Quantifying the roles of cell motility and cell proliferation in a circular barrier assay

Moving fronts of cells are essential features of embryonic development, wound repair and cancer metastasis. This paper describes a set of experiments to investigate the roles of random motility and proliferation in driving the spread of an initially confined cell population. The experiments include an analysis of cell spreading when proliferation was inhibited. Our data have been analysed using two mathematical models: a lattice-based discrete model and a related continuum partial differential equation model. We obtain independent estimates of the random motility parameter, D, and the intrinsic proliferation rate, λ, and we confirm that these estimates lead to accurate modelling predictions of the position of the leading edge of the moving front as well as the evolution of the cell density profiles. Previous work suggests that systems with a high λ/D ratio will be characterized by steep fronts, whereas systems with a low λ/D ratio will lead to shallow diffuse fronts and this is confirmed in the present study. Our results provide evidence that continuum models, based on the Fisher–Kolmogorov equation, are a reliable platform upon which we can interpret and predict such experimental observations.

Fractional models in space for diffusive processes in heterogeneous media with applications in cell motility and electrical signal propagation

This work addresses fundamental issues in the mathematical modelling of the diffusive motion of particles in biological and physiological settings. New mathematical results are proved and implemented in computer models for the colonisation of the embryonic gut by neural cells and the propagation of electrical waves in the heart, offering new insights into the relationships between structure and function. In particular, the thesis focuses on the use of non-local differential operators of non-integer order to capture the main features of diffusion processes occurring in complex spatial structures characterised by high levels of heterogeneity.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

