arXiv subjects

D. Thirumalai

Publications and source records attributed to D. Thirumalai.

At least 145 records · Page 8Linked to original sources

arXiv2007

Allosteric communication in Dihydrofolate Reductase: Signaling network and pathways for closed to occluded transition and back

E. Coli. dihydrofolate reductase (DHFR) undergoes conformational transitions between the closed (CS) and occluded (OS) states which, respectively, describe whether the active site is closed or occluded by the Met20 loop. A sequence-based approach is used to identify a network of residues that represents the allostery wiring diagram. We also use a self-organized polymer model to monitor the kinetics of the CS->OS and the reverse transitions. a sliding motion of Met20 loop is observed. The residues that facilitate the Met20 loop motion are part of the network of residues that transmit allosteric signals during the CS->OS transition.

q-bio.BM↗

arXiv2007

Stretching Homopolymers

Force induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with $N$ monomers, to force ($f$) in good and poor solvents. In good solvents and for {sufficiently large} $N$ we show, in accord with scaling predictions, that the mean extension along the $f$ axis $ \sim f$ for small $f$, and $ \sim f^{2/3}$ (the Pincus regime) for intermediate values of $f$. The theoretical predictions for $\la Z\ra$ as a function of $f$ are in excellent agreement with simulations for N=100 and 1600. However, even with N=1600, the expected Pincus regime is not observed due to the the breakdown of the assumptions in the blob picture for finite $N$. {We predict the Pincus scaling in a good solvent will be observed for $N\gtrsim 10^5$}. The force-dependent structure factors for a polymer in a poor solvent show that there are a hierarchy of structures, depending on the nature of the solvent. For a weakly hydrophobic polymer, various structures (ideal conformations, self-avoiding chains, globules, and rods) emerge on distinct length scales as $f$ is varied. A strongly hydrophobic polymer remains globular as long as $f$ is less than a critical value $f_c$. Above $f_c$, an abrupt first order transition to a rod-like structure occurs. Our predictions can be tested using single molecule experiments.

cond-mat.soft↗

arXiv2006

Effect of finite size on cooperativity and rates of protein folding

We analyze the dependence of cooperativity of the thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, $N$, using lattice models with side chains,off-lattice Go models and the available experimental data. A dimensionless measure of cooperativity, $Ω_c$ ($0 < Ω_c < \infty$), scales as $Ω_c \sim N^ζ$. The results of simulations and the analysis of experimental data further confirm the earlier prediction that $ζ$ is universal with $ζ= 1 +γ$, where exponent $γ$ characterizes the susceptibility of a self-avoiding walk. This finding suggests that the structural characteristics in the denaturated state are manifested in the folding cooperativity at the transition temperature. The folding rates $k_F$ for the Go models and a dataset of 69 proteins can be fit using $k_F = k_F^0 \exp(-cN^β)$. Both $β= 1/2$ and 2/3 provide a good fit of the data. We find that $k_F = k_F^0 \exp(-cN^{1/2})$, with the average (over the dataset of proteins) $k_F^0 \approx (0.2μs)^{-1}$ and $c \approx 1.1$, can be used to estimate folding rates to within an order of magnitude in most cases. The minimal models give identical $N$ dependence with $c \approx 1$. The prefactor for off-lattice Go models is nearly four orders of magnitude larger than the experimental value.

q-bio.BM↗

arXiv2006

Measuring the energy landscape roughness and the transition state location of biomolecules using single molecule mechanical unfolding experiments

Single molecule mechanical unfolding experiments are beginning to provide profiles of the complex energy landscape of biomolecules. In order to obtain reliable estimates of the energy landscape characteristics it is necessary to combine the experimental measurements with sound theoretical models and simulations. Here, we show how by using temperature as a variable in mechanical unfolding of biomolecules in laser optical tweezer or AFM experiments the roughness of the energy landscape can be measured without making any assumptions about the underlying reaction oordinate. The efficacy of the formalism is illustrated by reviewing experimental results that have directly measured roughness in a protein-protein complex. The roughness model can also be used to interpret experiments on forced-unfolding of proteins in which temperature is varied. Estimates of other aspects of the energy landscape such as free energy barriers or the transition state (TS) locations could depend on the precise model used to analyze the experimental data. We illustrate the inherent difficulties in obtaining the transition state location from loading rate or force-dependent unfolding rates. Because the transition state moves as the force or the loading rate is varied it is in general difficult to invert the experimental data unless the curvature at the top of the one dimensional free energy profile is large, i.e the barrier is sharp. The independence of the TS location on force holds good only for brittle or hard biomolecules whereas the TS location changes considerably if the molecule is soft or plastic. We also comment on the usefulness of extension of the molecule as a surrogate reaction coordinate especially in the context of force-quench refolding of proteins and RNA.

