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1. Neuronal death following excitotoxic insult appears to be a stochastic process involving transition through an intermediate biochemical state. 2. Hydrogen ion accumulation in the hours after toxic glutamate exposure may indicate that this transition has occurred.
The time-dependent measurement probabilities for the simple two-state quantum oscillator seem to invite description as a classical two-state stochastic process. It has been shown that such a description cannot be achieved using a Markov process. Constructing a more general non-Markov process is a challenging task, requiring as it does the proper generalizations of the Markovian Chapman-Kolmogorov and master equations. Here we describe those non-Markovian generalizations in some detail, and we then apply them to the two-state quantum oscillator. We devise two non-Markovian processes that correctly model the measurement statistics of the oscillator, we clarify a third modeling process that was proposed earlier by others, and we exhibit numerical simulations of all three processes. Our results illuminate some interesting though widely unappreciated points in the theory of non-Markovian stochastic processes. But since quantum theory does not tell us which one of these quite different modeling processes "really" describes the behavior of the oscillator, and also since none of these processes says anything about the dynamics of other (noncommuting) oscillator observables, we can see no justification for regarding any of these processes as being fundamentally descriptive of quantum dynamics. (c) 2001 American Institute of Physics.
An asynchronous Boolean network with N nodes whose states at each time point are determined by certain parent nodes is considered. We make use of the models developed by Matache and Heidel [Matache, M.T., Heidel, J., 2005. Asynchronous random Boolean network model based on elementary cellular automata rule 126. Phys. Rev. E 71, 026232] for a constant number of parents, and Matache [Matache, M.T., 2006. Asynchronous random Boolean network model with variable number of parents based on elementary cellular automata rule 126. IJMPB 20 (8), 897-923] for a varying number of parents. In both these papers the authors consider an asynchronous updating of all nodes, with asynchrony generated by various random distributions. We supplement those results by using various stochastic processes as generators for the number of nodes to be updated at each time point. In this paper we use the following stochastic processes: Poisson process, random walk, birth and death process, Brownian motion, and fractional Brownian motion. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed-point analysis. The dynamics of the system show that the number of nodes to be updated at each time point is of great importance, especially for the random walk, the birth and death, and the Brownian motion processes. Small or moderate values for the number of updated nodes generate order, while large values may generate chaos depending on the underlying parameters. The Poisson process generates order. With fractional Brownian motion, as the values of the Hurst parameter increase, the system exhibits order for a wider range of combinations of the underlying parameters.
Bone metastasis may be considered a non-stochastic process, since the blood flow in bone is lower than that in other organs and most cancers do not have a tendency to metastasize to bone in in vivo experiments. Furthermore, the experimental model of bone metastasis, based on the ligation of major venous flow, can not explain the wide-spread bone metastasis which is commonly observed in clinical cases. These observations may be explained by the hypothesis that tumor cells have a phenotype for translocating to specific tissues and that tumor cell growth is controlled by the microenvironmental factors in situ.
This study examined the influence of deterministic and stochastic processes (including white Gaussian noise) on reductions in the amount of force output variability through childhood. The structure of the force signal produced during a constant isometric pinch grip task was examined as a function of age (6, 8, and 10 years, and young adults), availability of feedback information (with and without vision), digit (thumb and index finger), and force level (5, 15, 25, and 35% of maximal voluntary contraction). The amount of white Gaussian noise in the force signals was negligible and not age related. The availability of vision led increasingly over the older age groups to lower long-range correlations with more than a single scaling range in a 1/f-like decay process. The reductions in the amount of force variability from childhood to adulthood were related in large part to deterministic organization that increased the adaptive use of higher frequency components, due to the more flexible use of information feedback and feedforward processes.
Cancer is a multistage process in which cell proliferation determines the growth of cells within stages and is associated with the transition of cells from one stage to the next. The usual model for cancer risk assessment, the linearized multistage model, does not explicitly include cell proliferation. More realistic cancer models are needed to reduce uncertainty in cancer risk assessment and to provide basic insights into the quantitative roles of cell proliferation and mutation. This report describes a simulation model for the transition of cells from one stage to the next and for clonal growth within stages. The model is intended to facilitate the use of experimental data on cell replication and preneoplastic lesions in risk assessment. When a population of cells is small its growth may be governed by stochastic processes. Such a population may disappear by chance even when the probability of cell division on a given time interval exceeds the probability of cell death. Procedures for estimating cell proliferation and mutation parameters from data for use in risk assessment should account for this random aspect of growth. The present model describes cell growth governed by stochastic processes, is consistent with earlier analytical expressions for such growth (Dewanjii et al., Risk Anal. 9, 179, 1989), and is flexible with respect to time-dependent data. A data set for spontaneous basophilic clones in male F344 rats (Popp et al., Fundam. Appl. Toxicol. 5, 314, 1985) is analyzed and predictions are made for (a) the probability of mutation to the basophilic genotype per division of a normal hepatocyte (3.5 x 10(-8)), (b) number of basophilic clones too small to be detected, and (c) number of basophilic clones that disappear by chance. This work illustrates the potential of computer simulation for quantitative analysis of the roles of cell division, cell death, and mutation in cancer.
