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PubMed2006

Difference between evolutionarily effective and germ line mutation rate due to stochastically varying haplogroup size.

Within a Y-chromosome haplogroup defined by unique event mutations, variation in microsatellites can accumulate due to their rapid mutation. Estimates based on pedigrees for the Y-chromosome microsatellite mutation rate are 3 or more times greater than the same estimates from evolutionary considerations. We show by simulation that the haplogroups that survive the stochastic processes of drift and extinction accumulate microsatellite variation at a lower rate than predicted from corresponding pedigree estimates; in particular, under constant total population size, the accumulated variance is on average 3-4 times smaller.

Chromosomes, Human, Y↗
PubMed1990

Graphs, random sums, and sojourn time distributions, with application to ion-channel modeling.

This paper considers the distribution of a sojourn time in a class of states of a stochastic process having finite discrete state space where sojourn times in any individual state are independent and identically distributed, and transitions between states follow a Markov chain. The state space and possible transitions of the process are represented by a graph. Class sojourn time distributions are derived by modifying this graph using 'composition' of states, defining a new Markov chain on the modified graph, and expressing the sojourn time in a composition state as a random sum. Appropriate compositions are chosen according to the possible "cores" of sojourns in the particular class, where a core describes the structure of a sojourn in terms of a single state or a chain in the original graph. Graph methods provide an algorithmic basis for the derivation, which can be simplified by using symmetry results. Models of ion-channel kinetics are used throughout for illustration; class sojourn time distributions are important in such models because individual states are often indistinguishable experimentally. Markov processes are the special case where sojourn times in individual states are exponentially distributed. In this case kinetic parameter estimation based on the observed class sojourn time distribution is briefly discussed; explicit estimating equations applicable to sequential models of nicotinic receptor kinetics are given.

Ion Channels↗
PubMed1993

Images of evolution: origin of spontaneous RNA replication waves.

Self-replicating molecules set up traveling concentration waves that propagate in an aqueous enzyme solution. The velocity of each wave provides an accurate (+/- 0.1%) noninvasive measure of fitness for the RNA species currently growing in its front. Evolution may be followed from changes in the front velocity, and these differ from wave to wave. Thousands of controlled evolution reactions in traveling waves have been monitored in parallel to obtain quantitative images of the stochastic process of natural selection. An RNA polymerase (RNA-dependent RNA nucleotidyltransferase, EC 2.7.7.6), extracted from bacteria infected by the Q beta RNA virus, catalyzes the replication. The traveling waves that arise spontaneously without added RNA provide a model system for major evolutionary change.

Biological Evolution↗
PubMed2004

Stochastic model for the species abundance problem in an ecological community.

We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical expression for the marginalized stationary distribution. Our solution is found in excellent agreement with numerical simulations and compares rather well with observational data from tropical forests.

Animals↗
PubMed2004

Stochastic and epigenetic changes of gene expression in Arabidopsis polyploids.

Polyploidization is an abrupt speciation mechanism for eukaryotes and is especially common in plants. However, little is known about patterns and mechanisms of gene regulation during early stages of polyploid formation. Here we analyzed differential expression patterns of the progenitors' genes among successive selfing generations and independent lineages. The synthetic Arabidopsis allotetraploid lines were produced by a genetic cross between A. thaliana and A. arenosa autotetraploids. We found that some progenitors' genes are differentially expressed in early generations, whereas other genes are silenced in late generations or among different siblings within a selfing generation, suggesting that the silencing of progenitors' genes is rapidly and/or stochastically established. Moreover, a subset of genes is affected in autotetraploid and multiple independent allotetraploid lines and in A. suecica, a natural allotetraploid derived from A. thaliana and A. arenosa, indicating locus-specific susceptibility to ploidy-dependent gene regulation. The role of DNA methylation in silencing progenitors' genes is tested in DNA-hypomethylation transgenic lines of A. suecica using RNA interference (RNAi). Two silenced genes are reactivated in both ddm1- and met1-RNAi lines, consistent with the demethylation of centromeric repeats and gene-specific regions in the genome. A rapid and stochastic process of differential gene expression is reinforced by epigenetic regulation during polyploid formation and evolution.

Arabidopsis↗
PubMed1983

A stochastic model for helix bending in B-DNA.

