arXiv subjects

D. Thirumalai

Publications and source records attributed to D. Thirumalai.

At least 55 records · Page 3Linked to original sources

arXiv2020

Spatially Heterogeneous Dynamics of Cells in a Growing Tumor Spheroid: Comparison Between Theory and Experiments

Collective cell movement, characterized by multiple cells that are in contact for substantial periods of time and undergo correlated motion, plays a central role in cancer and embryogenesis. Recent imaging experiments have provided time-dependent traces of individual cells, thus providing an unprecedented picture of tumor spheroid growth. By using simulations of a minimal cell model, we analyze the experimental data that map the movement of cells in fibrosarcoma tumor spheroid embedded in a collagen matrix. Both simulations and experiments show that cells in the core of the spheroid exhibit subdiffusive glassy dynamics (mean square displacement, $Δ(t) \approx t^α$ with $α< 1$), whereas cells in the periphery exhibit superdiffusive motion, $Δ(t) \approx t^α$ with $α>1)$. The motion of most of the cells near the periphery undergo highly persistent and correlated directional motion, thus explaining the observed superdiffusive behavior. The $α$ values for cells in the core and periphery, extracted from simulations and experiments are in near quantitative agreement with each other, which is surprising given that no parameter in the model was used to fit the measurements. The qualitatively different dynamics of cells in the core and periphery is captured by the fourth order susceptibility, introduced to characterize metastable states in glass forming systems. Analyses of the velocity autocorrelation of individual cells show remarkable spatial heterogeneity with no two cells exhibiting similar behavior. The prediction that $α$ should depend on the location of the cells in the tumor is amenable to experimental test. The highly heterogeneous dynamics of cells in the tumor spheroid provides a plausible mechanism for the origin of intratumor heterogeneity.

physics.bio-ph↗

arXiv2020

Cooperation among tumor cell subpopulations leads to intratumor heterogeneity

Heterogeneity is a hallmark of all cancers. Tumor heterogeneity is found at different levels -- interpatient, intrapatient, and intratumor heterogeneity. All of them pose challenges for clinical treatments. The latter two scenarios can also increase the risk of developing drug resistance. Although the existence of tumor heterogeneity has been known for two centuries, a clear understanding of its origin is still elusive, especially at the level of intratumor heterogeneity (ITH). The coexistence of different subpopulations within a single tumor has been shown to play crucial roles during all stages of carcinogenesis. Here, using concepts from evolutionary game theory and public goods game, often invoked in the context of the tragedy of commons, we explore how the interactions among subclone populations influence the establishment of ITH. By using an evolutionary model, which unifies several experimental results in distinct cancer types, we develop quantitative theoretical models for explaining data from {\it in vitro} experiments involving pancreatic cancer as well as {\it vivo} data in glioblastoma multiforme. Such physical and mathematical models complement experimental studies, and could optimistically also provide new ideas for the design of efficacious therapies for cancer patients.

cond-mat.soft↗

arXiv2020

Dual Role of Cell-Cell Adhesion In Tumor Suppression and Proliferation Due to Collective Mechanosensing

It is known that mechanical interactions couple a cell to its neighbors, enabling a feedback loop to regulate tissue growth. However, the interplay between cell-cell adhesion strength, local cell density and force fluctuations in regulating cell proliferation is poorly understood. Here, we show that spatial variations in the tumor growth rates, which depend on the location of cells within tissue spheroids, are strongly influenced by cell-cell adhesion. As the strength of the cell-cell adhesion increases, intercellular pressure initially decreases, enabling dormant cells to more readily enter into a proliferative state. We identify an optimal cell-cell adhesion regime where pressure on a cell is a minimum, allowing for maximum proliferation. We use a theoretical model to validate this novel collective feedback mechanism coupling adhesion strength, local stress fluctuations and proliferation.Our results, predicting the existence of a non-monotonic proliferation behavior as a function of adhesion strength, are consistent with experimental results. Several experimental implications of the proposed role of cell-cell adhesion in proliferation are quantified, making our model predictions amenable to further experimental scrutiny. We show that the mechanism of contact inhibition of proliferation, based on a pressure-adhesion feedback loop, serves as a unifying mechanism to understand the role of cell-cell adhesion in proliferation.

