Considerations for the use of cellular electrophysiology models within cardiac tissue simulations

The use of mathematical models to study cardiac electrophysiology has a long history, and numerous cellular scale models are now available, covering a range of species and cell types. Their use to study emergent properties in tissue is also widespread, typically using the monodomain or bidomain equations coupled to one or more cell models. Despite the relative maturity of this field, little has been written looking in detail at the interface between the cellular and tissue-level models. Mathematically this is relatively straightforward and well-defined. There are however many details and potential inconsistencies that need to be addressed, in order to ensure correct operation of a cellular model within a tissue simulation. This paper will describe these issues and how to address them.Simply having models available in a common format such as CellML is still of limited utility, with significant manual effort being required to integrate these models within a tissue simulation. We will thus also discuss the facilities available for automating this in a consistent fashion within Chaste, our robust and high-performance cardiac electrophysiology simulator.It will be seen that a common theme arising is the need to go beyond a representation of the model mathematics in a standard language, to include additional semantic information required in determining the model’s interface, and hence to enhance interoperability. Such information can be added as metadata, but agreement is needed on the terms to use, including development of appropriate ontologies, if reliable automated use of CellML models is to become common.     

Random deaths in a computational model for age-structured populations

Summary The concept of random deaths in a computational model for population dynamics is critically examined. We claim that it is just an artifact, albeit useful, of computational models to limit the size of the populations through the use of the socalled Verhulst factor and has no biological foundation. Alternative implementations of random deaths strategies are discussed and compared.     

Steady-states of receptor-ligand dynamics: a theoretical framework

This paper studies aspects of the dynamics of a conventional mechanism of ligand-receptor interactions, with a focus on the stability and location of steady-states. A theoretical framework is developed, which is based upon the rich and deep formalism of irreducible biochemical networks. When represented in this manner, the mass action kinetics of biochemical processes can be clearly seen in terms of their component biochemical interactions, their kinetic rate constants, and the stoichiometry for the system. A minimal parametrization is provided for models for two- or multi-state receptor interaction with ligand, and an "affinity quotient" is introduced, which allows an elegant classification of ligands into agonists, neutral agonists, and inverse agonists.     

A general framework for neutral models of community dynamics

Neutral models of community dynamics are a powerful tool for ecological research, but their applications are currently limited to unrealistically simple types of dynamics and ignore much of the complexity that characterize natural ecosystems. Here, we present a new analytical framework for neutral models that unifies existing models of neutral communities and extends the applicability of existing models to a much wider spectrum of ecological phenomena. The new framework extends the concept of neutrality to fitness equivalence and in spite of its simplicity explains a wide spectrum of empirical patterns of species diversity including positive, negative and unimodal productivity–diversity relationships; gradual and highly delayed declines in species diversity with habitat loss; and positive and negative responses of species diversity to habitat heterogeneity. Surprisingly, the abundance distribution in all of these cases is given by the dispersal limited multinomial (DLM), the abundance distribution in Hubbell's zero-sum model, showing DLM's robustness and demonstrating that it cannot be used to infer the underlying community dynamics. These results support the hypothesis that ecological communities are regulated by a limited set of fundamental mechanisms much simpler than could be expected from their immense complexity.     

Stochastic dynamics of immunity in small populations: a general framework

Assessment of immunological status is a powerful tool in the surveillance and control of infectious pathogens in livestock and human populations. The distribution of immunity levels in the population provides information on time and age dependent transmission. A stochastic model is developed for a livestock population which relates the dynamics of the distribution of immunity levels at the population level to those of pathogen transmission. A general model with K immunity level categories is first proposed, taking into account the increase of the immunity level due to an infection or a re-exposure, the decrease of the immunity level with time since infection or exposure, and the effect of immunity level on the susceptibility and the infectivity of individuals. Numerical results are presented in the particular cases with K=2 and K=3 immunity level categories. We demonstrate that for a given distribution of the immunity levels at the population level, the model can be used to identify quantities such as most likely periods of time since introduction of infection. We discuss this approach in relation to analysis of serological data.     

