Biomedical subjects

Anatoly B Kolomeisky

Publications and source records attributed to Anatoly B Kolomeisky.

17 recordsLinked to original sources

PubMed2007

Molecular motors: a theorist's perspective.

Individual molecular motors, or motor proteins, are enzymatic molecules that convert chemical energy, typically obtained from the hydrolysis of ATP (adenosine triphosphate), into mechanical work and motion. Processive motor proteins, such as kinesin, dynein, and certain myosins, step unidirectionally along linear tracks, specifically microtubules and actin filaments, and play a crucial role in cellular transport processes, organization, and function. In this review some theoretical aspects of motor-protein dynamics are presented in the light of current experimental methods that enable the measurement of the biochemical and biomechanical properties on a single-molecule basis. After a brief discussion of continuum ratchet concepts, we focus on discrete kinetic and stochastic models that yield predictions for the mean velocity, V(F, [ATP], ...), and other observables as a function of an imposed load force F, the ATP concentration, and other variables. The combination of appropriate theory with single-molecule observations should help uncover the mechanisms underlying motor-protein function.

Models, Biological↗

PubMed2006

Effect of orientation in translocation of polymers through nanopores.

The motion of polymers with inhomogeneous structure through nanopores is discussed theoretically. Specifically, we consider the translocation dynamics of polymers consisting of double-stranded and single-stranded blocks. Since only the single-stranded chain can go through the nanopore the double-stranded segment has to unzip before the translocation. Utilizing a simple analytical model, translocation times are calculated explicitly for different polymer orientations, i.e., when the single-stranded block enters the pore first and when the double-stranded segment is a leading one. The dependence of the translocation dynamics on external fields, energy of interaction in the double-stranded segment, size of the polymer, and the fraction of double-stranded monomers is analyzed. It is found that the order of entrance into the pore has a significant effect on the translocation dynamics. The theoretical results are discussed using free-energy landscape arguments.

Biophysical Phenomena↗

PubMed2006

Transport of single molecules along the periodic parallel lattices with coupling.

General discrete one-dimensional stochastic models to describe the transport of single molecules along coupled parallel lattices with period N are developed. Theoretical analysis that allows to calculate explicitly the steady-state dynamic properties of single molecules, such as mean velocity V and dispersion D, is presented for N=1 and N=2 models. For the systems with N>2 exact analytic expressions for the large-time dynamic properties are obtained in the limit of strong coupling between the lattices that leads to dynamic equilibrium between two parallel kinetic pathways. It is shown that for all systems dispersion is maximal when the coupling between channels is weak.

Algorithms↗

PubMed2006

Dynamic transitions in coupled motor proteins.

The effect of interactions on dynamics of coupled motor proteins is investigated theoretically. A simple stochastic discrete model, which allows one to calculate explicitly the dynamic properties, is developed. It is shown that there are two dynamic regimes, depending on the interaction between the particles. For strong interactions the motor proteins move as one tight cluster, while for weak interactions there is no correlation in the motion of the proteins, and the particle separation increases steadily with time. The boundary between the two regimes is specified by a critical interaction that has a nonzero value only for the coupling of the asymmetric motor proteins, and it depends on the temperature and transition rates. At the critical interaction there is a change in slope for the mean velocities and a discontinuity in the dispersions of the motor proteins as a function of interactions.

Binding Sites↗

PubMed2006

Dynamics of polymer translocation through nanopores: theory meets experiment.

The dynamics of translocation of polymer molecules through nanopores is investigated via molecular dynamics. We find that an off-lattice minimalist model of the system is sufficient to reproduce quantitatively all the experimentally observed trends and scaling behavior. Specifically, simulations show (i) two translocation regimes depending on the ratio of pore and polymer length, (ii) two different regimes for the probability of translocation depending on applied voltage, (iii) an exponential dependence of translocation velocity upon applied voltage, and (iv) an exponential decrease of the translocation time with temperature. We also propose a simple theoretical explanation of each of the observed trends within a free energy landscape framework.

Computer Simulation↗

PubMed2006

ATP hydrolysis stimulates large length fluctuations in single actin filaments.

