arXiv subjects

D. Thirumalai

Publications and source records attributed to D. Thirumalai.

At least 37 records · Page 2Linked to original sources

arXiv2023

Scaling regimes for wormlike chains confined to cylindrical surfaces under tension

We compute the free energy of confinement ${\cal{F}}$ for a wormlike chain (WLC), with persistence length $l_p$, that is confined to the surface of a cylinder of radius $R$ under an external tension $f$ using a mean field variational approach. For long chains, we analytically determine the behavior of the chain in a variety of regimes, which are demarcated by the interplay of $l_p$, the Odijk deflection length ($l_d=(R^2l_p)^{1/3}$), and the Pincus length ($l_f = {k_BT}/{f}$, with $k_BT$ being the thermal energy). The theory accurately reproduces the Odijk scaling for strongly confined chains at $f=0$, with ${\cal{F}}\sim Ll_p^{-1/3}R^{-2/3}$. For moderate values of $f$, the Odijk scaling is discernible only when ${l_p}\gg R$ for strongly confined chains. Confinement does not significantly alter the scaling of the mean extension for sufficiently high tension. The theory is used to estimate unwrapping forces for DNA from nucleosomes.

cond-mat.soft↗

arXiv2023

Watching ion-driven kinetics of ribozyme folding and misfolding caused by energetic and topological frustration one molecule at a time

Folding of ribozymes into well-defined tertiary structures usually requires divalent cations. How Mg$^{2+}$ ions direct the folding kinetics has been a long-standing unsolved problem because experiments cannot detect the positions and dynamics of ions. To address this problem, we used molecular simulations to dissect the folding kinetics of the Azoarcus ribozyme by monitoring the path each molecule takes to reach the folded state. We quantitatively establish that Mg$^{2+}$ binding to specific sites, coupled with counter-ion release of monovalent cations, stimulate the formation of secondary and tertiary structures, leading to diverse pathways that include direct rapid folding and trapping in misfolded structures. In some molecules, key tertiary structural elements form when Mg$^{2+}$ ions bind to specific RNA sites at the earliest stages of the folding, leading to specific collapse and rapid folding. In others, the formation of non-native base pairs, whose rearrangement is needed to reach the folded state, is the rate-limiting step. Escape from energetic traps, driven by thermal fluctuations, occurs readily. In contrast, the transition to the native state from long-lived topologically trapped native-like metastable states is extremely slow. Specific collapse and formation of energetically or topologically frustrated states occur early in the assembly process.

q-bio.BM↗

arXiv2023

From Effective Interactions Extracted Using Hi-C Data to Chromosome Structures in Conventional and Inverted Nuclei

Contact probabilities between loci, separated by arbitrary genomic distance, for a number of cell types have been reported using genome-wide chromosome conformation capture (Hi-C) experiments. How to extract the effective interaction energies between active euchromatin (A) and inactive heterochromatin (B) directly from the experimental data, without an underlying polymer model, is unsolved. Here, we first calculate the pairwise effective interaction energies (A-A, B-B, or A-B) for interphase chromosomes based on Hi-C data by using the concept of Statistical Potential (SP), which assumes that the interaction energy between two loci is proportional to the logarithm of the frequency with which they interact. Polymer simulations, using the extracted interaction energy values $\textit{without any parameter}$, reproduce the segregation between A and B type loci (compartments), and the emergence of topologically associating domains (TADs), features that are prominent in the Hi-C data for interphase chromosomes. Remarkably, the values of the SP automatically satisfy the Flory-Huggins phase separation criterion for all the chromosomes, which explains the mechanism of compartment formation in interphase chromosomes. Strikingly, simulations using the SP that accounts for pericentromeric constitutive heterochromatin (C-type), show hierarchical structuring with the high density of C-type loci in the nuclear center, followed by localization of the B type loci, with euchromatin being confined to the nuclear periphery, which differs from the expected nuclear organization of interphase chromosomes, but is in accord with the imaging data of the inverted nuclei found in photoreceptor rods in nocturnal mammals. The proposed parameter free method and applications show that compartment formation in conventional and inverted nuclei is best explained by the inequality between the effective interaction energies.

cond-mat.soft↗

arXiv2023

Conformational Fluctuations and Phases in Fused in Sarcoma (FUS) Low-Complexity Domain

