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PubMed2005

Computation in the olfactory system.

Computational models are increasingly essential to systems neuroscience. Models serve as proofs of concept, tests of sufficiency, and as quantitative embodiments of working hypotheses and are important tools for understanding and interpreting complex data sets. In the olfactory system, models have played a particularly prominent role in framing contemporary theories and presenting novel hypotheses, a role that will only grow as the complexity and intricacy of experimental data continue to increase. This review will attempt to provide a comprehensive, functional overview of computational ideas in olfaction and outline a computational framework for olfactory processing based on the insights provided by these diverse models and their supporting data.

Action Potentials↗
PubMed1993

Summarization, smoothing, and inference in epidemiologic analysis. 1991 Ipsen Lecture, Hindsgavl, Denmark.

In a recent article (Epidemiology 1990; 1: 421-429) I resurrected some historical criticisms of conventional statistics in non-randomized, non-randomly sampled studies, and suggested some improvements to current practice in response to these criticisms. Here, I propose that some resolution can be achieved by separating data analysis into summarization, smoothing, and inferential phases. Methods of statistical inference are in fact smoothing methods, as are many methods of descriptive statistics, and as such can be viewed as pattern-recognition devices. Scientific inference is not a statistical process, but instead concerns derivation of explanations for patterns detected by statistical methods. Improvements could be made to all three phases simply by keeping the phases distinct.

Analysis of Variance↗
PubMed2004

A weather-driven model of malaria transmission.

BACKGROUND: Climate is a major driving force behind malaria transmission and climate data are often used to account for the spatial, seasonal and interannual variation in malaria transmission. METHODS: This paper describes a mathematical-biological model of the parasite dynamics, comprising both the weather-dependent within-vector stages and the weather-independent within-host stages. RESULTS: Numerical evaluations of the model in both time and space show that it qualitatively reconstructs the prevalence of infection. CONCLUSION: A process-based modelling structure has been developed that may be suitable for the simulation of malaria forecasts based on seasonal weather forecasts.

Africa↗
PubMed2006

Pathogen transmission and clinic scheduling.

We developed a model of pathogen dissemination in the outpatient clinic that incorporates key kinetic aspects of the transmission process, as well as uncertainty regarding whether or not each incident patient is contagious. Assigning appointments late in the day to patients suspected of being infectious should decrease pathogen dissemination.

Ambulatory Care Facilities↗
PubMed1989

On the formulation of discrete-time epidemic models.

Jacquez constructed a properly posed, more general model for the Reed-Frost epidemic process by assuming independent behaviors for the susceptibles and introducing the generating function for the number of contacts per person. An alternative approach is proposed here that relies on similar hypotheses for the infectives and allows the usual chain-binomial structure of the infection process to be extended. For this new model, the derivation of the final size and the threshold phenomenon becomes much simpler. A detailed analysis and its generalization to heterogeneous populations and continuous-time models will be the subject of a forthcoming paper.

Disease Outbreaks↗
PubMed1994

A duality in aging: the equivalence of mortality models based on radically different concepts.

Several alternative mortality models fit Swedish old-age mortality data equally well. The models build on two different concepts of the heterogeneity of individuals in a population. The first concept concerns fixed, genetic differences among individuals in their risk of death. The second concept involves acquired susceptibility to death due to physiological changes and environmental influences. We show that alternative mortality models based on either of these two concepts or some mix of them lead to the same parametric form of observed age-specific death rates. We discuss this duality property of mortality processes and show that even when a mortality model fits the data, the concepts used to construct the model may not be correct.

Adult↗
PubMed2005

Real-time kinetics of gene activity in individual bacteria.

Protein levels have been shown to vary substantially between individual cells in clonal populations. In prokaryotes, the contribution to such fluctuations from the inherent randomness of gene expression has largely been attributed to having just a few transcripts of the corresponding mRNAs. By contrast, eukaryotic studies tend to emphasize chromatin remodeling and burst-like transcription. Here, we study single-cell transcription in Escherichia coli by measuring mRNA levels in individual living cells. The results directly demonstrate transcriptional bursting, similar to that indirectly inferred for eukaryotes. We also measure mRNA partitioning at cell division and correlate mRNA and protein levels in single cells. Partitioning is approximately binomial, and mRNA-protein correlations are weaker earlier in the cell cycle, where cell division has recently randomized the relative concentrations. Our methods further extend protein-based approaches by counting the integer-valued number of transcript with single-molecule resolution. This greatly facilitates kinetic interpretations in terms of the integer-valued random processes that produce the fluctuations.

Algorithms↗
PubMed2006

Chromatin assembly factor 1 ensures the stable maintenance of silent chromatin states in Arabidopsis.

