二维细胞运动模型的数值模拟

研究了一个二维细胞运动模型,该模型是个动边界问题．我们运用运动网格的有限元算法对此模型进行了数值模拟,数值结果表明,细胞最终收敛到固定形状,并且以固定速度向前运动．     

Modelling Directional Guidance and Motility Regulation in Cell Migration

Although cell migration is an essential process in development, how cells reach their final destination is not well understood. Secreted molecules are known to have a migratory effect, but it remains unclear whether such molecules act as directional guidance cues or as motility regulators. There is potential to use signalling molecules in new medical therapies, so it is important to identify the exact role these molecules play. This paper focuses on distinguishing between inhibitory and repulsive effects produced by signalling molecules, based on recent experiments examining the effect of Slit, a secreted protein, on the migration of neurons from the brain. The primary role of Slit, whether it is an inhibitor or repellent of neurons, is in dispute. We present population-level continuum models and recast these in terms of transition probabilities governing individual cells. Various cell-sensing strategies are considered within this framework. The models are applied to the neuronal migration experiments. To resolve the particular role of Slit, simulations of the models characterising different cell-sensing strategies are compared at the population and individual cell level, providing two complementary perspectives on the system. Difficulties and limitations in deducing cell migration rules from time-lapse imaging are discussed.     

癌细胞运动与迁移的分子机制

癌细胞运动和迁移的分子机制远较我们想象的复杂,癌细胞的运动和迁移性和接触性刺激相应答的细胞膜突起形成所启动的多步骤过程的结果.人们普遍想相信,片状伪足在驱动癌细胞迁移中起着主要作用,它通过附着在基底膜上而产生拉动细胞体向前的力量.近来的研究证明,切丝蛋白是癌细胞运动和迁移的一个重要调节因子, 切丝蛋白的局部激活可以诱导片状伪足的形成,并设定细胞运动方向.此外,成束蛋白.Arp2/3复合物、Cdc42、LIM激酶和黏着斑激酶常常协同调节癌细胞的运动和迁移.虽然调节癌细胞运动和迁移的信号通路和分子机制尚未完全阐明,但现有的资料清楚地表明,抑制癌细胞的迁移性将可能成为抑制恶性肿瘤生长和扩散的一个有用的策略.     

肿瘤细胞迁移特性及细胞迁移能力表征

细胞运动特征及其变化主要受细胞自身状况和微环境二方面的影响,细胞适应不同环境的运动响应方式存在差异,在二维培养基质上细胞迁移方式主要分为个体迁移和群体迁移,而在三维培养基质中其迁移模式主要为间充质迁移和阿米巴迁移.肿瘤细胞因其结构功能状况异常,在上述环境中的迁移特征出现不同程度的异化,其主要倾向为顽固、无目的和侵袭性的迁移运动.对细胞的迁移能力进行量化表征,有助于对细胞迁移本质的进一步认识.根据细胞培养环境的不同,分别介绍了二维和三维培养基质上细胞的不同迁移模式及肿瘤细胞的迁移运动特征,以及测量细胞迁移能力的体外测试手段和方法,并分析总结了这些方法的优缺点.     

A Mechanochemical Model of Cell Reorientation on Substrates under Cyclic Stretch

We report a theoretical study on the cyclic stretch-induced reorientation of spindle-shaped cells. Specifically, by taking into account the evolution of sub-cellular structures like the contractile stress fibers and adhesive receptor-ligand clusters, we develop a mechanochemical model to describe the dynamics of cell realignment in response to cyclically stretched substrates. Our main hypothesis is that cells tend to orient in the direction where the formation of stress fibers is energetically most favorable. We show that, when subjected to cyclic stretch, the final alignment of cells reflects the competition between the elevated force within stress fibers that accelerates their disassembly and the disruption of cell-substrate adhesion as well, and an effectively increased substrate rigidity that promotes more stable focal adhesions. Our model predictions are consistent with various observations like the substrate rigidity dependent formation of stable adhesions and the stretching frequency, as well as stretching amplitude, dependence of cell realignment. This theory also provides a simple explanation on the regulation of protein Rho in the formation of stretch-induced stress fibers in cells.     

A Dynamic Model of Chemoattractant-Induced Cell Migration

Cell migration refers to a directional cell movement in response to chemoattractant stimulation. In this work, we developed a cell-migration model by mimicking in vivo migration using optically manipulated chemoattractant-loaded microsources. The model facilitates a quantitative characterization of the relationship among the protrusion force, cell motility, and chemoattractant gradient for the first time (to our knowledge). We verified the correctness of the model using migrating leukemia cancer Jurkat cells. The results show that one can achieve the ideal migrating capacity by choosing the appropriate chemoattractant gradient and concentration at the leading edge of the cell.     