cond-mat.soft↗

arXiv2019

Generalized Rayleigh-Plesset Theory for Cell Size Maintenance in Viruses and Bacteria

The envelopes covering bacterial cytoplasm possess remarkable elastic properties. They are rigid enough to resist large pressures while being flexible enough to adapt to growth under environmental constraints. Similarly, the virus shells play an important role in their functions. However, the effects of mechanical properties of the outer shell in controlling and maintaining the sizes of bacteria or viruses are unknown. Here, we present a hydrodynamic "bubbles with shell" model, motivated by the study of bubble stability in fluids, to demonstrate that shell rigidity and turgor pressure control the sizes of bacteria and viruses. A dimensionless compliance parameter, expressed in terms of the elastic modulus of the shell, its thickness and the turgor pressure, determines membrane response to deformation and the size of the organisms. By analyzing experiment data, we show that bacterial and viral sizes correlate with shell elasticity, which plays a critical role in regulating size.

physics.bio-ph↗

arXiv2019

Iterative Annealing Mechanism Explains the Functions of the GroEL and RNA Chaperones

Molecular chaperones are ATP-consuming biological machines, which facilitate the folding of proteins and RNA molecules that are kinetically trapped in misfolded states for long times. Unassisted folding occurs by the kinetic partitioning mechanism according to which folding to the native state, with low probability as well as misfolding to one of the many metastable states, with high probability, occur rapidly on similar time scales. GroEL is an all-purpose stochastic machine that assists misfolded substrate proteins (SPs) to fold. The RNA chaperones (CYT-19) help the folding of ribozymes that readily misfold. GroEL does not interact with the folded proteins but CYT-19 disrupts both the folded and misfolded ribozymes. Despite this major difference, the Iterative Annealing Mechanism (IAM) quantitatively explains all the available experimental data for assisted folding of proteins and ribozymes. Driven by ATP binding and hydrolysis and GroES binding, GroEL undergoes a catalytic cycle during which it samples three allosteric states, referred to as T (apo), R (ATP bound), and R'' (ADP bound). In accord with the IAM predictions, analyses of the experimental data shows that the efficiency of the GroEL-GroES machinery and mutants is determined by the resetting rate $k_{R''\rightarrow T}$, which is largest for the wild type GroEL. Generalized IAM accurately predicts the folding kinetics of Tetrahymena ribozyme and its variants. Chaperones maximize the product of the folding rate and the steady state native state fold by driving the substrates out of equilibrium. Neither the absolute yield nor the folding rate is optimized.

q-bio.BM↗

arXiv2019

Fragile-to-Strong Crossover, growing length scales, and dynamic heterogeneity in Wigner Glasses

Colloidal particles, which are ubiquitous, have become ideal testing grounds for the structural glass transition (SGT) theories. In these systems glassy behavior is manifested as the density of the particles is increased. Thus, soft colloidal particles with varying degree of softness capture diverse glass forming properties, observed normally in molecular glasses. By performing Brownian dynamics simulations for a binary mixture of micron-sized charged colloidal suspensions, known to form Wigner glasses, we show that by tuning the softness of the potential, achievable by changing the monovalent salt concentration, there is a continuous transition between fragile to strong behavior. Remarkably, this is found in a system where the well characterized potential between the colloidal particles is isotropic. We also show that the predictions of the random first order transition (RFOT) theory quantitatively describes the universal features such as the growing correlation length, $ξ\sim (ϕ_K/ϕ- 1)^{-ν}$ with $ν= 2/3$ where $ϕ_K$, the analogue of the Kauzmann temperature, depends on the salt concentration. As anticipated by the RFOT predictions, we establish a causal relationship between the growing correlation length and a steep increase in the relaxation time and dynamic heterogeneity. The broad range of fragility observed in Wigner glasses is used to draw analogies with molecular glasses. The large variations in the fragility is found only when the temperature dependence of the viscosity is examined for a large class of diverse glass forming materials. In sharp contrast, this is vividly illustrated in a single system that can be experimentally probed. Our work also shows that the RFOT predictions are accurate in describing the dynamics over the entire density range, regardless of the fragility of the glasses, implying that the physics describing the SGT is universal.

