arXiv subjects

D. Thirumalai

Publications and source records attributed to D. Thirumalai.

At least 127 records · Page 7Linked to original sources

arXiv2010

Factors governing fibrillogenesis of polypeptide chains

Using lattice models we explore the factors that determine the tendencies of polypeptide chains to aggregate by exhaustively sampling the sequence and conformational space. The morphologies of the fibril-like structures and the time scales ($τ_{fib}$) for their formation depend on a balance between hydrophobic and coulomb interactions. The extent of population of an ensemble of \textbf{N$^*$} structures, which are fibril-prone structures in the spectrum of conformations of an isolated protein, is the major determinant of $τ_{fib}$. This observation is used to determine the aggregating sequences by exhaustively exploring the sequence space, thus providing a basis for genome wide search of fragments that are aggregation prone.

cond-mat.soft↗

arXiv2010

Theoretical Perspectives on Protein Folding

Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing the folding mechanisms of globular proteins. The experimental data and theoretical methods have revealed the multifaceted character of proteins. Proteins exhibit universal features that can be determined using only the number of amino acid residues (N) and polymer concepts. The sizes of proteins in the denatured and folded states, cooperativity of the folding transition, dispersions in the melting temperatures at the residue level, and time scales of folding are to a large extent determined by N. The consequences of finite N especially on how individual residues order upon folding depends on the topology of the folded states. Such intricate details can be predicted using the Molecular Transfer Model that combines simulations with measured transfer free energies of protein building blocks from water to the desired concentration of the denaturant. By watching one molecule fold at a time, using single molecule methods, the validity of the theoretically anticipated heterogeneity in the folding routes, and the N-dependent time scales for the three stages in the approach to the native state have been established. Despite the successes of theory, of which only a few examples are documented here, we conclude that much remains to be done to solve the "protein folding problem" in the broadest sense.

cond-mat.soft↗

arXiv2010

Determination of factors governing fibrillogenesis of polypeptide chains using lattice models

Using lattice models we explore the factors that determine the tendencies of polypeptide chains to aggregate by exhaustively sampling the sequence and conformational space. The morphologies of the fibril-like structures and the time scales ($τ_{fib}$) for their formation depend on a subtle balance between hydrophobic and coulomb interactions. The extent of population of a fibril-prone structure in the spectrum of monomer conformations is the major determinant of $τ_{fib}$. This observation is used to determine the aggregation-prone consensus sequences by exhaustively exploring the sequence space. Our results provide a basis for genome wide search of fragments that are aggregation prone.

q-bio.BM↗

arXiv2009

Random First Order Phase Transition Theory of the Structural Glass Transition

We describe our perspective on the Structural Glass Transition (SGT) problem built on the premise that a viable theory must provide a consistent picture of the dynamics and statics, which are manifested by large increase in shear viscosity and thermodynamic anamolies respectively. For the static and dynamic description to be consistent we discovered, using a density functional description without explicit inclusion of quenched random interactions and a mean-field theory, that there be an exponentially large number of metastable states at temperatures less than a critical transition temperature, $T_A$. At a lower temperature ($T_K < T_A$), which can be associated with the Kauzmann temperature, the number of glassy states is non-extensive. Based on this theory we formulated an entropic droplet picture to describe transport in finite dimensions in the temperature range $T_K < T < T_A$. From the finding that glasses are trapped in one of many metastable states below $T_A$ we argue that during the SGT law of large numbers is violated. As a consequence in glasses there are sub sample to sub sample fluctuations provided the system is observed for times longer than the typical relaxation time in a liquid. These considerations, which find support in computer simulations and experiments, also link the notion of dynamic heterogeneity to the violation of law of large numbers. Thus, the finding that there is an extensive number of metastable states in the range $T_K < T < T_A$ offers a coherent explanation of many of the universal features of glass forming materials.

cond-mat.soft↗

arXiv2009

Urea destabilizes RNA by forming stacking interactions and multiple hydrogen bonds with nucleic acid bases

