arXiv subjects

Saumyak Mukherjee

Publications and source records attributed to Saumyak Mukherjee.

14 recordsLinked to original sources

arXiv2026

Bayesian Learning of Distance Metrics Beyond RMSD for Biomolecule Alignment, Clustering, and Domain Identification

Root-mean-square deviation (RMSD) is the standard metric of structural comparison in molecular dynamics (MD) simulations. In its conventional form, RMSD assigns equal weight to all atoms regardless of mobility. Hence, flexible loops and disordered regions can dominate a global RMSD, while the rigid functional core contributes negligibly to the overall metric. To address this issue, we introduce the Bayes-optimal RMSD (BRMSD), which optimizes per-atom weights jointly with structural averages by maximizing a Bayesian posterior. In a trade-off between low RMSD and weight uniformity, a position-fluctuation parameter $σ$ controls the transition from classical RMSD ($σ\to \infty$) to a progressive focus on a rigid core ($σ\to 0$). The BRMSD framework supports analysis modules for structural alignment, focused alignment onto a user-specified domain, trajectory smoothing, soft $K$-means conformational clustering, and rigid-domain identification. These modules are implemented in the open-source Python package BRMSD (https://github.com/bio-phys/BRMSD) and benchmarked on two MD systems, the endoplasmic reticulum translocon-associated protein SND3 and the phosphotransferase adenylate kinase.

q-bio.BM↗

arXiv2025

Surface Induced Frustration of Inherent Dipolar Order in Nanoconfined Water

Surface effects could play a dominant role in modifying the natural liquid order. In some cases, the effects of the surface interactions can propagate inwards, and even can interfere with a similar propagation from opposite surfaces. This can be particularly evident in liquid water under nano-confinement. The large dipolar cross-correlations among distinct molecules that give rise to the unusually large dielectric constant of water (and in turn owe their origin to the extended hydrogen bond (HB) network) can get perturbed by surfaces. The perturbation can propagate inwards and then interfere with the one from the opposite surface if confinement is only a few layers wide. This can give rise to short-to-intermediate range solvent-mediated interaction between two surfaces. Here we study the effects of such interactions on the dielectric constant of nano-confined liquids, not just water but also ordering at protein surfaces. The surfaces work at two levels: (i) induce orientational realignment, and (ii) alter the cross-correlations between water molecules. Molecular dynamics simulations and statistical analyses are used to address these aspects in confinement of slit pores, nano tube/cylinder, and nano sphere. In addition, we consider the hydration layers of multiple proteins with vastly different structural features. These studies give us a measure of the extent or the length scale of cross-correlations between dipole moments of water molecules. We find an interesting orientational arrangement in the protein hydration layers, giving rise to long-range molecular cross-correlations. To decouple the effect of HB from the effect of geometry, we additionally study acetonitrile under nanoconfinement. Importantly, while a protein's interior is characterized by a small dielectric constant, the dipole moment of a peptide bond is large, and thus susceptible to fluctuations in water.

cond-mat.soft↗

arXiv2025

BEER: Biochemical Estimator and Explorer of Residues -- A Comprehensive Software Suite for Protein Sequence Analysis

Protein sequence analysis underpins research in biophysics, computational biology, and bioinformatics. We introduce BEER, a crossplatform graphical interface that accepts FASTA or Protein Data Bank (PDB) files, or manual sequence entry, and instantly computes a suite of physicochemical metrics, such as amino acid composition, Kyte Doolittle hydrophobicity profiles, net charge versus pH curves with automatic isoelectric point determination, solubility predictions, and key indices such as molecular weight, extinction coefficient, GRAVY (grand average of hydropathicity) score, instability index, and aromaticity. BEER's interactive visualizations, including bar and pie charts, hydropathy plots, residue level bead models, and radar diagrams make it easy to explore physicochemical properties of protein chains. A multichain module also enables direct comparison of complex assemblies. Built in Python with BioPython, PyQt5, and matplotlib, BEER delivers complete analyses of sequences up to 10000 residues in under one second.

