Distinguishing between Directed and Undirected Cell Motility within an Invading Cell Population

Cell invasion is the basis of several fundamental biological systems including developmental morphogenesis and disease progression. Invasion processes involve combined cell motility and proliferation. Standard experimental approaches to characterize invasion systems focus on measuring population-level wavespeed data. However, continuum models which incorporate either directed or undirected motility both give rise to traveling wave solutions with a well-defined wavespeed in terms of the motility parameters. Therefore, such population-level models and experimental data cannot be used to determine whether the motility is directed or undirected. This is a major impediment limiting our ability to interpret experimental observations of cell invasion. We demonstrate how to overcome this difficulty using individual-level data and discrete models. This approach can be used to interpret and design time-lapse imaging data to determine whether the cell motility is directed or undirected. Making a distinction between directed and undirected motility has profound implications regarding our ability to design strategies to manage development and disease associated with cell invasion. The authors gratefully acknowledge the support from the Australian Research Council (ARC) Discovery Project DP0662804. MS is an ARC postdoctoral fellow, KL is an ARC professorial fellow.     

Looking inside an invasion wave of cells using continuum models: proliferation is the key

Recently, a suite of cell migration assays were conducted to investigate the migration of neural crest (NC) cells along the gut during the development of the enteric nervous system (ENS). The NC cells colonise the gastro-intestinal tract as a rostro-caudal wave. Local behaviour was shown to be controlled by position relative to the leading edge of the wavefront. The assays involved chick-quail grafting techniques allowing the total invading population to be considered as a two-species system. A two-species continuum model with logistic proliferation and a migration mechanism is developed here to simulate the chick-quail graft experiments and provide a means of looking at the processes occurring within the invasion wave. Five migration mechanisms are considered--linear diffusion, two cases of nonlinear diffusion, chemokinesis and chemotaxis. The model results agree with the experimental observations, regardless of the specific type of migration mechanism. The results show that NC cell invasion is driven by proliferation and cell motility at the leading edge of the wave. Furthermore, logistic proliferation exerts the dominant control on the system. This observation is confirmed by analysing some simplified invasion models. Once the basic experiments were mathematically replicated, the mathematical models were used in turn to make some predictions that were yet to be experimentally tested. This involved conducting a sensitivity analysis of the system by interrupting the proliferation and/or migration ability of the leading edge. Numerical results show that the system is stable against these changes. Of the three experiments suggested, one was carried out and the experimental results were concordant with the theoretical predictions. The outcome of two other suggested experiments are predicted and left for future experimental validation.     

Cell proliferation drives neural crest cell invasion of the intestine

A general mathematical model of cell invasion is developed and validated with an experimental system. The model incorporates two basic cell functions: non-directed (diffusive) motility and proliferation to a carrying capacity limit. The model is used here to investigate cell proliferation and motility differences along the axis of an invasion wave. Mathematical simulations yield surprising and counterintuitive predictions. In this general scenario, cells at the invasive front are proliferative and migrate into previously unoccupied tissues while those behind the front are essentially nonproliferative and do not directly migrate into unoccupied tissues. These differences are not innate to the cells, but are a function of proximity to uninvaded tissue. Therefore, proliferation at the invading front is the critical mechanism driving apparently directed invasion. An appropriate system to experimentally validate these predictions is the directional invasion and colonization of the gut by vagal neural crest cells that establish the enteric nervous system. An assay using gut organ culture with chick-quail grafting is used for this purpose. The experimental results are entirely concordant with the mathematical predictions. We conclude that proliferation at the wavefront is a key mechanism driving the invasive process. This has important implications not just for the neural crest, but for other invasion systems such as epidermal wound healing, carcinoma invasion and other developmental cell migrations.     

Cell sorting by differential cell motility: a model for pattern formation in Dictyostelium

In the slug stage of the cellular slime mold Dictyostelium discoideum, prespore cells and four types of prestalk cells show a well-defined spatial distribution in a migrating slug. We have developed a continuous mathematical model for the distribution pattern of these cell types based on the balance of force in individual cells. In the model, cell types are assumed to have different properties in cell motility, i.e. different motive force, the rate of resistance against cell movement, and diffusion coefficient. Analysis of the stationary solution of the model shows that combination of these parameters and slug speed determines the three-dimensional shape of a slug and cell distribution pattern within it. Based on experimental data of slug motive force and velocity measurements, appropriate sets of parameters were chosen so that the cell-type distribution at stationary state matches the distribution in real slugs. With these parameters, we performed numerical calculation of the model in two-dimensional space using a moving particle method. The results reproduced many of the basic features of slug morphogenesis, i.e. cell sorting, translocation of the prestalk region, elongation of the slug, and its steady migration.     

