arXiv subjects

D. Thirumalai

Publications and source records attributed to D. Thirumalai.

At least 19 recordsLinked to original sources

arXiv2026

Persistence length of short homopolymeric single-stranded DNA sequences in polyvalent cations

We used simulations of short single stranded DNA (ssDNA) homopolymers, based on the sequence dependent Three Interaction Site (TIS) model, to calculate the persistence length ($l_p$) in polyvalent cations. The TIS model accounts for stacking interactions and electrostatic interactions are treated using the Coulomb potential. We find that $l_p$ for $\mathrm{dT_{30}}$ (T is thymine) and $\mathrm{dA_{30}}$ (A is adenine) is quantitatively fit using $l_p = l_p^0 + λκ^{-1}$ ($l_p^0$ is the bare persistence length, $λ$ is a dimensionless constant, and $κ$ is the inverse Debye length) in the divalent cations $\mathrm{Mg^{2+}}$ and $\mathrm{Ca^{2+}}$. The dependence of $l_p$ on $κ$ is surprising because it was derived for long flexible polyelectrolytes in which the charges interact via the Debye-Hückel potential. The $l_p^0$ values are 0.4 nm and 1.1 nm for polyT and polyA, respectively. Strikingly, $l_p$ is almost independent of the tetravalent spermine concentration. There is no clear theoretical explanation although simulations suggest that the number of spermine molecules that bind to the ssDNA saturates at a small value. A qualitative picture, based on the restrictions of access to the phosphate groups due to volume exclusion of the anisotropic structure of $\mathrm{Spm^{4+}}$, rationalizes the simulation results. The predicted dependence of $l_p$ in spermine awaits experimental test.

cond-mat.soft↗

arXiv2026

Shear effects in active models of normal and cancer cells

Mechanical properties of biological tissues, driven by passive and active forces, play a vital role in several processes ranging from development to cancer metastasis. However, the dynamical responses of cells in tissues, subject to mechanical deformations such as shear and the associated rheological properties, are not well characterized. Here, we use three-dimensional agent-based models for normal and cancer tissues to investigate their responses to simple shear as a function of cell stiffness and stochastic active forces. In the normal epithelium, with uniform strength of active force, the yield stress as a function of shear rate follows the Herschel-Bulkley form over a range of cell volume fraction. Strikingly, the shear rate dependence and the elasticity-dependent changes in the yield stress fall on master curves upon suitable scaling. To model cancer-like behavior, a certain fraction ($N_p$) of cells was chosen to have enhanced activity and decreased stiffness. As $N_p$ increases, the extent of collective cell movement decreases, transitioning from affine (collective) to non-affine (individualistic) movement, a finding that is in accord with imaging experiments. Simulations of a model of a stiff solid tumor, with radius $R_s$ embedded in normal tissue, show that as $R_s$ increases, the yield stress increases. Interestingly, the cells migrate collectively as $R_s$ increases. A Gaussian Mixture Model (GMM) and a mean field theory quantitatively account for the simulation as well as experimental results on cancerous, non-cancerous, and a mixture of these two types. The combined theoretical and experimental study establishes that heterogeneity in stiffness and activity determines non-affine movements in normal and cancer tissues.

cond-mat.soft↗

arXiv2026

Loop Extrusion Reversal by Condensin Motor is Mediated by Catch Bonds

Structural Maintenance Complexes (SMC) are energy consuming motors that are important in folding the genome by loop extrusion (LE) in all stages of the cell cycle. Single molecule magnetic tweezer pulling experiments have revealed that condensin, a member of the SMC family involved in mitosis, takes occasional backward steps, thus coughing up the gains in the length of the extruded loop. To reveal the mechanism of the forward and backward steps simultaneously, we developed a theory using the stochastic kinetic model and the scrunching mechanism for LE. The calculations quantitatively account for the measured force-dependent step size and dwell time distributions in both the directions. By postulating the existence of an intermediate state in the ATP-driven cycle that is poised to take a forward or a backward step, we predict that its lifetime increases as the external mechanical force increases till a critical value and subsequently decreases at higher forces. The surprising finding of lifetime increase in an active motor, at sub-piconewton forces, is the characteristic of catch bonds, known in force-induced rupture of several passive protein complexes. The identification of catch bond-like states in condensin not only expands our understanding of LE but also highlights the significance of mechanical forces in regulating genome organization.