Continual Cell Deformation Induced via Attachment to Oriented Fibers Enhances Fibroblast Cell Migration

Fibroblast migration is critical to the wound healing process. In vivo, migration occurs on fibrillar substrates, and previous observations have shown that a significant time lag exists before the onset of granulation tissue. We therefore conducted a series of experiments to understand the impact of both fibrillar morphology and migration time. Substrate topography was first shown to have a profound influence. Fibroblasts preferentially attach to fibrillar surfaces, and orient their cytoplasm for maximal contact with the fiber edge. In the case of en-mass cell migration out of an agarose droplet, fibroblasts on flat surfaces emerged with an enhanced velocity, v = 52μm/h, that decreases to the single cell value, v = 28μm/h within 24 hours and remained constant for at least four days. Fibroblasts emerging on fibrillar surfaces emerged with the single cell velocity, which remained constant for the first 24 hours and then increased reaching a plateau with more than twice the initial velocity within the next three days. The focal adhesions were distributed uniformly in cells on flat surfaces, while on the fibrillar surface they were clustered along the cell periphery. Furthermore, the number of focal adhesions for the cells on the flat surfaces remained constant, while it decreased on the fibrillar surface during the next three days. The deformation of the cell nuclei was found to be 50% larger on the fiber surfaces for the first 24 hours. While the mean deformation remained constant on the flat surface, it increased for the next three days by 24% in cells on fibers. On the fourth day, large actin/myosin fibers formed in cells on fibrillar surfaces only and coincided with a change from the standard migration mechanism involving extension of lamellipodia, and retraction of the rear, to one involving strong contractions oriented along the fibers and centered about the nucleus.     

Describing Directional Cell Migration with a Characteristic Directionality Time

Many cell types can bias their direction of locomotion by coupling to external cues. Characteristics such as how fast a cell migrates and the directedness of its migration path can be quantified to provide metrics that determine which biochemical and biomechanical factors affect directional cell migration, and by how much. To be useful, these metrics must be reproducible from one experimental setting to another. However, most are not reproducible because their numerical values depend on technical parameters like sampling interval and measurement error. To address the need for a reproducible metric, we analytically derive a metric called directionality time, the minimum observation time required to identify motion as directionally biased. We show that the corresponding fit function is applicable to a variety of ergodic, directionally biased motions. A motion is ergodic when the underlying dynamical properties such as speed or directional bias do not change over time. Measuring the directionality of nonergodic motion is less straightforward but we also show how this class of motion can be analyzed. Simulations are used to show the robustness of directionality time measurements and its decoupling from measurement errors. As a practical example, we demonstrate the measurement of directionality time, step-by-step, on noisy, nonergodic trajectories of chemotactic neutrophils. Because of its inherent generality, directionality time ought to be useful for characterizing a broad range of motions including intracellular transport, cell motility, and animal migration.     

A Mathematical Model of Collective Cell Migration in a Three-Dimensional,Heterogeneous Environment

Cell migration is essential in animal development, homeostasis, and disease progression, but many questions remain unanswered about how this process is controlled. While many kinds of individual cell movements have been characterized, less effort has been directed towards understanding how clusters of cells migrate collectively through heterogeneous, cellular environments. To explore this, we have focused on the migration of the border cells during Drosophila egg development. In this case, a cluster of different cell types coalesce and traverse as a group between large cells, called nurse cells, in the center of the egg chamber. We have developed a new model for this collective cell migration based on the forces of adhesion, repulsion, migration and stochastic fluctuation to generate the movement of discrete cells. We implement the model using Identical Math Cells, or IMCs. IMCs can each represent one biological cell of the system, or can be aggregated using increased adhesion forces to model the dynamics of larger biological cells. The domain of interest is filled with IMCs, each assigned specific biophysical properties to mimic a diversity of cell types. Using this system, we have successfully simulated the migration of the border cell cluster through an environment filled with larger cells, which represent nurse cells. Interestingly, our simulations suggest that the forces utilized in this model are sufficient to produce behaviors of the cluster that are observed in vivo, such as rotation. Our framework was developed to capture a heterogeneous cell population, and our implementation strategy allows for diverse, but precise, initial position specification over a three- dimensional domain. Therefore, we believe that this model will be useful for not only examining aspects of Drosophila oogenesis, but also for modeling other two or three-dimensional systems that have multiple cell types and where investigating the forces between cells is of interest.     