cond-mat.soft↗

arXiv2006

Dynamics of allosteric transitions in GroEL

The chaperonin GroEL-GroES, a machine which helps some proteins to fold, cycles through a number of allosteric states, the $T$ state, with high affinity for substrate proteins (SPs), the ATP-bound $R$ state, and the $R^{\prime\prime}$ ($GroEL-ADP-GroES$) complex. Structures are known for each of these states. Here, we use a self-organized polymer (SOP) model for the GroEL allosteric states and a general structure-based technique to simulate the dynamics of allosteric transitions in two subunits of GroEL and the heptamer. The $T \to R$ transition, in which the apical domains undergo counter-clockwise motion, is mediated by a multiple salt-bridge switch mechanism, in which a series of salt-bridges break and form. The initial event in the $R \to R^{\prime\prime}$ transition, during which GroEL rotates clockwise, involves a spectacular outside-in movement of helices K and L that results in K80-D359 salt-bridge formation. In both the transitions there is considerable heterogeneity in the transition pathways. The transition state ensembles (TSEs) connecting the $T$, $R$, and $R^{\prime\prime}$ states are broad with the the TSE for the $T \to R$ transition being more plastic than the $R\to R^{\prime\prime}$ TSE. The results suggest that GroEL functions as a force-transmitting device in which forces of about (5-30) pN may act on the SP during the reaction cycle.

q-bio.BM↗

arXiv2006

Pathways and kinetic barriers in mechanical unfolding and refolding of RNA and proteins

Using self-organized polymer models, we predict mechanical unfolding and refolding pathways of ribo-zymes, and the green fluorescent protein. In agreement with experiments, there are between six and eight unfolding transitions in the Tetrahymena ribozyme. Depending on the loading rate, the number of rips in the force-ramp unfolding of the Azoarcus ribozymes is between two and four. Force-quench refolding of the P4-P6 subdomain of the Tetrahymena ribozyme occurs through a compact intermediate. Subsequent formation of tertiary contacts between helices P5b-P6a and P5a/P5c-P4 leads to the native state. The force-quench refolding pathways agree with ensemble experiments. In the dominant unfolding route, the N-terminal a helix of GFP unravels first, followed by disruption of the N terminus b strand. There is a third intermediate that involves disruption of three other strands. In accord with experiments, the force-quench refolding pathway of GFP is hierarchic, with the rate-limiting step being the closure of the barrel.

q-bio.BM↗

arXiv2006

Size, shape, and flexibility of RNA structures

Determination of sizes and flexibilities of RNA molecules is important in understanding the nature of packing in folded structures and in elucidating interactions between RNA and DNA or proteins. Using the coordinates of the structures of RNA in the Protein Data Bank we find that the size of the folded RNA structures, measured using the radius of gyration, $R_G$, follows the Flory scaling law, namely, $R_G =5.5 N^{1/3}$ Åwhere N is the number of nucleotides. The shape of RNA molecules is characterized by the asphericity $Δ$ and the shape $S$ parameters that are computed using the eigenvalues of the moment of inertia tensor. From the distribution of $Δ$, we find that a large fraction of folded RNA structures are aspherical and the distribution of $S$ values shows that RNA molecules are prolate ($S>0$). The flexibility of folded structures is characterized by the persistence length $l_p$. By fitting the distance distribution function $P(r)$ to the worm-like chain model we extracted the persistence length $l_p$. We find that $l_p\approx 1.5 N^{0.33}$ Å. The dependence of $l_p$ on $N$ implies the average length of helices should increases as the size of RNA grows. We also analyze packing in the structures of ribosomes (30S, 50S, and 70S) in terms of $R_G$, $Δ$, $S$, and $l_p$. The 70S and the 50S subunits are more spherical compared to most RNA molecules. The globularity in 50S is due to the presence of an unusually large number (compared to 30S subunit) of small helices that are stitched together by bulges and loops. Comparison of the shapes of the intact 70S ribosome and the constituent particles suggests that folding of the individual molecules might occur prior to assembly.