cond-mat.soft↗

arXiv2025

Epigenetic state encodes locus-specific chromatin mechanics

Chromatin is repeatedly deformed in vivo during transcription, nuclear remodeling, and confined migration - yet how mechanical response varies from locus to locus, and how it relates to epigenetic state, remains unclear. We develop a theory to infer locus-specific viscoelasticity from three-dimensional genome organization. Using chromatin structures derived from contact maps, we calculate frequency-dependent storage and loss moduli for individual loci and establish that the mechanical properties are determined both by chromatin epigenetic marks and organization. On large length scales, chromatin exhibits Rouse-like viscoelastic scaling, but this coarse behavior masks extensive heterogeneity at the single-locus level. Loci segregate into two mechanical subpopulations with distinct longest relaxation times: one characterized by single-timescale and another by multi-timescale relaxation. The multi-timescale loci are strongly enriched in active marks, and the longest relaxation time for individual loci correlates inversely with effective local stiffness. Pull-release simulations further predict a time-dependent susceptibility: H3K27ac-rich loci deform more under sustained forcing yet can resist brief, large impulses. At finer genomic scales, promoters, enhancers, and gene bodies emerge as "viscoelastic islands" aligned with their focal interactions. Together, these results suggest that chromatin viscoelasticity is an organized, epigenetically coupled property of the 3D genome, providing a mechanistic layer that may influence enhancer-promoter communication, condensate-mediated organization, and response to cellular mechanical stress. The prediction that locus-specific mechanics in chromatin are controlled by 3D structures as well as the epigenetic states is amenable to experimental test.

cond-mat.soft↗

arXiv2025

Rotational migration in human pancreatic ductal organoids depends on actin and myosin activity

Rotational migration is one specific form of collective cell migration when epithelial cells are confined in a spherical geometry, such as in the epithelial acini. This tissue-level rotation motion is crucial for the morphogenesis of multiple epithelial systems. Here, we introduce a new primary human model for the study of rotational migration, pancreatic ductal organoids. Live imaging revealed the persistent rotation of the organoids over time. By tracking the nuclei, the three-dimensional trajectory of the cellular movement was reconstructed and the velocity of the rotation was quantified. The presence of focal adhesion clusters and prominent actin stress fibers were observed at the basal side of the organoids, suggesting the interactions between the cells and the surrounding extracellular matrix. Finally, our inhibition study showed the dependence of pancreatic ductal organoid rotational migration on myosin activity, actin polymerization, and actin branching. We hope that this model will enable future studies with human primary cells, which are more faithful to normal epithelial cells.

cond-mat.soft↗

arXiv2025

Droplet growth, Ostwald's rule, and emergence of order in Fused in Sarcoma

The low complexity domain of Fused in Sarcoma (FUS-LC consisting of 214 residues) undergoes phase separation, resulting in a dense liquid-like phase that forms early and slowly matures to reach ordered gel-like state on long time scales. Upon maturation, core-1, comprising of the 57 residues (39-95) in the N-terminus become structured, resulting in the formation of a non-polymorphic fibril. The truncated FUS-LC-C (residues 110-214) construct forms a fibril in which core-2 (residues 112-150) adopts a $β$-sheet structure. Using coarse-grained monomer SOP-IDP model simulations of FUS-LC, we predict that residues 155-190 in the C-terminal (core-3) form rapidly, followed by core-2, and finally core-1. The time scale of formation of the cores and their stabilities are inversely correlated, as anticipated by the Ostwald's rule of stages. Unbiased multichain simulations show that the chemical potentials in the two phases are equal and the calculated densities of the dense and dilute phases are in agreement with experiments. The dense phase, which forms by a nucleation mechanism, coarsens over time by a process that is reminiscent of Ostwald ripening. AlphaFold predictions of the core-3 structure and the simulations show that $β$-strand emerges in the core-3 region early during the droplet formation, and drives the initiation of FUS-LC assembly. The techniques introduced here are general and could be used to probe assembly of other IDPs such as TDP-43, which shares many features with FUS-LC.

cond-mat.soft↗

arXiv2025

Static Three-Dimensional Structures Determine Fast Dynamics Between Distal Loci Pairs in Interphase Chromosomes

