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PubMed2004

Predictive modelling of the microbial lag phase: a review.

This paper summarises recent trends in predictive modelling of microbial lag phenomena. The lag phase is approached from both a qualitative and a quantitative point of view. First, a definition of lag and an analysis of the prevailing measuring techniques for the determination of lag time is presented. Furthermore, based on experimental results presented in literature, factors influencing the lag phase are discussed. Major modelling approaches concerning lag phase estimation are critically assessed. In predictive microbiology, a two-step modelling approach is used. Primary models describe the evolution of microbial numbers with time and can be subdivided into deterministic and stochastic models. Primary deterministic models, e.g., Baranyi and Roberts [Int. J. Food Microbiol. 23 (1994) 277], Hills and Wright [J. Theor. Biol. 168 (1994) 31] and McKellar [Int. J. Food Microbiol. 36 (1997) 179], describe the evolution of microorganisms, using one single (deterministic) set of model parameters. In stochastic models, e.g., Buchanan et al. [Food Microbiol. 14 (1997) 313], Baranyi [J. Theor. Biol. 192 (1998) 403] and McKellar [J. Appl. Microbiol. 90 (2001) 407], the model parameters are distributed or random variables. Secondary models describe the relation between primary model parameters and influencing factors (e.g., environmental conditions). This survey mainly focuses on the influence of temperature and culture history on the lag phase during growth of bacteria.

Bacteria↗
PubMed2003

Synchronous loss of quasispecies memory in parallel viral lineages: a deterministic feature of viral quasispecies.

Viral quasispecies are endowed with a memory of their past evolutionary history in the form of minority genomes of their mutant spectra. To determine the fate of memory genomes in evolving viral quasispecies, we have measured memory levels of antigenic variant of foot-and-mouth disease virus (FMDV) RED, which includes an Arg-Glu-Asp (RED) at a surface antigenic loop of the viral capsid. The RED reverted to the standard Arg-Gly-Asp (RGD), and the RED remained as memory in the evolving quasispecies. In four parallel evolutionary lineages, memory reduction followed a strikingly similar pattern, and at passage 60 memory levels were indistinguishable from those of control populations (devoid of memory). Nucleotide sequence analyses indicated that memory loss occurred synchronously despite its ultimate molecular basis being the stochastic occurrence of mutations in the evolving quasispecies. These results on the kinetics of memory levels have unveiled a deterministic feature of viral quasispecies. Molecular mechanisms that may underlie synchronous memory loss are the averaging of noise signals derived from mutational input, and constraints to genome diversification imposed by a nucleotide sequence context in the viral genome. Possible implications of the behaviour of complex, adaptive viral systems as experimental models to address primary mechanisms of neurological memory are discussed.

Amino Acid Sequence↗
PubMed1987

Selection, generalized transmission and the evolution of modifier genes. I. The reduction principle.

Modifier gene models are used to explore the evolution of features of organisms, such as the genetic system, that are not directly involved in the determination of fitness. Recent work has shown that a general "reduction principle" holds in models of selectively neutral modifiers of recombination, mutation, and migration. Here we present a framework for models of modifier genes that shows these reduction results to be part of a more general theory, for which recombination and mutation are special cases. The deterministic forces that affect the genetic composition of a population can be partitioned into two categories: selection and transmission. Selection includes differential viabilities, fertilities, and mating success. Imperfect transmission occurs as a result of such phenomena as recombination, mutation and migration, meiosis, gene conversion, and meiotic drive. Selectively neutral modifier genes affect transmission, and a neutral modifier gene can evolve only by generating association with selected genes whose transmission it affects. We show that, in randomly mating populations at equilibrium, imperfect transmission of selected genes allows a variance in their marginal fitnesses to be maintained. This variance in the marginal fitnesses of selected genes is what drives the evolution of neutral modifier genes. Populations with a variance in marginal fitnesses at equilibrium are always subject to invasion by modifier genes that bring about perfect transmission of the selected genes. It is also found, within certain constraints, that for modifier genes producing what we call "linear variation" in the transmission processes, a new modifier allele can invade a population at equilibrium if it reduces the level of imperfect transmission acting on the selected genes, and will be expelled if it increases the level of imperfect transmission. Moreover, the strength of the induced selection on the modifier gene is shown to range up to the order of the departure of the genetic system from perfect transmission.

