Statistical properties of multistep enzyme-mediated reactions

Enzyme-mediated reactions may proceed through multiple intermediate conformational states before creating a final product molecule, and one often wishes to identify such intermediate structures from observations of the product creation. In this paper, we address this problem by solving the chemical master equations for various enzymatic reactions. We devise a perturbation theory analogous to that used in quantum mechanics that allows us to determine the first () and the second (variance) cumulants of the distribution of created product molecules as a function of the substrate concentration and the kinetic rates of the intermediate processes. The mean product flux V=d/dt (or "dose-response" curve) and the Fano factor F=variance/ are both realistically measurable quantities, and while the mean flux can often appear the same for different reaction types, the Fano factor can be quite different. This suggests both qualitative and quantitative ways to discriminate between different reaction schemes, and we explore this possibility in the context of four sample multistep enzymatic reactions. We argue that measuring both the mean flux and the Fano factor can not only discriminate between reaction types, but can also provide some detailed information about the internal, unobserved kinetic rates, and this can be done without measuring single-molecule transition events.Comment: 8 pages, 3 figure

Energy transfer in nonlinear network models of proteins

We investigate how nonlinearity and topological disorder affect the energy relaxation of local kicks in coarse-grained network models of proteins. We find that nonlinearity promotes long-range, coherent transfer of substantial energy to specific, functional sites, while depressing transfer to generic locations. Remarkably, transfer can be mediated by the self-localization of discrete breathers at distant locations from the kick, acting as efficient energy-accumulating centers.Comment: 4 pages, 3 figure

On the suppression of the nnˉn\bar{n} transitions in medium

The new model of $n\bar{n}$ transitions in the medium based on unitary $S$-matrix is considered. The time-dependence and corrections to the model are studied. The lower limit on the free-space $n\bar{n}$ oscillation time $\tau$ is in the range $10^{16}\; {\rm yr}>\tau >1.2\cdot 10^{9}\; {\rm s}$Comment: 15 pages, 3 figure

Residence Time Statistics for Normal and Fractional Diffusion in a Force Field

We investigate statistics of occupation times for an over-damped Brownian particle in an external force field. A backward Fokker-Planck equation introduced by Majumdar and Comtet describing the distribution of occupation times is solved. The solution gives a general relation between occupation time statistics and probability currents which are found from solutions of the corresponding problem of first passage time. This general relationship between occupation times and first passage times, is valid for normal Markovian diffusion and for non-Markovian sub-diffusion, the latter modeled using the fractional Fokker-Planck equation. For binding potential fields we find in the long time limit ergodic behavior for normal diffusion, while for the fractional framework weak ergodicity breaking is found, in agreement with previous results of Bel and Barkai on the continuous time random walk on a lattice. For non-binding potential rich physical behaviors are obtained, and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite. Our work establishes a link between fractional calculus and ergodicity breaking.Comment: 12 page

Bayesian inference of accurate population sizes and FRET efficiencies from single diffusing biomolecules.

It is of significant biophysical interest to obtain accurate intramolecular distance information and population sizes from single-molecule Förster resonance energy transfer (smFRET) data obtained from biomolecules in solution. Experimental methods of increasing cost and complexity are being developed to improve the accuracy and precision of data collection. However, the analysis of smFRET data sets currently relies on simplistic, and often arbitrary methods, for the selection and denoising of fluorescent bursts. Although these methods are satisfactory for the analysis of simple, low-noise systems with intermediate FRET efficiencies, they display systematic inaccuracies when applied to more complex systems. We have developed an inference method for the analysis of smFRET data from solution studies based on rigorous model-based Bayesian techniques. We implement a Monte Carlo Markov chain (MCMC) based algorithm that simultaneously estimates population sizes and intramolecular distance information directly from a raw smFRET data set, with no intermediate event selection and denoising steps. Here, we present both our parametric model of the smFRET process and the algorithm developed for data analysis. We test the algorithm using a combination of simulated data sets and data from dual-labeled DNA molecules. We demonstrate that our model-based method systematically outperforms threshold-based techniques in accurately inferring both population sizes and intramolecular distances.This is the final published version. It's also available from ACS in Analytical Chemistry: http://pubs.acs.org/doi/pdf/10.1021/ac501188r