Live-cell imaging experiments have shown that the distal dynamics between enhancers and promoters are unexpectedly rapid and incompatible with standard polymer models. The discordance between the compact static chromatin organization and dynamics is a conundrum that violates the expected structure-function relationship. We developed a theory to predict chromatin dynamics by accurately determining three-dimensional (3D) structures from static Hi-C contact maps or fixed-cell imaging data. Using the calculated 3D coordinates, the theory accurately forecasts experimentally observed two-point chromatin dynamics. It predicts rapid enhancer-promoter interactions and uncovers a scaling relationship between two-point relaxation time and genomic separation, closely matching recent measurements. The theory predicts that cohesin depletion accelerates single-locus diffusion while significantly slowing relaxation dynamics within topologically associating domains (TADs). Our results demonstrate that chromatin dynamics can be reliably inferred from static structural data, reinforcing the notion that 3D chromatin structure governs dynamic behavior. This general framework offers powerful tools for exploring chromatin dynamics across diverse biological contexts.

physics.bio-ph↗

arXiv2025

Iterative Annealing Mechanism for Protein and RNA Chaperones

Molecular chaperones are machines that consume copious amount of ATP to drive misfolded proteins or RNA to fold into functionally competent native states. Because the folding landscapes of biomolecules with complex native state topology are rugged consisting of multiple minima that are separated by large free energy barriers, folding occurs by the kinetic partitioning mechanism according to which only a small fraction of the molecules reach the folded state in biologically viable times. The rescue of such proteins and RNA require chaperones. Although the protein and RNA chaperones are profoundly different in their structure and action, the principles underlying their activity to produce the folded structures can be understood using a unified theoretical framework based on iterative annealing mechanism (IAM). Our theory shows that both these machines have evolved to the maximize the production of the steady state yield on biological times. Strikingly, theory predicts that only at a moderate level of RNA chaperone activity is the yield of the self-splicing pre-RNA is maximized in \textit{in vivo}.

physics.bio-ph↗

arXiv2025

Emergence of cellular nematic order is a conserved feature of gastrulation in animal embryos

Cells undergo dramatic morphological changes during embryogenesis, yet how these changes affect the formation of ordered tissues remains elusive. Here, we show that a phase transition leading to the formation of a nematic liquid crystal state during gastrulation in the development of embryos of fish, frogs, and fruit flies occurs by a common mechanism despite substantial differences between these evolutionarily distant animals. Importantly, nematic order forms early before any discernible changes in the shapes of cells. All three species exhibit similar propagation of the nematic phase, reminiscent of nucleation and growth mechanisms. The spatial correlations in the nematic phase in the notochord region are long-ranged and follow a similar power-law decay (y~$x^{-α}$ ) with $α$ less than unity, indicating a common underlying physical mechanism. To explain the common physical mechanism, we created a theoretical model that not only explains the experimental observations but also predicts that the nematic phase should be disrupted upon loss of planar cell polarity (frog), cell adhesion (frog), and notochord boundary formation (zebrafish). Gene knockdown or mutational studies confirm the theoretical predictions. The combination of experiments and theory provides a unified framework for understanding the potentially universal features of metazoan embryogenesis, in the process shedding light on the advent of ordered structures during animal development.

cond-mat.soft↗

arXiv2025

Minimal Models for RNA Simulations

The increasing importance of RNA as a prime player in biology can hardly be overstated. Problems in RNA, such as folding and RNA-RNA interactions that drive phase separation, require cations. Because experiments alone cannot reveal the dynamics of cation-RNA interactions, well calibrated theory and computations are needed to predict how ions control the behavior of RNA. The perspective describes the development and use of coarse-grained models at different resolutions. We focus on single- and three-interaction site interaction models, in which electrostatic interactions are treated using a combination of explicit and implicit representations. Applications to the folding of ribozymes and riboswitches are discussed, with emphasis on the role of monovalent and divalent cations. We also discuss phase separation in low complexity sequences. Challenges in the simulation of complex problems such as ribosome assembly and RNA chaperones, requiring developments of models for RNA-protein interactions, are pointed out.

