arXiv subjects

Tanmoy Pal

Publications and source records attributed to Tanmoy Pal.

12 recordsLinked to original sources

arXiv2026

Homeostatic Noise Buffering in Biomolecular Condensates Hinges on Phase Multiplicity Modulated by Interfacial and Droplet Size Effects

Specific mixing or demixing of molecular species is a characteristic feature of condensed intracellular membraneless compartments. How sequence patterns of intrinsically disordered proteins (IDPs) fundamentally impact subcompartmentalization of biomolecular condensates and their role in buffering against concentration fluctuations are hereby addressed by modeling liquid-liquid phase separation (LLPS) of polyampholytic sequence pairs using random phase approximation (RPA) polymer theory and molecular dynamics (MD). RPA theory predicts both binary and ternary LLPS in a temperature-sensitive manner. We observe demixing underpinned by ternary LLPS for pairs with dissimilar sequence charge patterns but not for pairs with similar sequence charge patterns. Notably, the predicted behaviors are corroborated by MD when RPA is augmented with interfacial tension and/or a finite-size formalism commensurating with the typical small sizes of MD model systems, supporting our stipulation that RPA theory is a useful sequence-specific modeling tool for biomolecular condensates with larger, more realistic sizes when finite-size effects are much less significant. In principle, when the condensate size is sufficiently large, ternary LLPS is superior to binary LLPS in noise buffering because the IDP compositions of the three coexisting phases in ternary LLPS remain unchanged over an extended two-dimensional concentration regime, whereas the two coexisting phases in binary LLPS are fixed only along a tieline. However, when condensate sizes are sufficiently small, the buffering capacities of ternary versus binary LLPSs are more complex as they are modulated differently by finite-size effects. Biophysical ramifications of this interplay are discussed in view of the size diversity of natural biomolecular condensates.

q-bio.BM↗

arXiv2024

Differential Effects of Sequence-Local versus Nonlocal Charge Patterns on Phase Separation and Conformational Dimensions of Polyampholytes as Model Intrinsically Disordered Proteins

Conformational properties of intrinsically disordered proteins (IDPs) are governed by a sequence-ensemble relationship. To differentiate the impact of sequence-local versus sequence-nonlocal features of an IDP's charge pattern on its conformational dimensions and its phase-separation propensity, the charge "blockiness'' $κ$ and the nonlocality-weighted sequence charge decoration (SCD) parameters are compared for their correlations with isolated-chain radii of gyration ($R_{\rm g}$s) and upper critical solution temperatures (UCSTs) of polyampholytes modeled by random phase approximation, field-theoretic simulation, and coarse-grained molecular dynamics. SCD is superior to $κ$ in predicting $R_{\rm g}$ because SCD accounts for effects of contact order, i.e., nonlocality, on dimensions of isolated chains. In contrast, $κ$ and SCD are comparably good, though nonideal, predictors of UCST because frequencies of interchain contacts in the multiple-chain condensed phase are less sensitive to sequence positions than frequencies of intrachain contacts of an isolated chain, as reflected by $κ$ correlating better with condensed-phase interaction energy than SCD.

q-bio.BM↗

arXiv2024

Electrostatics of Salt-Dependent Reentrant Phase Behaviors Highlights Diverse Roles of ATP in Biomolecular Condensates

Liquid-liquid phase separation (LLPS) involving intrinsically disordered protein regions (IDRs) is a major physical mechanism for biological membraneless compartmentalization. The multifaceted electrostatic effects in these biomolecular condensates are exemplified here by experimental and theoretical investigations of the different salt- and ATP-dependent LLPSs of an IDR of messenger RNA-regulating protein Caprin1 and its phosphorylated variant pY-Caprin1, exhibiting, e.g., reentrant behaviors in some instances but not others. Experimental data are rationalized by physical modeling using analytical theory, molecular dynamics, and polymer field-theoretic simulations, indicating that interchain ion bridges enhance LLPS of polyelectrolytes such as Caprin1 and the high valency of ATP-magnesium is a significant factor for its colocalization with the condensed phases, as similar trends are observed for other IDRs. The electrostatic nature of these features complements ATP's involvement in $\pi$-related interactions and as an amphiphilic hydrotrope, underscoring a general role of biomolecular condensates in modulating ion concentrations and its functional ramifications.