Bending in double-helical B-DNA apparently occurs only by rolling adjacent base pairs over one another along their long axes. The lifting apart of ends that would be required by tilt or wedge angle contributions is too costly in free energy and does not occur. Roll angles at base steps can be positive (compression of major groove) or negative (compression of minor groove), with the former somewhat easier. Individual steps may advance or oppose the overall direction of bend, or make lateral excursions, but the result of this series of "random roll" steps is the production of a net bending in the helix axis. Because the natural roll points for bending in a given plane occur every 5 base pairs, one would expect that double-helical DNA wrapped around a nucleosome core would exhibit bends with the same periodicity. Alternate bends might be particularly acute where the major groove faced the nucleosome core and was compressed against it. The "annealed kinking" model proposed by Fratini et al. (J. Biol. Chem. 257, 14686 (1982) was suggested from the observation that a major bend at a natural roll point is flanked by decreasing roll angles at the steps to either side, as though local strain was being minimized by somewhat blurring the bend out rather than keeping it localized. The random walk model suggested in this paper would describe this as a decreased roll angle as the helix step rotates toward a direction perpendicular to the overall bend. Bending of DNA is seen to be a more stochastic process than had been suspected. Detailed analysis of every helix step reveals both side excursions and backward or retrograde motion, as in any random walk situation. Yet these isolated steps counteract one another, to leave behind a residuum of overall bending in a specific direction.

Base Sequence↗
PubMed2006

Stochastic modeling of neurobiological time series: power, coherence, Granger causality, and separation of evoked responses from ongoing activity.

In this article we consider the stochastic modeling of neurobiological time series from cognitive experiments. Our starting point is the variable-signal-plus-ongoing-activity model. From this model a differentially variable component analysis strategy is developed from a Bayesian perspective to estimate event-related signals on a single trial basis. After subtracting out the event-related signal from recorded single trial time series, the residual ongoing activity is treated as a piecewise stationary stochastic process and analyzed by an adaptive multivariate autoregressive modeling strategy which yields power, coherence, and Granger causality spectra. Results from applying these methods to local field potential recordings from monkeys performing cognitive tasks are presented.

Action Potentials↗
PubMed2002

Surface-exposed positions in the transmembrane helices of the lactose permease of Escherichia coli determined by intermolecular thiol cross-linking.

Intermolecular thiol cross-linking was used to determine surface-exposed positions in 250 lactose permease mutants containing single-Cys replacements in each transmembrane helix. Significant cross-linking of monomers to produce homodimers is observed in nine mutants with a 5-A-long cross-linking agent containing bis-methane thiosulfonate reactive groups [position 78 (helix III); positions 185, 186, and 187 (helix VI); positions 263, 275, and 278 (helix VIII); and positions 308 (helix IX) and 398 (helix XII)]. The results are consistent with a current helix-packing model of the permease. Seven of the nine mutants that exhibit intermolecular cross-linking are located at or near the cytoplasmic ends of transmembrane helices; two are near periplasmic ends. The results suggest that only those Cys replacements accessible from the aqueous phase and not from the hydrophobic core of the membrane are susceptible to cross-linking because of the much higher reactivity of the thiolate anion relative to the thiol. Single-Cys mutants at positions 278 (helix VIII) and 398 (helix XII), which are located in opposite sides of the 12-helix bundle, exhibit similar rates of cross-linking with sigmoid kinetics. Furthermore, cross-linking is markedly decreased at 0 degrees C, suggesting that lateral diffusion of the permease within the plane of the membrane is important for intermolecular cross-linking. The findings confirm previous observations indicating that intermolecular cross-linking is a stochastic process resulting from random collisions and support a number of other lines of evidence that lactose permease is a monomer.

Amino Acid Sequence↗
PubMed1978

Origin and nature of correlations in the Ia feedback pathway of the muscle control system.

Mammalian primary muscle spindle endings receive two inputs from fusimotor fibres and length changes of their extrafusal environment. Both inputs are also powerful noise sources disturbing the discharge patterns of the receptors. In this paper emphasis is laid on the extrafusal component. It is shown that extrafusal muscle activity can be viewed as a stochastic process which, acting as a common source, can correlate discharge patterns of adjacent muscle spindles. Some quantitative characteristics of these correlations and their relation to the underlying mechanical events are investigated in some detail in order to provide data for more theoretical considerations on their possible physiological importance.

Action Potentials↗
PubMed1999

A method for estimating pharmacokinetic risks of concentration-dependent drug interactions from preclinical data.