The well known phenomenon of phase separation in synthetic polymers and proteins has become a major topic in biophysics because it has been invoked as a mechanism of compartment formation in cells, without the need for membranes. Most of the coacervates (or condensates) are composed of Intrinsically Disordered Proteins (IDPs) or regions that are structureless, often in interaction with RNA and DNA. One of the more intriguing IDPs is the 526-residue RNA binding protein, Fused In Sarcoma (FUS), whose monomer conformations and condensates exhibit unusual behavior that are sensitive to solution conditions. By focussing principally on the N-terminus low complexity domain (FUS-LC comprising residues 1-214) and other truncations, we rationalize the findings of solid state NMR experiments, which show that FUS-LC adopts a non-polymorphic fibril (core-1) involving residues 39-95, flanked by fuzzy coats on both the N- and C- terminal ends. An alternate structure (core-2), whose free energy is comparable to core-1, emerges only in the truncated construct (residues 110-214). Both core-1 and core-2 fibrils are stabilized by a Tyrosine ladder as well as hydrophilic interactions. The morphologies (gels, fibrils, and glass-like behavior) adopted by FUS seem to vary greatly, depending on the experimental conditions. The effect of phosphorylation is site specific and affects the stability of the fibril depending on the sites that are phosphorylated. Many of the peculiarities associated with FUS may also be shared by other IDPs, such as TDP43 and hnRNPA2. We outline a number of problems for which there is no clear molecular understanding.

q-bio.BM↗

arXiv2022

Topological transitions, turbulent-like motion and long-time-tails driven by cell division in biological tissues

The complex spatiotemporal flow patterns in living tissues, driven by active forces, have many of the characteristics associated with inertial turbulence even though the Reynolds number is extremely low. Analyses of experimental data from two-dimensional epithelial monolayers in combination with agent-based simulations show that cell division and apoptosis lead to directed cell motion for hours, resulting in rapid topological transitions in neighboring cells. These transitions in turn generate both long ranged and long lived clockwise and anticlockwise vortices, which gives rise to turbulent-like flows. Both experiments and simulations show that at long wavelengths the wave vector ($k$) dependent energy spectrum $E(k) \approx k^{-5/3}$, coinciding with the Kolmogorov scaling in fully developed inertial turbulence. Using theoretical arguments and simulations, we show that long-lived vortices lead to long-time tails in the velocity auto-correlation function, $C_v(t) \sim t^{-1/2}$, which has the same structure as in classical 2D fluids but with a different scaling exponent.

cond-mat.soft↗

arXiv2022

Friends in need: how chaperonins recognize and remodel proteins that require folding assistance

Chaperonins are biological nanomachines that help newly translated proteins to fold by rescuing them from kinetically trapped misfolded states. Protein folding assistance by the chaperonin machinery is obligatory in vivo for a subset of proteins in the bacterial proteome. Chaperonins are large oligomeric complexes, with unusual seven fold symmetry (group I) or eight/nine fold symmetry (group II), that form double-ring constructs, enclosing a central folding chamber. Dramatic large-scale conformational changes, that take place during ATP-driven cycles, allow chaperonins to bind misfolded proteins, encapsulate them into the expanded cavity and release them back into the cellular environment, regardless of whether they are folded or not. The theory associated with the iterative annealing mechanism, which incorporated the conformational free energy landscape description of protein folding, \textit{quantitatively} explains most, if not all, the available data. Misfolded conformations are associated with low energy minima in a rugged energy landscape. Random disruptions of these low energy conformations result in higher free energy, less folded, conformations that can stochastically partition into the native state. Group I chaperonins (GroEL homologues in eubacteria and endosymbiotic organelles), recognize a large number of misfolded proteins non-specifically and operate through highly coordinated cooperative motions. By contrast, the less well understood group II chaperonins (CCT in Eukarya and thermosome/TF55 in Archaea), assist a selected set of substrate proteins. Chaperonins are implicated in bacterial infection, autoimmune disease, as well as protein aggregation and degradation diseases. Understanding the chaperonin mechanism and their substrates is important not only for the fundamental aspect of cellular protein folding, but also for effective therapeutic strategies.

q-bio.BM↗

arXiv2022

A maximum-entropy model to predict 3D structural ensembles of chromatins from pairwise distances: Applications to Interphase Chromosomes and Structural Variants

