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D. Thirumalai

Publications and source records attributed to D. Thirumalai.

At least 163 records · Page 9Linked to original sources
arXiv2004

Finite size effects on calorimetric cooperativity of two-state proteins

Finite size effects on the calorimetric cooperatity of the folding-unfolding transition in two-state proteins are considered using the Go lattice models with and without side chains. We show that for models without side chains a dimensionless measure of calorimetric cooperativity kappa2 defined as the ratio of the van't Hoff to calorimetric enthalpy does not depend on the number of amino acids N. The average value of kappa2 is about 3/4 which is lower than the experimental value kappa2=1. For models with side chains kappa2 approaches unity as kappa2 \sim N^mu, where exponent mu=0.17. Above the critical chain length Nc =135 these models can mimic the truly all-or-non folding-unfolding transition.

q-bio.BM↗
arXiv2004

Finite size effects on thermal denaturation of globular proteins

Finite size effects on the cooperative thermal denaturation of proteins are considered. A dimensionless measure of cooperativity, Omega, scales as N^zeta, where N is the number of amino acids. Surprisingly, we find that zeta is universal with zeta = 1 + gamma, where the exponent gamma characterizes the divergence of the susceptibility for a self-avoiding walk. Our lattice model simulations and experimental data are consistent with the theory. Our finding rationalizes the marginal stability of proteins and substantiates the earlier predictions that the efficient folding of two-state proteins requires the folding transition temperature to be close to the collapse temperature.

q-bio.BM↗
arXiv2004

Proteins associated with diseases show enhanced sequence correlation between charged residues

Function of proteins or a network of interacting proteins often involves communication between residues that are well separated in sequence. The classic example is the participation of distant residues in allosteric regulation. Bioinformatic and structural analysis methods have been introduced to infer residues that are correlated. Recently, increasing attention has been paid to obtain the sequence properties that determine the tendency of disease related proteins (Abeta peptides, prion proteins, transthyretin etc.) to aggregate and form fibrils. Motivated in part by the need to identify sequence characteristics that indicate a tendency to aggregate, we introduce a general method that probes covariations in charged residues along the sequence in a given protein family. The method, which involves computing the Sequence Correlation Entropy (SCE) using the quenched probability Psk(i,j) of finding a residue pair at a given sequence separation sk, allows us to classify protein families in terms of their SCE. Our general approach may be a useful way in obtaining evolutionary covariations of amino acid residues on a genome wide level.

q-bio.BM↗
arXiv2003

Bending rigidity of stiff polyelectrolyte chains: Single chain and a bundle of multichains

We study the bending rigidity of highly charged stiff polyelectrolytes, for both a single chain and many chains forming a bundle. A theory is developed to account for the interplay between competitive binding of counterions and charge correlations in softening the polyelectrolyte (PE) chains. The presence of even a small concentration of multivalent counterions leads to a dramatic reduction in the bending rigidity of the chains that are nominally stiffened by the repulsion between their backbone charges. The variation of the bending rigidity as a function of $f_{0}$, the fraction of charged monomers on the chain, does not exhibits simple scaling behavior; it grows with increasing $f_{0}$ below a critical value of $f_{0}$. Beyond the critical value, however, the chain becomes softer as $f_{0}$ increases. The bending rigidity also exhibits intriguing dependence on the concentration of multivalent counterion $n_{2}$; for highly charged PEs, the bending rigidity decreases as $n_2$ increases from zero, while it increases with increasing $n_{2}$ beyond a certain value of $n_{2}$. When polyelectrolyte chains form a $N$-loop condensate (e.g., a toroidal bundle formed by $N$ turns (winds) of the chain), the inter-loop coupling further softens the condensate, resulting in the bending free energy of the condensate that scales as $N$ for large $N$.

cond-mat.soft↗
arXiv2003

Thermal denaturation and folding rates of single domain proteins: size matters

We analyze the dependence of thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, N. Using lattice Go models we show that DeltaT/T_F ~ N^-1, where T_F is the folding transition temperature and DeltaT is the folding transition width. This finding is consistent with finite size effects expected for the systems undergoing a phase transition from a disordered to an ordered phase. The dependence of the folding rates k_F on N for lattice models and the dataset of 57 proteins and peptides shows that k_F = k_F^0 exp(-CN^beta) provides a good fit, if 0 < beta <= 2/3 and C is a constant. We find that k_F = k_F^0 exp(-1.1N^0.5) with k_F^0 =(0.4x10^-6 s)^-1 can estimate optimal protein folding rates to within an order of magnitude in most cases. By using this fit for a set of proteins with beta-sheet topology we find that k_F^0 is approximately equal to k_U^0, the prefactor for unfolding rates. The maximum ratio of k_U^0/k_F^0 is 10 for this class of proteins.