This article evaluates a novel approach for estimating the pharmacokinetic risks associated with drug interactions in populations. Preclinical pharmacokinetic and metabolism data are analyzed with a stochastic differential equation-based pharmacokinetic model that recognizes that the risks associated with known drug interactions involve deterministic and stochastic components. Specifically, a Bernoulli jump-diffusion pharmacokinetic model that accounts for the pharmacokinetics, the variability inherent in the pharmacokinetics, and the idiosyncratic nature of the possibility of drug interactions is proposed. In addition, the variability inherent in the extent of drug interaction is explicitly accounted for. The approach provides useful mechanistic insights into the stochastic processes that "drive" drug interactions in populations because it yields analytical results. The validity of the model predictions was tested with experimental data from two previously investigated systems: N-1 and N-3 caffeine demethylation in populations with smokers and in the terfenadine-ketoconazole system.

Dose-Response Relationship, Drug↗
PubMed1995

On the distribution and convergence of feature space in self-organizing maps.

In this paper an analysis of the statistical and the convergence properties of Kohonen's self-organizing map of any dimension is presented. Every feature in the map is considered as a sum of a number of random variables. We extend the Central Limit Theorem to a particular case, which is then applied to prove that the feature space during learning tends to multiple gaussian distributed stochastic processes, which will eventually converge in the mean-square sense to the probabilistic centers of input subsets to form a quantization mapping with a minimum mean squared distortion either globally or locally. The diminishing effect, as training progresses, of the initial states on the value of the feature map is also shown.

Algorithms↗
PubMed2006

Parameter estimation of feedback gain in a stochastic model of renal hemodynamics: differences between spontaneously hypertensive and Sprague-Dawley rats.

Proximal tubular pressure shows periodic self-sustained oscillations in normotensive rats but highly irregular fluctuations in spontaneously hypertensive rats (SHR). Although we have suggested that the irregular fluctuations in SHR represent low-dimensional deterministic chaos in tubuloglomerular feedback (TGF), they could also arise from other mechanisms, such as intrinsic instabilities in preglomerular vessels or inputs from neighboring, coupled nephrons. To test this possibility, we applied a parameter estimation procedure to a model of TGF, where a stochastic process was added to represent mechanisms not included explicitly in the model. In its deterministic version, the model can have chaotic dynamics arising from TGF. The model introduces random fluctuations into a parameter that determines the gain of TGF. The model shows a rich variety of dynamics ranging from low-dimensional deterministic oscillations and chaos to high-dimensional random fluctuations. To fit the data from normotensive rats, the model must introduce only a small variation in the feedback gain, and its estimates of that gain agree well with experimental values. These results support the use of the deterministic model of nephron dynamics in normotensive rats. In contrast, the irregular tubular pressure fluctuations in SHR were best described by a model dominated by random parameter fluctuations. The results point to the failure of simple mathematical models of nephron dynamics adequately to describe processes that are important for the irregular tubular pressure fluctuations and the need to consider other factors, such as differences in vascular function or nephron-nephron interactions, in further work on this problem.

Animals↗
PubMed2002

Extinction dynamics in mainland-island metapopulations: an N-patch stochastic model.

A generalization of the well-known Levins' model of metapopulations is studied. The generalization consists of (i) the introduction of immigration from a mainland, and (ii) assuming the dynamics is stochastic, rather than deterministic. A master equation, for the probability that n of the patches are occupied, is derived and the stationary probability Ps(n), together with the mean and higher moments in the stationary state, determined. The time-dependence of the probability distribution is also studied: through a Gaussian approximation for general n when the boundary at n = 0 has little effect, and by calculating P(0, t), the probability that no patches are occupied at time t, by using a linearization procedure. These analytic calculations are supplemented by carrying out numerical solutions of the master equation and simulations of the stochastic process. The various approaches are in very good agreement with each other. This allows us to use the forms for Ps(0) and P(0,t) in the linearization approximation as a basis for calculating the mean time for a metapopulation to become extinct. We give an analytical expression for the mean time to extinction derived within a mean field approach. We devise a simple method to apply our mean field approach even to complex patch networks in realistic model metapopulations. After studying two spatially extended versions of this nonspatial metapopulation model--a lattice metapopulation model and a spatially realistic model--we conclude that our analytical formula for the mean extinction time is generally applicable to those metapopulations which are really endangered, where extinction dynamics dominates over local colonization processes. The time evolution and, in particular, the scope of our analytical results, are studied by comparing these different models with the analytical approach for various values of the parameters: the rates of immigration from the mainland, the rates of colonization and extinction, and the number of patches making up the metapopulation.

