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.     

On phytoplankton aggregation: a view from an IBM approach

In this paper, we build up an individual-based model (IBM) that describes the aggregative behavior in phytoplankton. The processes in play at the individual level (an individual=a phytoplankton cell) are: a random dispersal, a displacement due to the net effect of cells present in a suitable neighborhood (spatial interactions) and a branching (cell division and death). The IBM model provides a virtual world where phytoplankton cells appear to form clusters. Using this model, we explore the spatial structure of phytoplankton and present some numerical simulations that help the understanding of the aggregation phenomenon.     

A computational modeling and analysis in cell biological dynamics using electric cell-substrate impedance sensing (ECIS)

In this paper, a study of computational modeling and multi-scale analysis in cell dynamics is presented. Our study aims at: (1) deriving and validating a mathematical model for cell growth, and (2) quantitatively detecting and analyzing the biological interdependencies across multiple observational scales with a variety of time and frequency resolutions. This research was conducted using the time series data practically measured from a novel on-line cell monitoring technique, referred to as electric cell-substrate impedance sensing (ECIS), which allows continuously tracking the cellular behavior such as adhesion, proliferation, spreading and micromotion. First, comparing our ECIS-based cellular growth modeling analysis results with those determined by hematocytometer measurement using different time intervals, we found that the results obtained from both experimental methods consistently agreed. However, our study demonstrated that it is much easier and more convenient to operate with the ECIS system for on-line cellular growth monitoring. Secondly, for multi-scale analysis our results showed that the proposed wavelet-based methodology can effectively quantify the fluctuations associated with cell micromotions and quantitatively capture the biological interdependencies across multiple observational scales. Note that although the wavelet method is well known, its application into the ECIS time series analysis is novel and unprecedented in computational cell biology. Our analyses indicated that the proposed study on ECIS time series could provide a hopeful start and great potentials in both modeling and elucidating the complex mechanisms of cell biological systems.     

Modeling Imatinib-Treated Chronic Myelogenous Leukemia: Reducing the Complexity of Agent-Based Models

We develop a model for describing the dynamics of imatinib-treated chronic myelogenous leukemia. Our model is based on replacing the recent agent-based model of Roeder et al. (Nat. Med. 12(10):1181–1184, 2006) by a system of deterministic difference equations. These difference equations describe the time-evolution of clusters of individual agents that are grouped by discretizing the state space. Hence, unlike standard agent-base models, the complexity of our model is independent of the number of agents, which allows to conduct simulation studies with a realistic number of cells. This approach also allows to directly evaluate the expected steady states of the system. The results of our numerical simulations show that our model replicates the averaged behavior of the original Roeder model with a significantly reduced computational cost. Our general approach can be used to simplify other similar agent-based models. In particular, due to the reduced computational complexity of our technique, one can use it to conduct sensitivity studies of the parameters in large agent-based systems.     

A single-cell-based model of tumor growth in vitro: monolayers and spheroids

To what extent the growth dynamics of tumors is controlled by nutrients, biomechanical forces and other factors at different stages and in different environments is still largely unknown. Here we present a biophysical model to study the spatio-temporal growth dynamics of two-dimensional tumor monolayers and three-dimensional tumor spheroids as a complementary tool to in vitro experiments. Within our model each cell is represented as an individual object and parametrized by cell-biophysical and cell-kinetic parameters that can all be experimentally determined. Hence our modeling strategy allows us to study which mechanisms on the microscopic level of individual cells may affect the macroscopic properties of a growing tumor. We find the qualitative growth kinetics and patterns at early growth stages to be remarkably robust. Quantitative comparisons between computer simulations using our model and published experimental observations on monolayer cultures suggest a biomechanically-mediated form of growth inhibition during the experimentally observed transition from exponential to sub-exponential growth at sufficiently large tumor sizes. Our simulations show that the same transition during the growth of avascular tumor spheroids can be explained largely by the same mechanism. Glucose (or oxygen) depletion seems to determine mainly the size of the necrotic core but not the size of the tumor. We explore the consequences of the suggested biomechanical form of contact inhibition, in order to permit an experimental test of our model. Based on our findings we propose a phenomenological growth law in early expansion phases in which specific biological small-scale processes are subsumed in a small number of effective parameters.     

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.     

