Multiscale Stochastic Reaction–Diffusion Modeling: Application to Actin Dynamics in Filopodia

Two multiscale (hybrid) stochastic reaction–diffusion models of actin dynamics in a filopodium are investigated. Both hybrid algorithms combine compartment-based and molecular-based stochastic reaction–diffusion models. The first hybrid model is based on the models previously developed in the literature. The second hybrid model is based on the application of a recently developed two-regime method (TRM) to a fully molecular-based model, which is also developed in this paper. The results of hybrid models are compared with the results of the molecular-based model. It is shown that both approaches give comparable results, although the TRM model better agrees quantitatively with the molecular-based model.     

A discrete-time model with vaccination for a measles epidemic.

A discrete-time, age-independent SIR-type epidemic model is formulated and analyzed. The effects of vaccination are also included in the model. Three mathematically important properties are verified for the model: solutions are nonnegative, the population size is time-invariant, and the epidemic concludes with all individuals either remaining susceptible or becoming immune (a property typical of SIR models). The model is applied to a measles epidemic on a university campus. The simulated results are in good agreement with the actual data if it is assumed that the population mixes nonhomogeneously. The results of the simulations indicate that a rate of immunity greater than 98% may be required to prevent an epidemic in a university population. The model has applications to other contagious diseases of SIR type. Furthermore, the simulated results of the model can easily be compared to data, and the effects of a vaccination program can be examined.     

An adaptive model of sensory integration in a dynamic environment applied to human stance control

An adaptive estimator model of human spatial orientation is presented. The adaptive model dynamically weights sensory error signals. More specific, the model weights the difference between expected and actual sensory signals as a function of environmental conditions. The model does not require any changes in model parameters. Differences with existing models of spatial orientation are that: (1) environmental conditions are not specified but estimated, (2) the sensor noise characteristics are the only parameters supplied by the model designer, (3) history-dependent effects and mental resources can be modelled, and (4) vestibular thresholds are not included in the model; instead vestibular-related threshold effects are predicted by the model. The model was applied to human stance control and evaluated with results of a visually induced sway experiment. From these experiments it is known that the amplitude of visually induced sway reaches a saturation level as the stimulus level increases. This saturation level is higher when the support base is sway referenced. For subjects experiencing vestibular loss, these saturation effects do not occur. Unknown sensory noise characteristics were found by matching model predictions with these experimental results. Using only five model parameters, far more than five data points were successfully predicted. Model predictions showed that both the saturation levels are vestibular related since removal of the vestibular organs in the model removed the saturation effects, as was also shown in the experiments. It seems that the nature of these vestibular-related threshold effects is not physical, since in the model no threshold is included. The model results suggest that vestibular-related thresholds are the result of the processing of noisy sensory and motor output signals. Model analysis suggests that, especially for slow and small movements, the environment postural orientation can not be estimated optimally, which causes sensory illusions. The model also confirms the experimental finding that postural orientation is history dependent and can be shaped by instruction or mental knowledge. In addition the model predicts that: (1) vestibular-loss patients cannot handle sensory conflicting situations and will fall down, (2) during sinusoidal support-base translations vestibular function is needed to prevent falling, (3) loss of somatosensory information from the feet results in larger postural sway for sinusoidal support-base translations, and (4) loss of vestibular function results in falling for large support-base rotations with the eyes closed. These predictions are in agreement with experimental results. Received: 12 November 1999 / Accepted in revised form: 30 June 2000     

A coalescent model of recombination hotspots

Recent experimental findings suggest that the assumption of a homogeneous recombination rate along the human genome is too naive. These findings point to block-structured recombination rates; certain regions (called hotspots) are more prone than other regions to recombination. In this report a coalescent model incorporating hotspot or block-structured recombination is developed and investigated analytically as well as by simulation. Our main results can be summarized as follows: (1) The expected number of recombination events is much lower in a model with pure hotspot recombination than in a model with pure homogeneous recombination, (2) hotspots give rise to large variation in recombination rates along the genome as well as in the number of historical recombination events, and (3) the size of a (nonrecombining) block in the hotspot model is likely to be overestimated grossly when estimated from SNP data. The results are discussed with reference to the current debate about block-structured recombination and, in addition, the results are compared to genome-wide variation in recombination rates. A number of new analytical results about the model are derived.     

Steady flow of a viscous fluid through a network of tubes with applications to the human arterial system

The paper presents a finite-element model for the analysis of steady flow of a viscous fluid through a connected system of elastic tubes with the aim of simulating the conditions of blood flow through the human arterial system. The governing equations of the model are non-linear in character and are solved through an iterative computational procedure. This model is capable of incorporating the effects of stenosis on flow and pressure. Typical results are presented and discussed. Quantitative results have been obtained on blood flow through a model of the human arterial system corresponding to the sets of prescribed conditions at the terminations. Also computational results on the effect of stenosis in typical arteries of the system are presented.     