A Traveling Wave Model for Invasion by Precursor and Differentiated Cells

We develop and investigate a continuum model for invasion of a domain by cells that migrate, proliferate and differentiate. The model is applicable to neural crest cell invasion in the developing enteric nervous system, but is presented in general terms and is of broader applicability. Two cell populations are identified and modeled explicitly; a population of precursor cells that migrate and proliferate, and a population of differentiated cells derived from the precursors which have impaired migration and proliferation. The equation describing the precursor cells is based on Fisher’s equation with the addition of a carrying-capacity limited differentiation term. Two variations of the proliferation term are considered and compared. For most parameter values, the model admits a traveling wave solution for each population, both traveling at the same speed. The traveling wave solutions are investigated using perturbation analysis, phase plane methods, and numerical techniques. Analytical and numerical results suggest the existence of two wavespeed selection regimes. Regions of the parameter space are characterized according to existence, shape, and speed of traveling wave solutions. Our observations may be used in conjunction with experimental results to identify key parameters determining the invasion speed for a particular biological system. Furthermore, our results may assist experimentalists in identifying the resource that is limiting proliferation of precursor cells.     

Targeting of alpha(v) integrins interferes with FAK activation and smooth muscle cell migration and invasion

Aberrant migration of smooth muscle cells (SMCs) is a key feature of restenosis. Since extracellular matrix proteins and their receptors of the integrin family play a critical role in this process, it is instrumental to understand their contribution to cell migration and invasive motility of SMC on the molecular level. Therefore, we investigated the role of alpha(v)-containing integrins expressed by primary human coronary artery smooth muscle cells (hCASMCs) in vitronectin (VN)-initiated signaling events and cell migration. In hCASMC plated on VN, alpha(v)-containing integrins were localized at focal adhesion sites. Haptotactic stimulation through VN led to a dose-dependent increase in cell migration and concomitantly to enhanced tyrosine phosphorylation of focal adhesion kinase. Both events were completely blocked by a specific inhibitor of integrin alpha(v). Additionally, the integrin alpha(v) inhibitor abolished PDGF-BB-stimulated chemotactic migration. Confocal microscopy confirmed the increased tyrosine phosphorylation at VN-initiated focal contact sites in hCASMC, that was abolished upon alpha(v) inhibition. In vitro invasion of hCASMC was severely compromised in the presence of the integrin alpha(v) inhibitor paralleled by decreased levels of secreted matrix metalloprotease 2 (MMP-2). Together, integrin alpha(v) inhibition abrogates tyrosine phosphorylation at focal adhesion sites and diminishes MMP-2 secretion leading to reduced migration and invasion of hCASMCs.     

Quantitative studies of bacterial chemotaxis and microbial population dynamics

Although there is a long history of conjecture regarding the role and significance of bacterial chemotaxis in microbial ecology, only recently has a significant body of work appeared attempting to address this issue. The purpose of this paper is to provide a concise overview of this work, which combined mathematical modeling of bacterial population migration and experimental measurement of the model parameters with modeling of competitive microbial population dynamics in a nonmixed environment. Predictions from the population dynamics models, based on experimental estimates of the various motility and growth parameter values, are related to the small number of experimental observations available to date dealing with the effects of bacterial motility on competition in a nonmixed environment. Current results indicate that cell motility and chemotaxis properties can be as important to population dynamics as cell growth kinetic properties, so that greater attention to this aspect of microbial behavior is warranted in future studies of microbial ecology.     