q-bio.BM↗

arXiv2021

Signatures of Surprising Diffusion-Entropy Scaling across Pressure Induced Glass Transition in Water

Because of the negative inclination of the solid-liquid phase separation line in water, ice Ih melts on compression. On further increase in pressure the liquid water transforms into a high density metastable glassy state, characterized by a rapid approach to zero diffusion coefficient and an absence of any crystalline order in the static structure factor. The vitrification is found to occur even at high temperatures (T > 250 K). We study this glass transition process at four temperatures (80 K, 250 K, 300 K and 320 K). The transition pressure increases with increase in temperature, as expected. Interestingly, we find that the total entropy of the system exhibits a sharp crossover near the glass transition pressure where the diffusion of water goes to zero. The diffusion coefficient shows an exponential dependence on the properly defined excess entropy. In an interesting result not reported before, we find a pressure induced realignment of water molecules resulting in two well separated peaks in the O-O-O angle distribution among neighbouring molecules. The difference between the positions of these two peaks undergoes a sharp change at the vitrification pressure suggesting that it can serve as an appropriate order parameter to detect the glass transition point.

cond-mat.soft↗

arXiv2020

Origin of Multiple Infection Waves in a Pandemic: Effects of Inherent Susceptibility and External Infectivity Distributions

Two factors that are often ignored but could play a crucial role in the progression of an infectious disease are the distributions of inherent susceptibility ($σ_{inh}$) and external infectivity ($ι_{ext}$), in a given population. While the former is determined by the immunity of an individual towards a disease, the latter depends on the duration of exposure to the infection. We model the spatio-temporal propagation of a pandemic using a generalized SIR (Susceptible-Infected-Removed) model by introducing the susceptibility and infectivity distributions to understand their combined effects, which appear to remain inadequately addressed till date. We consider the coupling between $σ_{inh}$ and $ι_{ext}$ through a new Critical Infection Parameter (CIP) ($γ_c$). We find that the neglect of these distributions, as in the naive SIR model, results in an overestimation of the amount of infection in a population, which leads to incorrect (higher) estimates of the infections required to achieve the herd immunity threshold. Additionally, we include the effects of seeding of infection in a population by long-range migration. We solve the resulting master equations by performing Kinetic Monte Carlo Cellular Automata (KMC-CA) simulations. Importantly, our simulations can reproduce the multiple infection peak scenario of a pandemic. The latent interactions between disease migration and the distributions of susceptibility and infectivity can render the progression a character vastly different from the naive SIR model. In particular, inclusion of these additional features renders the problem a character of a living percolating system where the disease cluster survives by migrating from region to region.

q-bio.PE↗

arXiv2020

Attainment of Herd Immunity: Mathematical Modelling of Survival Rate

We study the influence of the rate of the attainment of herd immunity (HI), in the absence of an approved vaccine, on the vulnerable population. We essentially ask the question: how hard the evolution towards the desired herd immunity could be on the life of the vulnerables? We employ mathematical modelling (chemical network theory) and cellular automata based computer simulations to study the human cost of an epidemic spread and an effective strategy to introduce HI. Implementation of different strategies to counter the spread of the disease requires a certain degree of quantitative understanding of the time dependence of the outcome. In this paper, our main objective is to gather understanding of the dependence of outcome on the rate of progress of HI. We generalize the celebrated SIR model (Susceptible-Infected-Removed) by compartmentalizing the susceptible population into two categories- (i) vulnerables and (ii) resilients, and study dynamical evolution of the disease progression. We achieve such a classification by employing different rates of recovery of vulnerables vis-a-vis resilients. We obtain the relative fatality of these two sub-categories as a function of the percentages of the vulnerable and resilient population, and the complex dependence on the rate of attainment of herd immunity. Our results quantify the adverse effects on the recovery rates of vulnerables in the course of attaining the herd immunity. We find the important result that a slower attainment of the HI is relatively less fatal. However, a slower progress towards HI could be complicated by many intervening factors.

