Central Upwind Scheme for a Compressible Two-Phase Flow Model

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.     

Stochastic multitype epidemics in a community of households: estimation and form of optimal vaccination schemes

This paper treats a stochastic model for an SIR (susceptible-->infective-->removed) multitype household epidemic. The community is assumed to be closed, individuals are of different types and each individual belongs to a household. Previously obtained probabilistic and inferential results for the model are used to derive the optimal vaccination scheme. By this is meant the scheme that vaccinates the fewest among all vaccination schemes that reduce the threshold parameter below 1. This is done for the situation where all model parameters are known and also for the case where parameters are estimated from an outbreak in the community prior to vaccination. It is shown that the algorithm which chooses vaccines sequentially, at each step selecting the individual which reduces the threshold parameter the most, is not in general an optimal scheme. As a consequence, explicit characterisation of the optimal scheme is only possible in certain special cases. Two different types of vaccine responses, leaky and all-or-nothing, are considered and compared for the problems mentioned above. The methods are illustrated with some numerical examples.     

The role of carbon flux and biometric observations in constraining a terrestrial ecosystem model: a case study in disturbed forests in East Asia

The process of confining unnecessary freedom is a step toward advanced ecosystem modeling. This study demonstrates the importance of carbon flux and biometric observation in constraining a terrestrial ecosystem model with a simple optimization scheme. At the selected sites from AsiaFlux network, a simultaneous optimization scheme for both carbon flux and biomass was compared with carbon flux-oriented and biomass-oriented optimization schemes using the Biome-BGC model. The optimization scheme oriented to either carbon flux or biomass provided simulation results that were consistent with observations, but with reduced performance in unconstrained variables. The simultaneous optimization scheme yielded results that were consistent with observations for both carbon flux and biomass. By comparing long-term projections simulated by three schemes, it was found that the optimization oriented only to carbon flux has limited performance because misrepresented biomass significantly affected a projection of carbon exchange through heterotrophic respiration. From these experiments, we found that (1) a process model like Biome-BGC is capable of reproducing both carbon flux and biomass within acceptable proximity, (2) constraining biomass is importance not just because it is one of carbon cycle components, but also it significantly affects simulations of carbon flux. Thus, it is important to invest more effort to improve simulation of biomass as well as carbon flux.     

An unconditionally stable numerical method for the Luo-Rudy 1 model used in simulations of defibrillation

Numerical simulations of defibrillation using the Bidomain model coupled to a model of membrane kinetics represent a serious numerical challenge. This is because very high voltages close to defibrillation electrodes demand that extreme time step restrictions be placed on standard numerical schemes, e.g. the forward Euler scheme. A common solution to this problem is to modify the cell model by simple if-tests applied to several equations and rate functions. These changes are motivated by numerical problems rather than physiology, and should therefore be avoided whenever possible. The purpose of this paper is to present a numerical scheme that handles the original model without modifications and which is unconditionally stable for the Luo-Rudy phase 1 model. This also shows that the cell model is mathematically well-behaved, even in the presence of very high voltages. Our theoretical results are illustrated by numerical computations.     

An integrate-and-fire model for synchronized bursting in a network of cultured cortical neurons

It has been suggested that spontaneous synchronous neuronal activity is an essential step in the formation of functional networks in the central nervous system. The key features of this type of activity consist of bursts of action potentials with associated spikes of elevated cytoplasmic calcium. These features are also observed in networks of rat cortical neurons that have been formed in culture. Experimental studies of these cultured networks have led to several hypotheses for the mechanisms underlying the observed synchronized oscillations. In this paper, bursting integrate-and-fire type mathematical models for regular spiking (RS) and intrinsic bursting (IB) neurons are introduced and incorporated through a small-world connection scheme into a two-dimensional excitatory network similar to those in the cultured network. This computer model exhibits spontaneous synchronous activity through mechanisms similar to those hypothesized for the cultured experimental networks. Traces of the membrane potential and cytoplasmic calcium from the model closely match those obtained from experiments. We also consider the impact on network behavior of the IB neurons, the geometry and the small world connection scheme. Action Editor: David Golomb     

Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation

In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.     

Coupling field theory with continuum mechanics: a simulation of domain formation in giant unilamellar vesicles

Domain formation is modeled on the surface of giant unilamellar vesicles using a Landau field theory model for phase coexistence coupled to elastic deformation mechanics (e.g., membrane curvature). Smooth particle applied mechanics, a form of smoothed particle continuum mechanics, is used to solve either the time-dependent Landau-Ginzburg or Cahn-Hilliard free-energy models for the composition dynamics. At the same time, the underlying elastic membrane is modeled using smooth particle applied mechanics, resulting in a unified computational scheme capable of treating the response of the composition fields to arbitrary deformations of the vesicle and vice versa. The results indicate that curvature coupling, along with the field theory model for composition free energy, gives domain formations that are correlated with surface defects on the vesicle. In the case that external deformations are included, the domain structures are seen to respond to such deformations. The present simulation capability provides a significant step forward toward the simulation of realistic cellular membrane processes.     

