agreement with the existing potentiometric titration curves. The histidines are titrating very closely, and the Asp forms abundant salt bridges with the basic residues, displaying an unusually low pKa value. In addition, we could observe that the four peptides are very unstructured in the absence of copper, and not even the cyclic forms exhibit a significant β-sheet, unlike what could be expected from the presence of β-turn inducer units in this type of scaffold.