Polymerization dynamics of single actin filaments is investigated theoretically using a stochastic model that takes into account the hydrolysis of ATP-actin subunits, the geometry of actin filament tips, and the lateral interactions between the monomers as well as the processes at both ends of the polymer. Exact analytical expressions are obtained for the mean growth velocity, for the dispersion in the length fluctuations, and the nucleotide composition of the actin filaments. It is found that the ATP hydrolysis has a strong effect on dynamic properties of single actin filaments. At high concentrations of free actin monomers, the mean size of the unhydrolyzed ATP-cap is very large, and the dynamics is governed by association/dissociation of ATP-actin subunits. However, at low concentrations the size of the cap becomes finite, and the dissociation of ADP-actin subunits makes a significant contribution to overall dynamics. Actin filament length fluctuations reach a sharp maximum at the boundary between two dynamic regimes, and this boundary is always larger than the critical concentration for the actin filament's growth at the barbed end, assuming the sequential release of phosphate. Random and sequential mechanisms of hydrolysis are compared, and it is found that they predict qualitatively similar dynamic properties at low and high concentrations of free actin monomers with some deviations near the critical concentration. The possibility of attachment and detachment of oligomers in actin filament's growth is also discussed. Our theoretical approach is successfully applied to analyze the latest experiments on the growth and length fluctuations of individual actin filaments.

Actin Cytoskeleton↗

PubMed2005

Monte Carlo simulations of rigid biopolymer growth processes.

Rigid biopolymers, such as actin filaments, microtubules, and intermediate filaments, are vital components of the cytoskeleton and the cellular environment. Understanding biopolymer growth dynamics is essential for the description of the mechanisms and principles of cellular functions. These biopolymers are composed of N parallel protofilaments which are aligned with arbitrary but fixed relative displacements, thus giving rise to complex end structures. We have investigated rigid biopolymer growth processes by Monte Carlo simulations by taking into account the effects of such "end" properties and lateral interactions. Our simulations reproduce analytical results for the case of N = 2, which is biologically relevant for actin filaments. For the case of N = 13, which applies to microtubules, the simulations produced results qualitatively similar to the N = 2 case. The simulation results indicate that polymerization events are evenly distributed among the N protofilaments, which imply that both end-structure effects and lateral interactions are significant. The effect of different splittings in activation energy has been investigated for the case of N = 2. The effects of activation energy coefficients on the specific polymerization and depolymerization processes were found to be unsubstantial. By expanding the model, we have also obtained a force-velocity relationship of microtubules as observed in experiments. In addition, a range of lateral free-energy parameters was found that yields growth velocities in accordance with experimental observations and previous simulation estimates for the case of N = 13.

Actin Cytoskeleton↗

PubMed2005

Kinetics of two-step nucleation of crystals.

When the nucleation of a stable crystalline phase directly in a supersaturated old phase is greatly retarded, the crystal nuclei might nucleate within faster-forming particles of an intermediate phase. Here we present a theoretical investigation of the kinetics of this two-step nucleation of crystals and derive general expressions for the time dependence of the number of crystals nucleated within the particles of the intermediate phase. The results reveal that crystal nucleation can be strongly delayed by the slow growth of the particles and/or by the slow nucleation of the crystals in them. Furthermore, the linear part of the time dependence of the number of nucleated crystals is determined by the formation rate of the intermediate particles. This is in contrast with the one-step nucleation of crystals when this linear part is determined by the rate of crystal nucleation directly in the old phase. Criteria are proposed for distinction between the one- and two-step nucleation mechanisms, based on the supersaturation dependence of the delay time for nucleation. The application of the theoretical approach to the analysis of experimental data on the nucleation of crystals and other ordered aggregates of protein and other soluble materials is discussed.

Journal Article↗

PubMed2005

Coupling of two motor proteins: a new motor can move faster.