A three-dimensional vertex dynamics cell model of space-filling polyhedra simulating cell behavior in a cell aggregate

We developed a three-dimensional (3D) cell model of a multicellular aggregate consisting of several polyhedral cells to investigate the deformation and rearrangement of cells under the influence of external forces. The polyhedral cells fill the space in the aggregate without gaps or overlaps, consist of contracting interfaces and maintain their volumes. The interfaces and volumes were expressed by 3D vertex coordinates. Vertex movements obey equations of motion that rearrange the cells to minimize total free energy, and undergo an elementary process that exchanges vertex pair connections when vertices approach each other. The total free energy includes the interface energy of cells and the compression or expansion energy of cells. Computer simulations provided the following results: An aggregate of cells becomes spherical to minimize individual cell surface areas; Polygonal interfaces of cells remain flat; Cells within the 3D cell aggregate can move and rearrange despite the absence of free space. We examined cell rearrangement to elucidate the viscoelastic properties of the aggregate, e.g. when an external force flattens a cell aggregate (e.g. under centrifugation) its component cells quickly flatten. Under a continuous external force, the cells slowly rearrange to recover their original shape although the cell aggregate remains flat. The deformation and rearrangement of individual cells is a two-step process with a time lag. Our results showed that morphological and viscoelastic properties of the cell aggregate with long relaxation time are based on component cells where minimization of interfacial energy of cells provides a motive force for cell movement.     

First principle-based models in plant suspension cell cultures: a review

In this work, the development and application of published models for describing the behavior of plant cell cultures is reviewed. The structure of each type of model is analyzed and the new tendencies for the modeling of biotechnological processes that can be applied in plant cell cultures are presented. This review is a tool for clarifying the main features that characterize each type of model in the field of plant cell cultures and can be used as a support on the selection of the more suitable model type, taking into account the purpose of specific research.     

RBE variation in prostate carcinoma cells in active scanning proton beams: In-vitro measurements in comparison with phenomenological models

PurposeIn-vitro radiobiological studies are essential for modelling the relative biological effectiveness (RBE) in proton therapy. The purpose of this study was to experimentally determine the RBE values in proton beams along the beam path for human prostate carcinoma cells (Du-145). RBE-dose and RBE-LET_d (dose-averaged linear energy transfer) dependencies were investigated and three phenomenological RBE models, i.e. McNamara, Rørvik and Wilkens were benchmarked for this cell line.MethodsCells were placed at multiple positions along the beam path, employing an in-house developed solid phantom. The experimental setup reflected the clinical prostate treatment scenario in terms of field size, depth, and required proton energies (127.2–180.1 MeV) and the physical doses from 0.5 to 6 Gy were delivered. The reference irradiation was performed with 200 kV X-ray beams. Respective (α/β) values were determined using the linear quadratic model and LET_d was derived from the treatment planning system at the exact location of cells.Results and ConclusionIndependent of the cell survival level, all experimental RBE values were consistently higher in the target than the generic clinical RBE value of 1.1; with the lowest RBE value of 1.28 obtained at the beginning of the SOBP. A systematic RBE decrease with increasing dose was observed for the investigated dose range. The RBE values from all three applied models were considerably smaller than the experimental values. A clear increase of experimental RBE values with LET_d parameter suggests that proton LET must be taken into consideration for this low (α/β) tissue.     

Algorithms in nature: the convergence of systems biology and computational thinking

Computer science and biology have enjoyed a long and fruitful relationship for decades. Biologists rely on computational methods to analyze and integrate large data sets, while several computational methods were inspired by the high‐level design principles of biological systems. Recently, these two directions have been converging. In this review, we argue that thinking computationally about biological processes may lead to more accurate models, which in turn can be used to improve the design of algorithms. We discuss the similar mechanisms and requirements shared by computational and biological processes and then present several recent studies that apply this joint analysis strategy to problems related to coordination, network analysis, and tracking and vision. We also discuss additional biological processes that can be studied in a similar manner and link them to potential computational problems. With the rapid accumulation of data detailing the inner workings of biological systems, we expect this direction of coupling biological and computational studies to greatly expand in the future.     