The principles that govern the organization of genomes, which are needed for a deeper understanding of how chromosomes are packaged and function in eukaryotic cells, could be deciphered if the three-dimensional (3D) structures are known. Recently, single-cell imaging experiments have determined the 3D coordinates of a number of loci in a chromosome. Here, we introduce a computational method (Distance Matrix to Ensemble of Structures, DIMES), based on the maximum entropy principle, with experimental pair-wise distances between loci as constraints, to generate a unique ensemble of 3D chromatin structures. Using the ensemble of structures, we quantitatively account for the distribution of pair-wise distances, three-body co-localization and higher-order interactions. We demonstrate that the DIMES method can be applied to both small length-scale and chromosome-scale imaging data to quantify the extent of heterogeneity and fluctuations in the shapes on various length scales. We develop a perturbation method that is used in conjunction with DIMES to predict the changes in 3D structures from structural variations. Our method also reveals quantitative differences between the 3D structures inferred from Hi-C and the ones measured in imaging experiments. Finally, the physical interpretation of the parameters extracted from DIMES provides insights into the origin of phase separation between euchromatin and heterochromatin domains.

cond-mat.soft↗

arXiv2022

Information flow, Gating, and Energetics in dimeric molecular motors

Molecular motors belonging to the kinesin and myosin super family hydrolyze ATP by cycling through a sequence of chemical states. These cytoplasmic motors are dimers made up of two linked identical monomeric globular proteins. Fueled by the free energy generated by ATP hydrolysis, the motors walk on polar tracks (microtubule or filamentous actin) processively, which means that only one head detaches and executes a mechanical step while the other stays bound to the track. Thus, the one motor head must regulate chemical state of the other, referred to as "gating", a concept that is not fully understood. Inspired by experiments, showing that only a fraction of the energy from ATP hydrolysis is used to advance the kinesin motors against load, we demonstrate that additional energy is used for coordinating the chemical cycles of the two heads in the dimer - a feature that characterizes gating. To this end, we develop a general framework based on information theory and stochastic thermodynamics, and establish that gating could be quantified in terms of information flow between the motor heads. Applications of the theory to kinesin-1 and Myosin V show that information flow occurs, with positive cooperativity, at external resistive loads that are less than a critical value, $F_c$. When force exceeds $F_c$, effective information flow ceases. Interestingly, $F_c$, which is independent of the input energy generated through ATP hydrolysis, coincides with force at which the probability of backward steps starts to increase. Our findings suggest that transport efficiency is optimal only at forces less than $F_c$, which implies that these motors must operate at low loads under $\textit{in vivo}$ conditions.

physics.bio-ph↗

arXiv2022

Tracer particles sense local stresses in an evolving multicellular spheroid without affecting the anomalous dynamics of the cancer cells

Measurements of local stresses on the cancer cells (CCs), inferred by embedding inert compressible tracer particles (TPs) in a growing multicellular spheroid (MCS), show that pressure decreases monotonically as the distance from the core of the MCS increases. How faithfully do the TPs report the local stresses in the CCs is an important question because pressure buildup in the MCS is dynamically generated due to CC division, which implies that the CC dynamics should be minimally altered by the TPs. Here using theory and simulations, we show that although the TP dynamics is unusual, exhibiting sub-diffusive behavior on times less than the CC division times and hyper-diffusive dynamics on in the long-time limit, they do not affect the long-time CC dynamics or the local CC stress distributions. The CC pressure profile within the MCS, which decays from a high value at the core to the periphery, is almost identical with and without the TPs. That the TPs have insignificant effect on the local stresses in the MCS implies that they are reliable reporters of the CC microenvironment.

cond-mat.soft↗

arXiv2022

Mechanical feedback controls the emergence of dynamical memory in growing tissue monolayers

The growth of a tissue, which depends on cell-cell interactions and biologically relevant process such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal two-dimensional model in order to investigate the consequences of mechanical feedback, which is controlled by a critical pressure, $p_c$. A cell can only grow and divide if the pressure it experiences, due to interaction with its neighbors, is less than $p_c$. Because temperature is an irrelevant variable in the model, the cell dynamics is driven by self-generated active forces (SGAFs) that are created by cell division. It is shown that even in the absence of intercellular interactions, cells undergo diffusive behavior. The SGAF driven diffusion is indistinguishable from the well-known dynamics of a free Brownian particle at a fixed finite temperature. When intercellular interactions are taken into account, we find persistent temporal correlations in the force-force autocorrelation function ($FAF$) that extends over timescale of several cell division times. The time-dependence of the $FAF$ reveals memory effects, which increases as pc increases. The observed non-Markovian effects emerge due to the interplay of cell division and mechanical feedback, and is inherently a non-equilibrium phenomenon.

cond-mat.soft↗

arXiv2021

A mathematical model for phenotypic heterogeneity in breast cancer with implications for therapeutic strategies