Stimulation of cell surface plasminogen activation by membrane-bound melanotransferrin: a key phenomenon for cell invasion

The activation of plasminogen at the cell surface is a crucial step in cell migration and invasion. In the present study, the effect of membrane-bound melanotransferrin (mMTf), also known as human melanoma antigen p97, on cell surface plasminogen binding and activation was investigated by using Chinese Hamster Ovary (CHO) cells transfected with full-length melanotransferrin (MTf) cDNA and SK-MeL-28 melanoma cells. The expression of mMTf in CHO increased cell surface plasminogen binding by about 2-fold. In addition, application of the monoclonal antibody L235 against MTf as well as truncated, soluble MTf (sMTf) abolished plasminogen binding to MTf-transfected and SK-MeL-28 cells, indicating that mMTf is a potential cell surface plasminogen receptor. Moreover, mMTf expression in CHO cells stimulates plasminogen activation at the cell surface by about 2.5-fold. In addition to the induced binding and activation of plasminogen, cell motility, migration and invasion were about 3-fold higher in CHO cells expressing mMTf. Both monoclonal antibody L235 and truncated sMTf inhibited mMTf-stimulated CHO cell motility, migration and invasion. Overall, our results indicate a key role for mMTf in cell surface plasminogen binding and in activation processes involved during cell migration and invasion.     

Characterization of a synthetic peptide from type IV collagen that promotes melanoma cell adhesion, spreading, and motility

The adhesion and motility of tumor cells on basement membranes is a central consideration in tumor cell invasion and metastasis. Basement membrane type IV collagen directly promotes the adhesion and migration of various tumor cell types in vitro. Our previous studies demonstrated that tumor cells adhered and spread on surfaces coated with intact type IV collagen or either of the two major enzymatically purified domains of this protein. Only one of these major domains, the pepsin-generated major triple helical fragment, also supported tumor cell motility in vitro, implicating the involvement of the major triple helical region in type IV collagen-mediated tumor cell invasion in vivo. The present studies extend our previous observations using a synthetic peptide approach. A peptide, designated IV-H1, was derived from a continuous collagenous region of the major triple helical domain of the human alpha 1(IV) chain. This peptide, which has the sequence GVKGDKGNPGWPGAP, directly supported the adhesion, spreading, and motility of the highly metastatic K1735 M4 murine melanoma cell line, as well as the adhesion and spreading of other cell types, in a concentration-dependent manner in vitro. Furthermore, excess soluble peptide IV-H1, or polyclonal antibodies directed against peptide IV-H1, inhibited type IV collagen-mediated melanoma cell adhesion, spreading, and motility, but had no effect on these cellular responses to type I collagen. The full complement of cell adhesion, spreading, and motility promoting activities was dependent upon the preservation of the three prolyl residues in the peptide IV-H1 sequence. These studies indicate that peptide IV-H1 represents a cell-specific adhesion, spreading, and motility promoting domain that is active within the type IV collagen molecule.     

Protein kinase Cdelta signaling downstream of the EGF receptor mediates migration and invasiveness of prostate cancer cells

Tumor progression to the invasive phenotype occurs secondary to upregulated signaling from growth factor receptors that drive key cellular responses like proliferation, migration, and invasion. We hypothesized that Protein kinase Cdelta (PKCdelta)-mediated transcellular contractility is required for migration and invasion of prostate tumor cells. Two invasive human prostate cancer cell lines, DU145 cells overexpressing wildtype human EGFR (DU145WT) and PC3 cells, were studied. PKCdelta is overexpressed in these cells relative to normal prostate epithelial cells, and is activated downstream of EGFR leading to cell motility via modulation of myosin light chain activity. Abrogation of PKCdelta using Rottlerin and specific siRNA significantly decreased migration and invasion of both cell lines in vitro. Both PKCdelta and phosphorylated PKCdelta protein levels were higher in human prostate cancer tissue relative to normal donor prostate as assessed by Western blotting and immunohistochemistry. Thus, we conclude that PKCdelta inhibition can limit migration and invasion of prostate cancer cells.     

Collective dynamics of cancer cells confined in a confluent monolayer of normal cells

Tumorigenesis often involves specific changes in cell motility and intercellular adhesion. Understanding the collective cancer cell behavior associated with these specific changes could facilitate the detection of malignant characteristics during tumor growth and invasion. In this study, a cellular vertex model is developed to investigate the collective dynamics of a disk-like aggregate of cancer cells confined in a confluent monolayer of normal cells. The effects of intercellular adhesion and cell motility on tumor progression are examined. It is found that the stresses in both the cancer cells and the normal cells increase with tumor growth, resulting in a crowded environment and enhanced cell apoptosis. The intercellular adhesion between cancer cells and normal cells is revealed to promote tumor growth and invasion. The tumor invasion dynamics hinges on the motility of cancer cells. The cancer cells could orchestrate into different collective migration modes, e.g., directional migration and rotational oscillations, dictated by the competition between cell persistence and local coordination. Phase diagrams are established to reveal the competitive mechanisms. This work highlights the role of mechanics in regulating tumor growth and invasion.     

