Yuriy V. Pereverzev

Theoretical Aspects of the Biological Catch Bond

The biological catch bond is fascinating and counterintuitive. When an external force is applied to a catch bond, either in vivo or in vitro, the bond resists breaking and becomes stronger instead. In contrast, ordinary slip bonds, which represent the vast majority of biological and chemical bonds, dissociate faster when subjected to a force. Catch-bond behavior was first predicted theoretically 20 years ago and has recently been experimentally observed in a number of protein receptor-ligand complexes. In this Account, we review the simplest physical-chemical models that lead to analytic expressions for bond lifetime, the concise universal representations of experimental data, and the explicit requirements for catch binding. The phenomenon has many manifestations: increased lifetime with growing constant force is its defining characteristic. If force increases with time, as in jump-ramp experiments, catch binding creates an additional maximum in the probability density of bond rupture force. The new maximum occurs at smaller forces than the slip-binding maximum, merging with the latter at a certain ramp rate in a process resembling a phase transition. If force is applied periodically, as in blood flows, catch-bond properties strongly depend on force frequency. Catch binding results from a complex landscape of receptor-ligand interactions. Bond lifetime can increase if force (i) prevents dissociation through the native pathway and drives the system over a higher energy barrier or (ii) alters protein conformations in a way that strengthens receptor-ligand binding. The bond deformations can be associated with allostery; force-induced conformational changes at one end of the protein propagate to the binding site at the other end. Surrounding water creates further exciting effects. Protein-water tension provides an additional barrier that can be responsible for significant drops in bond lifetimes observed at low forces relative to zero force. This strong dependence of bond properties on weak protein-water interactions may provide universal activation mechanisms in many biological systems and create new types of catch binding. Molecular dynamics simulations provide atomistic insights: the molecular view of bond dissociation gives a foundation for theoretical models and differentiates between alternative interpretations of experimental data. The number of known catch bonds is growing; analogs are found in enzyme catalysis, peptide translocation through nanopores, DNA unwinding, photoinduced dissociation of chemical bonds, and negative thermal expansion of bulk materials, for example. Finer force resolution will likely provide many more. Understanding the properties of catch bonds offers insight into the behavior of biological systems subjected to external perturbations in general.

Quantized Hamilton dynamics for a general potential

The quantization of Hamilton dynamics (QHD) [J. Chem. Phys. 113, 6557 (2000)] that efficiently generalizes classical mechanics to include quantum tunneling and zero-point energy effects is extended to a general position dependent potential. A Taylor series expansion of the potential is considered both around a fixed point and around the moving instantaneous value of the position variable. The equations-of-motion obtained for the moving frame are significantly simpler than for the fixed frame, while still satisfying the classical limit. The number of the QHD variables and the order of the Taylor expansion of the potential constitute two independent approximation parameters. Conservation of the total energy and the Heisenberg commutator relationship is established for the second-order QHD that includes linear and quadratic variables. The formal results are illustrated by examples, including the harmonic oscillator, tunneling in a doublewell potential, and energy exchange between coupled Morse oscillators re...

Structural origin of the enhanced electro-optic response of dendrimeric systems

Abstract The structural origin of the enhancement of the electro-optic (EO) activity of a dendrimeric material, relative to the traditional guest–host polymer, is established within an analytic model. Chemical bonding between the chromophore fragments in the dendrimer suppresses the antiferroelectric correlation of the chromophore dipoles and assists in the macroscopic ordering of the dipoles by an applied field. The developed analytic model quantitatively agrees with the experimental data both for the increased EO coefficient of the cross-linkable dendrimer, and the decreased EO coefficient of the non-cross-linkable dendrimer. The model facilitates optimization of the structural and molecular properties of dendrimers and chromophore fragments in order to achieve materials with better EO response.

Atomistic simulation combined with analytic theory to study the response of the P-selectin/PSGL-1 complex to an external force.

Steered molecular dynamics simulations are combined with analytic theory in order to gain insights into the properties of the P-selectin/PSGL-1 catch-slip bond at the atomistic level of detail. The simulations allow us to monitor the conformational changes in the P-selectin/PSGL-1 complex in response to an external force, while the theory provides a unified framework bridging the simulation data with experiment over 9 orders of magnitude. The theory predicts that the probability of bond dissociation by the catch mechanism is extremely low in the simulations; however, a few or even a single trajectory can be sufficient for characterization of the slip mechanism. Theoretical analysis of the simulation data shows that the bond responds to the force in a highly nonlinear way, with the bond stiffness changing considerably as a function of the force ramp rate. The Langevin description of the simulation provides spring constants of the proteins and the binding interaction and gives the friction coefficient associated with the receptor-ligand motion in water. The estimated relaxation time shows that the simple probabilistic description is accurate for the experimental regime and remains approximately valid for the high ramp rates used in simulations. The simulations establish that bond deformation occurs primarily within the P-selectin receptor region. The two interaction sites within the binding pocket dissociate sequentially, raising the possibility of observing these independent rupture events in experiment. The stronger interaction that determines the overall properties of the bond dissociates first, indicating that the experimental data indeed capture the main rupture event and not the secondary weaker site rupture. The main rupture event involves the interaction between the calcium ion of the receptor and the ligand residue FUC-623. It is followed by new interactions, supporting the sliding-rebinding behavior observed in the earlier simulation [ Lou, J. Zhu, C. Biophys. J. 2007 , 92 , 1471 - 1485 ]. The weaker binding site shows fewer interaction features, suggesting that the sliding-rebinding behavior may be determined by the unique properties of the calcium site. The agreement between simulation and experiment provided by the two-pathway and deformation models, each containing only four parameters, indicates that the essential physics of the catch-slip bond should be relatively simple and robust over a wide range of pulling regimes.

