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PubMed1999

Simulating proton translocations in proteins: probing proton transfer pathways in the Rhodobacter sphaeroides reaction center.

A general method for simulating proton translocations in proteins and for exploring the role of different proton transfer pathways is developed and examined. The method evaluates the rate constants for proton transfer processes using the energetics of the relevant proton configurations. The energies (DeltaG((m))) of the different protonation states are evaluated in two steps. First, the semimicroscopic version of the protein dipole Langevin dipole (PDLD/S) method is used to evaluate the intrinsic energy of bringing the protons to their protein sites, when the charges of all protein ionized residues are set to zero. Second, the interactions between the charged groups are evaluated by using a Coulomb's Law with an effective dielectric constant. This approach, which was introduced in an earlier study by one of the authors of the current report, allows for a very fast determination of any DeltaG((m)) and for practical evaluation of the time-dependent proton population: That is, the rate constants for proton transfer processes are evaluated by using the corresponding DeltaG((m)) values and a Marcus type relationship. These rate constants are then used to construct a master equation, the integration of which by a fourth-order Runge-Kutta method yields the proton population as a function of time. The integration evaluates, 'on the fly,' the changes of the rate constants as a result of the time-dependent changes in charge-charge interaction, and this feature benefits from the fast determination of DeltaG((m)). The method is demonstrated in a preliminary study of proton translocation processes in the reaction center of Rhodobacter sphaeroides. It is found that proton transfer across water chains involves significant activation barriers and that ionized protein residues probably are involved in the proton transfer pathways. The potential of the present method in analyzing mutation experiments is discussed briefly and illustrated. The present study also examines different views of the nature of proton translocations in proteins. It is shown that such processes are controlled mainly by the electrostatic interaction between the proton site and its surroundings rather than by the local bond rearrangements of water molecules that are involved in the proton pathways. Thus, the overall rate of proton transport frequently is controlled by the highest barrier along the conduction pathway. Proteins 1999;36:484-500.

Computer Simulation↗
PubMed1990

Some mathematical problems of excitability.

The description of the electrical behaviour of nerve and muscle is one of the most quantitative areas of cellular physiology. There are detailed biophysical measurements of currents and potentials, that may be summarised as Master equations or stochastic differential equations for membrane channel and noise recordings, and nonlinear differential equations for macroscopic voltage clamp recordings. Propagation in excitable media is described by nonlinear reaction-diffusion equations. Computational approaches can provide solutions to these equations, but without qualitative studies on simplified caricatures contribute little to mathematical or physiological understanding.

Animals↗
PubMed1990

A stochastic simulation of tumor growth.

The growth of a tumor is described by a nonlinear stochastic representation. A systematic approach based on Taylor series expansion is adopted to solve the nonlinear master equation governing the variation of tumor weight as a function of time. The analysis of the available experimental data reveals that the growth rate of a tumor has a power law dependence on its weight.

Animals↗
PubMed1996

Collective dynamics of ion channels in biological membranes.

Master equation was used to describe the dynamics of coupled ion channels in biological membranes. From the stationary solution it was found that at a critical value of coupling strength the system undergoes phase transition of the second order, which can be of biological relevance.

Animals↗
PubMed2004

New theory of equation of state for surface monolayer.

A novel statistical-thermodynamic approach to deriving an equation of state for a surface monolayer has been elaborated on the basis of excluded area. A master differential equation relating surface (two-dimensional) pressure to excluded area has been derived to generate equations of state for a surface monolayer. The crudest solution (the zero approximation) of the master equation reproduces the known van Laar and Frumkin equations of state. The first approximation yields the two-dimensional van der Waals equation. The second, third, and fourth approximations lead to new and more accurate equations of state. The particular result of the fourth approximation is a precise equation of state for hard disks with deviation not more than 0.46% from data obtained by Monte Carlo and molecular-dynamics simulations within the whole range of surface density. The role of the third dimension for surface equations of state is discussed. An orientation equation of state has been proposed for monolayers containing anisometric particles. It follows from the orientation equation obtained that the orientation effect creates possibility for a two-dimensional phase transition.

Journal Article↗
PubMed2001

Models of venous admixture.

Medical students, residents, and allied health professionals often have difficulty quantitating ventilation-perfusion mismatch in ill patients. This manuscript quantitates ventilation-perfusion mismatch using the underlying physiological concepts and equations that describe mismatch. In addition, clinical problems with diagrams and worked-out solutions are supplied to help students master these equations as well as their practical limitations.

Education, Medical↗
PubMed2003

Dynamic tension spectroscopy and strength of biomembranes.

