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PubMed1986

Inactivation of macromolecules by ionizing radiation. Deterministic single-hit or stochastic multievent process?

A stochastic theory concerning the radiation inactivation of macromolecules such as enzymes or receptors is elaborated. In contrast with the single-hit theory, which assumes a complete inactivation of the target as the result of one hit, the stochastic theory postulates that the degree of inactivation by one hit is a random variable. This distinguishing feature has been considered in order to give a possible interpretation to the observed effect of temperature on the radiation-sensitivity of enzymes. As a consequence of the progressive inactivation during irradiation, the binding affinity of a ligand for the macromolecule is impaired by irradiation. Although this property might discriminate the stochastic theory from the classical single-hit theory on the basis of a statistical analysis of experimentally obtained data, it is shown that the commonly obtained degree of inaccuracy may render the statistical test non-conclusive.

Ligands↗
PubMed1967

Neuronal spike trains and stochastic point processes. I. The single spike train.

In a growing class of neurophysiological experiments, the train of impulses ("spikes") produced by a nerve cell is subjected to statistical treatment involving the time intervals between spikes. The statistical techniques available for the analysis of single spike trains are described and related to the underlying mathematical theory, that of stochastic point processes, i.e., of stochastic processes whose realizations may be described as series of point events occurring in time, separated by random intervals. For single stationary spike trains, several orders of complexity of statistical treatment are described; the major distinction is that between statistical measures that depend in an essential way on the serial order of interspike intervals and those that are order-independent. The interrelations among the several types of calculations are shown, and an attempt is made to ameliorate the current nomenclatural confusion in this field. Applications, interpretations, and potential difficulties of the statistical techniques are discussed, with special reference to types of spike trains encountered experimentally. Next, the related types of analysis are described for experiments which involve repeated presentations of a brief, isolated stimulus. Finally, the effects of nonstationarity, e.g. long-term changes in firing rate, on the various statistical measures are discussed. Several commonly observed patterns of spike activity are shown to be differentially sensitive to such changes. A companion paper covers the analysis of simultaneously observed spike trains.

Action Potentials↗
PubMed1984

Identification and estimation algorithm for stochastic neural system.

An algorithm for the estimation of stochastic processes in a neural system is presented. This process is defined here as the continuous stochastic process reflecting the dynamics of the neural system which has some inputs and generates output spike trains. The algorithm proposed here is to identify the system parameters and then estimate the stochastic process called neural system process here. These procedures carried out on the basis of the output spike trains which are supposed to be the data observed in the randomly missing way by the threshold time function in the neural system. The algorithm is constructed with the well-known Kalman filters and realizes the estimation of the neural system process by cooperating with the algorithm for the parameter estimation of the threshold time function presented previously (Nakao et al., 1983). The performance of the algorithm is examined by applying it to the various spike trains simulated by some artificial models and also to the neural spike trains recorded in cat's optic tract fibers. The results in these applications are thought to prove the effectiveness of the algorithm proposed here to some extent. Such attempts, we think, will serve to improve the characterizing and modelling techniques of the stochastic neural systems.

Animals↗
PubMed1991

Development of skin tumors in hairless mice after discontinuation of ultraviolet irradiation.

The development of skin tumors (mainly squamous cell carcinomas) in hairless Skh-HR1 mice after discontinuation of a course of daily UV irradiations (wavelengths, 280-370 nm) is compared to that when the daily irradiations are continued. Under conditions of continued daily exposures 50% of 22 animals contracted tumors with diameters of at least 4 mm in 135 days. With exposures stopped after 35 or 19 days (2 groups with 24 and 23 mice) this time interval increased to 280 and 645 days, respectively; the rate at which multiple tumors developed on the mice was correspondingly lower. A mathematical model, derived from a larger experiment (223 mice) with different levels of chronic UV exposure, successfully predicts the tumor development after discontinuation of UV exposure. This model is similar to those used in risk assessments for skin cancers in human populations, e.g., in relation to stratospheric ozone depletion, sunbeds, etc. The model separates UV-driven processes from purely time-dependent processes. These stochastic processes, described by Weibull statistics, form stages in the tumorigenesis. This interpretation of the data indicates that a late, UV-independent stage occurs between the smallest observable tumors and larger ones with diameters of over 4 mm. This could be a simple growth stage, but histopathology suggests that it may also entail a transition from actinic keratosis to squamous cell carcinoma.

