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At least 253 records · Page 14Linked to original sources
PubMed1996

Theory of gel electrophoresis of DNA: orientational effects.

Some aspects of the reptation model of gel electrophoresis of DNA, with emphasis on the orientational effects, are considered. A master equation for the reptational dynamics with the end boundary conditions is proposed. Based on this equation, the orientation and dynamics of the persistent-chain are investigated. In particular, the role of trap conformations for this chain, which essentially reduce the chain mobility, was analyzed. A transient orientation of the chain during pulsed field gel electrophoresis is also discussed.

DNA↗
PubMed2003

Structural and dynamical analysis of the hydration of the Alzheimer's beta-amyloid peptide.

An analysis of the water molecules in the first solvation shell obtained from the molecular dynamics simulation of the amyloid beta(10-35)NH2 peptide and the amyloid beta(10-35)NH2E22Q "Dutch" mutant peptide is presented. The structure, energetics, and dynamics of water in the hydration shell have been investigated using a variety of measures, including the hydrogen bond network, the water residence times for all the peptide residues, the diffusion constant, experimentally determined HN amide proton exchange, and the transition probabilities for water to move from one residue to another or into the bulk. The results of the study indicate that: (1) the water molecules at the peptide-solvent interface are organized in an ordered structure similar for the two peptide systems but different from that of the bulk, (2) the peptide structure inhibits diffusion perpendicular to the peptide surface by a factor of 3 to 5 relative to diffusion parallel to the peptide surface, which is comparable to diffusion of bulk water, (3) water in the first solvation shell shows dynamical relaxation on fast (1-2 ps) and slow (10-40 ps) time scales, (4) a novel solvent relaxation master equation is shown to capture the details of the fast relaxation of water in the peptide's first solvation shell, (5) the interaction between the peptide and the solvent is stronger in the wild type than in the E22Q mutant peptide, in agreement with earlier results obtained from computer simulations [Massi, F.; Straub, J. E. Biophys J 2001, 81, 697] correlated with the observed enhanced activity of the E22Q mutant peptide.

Alzheimer Disease↗
PubMed2004

A dual-level ab initio and hybrid density functional theory dynamics study on the unimolecular decomposition reaction C2H5O-->CH2O + CH3.

We present a direct ab initio and hybrid density functional theory dynamics study of the thermal rate constants of the unimolecular decomposition reaction of C2H5O-->CH2O + CH3 at a high-pressure limit. MPW1K/6-31+G(d,p), MP2/6-31+G(d,p), and MP2(full)/6-31G(d) methods were employed to optimize the geometries of all stationary points and to calculate the minimum energy path (MEP). The energies of all the stationary points were refined at a series of multicoefficient and multilevel methods. Among all methods, the QCISD(T)/aug-cc-pVTZ energies are in good agreement with the available experimental data. The rate constants were evaluated based on the energetics from the QCISD(T)/aug-cc-pVTZ//MPW1K/6-31+G(d,p) level of theory using both microcanonical variational transition state theory (microVT) and RRKM theory with the Eckart tunneling correction in the temperature range of 300-2500 K. The calculated rate constants at the QCISD(T)/aug-cc-pVTZ/MPW1K/6-31+G(d,p) level of theory are in good consistent with experimental data. The fitted three-parameter Arrhenius expression from the microVT/Eckart rate constants in the temperature range 200-2500 K is k = 2.52 x 10(12)T(0.41)e(-8894.0/T) s(-1). The falloff curves of pressure-dependent rate constants are performed using master-equation method within the temperature range of 391-471 K. The calculated results are in good agreement with the available experimental data.

Journal Article↗
PubMed1988

A reevaluation of the mathematical models for simulating single-channel and whole-cell ionic currents.

We have developed a technique that allows for the simulation of both single-channel and whole-cell ionic currents given any arbitrary first-order kinetic scheme for the conformational states of an ion channel. The procedure is based on the solution of the master equation, which, in turn, is a general expression for a Markov process. The solution is expressed in terms of the eigenvalues and eigenvectors of the kinetic system and the system's deviation from equilibrium. Our derived expression provides a general recipe for the calculation of whole-cell currents. By further manipulation of this expression, we show how conditional probabilities are derived that can be used for the simulation of single-channel currents. We discuss computer implementation of the results so that complicated kinetic schemes can be solved numerically. Finally, we demonstrate the procedure by providing a worked example of a simple model of activation followed by inactivation.

