Biology subjects

Dave Thirumalai

Publications and source records attributed to Dave Thirumalai.

9 recordsLinked to original sources

bioRxiv2016

Kinematics of the Lever Arm Swing in Myosin VI

Myosin VI (MVI) is the only known member of the myosin superfamily that, upon dimerization, walks processively towards the pointed end of the actin filament. The leading head of the dimer directs the trailing head forward with a power stroke, a conformational change of the motor domain exaggerated by the lever arm. Using a new coarse-grained model for the power stroke of a single MVI, we provide the molecular basis for its motility. We show that the power stroke occurs in two major steps: first, the motor domain attains the post-stroke conformation without directing the lever arm forward; second, the lever arm reaches the post-stroke orientation by undergoing a rotational diffusion. From the analysis of the trajectories, we discover that the potential that directs the rotating lever arm towards the post-stroke conformation is almost flat, implying that the lever arm rotation is mostly un-coupled from the motor domain. Because a backward load comparable with the largest inter-head tension in a MVI dimer prevents the rotation of the lever arm, our model suggests that the leading-head lever arm of a MVI dimer is uncoupled, in accord with the inference drawn from polarized Total Internal Reflection Fluorescence (polTIRF) experiments. Our simulations are in quantitative agreement with polTIRF experiments, which validates our structural insights. Finally, we discuss the implications of our model in explaining the broad step-size distribution of MVI stepping pattern, and we make testable predictions.

Biophysics↗

bioRxiv2016

Ripping RNA by Force using Gaussian Network Models

Using force as a probe to map the folding landscapes of RNA molecules has become a reality thanks to major advances in single molecule pulling experiments. Although the unfolding pathways under tension are complicated to predict studies in the context of proteins have shown that topology plays is the major determinant of the unfolding landscapes. By building on this finding we study the responses of RNA molecules to force by adapting Gaussian network model (GNM) that represents RNAs using a bead-spring network with isotropic interactions. Cross-correlation matrices of residue fluctuations, which are analytically calculated using GNM even upon application of mechanical force, show distinct allosteric communication as RNAs rupture. The model is used to calculate the force-extension curves at full thermodynamic equilibrium, and the corresponding unfolding pathways of four RNA molecules subject to a quasi-statically increased force. Our study finds that the analysis using GNM captures qualitatively the unfolding pathway of T. ribozyme elucidated by the optical tweezers measurement. However, the simple model is not sufficient to capture subtle features, such as bifurcation in the unfolding pathways or the ion effects, in the forced-unfolding of RNAs.

Biophysics↗

bioRxiv2016

Protein Collapse is Encoded in the Folded State Architecture

Folded states of single domain globular proteins, the workhorses in cells, are compact with high packing density. It is known that the radius of gyration, Rg, of both the folded and unfolded (created by adding denaturants) states increase as N{nu} where N is the number of amino acids in the protein. The values of the celebrated Flory exponent{nu} are, respectively, [Formula], and {approx} 0.6 in the folded and unfolded states, which coincide with those found in homopolymers in poor and good solvents, respectively. However, the extent of compaction of the unfolded state of a protein under low denaturant concentration, conditions favoring the formation of the folded state, is unknown. This problem which goes to the heart of how proteins fold, with implications for the evolution of foldable sequences, is unsolved. We develop a theory based on polymer physics concepts that uses the contact map of proteins as input to quantitatively assess collapsibility of proteins. The model, which includes only two-body excluded volume interactions and attractive interactions reflecting the contact map, has only expanded and compact states. Surprisingly, we find that although protein collapsibility is universal, the propensity to be compact depends on the protein architecture. Application of the theory to over two thousand proteins shows that the extent of collapsibility depends not only on N but also on the contact map reflecting the native fold structure. A major prediction of the theory is that {beta}-sheet proteins are far more collapsible than structures dominated by -helices. The theory and the accompanying simulations, validating the theoretical predictions, fully resolve the apparent controversy between conclusions reached using different experimental probes assessing the extent of compaction of a couple proteins. As a by product, we show that the theory correctly predicts the scaling of the collapse temperature of homopolymers as a function of the number of monomers. By calculating the criterion for collapsibility as a function of protein length we provide quantitative insights into the reasons why single domain proteins are small and the physical reasons for the origin of multi-domain proteins. We also show that non-coding RNA molecules, whose collapsibility is similar to proteins with {beta}-sheet structures, must undergo collapse prior to folding, adding support to \"Compactness Selection Hypothesis\" proposed in the context of RNA compaction.