q-bio.PE↗

arXiv2020

Dynamical Theory and Cellular Automata Simulations of Pandemic Spread: Understanding Different Temporal Patterns of Infections

Here we propose and implement a generalized mathematical model to find the time evolution of population in infectious diseases and apply the model to study the recent COVID-19 pandemic. Our model at the core is a non-local generalization of the widely used Kermack-McKendrick(KM) model where the susceptible(S) population evolves into two other categories, namely infectives(I) and removed(R). This is the well-known SIR model in which we further divide both S and I into high and low risk categories. We first formulate a set of non-local dynamical equations for the time evolution of distinct population distributions under this categorization in an attempt to describe the general scenario of infectious disease progression. We then solve the non-linear coupled differential equations-(i) numerically by the method of propagation, and (ii) a more flexible and versatile cellular automata (CA) simulation which provides a coarse-grained description of the generalized non-local model. In order to account for multiple factors such as role of spreaders before containment, we introduce a time dependent rate which appears to be essential to explain the sudden spikes before the plateau observed in many cases (for example like China). We demonstrate how this generalized approach allows us to handle the effects of (i) time-dependence of the rate-constants of spread, (ii) different population density, (iii) the age ratio, (iv) quarantine, (v) lockdown, and (vi) social distancing. Our study allows us to make certain predictions regarding the nature of spread with respect to several external parameters, treated as control variables. Analysis of the model clearly shows that due to the strong heterogeneity in the epidemic process originating from the distribution of initial infectives, the theory must be local in character but at the same time connect to a global perspective.

q-bio.PE↗

arXiv2019

Ice-water Interface: Correlation between Structure and Dynamics

To comprehend the complexities of the ice-water interface, we perform a study that attempts to correlate the altered dynamics of water to its perturbed structure at, and due to, the interface. The deviation from bulk values of structural and dynamical quantities at the interface are obtained by computer simulations. Water molecules are found to get exchanged between the ice-like and water-like domains of the interface with a time scale of the order of ~10 ps. To investigate the effect of interfaces in general, we study three other systems, namely (i) water between two hydrophobic nano-slabs, (ii) water at protein and (iii) DNA surfaces. In all these systems, we find that the difference from bulk properties become negligible beyond ~1 nm, with structural features converging to bulk values faster than the dynamical properties. Even in the case of the latter, we find that single-particle and collective properties behave differently. The approach to bulk values is rapid except for collective shell-dipole moments. We present a new insightful characterization of the surfaces by establishing a quantitative correlation between tetrahedrality order parameter (q_td) and dynamics by diffusion (D) and angular jumps. In the ice-water system, we find that the variation of qtd, as we move from solid to the liquid phase, correlated well with D. The correlation is found to be present in all the interfaces studied. Our results can be used to explain the experimental outcomes of the likes of dielectric relaxation and solvation dynamics.

cond-mat.soft↗

arXiv2018

In search of the origin of long-time power-law decay in DNA solvation dynamics

Experiments reveal that DNA solvation dynamics (SD) is characterized by multiple time scales ranging from a few ps to hundreds of ns and in some cases even up to microseconds. The last part of decay is slow and is characterized by a power law (PL). The microscopic origin of this PL is not yet clearly understood. Here we present a theoretical study based on time dependent statistical mechanics and computer simulations. Our investigations show that the primary candidates responsible for this exotic nature of SD are the counterions and ions from the buffer solution. We employ the model developed by Oosawa for polyelectrolyte solution that includes effects of counterion fluctuations to construct a frequency dependent dielectric function. We use it in the continuum model of Bagchi, Fleming and Oxtoby only to find that it fails to explain the slow PL decay of DNA solvation dynamics. We then extend the model by employing the continuous time random walk technique developed by Scher-Montroll-Lax. This approach can explain the long time PL decay, in terms of the collective response of the counter ions. From MD simulations we find frequent occurrence of random walk of tagged counter ions along the phosphate backbone. We propose a generalized random walk model for counterion hopping and carry out kinetic Monte Carlo simulations to show that the nonexponential contribution to solvation dynamics can indeed arise from dynamics of such ions. We also employ a Mode Coupling Theory analysis to understand the slow relaxation that originates from ions in solution. Explicit evaluation suggests that buffer ion contribution could explain logarithmic time dependence in the ns time scale, but not a power law. From MD simulations we find log-normal distributions of relaxation times of water dynamics inside the grooves. This is responsible for the initial faster multiexponential decay of SD.

