Biology subjects

Thirumalai, D.

Publications and source records attributed to Thirumalai, D..

At least 73 records · Page 4Linked to original sources

bioRxiv2021

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 is a major cause of drug resistance. Mathematical models that explain experiments quantitatively are useful in understanding the origin of intratumor heterogeneity, which then could be used to explore scenarios for efficacious therapy. Here, we develop a mathematical model to investigate intratumor heterogeneity 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, also agrees with experimental results, without tweaking any parameter in the model. The theory quantitatively explains experimental data on the responses of breast tumors 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.

cancer biology↗

bioRxiv2021

Multi-Scale Coarse Grained Model for the Stepping of Molecular Motors with application to Kinesin.

Conventional kinesin, a motor protein that transports cargo within cells, walks by taking multiple steps towards the plus end of the microtubule (MT). While significant progress has been made in understanding the details of the walking mechanism of kinesin there are many unresolved issues. From a computational perspective, a central challenge is the large size of the system, which limits the scope of time scales accessible in standard computer simulations. Here, we create a general multi-scale coarse-grained model for motors that enables us to simulate the stepping process of motors on polar tracks (actin and MT) with focus on kinesin. Our approach greatly shortens the computation times without a significant loss in detail, thus allowing us to better describe the molecular basis of the stepping kinetics. The small number of parameters, which are determined by fitting to experimental data, allows us to develop an accurate method that may be adopted to simulate stepping in other molecular motors. The model enables us to simulate a large number of steps, which was not possible previously. We show in agreement with experiments that due to the docking of the neck linker (NL) of kinesin, sometimes deemed as the power stroke, the space explored diffusively by the tethered head is severely restricted allowing the step to be in a tens of microseconds. We predict that increasing the interaction strength between the NL and the motor head, achievable by mutations in the NL, decreases the stepping time but reaches a saturation value. Furthermore, the full 3-dimensional dynamics of the cargo are fully resolved in our model, contributing to the predictive power and allowing us to study the important aspects of cargo-motor interactions.

biophysics↗

bioRxiv2021

Energy Landscape of Ubiquitin is Weakly Multidimensional

Single molecule pulling experiments report time-dependent changes in the extension (X) of a biomolecule as a function of the applied force (f). By fitting the data to one-dimensional analytical models of the energy landscape, the hopping rates between the folded and unfolded states in two-state folders, the height and the location of the transition state (TS) can be extracted. Although this approach is remarkably insightful, there are cases for which the energy landscape is multidimensional (catch bonds being the most prominent). To assess if the unfolding energy landscape in small single domain proteins could be one dimensional, we simulated force-induced unfolding of Ubiquitin (Ub) using the coarse-grained Self-Organized Polymer-Side Chain (SOP-SC) model. Brownian dynamics simulations using the SOP-SC model reveal that the Ub energy landscape is weakly multidimensional (WMD) governed predominantly by a single barrier. The unfolding pathway is confined to a narrow reaction pathway that could be described as diffusion in a quasi 1D X-dependent free energy profile. However, a granular analysis using the Pfold analysis, which does not assume any form for the reaction coordinate, shows that X alone does not account for the height, and more importantly, the location of the TS. The f-dependent TS location moves towards the folded state as f increases, in accord with the Hammond postulate. Our study shows that, in addition to analyzing the f-dependent hopping rates, the transition state ensemble must also be determined without resorting to X as a reaction coordinate in order to describe the unfolding energy landscapes of single domain proteins, especially if they are only WMD. TOC Graphic O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=91 SRC="FIGDIR/small/437368v1_ufig1.gif" ALT="Figure 1"> View larger version (20K): org.highwire.dtl.DTLVardef@1fd1480org.highwire.dtl.DTLVardef@4d12c8org.highwire.dtl.DTLVardef@c4839org.highwire.dtl.DTLVardef@59aab9_HPS_FORMAT_FIGEXP M_FIG C_FIG

biophysics↗

bioRxiv2021

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, P2. We find that the folded structures are nematic droplets with a broad distribution of P2. We argue that non-zero values of P2, leads to an arrangement of the SSEs that can resist external stresses 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).