Biophysics↗

bioRxiv2016

Noise Control In Gene Regulatory Networks With Negative Feedback

Genes and proteins regulate cellular functions through complex circuits of biochemical reactions. Fluctuations in the components of these regulatory networks result in noise that invariably corrupts the signal, possibly compromising function. Here, we create a practical formalism based on ideas introduced by Wiener and Kolmogorov (WK) for filtering noise in engineered communications systems to quantitatively assess the extent to which noise can be controlled in biological processes involving negative feedback. Application of the theory, which reproduces the previously proven scaling of the lower bound for noise suppression in terms of the number of signaling events, shows that a tetracycline repressor-based negative-regulatory gene circuit behaves as a WK filter. For the class of Hill-like nonlinear regulatory functions, this type of filter provides the optimal reduction in noise. Our theoretical approach can be readily combined with experimental measurements of response functions in a wide variety of genetic circuits, to elucidate the general principles by which biological networks minimize noise.

Biophysics↗

bioRxiv2016

Discrete step sizes of molecular motors lead to bimodal non-Gaussian velocity distributions under force

Fluctuations in the physical properties of biological machines are inextricably linked to their functions. Distributions of run-lengths and velocities of processive molecular motors, like kinesin-1, are accessible through single molecule techniques, yet there is lack a rigorous theoretical model for these probabilities up to now. We derive exact analytic results for a kinetic model to predict the resistive force (F) dependent velocity (P(v)) and run-length (P(n)) distribution functions of generic finitely processive molecular motors that take forward and backward steps on a track. Our theory quantitatively explains the zero force kinesin-1 data for both P(n) and P(v) using the detachment rate as the only parameter, thus allowing us to obtain the variations of these quantities under load. At non-zero F, P(v) is non-Gaussian, and is bimodal with peaks at positive and negative values of v. The prediction that P(v) is bimodal is a consequence of the discrete step-size of kinesin-1, and remains even when the step-size distribution is taken into account. Although the predictions are based on analyses of kinesin-1 data, our results are general and should hold for any processive motor, which walks on a track by taking discrete steps.

Biophysics↗

bioRxiv2016

Salt Effects on the Thermodynamics of a Frameshifting RNA Pseudoknot under Tension

Because of the potential link between -1 programmed ribosomal frameshifting and response of a pseudoknot (PK) RNA to force, a number of single molecule pulling experiments have been performed on PKs to decipher the mechanism of programmed ribosomal frameshifting. Motivated in part by these experiments, we performed simulations using a coarse-grained model of RNA to describe the response of a PK over a range of mechanical forces (fs) and monovalent salt concentrations (Cs). The coarse-grained simulations quantitatively reproduce the multistep thermal melting observed in experiments, thus validating our model. The free energy changes obtained in simulations are in excellent agreement with experiments. By varying f and C, we calculated the phase diagram that shows a sequence of structural transitions, populating distinct intermediate states. As f and C are changed, the stem-loop tertiary interactions rupture first, followed by unfolding of the 3-end hairpin (I{rightleftharpoons}F). Finally, the 5-end hairpin unravels, producing an extended state (E{rightleftharpoons}I). A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as (log Cm) with = 1 (0.5) for E{rightleftharpoons}I (I{rightleftharpoons}F) transition. This relation is used to obtain the preferential ion-RNA interaction coefficient, which can be quantitatively measured in single-molecule experiments, as done previously for DNA hairpins. A by-product of our work is the suggestion that the frameshift efficiency is likely determined by the stability of the 5 end hairpin that the ribosome first encounters during translation.

