arXiv subjects

Suman Das

Publications and source records attributed to Suman Das.

At least 37 records · Page 2Linked to original sources

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 $π$-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↗

arXiv2024

Gabriel's problem for harmonic Hardy spaces

We obtain inequalities of the form $$\int_C |f(z)|^p |dz| \leq A(p) \int_{\mathbb{T}} |f(z)|^p |dz|, \quad (p>1)$$ where $f$ is harmonic in the unit disk $\mathbb{D}$, $\mathbb{T}$ is the unit circle, and $C$ is any convex curve in $\mathbb{D}$. Such inequalities were originally studied for analytic functions by R. M. Gabriel [Proc. London Math. Soc. 28(2), 1928]. We show that these results, unlike in the case of analytic functions, cannot be true in general for $0< p \le 1$. Therefore, we produce an inequality of a slightly different type, which deals with the case $0<p<1$. An example is given to show that this result is "best possible", in the sense that an extension to $p=1$ fails. Then we consider the special case when $C$ is a circle, and prove a refined result which surprisingly holds for $p=1$ as well. We conclude with a maximal theorem which has potential applications.

math.CV↗

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.

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arXiv2024

Effect of Leaders Voice on Financial Market: An Empirical Deep Learning Expedition on NASDAQ, NSE, and Beyond

Financial market like the price of stock, share, gold, oil, mutual funds are affected by the news and posts on social media. In this work deep learning based models are proposed to predict the trend of financial market based on NLP analysis of the twitter handles of leaders of different fields. There are many models available to predict financial market based on only the historical data of the financial component but combining historical data with news and posts of the social media like Twitter is the main objective of the present work. Substantial improvement is shown in the result. The main features of the present work are: a) proposing completely generalized algorithm which is able to generate models for any twitter handle and any financial component, b) predicting the time window for a tweets effect on a stock price c) analyzing the effect of multiple twitter handles for predicting the trend. A detailed survey is done to find out the latest work in recent years in the similar field, find the research gap, and collect the required data for analysis and prediction. State-of-the-art algorithm is proposed and complete implementation with environment is given. An insightful trend of the result improvement considering the NLP analysis of twitter data on financial market components is shown. The Indian and USA financial markets are explored in the present work where as other markets can be taken in future. The socio-economic impact of the present work is discussed in conclusion.

cs.CE↗

arXiv2024

Brickwall, Normal Modes and Emerging Thermality

In this article, we demonstrate how black hole quasi-normal modes can emerge from a Dirichlet brickwall model normal modes. We consider a probe scalar field in a BTZ geometry with a Dirichlet brickwall and demonstrate that as the wall approaches the event horizon, the corresponding poles in the retarded correlator become dense and yield an effective branch-cut. The associated discontinuity of the correlator carries the information of the black hole quasi-normal modes. We further demonstrate that a non-vanishing angular momentum non-perturbatively enhances the pole-condensing. We hypothesize that it is also related to quantum chaotic features of the corresponding spectral form factor, which has been observed earlier. Finally, we discuss the underlying algebraic justification of this approximate thermalization in terms of the trace of the algebra.

hep-th↗

arXiv2024

What is the Simplest Linear Ramp?

We discuss conditions under which a deterministic sequence of real numbers, interpreted as the set of eigenvalues of a Hamiltonian, can exhibit features usually associated to random matrix spectra. A key diagnostic is the spectral form factor (SFF) -- a linear ramp in the SFF is often viewed as a signature of random matrix behavior. Based on various explicit examples, we observe conditions for linear and power law ramps to arise in deterministic spectra. We note that a very simple spectrum with a linear ramp is $E_n \sim \log n$. Despite the presence of ramps, these sequences do $not$ exhibit conventional level repulsion, demonstrating that the lore about their concurrence needs refinement. However, when a small noise correction is added to the spectrum, they lead to clear level repulsion as well as the (linear) ramp. We note some remarkable features of logarithmic spectra, apart from their linear ramps: they are closely related to normal modes of black hole stretched horizons, and their partition function with argument $s=β+it$ is the Riemann zeta function $ζ(s)$. An immediate consequence is that the spectral form factor is simply $\sim |ζ(it)|^2$. Our observation that log spectra have a linear ramp, is closely related to the Lindelöf hypothesis on the growth of the zeta function. With elementary numerics, we check that the slope of a best fit line through $|ζ(it)|^2$ on a log-log plot is indeed $1$, to the fourth decimal. We also note that truncating the Riemann zeta function sum at a finite integer $N$ causes the would-be-eternal ramp to end on a plateau.