Animals↗
PubMed1991

Stochastic interactive processes and the effect of context on perception.

The effects of context on perceptual identification responses given without time pressure are well-described by classical models in which contextual and stimulus information exert independent effects. A recent article by Massaro (1989) raises the possibility that interactive models, such as the TRACE model of speech perception, are inherently incompatible with these classical context effects. The present article shows that this incompatibility hypothesis can be rejected. Mathematical analysis and computer simulation methods are used to show that interactive models can exhibit the classical effects of context, if there is variability in the input to the network or if there is intrinsic variability in the network itself. A variety of interactive models which incorporate variability can all produce the classical context effects, at least under some conditions; the conditions are rather general in the case of one of the variants. The findings suggest that interactive models should not be viewed as alternatives to classical accounts, but as hypotheses about the dynamics of information processing that lead to the global asymptotic behavior that the classical models describe.

Attention↗
PubMed1989

Pharmacokinetics from a dynamical systems point of view.

The pharmacological action of many drugs depends on several variables at the same time and therefore will be dominated by an attractor of a dimension greater than zero. The pharmacokinetic behavior is likely to be dominated by a zero dimensional point attractor so that it is highly predictable. Pharmacokinetics is discussed from a dynamical systems point of view, whereby the transport of drugs in the tissues and organs is considered a stochastic process characterized by density functions of transit times and blood flows. In the body, the tissues and organs are arranged in parallel, in series, and in a feedback-loop fashion. Consequently, the single-pass transport of drugs through the body is again a stochastic process characterized by the density function of total body transit times, the cardiac output, and the total body extraction. The drug molecules, however, may pass through the body several times before ultimately leaving the system by metabolism or excretion. As a result, the body may be regarded as a positive feedback system with the pulmonary circulation (and its tissues) as the forward transfer function and the systemic circulation (with all its tissues) as the feedback transfer function. Consequently, the total body transport function (closed loop) is again a stochastic process characterized by a density function of total body residence times. The relationship between the body transit time distribution and the body residence distribution is determined by the feedback-loop arrangement, the cardiac output, and the extraction ratio which can easily be written in the Laplace domain. The pharmacokinetic parameters logically follow from the systems approach. They are the cardiac output, the mean transit time, the extraction ratio, the clearance, the volume of distribution in steady state, the mean residence time, and the average number of recirculations. The dynamic systems approach in pharmacokinetics has been illustrated with some examples notably with caffeine.

Absorption↗
PubMed1992

On inherited fertility in biological systems: a model of correlated fluctuations in the stochastic branching process.

A new evolutionary model with hereditary modes considered as correlated fluctuations of fertility has been proposed. It has been demonstrated that the model allows the global statistical properties of the system to be evaluated, e.g. the ensemble average and the probability of extinction. The results obtained show the increase of instability of a population with the enhancement of inheritance efficiency. The existence of at least an exponential stratification in the population has also been shown. Possible applications of the present model are discussed.

Animals↗
PubMed1982

A hybrid computer model of stochastic activity of the neurone.

The authors describe a hybrid computer neurone model intended for the investigation of stochastic transformations effected by neurones in correlation to some of their physiological parameters. The model is designed so as to give the best possible characterization of the internal dynamics of a neurone with minimum limiting conditions. It allows the generation of suitable input stochastic processes or operates with input processes obtained experimentally in the living neurone and it carries out basic statistical tests of the output stochastic process.

