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PubMed2004

Surface electromyogram signal modelling.

The paper reviews the fundamental components of stochastic and motor-unit-based models of the surface electromyogram (SEMG). Stochastic models used in ergonomics and kinesiology consider the SEMG to be a stochastic process whose amplitude is related to the level of muscle activation and whose power spectral density reflects muscle conduction velocity. Motor-unit-based models for describing the spatio-temporal distribution of individual motor-unit action potentials throughout the limb are quite robust, making it possible to extract precise information about motor-unit architecture from SEMG signals recorded by multi-electrode arrays. Motor-unit-based models have not yet been proven as successful, however, for extracting information about recruitment and firing rates throughout the full range of contraction. The relationship between SEMG and force during natural dynamic movements is much too complex to model in terms of single motor units.

Action Potentials↗
PubMed1991

Molecular and cellular lesions associated with breast cancer progression.

Breast cancer may be more than one disease with differing etiologies. At the molecular level, breast cancer may be the result of a complex, dynamic, and stochastic process where there is more than one way to accomplish each of the steps necessary for malignant growth. The well documented biologic heterogeneity of breast cancers may arise from the many possible molecular changes that can accomplish a given step with variable efficiency. Alternatively, this heterogeneity may also reflect various possible orders of acquiring the sum of steps necessary for malignant growth. We have attempted to describe some of the molecular changes associated with breast cancer in the context of this broad conceptual framework. We have found that the capacity for infinite growth in culture usually occurs at a late stage of malignant progression and is frequently associated with activating ras mutations. Loss of heterozygosity at chromosome 11p can occur either early or late in progression, while losses at chromosome loci 1q and 17p, although independent of each other, are found in primary breast cancers. Whether the same molecular and cellular changes are to be found in Japanese patients remains to be determined.

Alleles↗
PubMedDate not supplied

Two tools to test time series data for evidence of chaos and/or nonlinearity.

Two computer programs are described for evaluating the evidence for chaos and nonlinearity in time series data. "bx" is an efficient algorithm for computing the correlation integral (from which correlation dimension can be estimated); and "surrogat" is a Fourier-transform-based algorithm for generating surrogate data consistent with a null hypothesis that the data arise as a result of a linear stochastic process.

Algorithms↗
PubMed2003

The devil in the details of life-history evolution: instability and reversal of genetic correlations during selection on Drosophila development.

The evolutionary relationships between three major components of Darwinian fitness, development rate, growth rate and preadult survival, were estimated using a comparison of 55 distinct populations of Drosophila melanogaster variously selected for age-specific fertility, environmental-stress tolerance and accelerated development. Development rate displayed a strong net negative evolutionary correlation with weight at eclosion across all selection treatments, consistent with the existence of a size-versus-time tradeoff between these characters. However, within the data set, the magnitude of the evolutionary correlation depended upon the particular selection treatments contrasted. A previously proposed tradeoff between preadult viability and growth rate was apparent only under weak selection for juvenile fitness components. Direct selection for rapid development led to sharp reductions in both growth rates and viability. These data add to the mounting results from experimental evolution that illustrate the sensitivity of evolutionary correlations to (i) genotype-by-environment (G x E) interaction, (ii) complex functional-trait interactions, and (iii) character definition. Instability, disappearance and reversal of patterns of genetic covariation often occur over short evolutionary time frames and as the direct product of selection, rather than some stochastic process. We suggest that the functional architecture of fitness is a rapidly evolving matrix with reticulate properties, a matrix that we understand only poorly.

Animals↗
PubMed1992

Ion flow through biomembranes. Physical theory explains its high sensitivity.

Numerous biomembranes exhibit a sensitivity to changes in electrical potential greater than predicted as possible from the classical application of the Boltzmann relation, a phenomenon which has long defied explanation, the actual sensitivity of some Na+ channels being many times greater than the classical limit. This paper explains, using a minimum of mathematics, how the very rapid gating effect of adsorbed Ca2+ (or other impermeable divalent cations) can directly affect the conductance of channels, and thus interact with the electric field within the channel to produce a change in the potential across the channel's gate much greater than the change in the membrane potential, with a corresponding change in the fraction of open conformational gates and change in conductance. These results are not in conflict with the Boltzmann relation, the necessary energy being made available from the total potential difference across the membrane by a long unrecognized stochastic process; the full mathematical theory is given in cited references.

