The mechanical rigidity of the extracellular matrix regulates the structure, motility, and proliferation of glioma cells

Glioblastoma multiforme (GBM) is a malignant astrocytoma of the central nervous system associated with a median survival time of 15 months, even with aggressive therapy. This rapid progression is due in part to diffuse infiltration of single tumor cells into the brain parenchyma, which is thought to involve aberrant interactions between tumor cells and the extracellular matrix (ECM). Here, we test the hypothesis that mechanical cues from the ECM contribute to key tumor cell properties relevant to invasion. We cultured a series of glioma cell lines (U373-MG, U87-MG, U251-MG, SNB19, C6) on fibronectin-coated polymeric ECM substrates of defined mechanical rigidity and investigated the role of ECM rigidity in regulating tumor cell structure, migration, and proliferation. On highly rigid ECMs, tumor cells spread extensively, form prominent stress fibers and mature focal adhesions, and migrate rapidly. As ECM rigidity is lowered to values comparable with normal brain tissue, tumor cells appear rounded and fail to productively migrate. Remarkably, cell proliferation is also strongly regulated by ECM rigidity, with cells dividing much more rapidly on rigid than on compliant ECMs. Pharmacologic inhibition of nonmuscle myosin II–based contractility blunts this rigidity-sensitivity and rescues cell motility on highly compliant substrates. Collectively, our results provide support for a novel model in which ECM rigidity provides a transformative, microenvironmental cue that acts through actomyosin contractility to regulate the invasive properties of GBM tumor cells.

Involvement of focal adhesion kinase in inhibition of motility of human breast cancer cells by sphingosine 1-phosphate

Sphingosine 1-phosphate (SPP), a bioactive sphingolipid metabolite, inhibits chemoinvasiveness of the aggressive, estrogen-independent MDA-MB-231 human breast cancer cell line. As in many other cell types, SPP stimulated proliferation of MDA-MB-231 cells, albeit to a lesser extent. Treatment of MDA-MB-231 cells with SPP had no significant effect on their adhesiveness to Matrigel, and only high concentrations of SPP partially inhibited matrix metalloproteinase-2 activation induced by Con A. However, SPP at a concentration that strongly inhibited invasiveness also markedly reduced chemotactic motility. To investigate the molecular mechanisms by which SPP interferes with cell motility, we examined tyrosine phosphorylation of focal adhesion kinase (FAK) and paxillin, which are important for organization of focal adhesions and cell motility. SPP rapidly increased tyrosine phosphorylation of FAK and paxillin and of the paxillin-associated protein Crk. Overexpression of FAK and kinase-defective FAK in MDA-MB-231 cells resulted in a slight increase in motility without affecting the inhibitory effect of SPP, whereas expression of FAK with a mutation of the major autophosphorylation site (F397) abolished the inhibitory effect of SPP on cell motility. In contrast, the phosphoinositide 3'-kinase inhibitor, wortmannin, inhibited chemotactic motility in both vector and FAK-F397- transfected cells. Our results suggest that autophosphorylation of FAK on Y397 may play an important role in SPP signaling leading to decreased cell motility.

Heregulin regulates the actin cytoskeleton and promotes invasive properties in breast cancer cell lines