Structural Heterogeneity and Quantitative FRET Efficiency Distributions of Polyprolines through a Hybrid Atomistic Simulation and Monte Carlo Approach

Förster Resonance Energy Transfer (FRET) experiments probe molecular distances via distance dependent energy transfer from an excited donor dye to an acceptor dye. Single molecule experiments not only probe average distances, but also distance distributions or even fluctuations, and thus provide a powerful tool to study biomolecular structure and dynamics. However, the measured energy transfer efficiency depends not only on the distance between the dyes, but also on their mutual orientation, which is typically inaccessible to experiments. Thus, assumptions on the orientation distributions and averages are usually made, limiting the accuracy of the distance distributions extracted from FRET experiments. Here, we demonstrate that by combining single molecule FRET experiments with the mutual dye orientation statistics obtained from Molecular Dynamics (MD) simulations, improved estimates of distances and distributions are obtained. From the simulated time-dependent mutual orientations, FRET efficiencies are calculated and the full statistics of individual photon absorption, energy transfer, and photon emission events is obtained from subsequent Monte Carlo (MC) simulations of the FRET kinetics. All recorded emission events are collected to bursts from which efficiency distributions are calculated in close resemblance to the actual FRET experiment, taking shot noise fully into account. Using polyproline chains with attached Alexa 488 and Alexa 594 dyes as a test system, we demonstrate the feasibility of this approach by direct comparison to experimental data. We identified cis-isomers and different static local environments as sources of the experimentally observed heterogeneity. Reconstructions of distance distributions from experimental data at different levels of theory demonstrate how the respective underlying assumptions and approximations affect the obtained accuracy. Our results show that dye fluctuations obtained from MD simulations, combined with MC single photon kinetics, provide a versatile tool to improve the accuracy of distance distributions that can be extracted from measured single molecule FRET efficiencies

Relative Contributions of Intrinsic Structural–Functional Constraints and Translation Rate to the Evolution of Protein-Coding Genes

A long-standing assumption in evolutionary biology is that the evolution rate of protein-coding genes depends, largely, on specific constraints that affect the function of the given protein. However, recent research in evolutionary systems biology revealed unexpected, significant correlations between evolution rate and characteristics of genes or proteins that are not directly related to specific protein functions, such as expression level and protein–protein interactions. The strongest connections were consistently detected between protein sequence evolution rate and the expression level of the respective gene. A recent genome-wide proteomic study revealed an extremely strong correlation between the abundances of orthologous proteins in distantly related animals, the nematode Caenorhabditis elegans and the fruit fly Drosophila melanogaster. We used the extensive protein abundance data from this study along with short-term evolutionary rates (ERs) of orthologous genes in nematodes and flies to estimate the relative contributions of structural–functional constraints and the translation rate to the evolution rate of protein-coding genes. Together the intrinsic constraints and translation rate account for approximately 50% of the variance of the ERs. The contribution of constraints is estimated to be 3- to 5-fold greater than the contribution of translation rate

Extreme disorder in an ultrahigh-affinity protein complex

Molecular communication in biology is mediated by protein interactions. According to the current paradigm, the specificity and affinity required for these interactions are encoded in the precise complementarity of binding interfaces. Even proteins that are disordered under physiological conditions or that contain large unstructured regions commonly interact with well-structured binding sites on other biomolecules. Here we demonstrate the existence of an unexpected interaction mechanism: the two intrinsically disordered human proteins histone H1 and its nuclear chaperone prothymosin-α associate in a complex with picomolar affinity, but fully retain their structural disorder, long-range flexibility and highly dynamic character. On the basis of closely integrated experiments and molecular simulations, we show that the interaction can be explained by the large opposite net charge of the two proteins, without requiring defined binding sites or interactions between specific individual residues. Proteome-wide sequence analysis suggests that this interaction mechanism may be abundant in eukaryotes