biophysics↗

bioRxiv2021

Condensates in RNA Repeat Sequences are Heterogeneously Organized and Exhibit Reptation-like Dynamics

Although it is known that RNA undergoes liquid-liquid phase separation (LLPS), the interplay between the molecular driving forces and the emergent features of the condensates, such as their morphologies and dynamical properties, is not well understood. We introduce a coarse-grained model to simulate phase separation of trinucleotide repeat RNAs, which are implicated in neurological disorders such as Huntington disease and amyotrophic lateral sclerosis. After establishing that the simulations reproduce key experimental findings (length and concentration dependence of the phase transition in (CAG)n repeats), we show that once recruited inside the liquid droplets, the monomers transition from hairpin-like structures to extended states. Interactions between the monomers in the condensates result in the formation of an intricate and dense intermolecular network, which severely restrains the fluctuations and mobilities of the RNAs inside large droplets. In the largest densely packed high viscosity droplets, the mobility of RNA chains is best characterized by reptation, reminiscent of the dynamics in polymer melts. Our work provides a microscopic framework for understanding liquid-liquid phase separation in RNA, which is not easily discernible in current experiments.

biophysics↗

bioRxiv2021

Chromatin dynamics controls epigenetic domain formation

In multicellular organisms, nucleosomes carry epigenetic information that defines distinct patterns of gene expression, which are inherited over multiple generations. The enhanced capacity for information storage arises by nucleosome modifications, triggered by enzymes. Modified nucleosomes can transfer the mark to others that are in proximity by a positive feedback (modification begets modification) mechanism. We created a polymer model in which each bead, representing a nucleosome, stochastically switches between unmodified (U) and modified (M) states depending on the states of the neighbors. Spreading is initiated at a specific nucleation site (NS) that is permanently in the M state. Modifications spread among the non-nucleation loci probabilistically. If the spreading rate is higher than the chromatin relaxation rate, domains containing the modified nucleosomes form without bound. In the opposite biologically relevant limit, finite-sized domains form, driven by contacts between nucleosomes through a three-dimensional looping mechanism, with chromatin remaining in an expanded state, as is appropriate for fission yeast. Surprisingly, finite bounded domains arise without the need for any boundary elements as long as the spreading is slow. Maintenance of spatially and temporally stable domains require the presence of the NS whose removal eliminates finite-sized modified domains. By varying the solvent quality we show that finite heterochromatin domains form as long as initially chromatin is not fully condensed. The predictions compare well with experimental data for H3K9me3 spreading in Mouse Embryonic Stem cell.

biophysics↗

bioRxiv2020

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 ku(f), as a function of mechanical force, f, measurable in single molecule experiments, can arise for many reasons. In particular, upward curvature in log ku(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 {beta}-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 ku(f) as a function of force (or log ku[C] where [C] is the denaturant concentration).

biophysics↗

bioRxiv2020

Theory and simulations for crowding-induced changes in stability of proteins with applications to {lambda} 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 ({Phi}C) dependent increase in the melting temperature of globular proteins, [Formula], where [Formula]. The effective Flory exponent,{nu} 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 [≤] [≤] 2.0. The theoretical predictions are confirmed using molecular simulations of {lambda} repressor in the presence of spherical crowding particles. Analyses of previous simulations and experiments confirm the predicted theoretical bound for . 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. In vitro experiments containing mixtures of crowding particles could validate or invalidate the predictions.

biophysics↗

bioRxiv2020

Molecular Transfer Model for pH effects on Intrinsically Disordered Proteins: Theory and Applications