Analytic formulas for discrete stochastic models of cell populations with both differentiation and de-differentiation

Cell differentiation often appears to be a stochastic process particularly in the hemopoietic system. One of the earliest stochastic models for the growth of stem cell populations was proposed by Till et al. in 1964. In this model there are just two cell types: stem cells and specialized cells. At each time step there is a fixed probability that a stem cell differentiates into a specialized cell and a fixed probability that it undergoes mitosis to produce two stem cells. Even though this model is conceptually simple the myriad of possible outcomes has made it difficult to analyse. We present original closed-form expressions for the probability functions and a fast algorithm for computing them. Renewed interest in stem cells has raised questions about the effect de-differentiation has on stem cell populations. We have extended the stochastic model to include de-differentiation and show that even a small amount of de-differentiation can have a large effect on stem cell population growth.     

Empirical phylogenies and species abundance distributions are consistent with preequilibrium dynamics of neutral community models with gene flow

Community characteristics reflect past ecological and evolutionary dynamics. Here, we investigate whether it is possible to obtain realistically shaped modeled communities–that is with phylogenetic trees and species abundance distributions shaped similarly to typical empirical bird and mammal communities–from neutral community models. To test the effect of gene flow, we contrasted two spatially explicit individual‐based neutral models: one with protracted speciation, delayed by gene flow, and one with point mutation speciation, unaffected by gene flow. The former produced more realistic communities (shape of phylogenetic tree and species‐abundance distribution), consistent with gene flow being a key process in macro‐evolutionary dynamics. Earlier models struggled to capture the empirically observed branching tempo in phylogenetic trees, as measured by the gamma statistic. We show that the low gamma values typical of empirical trees can be obtained in models with protracted speciation, in preequilibrium communities developing from an initially abundant and widespread species. This was even more so in communities sampled incompletely, particularly if the unknown species are the youngest. Overall, our results demonstrate that the characteristics of empirical communities that we have studied can, to a large extent, be explained through a purely neutral model under preequilibrium conditions.     

IPBES框架下生物多样性和生态系统服务情景和模型方法评估及对我国的影响

随着国际社会对生物多样性保护关注度的提升, 生物多样性和生态系统服务情景和模型方法逐渐成为国际进程和条约关注的焦点问题。生物多样性和生态系统服务政府间科学-政策平台(Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services, IPBES)将“生物多样性和生态系统服务情景和模型方法评估”列入2014-2018年工作方案, 作为IPBES首批评估活动之一, 其评估报告及决策者摘要已在IPBES第四次全体会议上获得通过。本文概述了该评估报告的主要内容和结论, 探讨了报告与其他国际进程的关系及其可能对中国的影响。该报告梳理了国际上现有的生物多样性和生态系统服务相关情景和模型方法, 综合分析了它们的优缺点、适用范围和限制条件, 提出了使用过程中应对数据和知识空缺的方法, 为制定、使用及优化情景和模型提供了指导。IPBES的一系列评估报告将引领生物多样性和生态系统服务相关科学领域的发展, 为各国在生物多样性领域进行对话、权衡与博弈, 实现本国利益最大化提供一个高效的平台。中国作为一个发展中的生物多样性大国, 积极参与、发声必然是应对IPBES未来发展的最优方式。     