Stiffness-distortion sarcomere model for muscle simulation.

A relatively simple method is presented for incorporating cross-bridge mechanisms into a muscle model. The method is based on representing force in a half sarcomere as the product of the stiffness of all parallel cross bridges and their average distortion. Differential equations for sarcomeric stiffness are derived from a three-state kinetic scheme for the cross-bridge cycle. Differential equations for average distortion are derived from a distortional balance that accounts for distortion entering and leaving due to cross-bridge cycling and for distortion imposed by shearing motion between thick and thin filaments. The distortion equations are unique and enable sarcomere mechanodynamics to be described by only a few ordinary differential equations. Model predictions of small-amplitude step and sinusoidal responses agreed well with previously described experimental results and allowed unique interpretations to be made of various response components. Similarly good results were obtained for model reproductions of force-velocity and large-amplitude step and ramp responses. The model allowed reasonable predictions of contractile behavior by taking into account what is understood to be basic muscle contractile mechanisms.     

Quantitative analysis of a fully generalized four-state kinetic scheme

To describe the macroscopic behavior of many ion channels, at a minimum a four-state kinetic scheme is needed to provide for three processes: a delay in activation development, the activation process, and inactivation. I present here an analytical solution for a fully generalized four-state kinetic scheme in which every state can transit to every other state and any initial conditions can be specified. The solution describes the time courses of the probabilities of occupancy of each state during a step change in the rate constants of the scheme and includes closed-form expressions for the relaxation time constants and steady-state probabilities of occupancy as functions of the rate constants. Solutions for several relevant special cases are also included along with demonstrations that the general solution yields the correct behavior for several reduced or special cases where the result is independently known.     

Extended theoretical analysis of irreversible protein thermal unfolding

The theoretical analysis of the protein denaturation model which includes an irreversible, exothermic and rate-limited step has been improved and applied to the DSC profile of Azurin. The two-step nature of the irreversible denaturation of globular proteins is usually depicted in the following simplified scheme: N <--> U <--> F, which is known as the Lumry and Eyring model. In most of the works concerning the thermal unfolding of proteins, it is usually assumed that the irreversible step of the process does not take place significantly during the short time the protein spends in the temperature range of the DSC transition, or if this is not the case, that this irreversible step occurs with a negligible thermal effect. As we will show, this last assumption cannot be accepted acritically; in fact we have found that in the case of Azurin an evident exothermic effect occurs at the end of the transition. In order to fit the experimental Cp(exc) profile of Azurin, we have analyzed a model in which the exothermic effects of the irreversible step and the variations of DeltaH with temperature are taken into account. Our model was first tested simulating a series of profiles and considering the effects of the variation of the parameters on the shape of the curves, and successfully used to fit the experimental calorimetric profile of Azurin.     

Efficient simulations of tubulin-driven axonal growth

This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman–Rachford splitting scheme combined with temporal and spatial scalings of the model. Simulations based on this scheme have shown to be efficient, accurate, and reliable which makes it possible to evaluate the model, e.g. its dependency on biological and physical model parameters. These evaluations show among other things that the initial axon growth is very fast, that the active transport is the dominant reason over diffusion for the growth velocity, and that the polymerization rate in the growth cone does not affect the final axon length.     

Inference in MCMC step selection models

Habitat selection models are used in ecology to link the spatial distribution of animals to environmental covariates and identify preferred habitats. The most widely used models of this type, resource selection functions, aim to capture the steady-state distribution of space use of the animal, but they assume independence between the observed locations of an animal. This is unrealistic when location data display temporal autocorrelation. The alternative approach of step selection functions embed habitat selection in a model of animal movement, to account for the autocorrelation. However, inferences from step selection functions depend on the underlying movement model, and they do not readily predict steady-state space use. We suggest an analogy between parameter updates and target distributions in Markov chain Monte Carlo (MCMC) algorithms, and step selection and steady-state distributions in movement ecology, leading to a step selection model with an explicit steady-state distribution. In this framework, we explain how maximum likelihood estimation can be used for simultaneous inference about movement and habitat selection. We describe the local Gibbs sampler, a novel rejection-free MCMC scheme, use it as the basis of a flexible class of animal movement models, and derive its likelihood function for several important special cases. In a simulation study, we verify that maximum likelihood estimation can recover all model parameters. We illustrate the application of the method with data from a zebra.     