In vitro and in vivo examination of the cell surface glycoprotein CDCP1

A number of reports have demonstrated the importance of the CUB domaincontaining protein 1 (CDCP1) in facilitating cancer progression in animal models and the potential of this protein as a prognostic marker in several malignancies. CDCP1 facilitates metastasis formation in animal models by negatively regulating anoikis, a type of apoptosis triggered by the loss of attachment signalling from cell-cell contacts or cell-extra cellular matrix (ECM) contacts. Due to the important role CDCP1 plays in cancer progression in model systems, it is considered a potential drug target to prevent the metastatic spread of cancers. CDCP1 is a highly glycosylated 836 amino acid cell surface protein. It has structural features potentially facilitating protein-protein interactions including 14 N-glycosylation sites, three CUB-like domains, 20 cysteine residues likely to be involved in disulfide bond formation and five intracellular tyrosine residues. CDCP1 interacts with a variety of proteins including Src family kinases (SFKs) and protein kinase C ä (PKCä). Efforts to understand the mechanisms regulating these interactions have largely focussed on three CDCP1 tyrosine residues Y734, Y743 and Y762. CDCP1-Y734 is the site where SFKs phosphorylate and bind to CDCP1 and mediate subsequent phosphorylation of CDCP1-Y743 and -Y762 which leads to binding of PKCä at CDCP1-Y762. The resulting trimeric protein complex of SFK•CDCP1•PKCä has been proposed to mediate an anti-apoptotic cell phenotype in vitro, and to promote metastasis in vivo. The effect of mutation of the three tyrosines on interactions of CDCP1 with SFKs and PKCä and the consequences on cell phenotype in vitro and in vivo have not been examined. CDCP1 has a predicted molecular weight of ~90 kDa but is usually detected as a protein which migrates at ~135 kDa by Western blot analysis due to its high degree of glycosylation. A low molecular weight form of CDCP1 (LMWCDCP1) of ~70 kDa has been found in a variety of cancer cell lines. The mechanisms leading to the generation of LMW-CDCP1 in vivo are not well understood but an involvement of proteases in this process has been proposed. Serine proteases including plasmin and trypsin are able to proteolytically process CDCP1. In addition, the recombinant protease domain of the serine protease matriptase is also able to cleave the recombinant extracellular portion of CDCP1. Whether matriptase is able to proteolytically process CDCP1 on the cell surface has not been examined. Importantly, proteolytic processing of CDCP1 by trypsin leads to phosphorylation of its cell surface-retained portion which suggests that this event leads to initiation of an intracellular signalling cascade. This project aimed to further examine the biology of CDCP1 with a main of focus on exploring the roles played by CDCP1 tyrosine residues. To achieve this HeLa cells stably expressing CDCP1 or the CDCP1 tyrosine mutants Y734F, Y743F and Y762F were generated. These cell lines were used to examine: • The roles of the tyrosine residues Y734, Y743 and Y762 in mediating interactions of CDCP1 with binding proteins and to examine the effect of the stable expression on HeLa cell morphology. • The ability of the serine protease matriptase to proteolytically process cell surface CDCP1 and to examine the consequences of this event on HeLa cell phenotype and cell signalling in vitro. • The importance of these residues in processes associated with cancer progression in vitro including adhesion, proliferation and migration. • The role of these residues on metastatic phenotype in vivo and the ability of a function-blocking anti-CDCP1 antibody to inhibit metastasis in the chicken embryo chorioallantoic membrane (CAM) assay. Interestingly, biochemical experiments carried out in this study revealed that mutation of certain CDCP1 tyrosine residues impacts on interactions of this protein with binding proteins. For example, binding of SFKs as well as PKCä to CDCP1 was markedly decreased in HeLa-CDCP1-Y734F cells, and binding of PKCä was also reduced in HeLa-CDCP1-Y762F cells. In contrast, HeLa-CDCP1-Y743F cells did not display altered interactions with CDCP1 binding proteins. Importantly, observed differences in interactions of CDCP1 with binding partners impacted on basal phosphorylation of CDCP1. It was found that HeLa-CDCP1, HeLa-CDCP1-Y743F and -Y762F displayed strong basal levels of CDCP1 phosphorylation. In contrast, HeLa-CDCP1-Y734F cells did not display CDCP1 phosphorylation but exhibited constitutive phosphorylation of focal adhesion kinase (FAK) at tyrosine 861. Significantly, subsequent investigations to examine this observation suggested that CDCP1-Y734 and FAK-Y861 are competitive substrates for SFK-mediated phosphorylation. It appeared that SFK-mediated phosphorylation of CDCP1- Y734 and FAK-Y861 is an equilibrium which shifts depending on the level of CDCP1 expression in HeLa cells. This suggests that the level of CDCP1 expression may act as a regulatory mechanism allowing cells to switch from a FAK-Y861 mediated pathway to a CDCP1-Y734 mediated pathway. This is the first time that a link between SFKs, CDCP1 and FAK has been demonstrated. One of the most interesting observations from this work was that CDCP1 altered HeLa cell morphology causing an elongated and fibroblastic-like appearance. Importantly, this morphological change depended on CDCP1- Y734. In addition, it was observed that this change in cell morphology was accompanied by increased phosphorylation of SFK-Y416. This suggests that interactions of SFKs with CDCP1-Y734 increases SFK activity since SFKY416 is critical in regulating kinase activity of these proteins. The essential role of SFKs in mediating CDCP1-induced HeLa cell morphological changes was demonstrated using the SFK-selective inhibitor