Biophysics↗

bioRxiv2016

On the Importance of Hydrodynamic Interactions in the Stepping Kinetics of Kinesin

Conventional kinesin walks by a hand-over-hand mechanism on the microtubule (MT) by taking ~ 8nm discrete steps, and consumes one ATP molecule per step. The time needed to complete a single step is on the order of twenty microseconds. We show, using simulations of a coarse-grained model of the complex containing the two motor heads, the MT, and the coiled coil that in order to obtain quantitative agreement with experiments for the stepping kinetics hydrodynamic interactions (HI) have to be included. In simulations without hydrodynamic interactions spanning nearly twenty s not a single step was completed in hundred trajectories. In sharp contrast, nearly 14% of the steps reached the target binding site within 6s when HI were included. Somewhat surprisingly, there are qualitative differences in the diffusion pathways in simulations with and without HI. The extent of movement of the trailing head of kinesin on the MT during the diffusion stage of stepping is considerably greater in simulations with HI than in those without HI. Our results suggest that inclusion of HI is crucial in the accurate description of motility of other motors as well.

Biophysics↗

bioRxiv2016

How do metal ions direct ribozyme folding?

Ribozymes, which carry out phosphoryl transfer reactions, often require Mg2+ ions for catalytic activity. The correct folding of the active site and ribozyme tertiary structure is also regulated by metal ions in a manner which is not fully understood. Here, we employ coarse-grained molecular simulations to show that individual structural elements of the group I ribozyme from the bacterium Azoarcus form spontaneously in the unfolded ribozyme even at very low Mg2+ concentrations, and are transiently stabilized by coordination of Mg2+ ions to specific nucleotides. However, competition for scarce Mg2+ and topological constraints arising from chain connectivity prevent complete folding of the ribozyme. A much higher Mg2+ concentration is required for complete folding of the ribozyme and stabilization of the active site. When Mg2+ is replaced by Ca2+ the ribozyme folds but the active site remains unstable. Our results suggest that group I ribozymes utilize the same interactions with specific metal ligands for both structural stability and chemical activity.

Biophysics↗

bioRxiv2016

Folding PDZ2 domain using the Molecular Transfer Model

A major challenge in molecular simulations is to describe denaturant-dependent folding of proteins order to make direct comparisons with in vitro experiments. We use the molecular transfer model (MTM), which is currently the only method that accomplishes this goal albeit phenomenologically, to quantitatively describe urea-dependent folding of PDZ domain, which plays a significant role in molecular recognition and signaling. Experiments show that urea-dependent unfolding rates of the PDZ2 domain exhibit a downward curvature at high urea concentrations ([C]s), which has been interpreted by invoking the presence of a sparsely populated high energy intermediate. Simulations using the MTM and a coarse-grained Self-Organized Polymer (SOP) representation of PDZ2 are used to show that the intermediate (IEQ), which has some native-like character, is present in equilibrium both in the presence and absence of urea. The free energy profiles as a function of the structural overlap order parameter show that there are two barriers separating the folded and unfolded states. Structures of the transition state ensembles, (TSE1 separating the unfolded and IEQ and TSE2 separating IEQ and the native state), determined using the Pfold method, show that TSE1 is greatly expanded while TSE2 is compact and native-like. Folding trajectories reveal that PDZ2 folds by parallel routes. In one pathway folding occurs exclusively through I1, which resembles IEQ. In a fraction of trajectories, constituting the second pathway, folding occurs through a combination of I1 and a kinetic intermediate. We establish that the radius of gyration ([Formula]) of the unfolded state is more compact (by [~] 9%) under native conditions. Theory and simulations show that the decrease in [Formula] occurs on the time scale on the order of utmost ~ 20 {beta}. The modest decrease in [Formula] and the rapid collapse suggest that high spatial and temporal resolution, currently beyond the scope of most small angle X-ray scattering experiments, are needed to detect compaction in finite-sized proteins. The present work further establishes that MTM is efficacious in producing nearly quantitative predictions for folding of proteins under conditions used to carry out experiments.

Biophysics↗