q-bio.BM↗

arXiv2025

Controlling the morphologies and dynamics in three-dimensional tissues

A number of factors, such as, cell-cell interactions and self-propulsion of cells driven by cytoskeletal forces determine tissue morphologies and dynamics. To explore the interplay between these factors in controlling the dynamics at the tissue scale, we created a minimal three dimensional model in which short-range repulsive elastic forces account for cell-cell interactions. Self-propulsion is modeled as active uncorrelated random stochastic forces, with strength $μ$, that act on individual cells and is the only source of cell motility. Strikingly, variations in polydispersity in cell sizes ($Σ$) and cell elasticity ($E$), results in the formation of a variety of distinct ``phases", driven entirely by $μ$. At low $E$, the tissue behaves like a liquid, at all values of $Σ$, whereas at high $E$ and $Σ$, it has the characteristics of a glass. The tissue crystallizes at low $Σ$ provided $E$ exceeds a critical value. Over a narrow range of $E$ and $Σ$, that lies between the boundaries of the liquid and glass phase, the effective viscosity increases like in a glass as the cell density increases and saturates as the cells are compressed beyond a certain value, creating the viscosity saturation (VS) phase. The VS phase does not form in systems at finite temperature in which the dynamics satisfies the Fluctuation Dissipation Theorem. In the glass phase, the tissue exhibits aging (relaxation times depend on the waiting time) behavior at high $E$ values. Our findings provide a framework for designing tissues with tunable material properties by controlling the physical characteristics of cells.

cond-mat.soft↗

arXiv2024

Collective dynamic length increases monotonically in pinned and unpinned glass forming systems

The Random First Order Transition Theory (RFOT) predicts that transport proceeds by cooperative movement of particles in domains whose sizes increase as a liquid is compressed above a characteristic volume fraction, $ϕ_d$. The rounded dynamical transition around $ϕ_d$, which signals a crossover to activated transport, is accompanied by a growing correlation length that is predicted to diverge at the thermodynamic glass transition density ($> ϕ_d$). Simulations and imaging experiments probed the single particle dynamics of mobile particles in response to pinning all the particles in a semi-infinite space or randomly pinning (RP) a fraction of particles in a liquid at equilibrium. The extracted dynamic length increases non-monotonically with a peak around $ϕ_d$, which not only depends on the pinning method but is different from $ϕ_d$ of the actual liquid. This finding is at variance with the results obtained using the small wave length limit of a four-point structure factor for unpinned systems. To obtain a consistent picture of the growth of the dynamic length, one that is impervious to the use of RP, we introduce a multi particle structure factor, $S^c_{mp}(q,t)$, that probes collective dynamics. The collective dynamic length, calculated from the small wave vector limit of $S^c_{mp}(q,t)$, increases monotonically as a function of the volume fraction in glass forming binary mixture of charged colloidal particles in both unpinned and pinned systems. This prediction, which also holds in the presence of added monovalent salt, may be validated using imaging experiments.

cond-mat.soft↗

arXiv2024

Organization and Dynamics of Chromosomes

How long threadlike eukaryotic chromosomes fit tidily in the small volume of the nucleus without significant entanglement is just beginning to be understood, thanks to major advances in experimental techniques. Several polymer models, which reproduce contact maps that measure the probabilities that two loci are in spatial contact, have predicted the three-dimensional structures of interphase chromosomes. Data-driven approaches, using contact maps as input, predict that mitotic helical chromosomes are characterized by switch in handedness, referred to as "perversion". By using experimentally derived effective interactions between chromatin loci in simulations, structures of conventional and inverted nuclei have been accurately predicted. Polymer theory and simulations show that the dynamics of individual loci in chromatin exhibit subdiffusive behavior but the diffusion exponents are broadly distributed, which accords well with experiments. Although coarse-grained models are successful, many challenging problems remain, which require the creation of new experimental and computational tools to understand genome biology.

cond-mat.soft↗

arXiv2024

Universal aspects of the random first order phase transition theory of the structural glass transition

We analyze the ways in which the random first order phase transition (RFOT) of the glass transition differs from the well-studied regular first order and second order (or continuous) phase transitions. Just as is the case in the latter two classes of phase transitions, the RFOT also exhibits universal features. Here, we discuss these features and compare and contrast the RFOT with other types of transitions with an emphasis on the structural glass transition problem. An important feature of the complete RFOT theory is that it has at least two distinct transition temperatures, one of which is a dynamical (avoided) transition signaling loss of effective ergodicity, and the other is an equilibrium ideal glass transition. Particular attention is paid to the coherence, or correlation, length associated with these transitions in the RFOT. We also derive universal scaling relations for several experimentally measurable quantities that are valid near the ideal glass transition. In particular, activated scaling ideas are used to obtain a scaling equation for the non-linear structural glass susceptibility as the ideal glass transition is approached. Important finite corrections to the ideal glass transition temperature are also discussed. Our work provides additional criteria for assessing the validity of RFOT theory of the liquid to glass transition, and provides a firm theoretical foundation for analyzing experimental data on the temperature dependence of the relaxation times.