Urea titration of RNA by urea is an effective approach to investigate the forces stabilizing this biologically important molecule. We used all atom molecular dynamics simulations using two urea force fields and two RNA constructs to elucidate in atomic detail the destabilization mechanism of folded RNA in aqueous urea solutions. Urea denatures RNA by forming multiple hydrogen bonds with the RNA bases and has little influence on the phosphodiester backbone. Most significantly we discovered that urea engages in stacking interactions with the bases. We also estimate, for the first time, m-value for RNA, which is a measure of the strength of urea-RNA interactions. Our work provides a conceptual understanding of the mechanism by which urea enhances RNA folding rates.

q-bio.BM↗

arXiv2009

Refolding dynamics of stretched biopolymers upon force quench

Single molecule force spectroscopy methods can be used to generate folding trajectories of biopolymers from arbitrary regions of the folding landscape. We illustrate the complexity of the folding kinetics and generic aspects of the collapse of RNA and proteins upon force quench, using simulations of an RNA hairpin and theory based on the de Gennes model for homopolymer collapse. The folding time, $τ_F$, depends asymmetrically on $δf_S = f_S - f_m$ and $δf_Q = f_m - f_Q$ where $f_S$ ($f_Q$) is the stretch (quench) force, and $f_m$ is the transition mid-force of the RNA hairpin. In accord with experiments, the relaxation kinetics of the molecular extension, $R(t)$, occurs in three stages: a rapid initial decrease in the extension is followed by a plateau, and finally an abrupt reduction in $R(t)$ that occurs as the native state is approached. The duration of the plateau increases as $λ=τ_Q/τ_F$ decreases (where $τ_Q$ is the time in which the force is reduced from $f_S$ to $f_Q$). Variations in the mechanisms of force quench relaxation as $λ$ is altered are reflected in the experimentally measurable time-dependent entropy, which is computed directly from the folding trajectories. An analytical solution of the de Gennes model under tension reproduces the multistage stage kinetics in $R(t)$. The prediction that the initial stages of collapse should also be a generic feature of polymers is validated by simulation of the kinetics of toroid (globule) formation in semiflexible (flexible) homopolymers in poor solvents upon quenching the force from a fully stretched state. Our findings give a unified explanation for multiple disparate experimental observations of protein folding.

physics.bio-ph↗

arXiv2009

Theory of biopolymer stretching at high forces

We provide a unified theory for the high force elasticity of biopolymers solely in terms of the persistence length, $ξ_p$, and the monomer spacing, $a$. When the force $f>\fh \sim k_BTξ_p/a^2$ the biopolymers behave as Freely Jointed Chains (FJCs) while in the range $\fl \sim k_BT/ξ_p < f < \fh$ the Worm-like Chain (WLC) is a better model. We show that $ξ_p$ can be estimated from the force extension curve (FEC) at the extension $x\approx 1/2$ (normalized by the contour length of the biopolymer). After validating the theory using simulations, we provide a quantitative analysis of the FECs for a diverse set of biopolymers (dsDNA, ssRNA, ssDNA, polysaccharides, and unstructured PEVK domain of titin) for $x \ge 1/2$. The success of a specific polymer model (FJC or WLC) to describe the FEC of a given biopolymer is naturally explained by the theory. Only by probing the response of biopolymers over a wide range of forces can the $f$-dependent elasticity be fully described.

cond-mat.stat-mech↗

arXiv2009

How accurate are polymer models in the analysis of Forster resonance energy transfer experiments on proteins?

Single molecule Forster resonance energy transfer (FRET) experiments are used to infer the properties of the denatured state ensemble (DSE) of proteins. From the measured average FRET efficiency, , the distance distribution P(R) is inferred by assuming that the DSE can be described as a polymer. The single parameter in the appropriate polymer model (Gaussian chain, Wormlike chain, or Self-avoiding walk) for P(R) is determined by equating the calculated and measured . In order to assess the accuracy of this "standard procedure," we consider the generalized Rouse model (GRM), whose properties [ and P(R)] can be analytically computed, and the Molecular Transfer Model for protein L for which accurate simulations can be carried out as a function of guanadinium hydrochloride (GdmCl) concentration. Using the precisely computed for the GRM and protein L, we infer P(R) using the standard procedure. We find that the mean end-to-end distance can be accurately inferred (less than 10% relative error) using and polymer models for P(R). However, the value extracted for the radius of gyration (Rg) and the persistence length (lp) are less accurate. The relative error in the inferred R-g and lp, with respect to the exact values, can be as large as 25% at the highest GdmCl concentration. We propose a self-consistency test, requiring measurements of by attaching dyes to different residues in the protein, to assess the validity of describing DSE using the Gaussian model. Application of the self-consistency test to the GRM shows that even for this simple model the Gaussian P(R) is inadequate. Analysis of experimental data of FRET efficiencies for the cold shock protein shows that at there are significant deviations in the DSE P(R) from the Gaussian model.