Adsorption↗
PubMed1990

Studies on human CFU-Mix microvolume culture by use of limiting dilution assay.

By use of limiting dilution assay we investigated the bipotent and pluripotent hemopoietic progenitor cells (CFU-Mix) from 21 normal adults, cultured for 32 times. The CFU-Mix counts were 35.7 colonies/10(6) bone marrow cells. According to different cellular elements they could be divided into 5 groups, namely GEMM, GE, GL, GMeg and GM phi. It was suggested that differentiation of the stem cell is of stochastic process, influenced by different hemopoietic growth factors and cellular microenvironment. Our model seems to be suitable for studying differentiation of the stem cells. The rates of 3H-TdR and 55 + 59Fe incorporation were determined, and the 2nd day of culture was found to be the delayed stage of cell growth.

Adolescent↗
PubMed1998

The estimation of rapid rate constants from current-amplitude frequency distributions of single-channel recordings.

A method is described for estimating rapid rate constants from the distributions of current amplitude observed in single-channel electrical recordings. It has the advantages over previous, similar approaches that it can accommodate both multistate kinetic models and adjustable filtering of the data using an 8-pole Bessel filter. The method is conceptually straightforward: the observed distributions of current amplitude are compared with theoretical distributions derived by combining several simplifying assumptions about the underlying stochastic process with a model of the filter and electrical noise. Parameters are estimated by approximate maximum likelihood. The method was used successfully to estimate rate constants for both a simple two-state kinetic model (the transitions between open and closed states during the rapid gating of an outward-rectifying K(+)-selective channel in the plasma membrane of Acetabularia) and a complex multistate kinetic model (the blockade of the maxi cation channel in the plasma membrane of rye roots by verapamil). For the two-state model, parameters were estimated well, provided that they were not too fast or too slow in relation to the sampling rate. In the three-state model the precision of estimates depended in a complex way on the values of all rate parameters in the model.

Acetabularia↗
PubMed2002

When and where was the most recent common ancestor?

The structured coalescent is investigated for single-locus, digenic samples in the diffusion limit of the unidimensional stepping-stone model for homogeneous, isotropic migration and random genetic drift. Let T denote the scaled time to the most recent common ancestor (MRCA) of the two genes, and let Z designate the scaled deviation of the position of the MRCA from the average position of the two genes. The joint probability density of T and Z is evaluated explicitly. Both the marginal and conditional distributions of T have infinite expectation, as does the marginal distribution of Z. Conditioned on T = tau, the distribution of Z is Gaussian with mean zero and variance 2tau. The main results are extended to anisotropic migration. The results establish the existence of and define in the diffusion limit a retrospective stochastic process for digenic samples in one spatial dimension.

Animals↗
PubMed2006

Modeling intercellular interactions in early Mycobacterium infection.

Infection with Mycobacterium tuberculosis (Mtb) is characterized by localized, roughly spherical lesions within which the pathogen interacts with host cells. Containment of the infection or progression of disease depends on the behavior of individual cells, which, in turn, depends on the local molecular environment and on contact with neighboring cells. Modeling can help us understand the nonlinear interactions that drive the overall dynamics in this system. Early events in infection are particularly important, as are spatial effects and inherently stochastic processes. We describe a model of early Mycobacterium infection using the CyCells simulator, which was designed to capture these effects. We relate CyCells simulations of the model to several experimental observations of individual components of the response to Mtb.

Computer Simulation↗
PubMed1994

Spontaneous activity of first- and second-order neurons in the frog olfactory system.