Computers, Hybrid↗
PubMed1989

Ordered appearance of antigenic variants of African trypanosomes explained in a mathematical model based on a stochastic switch process and immune-selection against putative switch intermediates.

Antigenic variation of African trypanosomes results from the periodic activation of a single new variant cell surface glycoprotein (VSG) gene out of a repertoire of about a 1000 VSG genes. In spite of the apparently random genetic basis of the process of antigenic variation, the relapsing parasitemias are characterized by an as yet unexplained order of appearance of major VSG variants. Here we mathematically test hypotheses concerning the blood-based parasitemia. In our model the antigenic switches occur at random at the DNA level. A variable proportion of the switches has a short intermediate phase in which two different VSGs simultaneously occur on the cell surface. We show that, in a theoretical population of 230 single expressor variants in an immunocompetent or in an immunodeficient host, it is not possible to explain the ordered appearance of variants by affecting the growth coefficients of single expressors or double expressors or by affecting the antigen switch probabilities. Rather, a realistic parasitemia can be obtained if the majority of switches has a double expressor switch-intermediate phase and if the double expressors have a differential susceptibility to the immune control. This study is significant in providing a theoretical basis for the ordered appearance of variants and in explaining previously unresolved discrepancies between the rate of appearance of new variants in culture and in vivo. In addition, testable predictions as to the development of the infections, switch rate of variants, fraction of double expressors, and parasite mortality coefficients are generated.

Animals↗
PubMed1985

Statistics and quantum bumps in arthropod photoreceptors.

Discrete waves of depolarizing membrane potential in arthropod photoreceptors, called quantum bumps, appear to result from single-photon absorptions of the visual pigment. Statistical analysis of bump records suggest a model for bump occurrence in dark-adapted receptors at low levels of illumination. This model assumes that a photon that isomerizes a visual pigment molecule can trigger a stochastic process that can produce no more than one bump under normal conditions, and that the stochastic processes triggered by different isomerized visual pigment molecules are independent of each other.

Animals↗
PubMed1986

Evidence that the process of murine melanoma metastasis is sequential and selective and contains stochastic elements.

Malignant neoplasms are heterogeneous for many different biological characteristics, including invasion and metastasis. The pathogenesis of metastasis involves a series of sequential steps which must be completed by metastatic cells. In the present study we examined the metastatic behavior of three highly metastatic and three nonmetastatic subpopulations isolated from the K-1735 melanoma syngeneic to the C3H/HeN mouse. Cells were labeled with [125I]iodo-2'-deoxyuridine, and their initial organ distribution, fate, and production of experimental metastases were determined. Highly metastatic cells survived in lung parenchyma to produce metastases, whereas nonmetastatic cells did not. However, even with the highly metastatic cells only 2% of the original inoculum was responsible for the final production of metastases. The results support the concept that the fate of tumor cells released into the bloodstream is determined by sequential and selective events and introduces a third regulatory factor. Cells endowed with metastatic properties have a higher probability of forming metastases than cells not so endowed, but this probability is not 100%. Hence, metastasis should be considered as a sequential, selective, and stochastic process.

Animals↗
PubMed1992

Graphical representation of survival curves associated with a binary non-reversible time dependent covariate.

The use of time dependent covariates has allowed for incorporation into analysis of survival data intervening events that are binary and non-reversible (for example, heart transplant, initial response to chemotherapy). We can represent this type of intervening event as a three-state stochastic process with a starting state (S), an intervening state (I), and an absorbing state (D), which usually represents death. In this paper we present three procedures for calculating survivorship functions which attempt to display the prognostic significance of the time dependent covariate. The first method compares survival from baseline for the two possible paths through the stochastic process; the second method compares overall survival to survival with state I removed from the process; and, the third method compares survival for those already in state I at a landmark time x to those in state S at time x who will never enter state I. We develop discrete hazard estimates for the survival curves associated with the three methods. Two examples illustrate how these methods can yield different results and in which situations one might employ each of the three methods. Extensions to applications with reversible binary time dependent covariates and models with both baseline and time dependent covariates are suggested.