q-bio.BM↗

arXiv2006

Mechanical unfolding of RNA: From hairpins to structures with internal multiloops

Mechanical unfolding of RNA structures, ranging from hairpins to ribozymes, using laser optical tweezer (LOT) experiments have begun to reveal the features of the energy landscape that cannot be easily explored using conventional experiments. Upon application of constant force ($f$), RNA hairpins undergo cooperative transitions from folded to unfolded states whereas subdomains of ribozymes unravel one at a time. Here, we use a self-organized polymer (SOP) model and Brownian dynamics simulations to probe mechanical unfolding at constant force and constant-loading rate of four RNA structures of varying complexity. Our work shows (i) the response of RNA to force is largely determined by the native structure; (ii) only by probing mechanical unfolding over a wide range of forces can the underlying energy landscape be fully explored.

q-bio.BM↗

arXiv2006

Hydrophobic and Ionic Interactions in Nano-sized Water Droplets

We investigate the solvation of methane and methane decorated with charges in spherically confined water droplets. Free energy profiles for a single methane molecule in droplets, ranging in diameter D, from 1 to 4 nm, show that the droplet surfaces are strongly favorable as compared to the interior. From the temperature dependence of the free energy in D=3 nm, we show that this effect is entropically driven. The potentials of mean force (PMFs) between two methane molecules show that the solvent separated minimum in the bulk is completely absent in confined water, independent of the droplet size since the solute particles are primarily associated with the droplet surface. The tendency of methanes with charges (Mq+ and Mq- with q+ = q- = 0.4e, where e is the electronic charge) to be pinned at the surface depends dramatically on the size of the water droplet. When D=4 nm, the ions prefer the interior whereas for D<4 nm the ions are localized at the surface, but with much less tendency than for methanes. Increasing the ion charge to e makes the surface strongly unfavorable. Reflecting the charge asymmetry of the water molecule, negative ions have a stronger preference for the surface compared to positive ions of the same charge magnitude. With increasing droplet size, the PMFs between Mq+ and Mq- show decreasing influence of the boundary due to the reduced tendency for surface solvation. We also show that as the solute charge density decreases the surface becomes less unfavorable. The implications of our results for the folding of proteins in confined spaces are outlined.

physics.chem-ph↗

arXiv2006

Scenarios for protein aggregation: Molecular Dynamics simulations and Bioinformatic Analysis

The need to understand the assembly kinetics of fibril formation has become urgent because of the realization that soluble oligomers of amyloidogenic peptides may be even more neurotoxic than the end product, namely, the amyloid fibrils. In order to fully understand the routes to fibril formation one has to characterize the major species in the assembly pathways. The characterization of the energetics and dynamics of oligomers (dimers, trimers etc) is difficult using experiments alone because they undergo large conformational fluctuations. In this context, carefully planned molecular dynamics simulation studies, computations using coarse-grained models, and bioinformatic analysis have given considerable insights into the early events in the route to fibril formation. Here, we describe progress along this direction using examples taken largely from our own work. In this chapter, we focus on aspects of protein aggregation using Abeta-peptides and prion proteins as examples.

q-bio.BM↗

arXiv2006

Forced-unfolding and force-quench refolding of RNA hairpins

Using coarse-grained model we have explored forced-unfolding of RNA hairpin as a function of $f_S$ and the loading rate ($r_f$). The simulations and theoretical analysis have been done without and with the handles that are explicitly modeled by semiflexible polymer chains. The mechanisms and time scales for denaturation by temperature jump and mechanical unfolding are vastly different. The directed perturbation of the native state by $f_S$ results in a sequential unfolding of the hairpin starting from their ends whereas thermal denaturation occurs stochastically. From the dependence of the unfolding rates on $r_f$ and $f_S$ we show that the position of the unfolding transition state (TS) is not a constant but moves dramatically as either $r_f$ or $f_S$ is changed. The TS movements are interpreted by adopting the Hammond postulate for forced-unfolding. Forced-unfolding simulations of RNA, with handles attached to the two ends, show that the value of the unfolding force increases (especially at high pulling speeds) as the length of the handles increases. The pathways for refolding of RNA from stretched initial conformation, upon quenching $f_S$ to the quench force $f_Q$, are highly heterogeneous. The refolding times, upon force quench, are at least an order of magnitude greater than those obtained by temperature quench. The long $f_Q$-dependent refolding times starting from fully stretched states are analyzed using a model that accounts for the microscopic steps in the rate limiting step which involves the trans to gauche transitions of the dihedral angles in the GAAA tetraloop. The simulations with explicit molecular model for the handles show that the dynamics of force-quench refolding is strongly dependent on the interplay of their contour length and the persistence length, and the RNA persistence length.