We study the effect of a coupling between two motor domains in highly processive motor protein complexes. A simple stochastic discrete model, in which the two parts of the protein molecule interact through some energy potential, is presented. The exact analytical solutions for the dynamic properties of the combined motor species, such as the velocity and dispersion, are derived in terms of the properties of free individual motor domains and the interaction potential. It is shown that the coupling between the motor domains can create a more efficient motor protein that can move faster than individual particles. The results are applied to analyze the motion of RecBCD helicase molecules.

DNA↗

PubMed2005

Nucleation of ordered solid phases of proteins via a disordered high-density state: phenomenological approach.

Nucleation of ordered solid phases of proteins triggers numerous phenomena in laboratory, industry, and in healthy and sick organisms. Recent simulations and experiments with protein crystals suggest that the formation of an ordered crystalline nucleus is preceded by a disordered high-density cluster, akin to a droplet of high-density liquid that has been observed with some proteins; this mechanism allowed a qualitative explanation of recorded complex nucleation kinetics curves. Here, we present a simple phenomenological theory that takes into account intermediate high-density metastable states in the nucleation process. Nucleation rate data at varying temperature and protein concentration are reproduced with high fidelity using literature values of the thermodynamic and kinetic parameters of the system. Our calculations show that the growth rate of the near-critical and supercritical ordered clusters within the dense intermediate is a major factor for the overall nucleation rate. This highlights the role of viscosity within the dense intermediate for the formation of the ordered nucleus. The model provides an understanding of the action of additives that delay or accelerate nucleation and presents a framework within which the nucleation of other ordered protein solid phases, e.g., the sickle cell hemoglobin polymers, can be analyzed.

Computer Simulation↗

PubMed2005

Dynamic force spectroscopy of glycoprotein Ib-IX and von Willebrand factor.

The first stage in hemostasis is the binding of the platelet membrane receptor glycoprotein (GP) Ib-IX complex to the A1 domain of von Willebrand factor in the subendothelium. A bleeding disorder associated with this interaction is platelet-type von Willebrand disease, which results from gain-of-function (GOF) mutations in amino acid residues 233 or 239 of the GP Ibalpha subunit of GP Ib-IX. Using optical tweezers and a quadrant photodetector, we investigated the binding of A1 to GOF and loss-of-function mutants of GP Ibalpha with mutations in the region containing the two known naturally occurring mutations. By dynamically measuring unbinding force profiles at loading rates ranging from 200-20,000 pN/s, we found that the bond strengths between A1 and GP Ibalpha GOF mutants (233, 235, 237, and 239) were significantly greater than the A1/wild-type GP Ib-IX bond at all loading rates examined (p < 0.05). In addition, mutants 231 and 232 exhibited significantly lower bond strengths with A1 than the wild-type receptors (p < 0.05). We computed unloaded dissociation rate constant (k(off)(0)) values for interactions involving mutant and wild-type GP Ib-IX receptors with A1 and found the A1/wild-type GP Ib-IX k(off)(0) value of 5.47 +/- 0.25 s(-1) to be significantly greater than the GOF k(off)(0) values and significantly less than the loss-of-function k(off)(0) values. Our data illustrate the importance of the bond kinetics associated with the VWF/GP Ib-IX interaction in hemostasis and also demonstrate the drastic changes in binding that can occur when only a single amino acid of GP Ibalpha is altered.

Amino Acid Sequence↗

PubMed2005

Polymerization dynamics of double-stranded biopolymers: chemical kinetic approach.

The polymerization dynamics of double-stranded polymers, such as actin filaments, is investigated theoretically using simple chemical kinetic models that explicitly take into account some microscopic details of the polymer structure and the lateral interactions between the protofilaments. By considering all possible molecular configurations, the exact analytical expressions for the growth velocity and dispersion for two-stranded polymers are obtained in the case of the growing at only one end, and for the growth from both polymer ends. Exact theoretical calculations are compared with the predictions of approximate multilayer models that consider only a finite number of the most relevant polymer configurations. Our theoretical approach is applied to analyze the experimental data on the growth and fluctuations dynamics of individual single actin filaments.

Journal Article↗

PubMed2005

Understanding mechanochemical coupling in kinesins using first-passage-time processes.

