PUBLICATIONS
Pollination
Random Search with Resetting as a Strategy for Optimal Pollination (2019)
Robin, T., Sokolov, I.M. and Urbakh, M., 2018. Physical Review E., 99, 052119.
The problem of pollination is unique among a wide scope of search problems, since it requires optimization of benefits for both the searcher (pollinator) and its targets (plants). To address this challenge, we propose a pollination model which is based on a framework of first passage under stochastic restart. We derive equations for the search time and number of visited plants as functions of the distribution of nectar in the plant population and of the probability that a pollinator will leave the plant after examining a flower, thus effectively restarting the search. We demonstrate that nectar variation in plants serves as a driving force for pollination and establish conditions required for optimal pollination, which provides an efficient pollinator search strategy and the maximum number of plants visited by the pollinator.
Clusters
Life Time of Catch Bond Clusters (2018)
Robin, T., Sokolov, I.M. and Urbakh, M., 2018. Physica A: Statistical Mechanics and its Applications, 507, pp.398-405.
We consider the mean lifetime of adhesion clusters under a constant applied force and discuss in details different approximate solutions of this problem focusing on catch bond clusters. The analytical equation for the lifetime is derived that is accurate for a broad range of cluster parameters. A scaling equation for the variation of the cluster lifetime with the total number of available bonds is presented that holds already for relatively small clusters. While we focus on consideration of catch bond clusters, the derived equations are applicable also for description of lifetime of clusters including standard slip bonds.
Inhibitors
Single-Molecule Theory of Enzymatic Inhibition (2018)
Robin, T., Reuveni, S. and Urbakh, M., 2018. Nature communications, 9(1), p.779.
The classical theory of enzymatic inhibition takes a deterministic, bulk based approach to quantitatively describe how inhibitors affect the progression of enzymatic reactions. Catalysis at the single-enzyme level is, however, inherently stochastic which could lead to strong deviations from classical predictions. To explore this, 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 should strongly change our view on the uncompetitive and mixed modes of inhibition. There, stochastic fluctuations at the single-enzyme level could make inhibitors act as activators; and we state—in terms of experimentally measurable quantities—a mathematical condition for the emergence of this surprising phenomenon. Our findings could explain why certain molecules that inhibit enzymatic activity when substrate concentrations are high, elicit a non-monotonic dose response when substrate concentrations are low.
Enzymes II
On the Dependence of the Enzymatic Velocity on the Substrate Dissociation Rate (2016)
Berezhkovskii, A.M., Szabo, A., Rotbart, T., Urbakh, M. and Kolomeisky, A.B., 2016. The Journal of Physical Chemistry B, 121(15), pp.3437-3442.
Enzymes are biological catalysts that play a fundamental role in all living systems by supporting the selectivity and the speed for almost all cellular processes. While the general principles of enzyme functioning are known, the specific details of how they work at the microscopic level are not always available. Simple Michaelis–Menten kinetics assumes that the enzyme–substrate complex has only one conformation that decays as a single exponential. As a consequence, the enzymatic velocity decreases as the dissociation (off) rate constant of the complex increases. Recently, Reuveni et al. [ Proc. Natl. Acad. Sci. USA 2014, 111, 4391−4396] showed that it is possible for the enzymatic velocity to increase when the off rate becomes higher, if the enzyme–substrate complex has many conformations which dissociate with the same off rate constant. This was done using formal mathematical arguments, without specifying the nature of the dynamics of the enzyme–substrate complex. In order to provide a physical basis for this unexpected result, we derive an analytical expression for the enzymatic velocity assuming that the enzyme–substrate complex has multiple states and its conformational dynamics is described by rate equations with arbitrary rate constants. By applying our formalism to a complex with two conformations, we show that the unexpected off rate dependence of the velocity can be readily understood: If one of the conformations is unproductive, the system can escape from this “trap” by dissociating, thereby giving the enzyme another chance to form the productive enzyme–substrate complex. We also demonstrate that the nonmonotonic off rate dependence of the enzymatic velocity is possible not only when all off rate constants are identical, but even when they are different. We show that for typical experimentally determined rate constants, the nonmonotonic off rate dependence can occur for micromolar substrate concentrations. Finally, we discuss the relation of this work to the problem of optimizing the flux through singly occupied membrane channels and transporters.
Enzymes I
Michaelis-Menten Reaction Scheme as a Unified Approach Towards the Optimal Restart Problem (2015)
Rotbart, T., Reuveni, S. and Urbakh, M., 2015. Physical Review E, 92(6), p.060101.
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.