SU6656. This inhibitor caused reversion of HeLa-CDCP1 cell morphology to an epithelial appearance characteristic of HeLa-vector cells. Significantly, in vitro studies revealed that certain CDCP1-mediated cell phenotypes are mediated by cellular pathways dependent on CDCP1 tyrosine residues whereas others are independent of these sites. For example, CDCP1 expression caused a marked increase in HeLa cell motility that was independent of CDCP1 tyrosine residues. In contrast, CDCP1- induced decrease in HeLa cell proliferation was most prominent in HeLa- CDCP1-Y762F cells, potentially indicating a role for this site in regulating proliferation in HeLa cells. Another cellular event which was identified to require phosphorylation of a particular CDCP1 tyrosine residue is adhesion to fibronectin. It was observed that the CDCP1-mediated strong decrease in adhesion to fibronectin is mostly restored in HeLa-CDCP1-Y743F cells. This suggests a possible role for CDCP1-Y743 in causing a CDCP1-mediated decrease in adhesion. Data from in vivo experiments indicated that HeLa-CDCP1-Y734F cells are more metastic than HeLa-CDCP1 cells in vivo. This indicates that interaction of CDCP1 with SFKs and PKCä may not be required for CDCP1-mediated metastasis formation of HeLa cells in vivo. The metastatic phenotype of these cells may be caused by signalling involving FAK since HeLa-CDCP1- Y734F cells are the only CDCP1 expressing cells displaying constitutive phosphorylation of FAK-Y861. HeLa-CDCP1-Y762F cells displayed a very low metastatic ability which suggests that this CDCP1 tyrosine residue is important in mediating a pro-metastatic phenotype in HeLa cells. More detailed exploration of cellular events occurring downstream of CDCP1-Y734 and -Y762 may provide important insights into the mechanisms altering the metastatic ability of CDCP1 expressing HeLa cells. Complementing the in vivo studies, anti-CDCP1 antibodies were employed to assess whether these antibodies are able to inhibit metastasis of CDCP1 and CDCP1 tyrosine mutants expressing HeLa cells. It was found that HeLa- CDCP1-Y734F cells were the only cell line which was markedly reduced in the ability to metastasise. In contrast, the ability of HeLa-CDCP1, HeLa- CDCP1-Y743F and -Y762F cells to metastasise in vivo was not inhibited. These data suggest a possible role of interactions of CDCP1 with SFKs, occurring at CDCP1-Y734, in preventing an anti-metastatic effect of anti- CDCP1 antibodies in vivo. The proposal that SFKs may play a role in regulating anti-metastatic effects of anti-CDCP1 antibodies was supported by another experiment where differences between HeLa-CDCP1 cells and CDCP1 expressing HeLa cells (HeLa-CDCP1-S) from collaborators at the Scripps Research Institute were examined. It was found that HeLa-CDCP1-S cells express different SFKs than CDCP1 expressing HeLa cells generated for this study. This is important since HeLa-CDCP1-S cells can be inhibited in their metastatic ability using anti-CDCP1 antibodies in vivo. Importantly, these data suggest that further examinations of the roles of SFKs in facilitating anti-metastatic effects of anti-CDCP1 antibodies may give insights into how CDCP1 can be blocked to prevent metastasis in vivo. This project also explored the ability of the serine protease matriptase to proteolytically process cell surface localised CDCP1 because it is unknown whether matriptase can cleave cell surface CDCP1 as it has been reported for other proteases such as trypsin and plasmin. Furthermore, the consequences of matriptase-mediated proteolysis on cell phenotype in vitro and cell signalling were examined since recent reports suggested that proteolysis of CDCP1 leads to its phosphorylation and may initiate cell signalling and consequently alter cell phenotype. It was found that matriptase is able to proteolytically process cell surface CDCP1 at low nanomolar concentrations which suggests that cleavage of CDCP1 by matriptase may facilitate the generation of LWM-CDCP1 in vivo. To examine whether matriptase-mediated proteolysis induced cell signalling anti-phospho Erk 1/2 Western blot analysis was performed as this pathway has previously been examined to study signalling in response to proteolytic processing of cell surface proteins. It was found that matriptase-mediated proteolysis in CDCP1 expressing HeLa cells initiated intracellular signalling via Erk 1/2. Interestingly, this increase in phosphorylation of Erk 1/2 was also observed in HeLa-vector cells. This suggested that initiation of cell signalling via Erk 1/2 phosphorylation as a result of matriptase-mediated proteolysis occurs by pathways independent of CDCP1. Subsequent investigations measuring the flux of free calcium ions and by using a protease-activated receptor 2 (PAR2) agonist peptide confirmed this hypothesis. These data suggested that matriptase-mediated proteolysis results in cell signalling via a pathway induced by the activation of PAR2 rather than by CDCP1. This indicates that induction of cell signalling in HeLa cells as a consequence of matriptase-mediated proteolysis occurs via signalling pathways which do not involve phosphorylation of Erk 1/2. Consequently, it appears that future attempts should focus on the examination of cellular pathways other than Erk 1/2 to elucidate cell signalling initiated by matriptase-mediated proteolytic processing of CDCP1. The data presented in this thesis has explored in vitro and in vivo aspects of the biology of CDCP1. The observations summarised above will permit the design of future studies to more precisely determine the role of CDCP1 and its binding partners in processes relevant to cancer progression. This may contribute to further defining CDCP1 as a target for cancer treatment.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Lattice-free models of cell invasion : discrete simulations and travelling waves