cond-mat.stat-mech↗

arXiv2018

Towards Understanding the Structure, Dynamics and Bio-activity of Diabetic Drug Metformin

Small molecules are often found to exhibit extraordinarily diverse biological activities. Metformin is one of them. It is widely used as anti-diabetic drug for type-two diabetes. In addition to that, metformin hydrochloride shows anti-tumour activities and increases the survival rate of patients suffering from certain types of cancer namely colorectal, breast, pancreas and prostate cancer. However, theoretical studies of structure and dynamics of metformin have not yet been fully explored. In this work, we investigate the characteristic structural and dynamical features of three mono-protonated forms of metformin hydrochloride with the help of experiments, quantum chemical calculations and atomistic molecular dynamics simulations. We validate our force field by comparing simulation results to that of the experimental findings. Nevertheless, we discover that the non-planar tautomeric form is the most stable. Metformin forms strong hydrogen bonds with surrounding water molecules and its solvation dynamics show unique features. Because of an extended positive charge distribution, metformin possesses features of being a permanent cationic partner toward several targets. We study its interaction and binding ability with DNA using UV spectroscopy, circular dichroism, fluorimetry and metadynamics simulation. We find a non-intercalating mode of interaction. Metformin feasibly forms a minor/major groove-bound state within a few tens of nanoseconds, preferably with AT rich domains. A significant decrease in the free-energy of binding is observed when it binds to a minor groove of DNA.

q-bio.BM↗

arXiv2017

Cavity Waters Govern Insulin Association and Release: Inferences from Experimental Data and Molecular Dynamics Simulations

While a monomer of the ubiquitous hormone insulin is the biologically active form in the human body, its hexameric assembly acts as an efficient storage unit. However, the role of water molecules in the structure, stability and dynamics of the insulin hexamer is poorly understood. Here we combine experimental data with molecular dynamics simulations to investigate the shape, structure and stability of an insulin hexamer focusing on the role of water molecules. Both X-Ray analysis and computer simulations show that the core of the hexamer cavity is barrel-shaped, holding, on an average, sixteen water molecules. These encapsulated and constrained molecules impart structural stability to the hexamer. Apart from the electrostatic interactions with Zn2+ ions, an intricate hydrogen bond network amongst cavity water and neighboring protein residues stabilizes the hexameric association. These water molecules solvate six glutamate residues inside the cavity decreasing electrostatic repulsions amongst the negatively charged carboxylate groups. They also prevent association between glutamate residues and Zn2+ ions and maintain the integrity of the cavity. Simulations reveal that removal of these waters results in a collapse of the cavity. Subsequent analyses also show that the hydrogen bond network among these water molecules and protein residues that face the inner side of the cavity is more rigid with a slower relaxation as compared to that of the bulk solvent. Dynamics of cavity water reveal certain slow water molecules which form the back bone of the stable hydrogen bond network. The analysis presented here suggests a dominant role of structurally conserved water molecules in maintaining the integrity of the hexameric assembly and potentially modulating the dissociation of this assembly into the functional monomeric form.

q-bio.BM↗

arXiv2017

On the origin of diverse time scales in the protein hydration layer solvation dynamics: A molecular dynamics simulation study