Kinesins are processive motor proteins that move along microtubules in a stepwise manner, and their motion is powered by the hydrolysis of ATP. Recent experiments have investigated the coupling between the individual steps of single kinesin molecules and ATP hydrolysis, taking explicitly into account forward steps, backward steps, and detachments. A theoretical study of mechanochemical coupling in kinesins, which extends the approach used successfully to describe the dynamics of motor proteins, is presented. The possibility of irreversible detachments of kinesins from the microtubules is explicitly taken into account. Using the method of first-passage times, experimental data on the mechanochemical coupling in kinesins are fully described using the simplest two-state model. It is shown that the dwell times for the kinesin to move one step forward or backward, or to dissociate irreversibly, are the same, although the probabilities of these events are different. It is concluded that the current theoretical view-that only the forward motion of the motor protein molecule is coupled to ATP hydrolysis--is consistent with all available experimental observations for kinesins.

Adenosine Triphosphate↗

PubMed2004

Simple growth models of rigid multifilament biopolymers.

The growth dynamics of rigid biopolymers, consisting of N parallel protofilaments, is investigated theoretically using simple approximate models. In our approach, the structure of a polymer's growing end and lateral interactions between protofilaments are explicitly taken into account, and it is argued that only few configurations are important for a biopolymer's growth. As a result, exact analytic expressions for growth velocity and dispersion are obtained for any number of protofilaments and arbitrary geometry of the growing end of the biopolymer. Our theoretical predictions are compared with a full description of biopolymer growth dynamics for the simplest N=2 model. It is found that the results from the approximate theory are approaching the exact ones for large lateral interactions between the protofilaments. Our theory is also applied to analyze the experimental data on the growth of microtubules.

Biopolymers↗

PubMed2004

Polymer dynamics in repton model at large fields.

Polymer dynamics at large fields in Rubinstein-Duke repton model is investigated theoretically. Simple diagrammatic approach and analogy with asymmetric simple exclusion models are used to analyze the reptation dynamics of polymers. It is found that for polyelectrolytes the drift velocity decreases exponentially as a function of the external field with an exponent depending on polymer size and parity, while for polyampholytes the drift velocity is independent of polymer chain size. However, for polymers, consisting of charged and neutral blocks, the drift velocity approaches the constant limit which is determined by the size of the neutral block. The theoretical arguments are supported by extensive numerical calculations by means of density-matrix renormalization group techniques.

Journal Article↗

PubMed2003

Thermodynamics of electrolytes on anisotropic lattices.

The phase behavior of ionic fluids on simple cubic and tetragonal (anisotropic) lattices has been studied by grand canonical Monte Carlo simulations. Systems with both the true lattice Coulombic potential and continuous-space 1/r electrostatic interactions have been investigated. At all degrees of anisotropy, only coexistence between a disordered low-density phase and an ordered high-density phase with the structure similar to ionic crystal was found, in contrast to recent theoretical predictions. Tricritical parameters were determined to be increasing functions of anisotropy parameters which is consistent with theoretical calculations based on the Debye-Hückel approach. At large anisotropies a two-dimensional-like behavior is observed, from which we estimated the dimensionless tricritical temperature and density for the two-dimensional square lattice electrolyte to be T*(tri)=0.14 and rho*(tri)=0.70.

Journal Article↗

PubMed2003

A simple kinetic model describes the processivity of myosin-v.

Myosin-V is a motor protein responsible for organelle and vesicle transport in cells. Recent single-molecule experiments have shown that it is an efficient processive motor that walks along actin filaments taking steps of mean size close to 36 nm. A theoretical study of myosin-V motility is presented following an approach used successfully to analyze the dynamics of conventional kinesin but also taking some account of step-size variations. Much of the present experimental data for myosin-V can be well described by a two-state chemical kinetic model with three load-dependent rates. In addition, the analysis predicts the variation of the mean velocity and of the randomness-a quantitative measure of the stochastic deviations from uniform, constant-speed motion-with ATP concentration under both resisting and assisting loads, and indicates a substep of size d(0) approximately 13-14 nm (from the ATP-binding state) that appears to accord with independent observations.

Adenosine Diphosphate↗