An Oncogenic Protein Golgi Phosphoprotein 3 Up-regulates Cell Migration via Sialylation

Recently, the Golgi phosphoprotein 3 (GOLPH3) and its yeast homolog Vps74p have been characterized as essential for the Golgi localization of glycosyltransferase in yeast. GOLPH3 has been identified as a new oncogene that is commonly amplified in human cancers to modulate mammalian target of rapamycin signaling. However, the molecular mechanisms of the carcinogenic signaling pathway remain largely unclear. To investigate whether the expression of GOLPH3 was involved in the glycosylation processes in mammalian cells, and whether it affected cell behavior, we performed a loss-of-function study. Cell migration was suppressed in GOLPH3 knockdown (KD) cells, and the suppression was restored by a re-introduction of the GOLPH3 gene. HPLC and LC/MS analysis showed that the sialylation of N-glycans was specifically decreased in KD cells. The specific interaction between sialyltransferases and GOLPH3 was important for the sialylation. Furthermore, overexpression of α2,6-sialyltransferase-I rescued cell migration and cellular signaling, both of which were blocked in GOLPH3 knockdown cells. These results are the first direct demonstration of the role of GOLPH3 in N-glycosylation to regulate cell biological functions.     

WIP Regulates Persistence of Cell Migration and Ruffle Formation in Both Mesenchymal and Amoeboid Modes of Motility

The spatial distribution of signals downstream from receptor tyrosine kinases (RTKs) or G-protein coupled receptors (GPCR) regulates fundamental cellular processes that control cell migration and growth. Both pathways rely significantly on actin cytoskeleton reorganization mediated by nucleation-promoting factors such as the WASP-(Wiskott-Aldrich Syndrome Protein) family. WIP (WASP Interacting Protein) is essential for the formation of a class of polarised actin microdomain, namely dorsal ruffles, downstream of the RTK for PDGF (platelet-derived growth factor) but the underlying mechanism is poorly understood. Using lentivirally-reconstituted WIP-deficient murine fibroblasts we define the requirement for WIP interaction with N-WASP (neural WASP) and Nck for efficient dorsal ruffle formation and of WIP-Nck binding for fibroblast chemotaxis towards PDGF-AA. The formation of both circular dorsal ruffles in PDGF-AA-stimulated primary fibroblasts and lamellipodia in CXCL13-treated B lymphocytes are also compromised by WIP-deficiency. We provide data to show that a WIP-Nck signalling complex interacts with RTK to promote polarised actin remodelling in fibroblasts and provide the first evidence for WIP involvement in the control of migratory persistence in both mesenchymal (fibroblast) and amoeboid (B lymphocytes) motility.     

Tuning Cell Cycle Regulation with an Iron Key

Iron (Fe) is essential for cellular metabolism e.g., DNA synthesis and its depletion causes G1/S arrest and apoptosis. Considering this, Fe chelators have been shown to be effective anti-proliferative agents. In order to understand the anti-tumor activity of Fe chelators, the mechanisms responsible for G1/S arrest and apoptosis after Fe-depletion have been investigated. These studies reveal a multitude of cell cycle control molecules are regulated by Fe. These include p53, p27Kip1, cyclin D1 and cyclin-dependent kinase 2 (cdk2). Additionally, Fe-depletion up-regulates the mRNA levels of the cdk inhibitor, p21CIP1/WAF1, but paradoxically down-regulates its protein expression. This effect could contribute to the apoptosis observed after Fe-depletion. Iron-depletion also leads to proteasomal degradation of p21CIP1/WAF1 and cyclin D1 via an ubiquitin-independent pathway. This is in contrast to the mechanism in Fe-replete cells, where it occurs by ubiquitin-dependent proteasomal degradation. Up-regulation of p38 mitogen-activated protein kinase (MAPK) after Fe-depletion suggests another facet of cell cycle regulation responsible for inhibition of proliferation and apoptosis induction. Elucidation of the complex effects of Fe-depletion on the expression of cell cycle control molecules remains at its infancy. However, these processes are important to dissect for complete understanding of Fe-deficiency and the development of chelators for cancer treatment.     

A Cell-Based Model of Extracellular-Matrix-Guided Endothelial Cell Migration During Angiogenesis

Angiogenesis, the formation of new blood vessels sprouting from existing ones, occurs in several situations like wound healing, tissue remodeling, and near growing tumors. Under hypoxic conditions, tumor cells secrete growth factors, including VEGF. VEGF activates endothelial cells (ECs) in nearby vessels, leading to the migration of ECs out of the vessel and the formation of growing sprouts. A key process in angiogenesis is cellular self-organization, and previous modeling studies have identified mechanisms for producing networks and sprouts. Most theoretical studies of cellular self-organization during angiogenesis have ignored the interactions of ECs with the extra-cellular matrix (ECM), the jelly or hard materials that cells live in. Apart from providing structural support to cells, the ECM may play a key role in the coordination of cellular motility during angiogenesis. For example, by modifying the ECM, ECs can affect the motility of other ECs, long after they have left. Here, we present an explorative study of the cellular self-organization resulting from such ECM-coordinated cell migration. We show that a set of biologically-motivated, cell behavioral rules, including chemotaxis, haptotaxis, haptokinesis, and ECM-guided proliferation suffice for forming sprouts and branching vascular trees.     