Computer Simulation↗
PubMed2000

Molecular clocks reduce plasmid loss rates: the R1 case.

Plasmids control their replication so that the replication frequency per plasmid copy responds to the number of plasmid copies per cell. High sensitivity amplification in replication response to copy number deviations generally reduces variation in copy numbers between different single cells, thereby reducing the plasmid loss rate in a cell population. However, experiments show that plasmid R1 has a gradual, insensitive replication control predicting considerable copy number variation between single cells. The critical step in R1 copy number control is regulation of synthesis of a rate-limiting cis-acting replication protein, RepA. De novo synthesis of a large number of RepA molecules is required for replication, suggesting that copy number control is exercised at multiple steps. In this theoretical kinetic study we analyse R1 multistep copy number control and show that it results in the insensitive replication response found experimentally but that it at the same time effectively prohibits the existence of only one plasmid copy in a dividing cell. In combination with the partition system of R1, this can lead to very high segregational stability. The R1 control mechanism is compared to the different multistep copy number control of plasmid ColE1 that is based on conventional sensitivity amplification. This implies that while copy number control for ColE1 efficiently corrects for fluctuations that have already occurred, R1 copy number control prevents their emergence in cells that by chance start their cycle with only one plasmid copy. We also discuss how regular, clock-like, behaviour of single plasmid copies becomes hidden in experiments probing collective properties of a population of plasmid copies because the individual copies are out of phase. The model is formulated using master equations, taking a stochastic approach to regulation, but the mathematical formalism is kept to a minimum and the model is simplified to its bare essence. This simplicity makes it possible to extend the analysis to other replicons with similar design principles.

Bacteriocin Plasmids↗
PubMed1996

The spin dynamics of heteronuclear multiple-spin systems formulated in the extended strong-narrowing limit.

Employing the perturbation approach directly in the multiply rotating frame, the master equation governing the spin dynamics of scalar-coupled heteronuclear multiple-spin systems has been derived. The resulting equation for the spin-density operator and the matrix form of the relaxation superoperator are relatively simple under the conditions of the "extended" strong-narrowing limit. The extended strong-narrowing limit, which requires that omega iI tau c << 1 and 2 pi Jij tau c << 1 [where I represents one of the spin types in the heteronuclear spin system, omega Ii is the chemical-shift range of spin type I in radians per second, Jij is the coupling constant J between spin i and spin j (like or unlike) in hertz, and tau c is the correlation time in seconds per radian], can be applied to heteronuclear spin systems of both small molecules and biopolymers in high-resolution liquid NMR. This newly developed formalism is used to investigate the effect of transverse cross relaxation on the apparent coupling constants in a heteronuclear 1H-1H-13C three-spin system. The calculation shows that, despite the strong dipolar interaction between directly bonded 1H and 13C, this perturbation on the apparent couplings is trivial. This result is in contrast to the homonuclear proton spin system, where the scalar coupling constants between two protons are significantly modulated if one proton is strongly dipole coupled to another proton. The underlying physical reasons for the different behavior of heteronuclear and homonuclear systems are explained.

Electron Spin Resonance Spectroscopy↗
PubMed2000

Coherent cross-polarization theory for a spin-12 coupled to a general object

Zero-order average-Hamiltonian theory is used to extend the product-operator description of coherent spin-spin cross-polarization to the case of a spin-12 coupled to a general object, like a molecular rotor or a quantum oscillator. The object, which is not necessarily in a Boltzmann equilibrium state, is assumed to have no interaction with the lattice and no internal relaxation capacity. The Bloch-Wangsness-Redfield (BWR) theory for incoherent processes like spin-lattice relaxation does not apply for such an isolated spin-object pair. Nevertheless spectral density at the Larmor frequency, of key importance in BWR theory, also plays a central role in object-induced spin polarization. Spectral density in our theory is represented by quantum operators J(-) and J(+). If J(-) and J(+) do not commute, the spin-object coupling may cause spin polarization in an initially saturated spin system. This represents a coherent mechanism for spin cooling, which in specific cases may lead to enhanced spin polarization above the thermal equilibrium value. A master equation is derived for general spin-object cross-polarization, and applied to the case of a spin pair inside a uniaxial rotor, and a spin coupled to a microelectronic LC circuit. Copyright 2000 Academic Press.

Journal Article↗
PubMed2001

Dynamics of spin I=3/2 under spin-locking conditions in an ordered environment.