Sensitivity and flexibility of regular and chaotic calcium oscillations

Sensitivity and flexibility are important properties of biological systems. These properties are here investigated for intracellular calcium oscillations. For a particular model, we comparatively investigate sensitivity and flexibility of regular and chaotic Ca(2+) oscillations. For this model, we obtain two main results. First, sensitivity of the model system to parameter shifting does not depend on the complexity of Ca(2+) oscillations. We observe, however, that both regular and chaotic Ca(2+) oscillations are highly sensitive in regions close to bifurcation points. Second, also flexibility of Ca(2+) oscillations does not significantly depend on the type of Ca(2+) oscillations. Our results show that regular as well as chaotic Ca(2+) oscillations in the studied model are highly flexible in regimes with weak dissipation. Both results are discussed in the sense of possible biological importance.     

SMOES: a simulation model for the Oosterschelde ecosystem

The model SMOES integrates the results of the ecological research program conducted in the Oosterschelde estuary before and during the construction of a storm surge barrier. Its aim is to provide a quantitative summary of the research findings and to provide a tool for analysis and prediction of the ecosystem in response to human manipulations. This chapter describes model background and formulations. An uncertainty analysis is used to analyze the effect of uncertainties in model parameters on model outcome. The results of the sensitivity analysis are classified by distinguishing groups of model parameters with a qualitatively different effect on model results. Within these groups, a quantitative ranking of the parameters is possible. It appears that the most sensitive parameters represent processes that are relatively little studied in the Oosterschelde, which may provide guidelines for further research.     

Predicting the effect of relative humidity on skin temperature and skin wettedness

The purpose of this research is to investigate the relative humidity effects on skin temperature and skin wettedness for different operative temperatures. For this aim, thermal interactions between human body and environment are simulated. In this simulation, Gagge 2-node model is used but includes some significant modifications. The simulation is to apply the Gagge 2-node model to individual segments rather than to whole body. Also, the results of the simulation are compared with present measurements, and available experimental data and simulated results in the literature in order to present reliability of the 16 segments-Gagge 2-node model. It is determined that the simulation results are in good agreement with measured results obtained from present experiments, and simulated results and experimental data in the literature.     

Considering Variations in Waste Composition during Waste Input‐Output Modeling

Concentrations of pollutants vary in wastes from different sources. However, existing waste input‐output (WIO) models do not take these differing concentrations into account. This article proposes a new category of model, which we are calling a waste input‐output model at the substance level (WIOS model). The WIOS model considers variations in waste composition. These variations potentially affect the life cycle inventory of the waste treatment stage. The proposed model is expected to produce more accurate results than existing WIO models that do not consider variations in the composition of wastes. In addition, the proposed model provides a method to trace substances undergoing waste treatment. In this article, use of the WIOS model is illustrated by simulating the overall environmental loads of total organic carbon from wastewater treatment at a facility in Germany. The results show that variations in the composition of wastes entering treatment significantly affect the modeled estimates of total environmental loads caused by wastewater treatment. In addition, the results of the proposed model are different from results given by existing hybrid input‐output WIO models that do not consider variations in the composition of wastewater as it undergoes treatment.     

Mathematical modeling and qualitative analysis of insulin therapies

Several insulin therapies are widely in clinical use with the basic strategy that mimics insulin secretion in a normal glucose-insulin endocrine metabolic regulatory system. In this paper, we model the insulin therapies using a delay differential equation model. We study the dynamics of the model both qualitatively and quantitatively. The analytical results show the existence and uniqueness of a stable periodic solution that corresponds to ultradian insulin secretion oscillations. Numerically we simulate the insulin administration based on our model. The numerical simulation results are in agreement with findings of clinical studies.     

固定化金霉素产生菌原生质体转化林可霉素反应模型的研究

建立了固定化金霉素产生菌金色链霉菌(Streptomyces aurofaciens)原生质体转化林可霉素反应动力学模型并模拟计算了反应过程,模型计算与实验结果有好的一致性。讨论了各反应参数对转化反应的影响,给出了转化率与反应时间的关系式和最大转化率计算式,还对转化反应动力学模型进一步应用进行了讨论。     

Evolution and intraspecific exploitative competition. II. A two-locus model for additive gene effects

A two-locus model corresponding to the model of Christiansen and Loeschcke (1980, theoret, Popul. Biol. 18, 297-313) is analysed. The two loci each have two alleles, and the loci influences a character which determines the utilization of resources in a one-dimensional continuum. The analysis of the model is supported by numerical iterations of the recurrence equations. The previous prediction of high linkage disequilibrium for small allele contributions to the character and close linkage between the loci is confirmed. For larger allele contributions results comparable to those for the symmetric viabilities model are obtained. The model degenerates when the allele contributions at the two loci are equal, i.e., in the most symmetric situation. The results are discussed as the outcome of a balance between optimizing selection and disruptive selection. For small allele contributions the results are virtually independent of which genotype is most favoured by the optimizing aspect of the selective forces.     

Stochastic and deterministic models for the kinetic behavior of certain structured enzyme systems II: consecutive two enzyme systems.