改性PET材料编织物引导小鼠BMSC迁移模型的建立

目的:壳聚糖接枝改性的聚对苯二甲酸乙二醇酯(PET)纤维编织材料是一种具有良好组织相容性的新型生物材料,小鼠骨髓间充质干细胞(BMSC)为主要的人工韧带种子细胞.本研究通过建立一种可应用于生物材料上的细胞迁移模型,旨在观察BMSC在改性PET材料编织物上的迁移能力,探讨该材料作为人工韧带应用的可行性.方法:利用316L医用不锈钢自主设计制作细胞迁移模具,置于六孔板,在模具加样孔内接种小鼠BMSC,培养24h后撤出模具,分别继续培养48 h、72 h和96h;在证实模具可有效用于量化细胞迁移过程后,将不同线密度的PET材料编织物平铺于六孔板底,利用本模型观察BMSC在3000D组和5000D组经改性的PET材料编织物上的迁移能力,吉姆萨染色法计算不同时间点BMSC的迁移面积.结果:细胞接种24 h后撤出模具,可见六孔板底中央出现与模具底面大小相当的无细胞空白区,周围接种BMSC,随培养时间延长,BMSC逐渐由周围向中央区域迁移;在经改性的PET材料编织物上成功建立细胞迁移模型后,随培养时间增加,两组细胞迁移面积均逐渐增大,其中3000D组细胞迁移面积显著大于5000D组(P＜0.05).结论:利用316L医用不锈钢模具建立的细胞迁移模型能够应用于平铺编织物引导细胞迁移的基础研究,本模型可作为传统模型无法观察人工材料对细胞迁移可能影响的良好补充;3000D经改性的PET材料编织物的线密度较5000D更有利于小鼠BMSC在材料上的迁移和生长.     

Continuous Models for Cell Migration in Tissues and Applications to Cell Sorting via Differential Chemotaxis

Chemotaxis, the guided migration of cells in response to chemical gradients, is vital to a wide variety of biological processes, including patterning of the slime mold Dictyostelium, embryonic morphogenesis, wound healing, and tumor invasion. Continuous models of chemotaxis have been developed to describe many such systems, yet few have considered the movements within a heterogeneous tissue composed of multiple subpopulations. In this paper, a partial differential equation (PDE) model is developed to describe a tissue formed from two distinct chemotactic populations. For a “crowded” (negligible extracellular space) tissue, it is demonstrated that the model reduces to a simpler one-species system while for an “uncrowded” tissue, it captures both movement of the entire tissue (via cells attaching to/migrating within an extracellular substrate) and the within-tissue rearrangements of the separate cellular subpopulations. The model is applied to explore the sorting of a heterogeneous tissue, where it is shown that differential-chemotaxis not only generates classical sorting patterns previously seen via differential-adhesion, but also demonstrates new classes of behavior. These new phenomena include temporal dynamics consisting of a traveling wave composed of spatially sorted subpopulations reminiscent of Dictyostelium slugs.     

Mathematical Models for Cell Migration with Real-Time Cell Cycle Dynamics

The fluorescent ubiquitination-based cell cycle indicator, also known as FUCCI, allows the visualization of the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of two fluorescent probes, so that cells in the G1 phase fluoresce red and cells in the S/G2/M phase fluoresce green. FUCCI reveals real-time information about cell cycle dynamics of individual cells, and can be used to explore how the cell cycle relates to the location of individual cells, local cell density, and different cellular microenvironments. In particular, FUCCI is used in experimental studies examining cell migration, such as malignant invasion and wound healing. Here we present, to our knowledge, new mathematical models that can describe cell migration and cell cycle dynamics as indicated by FUCCI. The fundamental model describes the two cell cycle phases, G1 and S/G2/M, which FUCCI directly labels. The extended model includes a third phase, early S, which FUCCI indirectly labels. We present experimental data from scratch assays using FUCCI-transduced melanoma cells, and show that the predictions of spatial and temporal patterns of cell density in the experiments can be described by the fundamental model. We obtain numerical solutions of both the fundamental and extended models, which can take the form of traveling waves. These solutions are mathematically interesting because they are a combination of moving wavefronts and moving pulses. We derive and confirm a simple analytical expression for the minimum wave speed, as well as exploring how the wave speed depends on the spatial decay rate of the initial condition.