In order to inquire the microscopic origin of observed multiple time scales in solvation dynamics we carry out several computer experiments. We perform atomistic molecular dynamics simulations on three protein-water systems namely, Lysozyme, Myoglobin and sweet protein Monellin. In these experiments we mutate the charges of the neighbouring amino acid side chains of certain natural probes (Tryptophan) and also freeze the side chain motions. In order to distinguish between different contributions, we decompose the total solvation energy response in terms of various components present in the system. This allows us to capture the interplay among different self and cross-energy correlation terms. Freezing the protein motions removes the slowest component that results from side chain fluctuations, but a part of slowness remains. This leads to the conclusion that the slow component in the ~20-80 ps range arises from slow water molecules present in the hydration layer. While the more than 100 ps component may arise from various sources namely, adjacent charges in amino acid side chains, the water molecules that are hydrogen bonded to them and a dynamically coupled motion between side chain and water. The charges, in addition, enforce a structural ordering of nearby water molecules and helps to form local long-lived hydrogen bonded network. Further separation of the spatial and temporal responses in solvation dynamics reveals different roles of hydration and bulk water. We find that the hydration layer water molecules are largely responsible for the slow component whereas the initial ultrafast decay arise predominantly (~80%) due to the bulk. This agrees with earlier theoretical observations. We also attempt to rationalise our results with the help of a molecular hydrodynamic theory that was developed using classical time dependent density functional theory in a semi quantitative manner.

cond-mat.soft↗

arXiv2017

Distinguishing dynamical features of water inside protein hydration layer: Distribution reveals what is hidden behind the average

Since the pioneering works of Pethig, Grant and Wuthrich on protein hydration layer, many studies have been devoted to find out if there are any general and universal characteristic features that can distinguish water molecules inside the protein hydration layer from bulk. Given that the surface itself varies from protein to protein, and that each surface facing the water is heterogeneous, search for universal features has been elusive. Here, we perform atomistic molecular dynamics simulation in order to propose and demonstrate that such defining characteristics can emerge if we look not at average properties but the distribution of relaxation times. We present results of calculations of distributions of residence times and rotational relaxation times for four different protein-water systems, and compare them with the same quantities in the bulk. The distributions in the hydration layer is unusually broad and log-normal in nature, due to the simultaneous presence of peptide backbones that form weak hydrogen bonds, hydrophobic amino acid side chains that form no hydrogen bond and charged polar groups that form strong hydrogen bond with the surrounding water molecules. The broad distribution is responsible for the non-exponential dielectric response and also agrees with large specific heat of the hydration water. Our calculations reveal that while the average time constant is just about 2-3 times larger than that of bulk water, it provides a poor representation of the real behaviour. In particular, the average leads to the erroneous conclusion that water in the hydration layer is bulk-like. However, the observed and calculated lower value of static dielectric constant of hydration layer remained difficult to reconcile with the broad distribution observed in dynamical properties. We offer a plausible explanation of these unique properties.

cond-mat.soft↗

arXiv2017

Dynamical coupling between protein conformational fluctuation and hydration water: Heterogeneous dynamics of biological water

We investigate dynamical coupling between water and amino acid side-chain residues in solvation dynamics by selecting residues often used as natural probes, namely tryptophan, tyrosine and histidine, located at different positions on protein surface and having various degrees of solvent exposure. Such differently placed residues are found to exhibit different timescales of relaxation. The total solvation response, as measured by the probe is decomposed in terms of its interactions with (i) protein core, (ii) side-chain atoms and (iii) water molecules. Significant anti cross-correlations among these contributions are observed as a result of side-chain assisted energy flow between protein core and hydration layer, which is important for the proper functionality of a protein. It is also observed that there are rotationally faster as well as slower water molecules than that of bulk solvent, which are considered to be responsible for the multitude of timescales that are observed in solvation dynamics. We also establish that slow solvation derives a significant contribution from protein side-chain fluctuations. When the motion of the protein side-chains is forcefully quenched, solvation either becomes faster or slower depending on the location of the probe.

q-bio.BM↗