Shlomi Reuveni

Anomalies in the vibrational dynamics of proteins are a consequence of fractal-like structure

Proteins have been shown to exhibit strange/anomalous dynamics displaying non-Debye density of vibrational states, anomalous spread of vibrational energy, large conformational changes, nonexponential decay of correlations, and nonexponential unfolding times. The anomalous behavior may, in principle, stem from various factors affecting the energy landscape under which a protein vibrates. Investigating the origins of such unconventional dynamics, we focus on the structure-dynamics interplay and introduce a stochastic approach to the vibrational dynamics of proteins. We use diffusion, a method sensitive to the structural features of the protein fold and them alone, in order to probe protein structure. Conducting a large-scale study of diffusion on over 500 Protein Data Bank structures we find it to be anomalous, an indication of a fractal-like structure. Taking advantage of known and newly derived relations between vibrational dynamics and diffusion, we demonstrate the equivalence of our findings to the existence of structurally originated anomalies in the vibrational dynamics of proteins. We conclude that these anomalies are a direct result of the fractal-like structure of proteins. The duality between diffusion and vibrational dynamics allows us to make, on a single-molecule level, experimentally testable predictions. The time dependent vibrational mean square displacement of an amino acid is predicted to be subdiffusive. The thermal variance in the instantaneous distance between amino acids is shown to grow as a power law of the equilibrium distance. Mean first passage time analysis is offered as a practical tool that may aid in the identification of amino acid pairs involved in large conformational changes.

Coexistence of Flexibility and Stability of Proteins: An Equation of State

We consider a recently suggested “equation of state” for natively folded proteins, and verify its validity for a set of about 5800 proteins. The equation is based on a fractal viewpoint of proteins, on a generalization of the Landau-Peierls instability, and on a marginal stability criterion. The latter allows for coexistence of stability and flexibility of proteins, which is required for their proper function. The equation of state relates the protein fractal dimension , its spectral dimension , and the number of amino acids N. Using structural data from the protein data bank (PDB) and the Gaussian network model (GNM), we compute and for the entire set and demonstrate that the equation of state is well obeyed. Addressing the fractal properties and making use of the equation of state may help to engineer biologically inspired catalysts.

First Passage under Restart

First passage under restart has recently emerged as a conceptual framework suitable for the description of a wide range of phenomena, but the endless variety of ways in which restart mechanisms and first passage processes mix and match hindered the identification of unifying principles and general truths. Hope that these exist came from a recently discovered universality displayed by processes under optimal, constant rate, restart-but extensions and generalizations proved challenging as they marry arbitrarily complex processes and restart mechanisms. To address this challenge, we develop a generic approach to first passage under restart. Key features of diffusion under restart-the ultimate poster boy for this wide and diverse class of problems-are then shown to be completely universal.

Optimal stochastic restart renders fluctuations in first passage times universal

Stochastic restart may drastically reduce the expected run time of a computer algorithm, expedite the completion of a complex search process, or increase the turnover rate of an enzymatic reaction. These diverse first-passage-time (FPT) processes seem to have very little in common but it is actually quite the other way around. Here we show that the relative standard deviation associated with the FPT of an optimally restarted process, i.e., one that is restarted at a constant (nonzero) rate which brings the mean FPT to a minimum, is always unity. We interpret, further generalize, and discuss this finding and the implications arising from it.

Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem.

We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of Michaelis and Menten. Stopping a process in its midst-only to start it all over again-may prolong, leave unchanged, or even shorten the time taken for its completion. Here we are interested in the optimal restart problem, i.e., in finding a restart rate which brings the mean completion time of a process to a minimum. We derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest. We then continue to discover regimes at which solutions to the problem take on universal, details independent forms which further give rise to optimal scaling laws. The formalism we develop, and the results obtained, can be utilized when optimizing stochastic search processes and randomized computer algorithms. An immediate connection with kinetic proofreading is also noted and discussed.