Newly synthesized DNA is rapidly assembled into mature nucleosomes by the deposition of pre-existing and nascent histones, and some parts of this process are facilitated by chromatin assembly factor 1 (CAF-1). Loss-of-function mutants of CAF-1 in Arabidopsis, fasciata (fas), show a variety of morphological abnormalities and unique defects in gene expression in the meristems. In order to clarify the implications of CAF-1 in the maintenance of chromatin states in higher eukaryotes, we investigated transcriptional gene silencing (TGS) of various genes in fas mutants. Here, we show that TGS of endogenous CACTA transposons was released in a stochastic manner in fas. Other endogenous silent genes, a transposon AtMu1 and a hypothetical gene T5L23.26 at a heterochromatin knob, were also transcriptionally activated, and the activation of the three different silent loci at different chromosomal sites occurred non-concomitantly with each other. Furthermore, TGS of the silent beta-glucuronidase (GUS) transgene was also de-repressed randomly in fas. We conclude that CAF-1 ensures the stable inheritance of epigenetic states through growth and development in Arabidopsis.

Arabidopsis↗
PubMed1991

Convergence of one-dimensional diffusion processes to a jump process related to population genetics.

A conjecture on the convergence of diffusion models in population genetics to a simple Markov chain model is proved. The notion of bi-generalized diffusion processes and their limit theorems are used systematically to prove the conjecture. Three limits; strong selection-weak mutation limit, moderate selection-weak mutation limit, weak selection-weak mutation limit are considered for typical diffusion models in population genetics.

Genetics, Population↗
PubMedDate not supplied

Modeling population kinetics of free fatty acids in isolated rat hepatocytes using Markov Chain Monte Carlo.

The aim of this study is the characterization, by means of mathematical models, of the activity of isolated hepatic rat cells as regards the conversion of free fatty acids (FFA) to ketone bodies (KB). A new physiologically based compartmental model of FFA metabolism is used within a context of population pharmacokinetics. This analysis is based on a hierarchical model, that differs from standard model formulations, to account for the fact that some data sets belong to the same animal but have been collected under different experimental conditions. The statistical inference problem has been addressed within a Bayesian context and solved by using Markov Chain Monte Carlo (MCMC) simulation. The results obtained in this study indicate that, although hormones epinephrine and insulin are important metabolic regulatory factors in vivo, the conversion of FFA to KB by isolated hepatic rat cells is not significantly affected by epinephrine and only little influenced by insulin. So we conclude that in vivo, the interaction of these two hormones with other compounds not considered in this study plays a fundamental role in ketogenesis. From this study it appears that mathematical models of metabolic processes can be successfully employed in population kinetic studies using MCMC methods.

Animals↗
PubMed1997

An exemplar-based random walk model of speeded classification.

The authors propose and test an exemplar-based random walk model for predicting response times in tasks of speeded, multidimensional perceptual classification. The model combines elements of R. M. Nosofsky's (1986) generalized context model of categorization and G. D. Logan's (1988) instance-based model of automaticity. In the model, exemplars race among one another to be retrieved from memory, with rates determined by their similarity to test items. The retrieved exemplars provide incremental information that enters into a random walk process for making classification decisions. The model predicts correctly effects of within- and between-categories similarity, individual-object familiarity, and extended practice on classification response times. It also builds bridges between the domains of categorization and automaticity.

Concept Formation↗
PubMed2004

Predicting auditory tone-in-noise detection performance: the effects of neural variability.

Collecting and analyzing psychophysical data is a fundamental mechanism for the study of auditory processing. However, because this approach relies on human listening experiments, it can be costly in terms of time and money spent gathering the data. The development of a theoretical, model-based procedure capable of accurately predicting psychophysical behavior could alleviate these issues by enabling researchers to rapidly evaluate hypotheses prior to conducting experiments. This approach may also provide additional insight into auditory processing by establishing a link between psychophysical behavior and physiology. Signal detection theory has previously been combined with an auditory model to generate theoretical predictions of psychophysical behavior. Commonly, the ideal processor outperforms human subjects. In order for this model-based technique to enhance the study of auditory processing, discrepancies must be eliminated or explained. In this paper, we investigate the possibility that neural variability, which results from the randomness inherent in auditory nerve fiber responses, may explain some of the previously observed discrepancies. In addition, we study the impact of combining information across nerve fibers and investigate several models of multiple-fiber signal processing. Our findings suggest that neural variability can account for much, but not all, of the discrepancy between theoretical and experimental data.

Acoustic Stimulation↗
PubMed2004

A multichannel order-statistic technique for cDNA microarray image processing.

This paper introduces an automated image processing procedure capable of processing complementary deoxyribonucleic acid (cDNA) microarray images. Microarray data is contaminated by noise and suffers from broken edges and visual artifacts. Without the utilization of a filter, subsequent tasks such as spot identification and gene expression determination cannot be completed. By employing, in a unique cascade processing cycle, nonlinear filtering solutions based on robust order statistics, the procedure: 1) removes both background and high-frequency corrupting noise and 2) correctly identifies edges and spots in cDNA microarray data. The proposed solution operates directly on the microarray data, does not rely on explicit data normalization or spot separation preprocessing, and operates in a robust manner without using heuristically determined design parameters. Other routine microarray processing operations such as shape manipulations and grid adjustments can be used in conjunction with the developed solution in the processing pipeline. Experimentation reported in this paper indicates that the proposed solution yields excellent performance by removing noise and enhancing spot location determination.