We present a theoretical method to study how changes in pH shape the heterogeneous conformational ensemble explored by intrinsically disordered proteins (IDPs). The theory is developed in the context of coarse-grained models, which enable a fast, accurate, and extensive exploration of conformational space at a given protonation state. In order to account for pH effects, we generalize the Molecular Transfer Model (MTM), in which conformations are re-weighted using the transfer free energy, which is the free energy necessary for bringing to equilibrium in a new environment a "frozen" conformation of the system. Using the semi-grand ensemble, we derive an exact expression of the transfer free energy, which amounts to the appropriate summation over all the protonation states. Because the exact result is computationally too demanding to be useful for large polyelectrolytes or IDPs, we introduce a mean-field (MF) approximation of the transfer free energy. Using a lattice model, we compare the exact and MF results for the transfer free energy and a variety of observables associated with the model IDP. We find that the precise location of the charged groups (the sequence), and not merely the net charge, determines the structural properties. We demonstrate that some of the limitations previously noted for MF theory in the context of globular proteins are mitigated when disordered polymers are studied. The excellent agreement between the exact and MF results poises us to use the method presented here as a computational tool to study the properties of IDPs and other biological systems as a function of pH.

biophysics↗

bioRxiv2020

Role of Long-range Allosteric Communication in Determining the Stability and Disassembly of SARS-COV-2 in Complex with ACE2

Severe acute respiratory syndrome (SARS) and novel coronavirus disease (COVID-19) are caused by two closely related beta-coronaviruses, SARS-CoV and SARS-CoV-2, respectively. The envelopes surrounding these viruses are decorated with spike proteins, whose receptor binding domains (RBDs) initiate invasion by binding to the human angiotensin-converting enzyme 2 (ACE2). Subtle changes at the interface with ACE2 seem to be responsible for the enhanced affinity for the receptor of the SARS-CoV-2 RBD compared to SARS-CoV RBD. Here, we use Elastic Network Models (ENMs) to study the response of the viral RBDs and ACE2 upon dissassembly of the complexes. We identify a dominant detachment mode, in which the RBD rotates away from the surface of ACE2, while the receptor undergoes a conformational transition which stretches the active-site cleft. Using the Structural Perturbation Method, we determine the network of residues, referred to as the Allostery Wiring Diagram (AWD), which drives the large-scale motion activated by the detachment of the complex. The AWD for SARS-CoV and SARS-CoV-2 are remarkably similar, showing a network that spans the interface of the complex and reaches the active site of ACE2, thus establishing an allosteric connection between RBD binding and receptor catalytic function. Informed in part by the AWD, we used Molecular Dynamics simulations to probe the effect of interfacial mutations in which SARS-CoV-2 residues are replaced by their SARS-CoV counterparts. We focused on a conserved glycine (G502 in SARS-CoV-2, G488 in SARS-CoV) because it belongs to a region that initiates the dissociation of the complex along the dominant detachment mode, and is prominent in the AWD. Molecular Dynamics simulations of SARS-CoV-2 wild-type and G502P mutant show that the affinity for the human receptor of the mutant is drastically diminished. Our results suggest that in addition to residues that are in direct contact with the interface those involved in long range allosteric communication are also a determinant of the stability of the RBD-ACE2 complex.

biophysics↗

bioRxiv2020

Water-mediated interactions determine helix formation of peptides in open nanotubes

Water-mediated interactions (WMIs) play diverse roles in molecular biology. They are particularly relevant in geometrically confined spaces such as the interior of the chaperonin, at the interface between ligands and their binding partners, and in the ribosome tunnel. Inspired in part by the geometry of the ribosome tunnel, we consider confinement effects on the stability of peptides. We describe results from replica exchange molecular dynamics simulations of a system containing a 23-alanine or 23-serine polypeptide confined to non-polar and polar nanotubes in the gas phase and when open to a water reservoir. We quantify the effect of water in determining the preferred conformational states of these polypeptides by calculating the difference in the solvation free energy for the helix and coil states in the open nanotube in the two phases. Our simulations reveal several possibilities. We find that nanoscopic confinement preferentially stabilizes the helical state of polypeptides with hydrophobic side chains, which is explained by the entropic stabilization mechanism proposed on the basis of polymer physics. Polypeptide chains with hydrophilic side chains can adopt helical structures within nanotubes, but helix formation is sensitive to the nature of the nanotube due to WMIs. We elaborate on the potential implications of our findings to the stability of peptides in the ribosome tunnel.