Inevitably, almost all cancer patients develop resistance to targeted therapy. Intratumor heterogeneity (ITH) is a major cause of drug resistance. Mathematical models that explain experiments quantitatively is useful in understanding the origin of ITH, which then could be used to explore scenarios for efficacious therapy. Here, we develop a mathematical model to investigate ITH in breast cancer by exploiting the observation that HER2+ and HER2- cells could divide symmetrically or asymmetrically. Our predictions for the evolution of cell fractions are in quantitative agreement with single-cell experiments. Remarkably, the colony size of HER2+ cells emerging from a single HER2- cell (or vice versa), which occurs in about four cell doublings, agrees perfectly with experimental results, without tweaking any parameter in the model. The theory quantitatively explains experimental data on the responses of breast cancer tumor under different treatment protocols. We then used the model to predict that, not only the order of two drugs, but also the treatment period for each drug and the tumor cell plasticity could be manipulated to improve the treatment efficacy. Mathematical models, when integrated with data on patients, make possible exploration of a broad range of parameters readily, which might provide insights in devising effective therapies.

cond-mat.soft↗

arXiv2021

On the emergence of orientational order in folded proteins with implications for allostery

The beautiful structures of single and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein structures are considered to be aperiodic, and may have evolved this way for functional purposes, especially in instances that require a combination of softness and rigidity within the same molecule. By analyzing the solved protein structures, we show that orientational symmetry is broken in the aperiodic arrangement of the secondary structural elements (SSEs), which we deduce by calculating the nematic order parameter, $P_{2}$. We find that the folded structures are nematic droplets with a broad distribution of $P_{2}$. We argue that non-zero values of $P_{2}$, leads to an arrangement of the SSEs that can resist mechanical forces, which is a requirement for allosteric proteins. Such proteins, which resist mechanical forces in some regions while being flexible in others, transmit signals from one region of the protein to another (action at a distance) in response to binding of ligands (oxygen, ATP or other small molecules).

cond-mat.soft↗

arXiv2021

From Hi-C Contact Map to Three-dimensional Organization of Interphase Human Chromosomes

The probability of two loci, separated by a certain genome length, being in contact can be inferred using the Chromosome Conformation Capture (3C) method and related Hi-C experiments. How to go from the contact map, a matrix listing the mean contact probabilities between a large number of pairs of loci, to an ensemble of three-dimensional structures is an open problem. A solution to this problem, without assuming an assumed energy function, would be the first step in understanding the way nature has solved the packaging of chromosomes in tight cellular spaces. We created a theory, based on polymer physics characteristics of chromosomes and the maximum entropy principles, referred to as HIPPS (Hi-C-Polymer-Physics-Structures) method, that allows us to calculate the 3D structures solely from Hi-C contact maps. We created an ensemble of 3D structures for the 23 chromosomes from lymphoblastoid cells using the measured contact maps as inputs. The HIPPS method shows that conformations of chromosomes are heterogeneous even in a single cell type. The differences in the conformational heterogeneity of the same chromosome in different cell types (normal as well as cancerous cells) can also be quantitatively discerned using our theory. We validate the method by showing that the calculated volumes of the 23 chromosomes from the predicted 3D structures are in good agreement with experimental estimates. Because the method is general, the 3D structures for any species may be calculated directly from the contact map without the need to assume a specific polymer model, as is customarily done.

cond-mat.soft↗

arXiv2020

Theory and simulations for crowding-induced changes in stability of proteins with applications to $λ$ repressor

Experiments and theories have shown that when steric interactions between crowding particles and proteins are dominant, which give rise to Asakura-Oosawa depletion forces, then the stabilities of the proteins increase compared to the infinite dilution case. We show using theoretical arguments that the crowder volume fraction ($Φ_C$) dependent increase in the melting temperature of globular proteins, $ΔT_m(Φ_C) \approx Φ_C^α$ where $α= \frac{1}{(3 ν_{eff} - 1)}$. The effective Flory exponent, $ν_{eff}$, relates the radius of gyration in the unfolded state to the number of amino acid residues in the protein. We derive the bound 1.25 $\le α\le$ 2.0. The theoretical predictions are confirmed using molecular simulations of $λ$ repressor in the presence of spherical crowding particles. Analyses of previous simulations and experiments confirm the predicted theoretical bound for $α$. We show that the non-specific attractions between crowding particles and amino acid residues have to be substantial to fully negate the enhanced protein stabilities due to intra protein attractive Asakura-Oosawa (AO) depletion potential. Using the findings, we provide an alternate explanation for the very modest (often less than 0.5 Kcal/mol) destabilization in certain proteins in the cellular milieu. Cellular environment is polydisperse containing large and small crowding agents. AO arguments suggest that proteins would be localized between large (sizes exceeding that of the proteins) crowders, which are predicted to have negligible effect on stability. {\it In vitro} experiments containing mixtures of crowding particles could validate or invalidate the predictions.

