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PubMed2004

Effects of electrode-to-fiber distance on temporal neural response with electrical stimulation.

This paper presents an analysis of the effects of the electrode-to-fiber distance on the temporal response properties of an auditory nerve fiber stimulated by electric current pulses. This analysis was based upon results from a computational model of a mammalian auditory nerve fiber axon having 50 nodes of Ranvier, each consisting of 130 stochastic sodium channels and 50 stochastic potassium channels, making it possible to represent the temporal fluctuations of action potential initiation and conduction. A monopolar stimulus electrode was located above a central (26th) node at electrode-to-fiber distances of 1, 4, and 7 mm, while the recording electrode was located at the 36th node. Action potentials (spikes) were generated by the biophysical model using the Crank-Nicholson method to solve a diffusive partial differential equation. By observing the occurrence times of spikes in response to 2000 cathodic monophasic stimulus pulses, temporal jitter (i.e., the standard deviation of spike times) was calculated and the poststimulus time (PST) histogram was generated as well. Furthermore, by computing the PST histogram for each initiation node as functions of space (node number) and time (PST), it was shown that spike initiation was distributed not only spatially but also temporally for stimulus levels producing firing efficiencies (FEs) near 0.5. However, at levels producing FEs near 0.99, while temporal variations approached zero, the spatial distribution of initiating nodes was comparable to that observed for the FE near 0.5. As temporal fluctuations are important for speech coding in cochlear implants, we conclude that spatial characteristics of the electrode-auditory nerve fiber interface may play a significant role in influencing these stochastic temporal processes.

Action Potentials↗
PubMed2006

Systemic cancer progression and tumor dormancy: mathematical models meet single cell genomics.

Metastatic progression is thought to result from genetically advanced "fully-malignant" tumor cells. Within the concept the prevailing view holds that such cells disseminate mostly from large tumors and are capable of growing into metastases once they arrive at a distant site. Support for this scenario comes from numerous mouse models in which transplanted tumor cells grow into metastases within days or weeks. However, the assumption of such fully-malignant disseminating cells in human cancer is misleading and is neither supported by mathematical modeling of survival data from cancer patients nor by ex-vivo genomic data from disseminated cancer cells. For example, in breast cancer the growth of metastases is highly homogeneous and takes on average six years, the number of disseminated tumor cells before diagnosis of metastasis is similar for different tumor stages, and the genomic aberrations of disseminated cancer cells do rarely correspond to those in the primary tumor. Since these facts question conventional concepts of metastatic progression we provide a model of cancer progression in which time considerations and direct ex-vivo data form a starting point. In the proposed model tumor dormancy is a characteristic of almost all migrated tumor cells and metastatic growth is a rare, stochastic, evolutionary process of selection and mutation of cells that often disseminate shortly after transformation at the primary site.

Animals↗
PubMed2001

Photosynthetic electron transfer controlled by protein relaxation: analysis by Langevin stochastic approach.

Relaxation processes in proteins range in time from picoseconds to seconds. Correspondingly, biological electron transfer (ET) could be controlled by slow protein relaxation. We used the Langevin stochastic approach to describe this type of ET dynamics. Two different types of kinetic behavior were revealed, namely: oscillating ET (that could occur at picoseconds) and monotonically relaxing ET. On a longer time scale, the ET dynamics can include two different kinetic components. The faster one reflects the initial, nonadiabatic ET, whereas the slower one is governed by the medium relaxation. We derived a simple relation between the relative extents of these components, the change in the free energy (DeltaG), and the energy of the slow reorganization Lambda. The rate of ET was found to be determined by slow relaxation at -DeltaG < or = Lambda. The application of the developed approach to experimental data on ET in the bacterial photosynthetic reaction centers allowed a quantitative description of the oscillating features in the primary charge separation and yielded values of Lambda for the slower low-exothermic ET reactions. In all cases but one, the obtained estimates of Lambda varied in the range of 70-100 meV. Because the vast majority of the biological ET reactions are only slightly exothermic (DeltaG > or = -100 meV), the relaxationally controlled ET is likely to prevail in proteins.

Crystallography, X-Ray↗
PubMed2006

Information coding capacity of cerebellar parallel fibers.