cond-mat.soft↗

arXiv2019

Theoretical Perspectives on Biological Machines

Many biological functions are executed by molecular machines, which consume energy and convert it into mechanical work. Biological machines have evolved to transport cargo, facilitate folding of proteins and RNA, remodel chromatin and replicate DNA. A common aspect of these machines is that their functions are driven out of equilibrium. It is a challenge to provide a general framework for understanding the functions of biological machines, such as molecular motors, molecular chaperones, and helicases. Using these machines as prototypical examples, we describe a few general theoretical methods providing insights into their functions. Although the theories rely on coarse-graining of these complex systems they have proven useful in not only accounting for many in vitro experiments but also addressing questions such as how the trade-off between precision, energetic costs and optimal performances are balanced. However, many complexities associated with biological machines will require one to go beyond current theoretical methods. Simple point mutations in the enzyme could drastically alter functions, making the motors bi-directional or result in unexpected diseases or dramatically restrict the capacity of molecular chaperones to help proteins fold. These examples are reminders that while the search for principles of generality in biology is intellectually stimulating, one also ought to keep in mind that molecular details must be accounted for to develop a deeper understanding of processes driven by biological machines. Going beyond generic descriptions of in vitro behavior to making genuine understanding of in vivo functions will likely remain a major challenge for some time to come. The combination of careful experiments and the use of physical principles will be useful in elucidating the rules governing the workings of biological machines.

physics.bio-ph↗

arXiv2019

How kinesin waits for ATP affects the nucleotide and load dependence of the stepping kinetics

Dimeric molecular motors walk on polar tracks by binding and hydrolyzing one ATP per step. Despite tremendous progress, the waiting state for ATP binding in the well-studied kinesin that walks on microtubule (MT), remains controversial. One experiment suggests that in the waiting state both heads are bound to the MT, while the other shows that ATP binds to the leading head after the partner head detaches. To discriminate between these two scenarios, we developed a theory to calculate accurately several experimentally measurable quantities as a function of ATP concentration and resistive force. In particular, we predict that measurement of the randomness parameter could discriminate between the two scenarios for the waiting state of kinesin, thereby resolving this standing controversy.

q-bio.SC↗

arXiv2019

Conformational Heterogeneity in Human Interphase Chromosome Organization Reconciles the FISH and Hi-C Paradox

Hi-C experiments are used to infer the contact probabilities between loci separated by varying genome lengths. Contact probability should decrease as the spatial distance between two loci increases. However, studies comparing Hi-C and FISH data show that in some cases the distance between one pair of loci, with larger Hi-C readout, is paradoxically larger compared to another pair with a smaller value of the contact probability. Here, we show that the FISH-Hi-C paradox can be resolved using a theory based on a Generalized Rouse Model for Chromosomes (GRMC). The FISH-Hi-C paradox arises because the cell population is highly heterogeneous, which means that a given contact is present in only a fraction of cells. Insights from the GRMC is used to construct a theory, without any adjustable parameters, to extract the distribution of subpopulations from the FISH data, which quantitatively reproduces the Hi-C data. Our results show that heterogeneity is pervasive in genome organization at all length scales, reflecting large cell-to-cell variations.

cond-mat.soft↗

arXiv2019

Ion Condensation onto Ribozyme is Site-Specific and Fold-Dependent

The highly charged RNA molecules, with each phosphate carrying a single negative charge, cannot fold into well-defined architectures with tertiary interactions, in the absence of ions. For ribozymes, divalent cations are known to be more efficient than monovalent ions in driving them to a compact state although Mg$^{2+}$ ions are needed for catalytic activities. Therefore, how ions interact with RNA is relevant in understanding RNA folding. It is often thought that most of the ions are territorially and non-specifically bound to the RNA, as predicted by the counterion condensation (CIC) theory. Here, we show using simulations of ${\it Azoarcus}$ ribozyme, based on an accurate coarse-grained Three Site Interaction (TIS) model, with explicit divalent and monovalent cations, that ion condensation is highly specific and depends on the nucleotide position. The regions with high coordination between the phosphate groups and the divalent cations are discernible even at very low Mg$^{2+}$ concentrations when the ribozyme does not form tertiary interactions. Surprisingly, these regions also contain the secondary structural elements that nucleate subsequently in the self-assembly of RNA, implying that ion condensation is determined by the architecture of the folded state. These results are in sharp contrast to interactions of ions (monovalent and divalent) with rigid charged rods in which ion condensation is uniform and position independent. The differences are explained in terms of the dramatic non-monotonic shape fluctuations in the ribozyme as it folds with increasing Mg$^{2+}$ or Ca$^{2+}$ concentration.