In this simulation study for bone adaptive remodeling, loading conditions are described as stochastic processes to catch the unpredictable characteristics of daily physical activities, which are observed to be closely related with bone adaptive remodeling. This will not only eliminate the necessity of arbitrary choices for loading conditions, but also generate greater flexibility for simulations of bone adaptive remodeling. The sensitivity of simulation outcomes to the parameters in the simulation algorithm was examined by applying stochastic loading conditions on finite element models of simplified spine structures. In this way, the limitations induced by simplifying loading conditions into constant or cyclic loads can be avoided and, potentially, more clinical observations could be accommodated when more comprehensive finite element models are available.
A model of human health history and aging, based on a multivariate stochastic process with both continuous diffusion and discrete jump components, is presented. Discrete changes generate non-Gaussian diffusion with time varying continuous state distributions. An approach to calculating transition rates in dynamically heterogeneous populations, which generalizes the conditional averaging of hazard rates done in "fixed frailty" population models, is presented to describe health processes with multiple jumps. Conditional semi-invariants are used to approximate the conditional p.d.f. of the unobserved health history components. This is useful in analyzing the age dependence of mortality and health changes at advanced age (e.g., 95+) where homeostatic controls weaken, and physiological dynamics and survival manifest nonlinear behavior.
Using the theory of branching age-dependent stochastic processes, probabilistic descriptions are given of the age distribution associated with cell generations, and of some processes containing the information on cells synthesizing DNA after the action of proliferative stimulus.
This study proposes that plasticity of dendritic spine formation may be modeled as distribution patterns imbedded in a spine length-dependent and density-dependent stochastic process. Modeling the jewel fish tectal interneuron revealed a critical 10-36 micron region where spine length plasticity was predicted to be most detectable. This hypothesis was tested by comparing neurons sampled from jewel fish reared for 4 years in a crowded environment (1 fish/5.64 l) with uncrowded controls (1 fish/25 l). The interaction between fish groups and the location of spine length differences was significant (p less than 0.01) within the basal 10-30 micron dendritic segment. Spine head widths were also significantly smaller (p less than 0.01) in the crowded fish over the entire dendrite. These findings suggest two modes of neuronal plasticity: (1) plasticity of spine length during formation, and (2) plasticity in spine head width after the spine is formed.
The classical definition of evolutionary stability assumes that the fitness of each phenotype is fully determined by the composition of phenotypes in the population and by the strategies of each of these phenotypes. In natural populations, however, stochasticity often plays a crucial role in determining the fitness of an individual and a deterministic fitness function is probably rather rare. For example, choices of a new host plant, prey or oviposition patch are completely stochastic processes. Here we introduce a new definition of ESS that takes into account the effect of stochasticity on individual fitness. Then we show an application of this definition in a realistic system.
The probabilistic description of cell generation numbers in the populations induced to proliferate is considered on the basis of the model of branching age-dependent stochastic process. The recurrent formulas for generating functions (and moments) are derived for the following process which are of interest for the analysis of induced proliferation in closed cell populations: the number of cells in n-th generation horn up to the moment of observation, and the number of cell in n-th generation existing at a given moment.
This study aims at formulating a dynamic model of particle sedimentation as applied to lipoprotein deposition during atheroma progression. The basic assumption is that all particles are identical and that the number of sedimented particles is relatively great. It is hypothised that sedimentation of a given particle is random; according to the theory of stochastic processes, the probability of a certain number of particles to sediment or deposit changes with time. The stochastic approach may explain some aspects of atherosclerosis development, i.e. its progression or regression.
Computer simulations in which selection acts on a quantitative character show that the randomness of mutations can contribute significantly to evolutionary divergence between populations. In different populations, different advantageous mutations occur, and are selected to fixation, so that the populations diverge even when they are initially identical, and are subject to identical selection. This stochastic process is distinct from random genetic drift. In some circumstances (large populations or strong selection, or both) mutational order can be greatly more important than random drift in bringing about divergence. It can generate a 'disconnection' between evolution at the phenotypic and genotypic levels, and can give rise to a rough 'molecular clock', albeit episodic, that is driven by selection. In the absence of selection, mutational order has little or no effect.