We have derived approximate analytic solutions to the master equation describing the evolution of the spin I=3/2 density operator in the presence of a radio-frequency (RF) field and both static and fluctuating quadrupolar interactions. Spectra resulting from Fourier transformation of the evolutions of the on-resonance spin-locked magnetization into the various coherences display two satellite pairs and, in some cases, a central line. The central line is generally trimodal, consisting of a narrow component related to a slowly relaxing mode and two broad components pertaining to two faster relaxing modes. The rates of the fast modes are sensitive to slow molecular motion. Neither the amplitude nor the width of the narrow component is affected by the magnitude of the static coupling, whereas the corresponding features of the broad components depend in a rather complicated manner on the spin-lock field strength and static quadrupolar interaction. Under certain experimental conditions, the dependencies of the amplitudes on the dynamics are seen to vanish and the relaxation rates reduce to relatively simple expressions. One of the promising emerging features is the fact that the evolutions into the selectively detected quadrupolar spin polarization order and the rank-two double-quantum coherence do not exhibit a slowly relaxing mode and are particularly sensitive to slow molecular motion. Furthermore, these coherences can only be excited in the presence of a static coupling and this makes it possible to discern nuclei in anisotropic from those in isotropic environment. The feasibility of the spin-lock pulse sequences with limited RF power and a nonvanishing average electric field gradient has been demonstrated through experiments on sodium in a dense lyotropic DNA liquid crystal.

Crystallization↗
PubMed2002

Control of neural information transmission by synaptic dynamics.

The computational processing of a neural system is strongly influenced by the dynamical characteristics of the information transmission between neurons. In this work, the control of neural information transmission by synaptic dynamics is investigated by means of a master-equation-based stochastic model of pre-synaptic release of neurotransmitter-containing vesicles. The model incorporates facilitation of vesicle fusion with the pre-synaptic membrane due to intracellular calcium ions and depletion of readily releasable vesicles. The message to be transmitted is coded by the pre-synaptic firing sequence, and the received signal corresponds to the post-synaptic membrane potential response. At the sending end, the stochastic character of the vesicle release contributes to the entropy of the probability distribution of the number of vesicles released and represents noise with respect to information transmission. At the receiving end, the generation of post-synaptic membrane potentials is influenced by the temporal behaviour of ionic currents and membrane charging and is determined by means of a low-dimensional model. The rate and temporal types of neural coding are compatible with limiting cases of the synaptic information transmission as a function of initial vesicle release probability and pre-synaptic firing rate. The effects of the nonlinear dependencies of the vesicle release probability on intracellular calcium concentration and number of available vesicles are analysed. The model is compared with phenomenological and reduced models, a principal advantage being the capability of also determining fluctuations of dynamic variables

Calcium↗
PubMed1993

DNA damage in non-proliferating cells subjected to ionizing irradiation at high or low dose rates.

Ionizing radiation damage to the genome of a non-cycling mammalian cell is analyzed using continuous time Markov chains. Immediate damage induced by the radiation is modeled as a batch Poisson arrival process of DNA double strand breaks (DSBs). Different kinds of radiation, for example gamma rays or alpha particles, have different batch probabilities. Enzymatic modulation of the immediate damage is modeled as a Markov process similar to the processes described by the master equation of stochastic chemical kinetics. An illustrative example is the restitution/complete exchange model, which postulates that radiation induced DSBs can subsequently either undergo enzymatically mediated repair (restitution) or can participate pairwise in chromosome exchanges, some of which make irremediable lesions such as dicentric chromosome aberrations. One may have rapid irradiation followed by enzymatic DSB processing or have prolonged irradiation with both DSB arrival and enzymatic DSB processing continuing throughout the irradiation period. A complete solution of the Markov chain is known for the case that the exchange rate constant is negligible so that no irremediable chromosome lesions are produced and DSBs are the only damage to the genome. Using PDEs for generating functions, a perturbation calculation is made assuming the exchange rate constant is small compared to the repair rate constant. Some non-perturbative results applicable to very prolonged irradiation are also obtained using matrix methods: Perron-Frobenius theory, variational methods and numerical approximations of eigenvalues. Applications to experimental results on expected values, variances and statistical distributions of DNA lesions are briefly outlined. Continuous time Markov chain models are the most systematic of those current radiation damage models which treat DSB-DSB interactions within the cell nucleus as homogeneous (e.g. ignore diffusion limitations). They contain most other homogeneous models as special cases, limiting cases or approximations. However, applying the continuous time Markov chain models to studying spatial dependence of DSB interactions, which is generally believed to be very important in some situations, presents difficulties.

