Mechanisms of seizure propagation in a cortical model

We consider a mathematical model of mesoscopic human cortical ictal electrical activity. We compare the model results with ictal electrocortical data recorded from three human subjects and show how the two agree. We determine that, in the model system, seizures result from increased connectivity between excitatory and inhibitory cell populations, or from decreased connectivity within either excitatory or inhibitory cell populations. We compare the model results with the disinhibition and 4-AP models of epilepsy and suggest how the model may guide the development of new anticonvulsant therapies.     

Mathematical modelling of anisotropy in fibrous connective tissue

We present two modelling frameworks for studying dynamic anistropy in connective tissue, motivated by the problem of fibre alignment in wound healing. The first model is a system of partial differential equations operating on a macroscopic scale. We show that a model consisting of a single extracellular matrix material aligned by fibroblasts via flux and stress exhibits behaviour that is incompatible with experimental observations. We extend the model to two matrix types and show that the results of this extended model are robust and consistent with experiment. The second model represents cells as discrete objects in a continuum of ECM. We show that this model predicts patterns of alignment on macroscopic length scales that are lost in a continuum model of the cell population.     

A biochemically semi-detailed model of auxin-mediated vein formation in plant leaves

We present here a model intended to capture the biochemistry of vein formation in plant leaves. The model consists of three modules. Two of these modules, those describing auxin signaling and transport in plant cells, are biochemically detailed. We couple these modules to a simple model for PIN (auxin efflux carrier) protein localization based on an extracellular auxin sensor. We study the single-cell responses of this combined model in order to verify proper functioning of the modeled biochemical network. We then assemble a multicellular model from the single-cell building blocks. We find that the model can, under some conditions, generate files of polarized cells, but not true veins.     

Evaluating temporal variation in Citizen Science Data against temporal variation in the environment

Citizen Science Data (CSD) is increasingly contributing to the assessment of biodiversity and ecosystems. However, there is a need to evaluate the usefulness of CSD for different purposes. Ideally, CSD from populations should be evaluated against independent population data collected using a proper sampling design, but such data are lacking for almost all species. We propose an approach for evaluating CSD against environmental data. First, an evaluation model is formulated based on knowledge of how environmental variables affect population dynamics. Second, the hypotheses of the evaluation model are tested statistically. Support for the evaluation model is interpreted as support for the CSD. We applied the approach to six longhorn beetle species using Swedish data from 1930–2000. The evaluation model assumed that early summer temperature affects larval development time. We found support for the evaluation model in two species, and some evidence in its favour in one species. This suggests that the CSD from these species reflect true inter‐annual variation. We also found statistical evidence for population trends in three to four species. In two of these, the evaluation model was supported thus providing particular support for the trend estimates. Lack of support for the evaluation model may be due to biological inaccuracy, the general characteristics of CSD, or low resolution of the environmental evaluation data. We also discuss alternative environmental data for evaluating CSD.     

A dynamical system model of neurofilament transport in axons

We develop a dynamical system model for the transport of neurofilaments in axons, inspired by Brown's "stop-and-go" model for slow axonal transport. We use fast/slow time-scale arguments to lower the number of relevant parameters in our model. Then, we use experimental data of Wang and Brown to estimate all but one parameter. We show that we can choose this last remaining parameter such that the results of our model agree with pulse-labeling experiments from three different nerve cell types, and also agree with stochastic simulation results.     

A phylogenetic mixture model for detecting pattern-heterogeneity in gene sequence or character-state data

We describe a general likelihood-based 'mixture model' for inferring phylogenetic trees from gene-sequence or other character-state data. The model accommodates cases in which different sites in the alignment evolve in qualitatively distinct ways, but does not require prior knowledge of these patterns or partitioning of the data. We call this qualitative variability in the pattern of evolution across sites "pattern-heterogeneity" to distinguish it from both a homogenous process of evolution and from one characterized principally by differences in rates of evolution. We present studies to show that the model correctly retrieves the signals of pattern-heterogeneity from simulated gene-sequence data, and we apply the method to protein-coding genes and to a ribosomal 12S data set. The mixture model outperforms conventional partitioning in both these data sets. We implement the mixture model such that it can simultaneously detect rate- and pattern-heterogeneity. The model simplifies to a homogeneous model or a rate-variability model as special cases, and therefore always performs at least as well as these two approaches, and often considerably improves upon them. We make the model available within a Bayesian Markov-chain Monte Carlo framework for phylogenetic inference, as an easy-to-use computer program.     