q-bio.BM↗

arXiv2022

PT-Symmetry Breaking Transitions in Polymeric Systems

We show that classical DNA unzipping transition which is equivalently described by quantum mechanical localization-delocalization transition in the ground state of non-Hermitian single impurity Hatano-Nelson Hamiltonian is underpinned by generalized parity ({\bf P})-time reversal ({\bf T}) symmetry breaking transition. We also study the one-dimensional discretized version of Hatano-Nelson model in the presence of the single impurity and random disorder on a finite-size lattice. These discrete models are useful to study unzipping of a single adsorbed polymer from a surface. Our results show that the discrete models also undergo a phase transition from a PT unbroken phase to a broken phase. Interestingly, the generalized PT phase transition points coincide with the localization-delocalization transition for continuum as well as lattice models.

cond-mat.stat-mech↗

arXiv2022

Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Proteinlike Heteropolymers with Short- and Long-Spatial-Range Interactions

A theory for sequence dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints. A mean-field approximation leads to an effective Flory $χ$ parameter, which, in conjunction with RPA, accounts for the contact-interaction effects of amino acid composition and the sequence-pattern effects of long-range electrostatics in IDP LLPS, whereas FTS based on the formulation provides full sequence dependence for both short- and long-range interactions. This general approach is illustrated here by applications to variants of a natural IDP in the context of several different amino-acid interaction schemes as well as a set of different model hydrophobic-polar sequences sharing the same composition. Effectiveness of the methodology is verified by coarse-grained explicit-chain molecular dynamics simulations.

q-bio.BM↗

arXiv2022

Numerical Techniques for Applications of Analytical Theories to Sequence-Dependent Phase Separations of Intrinsically Disordered Proteins

Biomolecular condensates, physically underpinned to a significant extent by liquid-liquid phase separation (LLPS), are now widely recognized by numerous experimental studies to be of fundamental biological, biomedical, and biophysical importance. In the face of experimental discoveries, analytical formulations emerged as a powerful yet tractable tool in recent theoretical investigations of the role of LLPS in the assembly and dissociation of these condensates. The pertinent LLPS often involves, though not exclusively, intrinsically disordered proteins engaging in multivalent interactions that are governed by their amino acid sequences. For researchers interested in applying these theoretical methods, here we provide a practical guide to a set of computational techniques devised for extracting sequence-dependent LLPS properties from analytical formulations. The numerical procedures covered include those for the determinination of spinodal and binodal phase boundaries from a general free energy function with examples based on the random phase approximation in polymer theory, construction of tie lines for multiple-component LLPS, and field-theoretic simulation of multiple-chain heteropolymeric systems using complex Langevin dynamics. Since a more accurate physical picture often requires comparing analytical theory against explicit-chain model predictions, a commonly utilized methodology for coarse-grained molecular dynamics simulations of sequence-specific LLPS is also briefly outlined.

q-bio.BM↗

arXiv2022

Field theory description of ion association in re-entrant phase separation of polyampholytes

Phase separation of several different overall neutral polyampholyte species (with zero net charge) is studied in solution with two oppositely charged ion species that can form ion-pairs through an association reaction. A field theory description of the system, that treats polyampholyte charge sequence dependent electrostatic interactions as well as excluded volume effects, is hereby given. Interestingly, analysis of the model using random phase approximation and field theoretic simulation consistently show evidence of a re-entrant polyampholyte phase separation at high ion concentrations when there is an overall decrease of volume upon ion-association. As an illustration of the ramifications of our theoretical framework, several polyampholyte concentration vs ion concentration phase diagrams under constant temperature conditions are presented to elucidate the dependence of phase separation behavior on polyampholyte sequence charge pattern as well as ion-pair dissociation constant, volumetric effects on ion association, solvent quality, and temperature.