Animals↗
PubMed1987

Exact results for the average dynamic behavior of some non-linear neural networks.

We have studied the global dynamic behavior of neural-like networks of synchronous threshold elements by writing a master equation as a function of parameter values using statistical methods. Exact results for highly connected networks and no correlation are obtained, showing that in this case (contrary to previous results) the average activity can only display simple stable behaviour, the sole exception being special cases of a slow passage through a tangent bifurcation, and a limit cycle of length two. By introducing an appropriate probabilistic hypothesis, we also study the average activity and correlation for highly connected networks with the topology of a (Cayley) tree. In this case the dynamic is ruled by a pair of coupled equations linking activity and correlation, and the tendency is for the correlation to disappear over time. However, under reasonable biological conditions, this tendency will be extremely slow, giving rise to a region of pseudo-stability.

Animals↗
PubMed1979

Theory of transport noise in membrane channels with open-closed kinetics.

A theoretical approach to transport noise in kinetic systems, which has recently been developed, is applied to electric fluctuations around steady-states in membrane channels with different conductance states. The channel kinetics may be simple two state (open-closed) kinetics or more complicated. The membrane channel is considered as a sequence of binding sites separated by energy barriers over which the ions have to jump according to the usual single-file diffusion model. For simplicity the channels are assumed to act independently. In the special case of ionic movement fast compared with the channel open-closed kinetics the results agree with those derived from the usual Master equation approach to electric fluctuations in nerve membrane channels. For the simple model of channels with one binding site and two energy barries the coupling between the fluctuations coming from the open-closed kinetics and from the jump diffusion is investigated.

Binding Sites↗
PubMed1996

The dynamical theory of coevolution: a derivation from stochastic ecological processes.

In this paper we develop a dynamical theory of coevolution in ecological communities. The derivation explicitly accounts for the stochastic components of evolutionary change and is based on ecological processes at the level of the individual. We show that the coevolutionary dynamic can be envisaged as a directed random walk in the community's trait space. A quantitative description of this stochastic process in terms of a master equation is derived. By determining the first jump moment of this process we abstract the dynamic of the mean evolutionary path. To first order the resulting equation coincides with a dynamic that has frequently been assumed in evolutionary game theory. Apart from recovering this canonical equation we systematically establish the underlying assumptions. We provide higher order corrections and show that these can give rise to new, unexpected evolutionary effects including shifting evolutionary isoclines and evolutionary slowing down of mean paths as they approach evolutionary equilibria. Extensions of the derivation to more general ecological settings are discussed. In particular we allow for multi-trait coevolution and analyze coevolution under nonequilibrium population dynamics.

Animals↗
PubMed2003

Aging dynamics in globular proteins: summary and analysis of experimental results and simulation by a modified trap model.

Recent results of spectral diffusion experiments by spectral hole-burning techniques carried out at cryogenic temperatures on various monomeric heme proteins unequivocally show interesting new features of conformational dynamics of globular proteins that were not emphasized in the literature until now. These new aspects of the protein dynamics are anomalous diffusion and the aging effect. Here, using the similarities between proteins and glassy systems, we present a model which can interpret the line broadening and-through this effect-the aging phenomenon as well. Leaving untouched the widely accepted energy landscape (EL) concept for the general description of protein dynamics, we concentrate on the bottom of the funnel-like EL, because this part corresponds to the native state(s) at low temperature. We suggest that the overall shape of the EL at the lowest energy range is rather smooth, but on a finer scale it consists of traps. The dynamics is defined by sequential jumps among these traps and the process is described by a Master equation, where the hopping rate only depends on the parameters of the starting state. This model was adapted to interpret the common results of spectral diffusion experiments. We tested our model in the simplest case by computer simulation, and it shows excellent agreement with the experimental data. To our knowledge this is the first work where a theoretical interpretation of the aging dynamics of proteins is directly and quantitatively related to the experimental observations. We also show that the model, after the generalization that the traps are hierarchically organized, is in accordance with the concept of other well-known EL models.

Biophysical Phenomena↗
PubMed2006

Stochastic kinetics description of a simple transcription model.