Improvement and validation of a computational model of flow in the swirling well cell culture model

Effects of fluid dynamics on cells are often studied by growing the cells on the base of cylindrical wells or dishes that are swirled on the horizontal platform of an orbital shaker. The swirling culture medium applies a shear stress to the cells that varies in magnitude and directionality from the center to the edge of the vessel. Computational fluid dynamics methods are used to simulate the flow and hence calculate shear stresses at the base of the well. The shear characteristics at each radial location are then compared with cell behavior at the same position. Previous simulations have generally ignored effects of surface tension and wetting, and results have only occasionally been experimentally validated. We investigated whether such idealized simulations are sufficiently accurate, examining a commonly-used swirling well configuration. The breaking wave predicted by earlier simulations was not seen, and the edge-to-center difference in shear magnitude (but not directionality) almost disappeared, when surface tension and wetting were included. Optical measurements of fluid height and velocity agreed well only with the computational model that incorporated surface tension and wetting. These results demonstrate the importance of including accurate fluid properties in computational models of the swirling well method.     

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.     

Kinetic analysis of the effect of cell density on hybridoma cell growth in batch culture

The effect of cell density on cell growth was investigated in a suspension batch culture of hybridoma cells. The specific growth rate was found to increase with increasing initial cell density and then to decrease with further increases in initial cell density. In order to quantitatively describe the dependence of specific growth rate on cell density, a kinetic model is proposed, which satisfactorily represents the experimental data.     

Effective water model for Monte Carlo simulations of proteins

We present an effective theory for water. Our goal is to formulate on accurate model for the effects of solvation on protein dynamics, without incurring the huge computational cost and the slow temporal evolution typical of molecular dynamics simulations of liquids. We replace the individual water molecules in an all-atom potential with a local dielectric density field, with self interactions given by the Landau-Ginzburg free energy and external interactions by Lennard-Jones forces at the surface of the protein atoms. We explore conformational space with finite temperature Monte Carlo dynamics, using parallel Langevin and Fourier acceleration algorithms well suited to data-parallel computer architectures such as the Connection Machine. To establish the validity of our approximations, we compare our electrostatic contribution to the solvalion energy with the results of Lim, Bashford, and Karplus using a conventional static continuum dielectric cavity model, and the non electrostatic contributions with estimates of hydrophohic surface free energy. Our model can also accommodate ionic charges and temperature fluctuations, We propose future investigations extending our effective theory of solvation to include explicit orientational entropy and hydroxen-bonding terms. © 1995 John Wiley & Sons, Inc.     

Stochastic model of autocrine and paracrine signals in cell culture assays

Autocrine signaling systems are commonly studied under cell culture conditions. In a typical cell culture assay, a layer of liquid medium covers a random two-dimensional dispersion of cells, which secrete ligands. In a growing number of experiments, it is important to characterize the spatial range of autocrine and paracrine cell communication. Currently, the spatial distribution of diffusing signals can be analyzed only indirectly, from their effects on the intracellular signaling or physiological responses of autocrine cells. To directly characterize the spatial range of secreted ligands, we propose a stochastic model for autocrine cell cultures and analyze it using a combination of analytical and computational tools. The two main results derived within the framework of this model are 1), an expression for the fraction of autocrine trajectories, i.e., the probability for a ligand to be trapped by the same cell from which it has been secreted; and 2), an expression for the spatial distribution of trapping points of paracrine trajectories. We test these analytical results by stochastic simulations with efficient Brownian dynamics code and apply our model to analyze the spatial operation of autocrine epidermal growth factor receptor systems.     

A well-mixed, polymer-based microbioreactor with integrated optical measurements

We describe a 150 microL microbioreactor fabricated in poly(methylmethacrylate) (PMMA) and poly(dimethylsiloxane) (PDMS) to cultivate microbial cell cultures. Mixing is achieved by a small magnetic stir bar and fluorescent sensors are integrated for on-line measurement of pH and dissolved oxygen. Optical transmission measurements are used for cell density. The body of the reactor is poly(methylmethacrylate) with a thin layer of poly (dimethylsiloxane) for aeration, oxygen diffuses through this gas-permeable membrane into the microbioreactor to support metabolism of bacterial cells. Mixing in the reactor is characterized by observation of mixing of dyes and computational fluid dynamics simulations. The oxygenation is described in terms of measured K(L)a values for microbioreactor, 20-75/h corresponding to increasing stirring speed 200-800 rpm. Escherichia coli cell growth in the microbioreactor is demonstrated and the growth behavior is benchmarked with conventional bench-scale bioreactors, flasks and tubes. Batch culture experiments with Saccharomyces cerevisiae further demonstrate the reproducibility and flexibility of the microbioreactor system.     