q-bio.BM↗

arXiv2006

Kinetics of Interior Loop Formation in Semiflexible Chains

Loop formation between monomers in the interior of semiflexible chains describes elementary events in biomolecular folding and DNA bending. We calculate analytically the interior distance distribution function for semiflexible chains using a mean-field approach. Using the potential of mean force derived from the distance distribution function we present a simple expression for the kinetics of interior looping by adopting Kramers theory. For the parameters, that are appropriate for DNA, the theoretical predictions in comparison to the case are in excellent agreement with explicit Brownian dynamics simulations of worm-like chain (WLC) model. The interior looping times ($τ_{IC}$) can be greatly altered in cases when the stiffness of the loop differs from that of the dangling ends. If the dangling end is stiffer than the loop then $τ_{IC}$ increases for the case of the WLC with uniform persistence length. In contrast, attachment of flexible dangling ends enhances rate of interior loop formation. The theory also shows that if the monomers are charged and interact via screened Coulomb potential then both the cyclization ($τ_c$) and interior looping ($τ_{IC}$) times greatly increase at low ionic concentration. Because both $τ_c$ and $τ_{IC}$ are determined essentially by the effective persistence length ($l_p^{(R)}$) we computed $l_p^{(R)}$ by varying the range of the repulsive interaction between the monomers. For short range interactions $l_p^{(R)}$ nearly coincides with the bare persistence length which is determined largely by the backbone chain connectivity. This finding rationalizes the efficacy of describing a number of experimental observations (response of biopolymers to force and cyclization kinetics) in biomolecules using WLC model with an effective persistence length.

cond-mat.soft↗

arXiv2006

Mapping the energy landscape of biomolecules using single molecule force correlation spectroscopy (FCS): Theory and applications

In the current AFM experiments the distribution of unfolding times, P(t), is measured by applying a constant stretching force f_s from which the apparent unfolding rate is obtained. To describe the complexity of the underlying energy landscape requires additional probes that can incorporate the dynamics of tension propagation and relaxation of the polypeptide chain upon force quench. We introduce a theory of force correlation spectroscopy (FCS) to map the parameters of the energy landscape of proteins. In the FCS the joint distribution, P(T,t) of folding and unfolding times is constructed by repeated application of cycles of stretching at constant fs, separated by release periods T during which the force is quenched to f_q<f_s. During the release period, the protein can collapse to a manifold of compact states or refold. We show that P(T,t) can be used to resolve the kinetics of unfolding as well as formation of native contacts and to extract the parameters of the energy landscape using chain extension as the reaction coordinate and P(T,t). We illustrate the utility of the proposed formalism by analyzing simulations of unfolding-refolding trajectories of a coarse-grained protein S1 with beta-sheet architecture for several values of f_s, T and f_q=0. The simulations of stretch-relax trajectories are used to map many of the parameters that characterize the energy landscape of S1.

cond-mat.soft↗

arXiv2005

Persistence Length Changes Dramatically as RNA Folds

We determine the persistence length, $l_p$, for a bacterial group I ribozyme as a function of concentration of monovalent and divalent cations by fitting the distance distribution functions $P(r)$ obtained from small angle X-ray scattering intensity data to the asymptotic form of the calculated $P_{WLC}(r)$ for a worm-like chain (WLC). The $l_p$ values change dramatically over a narrow range of \Mg concentration from $\sim$21 Åin the unfolded state (\textbf{U}) to $\sim$10 Åin the compact ($\mathrm{I_C}$) and native states. Variations in $l_p$ with increasing \Na concentration are more gradual. In accord with the predictions of polyelectrolyte theory we find $l_p \propto 1/ κ^2$ where $κ$ is the inverse Debye-screening length.