q-bio.BM↗

arXiv2018

Symmetry, Rigidity, and Allosteric Signaling: From Monomeric Proteins to Molecular Machines

Allosteric signaling in biological molecules, which may be viewed as specific action at a distance due to localized perturbation upon binding of ligands or changes in environmental cues, is pervasive in biology. Phenomenological MWC and KNF models galvanized research for over five decades, and these models continue to be the basis for describing the allostery in an array of systems. However, understanding allosteric signaling and the associated dynamics between distinct allosteric states is challenging. In this review, we first describe symmetry and rigidity as essential requirements for allosteric proteins. The general features, with MWC and KNF as two extreme scenarios, emerge when allosteric signaling is viewed from an energy landscape perspective. To go beyond the general theories, we describe computational tools to predict the network of residues that carry allosteric signals. Methods to obtain molecular insights into the dynamics of allosteric transitions are briefly mentioned. The utility of the methods is illustrated by applications to systems ranging from monomeric proteins to multisubunit proteins. Finally, the role allostery plays in the functions of ATP-consuming molecular machines, bacterial chaperonin GroEL and molecular motors, is described. Although universal molecular principles governing allosteric signaling do not exist, we can draw the following general conclusions. (1) Multiple pathways connecting allosteric states are highly heterogeneous. (2) Allosteric signaling is exquisitely sensitive to the architecture of the system, which implies that the capacity for allostery is encoded in the structure itself. (3) The mechanical modes that connect distinct allosteric states are robust to sequence variations. (4) Extensive investigations of allostery in Hemoglobin and more recently GroEL, show that a network of salt-bridge rearrangements serves as allosteric switches.

cond-mat.soft↗

arXiv2018

Share, but unequally: A plausible mechanism for emergence and maintenance of intratumor heterogeneity

Intratumor heterogeneity (ITH), referring to coexistence of different cell subpopulations in a single tumor, has been a major puzzle in cancer research for almost half a century. The lack of understanding of the underlying mechanism of ITH hinders progress in developing effective therapies for cancers. Based on the findings in a recent quantitative experiment on pancreatic cancer, we developed a general evolutionary model for one type of cancer, accounting for interactions between different cell populations through paracrine or juxtacrine factors. We show that the emergence of a stable heterogeneous state in a tumor requires an unequal allocation of paracrine growth factors ("public goods") between cells that produce them and those that merely consume them. Our model provides a quantitative explanation of recent {\it in vitro} experimental studies in pancreatic cancer in which insulin growth factor (IGF-II) plays the role of public goods. The calculated phase diagrams as a function of exogenous resources and fraction of growth factor producing cells show ITH persists only in a narrow range of concentration of exogenous IGF-II. Remarkably, maintenance of ITH requires cooperation among tumor cell subpopulations in harsh conditions, specified by lack of exogenous IGF-II, whereas surplus exogenous IGF-II elicits competition. Our theory also quantitatively accounts for measured {\it in vivo} tumor growth in glioblastoma multiforme (GBM). The predictions for GBM tumor growth as a function of the fraction of tumor cells are amenable to experimental tests. The mechanism for ITH also provides hints for devising efficacious therapies.