q-bio.BM↗

arXiv2009

Crowding effects on the structural transitions in a flexible helical homopolymer

We elucidate the structural transitions in a helical off-lattice homopolymer induced by crowding agents, as function of the number of monomers ($N$) and volume fraction ($ϕ_c$) of crowding particles. At $ϕ_c = 0$, the homopolymer undergoes transitions from a random coil to a helix, helical hairpin \textbf{HH}, and helix bundle \textbf{HB} structures depending on $N$, and temperature. Crowding induces chain compaction that can promote \textbf{HH} or \textbf{HB} formation depending on $ϕ_c$. Typically, the helical content decreases which is reflected in the decrease in the transition temperatures that depend on $ϕ_c$, $N$, and the size of the crowding particles.

cond-mat.soft↗

arXiv2009

Water-mediated interactions between hydrophobic and ionic species in cylindrical nanopores

We use Metropolis Monte Carlo and umbrella sampling to calculate the free energies of interaction of two methane molecules and their charged derivatives in cylindrical water-filled pores. Confinement strongly alters the interactions between the nonpolar solutes, and completely eliminates the solvent separated minimum (SSM) that is seen in bulk water. The free energy profiles show that the methane molecules are either in contact or at separations corresponding to the diameter and the length of the cylindrical pore. Analytic calculations that estimate the entropy of the solutes, which are solvated at the pore surface, qualitatively explain the shape of the free energy profiles. Adding charges of opposite sign and magnitude $0.4e$ or $e$ (where $e$ is the electronic charge) to the methane molecules decreases their tendency for surface solvation and restores the SSM. We show that confinement induced ion-pair formation occurs whenever $l_B/D \sim O(1)$, where $l_B$ is the Bjerrum length, and $D$ is the pore diameter. The extent of stabilization of the SSM increases with ion charge density as long as $l_B/D < 1$. In pores with $D \le 1.2$ nm, in which the water is strongly layered, increasing the charge magnitude from $0.4e$ to $e$ reduces the stability of the SSM. As a result, ion-pair formation which occurs with negligible probability in the bulk, is promoted. In larger diameter pores that can accomodate a complete hydration layer around the solutes, the stability of the SSM is enhanced.

cond-mat.soft↗

arXiv2008

Probing the Mechanisms of Fibril Formation Using Lattice Models

Using exhaustive Monte Carlo simulations we study the kinetics and mechanism of fibril formation using lattice models as a function of temperature and the number of chains. While these models are, at best, caricatures of peptides, we show that a number of generic features thought to govern fibril assembly are present in the toy model. The monomer, which contains eight beads made from three letters (hydrophobic, polar, and charged), adopts a compact conformation in the native state. The kinetics of fibril assembly occurs in three distinct stages. In each stage there is a cascade of events that transforms the monomers and oligomers to ordered structures. In the first "burst" stage highly mobile oligomers of varying sizes form. The conversion to the aggregation-prone conformation occurs within the oligomers during the second stage. As time progresses, a dominant cluster emerges that contains a majority of the chains. In the final stage, the aggregation-prone conformation particles serve as a template onto which smaller oligomers or monomers can dock and undergo conversion to fibril structures. The overall time for growth in the latter stages is well described by the Lifshitz-Slyazov growth kinetics for crystallization from super-saturated solutions.