q-bio.BM↗

arXiv2005

Influence of surface interactions on folding and forced unbinding of semiflexible chains

We investigate the folding and forced-unbinding transitions of adsorbed semiflexible polymer chains using theory and simulations. These processes describe biologically relevant phenomena that include adhesive interactions between proteins and tethering of receptors to cell walls. The binding interface is modeled as a solid surface and the worm-like chain is used for the semiflexible chain. Using Langevin simulations we examine the ordering kinetics of racquet-like and toroidal structures in the presence of attractive interaction between the surface and the polymer chain. For a range of interactions, temperature, and the persistence length l_p we obtained the monomer density distribution n(x) for all the relevant morphologies. The simulated results for n(x) are in good agreement with theory. The formation of toroids on the surface appears to be a first order transition. Chain-surface interaction is probed by subjecting the surface structures to a pulling force f. The average extension x as a function of f exhibit sigmoidal profile with sharp all-or-none transition at the unfolding f_c which increases for more structured states. Simulated x compare well with the theoretical predictions. The critical force f_c is a function of l_s/l_c for a fixed temperature, where l_c, l_s are the length scales that express the strength of the intramolecular and chain-surface attraction, respectively. For a fixed l_s, f_c increases as l_p decreases.

cond-mat.soft↗

arXiv2005

Probing protein-protein interactions by dynamic force correlated spectroscopy (FCS)

We develop a formalism for single molecule dynamic force spectroscopy to map the energy landscape of protein-protein complex ($P_1$$P_2$). The joint distribution $P(τ_1,τ_2)$ of unbinding lifetimes $τ_1$ and $τ_2$ measurable in a compression-tension cycle, which accounts for the internal relaxation dynamics of the proteins under tension, shows that the histogram of $τ_1$ is not Poissonian. The theory is applied to the forced unbinding of protein $P_1$, modeled as a wormlike chain, from $P_1$$P_2$. We propose a new class of experiments which can resolve the effect of internal protein dynamics on the unbinding lifetimes.

cond-mat.soft↗

arXiv2005

The shape of a flexible polymer in a cylindrical pore

We calculate the mean end-to-end distance ($R$) of a self-avoiding polymer encapsulated in an infinitely long cylinder with radius $D$. A self-consistent perturbation theory is used to calculate $R$ as a function of $D$ for impenetrable hard walls and soft walls. In both cases, $R$ obeys the predicted scaling behavior in the limit of large and small $D$. The crossover from the three dimensional behavior ($D\to\infty$) to the fully stretched one dimensional case ($D\to 0$) is non-monotonic. The minimum value of $R$ is found at $D\sim 0.46 R_F$, where $R_F$ is the Flory radius of $R$ at $D \to \infty$. The results for soft walls map onto the hard wall case with a larger cylinder radius.

cond-mat.soft↗

arXiv2005

Mechanical unfolding of RNA hairpins

Mechanical unfolding trajectories, generated by applying constant force in optical tweezer experiments, show that RNA hairpins and the P5abc subdomain of the group I intron unfold reversibly. We use coarse-grained Go-like models for RNA hairpins to explore forced-unfolding over a broad range of temperatures. A number of predictions that are amenable to experimental tests are made. At the critical force the hairpin jumps between folded and unfolded conformations without populating any discernible intermediates. The phase diagram in the force-temperature (f,T) plane shows that the hairpin unfolds by an all-or-none process. The cooperativity of the unfolding transition increases dramatically at low temperatures. Free energy of stability, obtained from time averages of mechanical unfolding trajectories, coincide with ensemble averages which establishes ergodicity. The hopping time between the the native basin of attraction (NBA) and the unfolded basin increases dramatically along the phase boundary. Thermal unfolding is stochastic whereas mechanical unfolding occurs in "quantized steps" with great variations in the step lengths. Refolding times, upon force quench, from stretched states to the NBA is "at least an order of magnitude" greater than folding times by temperature quench. Upon force quench from stretched states the NBA is reached in at least three stages. In the initial stages the mean end-to-end distance decreases nearly continuously and only in the last stage there is a sudden transition to the NBA. Because of the generality of the results we propose that similar behavior should be observed in force quench refolding of proteins.

q-bio.BM↗