Biological Evolution↗
PubMed2000

Rate processes in a delayed, stochastically driven, and overdamped system

A Fokker-Planck formulation of systems described by stochastic delay differential equations has been recently proposed. A separation of time scales approximation allowing this Fokker-Planck equation to be simplified in the case of multistable systems is hereby introduced, and applied to a system consisting of a particle coupled to a delayed quartic potential. In that approximation, population numbers in each well obey a phenomenological rate law. The corresponding transition rate is expressed in terms of the noise variance and the steady-state probability density. The same type of expression is also obtained for the mean first passage time from a given point to another one. The steady-state probability density appearing in these formulas is determined both from simulations and from a small delay expansion. The results support the validity of the separation of time scales approximation. However, the results obtained using a numerically determined steady-state probability are more accurate than those obtained using the small delay expansion, thereby stressing the high sensitivity of the transition rate and mean first passage time to the shape of the steady-state probability density. Simulation results also indicate that the transition rate and the mean first passage time both follow Arrhenius' law when the noise variance is small, even if the delay is large. Finally, deterministic unbounded solutions are found to coexist with the bounded ones. In the presence of noise, the transition rate from bounded to unbounded solutions increases with the delay.

Journal Article↗
PubMed2005

Predator-prey cycles from resonant amplification of demographic stochasticity.

We present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is infinitely large, is the Volterra system (with density-dependent prey reproduction) which is well known to fail to predict cycles. This difference in behavior can be traced to a resonant amplification of demographic fluctuations which disappears only when the number of individuals is strictly infinite. Our results indicate that additional biological mechanisms, such as predator satiation, may not be necessary to explain observed predator-prey cycles in real (finite) populations.

Animals↗
PubMed1999

Stochastic model revisited.

Micromanipulation of murine and human hematopoietic progenitors has demonstrated various combinations of lineages in multilineage colonies, a finding consistent with the stochastic model of stem cell differentiation. Debate continued, however, on the mechanisms of stem cell differentiation, partly because some studies of cell lines suggested a deterministic model. Recently, transfection of primary hematopoietic progenitors with natural or chimeric cytokine receptors demonstrated that forced expression of cytokine receptors does not change the intrinsic differentiation potential of the primary progenitors. Studies also have demonstrated remarkable absence of specificity of signaling pathways in the primary progenitors. These studies are consistent with the stochastic model of stem cell differentiation in which cytokines play permissive and not instructive roles. This review summarizes some of the pertinent literature and discusses the cellular and molecular mechanisms of stem cell differentiation.

Animals↗
PubMed1990

Receptor-mediated cell attachment and detachment kinetics. II. Experimental model studies with the radial-flow detachment assay.

Quantitative information regarding the kinetics of receptor-mediated cell adhesion to a ligand-coated surface are crucial for understanding the role of certain key parameters in many physiological and biotechnology-related processes. Here, we use the probabilistic attachment and detachment models developed in the preceding paper to interpret transient data from well-defined experiments. These data are obtained with a simple model cell system that consists of receptor-coated latex beads (prototype cells) and a Radial-Flow Detachment Assay (RFDA) using a ligand-coated glass disc. The receptors and ligands used in this work are complementary antibodies. The beads enable us to examine transient behavior with particles that possess fairly uniform properties that can be varied systematically, and the RFDA is designed for direct observation of adhesion to the ligand-coated glass surface over a range of shear stresses. Our experiments focus on the effects of surface shear stress, receptor density, and ligand density. These data provide a crucial test of the probabilistic framework. We show that these data can be explained with the probabilistic analyses, whereas they cannot be readily interpreted on the basis of a deterministic analysis. In addition, we examine transient data on cell adhesion reported from other assays, demonstrating the consistency of these data with the predictions of the probabilistic models.

