A 3D Individual-Based Model to Study Effects of Chemotaxis,Competition and Diffusion on the Motile-Phytoplankton Aggregation

In this paper, we develop a 3D-individual-based model (IBM) to understand effect of various small-scale mechanisms in phytoplankton cells, on the cellular aggregation process. These mechanisms are: spatial interactions between cells due to their chemosensory abilities (chemotaxis), a molecular diffusion and a demographical process. The latter is considered as a branching process with a density-dependent death rate to take into account the local competition on resources. We implement the IBM and simulate various scenarios under real parameter values for phytoplankton cells. To quantify the effects of the different processes quoted above on the spatial and temporal distribution of phytoplankton, we used two spatial statistics: the Clark–Evans index and the group belonging percentage. Our simulation study highlights the role of the branching process with a weak-to-medium competition in reinforcing the aggregating structure that forms from attraction mechanisms (under suitable conditions for diffusion and attraction forces), and shows by contrast that aggregations cannot form when competition is high.     

Individual-based modeling of phytoplankton: evaluating approaches for applying the cell quota model

Present phytoplankton models typically use a population-level (lumped) modeling (PLM) approach that assumes average properties of a population within a control volume. For modern biogeochemical models that formulate growth as a nonlinear function of the internal nutrient (e.g. Droop kinetics), this averaging assumption can introduce a significant error. Individual-based (agent-based) modeling (IBM) does not make the assumption of average properties and therefore constitutes a promising alternative for biogeochemical modeling. This paper explores the hypothesis that the cell quota (Droop) model, which predicts the population-average specific growth or cell division rate, based on the population-average nutrient cell quota, can be applied to individual algal cells and produce the same population-level results. Three models that translate the growth rate calculated using the cell quota model into discrete cell division events are evaluated, including a stochastic model based on the probability of cell division, a deterministic model based on the maturation velocity and fraction of the cell cycle completed (maturity fraction), and a deterministic model based on biomass (carbon) growth and cell size. The division models are integrated into an IBM framework (iAlgae), which combines a lumped system representation of a nutrient with an individual representation of algae. The IBM models are evaluated against a conventional PLM (because that is the traditional approach) and data from a number of steady and unsteady continuous (chemostat) and batch culture laboratory experiments. The stochastic IBM model fails the steady chemostat culture test, because it produces excessive numerical randomness. The deterministic cell cycle IBM model fails the batch culture test, because it has an abrupt drop in cell quota at division, which allows the cell quota to fall below the subsistence quota. The deterministic cell size IBM model reproduces the data and PLM results for all experiments and the model parameters (e.g. maximum specific growth rate, subsistence quota) are the same as those for the PLM. In addition, the model-predicted cell age, size (carbon) and volume distributions are consistent with those derived analytically and compare well to observations. The paper discusses and illustrates scenarios where intra-population variability in natural systems leads to differences between the IBM and PLM models.     

Spatial organization of mesenchymal stem cells in vitro--results from a new individual cell-based model with podia

Therapeutic application of mesenchymal stem cells (MSC) requires their extensive in vitro expansion. MSC in culture typically grow to confluence within a few weeks. They show spindle-shaped fibroblastoid morphology and align to each other in characteristic spatial patterns at high cell density. We present an individual cell-based model (IBM) that is able to quantitatively describe the spatio-temporal organization of MSC in culture. Our model substantially improves on previous models by explicitly representing cell podia and their dynamics. It employs podia-generated forces for cell movement and adjusts cell behavior in response to cell density. At the same time, it is simple enough to simulate thousands of cells with reasonable computational effort. Experimental sheep MSC cultures were monitored under standard conditions. Automated image analysis was used to determine the location and orientation of individual cells. Our simulations quantitatively reproduced the observed growth dynamics and cell-cell alignment assuming cell density-dependent proliferation, migration, and morphology. In addition to cell growth on plain substrates our model captured cell alignment on micro-structured surfaces. We propose a specific surface micro-structure that according to our simulations can substantially enlarge cell culture harvest. The 'tool box' of cell migratory behavior newly introduced in this study significantly enhances the bandwidth of IBM. Our approach is capable of accommodating individual cell behavior and collective cell dynamics of a variety of cell types and tissues in computational systems biology.     

Spatial Moment Description of Birth–Death–Movement Processes Incorporating the Effects of Crowding and Obstacles

Birth–death–movement processes, modulated by interactions between individuals, are fundamental to many cell biology processes. A key feature of the movement of cells within in vivo environments is the interactions between motile cells and stationary obstacles. Here we propose a multi-species model of individual-level motility, proliferation and death. This model is a spatial birth–death–movement stochastic process, a class of individual-based model (IBM) that is amenable to mathematical analysis. We present the IBM in a general multi-species framework and then focus on the case of a population of motile, proliferative agents in an environment populated by stationary, non-proliferative obstacles. To analyse the IBM, we derive a system of spatial moment equations governing the evolution of the density of agents and the density of pairs of agents. This approach avoids making the usual mean-field assumption so that our models can be used to study the formation of spatial structure, such as clustering and aggregation, and to understand how spatial structure influences population-level outcomes. Overall the spatial moment model provides a reasonably accurate prediction of the system dynamics, including important effects such as how varying the properties of the obstacles leads to different spatial patterns in the population of agents.     