q-bio.PE↗

arXiv2018

On the origin of super-diffusive behavior in a class of non-equilibrium systems

Experiments and simulations have established that dynamics in a class of living and abiotic systems that are far from equilibrium exhibit super diffusive behavior at long times, which in some cases (for example evolving tumor) is preceded by slow glass-like dynamics. By using the evolution of a collection of tumor cells, driven by mechanical forces and subject to cell birth and apoptosis, as a case study we show theoretically that on short time scales the mean square displacement is sub-diffusive due to jamming, whereas at long times it is super diffusive. The results obtained using stochastic quantization method, which is needed because of the absence of fluctuation-dissipation theorem (FDT), show that the super-diffusive behavior is universal and impervious to the nature of cell-cell interactions. Surprisingly, the theory also quantitatively accounts for the non-trivial dynamics observed in simulations of a model soap foam characterized by creation and destruction of spherical bubbles, which suggests that the two non-equilibrium systems belong to the same universality class. The theoretical prediction for the super diffusion exponent is in excellent agreement with simulations for collective motion of tumor cells and dynamics associated with soap bubbles.

cond-mat.stat-mech↗

arXiv2018

Frictional Effects on RNA Folding: Speed Limit and Kramers Turnover

We investigated frictional effects on the folding rates of a human telomerase hairpin (hTR HP) and H-type pseudoknot from the Beet Western Yellow Virus (BWYV PK) using simulations of the Three Interaction Site (TIS) model for RNA. The heat capacity from TIS model simulations, calculated using temperature replica exchange simulations, reproduces nearly quantitatively the available experimental data for the hTR HP. The corresponding results for BWYV PK serve as predictions. We calculated the folding rates ($k_\mathrm{F}$) from more than 100 folding trajectories for each value of the solvent viscosity ($η$) at a fixed salt concentration of 200 mM. By using the theoretical estimate ($\propto$$\sqrt{N}$ where $N$ is the number of nucleotides) for folding free energy barrier, $k_\mathrm{F}$ data for both the RNAs are quantitatively fit using one-dimensional Kramers' theory with two parameters specifying the curvatures in the unfolded basin and the barrier top. In the high-friction regime ($η\gtrsim10^{-5}\,\textrm{Pa\ensuremath{\cdot}s}$), for both HP and PK, $k_\mathrm{F}$s decrease as $1/η$ whereas in the low friction regime, $k_\mathrm{F}$ values increase as $η$ increases, leading to a maximum folding rate at a moderate viscosity ($\sim10^{-6}\,\textrm{Pa\ensuremath{\cdot}s}$), which is the Kramers turnover. From the fits, we find that the speed limit to RNA folding at water viscosity is between 1 and 4 $\mathrm{μs}$, which is in accord with our previous theoretical prediction as well as results from several single molecule experiments. Both the RNA constructs fold by parallel pathways. Surprisingly, we find that the flux through the pathways could be altered by changing solvent viscosity, a prediction that is more easily testable in RNA than in proteins.

q-bio.BM↗

arXiv2018

Charge fluctuation effects on the shape of flexible polyampholytes with applications to Intrinsically disordered proteins

Random polyampholytes (PAs) contain positively and negatively charged monomers that are distributed randomly along the polymer chain. The interaction between charges is assumed to be given by the Debye-Huckel potential. We show that the size of the PA is determined by an interplay between electrostatic interactions, giving rise to the polyelectrolyte (PE) effect due to net charge per monomer ($σ$), and an effective attractive PA interaction due to charge fluctuations, $δσ$. The interplay between these terms gives rise to non-monotonic dependence of the radius of gyration, $R_g$ on the inverse Debye length, $κ$ when PA effects are important (${\frac{δσ}σ} > 1$). In the opposite limit, $R_g$ decreases monotonically with increasing $κ$. Simulations of PA chains, using a charged bead-spring model, further corroborates our theoretical predictions. The simulations unambiguously show that conformational heterogeneity manifests itself among sequences that have identical PA parameters. A clear implication is that the phases of PA sequences, and by inference IDPs, cannot be determined using only the bare PA parameters ($σ$ and $δσ$). The theory is used to calculate the changes in $R_g$ on $N$, the number of residues for a set of Intrinsically Disordered Proteins (IDPs). For a certain class of IDPs, with $N$ between 24 to 441, the size grows as $R_g \sim N^{0.6}$, which agrees with data from Small Angle X-ray Scattering (SAXS) experiments.