Data Interpretation, Statistical↗
PubMed1987

Weak convergence of a sequence of stochastic difference equations to a stochastic ordinary differential equation.

We consider a sequence of discrete parameter stochastic processes defined by solutions to stochastic difference equations. A condition is given that this sequence converges weakly to a continuous parameter process defined by solutions to a stochastic ordinary differential equation. Applying this result, two limit theorems related to population biology are proved. Random parameters in stochastic difference equations are autocorrelated stationary Gaussian processes in the first case. They are jump-type Markov processes in the second case. We discuss a problem of continuous time approximations for discrete time models in random environments.

Genetics, Population↗
PubMed1967

Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains.

The statistical analysis of two simultaneously observed trains of neuronal spikes is described, using as a conceptual framework the theory of stochastic point processes.The first statistical question that arises is whether the observed trains are independent; statistical techniques for testing independence are developed around the notion that, under the null hypothesis, the times of spike occurrence in one train represent random instants in time with respect to the other. If the null hypothesis is rejected-if dependence is attributed to the trains-the problem then becomes that of characterizing the nature and source of the observed dependencies. Statistical signs of various classes of dependencies, including direct interaction and shared input, are discussed and illustrated through computer simulations of interacting neurons. The effects of nonstationarities on the statistical measures for simultaneous spike trains are also discussed. For two-train comparisons of irregularly discharging nerve cells, moderate nonstationarities are shown to have little effect on the detection of interactions.Combining repetitive stimulation and simultaneous recording of spike trains from two (or more) neurons yields additional clues as to possible modes of interaction among the monitored neurons; the theory presented is illustrated by an application to experimentally obtained data from auditory neurons.A companion paper covers the analysis of single spike trains.

Action Potentials↗
PubMed1991

Stochastic differential equations, their interpretation and application.

The work is recommended to readers with some, maybe heuristic, imagine about stochastic processes that want to meet the notion stochastic differential equation and its interpretation. The notions like Brownian motion and stochastic integral with interpretations in concrete situations in areas of biology and medicine are discussed. The questions are related to mathematical modelling and they may be interpreted in connection with stochastic signal filtering and optimal queuing theory.

Stochastic Processes↗
PubMed1983

Statistical analysis of ongoing activity of neurones in the substantia gelatinosa and in lamina III of cat spinal cord.

Intracellular recordings from substantia gelatinosa (s.g.) neurones in chloralose-anaesthetized cats and in decerebrate preparations revealed the existence of ongoing synaptic activity. 59% of s.g. neurones showed ongoing spiking activity at rates of more than one per second. The ongoing activity of twenty s.g. neurones was subjected to statistical analysis. Stationarity was established for the activity of each neurone, the interspike interval (i.s.i.) distributions were bell-shaped, and no evidence of dependency of the length of an interval on the one preceding it was found. The mechanism of spike generation in these neurones is therefore an example of a renewal stochastic process. The pattern of ongoing discharge of twelve neurones recorded in lamina III was markedly different, and generated in each case a unimodal asymmetric i.s.i. histogram with a sharp rise to mode after a short dead time and a slow decay. The activity was stationary only in the long term, and there was strong evidence of dependency of intervals. The spike generating mechanism was therefore an example of a non-renewal stochastic process. The different patterns of activity are discussed in relation to differences in cutaneous input, and it is suggested that the pattern of activity in the s.g. neurones is the result of convergence on the neurones of a large number of small independent excitatory influences, whereas that of the neurones in lamina III is the result of excitation by powerful synchronous synaptic inputs. It is re-emphasized that statistical analysis of neural impulse sequences is a valuable technique in investigation of the function of a neurone within its network.

Anesthesia, General↗