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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↗
PubMed1990

Reducing bias in estimates of the richards growth function shape parameter.

A process error model developed by White and Brisbin (1980) is used frequently for estimation of the parameters of the Richards sigmoid growth function. The Richards function includes a parameter, m, that describes the shape of familiar three-parameter functions, such as the monomolecular (m = 0), von Bertalanffy (m = 2/3), Gompertz (m----1) and logistic m = 2), as well as other sigmoid functions. We show that this model systematically underestimates the shape parameter, m. In calibration runs and simulations, bias decreased with increased frequency of sampling during the period of rapid growth and with smaller values of true m. Relative bias was insensitive to the magnitude of m. A simple correction reduced the bias to negligible values for both deterministic and stochastic process error models. Biases in estimated asymptote, A, and growing time, T, were small for a variety of sampling intervals and shape parameters.

Animals↗
PubMed1966

State vector description of the proliferation of mammalian cells in tissue culture. I. Exponential growth.

Proliferation of mammalian cells, even under conditions of unlimited growth, presents a complex problem because of the interaction of deterministic and stochastic processes. Division of the cell cycle into a finite number of parts establishes a multidimensional vector space. In this space an arbitrary culture can be represented by a vector called the state vector. The culture's subsequent growth is represented mathematically as a series of transformations of the state vector. The operators effecting these transformations are presented in matrix form and their relationship to the distribution of cell generation times is described. As an application of the model, the growth of an initially synchronized culture is considered and an unambiguous measure of the degree of synchrony is proposed. Results of a computer simulation of such a culture show the behavior with time of the degree of synchrony, the total cell number, and the mitotic index. In particular the importance of the magnitude of the coefficient of variation of the generation time distribution is illustrated.

Animals↗
PubMed1992

Aging and mortality: manifestations of natural 'non-selection'.

Aging and mortality have long been a source of concern, fascination and investigation. The ultimate question being, why do we age and die? The method of longitudinal Gompertzian analysis demonstrates that aging and mortality are deterministically linked. Moreover, this method of analysis reveals that with enhanced human survival, mortality patterns have changed primarily as the result of the unmasking of latent susceptibilities to other Gompertzian diseases rather than altered environmental etiopathogenic influences. That is, the Gompertzian model of human aging and mortality suggests that redundant programmed failure is the primary reason for ultimate and inevitable mortality. A process by which redundant deterministic disease susceptibilities could accumulate within the genome is natural 'non-selection'. Random genetic mutations which enhance survival until reproduction facilitate the processes of natural selection and evolution. However, random genetic mutations that program for late failure or disease susceptibility would not be eliminated from the gene pool. Thus, random genetic mutations which have programmed for late susceptibility to Gompertzian diseases, and their cumulative non-selection, may be the basis for the deterministic relationship between aging and mortality.

Adult↗
PubMed1988

A Markov process based model of the neurotransmitter-receptor binding process in the brain.

A non-deterministic model, based on the assumption that the binding of a neurotransmitter to its receptor is a Markov process, is developed. This model is capable of describing the kinetic processes that occur when a neurotransmitter binds to its receptor under normal and abnormal (pathological) conditions. The model assumes the presence of four states and develops transition probability functions for these states, the expected number of visits to a given state, and the probability of ever reaching a given state. The model explains the probable causes of related disease situations such as Parkinson's disease and schizophrenia, and develops transition probability function and other related statistical properties appropriate to these disease situations. Model parameters of the normal condition were generated by a computer simulation program and compared to those of the pathological conditions. The results of these sample calculations support the assumptions made in the model for normal and disease situations.

Brain↗
PubMed1992

A calcium model with random absorption: a stochastic approach.

Absorption of calcium, or any mineral, by the body is subject to the random fluctuations typical of diffusion through membranes. In this paper we consider the absorption of calcium from the gut as a white noise process added to the deterministic model of Sen & Mohr (1990, J. theor. Biol. 142, 179-188). The first two moments for the amount of calcium in the extracellular fluid (ECF) have been derived using the Ito Calculus. A confidence interval for the total amount of calcium in the ECF is constructed. The equations for the first two moments of the fraction of dose calcium in the ECF are also given. Suggestions are made for the collection of experimental data in a form which should be helpful in investigating the magnitude of the stochastic effect.

Calcium↗
PubMed1987

Selection by differential molecular survival: a possible mechanism of early chemical evolution.