q-bio.BM↗
arXiv2003

Asymmetry in the shapes of folded and denatured states of proteins

The asymmetry in the shapes of folded and unfolded states are probed using two parameters, one being a measure of the sphericity and the other that describes the shape. For the folded states, whose interiors are densely packed, the radii of gyration (Rg) and these two parameters are calculated using the coordinates of the experimentally determined structures. Although Rg scales as expected for maximally compact structures, the distributions of the shape parameters show that there is considerable asymmetry in the shapes of folded structures. The degree of asymmetry is greater for proteins that form oligomers. Analysis of the two- and three-body contacts in the native structures shows that the presence of near equal number of contacts between backbone and side-chains and between side-chains gives rise to dense packing. We suggest that proteins with relatively large values of shape parameters can tolerate volume mutations without greatly affecting the network of contacts or their stability. To probe shape characteristics of denatured states we have developed a model of a WW-like domain. The shape parameters, which are calculated using Langevin simulations, change dramatically in the course of coil to globule transition. Comparison of the values of shape parameters between the globular state and the folded state of WW domain shows that both energetic (especially dispersion in the hydrophobic interactions) and steric effects are important in determining packing in proteins.

q-bio.BM↗
arXiv2003

Anisotropic coarse-grained statistical potentials improve the ability to identify native-like protein structures

We present a new method to extract distance and orientation dependent potentials between amino acid side chains using a database of protein structures and the standard Boltzmann device. The importance of orientation dependent interactions is first established by computing orientational order parameters for proteins with alpha-helical and beta-sheet architecture. Extraction of the anisotropic interactions requires defining local reference frames for each amino acid that uniquely determine the coordinates of the neighboring residues. Using the local reference frames and histograms of the radial and angular correlation functions for a standard set of non-homologue protein structures, we construct the anisotropic pair potentials. The performance of the orientation dependent potentials was studied using a large database of decoy proteins. The results demonstrate that the new distance and orientation dependent residue-residue potentials present a significantly improved ability to recognize native folds from a set of native and decoy protein structures.

physics.chem-ph↗
arXiv2002

Dependence of folding rates on protein length

Using three-dimensional Go lattice models with side chains for proteins, we investigate the dependence of folding times on protein length. In agreement with previous theoretical predictions, we find that the folding time grows as a power law with the chain length N with exponent $λ\approx 3.6$ for the Go model, in which all native interactions (i.e., between all side chains and backbone atoms) are uniform. If the interactions between side chains are given by pairwise statistical potentials, which introduce heterogeneity in the contact energies, then the power law fits yield large $λ$ values that typically signifies a crossover to an underlying activated process. Accordingly, the dependence of folding time is best described by the stretched exponential \exp(\sqrt{N}). The study also shows that the incorporation of side chains considerably slows down folding by introducing energetic and topological frustration.

cond-mat.soft↗
arXiv2002

Folding in lattice models with side chains

The folding kinetics of three-dimensional lattice Go models with side chains is studied using two different Monte Carlo move sets. A flexible move set based on single, double and triple backbone moves is found to be far superior compared to the standard Monte Carlo dynamics. It was found that the folding time grows as a power law with the chain length and the corresponding exponent $λ\approx 3.6$ for Go models. The study shows that the incorporation of side chains dramatically slows down folding rates.

cond-mat.soft↗
arXiv2001

Introducing Protein Folding Using Simple Models

We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use of lattice models to understand the selection of the limited set of viable protein folds; (ii) the relationship between structure and sequence spaces; (iii) the application of lattice models for studying folding mechanisms (topological frustration, kinetic partitioning mechanism). Classification of folding scenarios based on the intrinsic thermodynamic properties of a sequence (namely, the collapse and folding transition temperatures) is outlined. A brief discussion of random heteropolymer model is also presented.

cond-mat.soft↗
arXiv2000

Kinetics of condensation of flexible polyelectrolytes in poor solvents: effects of solvent quality, valence and size of counterions

The collapse kinetics of strongly charged polyelectrolytes in poor solvents is investigated by Langevin simulations and scaling arguments. The rate of collapse increases sharply as the valence of counterions, z, increases from one to four. The combined system of the collapsed chain and the condensed counterions forms a Wigner crystal when the solvent quality is not too poor provided z >= 2. For very poor solvents the morphology of the collapsed structure resembles a Wigner glass. For a fixed z and quality of the solvent the efficiency of collapse decreases dramatically as the size of the counterion increases. A valence dependent diagram of states in poor solvents is derived.