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.

Platelet-derived endothelial cell growth factor (thymidine phosphorylase) expression in lung cancer

Platelet-derived endothelial cell growth factor/thymidine phosphorylase (PD-ECGF/TP) is an enzyme with angiogenic and cell motility properties. Moreover, it is involved in the transformation of fluoropyrimidines into active cytotoxic metabolites, In the present study, the expression of PD-ECGF in normal lung and lung cancer was immunohistochemically evaluated using the P-GF.44C monoclonal antibody. Alveolar and tumoural macrophages mere invariably stained and mere used as an internal control for assessment of the staining. Alveolar epithelium was always negative, whilst bronchiolar epithelium showed occasional positive reactivity. Normal lung and tumour endothelium was occasionally positive, Positive staining in more than 50 per cent of cells was observed in 23/71 squamous carcinomas (32 per cent), 16/38 (42 per cent) adenocarcinomas, and 2/6 (33 per cent) adenosquamous carcinomas. Differentiated areas and areas of squamous metaplasia mere more strongly positive than other tumour areas. All 22 small cell carcinomas and one carcinoid tumour were negative. The present study provides a baseline for future studies in non-small cell lung cancer to correlate PD-ECGF expression with tumour vascularization, prognosis, and response to chemotherapy.

Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies

Background The expansion of cell colonies is driven by a delicate balance of several mechanisms including cell motility, cell-to-cell adhesion and cell proliferation. New approaches that can be used to independently identify and quantify the role of each mechanism will help us understand how each mechanism contributes to the expansion process. Standard mathematical modelling approaches to describe such cell colony expansion typically neglect cell-to-cell adhesion, despite the fact that cell-to-cell adhesion is thought to play an important role. Results We use a combined experimental and mathematical modelling approach to determine the cell diffusivity, D, cell-to-cell adhesion strength, q, and cell proliferation rate, ?, in an expanding colony of MM127 melanoma cells. Using a circular barrier assay, we extract several types of experimental data and use a mathematical model to independently estimate D, q and ?. In our first set of experiments, we suppress cell proliferation and analyse three different types of data to estimate D and q. We find that standard types of data, such as the area enclosed by the leading edge of the expanding colony and more detailed cell density profiles throughout the expanding colony, does not provide sufficient information to uniquely identify D and q. We find that additional data relating to the degree of cell-to-cell clustering is required to provide independent estimates of q, and in turn D. In our second set of experiments, where proliferation is not suppressed, we use data describing temporal changes in cell density to determine the cell proliferation rate. In summary, we find that our experiments are best described using the range D = 161 - 243 ?m2 hour-1, q = 0.3 - 0.5 (low to moderate strength) and ? = 0.0305 - 0.0398 hour-1, and with these parameters we can accurately predict the temporal variations in the spatial extent and cell density profile throughout the expanding melanoma cell colony. Conclusions Our systematic approach to identify the cell diffusivity, cell-to-cell adhesion strength and cell proliferation rate highlights the importance of integrating multiple types of data to accurately quantify the factors influencing the spatial expansion of melanoma cell colonies.