Algorithms↗
PubMedDate not supplied

Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects.

In the case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks. In this paper, the Dirichlet process prior was used to provide nonparametric Bayesian estimates for correlated random effects. This goal was achieved by providing a Gibbs sampler algorithm that allows these correlated random effects to have a nonparametric prior distribution. A sampling based method is illustrated. This method which is employed by transforming the genetic covariance matrix to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and the results of previous researchers. Also by using Gibbs sampling and data augmentation a simulation procedure was derived for estimating the precision parameter M associated with the Dirichlet process prior. All needed conditional posterior distributions are given. To illustrate the application, data from the Elsenburg Dormer sheep stud were analysed. A total of 3325 weaning weight records from the progeny of 101 sires were used.

Algorithms↗
PubMedDate not supplied

Accurate spike synchronization in cortex.

In view of the enormous capacity and complexity of mammalian brains it is evident that a detailed account of their anatomy and physiology alone cannot lead to a complete understanding of their function. Computer simulation and mathematical analysis of abstract, yet biologically realistic models for neurons and networks yield additional and useful information about the interplay of the underlying anatomical structures, the physiological processes operating on the neuronal substrate, and the resulting brain functions during the performance of behavioral tasks. We discuss some contributions of such experiment-guided theory to the issue of accurate spike synchronization.

Animals↗
PubMed1999

Evaluation of the bias in using the time to the first event when the inter-event intervals have a Weibull distribution.

Currently the analysis of clinical trials for treatment of paroxysmal atrial fibrillation (PAF) relies on the assumption that the events are distributed according to a Poisson distribution. We contend that the occurrence of PAF events are clearly not Poisson and tend to occur in clusters. A candidate parametric model of the inter-event interval, the Weibull distribution, is presented. When the events are distributed according to a Poisson distribution, the time to the first event (TFE) has the same distribution as the inter-event intervals (IEI) due to the 'memoryless' property of the Poisson distribution, hence the TFE can be used instead of the IEI. When the events do not form a Poisson distribution, the TFE does not have the same distribution as the IEI. We show that for the Weibull distribution, when the TFE is used to model the IEI, both the mean and the survivor distribution are biased. The bias in the survivor function is a function both of time and the parameters of the distribution. Therefore when two groups have different parameters for their distributions (as in the case of different treatment effects), the discrepancy between the survivor distribution of the IEI and the survivor distribution of the TFE is affected differentially. We demonstrate the low coverage probabilities of the mean and the survivor function which result when the underlying distribution is Weibull with shape parameter kappa < 1.0. It is likely that this problem will arise for other clustered event processes. This suggests that careful empirical investigation of the distribution of IEI for recurrent events is necessary before choosing to analyse the data using the TFE.

Atrial Fibrillation↗
PubMed2004

Survival models based on the Ornstein-Uhlenbeck process.

When modelling survival data it may be of interest to imagine an underlying process leading up to the event in question. The Ornstein-Uhlenbeck process is a natural model to consider in a biological context because it stabilizes around some equilibrium point. This corresponds to the homeostasis often observed in biology, and also to some extent in the social sciences. First, we study the first-passage time distribution of an Ornstein-Uhlenbeck process, focussing especially on what is termed quasi-stationarity and the various shapes of the hazard rate. Next, we consider a model where the individual hazard rate is a squared function of an Ornstein-Uhlenbeck process. We extend known results on this model. The results on quasi-stationarity are relevant for recent discussions about mortality plateaus. In addition, we point out a connection to models for short-term interest rates in financial modeling.

Humans↗
PubMed1999

Investigating autocatalytic gene expression systems through mechanistic modeling.

A structured model of gene expression, which incorporates the stochastic behavior of cellular processes, was developed to examine the "all-or-none" phenomenon observed in autocatalytic systems (e.g. the lac operon). Autocatalytic expression systems typically have the genes encoding the inducer transport proteins controlled by internal inducer levels, so that transport of the inducer increases production of the transport protein. The model was able to predict the unique behaviors of autocatalytic expression systems that have been experimentally observed and provided valuable insight into the role of population heterogeneity in these systems. The simulations substantiate the importance of stochastic processes on induction of gene expression in autocatalytic systems. The simulation results show that the all-or-none phenomenon is governed largely by random cellular events, and that population-averaged variations in gene expression are due to changes in the frequency of full gene induction in individual cells rather than to uniform variations in gene expression across the entire population. In addition, the model shows how concentrations of inducer too low to induce expression in uninduced cells can maintain induction in pre-induced cultures. A comparison of induction behaviors from an autocatalytic system and a system having constitutive synthesis of the transport protein showed that transport protein levels must be decoupled from inducer control to achieve homogeneous expression of a gene of interest in all cells of a culture.

Biological Transport↗