biophysics↗

bioRxiv2020

Retardation of folding rates of substrate proteins in the nanocage of GroEL

The E. Coli. ATP-consuming chaperonin machinery, a complex between GroEL and GroES, has evolved to facilitate folding of substrate proteins (SPs) that cannot do so spontaneously. A series of kinetic experiments show that the SPs are encapsulated in the GroEL/ES nano cage for a short duration. If confining the SPs in the predominantly polar cage of GroEL in order to help folding, the assisted folding rate, relative to the bulk value, should always be enhanced. Here, we show that this is not the case for the folding of rhodanese in the presence of the full machinery of GroEL/ES and ATP. The assisted folding rate of rhodanese decreases. Based on our finding and those reported in other studies, we suggest that the ATP-consuming chaperonin machinery has evolved to optimize the product of the folding rate and the yield of the folded SPs on the biological time scale. Neither the rate nor the yield is separately maximized.

biophysics↗

bioRxiv2020

Asymmetry in Histone Rotation in Forced Unwrapping and Force Quench Rewrapping in a Nucleosome

Nucleosomes, the building blocks of chromosomes, are also transcription regulators. Single molecule pulling experiments have shown that nucleosomes unwrap in two major stages, releasing nearly equal length of DNA in each stage. The first stage, attributed to the rupture of the outer turn is reversible, occurs at low forces ({approx} (3 - 5) pNs) whereas in the second stage the inner turn ruptures irreversibly at high forces (between {approx} (9 - 15) or higher) pNs. We show that Brownian dynamics simulations using the Self-Organized Polymer model of the nucleosome capture the experimental findings, thus permitting us to discern the molecular details of the structural changes not only in DNA but also in the Histone Protein Core (HPC). Upon unwrapping of the outer turn, which is independent of the pulling direction, there is a transition from 1.6 turns to 1.0 turn DNA wound around the HPC. In contrast, the rupture of the inner turn, leading to less than 0.5 turn DNA around the HPC, depends on the pulling direction, and is controlled by energetic and kinetic barriers. The latter arises because the mechanical force has to produce sufficient torque to rotate (in an almost directed manner) the HPC by 180{degrees}. In contrast, during the rewrapping process, HPC rotation is stochastic, with the quenched force fQ playing no role. Interestingly, if fQ = 0 the HPC rotation is not required for rewrapping because the DNA ends are unconstrained. The assembly of the outer wrap upon force quench, as assessed by the decrease in the end-to-end distance (Ree) of the DNA, nearly coincides with the increase in Ree as force is increased, confirming the reversible nature of the 1.6 turns to 1.0 turn transition. The asymmetry in HPC rotation during unwrapping and rewrapping accounts for the observed hysteresis in the stretch-release cycles in single molecule pulling experiments. Experiments that could validate the prediction that HPC rotation, which gives rise to the kinetic barrier in the unwrapping process, are proposed.

biophysics↗

bioRxiv2020

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.