A fully continuous individual-based model of tumor cell evolution

The aim of this work is to develop and study a fully continuous individual-based model (IBM) for cancer tumor invasion into a spatial environment of surrounding tissue. The IBM improves previous spatially discrete models, because it is continuous in all variables (including spatial variables), and thus not constrained to lattice frameworks. The IBM includes four types of individual elements: tumor cells, extracellular macromolecules (MM), a matrix degradative enzyme (MDE), and oxygen. The algorithm underlying the IBM is based on the dynamic interaction of these four elements in the spatial environment, with special consideration of mutation phenotypes. A set of stochastic differential equations is formulated to describe the evolution of the IBM in an equivalent way. The IBM is scaled up to a system of partial differential equations (PDE) representing the limiting behavior of the IBM as the number of cells and molecules approaches infinity. Both models (IBM and PDE) are numerically simulated with two kinds of initial conditions: homogeneous MM distribution and heterogeneous MM distribution. With both kinds of initial MM distributions spatial fingering patterns appear in the tumor growth. The output of both simulations is quite similar.     

Modeling dengue outbreaks

We introduce a dengue model (SEIR) where the human individuals are treated on an individual basis (IBM) while the mosquito population, produced by an independent model, is treated by compartments (SEI). We study the spread of epidemics by the sole action of the mosquito. Exponential, deterministic and experimental distributions for the (human) exposed period are considered in two weather scenarios, one corresponding to temperate climate and the other to tropical climate. Virus circulation, final epidemic size and duration of outbreaks are considered showing that the results present little sensitivity to the statistics followed by the exposed period provided the median of the distributions are in coincidence. Only the time between an introduced (imported) case and the appearance of the first symptomatic secondary case is sensitive to this distribution. We finally show that the IBM model introduced is precisely a realization of a compartmental model, and that at least in this case, the choice between compartmental models or IBM is only a matter of convenience.     

Impact of the topology of metapopulations on the resurgence of epidemics rendered by a new multiscale hybrid modeling approach

Simulating epidemics in metapopulations is a challenging issue due to the large demographic and geographic scales to incorporate. Traditional epidemiologic models choose to simplify reality by ignoring both the spatial distribution of populations and possible intrapopulation heterogeneities, whereas more recent solutions based on Individual-Based Modeling (IBM) can achieve high precision but are costly to compute and analyze. We introduce here an original alternative to these two approaches, which relies on a novel hybrid modeling framework and incarnates a multiscale view of epidemics. The model relies on a technical fusion of two modeling paradigms: System Dynamics (SD) and Individual-Based Modeling. It features an aggregated representation of local outbreaks rendered in SD, and at the same time a spatially-explicit simulation of the spread between populations simulated in IBM. We first present the design of this deterministic model, show that it can reproduce the dynamics of real resurgent epidemics, and infer from the sensitivity of several spatial factors absent in compartmental models the importance of having large-scale epidemiological processes represented inside of an explicitly disaggregated metapopulation. After discussing the implications of results obtained from simulation runs and the applicability of this model, we conclude that SD–IB hybrid modeling can be an interesting choice to represent epidemics in a spatially-explicit way without necessarily taking into account individual heterogeneities, and therefore it can be considered as a valuable alternative to simple compartmental models suffering from detrimental effects of the well-mixed assumption.     

Modeling aggregation and growth processes in an algal population model: analysis and computations

 Aggregation, the formation of large particles through multiple collision of smaller ones is a highly visible phenomena in oceanic waters which can control material flux to the deep sea. Oceanic aggregates more than 1 cm in diameter have been observed and are frequently described to consist of phytoplankton cells as well as other organic matter such as fecel pellets and mucus nets from pteropods. Division of live phytoplankton cells within an aggregate can also increase the size of aggregate (assuming some daughter cells stay in the aggregate) and hence could be a significant factor in speeding up the formation process of larger aggregate. Due to the difficulty of modeling cell division within aggregates, few efforts have been made in this direction. In this paper, we propose a size structured approach that includes growth of aggregate size due to both cell division and aggregation. We first examine some basic mathematical issues associated with the development of a numerical simulation of the resulting algal aggregation model. The numerical algorithm is then used to examine the basic model behavior and present a comparison between aggregate distribution with and without division in aggregates. Results indicate that the inclusion of a growth term in aggregates, due to cell division, results in higher densities of larger aggregates; hence it has the impact to speed clearance of organic matter from the surface layer of the ocean. Received 1 July 1994; received in revised form 23 February 1996     