hep-th↗

arXiv2024

Entanglement from holography for five-dimensional charged Schrödinger black hole

We study entanglement entropy in a non-relativistic Schrödinger field theory at finite temperature and electric charge using the principle of gauge/gravity duality. The spacetime geometry is obtained from a charged AdS black hole by a null Melvin twist. By using an appropriate modification of the holographic Ryu-Takayanagi formula, we calculate the entanglement entropy, mutual information, and entanglement wedge cross-section for the simplest strip subsystem. The entanglement measures show non-trivial dependence on the black hole parameters.

hep-th↗

arXiv2023

Brickwall in Rotating BTZ: A Dip-Ramp-Plateau Story

In this article, building on our recent investigations and motivated by the fuzzball-paradigm, we explore normal modes of a probe massless scalar field in the rotating BTZ-geometry in an asymptotically AdS spacetime and correspondingly obtain the Spectral Form Factor (SFF) of the scalar field. In particular, we analyze the SFF obtained from the single-particle partition function. We observe that, a non-trivial Dip-Ramp-Plateau structure, with a Ramp of slope one (within numerical precision) exists in the SFF which is obtained from the grand-canonical partition function. This behaviour is observed to remain stable close to extremality as well. However, at exact extremality, we observe a loss of the DRP-structure in the corresponding SFF. Technically, we have used two methods to obtain our results: (i) An explicit and direct numerical solution of the boundary conditions to obtain the normal modes, (ii) A WKB-approximation, which yields analytic, semi-analytic and efficient numerical solutions for the modes in various regimes. We further re-visit the non-rotating case and elucidate the effectiveness of the WKB-approximation in this case, which allows for an analytic expression of the normal modes in the regime where a level-repulsion exists. This regime corresponds to the lower end of the spectrum as a function of the scalar angular momentum. By analyzing the classical stress-tensor of the probe sector, we further demonstrate that the back-reaction of the scalar field grows fast as the angular momenta of the scalar modes increase in the large angular momenta regime, while the back-reaction remains controllably small in the regime where the spectrum has non-trivial level correlations. This further justifies cutting the spectrum off at a suitable value of the scalar angular momenta, beyond which the scalar back-reaction significantly modifies the background geometry.

hep-th↗

arXiv2023

Fuzzballs and Random Matrices

Black holes are believed to have the fast scrambling properties of random matrices. If the fuzzball proposal is to be a viable model for quantum black holes, it should reproduce this expectation. This is considered challenging, because it is natural for the modes on a fuzzball microstate to follow Poisson statistics. In a previous paper, we noted a potential loophole here, thanks to the modes depending not just on the $n$-quantum number, but also on the $J$-quantum numbers of the compact dimensions. For a free scalar field $ϕ$, by imposing a Dirichlet boundary condition $ϕ=0$ at the stretched horizon, we showed that this $J$-dependence leads to a linear ramp in the Spectral Form Factor (SFF). Despite this, the status of level repulsion remained mysterious. In this letter, motivated by the profile functions of BPS fuzzballs, we consider a generic profile $ϕ= ϕ_0(θ)$ instead of $ϕ=0$ at the stretched horizon. For various notions of genericity (eg. when the Fourier coefficients of $ϕ_0(θ)$ are suitably Gaussian distributed), we find that the $J$-dependence of the spectrum exhibits striking evidence of level repulsion, along with the linear ramp. We also find that varying the profile leads to natural interpolations between Poisson and Wigner-Dyson(WD)-like spectra. The linear ramp in our previous work can be understood as arising via an extreme version of level repulsion in such a limiting spectrum. We also explain how the stretched horizon/fuzzball is different in these aspects from simply putting a cut-off in flat space or AdS (ie., without a horizon).

hep-th↗

arXiv2023

Synthetic Fuzzballs: A Linear Ramp from Black Hole Normal Modes

We consider a black hole with a stretched horizon as a toy model for a fuzzball microstate. The stretched horizon provides a cut-off, and therefore one can determine the normal (as opposed to quasi-normal) modes of a probe scalar in this geometry. For the BTZ black hole, we compute these as a function of the level $n$ and the angular quantum number $J$. Conventional level repulsion is absent in this system, and yet we find that the Spectral Form Factor (SFF) shows clear evidence for a dip-ramp-plateau structure with a linear ramp of slope $\sim 1$ on a log-log plot, with or without ensemble averaging. We show that this is a robust feature of stretched horizons by repeating our calculations on the Rindler wedge (times a compact space). We also observe that this is {\em not} a generic feature of integrable systems, as illustrated by standard examples like integrable billiards and random 2-site coupled SYK model, among others. The origins of the ramp can be traced to the hierarchically weaker dependence of the normal mode spectrum on the quantum numbers of the compact directions, and the resulting quasi-degeneracy. We conclude by noting an analogy between the 4-site coupled SYK model and the quartic coupling responsible for the non-linear instability of capped geometries. Based on this, we speculate that incorporating probe self-interactions will lead to stronger connections to random matrix behavior.