This paper contains extensions of results from a previous paper regarding structured one enzyme systems to a more complicated structured two enzyme system. A stochastic model and a deterministic model are developed for such systems and their steady state reaction kinetics are compared. These comparisons are in the form of graphs of the reaction kinetics versus substrate concentration. Two quantities are proposed as indications of lack of agreement between the two models. This lack of agreement corresponds to situations in which the model systems are more highly non-linear, in accord with Jensen's inequalities. Implications of these results, relative to experimental procedures are briefly discussed.     

Vaccination in density-dependent epidemic models

This paper examines the effect of vaccination for an epidemic model where the death rate depends on the number of individuals in the population. The basic model which is described is based on measles or other childhood diseases in developing countries or viral diseases such as rabies in animal populations. An equilibrium analysis of the model and the local stability of small perturbations about the equilibrium values are discussed. The biological implications of these results are examined and similar results presented for modifications of the basic model.     

Predictive multiscale computational model of shoe-floor coefficient of friction

Understanding the frictional interactions between the shoe and floor during walking is critical to prevention of slips and falls, particularly when contaminants are present. A multiscale finite element model of shoe-floor-contaminant friction was developed that takes into account the surface and material characteristics of the shoe and flooring in microscopic and macroscopic scales. The model calculates shoe-floor coefficient of friction (COF) in boundary lubrication regime where effects of adhesion friction and hydrodynamic pressures are negligible. The validity of model outputs was assessed by comparing model predictions to the experimental results from mechanical COF testing. The multiscale model estimates were linearly related to the experimental results (p < 0.0001). The model predicted 73% of variability in experimentally-measured shoe-floor-contaminant COF. The results demonstrate the potential of multiscale finite element modeling in aiding slip-resistant shoe and flooring design and reducing slip and fall injuries.     

Mechanochemical couplings of kinesin motors

Kinesins are molecular motors capable of moving processively along microtubule in a stepwise manner by hydrolyzing ATP. Numerous experimental results on various aspects of their dynamical behaviours are available in literature. Although a number of models of tightly coordinated mechanism have been proposed to explain some experimental results, up to now no good explanation has been given to all these experimental results by using a single model. We have recently proposed such a model of partially coordinated hand-over-hand moving mechanism. In this paper, we use this model to study in detail various aspects of the dynamical properties of single kinesin molecules. We show that kinesin dimers walk hand-over-hand along microtubules in a partially coordinated rather than a tightly coordinated manner. The degree of coordination depends on the ratio of the two heads' ATPase rates that are in turn determined by both internal elastic force and external load. We have tested this model using various available experimental results on different samples and obtained a good agreement between the theory and the experiments.     

The population genetics of adaptation on correlated fitness landscapes: the block model

Several recent theoretical studies of the genetics of adaptation have focused on the mutational landscape model, which considers evolution on rugged fitness landscapes (i.e., ones having many local optima). Adaptation in this model is characterized by several simple results. Here I ask whether these results also hold on correlated fitness landscapes, which are smoother than those considered in the mutational landscape model. In particular, I study the genetics of adaptation in the block model, a tunably rugged model of fitness landscapes. Considering the scenario in which adaptation begins from a high fitness wild-type DNA sequence, I use extreme value theory and computer simulations to study both single adaptive steps and entire adaptive walks. I show that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.     

Models of nearly neutral mutations with particular implications for nonrandom usage of synonymous codons

Summary The population dynamics of nearly neutral mutations are studied using a single-site and a multisite model. In the latter model, the nucleotides in a sequence are completely linked and the selection schemes employed are additive, multiplicative, and additive with a threshold. Although the third selection scheme is very different from the first two, the three schemes produce identical results for a wide range of parameter values. Thus the present study provides a general theory for the population dynamics of nearly neutral mutations because the results can also be used to draw inferences about other selection schemes such as stabilizing selection and synergistic selection. It is shown that the number of slightly deleterious mutations accumulated in a sequence can be considerably larger under the multisite model than under the single-site model, particularly if the sequence is long or if the mutation rate per site is high. The results show that even a very slight selective difference between synonymous codons can produce a strong bias in codon usage. Three alternative explanations for the strong bias in codon usage in bacterial and yeast genes are considered. The implications of the present results for molecular evolution are discussed.     

Neuronal Mechanisms Encoding Global-to-Fine Information in Inferior-Temporal Cortex

Sugase et al. found that global information is represented at the initial transient firing of a single face-responsive neuron in inferior-temporal (IT) cortex, and that finer information is represented at the subsequent sustained firing. A feed-forward model and an attractor network are conceivable models to reproduce this dynamics. The attractor network, specifically an associative memory model, is employed to elucidate the neuronal mechanisms producing the dynamics. The results obtained by computer simulations show that a state of neuronal population initially approaches to a mean state of similar memory patterns, and that it finally converges to a memory pattern. This dynamics qualitatively coincides with that of face-responsive neurons. The dynamics of a single neuron in the model also coincides with that of a single face-responsive neuron. Furthermore, we propose two physiological experiments and predict the results from our model. Both predicted results are not explainable by the feed-forward model. Therefore, if the results obtained by actual physiological experiments coincide with our predicted results, the attractor network might be the neuronal mechanisms producing the dynamics of face-responsive neurons.