Spatial coexistence of phytoplankton species in ecological timescale

The species diversity of phytoplankton is usually very high in wild aquatic systems, as seen in the paradox of plankton. Coexistence of many competitive phytoplankton species is extremely common in nature. However, experiments and mathematical theories show that interspecific competition often leads to the extinction of most inferior species. Here, we present a lattice version of a multi-species Lotka–Volterra competition model to demonstrate the importance of local interaction. Its mathematical equilibrium is the exclusion of all but one superior species. However, temporal coexistence of many competitive species is possible in an ecological time scale if interactions are local instead of global. This implies that the time scale is elongated many orders when interactions are local. Extremely high species diversity of phytoplankton in aquatic systems may be maintained by spatial coexistence in an ecological time scale.Tatsuo Miyazaki, Kei-ichi Tainaka, and Jin Yoshimura contributed equally to this study.     

Herbivores and the Spatial Distributions of the Phytoplankton. I. The Plankton Market

Planktonic herbivores forage on phytoplankton cells which were produced at some earlier time and at a distant place. A steady state, one dimension model of the birth, death and eddy diffusion of phytoplankton illustrates phytoplankton smooth both temporal and spatial variations as they are transported. When the eddy diffusivity is k and the phytoplankton doubling time is b, the average distance traveled by a phytoplankton cell is (kb)^1/2 and the average time spent doing so is b. Only those spatial variations with wavelengths greater than 2π(kb)^1/2 and temporal variations with periods greater than 2πb will be observed in the phytoplankton distributions at more than half their original amplitude. Both k and b control the length scale of phytoplankton distributions in a cartesian coordinate system. Planktonic herbivores view the phytoplankton from a diffusing coordinate system in which the spatial scales of the phytoplankton distribution are transformed into time scales.     

Autoantibodies Produced at the Site of Tissue Damage Provide Evidence of Humoral Autoimmunity in Inclusion Body Myositis

Inclusion body myositis (IBM) belongs to a group of muscle diseases known as the inflammatory myopathies. The presence of antibody-secreting plasma cells in IBM muscle implicates the humoral immune response in this disease. However, whether the humoral immune response actively contributes to IBM pathology has not been established. We sought to investigate whether the humoral immune response in IBM both in the periphery and at the site of tissue damage was directed towards self-antigens. Peripheral autoantibodies present in IBM serum but not control serum recognized self-antigens in both muscle tissue and human-derived cell lines. To study the humoral immune response at the site of tissue damage in IBM patients, we isolated single plasma cells directly from IBM-derived muscle tissue sections and from these cells, reconstructed a series of recombinant immunoglobulins (rIgG). These rIgG, each representing a single muscle-associated plasma cell, were examined for reactivity to self-antigens. Both, flow cytometry and immunoblotting revealed that these rIgG recognized antigens expressed by cell lines and in muscle tissue homogenates. Using a mass spectrometry-based approach, Desmin, a major intermediate filament protein, expressed abundantly in muscle tissue, was identified as the target of one IBM muscle-derived rIgG. Collectively, these data support the view that IBM includes a humoral immune response in both the periphery and at the site of tissue damage that is directed towards self-antigens.     

Phytoplankton cell size and the development of microenvironments

Abstract The effect of cell size on the development of extracellular microenvironments of pH produced by individual photosynthesizing phytoplankton cells was investigated. The presence of pH microenvironments was determined by detection of a chemical reaction known to occur in microenvironments of high pH produced by algal photosynthesis, specifically the extracellular oxidation of Mn(II) to MnO_x. The dye leukoberbelin blue was used to detect the reaction. It was experimentally determined that individual algal cells larger than 20 μm (length and/or width) produced microenvironments, while smaller cells did not unless present as cell aggregates larger than 20 μm. A mathematical model is presented and discussed.     

Flow cytometry: instrumentation and application in phytoplankton research

In flow cytometry, light scattering and fluorescence of individual particles in suspension is measured at high speed. When applied to planktonic particles, the light scattering and (auto-)fluorescence properties of algal cells can be used for cell identification and counting. Analysis of the wide size spectrum of phytoplankton species, generally present in eutrophic inland and coastal waters, requires flow cytometers specially designed for this purpose. This paper compares the performance in phytoplankton research of a commercial flow cytometer to a purpose built instrument. It reports on the identification of phytoplankton and indicates an area where flow cytometry may supersede more conventional techniques: the analysis of morphological and physiological characteristics of subpopulations in phytoplankton samples.     