The spontaneous activity of first-order neurons (neuroreceptors of the mucosa) and second-order neurons (mitral cells of the bulb) was recorded extracellularly in the frog olfactory system. To assess the influence of peripheral inputs upon mitral cells, the bulb was either normally connected or partially deafferented. Our first set of findings concern the firing behavior. We found that most neurons generated interspike intervals (ISIs) that were stationary in mean and variance, and were not serially correlated at first and second order. Individual spikes in mitral cells and bursts of spikes in neuroreceptors were found to be generated by a Poisson process. Stochastic modeling suggests that the Poissonian behavior depends on the mean value of the membrane potential at the axon hillock. In these models, the mean potential in mitral cells would be far below the firing threshold and in neuroreceptors it would fluctuate at random between two states, one close to resting potential (between bursts) and the other close to the firing threshold with occasional crossings (within bursts). Secondly, partially deafferented mitral cells had significantly higher activity and lower variance than mitral cells receiving normal afferent input. This effect gives evidence that peripheral inputs influence mitral cells at rest not only through direct excitation but also through indirect inhibition exerted by local neurons. Thus, the unstimulated state of the olfactory bulb would not be qualitatively different from its stimulated state in the sense that both states involve the same types of synaptic interactions. Consequently, understanding the synaptic relationships that take place in the bulb network can benefit from studies of its spontaneous activity.

Action Potentials↗
PubMed1984

Detection of periodic signals in noise: an iterative procedure.

A method for detection and estimation of periodic signals in the presence of noise is described. The algorithm is an iterative improvement of the autoregressive-moving average estimation of a stochastic process and gives an exact frequency resolution of sinusoidal signals additively mixed with noise in a low signal-to-noise ratio only from a small number of measurements. The iterative improvement of the spectral estimation compared with other methods is demonstrated by examples.

Computers↗
PubMed1984

Temporal characteristics of seizures and epileptiform discharges.

The time relations of epileptic events have been studied in 3 sets of data: (I) counts of individual epileptiform discharges in twelve 48 h EEG recordings, (IIa) seizure calendars of 30 therapy-resistant outpatients participating in a drug trial, (IIb) seizure calendars of 10 mentally subnormal epileptic patients resident in a long-stay unit. The EEG data I were characterized most often by a Poisson distribution of intervals between discharges and the occurrence of marked periodicities, particularly at night. The periods of rhythmic nocturnal events ranged from 13 to 142 min and did not appear to correspond to the REM/non-REM cycle. In the seizure data IIa and b a Poisson distribution of intervals between events was found in half the patients. Periodicities occurred only in group IIa and did not correspond to weekly or monthly cycles. A stochastic process is considered to be the model which best fits these data.

Adolescent↗
PubMed1985

Moments of the power spectral density estimated from samples of the autocorrelation function (a robust procedure for monitoring changes in the statistical properties of lengthy non-stationary time series such as the EEG.

Accurate estimates of the statistical moments of the power spectral density (PSD) are obtained without computing the Fourier transform of the associated time series. An innovative analytical procedure is derived which reduces the problem to that of summing a small number of weighted samples of the autocorrelation function (ACF). This result significantly reduces the computational requirements for generating meaningful PSD shape descriptors and thus is especially important in biomedical applications where the cost and effort of monitoring lengthy non-stationary time series is a serious practical limitation. In addition the procedure is robust and therefore can be rigorously applied to any stochastic process to estimate its fundamental statistical properties.

Adult↗
PubMedDate not supplied

Nonstationary properties of postural sway.

Postural sway during quite stance is usually assumed to be a stationary stochastic process. We tested this assumption by investigating the time invariance of the average value and variance of the postural sway of three subjects. The sway was measured with a force plate under three conditions: subject standing on two feet with eyes open; subject standing on two feet with eyes closed; and subject standing on one foot with eyes open. Data were collected in 1 min runs. More than 50 min of data were collected for each subject under each test condition. The data were averaged across all runs for each subject and condition. Trends were found to be present in the data. In addition, there were initial transient increases in the second-order moments about the trends. The transient changes in first- and second-order moments usually disappeared during the first 20 s. In light of these findings, we can reject the hypothesis that postural sway is a stationary process. The results imply that the usual methods to parameterize postural sway have to be either changed or reinterpreted.