CD151 is associated with prostate cancer cell invasion and lymphangiogenesis in vivo

CD151, a member of the tetraspanin family, is associated with regulation of migration of normal and tumour cells via cell surface microdomain formation. CD151 was found in our laboratory to have a prognostic value in prostate cancer and is a promoter of prostate cancer migration and invasion. These roles involve association with integrins on both cell-cell and cell-stroma levels. Furthermore, CD151 plays a role in endothelial cell motility. CD151 expression was examined in three commonly used prostate cancer cell lines. We investigated CD151 expression, angiogenesis (microvessel density; MVD) and lymphangiogenesis (lymphatic vessel density; LVD) in an orthotopic xenograft model of prostate cancer in matched tumours from primary and secondary sites. CD151 was found to be heterogeneously expressed across different prostate cancer cell lines and the levels of CD151 expression were significantly higher in the highly tumorigenic, androgen-insensitive cells PC-3 and DU-145 compared to the androgen-sensitive cell line LNCaP (P<0.05). The majority of in vivo xenografts developed pelvic lymph node metastases. Importantly, primary tumours that developed metastasis had significantly higher CD151 expression and MVD compared to those which did not develop metastasis (P<0.05). We identified, for the first time, that CD151 expression is associated with LVD in prostate cancer. These findings underscore the potential role of CD151 and angiogenesis in the metastatic potential of prostate cancer. CD151 has a prognostic value in this mouse model of prostate cancer and may play a role in lymphangiogenesis. CD151 is likely an important regulator of cancer cell communication with the surrounding microenvironment.

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

Many cell types form clumps or aggregates when cultured in vitro through a variety of mechanisms including rapid cell proliferation, chemotaxis, or direct cell-to-cell contact. In this paper we develop an agent-based model to explore the formation of aggregates in cultures where cells are initially distributed uniformly, at random, on a two-dimensional substrate. Our model includes unbiased random cell motion, together with two mechanisms which can produce cell aggregates: (i) rapid cell proliferation, and (ii) a biased cell motility mechanism where cells can sense other cells within a finite range, and will tend to move towards areas with higher numbers of cells. We then introduce a pair-correlation function which allows us to quantify aspects of the spatial patterns produced by our agent-based model. In particular, these pair-correlation functions are able to detect differences between domains populated uniformly at random (i.e. at the exclusion complete spatial randomness (ECSR) state) and those where the proliferation and biased motion rules have been employed - even when such differences are not obvious to the naked eye. The pair-correlation function can also detect the emergence of a characteristic inter-aggregate distance which occurs when the biased motion mechanism is dominant, and is not observed when cell proliferation is the main mechanism of aggregate formation. This suggests that applying the pair-correlation function to experimental images of cell aggregates may provide information about the mechanism associated with observed aggregates. As a proof of concept, we perform such analysis for images of cancer cell aggregates, which are known to be associated with rapid proliferation. The results of our analysis are consistent with the predictions of the proliferation-based simulations, which supports the potential usefulness of pair correlation functions for providing insight into the mechanisms of aggregate formation.

Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry?

Cells respond to various biochemical and physical cues during wound–healing and tumour progression. In vitro assays used to study these processes are typically conducted in one particular geometry and it is unclear how the assay geometry affects the capacity of cell populations to spread, or whether the relevant mechanisms, such as cell motility and cell proliferation, are somehow sensitive to the geometry of the assay. In this work we use a circular barrier assay to characterise the spreading of cell populations in two different geometries. Assay 1 describes a tumour–like geometry where a cell population spreads outwards into an open space. Assay 2 describes a wound–like geometry where a cell population spreads inwards to close a void. We use a combination of discrete and continuum mathematical models and automated image processing methods to obtain independent estimates of the effective cell diffusivity, D, and the effective cell proliferation rate, λ. Using our parameterised mathematical model we confirm that our estimates of D and λ accurately predict the time–evolution of the location of the leading edge and the cell density profiles for both assay 1 and assay 2. Our work suggests that the effective cell diffusivity is up to 50% lower for assay 2 compared to assay 1, whereas the effective cell proliferation rate is up to 30% lower for assay 2 compared to assay 1.