cond-mat.soft↗
arXiv2000

Dynamics of Collapse of flexible Polyelectrolytes and Polyampholytes

We provide a theory for the dynamics of collapse of strongly charged polyelectrolytes (PEs) and flexible polyampholytes (PAs) using Langevin equation. After the initial stage, in which counterions condense onto PE, the mechanism of approach to the globular state is similar for PE and PA. In both instances, metastable pearl-necklace structures form in characteristic time scale that is proportional to N^{4/5} where N is the number of monomers. The late stage of collapse occurs by merger of clusters with the largest one growing at the expense of smaller ones (Lifshitz- Slyozov mechanism). The time scale for this process T_{COLL} N. Simulations are used to support the proposed collapse mechanism for PA and PE.

cond-mat.soft↗
arXiv1999

Emergence of stable and fast folding protein structures

The number of protein structures is far less than the number of sequences. By imposing simple generic features of proteins (low energy and compaction) on all possible sequences we show that the structure space is sparse compared to the sequence space. Even though the sequence space grows exponentially with N (the number of amino acids) we conjecture that the number of low energy compact structures only scales as ln N. This implies that many sequences must map onto countable number of basins in the structure space. The number of sequences for which a given fold emerges as a native structure is further reduced by the dual requirements of stability and kinetic accessibility. The factor that determines the dual requirement is related to the sequence dependent temperatures, T_θ(collapse transition temperature) and T_F (folding transition temperature). Sequences, for which σ=(T_θ-T_F)/T_θis small, typically fold fast by generically collapsing to the native-like structures and then rapidly assembling to the native state. Such sequences satisfy the dual requirements over a wide temperature range. We also suggest that the functional requirement may further reduce the number of sequences that are biologically competent. The scheme developed here for thinning of the sequence space that leads to foldable structures arises naturally using simple physical characteristics of proteins. The reduction in sequence space leading to the emergence of foldable structures is demonstrated using lattice models of proteins.

cond-mat.soft↗
arXiv1999

Stretching Single Domain Proteins: Phase Diagram and Kinetics of Force-Induced Unfolding

Single molecule force spectroscopy reveals unfolding of domains in titin upon stretching. We provide a theoretical framework for these experiments by computing the phase diagrams for force-induced unfolding of single domain proteins using lattice models. The results show that two-state folders (at zero force) unravel cooperatively whereas stretching of non-two-state folders occurs through intermediates. The stretching rates of individual molecules show great variations reflecting the heterogeneity of force-induced unfolding pathways. The approach to the stretched state occurs in a step-wise "quantized" manner. Unfolding dynamics depends sensitively on topology. The unfolding rates increase exponentially with force f till an optimum value which is determined by the barrier to unfolding when f=0. A mapping of these results to proteins shows qualitative agreement with force-induced unfolding of Ig-like domains in titin. We show that single molecule force spectroscopy can be used to map the folding free energy landscape of proteins in the absence of denaturants.

cond-mat.soft↗
arXiv1998

Persistence Length of Flexible Polyelectrolyte Chains

We calculate the dependence of the electrostatic persistence length, l_e, of weakly charged flexible polyelectrolyte chains using a self-consistent variational theory. The variation of l_e with κ, the inverse Debye screening length, is controlled by the parameter l_0 l_B/A^2, where l_0 is the bare persistence length, l_B is the Bjerrum length, and A is the mean distance between charges along the chain. Several distinct regimes for the dependence of l_e on κemerge depending on the value of l_0 l_B/A^2. We show that when l_0 l_B /A^2 << 1 we recover the classical result, l_e \propto κ^{-2}. For intermediate values of l_0 l_B /A^2, l_e \propto κ^{-1}. In this regime one can also get l_e \propto κ^{-y} with y < 1 depending on the strength of the Coulomb interaction. Qualitative comparisons between our theory and simulations as well as other theories are presented.

cond-mat.stat-mech↗
arXiv1998

Stretching DNA: Role of electrostatic interaction

The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find theoreticlly and by a simple blob picture that the extension scales as fr_D where r_D is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like conformations are possible. In this regime the extension approaches the contour length as f^{-1/2} where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out.

cond-mat.soft↗
arXiv1998

Fractal Analysis of Protein Potential Energy Landscapes

The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the exponent γ, is almost independent of temperature and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior.

cond-mat.soft↗