A model for phase transitions in lipid bilayers and biological membranes

We wish to present an order-disorder model for the observed phase transitions in lipid bilayers and biological membranes. We show that the model may, under certain circumstances, exhibit two phase transitions, one corresponding to positional disordering of entire lipid molecules, and the other corresponding to orientational disordering in the hydrocarbon chains. We then give results of our numerical analysis of the model and compare them with experimental data. Shortcomings of the model and future directions for analyses of this type are also discussed.     

协方差阵扰动增长曲线模型中回归参数阵B的影响分析

本文利用协方差阵扰动模型讨论增长曲线模型回归参数阵B的影响分析,获得了扰动前后B的最小二乘估计关系式,同时还得到了度量扰动影响的广义Cook距离．     

Stochastic effects in intercellular calcium spiking in hepatocytes

We carry out a Monte Carlo simulation of stochastic effects for two models of intercellular calcium wave propagation in rat hepatocytes. Both models involve gap junction diffusion by a second messenger. We find that, in general, the stochastic effects improve agreement with experiment, for a reasonable choice of model parameters. Both stochastic models exhibit baseline fluctuations and variations in the peak heights of Ca(2+). In addition, we find for one model that there is a distribution of latency times, rather than a single latency time, with a distribution width which is comparable to the experimental observation of spike widths. We also find for the other model with low gap junction diffusion that it is possible for cell multiplets to oscillate independently initially, but to subsequently become synchronized.     

Pattern storage in a sparsely coded neural network with cyclic activation

We investigate an artificial neural network model with a modified Hebb rule. It is an auto-associative neural network similar to the Hopfield model and to the Willshaw model. It has properties of both of these models. Another property is that the patterns are sparsely coded and are stored in cycles of synchronous neural activities. The cycles of activity for some ranges of parameter increase the capacity of the model. We discuss basic properties of the model and some of the implementation issues, namely optimizing of the algorithms. We describe the modification of the Hebb learning rule, the learning algorithm, the generation of patterns, decomposition of patterns into cycles and pattern recall.     

A general model to explore complex dominance patterns in plant sporophytic self-incompatibility systems

We developed a general model of sporophytic self-incompatibility under negative frequency-dependent selection allowing complex patterns of dominance among alleles. We used this model deterministically to investigate the effects on equilibrium allelic frequencies of the number of dominance classes, the number of alleles per dominance class, the asymmetry in dominance expression between pollen and pistil, and whether selection acts on male fitness only or both on male and on female fitnesses. We show that the so-called "recessive effect" occurs under a wide variety of situations. We found emerging properties of finite population models with several alleles per dominance class such as that higher numbers of alleles are maintained in more dominant classes and that the number of dominance classes can evolve. We also investigated the occurrence of homozygous genotypes and found that substantial proportions of those can occur for the most recessive alleles. We used the model for two species with complex dominance patterns to test whether allelic frequencies in natural populations are in agreement with the distribution predicted by our model. We suggest that the model can be used to test explicitly for additional, allele-specific, selective forces.     

Bubbling and hydra effect in a population system with Allee effect

We present a continuous time predator-prey model and predator’s growth subjected to component Allee effect. The model also includes density dependent mortality of predator. We investigate our model both analytically and numerically, and highlighted the effect of density independent mortality and Allee effect. In our system, we find that a fixed point representing the extinction of predator is always a stable point. When coexistence equilibria exists our system is bistable. We have observed that tristability is possible for our model that includes two stable co-existence fixed point. The most important phenomena which we have observed are hydra effect and cascading effect. Due to component Allee effect in predator the system shows multiple hydra effect. We discuss the phenomenon of bubbling, which indicates increasing and decreasing of amplitudes of cycles. We have presented one-parametric as well as two-parametric bifurcation diagram and also all possible bifurcations that the system could go through.     