A model is proposed to account for selective chemical evolution, progressing from a relatively simple initial set of abiotic synthetic phenomena up to the elaborately sophisticated processes that are almost certainly required to produce the complex molecules, such as replicatable RNA-like oligonucleotides, needed for a Darwinian form of selection to start operating. The model makes the following assumptions: (i) that a small number of micromolecular substances were present at high concentration; (ii) that a random assembly mechanism combined these molecules into a variety of multimeric compounds comprising a wide repertoire of rudimentary catalytic activities; and (iii) that a lytic system capable of breaking down the assembled products existed. The model assumes further that catalysts supplied with substrates were significantly protected against breakdown. It is shown that, by granting these assumptions, an increasingly complex network of metabolic pathways would progressively be established. At the same time, the catalysts concerned would accumulate selectively to become choice substrates for elongation and other modifications that could enhance their efficiency, as well as their survival. Chemical evolution would thus proceed by a dual process of metabolic extension and catalytic innovation. Such a process should be largely deterministic and predictable from initial conditions.

Biochemical Phenomena↗
PubMed1992

Chaotic dynamics in autonomic nervous system activity of a patient during a psychotherapy session.

Chaos theory and nonlinear dynamical modeling have been applied successfully in a variety of scientific fields ranging from the physical sciences to population biology. More recently, investigators have modeled long-term psychological processes by applying this paradigm to subjective measures. Yet, mathematically rigorous dynamical modeling of transient psychodynamic processes remains uncharted. Human behaviors and intrapsychic processes often defy prediction, yet psychodynamic theory views these as fundamentally deterministic. We postulate that a nonlinear dynamical analysis of mental states and mental control processes may help reconcile the paradox that seemingly random mental states are thought ultimately to result from deterministic, rather than stochastic, psychological processes. As an initial empirical approach, we examined spontaneously occurring autonomic activity of a patient during 1 hr of psychotherapy and illustrate that cardiac responses associated with psychologically meaningful events possess nonlinear characteristics indicative of chaos. Such nonlinear analyses may shed light on fundamental issues of psychological functioning.

Adult↗
PubMed2025

Environmental Stresses Constrain Soil Microbial Community Functions by Regulating Deterministic Assembly and Niche Width.

Increasing evidence indicates that the loss of soil microbial α-diversity triggered by environmental stress negatively impacts microbial functions; however, the effects of microbial α-diversity on community functions under environmental stress are poorly understood. Here, we investigated the changes in bacterial and fungal α- diversity along gradients of five natural stressors (temperature, precipitation, plant diversity, soil organic C and pH) across 45 grasslands in China and evaluated their connection with microbial functional traits. By quantifying the five environmental stresses into an integrated stress index, we found that the bacterial and fungal α-diversity declined under high environmental stress across three soil layers (0-20 cm, 20-40 cm and 40-60 cm). Metagenomic-based analyses showed that the diversity of functional genes decreased along the stress gradients. High stress enhanced the abundance of genes associated with broad functional categories (e.g., glycolysis/gluconeogenesis, TCA cycle, DNA replication/repair and cell growth/death) but reduced the abundance of genes linked to specialised functional categories (e.g., C, N, S and methane metabolism). Phylogenetic null models and niche analyses indicated that stochastic assembly processes predominated in high-diversity communities, in which bacterial and fungal taxa had a narrow ecological niche. However, in low-diversity communities, deterministic assembly processes were dominant, and taxa had wide niches, correlating with the reduction in gene abundance observed for broad and specialised functional categories. Given the essential role of the microbiome in regulating ecosystem functions, our findings suggest that low-diversity-induced deterministic community assembly processes and a wide niche under high environmental stress may regulate microbial functions. These findings emphasise the ecological mechanisms through which microbial biodiversity regulates terrestrial ecosystem functioning.

Soil Microbiology↗
PubMed1987

Statistical properties of flip-flop processes associated to the chaotic behavior of systems with strange attractors.

The chaotic behavior of systems with strange attractors can be discussed by examining the flip-flop process associated to the system dynamics. This was already shown by Lorenz (1963) in his first seminal paper. A somewhat surprising result was obtained by Aizawa (1982), who, studying the same Lorenz attractor at the parameter value r = 28, reached the conclusion that the associated flip-flop was a typical Markov process. Since the process is generated in a deterministic way, one may wonder if the Aizawa result is accidental, depending on the particular parameter value, or if a similar conclusion can be extended to other systems, with different attractors. Our conclusions are that the Aizawa result is mostly accidental, because for other parameter values and for other attractors there are sharp deviations from the Markovian process.

Animals↗
PubMed2026

Methane and carbon dioxide emissions from wastewater treatment units linked to DOM stabilization and phosphonate-scavenging microbiomes.