cond-mat.stat-mech↗

arXiv2024

Proliferation-driven mechanical feedback regulates cell dynamics in growing tissues

Local stresses in a tissue, a collective property, regulate cell division and apoptosis. In turn, cell growth and division induce active stresses in the tissue. As a consequence, there is a feedback between cell growth and local stresses. However, how the cell dynamics depend on local stress-dependent cell division and the feedback strength is not fully understood. Here, we probe the consequences of stress-mediated growth and cell division on cell dynamics using agent-based simulations of a two-dimensional growing tissue. We discover a rich dynamical behavior of individual cells, ranging from jamming (mean square displacement, $Δ(t) \sim t^α$ with $α$ less than unity), to hyperdiffusion ($α> 2$) depending on cell division rate and the strength of the mechanical feedback. Strikingly, $Δ(t)$ is determined by the tissue growth law, which quantifies cell proliferation (number of cells $N(t)$ as a function of time). The growth law ($N(t) \sim t^λ$ at long times) is regulated by the critical pressure that controls the strength of the mechanical feedback and the ratio between cell division-apoptosis rates. We show that $λ\sim α$, which implies that higher growth rate leads to a greater degree of cell migration. The variations in cell motility are linked to the emergence of highly persistent forces extending over several cell cycle times. Our predictions are testable using cell-tracking imaging techniques.

cond-mat.soft↗

arXiv2024

Transcription-induced active forces suppress chromatin motion

The organization of interphase chromosomes in a number of species is starting to emerge thanks to advances in a variety of experimental techniques. However, much less is known about the dynamics, especially in the functional states of chromatin. Some experiments have shown that the motility of individual loci in human interphase chromosome decreases during transcription, and increases upon inhibiting transcription. This is a counter-intuitive finding because it is thought that the active mechanical force ($F$) on the order of ten pico-newtons, generated by RNA polymerase II (RNAPII) that is presumably transmitted to the gene-rich region of the chromatin, would render it more open, thus enhancing the mobility. We developed a minimal active copolymer model for interphase chromosomes to investigate how $F$ affects the dynamical properties of chromatin. The movements of the loci in the gene-rich region are suppressed in an intermediate range of $F$, and are enhanced at small $F$ values, which has also been observed in experiments. In the intermediate $F$, the bond length between consecutive loci increases, becoming commensurate with the distance at the minimum of the attractive interaction between non-bonded loci. This results in a transient disorder-to-order transition, leading to a decreased mobility during transcription. Strikingly, the $F$-dependent change in the locus dynamics preserves the organization of the chromosome at $F=0$. Transient ordering of the loci, which is not found in the polymers with random epigenetic profiles, in the gene-rich region might be a plausible mechanism for nucleating a dynamic network involving transcription factors, RNAPII, and chromatin.

physics.bio-ph↗

arXiv2023

On the role of mechanical feedback in synchronous to asynchronous transition during embryogenesis

Experiments have shown that during the initial stage of Zebrafish morphogenesis a synchronous to asynchronous transition (SAT) occurs, as the cells divide extremely rapidly. In the synchronous phase, the cells divide in unison unlike in the asynchronous phase. Despite the widespread observation of SAT in experiments, a theory to calculate the critical number of cell cycles, $n^{*}$, at which asynchronous growth emerges does not exist. Here, using a model for the cell cycle, with the assumption that cell division times are Gaussian distributed with broadening, we predict $n^{*}$ and the time at which the SAT occurs. The theoretical results are in excellent agreement with experiments. The theory, supplemented by agent based simulations, establish that the SAT emerges as a consequence of biomechanical feedback on cell division. The emergence of asynchronous phase is due to linearly increasing fluctuations in the cell cycle times with each round of cell division. We also make several testable predictions, which would further shed light on the role of biomechanical feedback on the growth of multicellular systems.

physics.bio-ph↗

arXiv2023

Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis

A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity (η) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction (ϕS). The increase in η up to ϕS is similar to the behavior observed in several glass-forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, η is a constant above ϕS. To determine the mechanism of this unusual dependence of η on ϕ, we performed extensive simulations using an agent-based model of a dense non-confluent two-dimensional tissue. We show that polydispersity in the cell size, and the propensity of the cells to deform, results in the saturation of the available free area per cell beyond a critical packing fraction. Saturation in the free space not only explains the viscosity plateau above ϕS but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.

cond-mat.soft↗