Animals↗
PubMed1998

Predicted and inferred waiting times for key mutations in the germinal centre reaction: evidence for stochasticity in selection.

The germinal centre reaction (GCR) is a fundamental component of the immune response to T-dependent antigens, during which the immunoglobulin (Ig) genes of B cells experience somatic hypermutation and selection. A maximum-likelihood method on DNA sequence data from 16 individual germinal centres was used to infer that the waiting time for position 33 key (high-affinity) mutations in the anti-(4-hydroxy-3-nitrophenyl) acetyl (NP) response is 8.3 days. This is in marked contrast to the prediction of a key mutant each generation (waiting time about 1/3 day) obtained from a simple model and parameters available in the literature. This disagreement is resolved in part by the finding that the targeted base occurs in a cold spot for hypermutation, raising the predicted waiting time to 2.3 days, although this value remains significantly lower than that inferred from the sequence data. It is proposed that the remaining disparity is attributable to some further stochastic process in the GCR: many early key mutations arise but fail to 'take root' within the GC, either due to emigration or failure of cognate T cell/B cell interaction. Furthermore, it is argued that the frequency with which position 33 mutations are found in secondary responses to NP indicates the presence of selection after the GCR.

Animals↗
PubMed1989

Stochastic models for heterogeneous DNA sequences.

The composition of naturally occurring DNA sequences is often strikingly heterogeneous. In this paper, the DNA sequence is viewed as a stochastic process with local compositional properties determined by the states of a hidden Markov chain. The model used is a discrete-state, discrete-outcome version of a general model for non-stationary time series proposed by Kitagawa (1987). A smoothing algorithm is described which can be used to reconstruct the hidden process and produce graphic displays of the compositional structure of a sequence. The problem of parameter estimation is approached using likelihood methods and an EM algorithm for approximating the maximum likelihood estimate is derived. The methods are applied to sequences from yeast mitochondrial DNA, human and mouse mitochondrial DNAs, a human X chromosomal fragment and the complete genome of bacteriophage lambda.

Base Sequence↗
PubMed1991

Generalized Stein's model for anatomically complex neurons.

A neuron with a large dendritic structure is considered. The number of synapses located on the dendrites is substantially higher than on the soma. The synaptic input effect on the neuronal excitability decreases with distance between a synapse ending and the trigger zone. Two areas are distinguished in accordance with the effect of synaptic input--dendritic and somatic. The dendritic area, when compared to the soma, is characterized by much higher intensity of its activation but the amplitudes of synaptically evoked changes of the membrane potential at the trigger zone are in general small. This situation is suitable for a diffusion approximation. However, on the soma, especially in the proximity of the trigger zone, the membrane potential changes are a large fraction of the threshold depolarization. The membrane potential at the trigger zone is modelled by a one-dimensional stochastic process. The diffusion Ornstein-Uhlenbeck process serves as a basis of the model; however, at the moments of somatic synapses activation its voltage changes in jumps. Their sizes represent the amplitudes of the evoked postsynaptic potentials. The unimodal histograms of interspike intervals can be explained by the model. The values of the coefficient of variation greater than one are connected with substantial inhibition.

Animals↗
PubMed2003

A model of aging and a shape of the observed force of mortality.

A probabilistic model of aging is considered. It is based on the assumption that a random resource, a stochastic process of aging (wear) and the corresponding anti-aging process are embedded at birth. A death occurs when the accumulated wear exceeds the initial random resource. It is assumed that the anti-aging process decreases wear in each increment. The impact of environment (lifestyle) is also taken into account. The corresponding relations for the observed and the conditional hazard rate (force of mortality) are obtained. Similar to some demographic models, the deceleration of mortality phenomenon is explained via the concept of frailty. Simple examples are considered.

Aged↗
PubMed1998

Cross-spectral analysis of physiological tremor and muscle activity. I. Theory and application to unsynchronized electromyogram.

We investigate the relationship between the extensor electromyogram (EMG) and tremor times series in physiological hand tremor by cross-spectral analysis. Special attention is directed to the phase spectrum and the effects of observational noise. We calculate the theoretical phase spectrum for a second-order linear stochastic process and compare the results to measured tremor data recorded from subjects who did not show a synchronized EMG activity in the corresponding extensor muscle. The results show that physiological tremor is well described by the proposed model and that the measured EMG represents a Newtonian force by which the muscle acts on the hand.

Biomechanical Phenomena↗