Mean-field theory of acentric order of chromophores with displaced dipoles

A mean-field model of acentric order of dipolar chromophores in polymeric electro-optic materials is developed by extension of our earlier results [Y.V. Pereverzev, O.V. Prezhdo, Phys. Rev. E 62 (2000) 8324] to allow for position and orientation flexibility of chromophore dipoles with respect of the molecular frame. The extended model quantitatively reproduces the experimental data for two sample chromophore systems. The model indicates that the disappearance of the acentric order and the related turnover and decay of the electro-optic coefficient are associated with a second-order phase transition in the dipolar system from para- to antiferroelectric state.

Correlation functions in quantized Hamilton dynamics and quantal cumulant dynamics

Quantized Hamilton dynamics (QHD) [O. V. Prezhdo and Y. V. Pereverzev, J. Chem. Phys. 113, 6557 (2000)] and quantal cumulant dynamics (QCD) [Shigeta et al., J. Chem. Phys. 125, 244102 (2006)] are used to obtain a semiclassical description of two-time correlation functions (CFs). Generally, lower-order CFs couple to higher-order CFs. The infinite hierarchy is terminated by a closure, which neglects higher-order irreducible correlators and provides an efficient approximation to quantum mechanics. The approach is illustrated with a simple nonlinear system, for which the real part of the classical CF continues a perfect oscillation and the imaginary part is identically zero. At little computational expense, the second-order QHD/QCD approximation reproduces the real and imaginary parts of the quantum-mechanical CF.

A model of phase transitions in the system of electro-optical dipolar chromophores subject to an electric field

An analytical model for the nonlinear behavior of the electro-optic (EO) coefficient in chromophore–polymeric materials is developed. The sharp decline of the EO coefficient above a threshold chromophore concentration is attributed to a second order phase transition transforming the chromophore dipolar system into an antiferroelectric state. The rise of antiferroelectric correlations between chromophore dipoles deteriorates the efficiency of the poling process aimed at achieving a noncentrosymmetric chromophore ordering by application of an electric field. The location of the phase transition and the magnitude of the EO coefficient are investigated as functions of molecular and thermodynamic parameters. Particularly remarkable observations are made regarding the dependence of the EO coefficient on the macroscopic shape of samples used for poling. Slab shaped samples that are common in practice are least efficient for the poling process. Any degree of sample elongation in the direction of the poling field ...

Dissipation of classical energy in nonlinear quantum systems

We show using two simple nonlinear quantum systems that the infinite set of quantum dynamical variables, as introduced in quantized Hamilton dynamics [O. V. Prezhdo and Y. V. Pereverzev, J. Chem. Phys. 113, 6557 (2000)], behave as a thermostat with respect to the finite number of classical variables. The coherent classical component of the evolution decays by coupling to the chaotic quantum reservoir. The classical energy, understood as the part of system energy expressible through the average values of coordinates and momenta, is transferred to the quantum energy expressible through the higher moments of coordinates and momenta and other quantum variables. At long times, the classical variables reach equilibrium, and the classical energy fluctuates around the equilibrium value. These phenomena are illustrated with the exactly solvable Jaynes-Cummings model and a nonlinear oscillator.

A new model of chemical bonding in ionic melts.

We developed a new physical model to predict macroscopic properties of inorganic molten systems using a realistic description of inter-atomic interactions. Unlike the conventional approach, which tends to overestimate viscosity by several times, our systems consist of a set of ions with an admixture of neutral atoms. The neutral atom subsystem is a consequence of the covalent/ionic state reduction, occurring in the liquid phase. Comparison of the calculated macroscopic properties (shear viscosity and self-diffusion constants) with the experiment demonstrates good performance of our model. The presented approach is inspired by a significant degree of covalent interaction between the alkali and chlorine atoms, predicted by the coupled cluster theory.

Anomalously increased lifetimes of biological complexes at zero force due to the protein-water interface.

A number of biological bonds show dramatically increased lifetimes at zero-force conditions, compared to lifetimes when even a small tensile force is applied to the ligand. The discrepancy is so great that it cannot be explained by the traditional receptor-ligand binding models. This generic phenomenon is rationalized here by considering the interaction of water with the receptor-ligand complex. It is argued that the water-protein interaction creates an energy barrier that prevents the ligand unbinding in the absence of the force. The properties of the interaction are such that even application of a relatively low force results in a dramatic drop of the bond lifetime due to the alteration of the water-receptor and water-ligand interaction network. The phenomenon is described by the presence of a second shallow interaction energy minimum for the bound ligand followed by a wide receptor-ligand dissociation barrier. The general analysis is applied quantitatively to the actin-myosin system, which demonstrates the gigantic drop of the bond lifetime at small forces and catch behavior (an increase in the lifetime) at moderate forces. The base hypothesis proposed to explain the small-force abnormal drop in the bond lifetime suggests that the majority of biological bonds may exhibit this phenomenon irrespectively whether they behave as slip or catch-slip bonds.