hep-th↗

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

RG Flows and Thermofield-Double States in Holography

In this article, we consider a Renormalization Group flow of the Thermofield-Double state in a UV-complete description of Holography, by introducing a relevant deformation to the ${\cal N}=4$ super Yang-Mills theory at strong coupling. This RG-flow is known to have a non-trivial, interacting ${\cal N}=1$ fixed point at the IR. Geometrically, an RG-flow of the TFD-state naturally continues radially and inside the black hole event horizon and yields a Kasner-structure near singularity, as has been observed in recent works. We show that for a generic value of the deformation, the putative IR fixed point remains inside the black hole. By fine-tuning this deformation, the "fixed point" can be brought arbitrarily close to the event horizon, while always remaining inside. Physically, this distinguishes between the vanishing temperature limit of the RG-flows with the one at exactly zero temperature. We further discuss its general implications in the context of Holography. We also discuss how correlations between the two-copies of the TFD-state depend on this explicit RG-flow.

hep-th↗

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.

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arXiv2020

Comparative Roles of Charge, $π$ and Hydrophobic Interactions in Sequence-Dependent Phase Separation of Intrinsically Disordered Proteins

Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS), we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess the roles of electrostatic, hydrophobic, cation-$π$, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated 3 residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation-$π$ interactions consistently accounted for the experimental LLPS data on the wildtype, a charge-scrambled, an FtoA, and an RtoK mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and LLPS experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, the important LLPS-driving $π$-related interactions are embodied in classical statistical potentials. Further elucidation will be necessary, however, especially of phenylalanine's role in condensate assembly because experiments on FtoA and YtoF mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than those posited by common statistical potentials. Protein-protein electrostatic interactions are modulated by relative permittivity, which depends on protein concentration. Analytical theory suggests that this dependence entails enhanced inter-protein interactions in the condensed phase but more favorable protein-solvent interactions in the dilute phase. The opposing trends lead to a modest overall impact on LLPS.

q-bio.BM↗

arXiv2020

Analytical Theory for Sequence-Specific Binary Fuzzy Complexes of Charged Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are important for biological functions. In contrast to folded proteins, molecular recognition among certain IDPs is "fuzzy" in that their binding and/or phase separation are stochastically governed by the interacting IDPs' amino acid sequences while their assembled conformations remain largely disordered. To help elucidate a basic aspect of this fascinating yet poorly understood phenomenon, the binding of a homo- or hetero-dimeric pair of polyampholytic IDPs is modeled statistical mechanically using cluster expansion. We find that the binding affinities of binary fuzzy complexes in the model correlate strongly with a newly derived simple "jSCD" parameter readily calculable from the pair of IDPs' sequence charge patterns. Predictions by our analytical theory are in essential agreement with coarse-grained explicit-chain simulations. This computationally efficient theoretical framework is expected to be broadly applicable to rationalizing and predicting sequence-specific IDP-IDP polyelectrostatic interactions.

q-bio.BM↗

arXiv2018

Coarse-Grained Residue-Based Models of Disordered Protein Condensates: Utility and Limitations of Simple Charge Pattern Parameters

Biomolecular condensates undergirded by phase separations of proteins and nucleic acids serve crucial biological functions. To gain physical insights into their genetic basis, we study how liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) depends on their sequence charge patterns using a continuum Langevin chain model wherein each amino acid residue is represented by a single bead. Charge patterns are characterized by the `blockiness' measure $κ$ and the `sequence charge decoration' (SCD) parameter. Consistent with random phase approximation (RPA) theory and lattice simulations, LLPS propensity as characterized by critical temperature $T^*_{\rm cr}$ increases with increasingly negative SCD for a set of sequences showing a positive correlation between $κ$ and $-$SCD. Relative to RPA, the simulated sequence-dependent variation in $T^*_{\rm cr}$ is often---though not always---smaller, whereas the simulated critical volume fractions are higher. However, for a set of sequences exhibiting an anti-correlation between $κ$ and $-$SCD, the simulated $T^*_{\rm cr}$'s are quite insensitive to either parameters. Additionally, we find that blocky sequences that allow for strong electrostatic repulsion can lead to coexistence curves with upward concavity as stipulated by RPA, but the LLPS propensity of a strictly alternating charge sequence was likely overestimated by RPA and lattice models because interchain stabilization of this sequence requires spatial alignments that are difficult to achieve in real space. These results help delineate the utility and limitations of the charge pattern parameters and of RPA, pointing to further efforts necessary for rationalizing the newly observed subtleties.

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