浮游植物细胞自噬作用特点及研究方法

自噬(Autophagy)是真核生物细胞中一类高度保守的、依赖于溶酶体或液泡途径对胞质蛋白和细胞器进行降解的生物学过程。细胞自噬除维持细胞稳态外,在细胞响应各种外界胁迫中也发挥重要作用。近年来,陆续发现浮游植物能够通过细胞自噬应答众多环境胁迫,并在浮游植物细胞中鉴定出了类似于哺乳动物细胞中的核心自噬功能单位。自噬作为一种独特的程序性细胞死亡(PCD)形式,对浮游植物遭受胁迫后的个体存活及种群延续具有至关重要的作用。因此,细胞自噬也将成为浮游植物研究领域的一个新的着力点。主要综述了浮游植物细胞中自噬的保守性、诱导因素、调控机制、自噬与凋亡的交互作用以及浮游植物自噬研究方法等研究进展。     

Spatial competition with Lactococcus lactis in mixed-species continuous-flow biofilms inhibits Listeria monocytogenes growth

Surfaces in industrial settings provide a home for resident biofilms that are likely to interact with the attachment, growth and survival of pathogens such as Listeria monocytogenes. Experimental results have indicated that L. monocytogenes cells were inhibited by the presence of a model resident flora (Lactococcus lactis) in dual-species continuous flow-biofilms, and are spatially restricted to the lower biofilm layers. Using a new, simplified individual-based model (IBM) that simulates bacterial cell growth in a three-dimensional space, the spatial arrangements of the two species were reconstructed and their cell counts successfully predicted. This model showed that the difference in generation times between L. monocytogenes and L. lactis cells during the initial stages of dual-species biofilm formation was probably responsible for the species spatialization observed and the subsequent inhibition of growth of the pathogen.     

Combining Individual-Based Modeling and Food Microenvironment Descriptions To Predict the Growth of Listeria monocytogenes on Smear Soft Cheese

An individual-based modeling (IBM) approach was developed to describe the behavior of a few Listeria monocytogenes cells contaminating smear soft cheese surface. The IBM approach consisted of assessing the stochastic individual behaviors of cells on cheese surfaces and knowing the characteristics of their surrounding microenvironments. We used a microelectrode for pH measurements and micro-osmolality to assess the water activity of cheese microsamples. These measurements revealed a high variability of microscale pH compared to that of macroscale pH. A model describing the increase in pH from approximately 5.0 to more than 7.0 during ripening was developed. The spatial variability of the cheese surface characterized by an increasing pH with radius and higher pH on crests compared to that of hollows on cheese rind was also modeled. The microscale water activity ranged from approximately 0.96 to 0.98 and was stable during ripening. The spatial variability on cheese surfaces was low compared to between-cheese variability. Models describing the microscale variability of cheese characteristics were combined with the IBM approach to simulate the stochastic growth of L. monocytogenes on cheese, and these simulations were compared to bacterial counts obtained from irradiated cheeses artificially contaminated at different ripening stages. The simulated variability of L. monocytogenes counts with the IBM/microenvironmental approach was consistent with the observed one. Contrasting situations corresponding to no growth or highly contaminated foods could be deduced from these models. Moreover, the IBM approach was more effective than the traditional population/macroenvironmental approach to describe the actual bacterial behavior variability.     

Are Tumor Cell Lineages Solely Shaped by Mechanical Forces?

This paper investigates cell proliferation dynamics in small tumor cell aggregates using an individual-based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as the impact of the orientation of the division plane on this morphology. Our IBM model is based on the hypothesis that cells are incompressible objects that grow in size and divide once a threshold size is reached, and that newly born cell adhere to the existing cell cluster. We performed comparisons between the simulation model and experimental data by using several statistical indicators. The results suggest that the emergence of particular morphologies can be explained by simple mechanical interactions.     

基于遥感数据的东海浮游植物生物量时空变化研究

基于地理位置、纬度和生态特征的不同在东海选取了9个面积相同的子区域,采用1997-2015年由SeaWiFS(Sea-Viewing Wide Field-of-View Sensor)和MODIS(Moderate-Resolution Imaging Spectroradiometer)传感器获得的叶绿素a浓度资料,对我国东海浮游植物生物量的时空变化和藻华现象进行了分析。通过高斯曲线模型拟合,得到了藻华爆发的起始时间、峰值时间、结束时间及持续时间。研究表明东海浮游植物生物量在空间上的分布规律为:外海浮游植物生物量小于近岸;长江口和台州列岛海域的浮游植物生物量较大,近黄海海域的两个区域次之,较小的位于南麂列岛海域和台湾海峡,越靠近南部海域浮游植物生物量越低。藻华发生的规律为:以南麂列岛为分界线,由高纬度到低纬度,浮游植物到达藻华发生峰值的时间持续推后,爆发持续时间增长。