Activation process of pepsinogen.

The activation process of pepsinogen was analyzed by a combination of computer simulation and experiment. In order to investigate in detail the behavior of the basic schemes proposed in the previous study, further computer simulations were conducted. Some experiments were performed based on the information obtained. The changes in the UV difference spectrum in the early stage was measured by the stopped-flow technique and the conversion of pepsinogen to pepsin [EC 3.4.23.1] was followed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. Furthermore, on the basis of the experimental results, the most reasonable scheme was selected and modified. As a result, a scheme for the activation process of pepsinogen was obtained (Scheme 8). On the basis of the above analyses, it was assumed that the first step and the third step are pH-dependent based on the change in the UV spectrum, that the second step is a nonlinear reaction containing a looped reaction with a dimeric intermediate (in this step, peptide fragments are released and pepsinogen is converted to a pepsin-like molecule), and that the third step is an equilibrium reaction involving proton binding.     

A classification model for the Leiden proteomics competition

A strategy is presented to build a discrimination model in proteomics studies. The model is built using cross-validation. This cross-validation step can simply be combined with a variable selection method, called rank products. The strategy is especially suitable for the low-samples-to-variables-ratio (undersampling) case, as is often encountered in proteomics and metabolomics studies. As a classification method, Principal Component Discriminant Analysis is used; however, the methodology can be used with any classifier. A data set containing serum samples from breast cancer patients and healthy controls is analysed. Double cross-validation shows that the sensitivity of the model is 82% and the specificity 86%. Potential putative biomarkers are identified using the variable selection method. In each cross-validation loop a classification model is built. The final classification uses a majority voting scheme from the ensemble classifier.     

Mechanism of gating of T-type calcium channels

We have analyzed the gating kinetics of T-type Ca channels in 3T3 fibroblasts. Our results show that channel closing, inactivation, and recovery from inactivation each include a voltage-independent step which becomes rate limiting at extreme potentials. The data require a cyclic model with a minimum of two closed, one open, and two inactivated states. Such a model can produce good fits to our data even if the transitions between closed states are the only voltage-dependent steps in the activating pathway leading from closed to inactivated states. Our analysis suggests that the channel inactivation step, as well as the direct opening and closing transitions, are not intrinsically voltage sensitive. Single-channel recordings are consistent with this scheme. As expected, each channel produces a single burst per opening and then inactivates. Comparison of the kinetics of T-type Ca current in fibroblasts and neuronal cells reveals significant differences which suggest that different subtypes of T-type Ca channels are expressed differentially in a tissue specific manner.     

Kinetics of protein subunit interactions: simulation of a polymerization overshoot

Theoretical calculations of the kinetics of a polymerization reaction have been carried out for a scheme in which there is a nucleation step that is slow relative to subsequent propagation steps. A transient maximum (overshoot) in molecular weight can be expected in such reversibly self-associating systems when polymerization is initiated suddenly. The extent of overshoot decreases with increasing initial concentration of true equilibrium is strongly dependent on the rate of nucleus formation and the rate of depolymerization when the absolute values of both are small relative to the rate of propagation.     

毛乌素沙地草地种植管理咨询系统的开发

 本研究初步开发了一个用于毛乌素沙地草地种植管理咨询的专家系统ASSG。这个系统将当地生态系统管理专家们的经验知识和对土壤水分动态的理论研究成果结合起来以产生对于土地利用和种植的作物种类及品种的最优管理策略和最适的植被覆盖率。本系统利用3个层次的推理过程和结构化的知识库,通过咨询过程—步步地引导用户得到最优种植管理策略。在每—层次的推理中,本系统提供给用户多重选择,根据用户的意愿进行下一步的推理。这一推理的交互作用机制为用户获得适宜的咨询结果提供了最大的便利性。本系统的主体部分山Turbo Prolog语言完成,该语言是一种用于开发专家系统的描述性语言。基于土壤水分平衡原理的最优植被覆盖率模型由C语言实现,并应用多语言编程技术将之嵌入程序主体中。系统的样本运行结果表明本系统运行便利,并能产生合理的种植管理策略。     

Transport of the substance through thin membranes with narrow pores after the preceding stage of surface diffusion

A model of the substance transport through thin membranes is discussed. Existence of a step of the surface diffusion of permeable particles is assumed preceding its entrance into membrane channel. An expression is given for the stationary flow, which has earlier been obtained for other transport models. It is shown that the permeant affinity to the membrane surface is the main condition for the validity of the scheme in question.