Understanding synaptic connectivity is a prerequisite to gaining insight on how the central nervous system processes information. Cerebellar parallel fibers make an impressive number of synapses with the Purkinje cells. These synapses are the major structural elements of a large information processing system. The objective of the present report is to describe a method to estimate the coding capacity of this information processing system. We propose to derive the coding capacity from the linear distribution pattern of synaptic varicosities along parallel fibers in a manner consistent with Shannon's information theory formalism. The coding capacity of an average parallel fiber synapse is S=-kappaSigmaP(l(i))lnP(l(i)), where kappa=1/ln2, P(l(i)) is the probability of observing a particular inter-varicosital distance l(i), and ln is the natural logarithm to the base e. In the cerebellar parallel fibers of the mouse, and in a number of other unmyelinated axonal systems, the distribution pattern of P(l(i)) as a function of l(i) is exponential-like. According to information theory, the exponential-like distribution pattern suggests that information transmission in these axonal synaptic systems is operating at near-optimal coding capacity. This optimization in information coding may be the result of a stochastic-like process regulating the formation or elimination of parallel fiber synapses during development and maturation. In the adult nervous system, neuroplasticity-mediated synaptic remodeling may also regulate the coding capacity of axonal synapses via a similar stochastic-like process. The conceptual framework herein may be applicable to other axonal systems in the nervous system.

Animals↗
PubMed1979

Model of hospital's inflow.

To be accepted as an inpatient in the Geneva Hospital one must proceed through a registration post. Data collecting sessions were set up there to study its working. Since many random components enter the registration procedure a stochastic queuing process is the appropriate model. The process main characteristics are determined by rather involved statistical and mathematical means. The values reckoned for the most relevant parameters (to both medical staff and general public) are found quite plausible.

Admitting Department, Hospital↗
PubMed1994

Asymptotic behaviour of reaction-diffusion systems in population and epidemic models. The role of cross diffusion.

Cross diffusion has been widely considered in the mathematical modelling of spatially structured ecological and epidemic systems, either in the mechanical description of diffusion or in the stochastic point process description of interacting populations. In this paper mathematical results recently obtained by the authors about the asymptotic behaviour of reaction-diffusion systems with full matrices of diffusion are applied to classes of biological systems.

Animals↗
PubMed2005

A ballistic model of choice response time.

Almost all models of response time (RT) use a stochastic accumulation process. To account for the benchmark RT phenomena, researchers have found it necessary to include between-trial variability in the starting point and/or the rate of accumulation, both in linear (R. Ratcliff & J. N. Rouder, 1998) and nonlinear (M. Usher & J. L. McClelland, 2001) models. The authors show that a ballistic (deterministic within-trial) model using a simplified version of M. Usher and J. L. McClelland's (2001) nonlinear accumulation process with between-trial variability in accumulation rate and starting point is capable of accounting for the benchmark behavioral phenomena. The authors successfully fit their model to R. Ratcliff and J. N. Rouder's (1998) data, which exhibit many of the benchmark phenomena.

Choice Behavior↗
PubMed1992

Stochastic aspects of leukocyte transit in hamster cheek pouch arterioles.

To clarify the dynamics of leukocyte delivery to the capillary network we measured leukocyte velocity (Vwbc), leukocyte flux and the intra-arrival times between successive leukocytes in terminal arterioles of the cheekpouch of eight hamsters. The sequences, generated electronically when fluorescent leukocytes passed a fixed point in the arteriole, were analyzed as stochastic point processes. Results showed that six sequences were stationary, and two with a linear trend in Vwbc, were not. Tests performed on the stationary sequences indicated conformity to a renewal process in all cases. Analysis of the distributional and sequential properties of the sequences indicated a good fit to a Poisson process. Overall these results show that leukocyte delivery to the capillary network can be characterized as a Poisson process if Vwbc remains relatively constant, if not, a non-homogeneous Poisson process is a more suitable model, with Vwbc being the explanatory variable. The demonstration of the applicability of these models may lead to a more complete understanding of both the physiological and patho-physiological dynamics of leukocytes within the microvasculature.

Animals↗
PubMed1989

A methodological study of a nonlinear stochastic model of an AIDS epidemic with recruitment.

A nonlinear stochastic model of an AIDS epidemic with recruitment of infectives, susceptibles, and AIDS cases into a randomly mixing population of male homosexuals was formulated and studied from a methodological point of view through intensive computer experimentation. Probability generating functions were used to formulate a model for the monthly probability that a susceptible individual becomes infected with HIV, under the assumption that the probability of infection per sexual contact varies as a function of the duration of infection. A method for taking into account the use of condoms to prevent infection with HIV was also introduced. Nonlinear difference equations, resembling deterministic epidemic models, were embedded in the stochastic population process by iterating an initial conditional expectation. Examples of Monte Carlo experiments are presented, illustrating that solutions of these nonlinear difference equations are not always good measures of central tendency for variations in the sample functions of the process. Two important substantive conclusions drawn from the Monte Carlo experiments were that efforts should be made to collect quantitative information on the probability of infection per sexual contact as a function of duration of infection and the frequency of condom use within and among risk categories in a population.