We study a stochastic model of transcription kinetics in order to characterize the distributions of transcriptional delay and of elongation rates. Transcriptional delay is the time which elapses between the binding of RNA polymerase to a promoter sequence and its dissociation from the DNA template strand with consequent release of the transcript. Transcription elongation is the process by which the RNA polymerase slides along the template strand. The model considers a DNA template strand with one promoter site and n nucleotide sites, and five types of reaction processes, which we think are key ones in transcription. The chemical master equation is a set of ordinary differential equations in 3(n) variables, where n is the number of bases in the template. This model is too huge to be handled if n is large. We manage to get a reduced Markov model which has only 2n independent variables and can well approximate the original dynamics. We obtain a number of analytical and numerical results for this model, including delay and transcript elongation rate distributions. Recent studies of single-RNA polymerase transcription by using optical-trapping techniques raise an issue of whether the elongation rates measured in a population are heterogeneous or not. Our model implies that in the cases studied, different RNA polymerase molecules move at different characteristic rates along the template strand. We also discuss the implications of this work for the mathematical modeling of genetic regulatory circuits.

Algorithms↗
PubMed1990

Theory of exciton annihilation in complexes of a finite number of molecular sites.

A theory of the kinematics of singlet exciton annihilation in complexes of a finite number of molecular sites is developed. The theory is based on a specific scheme suggested earlier by Gülen, Wittmershaus, and Knox [Biophys J. 49:469-477 (1986)]. It is adequate to address the excitation kinetics and dynamics in such systems, especially under high excitation intensities. A Pauli master equation is formulated and is solved to give explicit expressions for observables such as quantum yield and fluorescence intensity. The excitation intensity dependence of the observables is taken into account by introducing Poisson statistics. Details relevant to its application to the annihilation of excitons in photosynthetic systems and its connection to earlier theories are presented.

Energy Transfer↗
PubMed1992

DNA damage caused by ionizing radiation.

A survey is given of continuous-time Markov chain models for ionizing radiation damage to the genome of mammalian cells. In such models, immediate damage induced by the radiation is regarded as a batch-Poisson arrival process of DNA double-strand breaks (DSBs). Enzymatic modification of the immediate damage is modeled as a Markov process similar to those described by the master equation of stochastic chemical kinetics. An illustrative example is the restitution/complete-exchange model. The model postulates that, after being induced by radiation, DSBs subsequently either undergo enzymatically mediated restitution (repair) or participate pairwise in chromosome exchanges. Some of the exchanges make irremediable lesions such as dicentric chromosome aberrations. One may have rapid irradiation followed by enzymatic DSB processing or have prolonged irradiation with both DSB arrival and enzymatic DSB processing continuing throughout the irradiation period. Methods for analyzing the Markov chains include using an approximate model for expected values, the discrete-time Markov chain embedded at transitions, partial differential equations for generating functions, normal perturbation theory, singular perturbation theory with scaling, numerical computations, and certain matrix methods that combine Perron-Frobenius theory with variational estimates. Applications to experimental results on expected values, variances, and statistical distributions of DNA lesions are briefly outlined. Continuous-time Markov chains are the most systematic of those radiation damage models that treat DSB-DSB interactions within the cell nucleus as homogeneous (e.g., ignore diffusion limitations). They contain virtually all other relevant homogeneous models and semiempirical summaries as special cases, limiting cases, or approximations. However, the Markov models do not seem to be well suited for studying spatial dependence of DSB interactions, which is known to be important in some situations.

Animals↗
PubMed1992

Structured Biological Modelling: a method for the analysis and simulation of biological systems applied to oscillatory intracellular calcium waves.

In biology signal and information processing networks are widely known. Due to their inherent complexity and non-linear dynamics the time evolution of these systems can not be predicted by simple plausibility arguments. Fortunately, the power of modern computers allows the simulation of complex biological models. Therefore the problem becomes reduced to the question of how to develop a consistent mathematical model which comprises the essentials of the real biological system. As an interface between the phenomenological description and a computer simulation of the system the proposed method of Structured Biological Modelling (SBM) uses top-down levelled dataflow diagrams. They serve as a powerful tool for the analysis and the mathematical description of the system in terms of a stochastic formulation. The stochastic treatment, regarding the time evolution of the system as a stochastic process governed by a master equation, circumvents most difficulties arising from high dimensional and non-linear systems. As an application of SBM we develop a stochastic computer model of intracellular oscillatory Ca2+ waves in non-excitable cells. As demonstrated on this example, SBM can be used for the design of computer experiments which under certain conditions can be used as cheap and harmless counterparts to the usual time-consuming biological experiments.

Calcium↗