q-bio.BM↗

arXiv2008

Crowding effects on the mechanical stability and unfolding pathways of Ubiquitin

The interior of cells is crowded thus making it important to assess the effects of macromolecules on the folding of proteins. Using the Self-Organized Polymer (SOP) model, which is a coarse-grained representation of polypeptide chains, we probe the mechanical stability of Ubiquitin (Ub) monomers and trimers ((Ub)$_3$) in the presence of monodisperse spherical crowding agents. Crowding increases the volume fraction ($Φ_c$)-dependent average force ($ $), relative to the value at $Φ_c = 0$, needed to unfold Ub and the polyprotein. For a given $Φ_c$, the values of $ $ increase as the diameter ($σ_c$) of the crowding particles decreases. The average unfolding force $ $ depends on the ratio $\frac{D}{R_g}$, where $D \approx σ_c (\fracπ{6 Φ_c})^{1/3}$ with $R_g$ being the radius of gyration of Ub (or (Ub)$_3$) in the unfolded state. Examination of the unfolding pathways shows that, relative to $Φ_c = 0$, crowding promotes reassociation of ruptured secondary structural elements. Both the nature of the unfolding pathways and $ $ for (Ub)$_3$ are altered in the presence of crowding particles with the effect being most dramatic for the subunit that unfolds last. We predict, based on SOP simulations and theoretical arguments, that $ \sim Φ_c^{\frac{1}{3ν}}$, where $ν$ is the Flory exponent that describes the unfolded (random coil) state of the protein.

q-bio.BM↗

arXiv2008

Compression and stretching of a self-avoiding chain in cylindrical nanopores

Force-induced deformations of a self-avoiding chain confined inside a cylindrical cavity, with diameter $D$, are probed using molecular dynamics simulations, scaling analysis, and analytical calculations. We obtain and confirm a simple scaling relation $-f \cdot D \sim R^{-9/4}$ in the strong-compression regime, while for weak deformations we find $f \cdot D = -A(R/R_0) + B (R/R_0)^{-2}$, where $A$ and $B$ are constants, $f$ the external force, and $R$ the chain extension (with $R_0$ its unperturbed value). For a strong stretch, we present a universal, analytical force-extension relation. Our results can be used to analyze the behavior of biomolecules in confinement.

cond-mat.soft↗

arXiv2008

Minimal models for proteins and RNA: From folding to function

We present a panoramic view of the utility of coarse-grained (CG) models to study folding and functions of proteins and RNA. Drawing largely on the methods developed in our group over the last twenty years, we describe a number of key applications ranging from folding of proteins with disulfide bonds to functions of molecular machines. After presenting the theoretical basis that justifies the use of CG models, we explore the biophysical basis for the emergence of a finite number of folds from lattice models. The lattice model simulations of approach to the folded state show that non-native interactions are relevant only early in the folding process - a finding that rationalizes the success of structure-based models that emphasize native interactions. Applications of off-lattice $C_α$ and models that explicitly consider side chains ($C_α$-SCM) to folding of $β$-hairpin and effects of macromolecular crowding are briefly discussed. Successful application of a new class of off-lattice model, referred to as the Self-Organized Polymer (SOP), is shown by describing the response of Green Fluorescent Protein (GFP) to mechanical force. The utility of the SOP model is further illustrated by applications that clarify the functions of the chaperonin GroEL and motion of the molecular motor kinesin. We also present two distinct models for RNA, namely, the Three Site Interaction (TIS) model and the SOP model, that probe forced unfolding and force quench refolding of a simple hairpin and {\it Azoarcus} ribozyme. The predictions based on the SOP model show that force-induced unfolding pathways of the ribozyme can be dramatically changed by varying the loading rate. We conclude with a discussion of future prospects for the use of coarse-grained models in addressing problems of outstanding interest in biology.