Municipal wastewater treatment plants (WWTPs) are major engineered facilities for urban carbon removal, yet methane (CH4) formation and source mechanisms in downstream stages after aeration and biological nutrient removal remain poorly resolved. Process resolved monitoring at a full-scale WWTP showed that CH4 emissions were concentrated upstream, while measurable fluxes persisted in downstream sedimentation and denitrification units. Dissolved CH4 profiles showed strong attenuation of influent derived CH4 during upstream treatment, followed by a local increase after secondary clarification. Carbon dioxide (CO2) emissions peaked in the biochemical tank, consistent with rapid oxidation of labile organic carbon. Fluorescence and molecular analyses revealed a shift in dissolved organic matter (DOM) from protein like to more humic and processed molecules, while community assembly remained predominantly deterministic despite greater stochasticity in later stages. The C-P lyase catalytic core was enriched in these units, accompanied by higher phnJ transcript abundance, candidate organophosphonate features, and genomic potential. Together with BES insensitive CH4 formation in independent microcosms, these observations supported C-P lyase mediated organophosphonate utilization as a contributing pathway to local CH4 formation. Integrated evidence indicated that DOM stabilization, deterministic community filtering, potential succinate mediated cross feeding, and phosphonate scavenging jointly shaped this process. These findings show that advanced treatment units are not CH4 hotspots, but neither are they CH4 inactive zones; process resolved GHG assessments should therefore consider persistent local CH4 generation and its association with substrate restructuring and alternative phosphorus acquisition.

Dissolved organic matter↗
PubMed1986

Noise-induced neural impulses.

The firing pattern of neural pulses often show the following features: the shapes of individual pulses are nearly identical and frequency independent; the firing frequency can vary over a broad range; the time period between pulses shows a stochastic scatter. This behaviour cannot be understood on the basis of a deterministic non-linear dynamic process, e.g. the Bonhoeffer-van der Pol model. We demonstrate in this paper that a noise term added to the Bonhoeffer-van der Pol model can reproduce the firing patterns of neurons very well. For this purpose we have considered the Fokker-Planck equation corresponding to the stochastic Bonhoeffer-van der Pol model. This equation has been solved by a new Monte Carlo algorithm. We demonstrate that the ensuing distribution functions represent only the global characteristics of the underlying force field: lines of zero slope which attract nearby trajectories prove to be the regions of phase space where the distributions concentrate their amplitude. Since there are two such lines the distributions are bimodal representing repeated fluctuations between two lines of zero slope. Even in cases where the deterministic Bonhoeffer-van der Pol model does not show limit cycle behaviour the stochastic system produces a limit cycle. This cycle can be identified with the firing of neural pulses.

Acoustic Stimulation↗
PubMed1991

Adaptive processing techniques based on hidden Markov models for characterizing very small channel currents buried in noise and deterministic interferences.

Techniques for characterizing very small single-channel currents buried in background noise are described and tested on simulated data to give confidence when applied to real data. Single channel currents are represented as a discrete-time, finite-state, homogeneous, Markov process, and the noise that obscures the signal is assumed to be white and Gaussian. The various signal model parameters, such as the Markov state levels and transition probabilities, are unknown. In addition to white Gaussian noise, the signal can be corrupted by deterministic interferences of known form but unknown parameters, such as the sinusoidal disturbance stemming from AC interference and a drift of the base line owing to a slow development of liquid-junction potentials. To characterize the signal buried in such stochastic and deterministic interferences, the problem is first formulated in the framework of a Hidden Markov Model and then the Expectation Maximization algorithm is applied to obtain the maximum likelihood estimates of the model parameters (state levels, transition probabilities), signals, and the parameters of the deterministic disturbances. Using fictitious channel currents embedded in the idealized noise, we first show that the signal processing technique is capable of characterizing the signal characteristics quite accurately even when the amplitude of currents is as small as 5-10 fA. The statistics of the signal estimated from the processing technique include the amplitude, mean open and closed duration, open-time and closed-time histograms, probability of dwell-time and the transition probability matrix. With a periodic interference composed, for example, of 50 Hz and 100 Hz components, or a linear drift of the baseline added to the segment containing channel currents and white noise, the parameters of the deterministic interference, such as the amplitude and phase of the sinusoidal wave, or the rate of linear drift, as well as all the relevant statistics of the signal, are accurately estimated with the algorithm we propose. Also, if the frequencies of the periodic interference are unknown, they can be accurately estimated. Finally, we provide a technique by which channel currents originating from the sum of two or more independent single channels are decomposed so that each process can be separately characterized. This process is also formulated as a Hidden Markov Model problem and solved by applying the Expectation Maximization algorithm. The scheme relies on the fact that the transition matrix of the summed Markov process can be construed as a tensor product of the transition matrices of individual processes.