cond-mat.soft↗

arXiv2020

Low force unfolding of a single-domain protein by parallel pathways

Deviations from linearity in the dependence of the logarithm of protein unfolding rates, $\log k_u(f)$, as a function of mechanical force, $f$, measurable in single molecule experiments, can arise for many reasons. In particular, upward curvature in $\log k_u(f)$ as a function of $f$ implies that the underlying energy landscape must be multidimensional with the possibility that unfolding ensues by parallel pathways. Here, simulations using the SOP-SC model of a wild type $β$-sandwich protein and several mutants, with immunoglobulin folds, show upward curvature in the unfolding kinetics. There are substantial changes in the structures of the transition state ensembles as force is increased, signaling a switch in the unfolding pathways. Our results, when combined with previous theoretical and experimental studies, show that parallel unfolding of structurally unrelated single domain proteins can be determined from the dependence of $\log k_u(f)$ as a function of force (or $\log k_u[C]$ where $[C]$ is the denaturant concentration).

cond-mat.soft↗

arXiv2020

Far from equilibrium dynamics of tracer particles embedded in a growing multicellular spheroid

By embedding inert tracer particles (TPs) in a growing multicellular spheroid the local stresses on the cancer cells (CCs) can be measured. In order for this technique to be effective the unknown effect of the dynamics of the TPs on the CCs has to be elucidated to ensure that the TPs do not greatly alter the local stresses on the CCs. We show, using theory and simulations, that the self-generated (active) forces arising from proliferation and apoptosis of the CCs drive the dynamics of the TPs far from equilibrium. On time scales less than the division times of the CCs, the TPs exhibit sub-diffusive dynamics (the mean square displacement, $Δ_{TP}(t) \sim t^{β_{TP}}$ with $β_{TP}<1$), similar to glass-forming systems. Surprisingly, in the long-time limit, the motion of the TPs is hyper-diffusive ($Δ_{TP}(t) \sim t^{α_{TP}}$ with $α_{TP}>2$) due to persistent directed motion for long times. In comparison, proliferation of the CCs randomizes their motion leading to superdiffusive behavior with $α_{CC}$ exceeding unity. Most importantly, $α_{CC}$ is not significantly affected by the TPs. Our predictions could be tested using \textit{in vitro} imaging methods where the motion of the TPs and the CCs can be tracked.

physics.bio-ph↗

arXiv2020

RFOT theory for glassy dynamics in a single condensed polymer

The number of compact structures of a single condensed polymer (SCP), with similar free energies, grows exponentially with the degree of polymerization. In analogy with structural glasses (SGs), we expect that at low temperatures chain relaxation should occur by activated transitions between the compact metastable states. By evolving the states of the SCP that is linearly coupled to a reference state, we show that, below a dynamical transition temperature ($T_d$), the SCP is trapped in a metastable state leading to slow dynamics. At a lower temperature, $T_K \ne 0$, the configurational entropy vanishes, resulting in a thermodynamic random first order ideal glass transition. The relaxation time obeys the Vogel-Fulcher-Tamman law, diverging at $T=T_0 \approx T_K$. These findings, accord well with the random first order transition theory, establishing that SCP and SG exhibit similar universal characteristics.

cond-mat.soft↗

arXiv2020

Self-generated persistent random forces drive phase separation in growing tumors

A single solid tumor, composed of nearly identical cells, exhibits heterogeneous dynamics. Cells dynamics in the core is glass-like whereas those in the periphery undergo diffusive or super-diffusive behavior. Quantification of heterogeneity using the mean square displacement or the self-intermediate scattering function, which involves averaging over the cell population, hides the complexity of the collective movement. Using the t-distributed stochastic neighbor embedding (t-SNE), a popular unsupervised machine learning dimensionality reduction technique, we show that the phase space structure of an evolving colony of cells, driven by cell division and apoptosis, partitions into nearly disjoint sets composed principally of core and periphery cells. The non-equilibrium phase separation is driven by the differences in the persistence of self-generated active forces induced by cell division. Extensive heterogeneity revealed by t-SNE paves way towards understanding the origins of intratumor heterogeneity using experimental imaging data.

physics.bio-ph↗