Acquired Immunodeficiency Syndrome↗
PubMedDate not supplied

Morphological analysis and modeling of neuronal dendrites.

Morphological data on two classes of neurons from mammalian midbrain have quantitatively been analyzed for dendritic shape parameters. Their frequency distributions were used to optimize the parameters of a dendritic growth model which describes dendritic morphology by a stochastic growth process of segment branching. The model assumes randomness with respect to both the selection of the branching segment out of the tree segments and the occurrence of the branching event in time. Model-generated trees have shape properties closely matching the observed ones. The dendritic trees of each of the two classes of neurons are represented by a specific set of growth model parameters, thus achieving morphological data compression.

Animals↗
PubMed1995

Bovine tuberculosis in badger (Meles meles) populations in southwest England: the use of a spatial stochastic simulation model to understand the dynamics of the disease.

A spatial stochastic simulation model was developed to describe the dynamics of bovine tuberculosis in badger populations in southwest England, based on data from the literature and from unpublished sources. As there are no data on intra- and intergroup infection probabilities, estimates of these were obtained through repeated simulations based on field observations of the spread and prevalence of the disease. The model works on a grid-cell basis, with each grid cell potentially occupied by one badger social group; immigration to and emigration from the main grid are incorporated. Population regulation is assumed to occur at the group level through density-dependent fecundity and cub mortality, and the model can be run for various disease-free equilibrium group sizes (which are determined by the carrying capacity of the environment). The model works on a quarterly (three-monthly) basis and processes are stochastic at the individual level. Three classes of individual (adults, yearlings and cubs) and three classes of infection (susceptible, infected-but-not-infectious and infectious) are recognized. Bovine tuberculosis wa shown to persist in badger populations for long periods of time, even in populations with a disease-free equilibrium group size of only four adults and yearlings. However, with standard rates of intergroup infection and movement, the disease only became endemic in populations with a disease-free equilibrium group size greater than six adults and yearlings. In the endemic situation, the prevalence of the disease ranged between 11-22 degrees depending on the combination of inter- and intragroup infection probabilities used. Endemic infection within the homogeneous environment of the grid was characterized by a high degree of heterogeneity. Patches of infection were spatio-temporally unstable, but shifted in location relatively slowly. Spread of the disease from a point source of infection with standard rates of intergroup movement and infection only occurred to any marked extent in populations with disease-free equilibrium group sizes of eight or more adults and yearlings. Increasing the intergroup infection probability had a significant effect on increasing the probability and rate of spread, and considerably lowered the threshold group size for spread from a point source to around four adults and yearlings. However, increasing the rates of intergroup movement reduced the probability of spread of the disease except at the largest groups sizes. When both intergroup infection and movements were increased, the effects of increased infection in enhancing spread were offset to some degree by the increased movements. Perturbation to the badger population, as may be caused by control operations, could therefore increase the probability of persistence or spread of an infection.

Animals↗
PubMed1993

Somatic mutation, monoclonality and stochastic models of stem cell organization in the intestinal crypt.

Among highly proliferating tissues the intestinal tissue is of particular interest. Techniques are available that permit an insight into how intestinal crypts as the basic macroscopic tissue unit are regenerated from a small population of self-maintaining stem cells. However, neither the precise number of these stem cells nor their properties are known. We have recently suggested a model of stem cell organization which explains the life cycle of murine intestinal crypts, their birth (by crypt fission) and extinction rates, as well as their size distribution on a quantitative basis (Loeffler & Grossman, 1991). The model assumptions involve two stochastic branching processes, one for the growth of several independent indistinguishable stem cells and a second for a threshold dependent crypt fission process. New data have now become available challenging the above concept. They relate to the conversion of crypts to monoclonal phenotypic expression after mutagenic events, presumably taking place in single stem cells. A detailed analysis of these data is shown here utilizing a more elaborate version of the above model. The new data are consistent with this model within the range of parameters predicted previously. We conclude that the cellular regeneration of intestinal crypts can be explained on the basis of several indistinguishable stem cells which can replace each other.

Animals↗
PubMed2001

A parallel study on bacterial growth and inactivation.

Pure stochastic birth process models are used to establish the connection between the traditional food microbiology concept of bacterial lag period, before the exponential growth, and the distribution of the lag times of individual cells. In a parallel way, similar study is carried out on the connection between the "shoulder" period, before the exponential decay, and the distribution of the survival times of individual cells. Formulae are derived to calculate the parameters of the growth/survival curves from the distributions of the respective parameters of individual cells. It is shown that, in some aspects, analogy, in some aspects fundamental difference exists between growth and survival modelling.