Adult↗
PubMed1992

Analysis of insertions/deletions in protein structures.

An analysis of insertions and deletions (indels) occurring in a databank of multiple sequence alignments based on protein tertiary structure is reported. Indels prefer to be short (1 to 5 residues). The average intervening sequence length between them versus the percentage of residue identity in pairwise alignments shows an exponential behaviour, suggesting a stochastic process such that nearly every loop in an ancestral structure is a possible target for indels during evolution. The results also suggest a limit to the average size of indels accommodated by protein structures. The preferred indel conformations are reverse turn and coil as are the preferred conformations at the indel edges (N- and C-terminal sides). Interruptions in helices and strands were observed as very rare events.

Amino Acid Sequence↗
PubMed1996

Measures of concurrency in networks and the spread of infectious disease.

An investigation is made into the impact of concurrent partnerships on epidemic spread. Starting from a definition of concurrency on the level of individuals, the authors define ways to quantify concurrency on the population level. An index of concurrency based on graph theoretical considerations is introduced, and the way in which it is related to the degree distribution of the contact graph is demonstrated. Then the spread of an infectious disease on a dynamic partnership network is investigated. The model is based on a stochastic process of pair formation and separation and a process of disease transmission within partnerships of susceptible and infected individuals. Using Monte Carlo simulation, the spread of the epidemic is compared for contact patterns ranging from serial monogamy to situations where individuals can have many partners simultaneously. It is found that for a fixed mean number of partners per individual the distribution of these partnerships over the population has a major influence on the speed of the epidemic in its initial phase and consequently in the number of individuals who are infected after a certain time period.

Acquired Immunodeficiency Syndrome↗
PubMed1976

Stable mutants of mammalian cells that overproduce the first three enzymes of pyrimidine nucleotide biosynthesis.

Upon exposure to 0.1 mM N-phosphonacetyl-L-aspartate (PALA), a transition state analog inhibitor of aspartate transcarbamylase, most cells of a simian virus 40 (SV40)-transformed Syrian hamster line are killed within a few days, but resistant mutants form spontaneously with frequency 2-5 X 10(-5) in a stochastic process not dependent upon the presence of the inhibitor. The resistant phenotype is stable for many months in the absence of PALA. Other cell lines also give resistant mutants, but with substantially lower frequencies. Serial selection with PALA at concentrations up to 25 mM has yielded clones with more than 100 times the original aspartate transcarbamylase activity. The activities of carbamyl-P synthetase and dihydroorotase, which co-purify with aspartate transcarbamylase as a three-enzyme complex, increase in parallel with aspartate transcarbamylase activity in each resistant clone tested, but there is no substantial change in the activities of the last three enzymes of the de novo pathway, which are not in this complex. In each of the three resistant clones tested, there is an increase in the number of aspartate transcarbamylase active sites, determined by titration with 3H-PALA, which closely parallels the increase in enzyme activity. In one resistant clone tested, there is no change in the Ki for PALA or the Km for carbamyl-P. The only mechanism detected for achieving resistance to PALA is an increase in the steady state amount of the three enzyme complex.

Amidohydrolases↗
PubMed1983

Asynchronous switching of flagellar motors on a single bacterial cell.

Salmonella possesses several flagella, each capable of counterclockwise and clockwise rotation. Counterclockwise rotation produces swimming, clockwise rotation produces tumbling. Switching between senses occurs stochastically. The rotational sense of individual flagella on a single cell could be monitored under special conditions (partially de-energized cells of cheC and cheZ mutants). Switching was totally asynchronous, indicating that the stochastic process operates at the level of the individual organelle. Coordinated rotation in the flagellar bundle during swimming may therefore derive simply from a high counterclockwise probability enhanced by mechanical interactions, and not from a synchronizing switch mechanism. Different flagella on a given cell had different switching probabilities, on a time scale (greater than 2 min) spanning many switching events. This heterogeneity may reflect permanent structural differences, or slow fluctuations in some regulatory process.

Bacterial Proteins↗