Reversing invasion in bistable systems

In this paper, we discuss a class of bistable reaction-diffusion systems used to model the competitive interaction of two species. The interactions are assumed to be of classic “Lotka–Volterra” type and we will consider a particular problem with relevance to applications in population dynamics: essentially, we study under what conditions the interplay of relative motility (diffusion) and competitive strength can cause waves of invasion to be halted and reversed. By establishing rigorous results concerning related degenerate and near-degenerate systems, we build a picture of the dependence of the wave speed on system parameters. Our results lead us to conjecture that this class of competition model has three “zones of response”. In the central zone, varying the motility can slow, halt and reverse invasion. However, in the two outer zones, the direction of invasion is independent of the relative motility and is entirely determined by the relative competitive strengths. Furthermore, we conjecture that for a large class of competition models of the type studied here, the wave speed is an increasing function of the relative motility.     

STE20-related kinase adaptor protein α (STRADα) regulates cell polarity and invasion through PAK1 signaling in LKB1-null cells

LKB1 is a Ser/Thr kinase, and its activity is regulated by the pseudokinase, STE20-related adaptor α (STRADα). The STRADα-LKB1 pathway plays critical roles in epithelial cell polarity, neuronal polarity, and cancer metastasis. Though much attention is given to the STRADα-LKB1 pathway, the function of STRADα itself, including a role outside of the LKB1 pathway, has not been well-studied. Data in Caenorhabditis elegans suggest that STRADα has an LKB1-independent role in regulating cell polarity, and therefore we tested the hypothesis that STRADα regulates cancer cell polarity and motility when wild-type LKB1 is absent. These results show that STRADα protein is reduced in LKB1-null cell lines (mutation or homozygous deletion) and this partial degradation occurs through the Hsp90-dependent proteasome pathway. The remaining STRADα participates in cell polarity and invasion, such that STRADα depletion results in misaligned lamellipodia, improper Golgi positioning, and reduced invasion. To probe the molecular basis of this defect, we show that STRADα associates in a complex with PAK1, and STRADα loss disrupts PAK1 activity via Thr(423) PAK1 phosphorylation. When STRADα is depleted, PAK1-induced invasion could not occur, suggesting that STRADα is necessary for PAK1 to drive motility. Furthermore, STRADα overexpression caused increased activity of the PAK1-activating protein, rac1, and a constitutively active rac1 mutant (Q61L) rescued pPAK(Thr423) and STRADα invasion defects. Taken together, these results show that a STRADα-rac1-PAK1 pathway regulates cell polarity and invasion in LKB1-null cells. It also suggests that while the function of LKB1 and STRADα undoubtedly overlap, they may also have mutually exclusive roles.     

Tumor suppressor KAI1 affects integrin αvβ3-mediated ovarian cancer cell adhesion, motility, and proliferation

The tetraspanin KAI1 had been described as a metastasis suppressor in many different cancer types, a function for which associations of KAI1 with adhesion and signaling receptors of the integrin superfamily likely play a role. In ovarian cancer, integrin αvβ3 correlates with tumor progression and its elevation in vitro provoked enhanced cell adhesion accompanied by significant increases in cell motility and proliferation in the presence of its major ligand vitronectin. In the present study, we characterized integrin αvβ3-mediated tumor biological effects as a function of cellular KAI1 restoration and proved for the first time that KAI1, besides its already known physical crosstalk with β1-integrins, also colocalizes with integrin αvβ3. Functionally, elevated KAI1 levels drastically increased integrin αvβ3/vitronectin-dependent ovarian cancer cell adhesion. Since an intermediate level of cell adhesive strength is required for optimal cell migration, we next studied ovarian cancer cell motility as a function of KAI1 restoration. By time lapse video microscopy, we found impaired integrin αvβ3/vitronectin-mediated cell migration most probably due to strongly enhanced cellular immobilization onto the adhesion-supporting matrix. Moreover, KAI1 reexpression significantly diminished cell proliferation. These data strongly indicate that KAI1 may suppress ovarian cancer progression by inhibiting integrin αvβ3/vitronectin-provoked tumor cell motility and proliferation as important hallmarks of the oncogenic process.     