Rupturing fluid membrane vesicles with a steady ramp of micropipette suction produces a distribution of breakage tensions governed by the kinetic process of membrane failure. When plotted as a function of log(tension loading rate), the locations of distribution peaks define a dynamic tension spectrum with distinct regimes that reflect passage of prominent energy barriers along the kinetic pathway. Using tests on five types of giant phosphatidylcholine lipid vesicles over loading rates(tension/time) from 0.01-100 mN/m/s, we show that the kinetic process of membrane breakage can be modeled by a causal sequence of two thermally-activated transitions. At fast loading rates, a steep linear regime appears in each spectrum which implies that membrane failure starts with nucleation of a rare precursor defect. The slope and projected intercept of this regime are set by defect size and frequency of spontaneous formation, respectively. But at slow loading rates, each spectrum crosses over to a shallow-curved regime where rupture tension changes weakly with rate. This regime is predicted by the classical cavitation theory for opening an unstable hole in a two-dimensional film within the lifetime of the defect state. Under slow loading, membrane edge energy and the frequency scale for thermal fluctuations in hole size are the principal factors that govern the level of tension at failure. To critically test the model and obtain the parameters governing the rates of transition under stress, distributions of rupture tension were computed and matched to the measured histograms through solution of the kinetic master (Markov) equations for defect formation and annihilation or evolution to an unstable hole under a ramp of tension. As key predictors of membrane strength, the results for spontaneous frequencies of defect formation and hole edge energies were found to correlate with membrane thicknesses and elastic bending moduli, respectively.

Algorithms↗
PubMed1999

Microtubules: strange polymers inside the cell.

This paper provides a consistent approach (within a one-dimensional approximation) to the description of the evolution of the microtubule length at both low- and high-density concentrations. We derive general master-type equations which are based on the key chemical reactions involved in the assembly and disassembly of microtubules. The processes included are: polymerization and depolymerization of a single protein dimer, catastrophic disassembly affecting an a piori arbitrary number of dimers, and a rescue event. Solutions of the derived equations are compared with the existing experimental data. Important conclusions linking the emergence of bell-shaped histograms with the nature of catastrophe and rescue phenomena are drawn. Finally, we briefly discuss the emergence of coherent phenomena in microtubule polymerization, i.e., a transition to collective oscillations in the assembly and disassembly effects.

Biopolymers↗
PubMed2005

Stochastic chemical reactions in microdomains.

Traditional chemical kinetics may be inappropriate to describe chemical reactions in microdomains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a master-diffusion equation for the joint probability density of a mobile reactant and the number of bound substrate in a confined domain. We use the equation to calculate the fluctuations in the number of bound substrate molecules as a function of initial reactant distribution. A second model is presented based on a Markov description of the binding and unbinding and on the mean first passage time of a molecule to a small portion of the boundary. These models can be used for the description of noise due to gating of ionic channels by random binding and unbinding of ligands in biological sensor cells, such as olfactory cilia, photoreceptors, hair cells in the cochlea.

Journal Article↗
PubMed1999

Deuteron NMR study of a long-chain smectic liquid crystal: molecular order and dynamics.

Deuteron Zeeman (T(1Z)) and quadrupolar (T(1Q)) spin-lattice relaxation times and quadrupolar splittings were measured in the nematic and smectic A phases of a chain-deuterated 4-n-octyloxy-4'-cyanobiphenyl (8OCB-d17) at 15.1 and 46 MHz. To model the NMR observables, the so-called pentane effect is used to limit the number of possible conformations in the chain, and is found to be a good approximation. The additive potential method is employed to construct the potential of mean torque using the quadrupolar splittings. A decoupled model is used to describe correlated internal motions in the chain, which are independent of the molecular reorientation. The latter motion is treated using the small-step rotational diffusion model of Nordio (Tarroni and Zannoni), while the former motion is described using a master rate equation. In the nematic phase, order director fluctuations are found to be necessary. The relaxation data in both mesophases were treated using a global target method, and the derived motional parameters are acceptable in comparison with those found for 6OCB.

Journal Article↗
PubMed2001

Extremal properties of random trees.

We investigate extremal statistical properties such as the maximal and the minimal heights of randomly generated binary trees. By analyzing the master evolution equations we show that the cumulative distribution of extremal heights approaches a traveling wave form. The wave front in the minimal case is governed by the small-extremal-height tail of the distribution, and conversely, the front in the maximal case is governed by the large-extremal-height tail of the distribution. We determine several statistical characteristics of the extremal height distribution analytically. In particular, the expected minimal and maximal heights grow logarithmically with the tree size, N, h(min) approximately v(min) ln N, and h(max) approximately v(max) ln N, with v(min)=0.373365ellipsis and v(max)=4.31107ellipsis, respectively. Corrections to this asymptotic behavior are of order O(ln ln N).

Journal Article↗
PubMed2003

Synchronization and symmetry-breaking bifurcations in constructive networks of coupled chaotic oscillators.