biophysics↗

bioRxiv2020

Dramatic shape changes occur as Cytochrome c folds

Extensive experimental studies on the folding of Cytochrome c (Cyt c) make this small protein an ideal target for atomic detailed simulations for the purposes of quantitatively characterizing the structural transitions and the associated time scales for folding to the native state from an ensemble of unfolded states. We use previously generated atomically detailed folding trajectories by the Stochastic Difference Equation in Length (SDEL) to calculate the time-dependent changes in the Small Angle X-ray scattering (SAXS) profiles. Excellent agreement is obtained between experiments and simulations for the time dependent SAXS spectra, allowing us to identify the structures of the folding intermediates, which shows that Cyt c reaches the native state by a sequential folding mechanism. Using the ensembles of structures along the folding pathways we show that compaction and the sphericity of Cyt c change dramatically from the prolate ellipsoid shape in the unfolded state to the spherical native state. Our data, which provides unprecedented quantitative agreement with all aspects of time-resolved SAXS experiments, shows that hydrophobic collapse and amide group protection coincide on the 100 microseconds time scale, which is in accord with ultrafast Hydrogen/Deuterium exchange studies. Based on these results we propose that compaction of polypeptide chains, accompanied by dramatic shape changes, is a universal characteristic of globular proteins, regardless of the underlying folding mechanism.

biophysics↗

bioRxiv2020

On the theory of condensin mediated loop extrusion in genomes

Condensation of hundreds of mega-base-pair-long human chromosomes in a small nuclear volume is a spectacular biological phenomenon. This process is driven by the formation of chromosome loops. The ATP consuming motor, condensin, interacts with chromatin segments to actively extrude loops. Motivated by real-time imaging of loop extrusion (LE), we created an analytically solvable model, predicting the LE velocity and step size distribution as a function of external load. The theory fits the available experimental data quantitatively, and suggests that condensin must undergo a large conformational change, induced by ATP binding, bringing distant parts of the motor to proximity. Simulations using a simple model confirm that the motor transitions between an open and a closed state in order to extrude loops by a scrunching mechanism, similar to that proposed in DNA bubble formation during bacterial transcription. Changes in the orientation of the motor domains are transmitted over ~ 50 nm, connecting the motor head and the hinge, thus providing an allosteric basis for LE.

biophysics↗

bioRxiv2020

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. The first step in the HIPPS method is to relate the mean contact probability [Formula] between loci i and j and the average spatial distance, [Formula]. This is a difficult problem to solve because the cell population is heterogeneous, which means that a given contact exists only in a small unknown fraction of cells. Despite the population heterogeneity, we first prove that there is a theoretical lower bound connecting [<]pij[>] and [Formula] via a power-law relation. We show, using simulations of a precisely solvable model, that the overall organization is accurately captured by constructing the distance map from the contact map even when if the cell population is highly heterogeneous, thus justifying the use of the lower bound. In the second step, the mean distance matrix, with elements [Formula], is used as a constraint in the maximum entropy principle to obtain the joint distribution of spatial positions of the loci. Using the two steps, 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.

biophysics↗

bioRxiv2020

Tumor mutation burden signatures and relation to cancer risk in humans: A pan-cancer analysis

Cancers, resulting in uncontrolled cell proliferation, are driven by accumulation of somatic mutations. Genome-wide sequencing has produced a catalogue of millions of somatic mutations, which contain the evolutionary history of the cancers. However, the connection between the mutation accumulation and disease development and risks is poorly understood. Here, we analyzed more than 1,200,000 mutations from 5,000 cancer patients with whole-exome sequencing, and discovered two novel signatures for 16 cancer types in The Cancer Genome Atlas (TCGA) database. A strong correlation between Tumor Mutation Burden (TMB) and the Patient Age at Diagnosis (PAD) is observed for cancers with low TMB (mean value less than 3 mutations per million base pairs) but is absent in cancers with high TMB. We also validate this finding using whole-genome sequencing data from more than 2,000 patients for 24 cancer types. Surprisingly, the differences in cancer risk between the sexes are also mainly driven by the disparity in mutation burden. The TMB variations, imprinted at the chromosome level, also reflect accumulation of mutation clusters within small chromosome segments in high TMB cancers. By analyzing the characteristics of mutations based on multi-region sequencing, we found that a combination of TMB and intratumor heterogeneity could a potential biomarker for predicting the patient survival and response to treatment.

cancer biology↗