Steady size distributions for cells in one-dimensional plant tissues

We consider a population of cells growing and dividing steadily without mortality, so that the total cell population is increasing, but the proportion of cells in any size class remains constant. The cell division process is non-deterministic in the sense that both the size at which a cell divides, and the proportions into which it divides, are described by probability density functions. We derive expressions for the steady size/birth-size distribution (and the corresponding size/age distribution) in terms of the cell birth-size distribution, in the particular case of one-dimensional growth in plant organs, where the relative growth rate is the same for all cells but may vary with time. This birth-size distribution is shown to be the principal eigenfunction of a Fredholm integral operator. Some special cases of the cell birth-size distribution are then solved using analytical techniques, and in more realistic examples, the eigen-function is found using a simple, generally applicable numerical iteration.     

A cell surface chondroitin sulfate proteoglycan, immunologically related to CD44, is involved in type I collagen-mediated melanoma cell motility and invasion

The metastatic spread of tumor cells occurs through a complex series of events, one of which involves the adhesion of tumor cells to extracellular matrix (ECM) components. Multiple interactions between cell surface receptors of an adherent tumor cell and the surrounding ECM contribute to cell motility and invasion. The current studies evaluate the role of a cell surface chondroitin sulfate proteoglycan (CSPG) in the adhesion, motility, and invasive behavior of a highly metastatic mouse melanoma cell line (K1735 M4) on type I collagen matrices. By blocking mouse melanoma cell production of CSPG with p-nitrophenyl beta-D-xylopyranoside (beta-D-xyloside), a compound that uncouples chondroitin sulfate from CSPG core protein synthesis, we observed a corresponding decrease in melanoma cell motility on type I collagen and invasive behavior into type I collagen gels. Melanoma cell motility on type I collagen could also be inhibited by removing cell surface chondroitin sulfate with chondroitinase. In contrast, type I collagen-mediated melanoma cell adhesion and spreading were not affected by either beta-D-xyloside or chondroitinase treatments. These results suggest that mouse melanoma CSPG is not a primary cell adhesion receptor, but may play a role in melanoma cell motility and invasion at the level of cellular translocation. Furthermore, purified mouse melanoma cell surface CSPG was shown, by affinity chromatography and in solid phase binding assays, to bind to type I collagen and this interaction was shown to be mediated, at least in part, by chondroitin sulfate. Additionally we have determined that mouse melanoma CSPG is composed of a 110-kD core protein that is recognized by anti-CD44 antibodies on Western blots. Collectively, our data suggests that interactions between a cell surface CD44-related CSPG and type I collagen in the ECM may play an important role in mouse melanoma cell motility and invasion, and that the chondroitin sulfate portion of the proteoglycan seems to be a critical component in mediating this effect.     

Increase in fluidity in the membrane of MT3 breast cancer cells correlates with enhanced cell adhesion in vitro and increased lung metastasis in NOD/SCID mice

To study whether membrane fluidity of tumor cells have an influence on metastasis, MT3 breast cancer cells harvested during exponential growth and under confluent conditions were compared. Electron paramagnetic resonance (EPR) data revealed that, in comparison to growing cells, confluent cells have a significant higher fluidity in their membrane related to a higher relative portion of disordered domains and a reduced portion of the most ordered domains. Further, sialyl Lewis X and/or A ligand-mediated adhesion of these cells was 2-fold enhanced. Confocal laser scanning microscopy further demonstrated a higher motility of ligands in the membrane of confluent cells, together with an accumulation of these ligands in distinct areas. Both facts are suggested to be responsible for an enhanced cell adhesion observed. Finally, an increased number of large distinct metastatic foci was registered in lungs of mice after i.v. inoculation of confluent cells. The results indicate that domain organization and fluidity of the cell membrane affect tumor cell adhesion and can have in this way also an impact on the malignancy of breast cancer cells.