Bacteria↗
PubMed1998

A modified model for projecting age-structured populations in random environments.

A discrete-time age-structured population model with vital rates linked to a stochastic environmental process was developed as a generalization of an existing model by making the explicit link between variability in the vital rates and variability in the environment more flexible. This modified model uses biologically relevant probability distributions for the vital rates, and allows for temporal autocorrelation and an arbitrary covariance structure between vital rates. Through simulations, the properties of the projected population in the short-term were investigated and compared to analytical approximations. The distribution of the total population size did not quickly approach lognormality under all conditions. Furthermore, the sensitivity of the vital rates to the environmental process had a strong effect on the variance and distribution of the projected population size. These results suggest that short-term projections need to be carried out through simulation methods, as the analytical approximations technically apply only to the long-run asymptotic behavior. Techniques for parameter estimation were considered; recommendations depend on the form of the data available. The approach described allows the empirical calculation of the probability distribution for predicted population size, a quantity relevant to the use of formal decision analysis in natural resource management.

Age Factors↗
PubMed2003

Speciation in multidimensional evolutionary space.

Adaptive dynamics in two-dimensional phenotype space is investigated by computer simulation. The model assumes Lotka-Voltera-type competition and a stochastic mutation process. The carrying capacity has a single maximum in the origin of the strategy space and the competition coefficient decreases with strategy difference. Evolutionary branching, an asexual analog of adaptive speciation, is observed with suitable parameters. The branching at the singular point, which is a fixed point of the directional evolution, may occur into two or three, but not more, directions. Further branchings may occur after the initial separation. The probability of three-branching is studied as a function of several parameters. We conclude that the two-way branching is the predominant mode of adaptive speciation.

Adaptation, Physiological↗
PubMed1987

Demographic heterogeneity and uncertainty in population projections.

Recent developments in a class of stochastic population processes were used to study the impact of demographic heterogeneity on the uncertainty of population projections. Selected for study by computer simulation were population projections for East Africa designed to quantify opinions regarding expected fertility and mortality declines. Since both fertility and mortality declined in these projections, their laws of evolution may be described as time inhomogeneous. The computer simulation studies reported in this paper strongly suggest that randomized laws of evolution should be taken into account in further developments of population projection methodologies designed formally and computationally to accommodate uncertainty. Variability in fecundability, the kind of demographic heterogeneity studied in this paper, is only one aspect of these randomized laws.

Africa, Eastern↗
PubMed2001

Control motifs for intracellular regulatory networks.

A number of technological innovations are yielding unprecedented data on the networks of biochemical, genetic, and biophysical reactions that underlie cellular behavior and failure. These networks are composed of hundreds to thousands of chemical species and structures, interacting via nonlinear and possibly stochastic physical processes. A central goal of modern biology is to optimally use the data on these networks to understand how their design leads to the observed cellular behaviors and failures. Ultimately, this knowledge should enable cellular engineers to redesign cellular processes to meet industrial needs (such as optimal natural product synthesis), aid in choosing the most effective targets for pharmaceuticals, and tailor treatment for individual genotypes. The size and complexity of these networks and the inevitable lack of complete data, however, makes reaching these goals extremely difficult. If it proves possible to modularize these networks into functional subnetworks, then these smaller networks may be amenable to direct analysis and might serve as regulatory motifs. These motifs, recurring elements of control, may help to deduce the structure and function of partially known networks and form the basis for fulfilling the goals described above. A number of approaches to identifying and analyzing control motifs in intracellular networks are reviewed.

Animals↗
PubMed2005

Theory of frequency and phase synchronization in a rocked bistable stochastic system.

We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of stochastic resonance. We present an approach to the stochastic counting process of noise-induced switching events: starting from the Markovian dynamics of the nonstationary, continuous particle dynamics, one finds upon contraction onto two states a non-Markovian renewal dynamics. A proper definition of an output discrete phase is given, and the time rate of change of its noise average determines the corresponding output frequency. The phenomenon of noise-assisted phase synchronization is investigated in terms of an effective, instantaneous phase diffusion. The theory is applied to rectangular-shaped rocking signals versus increasing input-noise strengths. In this case, for an appropriate choice of the parameter values, the system exhibits a noise-induced frequency locking accompanied by a very pronounced suppression of the phase diffusion of the output signal. Precise numerical simulations corroborate very favorably our analytical results. The novel theoretical findings are also compared with prior ones.

Action Potentials↗