Random effects selection in linear mixed models

We address the important practical problem of how to select the random effects component in a linear mixed model. A hierarchical Bayesian model is used to identify any random effect with zero variance. The proposed approach reparameterizes the mixed model so that functions of the covariance parameters of the random effects distribution are incorporated as regression coefficients on standard normal latent variables. We allow random effects to effectively drop out of the model by choosing mixture priors with point mass at zero for the random effects variances. Due to the reparameterization, the model enjoys a conditionally linear structure that facilitates the use of normal conjugate priors. We demonstrate that posterior computation can proceed via a simple and efficient Markov chain Monte Carlo algorithm. The methods are illustrated using simulated data and real data from a study relating prenatal exposure to polychlorinated biphenyls and psychomotor development of children.     

The importance of 'memory' in statistical models for animal feeding behaviour

We investigate models for animal feeding behaviour, with the aim of improving understanding of how animals organise their behaviour in the short term. We consider three classes of model: hidden Markov, latent Gaussian and semi-Markov. Each can predict the typical 'clustered' feeding behaviour that is generally observed, however they differ in the extent to which 'memory' of previous behaviour is allowed to affect future behaviour. The hidden Markov model has 'lack of memory', the current behavioural state being dependent on the previous state only. The latent Gaussian model assumes feeding/non-feeding periods to occur by the thresholding of an underlying continuous variable, thereby incorporating some 'short-term memory'. The semi-Markov model, by taking into account the duration of time spent in the previous state, can be said to incorporate 'longer-term memory'. We fit each of these models to a dataset of cow feeding behaviour. We find the semi-Markov model (longer-term memory) to have the best fit to the data and the hidden Markov model (lack of memory) the worst. We argue that in view of effects of satiety on short-term feeding behaviour of animal species in general, biologically suitable models should allow 'memory' to play a role. We conclude that our findings are equally relevant for the analysis of other types of short-term behaviour that are governed by satiety-like principles.     

Predicting failure rate of PCR in large genomes

We have developed statistical models for estimating the failure rate of polymerase chain reaction (PCR) primers using 236 primer sequence-related factors. The model involved 1314 primer pairs and is based on more than 80 000 PCR experiments. We found that the most important factor in determining PCR failure is the number of predicted primer-binding sites in the genomic DNA. We also compared different ways of defining primer-binding sites (fixed length word versus thermodynamic model; exact match versus matches including 1–2 mismatches). We found that the most efficient prediction of PCR failure rates can be achieved using a combination of four factors (number of primer-binding sites counted in different ways plus GC% of the primer) combined into single statistical model GM1. According to our estimations from experimental data, the GM1 model can reduce the average failure rate of PCR primers nearly 3-fold (from 17% to 6%). The GM1 model can easily be implemented in software to premask genome sequences for potentially failing PCR primers, thus improving large-scale PCR-primer design.     

Spatial and spatio-temporal patterns in a cell-haptotaxis model

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation.     

Chaos in a periodically forced chemostat with algal mortality

We study the possibility of chaotic dynamics in the externally driven Droop model. This model describes a phytoplankton population in a chemostat under periodic nutrient supply. Previously, it has been proven under very general assumptions, that such systems are not able to exhibit chaotic dynamics. We show that the simple introduction of algal mortality may lead to chaotic oscillations of algal density in the forced chemostat. Our numerical simulations show that the existence of chaos is intimately related to plankton overshooting in the unforced model. We provide a simple measure, based on stability analysis, for estimating the amount of overshooting. These findings are not restricted to the Droop model but also hold for other chemostat models with mortality. Our results suggest periodically driven chemostats as a simple model system for the experimental verification of chaos in ecology.     

A simple mathematical model for Ebola in Africa

We deal with the following question: Can the consumption of contaminated bush meat, the funeral practices and the environmental contamination explain the recurrence and persistence of Ebola virus disease outbreaks in Africa? We develop an SIR-type model which, incorporates both the direct and indirect transmissions in such a manner that there is a provision of Ebola viruses. We prove that the full model has one (endemic) equilibrium which is locally asymptotically stable whereas, it is globally asymptotically stable in the absence of the Ebola virus shedding in the environment. For the sub-model without the provision of Ebola viruses, the disease dies out or stabilizes globally at an endemic equilibrium. At the endemic level, the number of infectious is larger for the full model than for the sub-model without provision of Ebola viruses. We design a nonstandard finite difference scheme, which preserves the dynamics of the model. Numerical simulations are provided.