Effect of partial oxygen pressure on survival, proliferation, and differentiation of mouse bone marrow mesenchymal stem cells

Effects of partial oxygen pressure in a gas mixture surrounding the culture medium on survival, proliferation and differentiation of mesenchymal stem cells (MSC) isolated from mouse bone marrow was studied. It was found that 3% oxygen increased the survival of cells seeded at low density; the rate and duration of the MSC proliferation were also elevated. Effect of oxygen concentration on replicative activity of MSC was manifested as early as the first few days after the onset of cell growth. Studies of colony formation revealed that preincubation of cells with 21% oxygen had a negative effect on cell growth under 3% oxygen, while preincubation with 3% oxygen stimulated MSC proliferation in the presence of 21% oxygen. Notwithstanding, this effect of oxygen cannot be interpreted as unequivocally deleterious. Low partial oxygen pressure inhibited osteogenic differentiation of MSC, but adipogenic differentiation was insensitive to oxygen concentration. It is concluded that proliferation and differentiation of MSC depend critically on oxygen content in the culture medium.     

A comparison of random vs. chemotaxis-driven contacts of T cells with dendritic cells during repertoire scanning

Generating adaptive immunity after infection or immunization requires physical interactions within a lymph node (LN) T-zone between antigen-bearing dendritic cells (DCs) that arrive from peripheral tissues and rare cognate T cells entering via high endothelial venules (HEVs). This interaction results in activation of cognate T cells, expansion of that T cell lineage and their exit from the LN T-zone via efferent lymphatics (ELs). How antigen-specific T cells locate DCs within this complex environment is controversial, and both random T cell migration and chemotaxis have been proposed. We developed an agent-based computational model of a LN that captures many features of T cell and DC dynamics observed by two-photon microscopy. Our simulations matched in vivo two-photon microscopy data regarding T cell speed, short-term directional persistence of motion and cell motility. We also obtained in vivo data regarding density of T cells and DCs within a LN and matched our model environment to measurements of the distance from HEVs to ELs. We used our model to compare chemotaxis with random motion and showed that chemotaxis increased total number of T cell DC contacts, but decreased unique contacts, producing fewer activated T cells. Our results suggest that, within a LN T-zone, a random search strategy is optimal for a rare cognate T cell to find its DC match and maximize production of activated T cells.     

Impact of oxygen environment on mesenchymal stem cell expansion and chondrogenic differentiation

Introduction:  In vitro expansion and differentiation of mesenchymal stem cells (MSC) rely on specific environmental conditions, and investigations have demonstrated that one crucial factor is oxygen environment.
Objectives:  In order to understand the impact of oxygen tension on MSC culture and chondrogenic differentiation in vitro , we developed a mathematical model of these processes and applied it in predicting optimal assays.
Methods and results:  We compared ovine MSCs under physiologically low and atmospheric oxygen tension. Low oxygen tension improved their in vitro population growth as demonstrated by monoclonal expansion and colony forming assays. Moreover, it accelerated induction of the chondrogenic phenotype in subsequent three-dimensional differentiation cultures. We introduced a hybrid stochastic multiscale model of MSC organization in vitro . The model assumes that cell adaptation to non-physiological high oxygen tension reversibly changes the structure of MSC populations with respect to differentiation. In simulation series, we demonstrated that these changes profoundly affect chondrogenic potential of the populations. Our mathematical model provides a consistent explanation of our experimental findings.
Conclusions:  Our approach provides new insights into organization of MSC populations in vitro. The results suggest that MSC differentiation is largely reversible and that lineage plasticity is restricted to stem cells and early progenitors. The model predicts a significant impact of short-term low oxygen treatment on MSC differentiation and optimal chondrogenic differentiation at 10–11% pO₂.     