壤中流模型研究的现状及存在问题

对国内外壤中流模型与模拟进行了较为系统的介绍,并针对这些模型提出了一种壤中流模型分类的方法,即根据模型所依据的主要原理将壤中流模型分为三大类：１）Ｒｉｃｈａｒｄｓ模型;２）动力波模型;３）贮水泄流模型．Ｒｉｃｈａｒｄｓ模型又可分为一维Ｒｉｃｈａｒｄｓ模型、二维Ｒｉｃｈａｒｄｓ模型和三维Ｒｉｃｈａｒｄｓ模型;贮水泄流模型又可分为动力贮水泄流模型和Ｂｏｕｓｉｎｅｓｑ贮水泄流模型．同时,将这３类模型进行对比,指出了它们各自优点和不足．     

Long-term demographic surveys reveal a consistent relationship between average occupancy and abundance within local populations of a butterfly metapopulation

Species distribution models are the tool of choice for large-scale population monitoring, environmental association studies and predictions of range shifts under future environmental conditions. Available data and familiarity of the tools rather than the underlying population dynamics often dictate the choice of specific method – especially for the case of presence–absence data. Yet, for predictive purposes, the relationship between occupancy and abundance embodied in the models should reflect the actual population dynamics of the modelled species. To understand the relationship of occupancy and abundance in a heterogeneous landscape at the scale of local populations, we built a spatio-temporal regression model of populations of the Glanville fritillary butterfly Melitaea cinxia in a Baltic Sea archipelago. Our data comprised nineteen years of habitat surveys and snapshot data of land use in the region. We used variance partitioning to quantify relative contributions of land use, habitat quality and metapopulation covariates. The model revealed a consistent and positive, but noisy relationship between average occupancy and mean abundance in local populations. Patterns of abundance were highly variable across years, with large uncorrelated random variation and strong local population stochasticity. In contrast, the spatio-temporal random effect, habitat quality, population connectivity and patch size explained variation in occupancy, vindicating metapopulation theory as the basis for modelling occupancy patterns in fragmented landscapes. Previous abundance was an important predictor in the occupancy model, which points to a spillover of abundance into occupancy dynamics. While occupancy models can successfully model large-scale population structure and average occupancy, extinction probability estimates for local populations derived from occupancy-only models are overconfident, as extinction risk is dependent on actual, not average, abundance.     

The role of migration in mutant dynamics in fragmented populations

Mutant dynamics in fragmented populations have been studied extensively in evolutionary biology. Yet, open questions remain, both experimentally and theoretically. Some of the fundamental properties predicted by models still need to be addressed experimentally. We contribute to this by using a combination of experiments and theory to investigate the role of migration in mutant distribution. In the case of neutral mutants, while the mean frequency of mutants is not influenced by migration, the probability distribution is. To address this empirically, we performed in vitro experiments, where mixtures of GFP-labelled (“mutant”) and non-labelled (“wid-type”) murine cells were grown in wells (demes), and migration was mimicked via cell transfer from well to well. In the presence of migration, we observed a change in the skewedness of the distribution of the mutant frequencies in the wells, consistent with previous and our own model predictions. In the presence of de novo mutant production, we used modelling to investigate the level at which disadvantageous mutants are predicted to exist, which has implications for the adaptive potential of the population in case of an environmental change. In panmictic populations, disadvantageous mutants can persist around a steady state, determined by the rate of mutant production and the selective disadvantage (selection-mutation balance). In a fragmented system that consists of demes connected by migration, a steady-state persistence of disadvantageous mutants is also observed, which, however, is fundamentally different from the mutation-selection balance and characterized by higher mutant levels. The increase in mutant frequencies above the selection-mutation balance can be maintained in small ($N<N_c$) demes as long as the migration rate is sufficiently small. The migration rate above which the mutants approach the selection-mutation balance decays exponentially with $N/N_c$. The observed increase in the mutant numbers is not explained by the change in the effective population size. Implications for evolutionary processes in diseases are discussed, where the pre-existence of disadvantageous drug-resistant mutant cells or pathogens drives the response of the disease to treatments.     