The underlying stochastic nature of many models of the actomyosin interaction should result in fluctuations in both force and shortening velocity. In classical experimental approaches involving intact or glycerinated muscle preparations these fluctuations are too small to resolve owing to the large numbers of crossbridges involved. However, new experimental techniques allow mechanical measurements to be made in systems in which small numbers of myosin heads act on a single actin filament, or small numbers of kinesin molecules act on a single tubulin filament. In these systems, stochastic effects should be evident. To understand better the nature of the expected stochastic effects, we have used computer simulation to investigate the fluctuations predicted by the original model for muscle crossbridge mechanics proposed by A.F. Huxley. We consider three situations: (1) the translation of actin or tubulin filaments by myosin or kinesin motors immobilized on a fixed substrate, (2) the production of tension by ensembles of immobilized myosin which involve the displacement of an elastic load, and (3) the fluctuations in axial displacement of a single, bipolar myosin thick filament interacting with actin filaments as in a sarcomere. In all three cases, fluctuations are clearly evident in simulations involving small numbers of motors. For case (1), we show that translation velocities can vary with crossbridge density. Whether one motor translates a filament faster, slower or at the same speed as many motors depends on the relative magnitudes of the attachment and detachment rate functions. Analytical expressions are provided to quantitate this relationship. For case (2), we show that fluctuations predicted assuming perfectly isometric conditions differ form those observed when the 'isometric state' is achieved against an elastic load. 'Elastic damping' of the fluctuations in the system results from the presence of many attached motors. In case (3) we show that in spite of the presence of stochastic fluctuations which can destabilize the uniformity of filament overlap in a sarcomere, the magnitude of thick filament displacement is less than might be anticipated over time periods of in vivo contraction. Taken together, these simulations allow one to better interpret experimental data in terms of current models of motor function.
We consider the problem of "discrete-time persistence," which deals with the zero crossings of a continuous stochastic process X(T) measured at discrete times T=nDeltaT. For a Gaussian stationary process the persistence (no crossing) probability decays as exp(-theta(D)T)=[rho(a)](n) for large n, where a=exp(-DeltaT/2) and the discrete persistence exponent theta(D) is given by theta(D)=(ln rho)/(2 ln a). Using the "independent interval approximation," we show how theta(D) varies with DeltaT for small DeltaT and conclude that experimental measurements of persistence for smooth processes, such as diffusion, are less sensitive to the effects of discrete sampling than measurements of a randomly accelerated particle or random walker. We extend the matrix method developed by us previously [Phys. Rev. E 64, 015101(R) (2001)] to determine rho(a) for a two-dimensional random walk and the one-dimensional random-acceleration problem. We also consider "alternating persistence," which corresponds to a<0, and calculate rho(a) for this case.
Understanding the evolutionary dynamics of influenza A virus is central to its surveillance and control. While immune-driven antigenic drift is a key determinant of viral evolution across epidemic seasons, the evolutionary processes shaping influenza virus diversity within seasons are less clear. Here we show with a phylogenetic analysis of 413 complete genomes of human H3N2 influenza A viruses collected between 1997 and 2005 from New York State, United States, that genetic diversity is both abundant and largely generated through the seasonal importation of multiple divergent clades of the same subtype. These clades cocirculated within New York State, allowing frequent reassortment and generating genome-wide diversity. However, relatively low levels of positive selection and genetic diversity were observed at amino acid sites considered important in antigenic drift. These results indicate that adaptive evolution occurs only sporadically in influenza A virus; rather, the stochastic processes of viral migration and clade reassortment play a vital role in shaping short-term evolutionary dynamics. Thus, predicting future patterns of influenza virus evolution for vaccine strain selection is inherently complex and requires intensive surveillance, whole-genome sequencing, and phenotypic analysis.
1. Slow waves were recorded from the circular muscle layer of the antral region of guinea-pig stomach. Slow waves were abolished by 2APB, an inhibitor of IP(3)-induced Ca2+ release. 2. When the rate of generation of slow waves was monitored it was found to vary from cycle to cycle around a mean value. The variation persisted after abolishing neuronal activity with tetrodotoxin. 3. When simultaneous recordings were made from interstitial cells in the myenteric region (ICC(MY)) and smooth muscle cells of the circular layer, variations in the rate of generation of slow waves were found to be linked with variations in the rate of generation of driving potentials by ICC(MY). 4. A preparation was devised which consisted of the longitudinal muscle layer and ICC(MY). In this preparation ICC(MY) and smooth muscle cells lying in the longitudinal muscle layer generated driving potentials and follower potentials, synchronously. 5. Driving potentials had two components, a rapid primary component that was followed by a prolonged plateau component. Caffeine (3 mM) abolished the plateau component; conversely reducing the external concentration of calcium ions [Ca2+](o) mainly affected the primary component. 6. Analysis of the variations in the rate of generation of driving potentials indicated that this arose because both the duration of individual driving potentials and the interval between successive driving potentials varied. 7. It is suggested that the initiation of pacemaker activity in a network of ICC(MY) is a stochastic process, with the probability of initiating a driving potential slowly increasing, after a delay, from a low to a higher value following the previous driving potential.