Algorithms↗
PubMed1989

The effect of a random initial value in neural first-passage-time models.

The effect of a random initial value is examined in several stochastic integrate-and-fire neural models with a constant threshold and a constant input. The three models considered are approximations of Stein's model, namely: (1) a leaky integrator with deterministic trajectories, (2) a Wiener process with drift, and (3) an Ornstein-Uhlenbeck process. For model 1, different distributions for the initial value lead to commonly observed interspike interval distributions. For model 2, a discrete and a uniform distribution for the initial value are examined along with some parameter estimation procedures. For model 3, with a truncated normal distribution for the initial value, the coefficient of variation is shown to be greater than 1, and as the threshold becomes large the first-passage-time distribution approaches an exponential distribution. The relationships among the models and between them and previous models are also discussed, along with the robustness of the model assumptions and methods of their verification. The effects of a random initial value are found to be most pronounced at high firing rates.

Action Potentials↗
PubMed1992

The catalytic power of pyruvate decarboxylase. A stochastic model for the molecular evolution of enzymes.

Pyruvate decarboxylase (PDC) catalyzes the decarboxylation of pyruvate anion by a factor of around 10(12), compared with the non-enzymic decarboxylation by thiamine, under standard state conditions of 1 mM pyruvate and thiamine diphosphate (TDP), pH 6.2. Free-energy diagrams constructed on the basis of earlier measurements for the enzymic and non-enzymic reactions give some information on catalysis by PDC. PDC stabilizes the reactant state preceding TDP addition to pyruvate by 76 kJ mol-1 and the transition state for the addition by 83 kJ mol-1. PDC stabilizes the reactant state preceding decarboxylation (presumably alpha-lactyl-TDP) by 27 kJ mol-1 and the transition state for decarboxylation by 68 kJ mol-1. In addition, the free-energy diagrams reveal a leveling of reactant-state free energies in the enzymic reaction compared with the non-enzymic reaction, in that the former are nearly equal to each other. The enzyme-bound transition-state energies are similarly leveled. The energetic leveling of reactant states has been noted by Albery, Knowles and their coworkers in many enzymic reactions and termed 'matched internal thermodynamics.' They showed that the result would arise naturally (and inevitably) in the 'evolution to perfection' of enzymes, when the evolutionary process was treated by a deterministic model. The critical assumption of this model was the validity of a Marcus-type or Brønsted-type linear free-energy relationship between rate and equilibrium constants for reactions occurring wholly within enzyme complexes. Here a completely stochastic simulation of molecular evolution, with no deterministic assumptions, is shown to reproduce both 'matched internal thermodynamics' and the 'matched internal kinetics' or leveling of transition-state energies noted here. The Albery-Knowles result is thus more general than might have been supposed.

Biological Evolution↗
PubMed1990

A deterministic model of the cell cycle.

The variability of the duration of the cell cycle is explained by the phenomenon of sensitive dependence upon initial conditions; as may occur in deterministic non-linear systems. Chaotic dynamics of a system is the result of this sensitive dependence. First a deterministic system is formulated that is equivalent to the Smith-Martin transition probability model of the cell cycle. Next the model is extended to a dynamic process that ranges over the cell generations. A deterministic non-linear relationship between the cycle time of the mother and daughter cell is established. It clarifies the variability of mother-daughter correlation for the different cell types. The model is fitted to two different cell cultures; it shows that the graph of the non-linear relation has the same shape for different cell types.

Animals↗
PubMed1991

Dependence of epidemic and population velocities on basic parameters.

This paper describes the use of linear deterministic models for examining the spread of population processes, discussing their advantages and limitations. Their main advantages are that their assumptions are relatively transparent and that they are easy to analyze, yet they generally give the same velocity as more complex linear stochastic and nonlinear deterministic models. Their simplicity, especially if we use the elegant reproduction and dispersal kernel formulation of Diekmann and van den Bosch et al., allows us greater freedom to choose a biologically realistic model and greatly facilitates examination of the dependence of conclusions on model components and of how these are incorporated into the model and fitted from data. This is illustrated by consideration of a range of examples, including both diffusion and dispersal models and by discussion of their application to both epidemic and population dynamic problems. A general limitation on fitting models results from the poor accuracy of most ecological data, especially on dispersal distances. Confirmation of a model is thus rarely as convincing as those cases where we can clearly reject one. We also need to be aware that linear models provide only an upper bound for the velocity of more realistic nonlinear stochastic models and are almost wholly inadequate when it comes to modeling more complex aspects such as the transition to endemicity and endemic patterns. These limitations are, however, to a great extent shared by linear stochastic and nonlinear deterministic models.

Animals↗