The spatiotemporal dynamics of networks based on a ring of coupled oscillators with regular shortcuts beyond the nearest-neighbor couplings is studied by using master stability equations and numerical simulations. The generic criterion for dynamic synchronization has been extended to arbitrary network topologies with zero row-sum. The symmetry-breaking oscillation patterns that resulted from the Hopf bifurcation from synchronous states are analyzed by the symmetry group theory.

Journal Article↗
PubMed2004

Enhancement of neural synchrony by time delay.

In a network of neuronal oscillators with time-delayed coupling, we uncover a phenomenon of enhancement of neural synchrony by time delay: a stable synchronized state exists at low coupling strengths for significant time delays. By formulating a master stability equation for time-delayed networks of Hindmarsh-Rose neurons, we show that there is always an extended region of stable synchronous activity corresponding to low coupling strengths. Such synchrony could be achieved in the undelayed system only by much higher coupling strengths. This phenomenon of enhanced neural synchrony by delay has important implications, in particular, in understanding synchronization of distant neurons and information processing in the brain.

Animals↗
PubMed2026

Clonal stochasticity in early NK cell response to mouse cytomegalovirus is generated by mature subsets of varying proliferative ability.

Natural killer (NK) cells are classically defined as innate immune cells, but experiments show that mouse cytomegalovirus (MCMV) infection in C57BL/6 mice can cause NK cells to undergo antigen-specific proliferation and memory formation, similar to adaptive CD8+ T cells. One shared behavior between CD8+ T cells and NK cells is clonal expansion, where a single stimulated cell proliferates rapidly to form a diverse population of cells. For example, clones derived from single cells are most abundant during expansion when they are primarily CD27- for NK cells and CD62L- for T cells, phenotypes derived from precursor CD27+ and CD62L + cells, respectively. Here we determined the mechanistic rules involving proliferation, cell death, and differentiation of endogenous and adoptively transferred NK cells in the expansion phase of the response to MCMV infection. We found that the interplay between cell proliferation and cell death of mature CD27- NK cells and a highly proliferative CD27-Ly6C- mature subtype and intrinsic stochastic fluctuations in these processes play key roles in regulating the heterogeneity and population of the NK cell subtypes. Furthermore, we estimate rates for maturation of endogenous NK cells in homeostasis and in MCMV infection and found that only NK cell growth rates, and not differentiation rates, are appreciably increased by MCMV. Taken together, these results quantify the differences between the kinetics of NK cell antigen-specific expansion from that of CD8+T cells and unique mechanisms that give rise to the observed heterogeneity in NK cell clones generated from single NK cells in the expansion phase.

Animals↗
PubMedDate not supplied

Advanced practice: do we know what it is?

The UKCC has proposed the development of an advanced practitioner role. The role is equated with master's and doctorate level of preparation. The development of the advanced practitioner role is outlined. The assumption that the nursing profession understands the term advanced practice is challenged. It is not possible to make explicit the role of the advanced practitioner unless nursing knowledge is used as its foundation. Two basic questions have yet to be answered: What is advanced practice? What is an advanced practitioner?

Education, Nursing, Graduate↗
PubMed1997

Master-slave synchronization and the Lorenz equations.

Since the seminal remark by Pecora and Carroll [Phys. Rev. Lett. 64, 821 (1990)] that one can synchronize chaotic systems, the main example in the related literature has been the Lorenz equations. Yet this literature contains a mixture of true and false, and of justified and unsubstantiated claims about the synchronization properties of the Lorenz equations. In this note we clarify some of the confusion. (c) 1997 American Institute of Physics.

Journal Article↗
PubMed2006

Theory of the statistics of kinetic transitions with application to single-molecule enzyme catalysis.

Single-molecule spectroscopy can monitor transitions between two microscopic states when these transitions are associated with the emission of photons. A general formalism is developed for obtaining the statistics of such transitions from a microscopic model when the dynamics is described by master or rate equations or their continuum analog, multidimensional reaction-diffusion equations. The focus is on the distribution of the number of transitions during a fixed observation time, the distribution of times between transitions, and the corresponding correlation functions. It is shown how these quantities are related to each other and how they can be explicitly calculated in a straightforward way for both immobile and diffusing molecules. Our formalism reduces to renewal theory when the monitored transitions either go to or originate from a single state. The influence of dynamics slow compared with the time between monitored transitions is treated in a simple way, and the probability distributions are expressed in terms of Mandel-type formulas. The formalism is illustrated by a detailed analysis of the statistics of catalytic turnovers of enzymes. When the rates of conformational changes are slower than the catalytic rates which are in turn slower than the binding relaxation rate, (1) the mean number of turnovers is shown to have the classical Michaelis-Menten form, (2) the correlation function of the number of turnovers is a direct measure of the time scale of catalytic rate fluctuations, and (3) the distribution of the time between consecutive turnovers is determined by the steady-state distribution.

Catalysis↗