Modeling of flow‐induced shear stress applied on 3D cellular scaffolds: Implications for vascular tissue engineering

Novel tissue‐culture bioreactors employ flow‐induced shear stress as a means of mechanical stimulation of cells. We developed a computational fluid dynamics model of the complex three‐dimensional (3D) microstructure of a porous scaffold incubated in a direct perfusion bioreactor. Our model was designed to predict high shear‐stress values within the physiological range of those naturally sensed by vascular cells (1–10 dyne/cm²), and will thereby provide suitable conditions for vascular tissue‐engineering experiments. The model also accounts for cellular growth, which was designed as an added cell layer grown on all scaffold walls. Five model variants were designed, with geometric differences corresponding to cell‐layer thicknesses of 0, 50, 75, 100, and 125 µm. Four inlet velocities (0.5, 1, 1.5, and 2 cm/s) were applied to each model. Wall shear‐stress distribution and overall pressure drop calculations were then used to characterize the relation between flow rate, shear stress, cell‐layer thickness, and pressure drop. The simulations showed that cellular growth within 3D scaffolds exposes cells to elevated shear stress, with considerably increasing average values in correlation to cell growth and inflow velocity. Our results provide in‐depth analysis of the microdynamic environment of cells cultured within 3D environments, and thus provide advanced control over tissue development in vitro. Biotechnol. Bioeng. 2010; 105: 645–654. © 2009 Wiley Periodicals, Inc.     

Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling

Vasculogenesis, the de novo growth of the primary vascular network from initially dispersed endothelial cells, is the first step in the development of the circulatory system in vertebrates. In the first stages of vasculogenesis, endothelial cells elongate and form a network-like structure, called the primary capillary plexus, which subsequently remodels, with the size of the vacancies between ribbons of endothelial cells coarsening over time. To isolate such intrinsic morphogenetic ability of endothelial cells from its regulation by long-range guidance cues and additional cell types, we use an in vitro model of human umbilical vein endothelial cells (HUVEC) in Matrigel. This quasi-two-dimensional endothelial cell culture model would most closely correspond to vasculogenesis in flat areas of the embryo like the yolk sac. Several studies have used continuum mathematical models to explore in vitro vasculogenesis: such models describe cell ensembles but ignore the endothelial cells' shapes and active surface fluctuations. While these models initially reproduce vascular-like morphologies, they eventually stabilize into a disconnected pattern of vascular "islands." Also, they fail to reproduce temporally correct network coarsening. Using a cell-centered computational model, we show that the endothelial cells' elongated shape is key to correct spatiotemporal in silico replication of stable vascular network growth. We validate our simulation results against HUVEC cultures using time-resolved image analysis and find that our simulations quantitatively reproduce in vitro vasculogenesis and subsequent in vitro remodeling.     

生长因子TGF-β1和bFGF促兔骨髓间质干细胞向韧带样细胞分化的实验研究

摘要目的：采用生长因子TGF-β1和bFGF诱导体外培养的兔骨髓间质干细胞（MSCs）,转化为韧带样细胞,并研究此种韧带样细胞的生物特性。方法：自幼兔四肢骨抽取骨髓分离纯化MSCs并培养、增殖;采用特定浓度TGF-β1（10ng／ml）和bFGF（25ng／mL）对MSCs进行诱导分化,观察生长因子对MSCs生长、形态的影响,使用MTT法绘制细胞生长曲线,使用天狼腥红染色法定量对比MSCs分泌胶原蛋白量。单纯培养和单一因子诱导组作为对照。结果：TGF-β1和bFGF联合使用组,细胞形态优于空白组及单一因子组,细胞增殖率、胶原分泌量也均高于对照组。结论：联合使用生长因子TGF-β1和bFGF刺激兔MSCs,能够促使兔MSCs定向转化为韧带样细胞,对组织工程前交叉韧带的构建具有积极意义。     

恒河猴骨髓间质干细胞的体外分离培养及形态学特征分析(英文)

探索恒河猴骨髓间质干细胞(MSC)的体外分离培养方法,为其应用提供实验基础。取恒河猴骨髓细胞悬液,经梯度离心去除大部分血细胞,取含有MSC的中间单核细胞层,在含10%胎牛血清及1ng/mL碱性成纤维细胞生长因子的L-DMEM中培养扩增,并不断换液去除杂细胞,经过18d的原代培养,获得呈致密单层生长的MSC,其形态为较规则的长梭形细胞,排列有方向性,呈现一定的漩涡状、辐射状生长趋势。将原代细胞以1∶2传代,传代培养后期,细胞增殖速度逐渐变缓,细胞形态逐渐出现三角形、多边形及扁平宽大形等不规则形态。结果显示,恒河猴骨髓间质干细胞可在体外进行传代培养,但需进一步优化其培养条件。