Biophysical Phenomena↗
PubMed2001

Multistationarity, the basis of cell differentiation and memory. I. Structural conditions of multistationarity and other nontrivial behavior.

A biological introduction serves to remind us that differentiation is an epigenetic process, that multistationarity can account for epigenetic differences, including those involved in cell differentiation, and that positive feedback circuits are a necessary condition for multistationarity and, by inference, for differentiation. The core of the paper is comprised of a formal description of feedback circuits and unions of disjoint circuits. We introduce the concepts of full-circuit (a circuit or union of disjoint circuits which involves all the variables of the system), and of ambiguous circuit (a circuit whose sign depends on the location in phase space). We describe the partition of phase space (a) according to the signs of the ambiguous circuits, and (b) according to the signs of the eigenvalues or their real part. We introduce a normalization of the system versus one of the circuits; in two variables, this permits an entirely general description in terms of a common diagram in the "circuit space." The paper ends with general statements concerning the requirements for multistationarity, stable periodicity, and deterministic chaos. (c) 2001 American Institute of Physics.

Journal Article↗
PubMed2007

Manipulation of the morphology of semiconductor-based nanostructures from core-shell nanoparticles to nanocables: the case of CdSe/SiO(2).

The morphology of CdSe/SiO(2) was manipulated from core-shell-structured nanoparticles to nanocables by using a chemical vapor deposition (CVD) process. The growth of nanocables, with cores no more than 20 nm in diameter, is initiated by the formation of core-shell nanoparticles with SiO(2) as matrix and CdSe clusters dispersed inside. After the subsequent vaporization of the SiO(2) matrix, the follow-up CdSe vapor crystallizes with the remaining CdSe clusters as nuclei to form CdSe nanowires as the furnace was cooled to 1200 degrees C. During the controlled cooling of the furnace, the SiO vapor re-deposits to sheathe the nanowires. The thickness of the shell and the diameter of core were successfully controlled. The photoluminescence measurements show that the CdSe/SiO(2) nanocables have strong visible-light emission bands located at 590 and 688 nm, which are attributed to the defects induced by SiO(2) sheaths nanowires and the quantum confinement effect of the CdSe, respectively. The UV/Vis absorption spectra of the naked CdSe nanowires further validate the above-mentioned quantum confinement effect. The deterministic growth of these nanocables is very important for the design of the nanodevices based on them.

Journal Article↗
PubMedDate not supplied

A model-based approach for the analysis of neuronal information transmission in multi-input and -output systems.

We present a new method to characterize multi-input and output neuronal systems using information theory. To obtain a lower bound of transinformation we take three steps: (1) Estimation of the deterministic response to isolate components carrying stimulus information. The deviation of the original response from the deterministic estimate is defined as noise. (2) Coordinate transformation using PCA yields an uncorrelated representation. (3) Partial transinformation values are calculated independently either by Shannon's formula assuming normality or based on density estimation for arbitrary distributions. We investigate the performance of the algorithms using simulated data and discuss suitable parameter settings. The approach allows to evaluate the degree to which stimulus features are encoded. Its potential is illustrated by analyses of neuronal activity in cat primary visual cortex evoked by electrical retina stimulation.

Action Potentials↗
PubMed2005

Deterministic and stochastic elements of axonal guidance.

An enormous literature has been developed on investigations of the growth and guidance of axons during development and after injury. In this review, we provide a guide to this literature as a resource for biomedical investigators. We first review briefly the molecular biology that is known to regulate migration of the growth cone and branching of axonal arbors. We then outline some important fundamental considerations that are important to the modeling of the phenomenology of these guidance effects and of what is known of their underlying internal mechanisms. We conclude by providing some thoughts on the outlook for future biomedical modeling in the field.

Actins↗
PubMed2005

Durability of marker-quantitative trait loci haplotypes in structured populations.