Understanding species distribution in dynamic populations: a new approach using spatio‐temporal point process models

Understanding and predicting a species’ distribution across a landscape is of central importance in ecology, biogeography and conservation biology. However, it presents daunting challenges when populations are highly dynamic (i.e. increasing or decreasing their ranges), particularly for small populations where information about ecology and life history traits is lacking. Currently, many modelling approaches fail to distinguish whether a site is unoccupied because the available habitat is unsuitable or because a species expanding its range has not arrived at the site yet. As a result, habitat that is indeed suitable may appear unsuitable. To overcome some of these limitations, we use a statistical modelling approach based on spatio‐temporal log‐Gaussian Cox processes. These model the spatial distribution of the species across available habitat and how this distribution changes over time, relative to covariates. In addition, the model explicitly accounts for spatio‐temporal dynamics that are unaccounted for by covariates through a spatio‐temporal stochastic process. We illustrate the approach by predicting the distribution of a recently established population of Eurasian cranes Grus grus in England, UK, and estimate the effect of a reintroduction in the range expansion of the population. Our models show that wetland extent and perimeter‐to‐area ratio have a positive and negative effect, respectively, in crane colonisation probability. Moreover, we find that cranes are more likely to colonise areas near already occupied wetlands and that the colonisation process is progressing at a low rate. Finally, the reintroduction of cranes in SW England can be considered a human‐assisted long‐distance dispersal event that has increased the dispersal potential of the species along a longitudinal axis in S England. Spatio‐temporal log‐Gaussian Cox process models offer an excellent opportunity for the study of species where information on life history traits is lacking, since these are represented through the spatio‐temporal dynamics reflected in the model.     

Spatial modelling of succession-disturbance dynamics in forest ecosystems: Concepts and examples

Over the last few decades it has become increasingly obvious that disturbance, whether natural or anthropogenic in origin, is ubiquitous in ecosystems. Disturbance-related processes are now considered to be important determinants of the composition, structure and function of ecological systems. However, because disturbance and succession processes occur across a wide range of spatio-temporal scales their empirical investigation is difficult. To counter these difficulties much use has been made of spatial modelling to explore the response of ecological systems to disturbance(s) occurring at spatial scales from the individual to the landscape and above, and temporal scales from minutes to centuries. Here we consider such models by contrasting two alternative motivations for their development and use: prediction and exploration, with a focus on forested ecosystems. We consider the two approaches to be complementary rather than competing. Predictive modelling aims to combine knowledge (understanding and data) with the goal of predicting system dynamics; conversely, exploratory models focus on developing understanding in systems where uncertainty is high. Examples of exploratory modelling include model-based explorations of generic issues of criticality in ecological systems, whereas predictive models tend to be more heavily data-driven (e.g. species distribution models). By considering predictive and exploratory modelling alongside each other, we aim to illustrate the range of methods used to model succession and disturbance dynamics and the challenges involved in the model-building and evaluation processes in this arena.     

Self-regulation within outbreak populations of feral house mice: a test of alternative models

1. Outbreaks of feral house mice, Mus domesticus, in Australia represent a fundamental failure of the behavioural control mechanisms of population density, as proposed in the hypothesis of self-regulation. 2. Mice have the potential to keep numbers in check via a suite of spacing behaviours; however, the self-regulation hypothesis implies that some social change occurs that permits the population to erupt. It also suggests that at different phases of an outbreak, distinct patterns of social activity are evident. 3. We compare predictions from two models encapsulating the self-regulation hypothesis as applied to feral house mice in south-eastern Australia. Each model may be distinguished by the timing of aggressiveness between mice that leads to a closed social system. We compare individual turnover, residency and territoriality in each sex and age cohort during the increase, peak and low phases of a population outbreak that peaked in 2001. 4. The activity of 438 mice was monitored via intensive mark-recapture trapping and an automated event recording system that detected the activity of 300 marked individuals at burrow entrances. 5. Our findings support the second model, which suggests that mice switch from an almost asocial structure at low densities to a territorial system as abundance increases. Adult females appear more likely than males or juveniles to make the significant social shift. The trigger for this change remains unclear and several alternative mechanisms are proposed.