cond-mat.stat-mech↗

arXiv2018

Cell growth rate dictates the onset of glass to fluid-like transition and long time super-diffusion in an evolving cell colony

Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight their implications in understanding similar behavior in seemingly unrelated soft glassy materials and possibly chemokine-induced migration of CD8$^{+}$ T cells. We performed simulations of tumor invasion using a minimal three dimensional model, accounting for cell elasticity and adhesive cell-cell interactions as well as cell birth and death to establish that cell growth rate-dependent tumor expansion results in the emergence of distinct topological niches. Cells at the periphery move with higher velocity perpendicular to the tumor boundary, while motion of interior cells is slower and isotropic. The mean square displacement, $Δ(t)$, of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting super-diffusive behavior, $Δ(t) \approx t^α$ ($α> 1$), at longer times. We derive the value of $α\approx 1.33$ using a field theoretic approach based on stochastic quantization. In the process we establish the universality of super-diffusion in a class of seemingly unrelated non-equilibrium systems. Super diffusion at long times arises only if there is an imbalance between cell birth and death rates. Our findings for the collective migration, which also suggests that tumor evolution occurs in a polarized manner, are in quantitative agreement with {\it in vitro} experiments. Although set in the context of tumor invasion the findings should also hold in describing collective motion in growing cells and in active systems where creation and annihilation of particles play a role.

q-bio.CB↗

arXiv2018

Signaling Networks and Dynamics of Allosteric Transitions in Bacterial Chaperonin GroEL: Implications for Iterative Annealing of Misfolded Proteins

Signal transmission at the molecular level in many biological complexes occurs through allosteric transitions. They describe the response a complex to binding of ligands at sites that are spatially well separated from the binding region. We describe the Structural Perturbation Method (SPM), based on phonon propagation in solids, that can be used to determine the signal transmitting allostery wiring diagram (AWD) in large but finite-sized biological complexes. Applications to the bacterial chaperonin GroEL-GroES complex shows that the AWD determined from structures also drive the allosteric transitions dynamically. Both from a structural and dynamical perspective these transitions are largely determined by formation and rupture of salt-bridges. The molecular description of allostery in GroEL provides insights into its function, which is quantitatively described by the Iterative Annealing Mechanism. Remarkably, in this complex molecular machine, a deep connection is established between the structures, reaction cycle during which GroEL undergoes a sequence of allosteric transitions, and function in a self-consistent manner.

q-bio.BM↗

arXiv2017

Forced-rupture of Cell-Adhesion Complexes Reveals abrupt switch between two Brittle States

Cell adhesion complexes (CACs), which are activated by ligand binding, play key roles in many cellular functions ranging from cell cycle regulation to mediation of cell extracellular matrix adhesion. Inspired by single molecule pulling experiments on leukocyte function-associated antigen-1 (LFA-1), expressed in T-cells, bound to intercellular adhesion molecules (ICAM), we performed constant loading rate ($r_f$) and constant force ($F$) simulations using the Self-Organized Polymer (SOP) model to describe the mechanism of ligand rupture from CACs. The simulations reproduce the major experimental finding on the kinetics of the rupture process, namely, the dependence of the most probable rupture forces ($f^*$s) on $\ln r_f$ ($r_f$ is the loading rate) exhibits two distinct linear regimes. The first, at low $r_f$, has a shallow slope whereas the slope at high $r_f$ is much larger, especially for LFA-1/ICAM-1 complex with the transition between the two occurring over a narrow $r_f$ range. Locations of the two transition states (TSs), extracted from the simulations show an abrupt change from a high value at low $r_f$ or $F$ to a low value at high $r_f$ or $F$. The unusual behavior in which the CACs switch from one brittle (TS position is a constant over a range of forces) state to another brittle state is not found in forced-rupture in other protein complexes. We explain this novel behavior by constructing the free energy profiles, $F(Λ)$s, as a function of a collective reaction coordinate ($Λ$), involving many key charged residues and a critical metal ion. The TS positions in F($Λ) change abruptly at a critical force, demonstrating that it, rather than the molecular extension is a good reaction coordinate. We reveal a new mechanism for the two loading regimes observed in the rupture kinetics in CACs.

q-bio.BM↗