Given the relative ease of identifying genetic markers linked to QTL (compared to finding the loci themselves), it is natural to ask whether linked markers can be used to address questions concerning the contemporary dynamics and recent history of the QTL. In particular, can a marker allele found associated with a QTL allele in a QTL mapping study be used to track population dynamics or the history of the QTL allele? For this strategy to succeed, the marker-QTL haplotype must persist in the face of recombination over the relevant time frame. Here we investigate the dynamics of marker-QTL haplotype frequencies under recombination, population structure, and divergent selection to assess the potential utility of linked markers for a population genetic study of QTL. For two scenarios, described as "secondary contact" and "novel allele," we use both deterministic and stochastic methods to describe the influence of gene flow between habitats, the strength of divergent selection, and the genetic distance between a marker and the QTL on the persistence of marker-QTL haplotypes. We find that for most reasonable values of selection on a locus (s < or = 0.5) and migration (m > 1%) between differentially selected populations, haplotypes of typically spaced markers (5 cM) and QTL do not persist long enough (>100 generations) to provide accurate inference of the allelic state at the QTL.

Alleles↗
PubMed1991

Reproduction numbers and thresholds in stochastic epidemic models. I. Homogeneous populations.

We compare threshold results for the deterministic and stochastic versions of the homogeneous SI model with recruitment, death due to the disease, a background death rate, and transmission rate beta cXY/N. If an infective is introduced into a population of susceptibles, the basic reproduction number, R0, plays a fundamental role for both, though the threshold results differ somewhat. For the deterministic model, no epidemic can occur if R0 less than or equal to 1 and an epidemic occurs if R0 greater than 1. For the stochastic model we find that on average, no epidemic will occur if R0 less than or equal to 1. If R0 greater than 1, there is a finite probability, but less than 1, that an epidemic will develop and eventuate in an endemic quasi-equilibrium. However, there is also a finite probability of extinction of the infection, and the probability of extinction decreases as R0 increases above 1.

Computer Simulation↗
PubMed2006

Stochastic or deterministic: what is the effective population size of HIV-1?

Various studies have attempted to estimate the effective population size of HIV-1 to determine the strength of stochastic effects in within-host evolution. The largely discrepant estimates, the complexity of the concept of the effective population size and the resulting uncertainty about the underlying assumptions make the interpretation of these estimates difficult. Here, we explain the concept and critically assess the current estimates. We discuss the biologically relevant factors that affect the estimate and use of the effective population size. We argue that these factors lead to an underestimation of the effective population size and, thus, to an overestimation of the strength of stochastic effects in HIV-1 evolution.

Evolution, Molecular↗
PubMed2006

Artifact reduction for EEG/fMRI recording: nonlinear reduction of ballistocardiogram artifacts.

OBJECTIVE: We present a new method of effectively removing the ballistocardiogram artifacts (BAs) of electroencephalography (EEG), recorded inside a 1.5 T static magnetic field scanner with no fMRI scanning, which conserves the time and frequency features of event-related EEG activity. METHODS: The BAs are approximated as deterministically chaotic dynamics. A Wavelet-based nonlinear noise reduction (WNNR) method consisting of: (a) wavelet transformation, (b) nonlinear noise reduction and (c) spatial average subtraction, is developed to effectively reduce the BAs so that the residual artifacts are smaller than the EEG signals. RESULTS: The effectiveness of the WNNR method to remove the BAs with conservation of the temporal EEG signals is evaluated by simulations and experiments inside a 1.5 T static magnetic field, with the visual evoked EEG dynamics. The WNNR method is also demonstrated to effectively retrieve alpha waves while the subjects' eyes are closed. CONCLUSIONS: The WNNR method has the abilities to effectively remove the BAs and conserve the time-frequency features of EEG activity. SIGNIFICANCE: The WNNR method provides us a significant technique to obtain clean temporal EEG signals during recording with MRI, especially for the event-related EEG dynamics. Notably, it might work effectively at higher field strengths as well. Moreover, it can be also used to process many other biological data contaminated by the cardiac pulses.