cond-mat.soft↗

arXiv2021

A Simple Explicit-Solvent Model of Polyampholyte Phase Behaviors and its Ramifications for Dielectric Effects in Biomolecular Condensates

Biomolecular condensates such as membraneless organelles, underpinned by liquid-liquid phase separation (LLPS), are important for physiological function, with electrostatics -- among other interaction types -- being a prominent force in their assembly. Charge interactions of intrinsically disordered proteins (IDPs) and other biomolecules are sensitive to the aqueous dielectric environment. Because the relative permittivity of protein is significantly lower than that of water, the interior of an IDP condensate is a relatively low-dielectric regime, which, aside from its possible functional effects on client molecules, should facilitate stronger electrostatic interactions among the scaffold IDPs. To gain insight into this LLPS-induced dielectric heterogeneity, addressing in particular whether a low-dielectric condensed phase entails more favorable LLPS than that posited by assuming IDP electrostatic interactions are uniformly modulated by the higher dielectric constant of the pure solvent, we consider a simplified multiple-chain model of polyampholytes immersed in explicit solvents that are either polarizable or possess a permanent dipole. Notably, simulated phase behaviors of these systems exhibit only minor to moderate differences from those obtained using implicit-solvent models with a uniform relative permittivity equals to that of pure solvent. Buttressed by theoretical treatments developed here using random phase approximation and polymer field-theoretic simulations, these observations indicate a partial compensation of effects between favorable solvent-mediated interactions among the polyampholytes in the condensed phase and favorable polyampholyte-solvent interactions in the dilute phase, often netting only a minor enhancement of overall LLPS propensity from the very dielectric heterogeneity that arises from the LLPS itself. Further ramifications of this principle are discussed.

q-bio.BM↗

arXiv2021

Subcompartmentalization of polyampholyte species in organelle-like condensates is promoted by charge pattern mismatch and strong excluded-volume interaction

Polyampholyte field theory and explicit-chain molecular dynamics models of sequence-specific phase separation of a system with two intrinsically disordered protein (IDP) species indicate consistently that a substantial polymer excluded volume and a significant mismatch of the IDP sequence charge patterns can act in concert, but not in isolation, to demix the two IDP species upon condensation. This finding reveals an energetic-geometric interplay in a stochastic, "fuzzy" molecular recognition mechanism that may facilitate subcompartmentalization of membraneless organelles.

q-bio.BM↗

arXiv2016

Rigidity of Melting DNA

The temperature dependence of DNA flexibility is studied in the presence of stretching and unzipping forces. Two classes of models are considered. In one case the origin of elasticity is entropic due to the polymeric correlations, and in the other the double-stranded DNA is taken to have an intrinsic rigidity for bending. In both cases single strands are completely flexible. The change in the elastic constant for the flexible case due to thermally generated bubbles is obtained exactly. For the case of intrinsic rigidity, the elastic constant is found to be proportional to the square root of the bubble number fluctuation.

cond-mat.soft↗

arXiv2015

Efimov like phase of a three stranded DNA (Efimov-DNA) and the renormalization group limit cycle

A three-stranded DNA with short range base pairings only is known to exhibit a classical analog of the quantum Efimov effect, viz., a three chain bound state at the two chain melting point where no two are bound. By using a non-perturbative renormalization group method for a rigid duplex DNA and a flexible third strand, with base pairings and strand exchange, we show that the Efimov-DNA is associated with a limit cycle type behavior of the flow of an effective three chain interaction. The analysis also shows that thermally generated bubbles play an essential role in producing the effect. A toy model for the flow equations shows the limit cycle in an extended three dimensional parameter space of the two-chain coupling and a complex three chain interaction.

cond-mat.soft↗

arXiv2012

Renormalization Group Limit Cycle for Three-Stranded DNA

We show that there exists an Efimov-like three strand DNA bound state at the duplex melting point and it is described by a renormalization group limit cycle. A nonperturbative RG is used to obtain this result in a model involving short range pairing only. Our results suggest that Efimov physics can be tested in polymeric systems.

cond-mat.soft↗