q-bio.BM↗

arXiv2008

Semiflexible Chains in Confined Spaces

We develop an analytical method for studying the properties of a non-interacting Wormlike Chain (WLC) in confined geometries. The mean field-like theory replaces the rigid constraints of confinement with average constraints, thus allowing us to develop a tractable method for treating a WLC wrapped on the surface of a sphere, and fully encapsulated within it. The efficacy of the theory is established by reproducing the exact correlation functions for a WLC confined to the surface of a sphere. In addition, the coefficients in the free energy are exactly calculated. We also describe the behavior of a surface-confined chain under external tension that is relevant for single molecule experiments on histone-DNA complexes. The force-extension curves display spatial oscillations, and the extension of the chain, whose maximum value is bounded by the sphere diameter, scales as $f^{-1}$ at large forces, in contrast to the unconfined chain that approaches the contour length as $f^{-1/2}$. A WLC encapsulated in a sphere, that is relevant for the study of the viral encapsulation of DNA, can also be treated using the MF approach. The predictions of the theory for various correlation functions are in excellent agreement with Langevin simulations. We find that strongly confined chains are highly structured by examining the correlations using a local winding axis. The predicted pressure of the system is in excellent agreement with simulations but, as is known, is significantly lower than the pressures seen for DNA packaged in viral capsids.

cond-mat.soft↗

arXiv2008

Force Dependent Hopping Rates of RNA Hairpins can be Estimated from Accurate Measurement of the Folding Landscapes

The sequence-dependent folding landscapes of nucleic acid hairpins reflect much of the complexity of biomolecular folding. Folding trajectories, generated using single molecule force clamp experiments by attaching semiflexible polymers to the ends of hairpins have been used to infer their folding landscapes. Using simulations and theory, we study the effect of the dynamics of the attached handles on the handle-free RNA free energy profile $F^o_{eq}(z_m)$, where $z_m$ is the molecular extension of the hairpin. Accurate measurements of $F^o_{eq}(z_m)$ requires stiff polymers with small $L/l_p$, where $L$ is the contour length of the handle, and $l_p$ is the persistence length. Paradoxically, reliable estimates of the hopping rates can only be made using flexible handles. Nevertheless, we show that the equilibrium free energy profile $F^o_{eq}(z_m)$ at an external tension $f_m$, the force ($f$) at which the folded and unfolded states are equally populated, in conjunction with Kramers' theory, can provide accurate estimates of the force-dependent hopping rates in the absence of handles at arbitrary values of $f$. Our theoretical framework shows that $z_m$ is a good reaction coordinate for nucleic acid hairpins under tension.

cond-mat.soft↗

arXiv2008

The role of internal chain dynamics on the rupture kinetics of adhesive contacts

We study the forced rupture of adhesive contacts between monomers that are not covalently linked in a Rouse chain. When the applied force ($f$) to the chain end is less than the critical force for rupture ($f_c$), the {\it reversible} rupture process is coupled to the internal Rouse modes. If $f/f_{c}$$>$1 the rupture is {\it irreversible}. In both limits, the non-exponential distribution of contact lifetimes, which depends sensitively on the location of the contact, follows the double-exponential (Gumbel) distribution. When two contacts are well separated along the chain, the rate limiting step in the {\it sequential} rupture kinetics is the disruption of the contact that is in the chain interior. If the two contacts are close to each other, they cooperate to sustain the stress, which results in an ``all-or-none'' transition.

cond-mat.soft↗

arXiv2007

Kinetics of Loop Formation in Polymer Chains

We investigate the kinetics of loop formation in flexible ideal polymer chains (Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is $τ_c\sim τ_0 N^2$ (where $τ_0$ is a microscopic time scale and $N$ is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when $a$, the capture radius for contact formation, exceeds $b$, the average distance between two connected beads. Simulations also show that, when $a < b$, $τ_c\sim N^{α_τ}$, where $1.5<{α_τ}\le 2$ in the range $7<N<200$ used in the simulations. By using a diffusion coefficient that is dependent on the length scales $a$ and $b$ (with $a<b$), which captures the two-stage mechanism by which looping occurs when $a < b$, we obtain an analytic expression for $τ_c$ that fits the simulation results well. The kinetics of contact formation between the ends of the chain are profoundly affected when interactions between monomers are taken into account. Remarkably, for $N < 100$ the values of $τ_c$ decrease by more than two orders of magnitude when the solvent quality changes from good to poor. Fits of the simulation data for $τ_c$ to a power law in $N$ ($τ_c\sim N^{α_τ}$) show that $α_τ$ varies from about 2.4 in a good solvent to about 1.0 in poor solvents. Loop formation in poor solvents, in which the polymer adopts dense, compact globular conformations, occurs by a reptation-like mechanism of the ends of the chain.

cond-mat.soft↗