A ribosome flow model for analyzing translation elongation

We describe the first genome wide analysis of translation based on a model aimed at capturing the physical and dynamical aspects of this process. The Ribosomal Flow Model (RFM) is a computationally efficient approximation of the Totally Asymmetric Exclusion Process (TASEP) model (e.g. see [1]). The RFM is sensitive to the order of codons in the coding sequence, the tRNA pool of the organism, interactions between ribosomes and their size (see Figure [1]). The RFM predicts fundamental outcomes of the translation process, including translation rates, protein abundance and ribosomal densities [2] and the relation between all these variables, better than alternative (’non-physical’) approaches (e.g. see [3,4]). In addition, we show that the RFM model can be used for accurate inference of initiation rates, the effect of codon order on protein abundance and the cost of translation. All these variables could not be inferred by previous predictors.

Proteins: coexistence of stability and flexibility

We introduce an equation for protein native topology based on recent analysis of data from the Protein Data Bank and on a generalization of the Landau-Peierls instability criterion for fractals. The equation relates the protein fractal dimension df, the spectral dimension ds, and the number of amino acids N. Deviations from the equation may render a protein unfolded. The fractal nature of proteins is shown to bridge their seemingly conflicting properties of stability and flexibility. Over 500 proteins have been analyzed (df, ds, and N) and found to obey this equation of state.

Multisite phosphorylation regulates phenotypic variability in antibiotic tolerance

Isogenic populations of cells exhibit phenotypic variability that has specific physiological consequences. For example, individual bacteria can differ in their sensitivity to an antibiotic, but whether this variability is regulated or an unavoidable consequence of stochastic fluctuations is unclear. We observed that a bacterial stress response gene, the (p)ppGpp synthetase sasA, exhibits high levels of extrinsic noise in expression, suggestive of a regulatory process. We traced this variability to the convergence of two signaling systems that together control an event largely unexplored in bacteria, the multisite phosphorylation of a transcription factor. We found that this regulatory intersection is crucial for controlling the appearance of outliers, rare cells with unusually high levels of sasA expression. Additionally, by examining the full distributions of gene expression we calculated the importance of multisite phosphorylation in setting the relative abundance of cells with a given a level of SasA. We then created a predictive model for the probability of a given cell surviving antibiotic treatment as a function of sasA expression. Therefore, our data show that multisite phosphorylation can be used to strongly regulate bacterial physiology and sensitivity to antibiotic treatment. Significance Statement Cells possess many signaling pathways for sensing and responding to their environment. Although these pathways are commonly characterized individually, signals between separate pathways are often integrated. One way that pathways can intersect is through multisite phosphorylation controlling the activity of a common target, where each phosphorylation is contributed by a separate signaling system. Bacteria are an ideal place to study the effects of these intersections on gene expression since the number of such intersections is comparatively small, and subsequent gene regulation relatively simple. Here we show that signal integration through multisite phosphorylation is important for setting the frequency of bacterial cells with increased antibiotic tolerance by controlling the heterogeneity, or noise, in gene expression across the population.

Single-molecule theory of enzymatic inhibition predicts the emergence of inhibitor-activator duality

The classical theory of enzymatic inhibition aims to quantitatively describe the effect of certain molecules—called inhibitors—on the progression of enzymatic reactions, but “non-classical effects” and “anomalies” which seem to fall beyond its scope have forced practitioners and others to repeatedly patch and mend it ad-hoc. For example, depending on concentrations, some molecules can either inhibit, or facilitate, the progression of an enzymatic reaction. This duality gives rise to non-monotonic dose response curves which seriously complicate high throughput inhibitor screens and drug development, but it is widely believed that the three canonical modes of inhibition—competitive, uncompetitive, and mixed—cannot account for it. To critically test this view, we take the single enzyme perspective and rebuild the theory of enzymatic inhibition from the bottom up. We find that accounting for multi-conformational enzyme structure and intrinsic randomness cannot undermine the validity of classical results in the case of competitive inhibition; but that it should strongly change our view on the uncompetitive and mixed modes of inhibition. In particular, we show that inhibitor-activator duality is inherent to these modes of “inhibition”, and state—in terms of experimentally measurable quantities—a condition assuring its emergence. Fundamental and practical implications of our findings are discussed.