Adult↗
PubMed1998

Stochastic dose/risk assessment uncertainty and the concept of potential exposures.

Assessments of future potential doses and risks (e.g. in connection with radioactive waste disposal) can be associated with substantial uncertainties. These uncertainties are often incorporated into assessments using stochastic models, and give rise to doses characterised in probabilistic terms. Questions about how doses should be related to risks arise even in the case of deterministic dose assessments. However, results of a probabilistic dose assessment may lead to additional issues when interpreting them or attempting to convert them to risk for regulatory purposes. Some problems are shown to originate from the difference between the meaning of a probabilistic dose value and the definition of potential exposure. Others relate to the appropriate choice of, or approach to compliance with, a regulatory limit. A possible method for setting limits on probabilistic (potential) doses or risks is proposed, based on an accepted technique for determining detection limits.

Computer Simulation↗
PubMed2004

Ancestral sequence reconstruction in primate mitochondrial DNA: compositional bias and effect on functional inference.

Reconstruction of ancestral DNA and amino acid sequences is an important means of inferring information about past evolutionary events. Such reconstructions suggest changes in molecular function and evolutionary processes over the course of evolution and are used to infer adaptation and convergence. Maximum likelihood (ML) is generally thought to provide relatively accurate reconstructed sequences compared to parsimony, but both methods lead to the inference of multiple directional changes in nucleotide frequencies in primate mitochondrial DNA (mtDNA). To better understand this surprising result, as well as to better understand how parsimony and ML differ, we constructed a series of computationally simple "conditional pathway" methods that differed in the number of substitutions allowed per site along each branch, and we also evaluated the entire Bayesian posterior frequency distribution of reconstructed ancestral states. We analyzed primate mitochondrial cytochrome b (Cyt-b) and cytochrome oxidase subunit I (COI) genes and found that ML reconstructs ancestral frequencies that are often more different from tip sequences than are parsimony reconstructions. In contrast, frequency reconstructions based on the posterior ensemble more closely resemble extant nucleotide frequencies. Simulations indicate that these differences in ancestral sequence inference are probably due to deterministic bias caused by high uncertainty in the optimization-based ancestral reconstruction methods (parsimony, ML, Bayesian maximum a posteriori). In contrast, ancestral nucleotide frequencies based on an average of the Bayesian set of credible ancestral sequences are much less biased. The methods involving simpler conditional pathway calculations have slightly reduced likelihood values compared to full likelihood calculations, but they can provide fairly unbiased nucleotide reconstructions and may be useful in more complex phylogenetic analyses than considered here due to their speed and flexibility. To determine whether biased reconstructions using optimization methods might affect inferences of functional properties, ancestral primate mitochondrial tRNA sequences were inferred and helix-forming propensities for conserved pairs were evaluated in silico. For ambiguously reconstructed nucleotides at sites with high base composition variability, ancestral tRNA sequences from Bayesian analyses were more compatible with canonical base pairing than were those inferred by other methods. Thus, nucleotide bias in reconstructed sequences apparently can lead to serious bias and inaccuracies in functional predictions.

Animals↗
PubMed2006

Optimal observability of sustained stochastic competitive inhibition oscillations at organellar volumes.

When molecules are present in small numbers, such as is frequently the case in cells, the usual assumptions leading to differential rate equations are invalid and it is necessary to use a stochastic description which takes into account the randomness of reactive encounters in solution. We display a very simple biochemical model, ordinary competitive inhibition with substrate inflow, which is only capable of damped oscillations in the deterministic mass-action rate equation limit, but which displays sustained oscillations in stochastic simulations. We define an observability parameter, which is essentially just the ratio of the amplitude of the oscillations to the mean value of the concentration. A maximum in the observability is seen as the volume is varied, a phenomenon we name system-size observability resonance by analogy with other types of stochastic resonance. For the parameters of this study, the maximum in the observability occurs at volumes similar to those of bacterial cells or of eukaryotic organelles.

Algorithms↗