The metastatic process requires changes in tumor cell adhesion properties, cell motility and remodeling of the extracellular matrix. The erbB2 proto-oncogene is overexpressed in approximately 30% of breast cancers and is a major prognostic parameter when present in invasive disease. A ligand for the erbB2 receptor has not yet been identified but it can be activated by heterodimerization with heregulin (HRG)-stimulated erbB3 and erbB4 receptors. The HRGs are a family of polypeptide growth factors that have been shown to play a role in embryogenesis, tumor formation, growth and differentiation of breast cancer cells. The erbB3 and erbB4 receptors are involved in transregulation of erbB2 signaling. The work presented here suggests biological roles for HRG including regulation of the actin cytoskeleton and induction of motility and invasion in breast cancer cells. HRG-expressing breast cancer cell lines are characterized by low erbB receptor levels and a high invasive and metastatic index, while those which overexpress erbB2 demonstrate minimal invasive potential in vitro and are non-tumorigenic in vivo. Treatment of the highly tumorigenic and metastatic HRG-expressing breast cancer cell line MDA-MB-231 with an HRG-neutralizing antibody significantly inhibited proliferation in culture and motility in the Boyden chamber assay. Addition of exogenous HRG to non-invasive erbB2 overexpressing cells (SKBr-3) at low concentrations induced formation of pseudopodia, enhanced phagocytic activity and increased chemomigration and invasion in the Boyden chamber assay. The specificity of the chemomigration response to HRG is demonstrated by inhibition with the anti-HRG neutralizing antibody. These results suggest that either HRG can act as an autocrine or paracrine ligand to promote the invasive behavior of breast cancer cells in vitro or thus may enhance the metastatic process in vivo.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.

Mathematical models for collective cell spreading

Collective cell spreading is frequently observed in development, tissue repair and disease progression. Mathematical modelling used in conjunction with experimental investigation can provide key insights into the mechanisms driving the spread of cell populations. In this study, we investigated how experimental and modelling frameworks can be used to identify several key features underlying collective cell spreading. In particular, we were able to independently quantify the roles of cell motility and cell proliferation in a spreading cell population, and investigate how these roles are influenced by factors such as the initial cell density, type of cell population and the assay geometry.

The cross-talk of LDL-cholesterol with cell migration: Insights from the Niemann Pick Type C1 mutation

Cholesterol is considered indispensible for the recruitment and functioning of integrins in focal adhesions for cell migration. However, the physiological cholesterol pools that control integrin trafficking and focal adhesion assembly remain unclear. Using Niemann Pick Type C1 (NPC) mutant cells, which accumulate Low Density lipoprotein (LDL)-derived cholesterol in late endosomes (LE), several recent studies indicate that LDL-cholesterol has multiple roles in regulating focal adhesion dynamics. Firstly, targeting of endocytosed LDL-cholesterol from LE to focal adhesions controls their formation at the leading edge of migrating cells. Other newly emerging literature suggests that this may be coupled to vesicular transport of integrins, Src kinase and metalloproteases from the LE compartment to focal adhesions. Secondly, our recent work identified LDL-cholesterol as a key factor that determines the distribution and ability of several Soluble NSF Attachment Protein (SNAP) Receptor (SNARE) proteins, key players in vesicle transport, to control integrin trafficking to the cell surface and extracellular matrix (ECM) secretion. Collectively, dietary, genetic and pathological changes in cholesterol metabolism may link with efficiency and speed of integrin and ECM cell surface delivery in metastatic cancer cells. This commentary will summarize how direct and indirect pathways enable LDL-cholesterol to modulate cell motility.

Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model

Background: Standard methods for quantifying IncuCyte ZOOM™ assays involve measurements that quantify how rapidly the initially-vacant area becomes re-colonised with cells as a function of time. Unfortunately, these measurements give no insight into the details of the cellular-level mechanisms acting to close the initially-vacant area. We provide an alternative method enabling us to quantify the role of cell motility and cell proliferation separately. To achieve this we calibrate standard data available from IncuCyte ZOOM™ images to the solution of the Fisher-Kolmogorov model. Results: The Fisher-Kolmogorov model is a reaction-diffusion equation that has been used to describe collective cell spreading driven by cell migration, characterised by a cell diffusivity, D, and carrying capacity limited proliferation with proliferation rate, λ, and carrying capacity density, K. By analysing temporal changes in cell density in several subregions located well-behind the initial position of the leading edge we estimate λ and K. Given these estimates, we then apply automatic leading edge detection algorithms to the images produced by the IncuCyte ZOOM™ assay and match this data with a numerical solution of the Fisher-Kolmogorov equation to provide an estimate of D. We demonstrate this method by applying it to interpret a suite of IncuCyte ZOOM™ assays using PC-3 prostate cancer cells and obtain estimates of D, λ and K. Comparing estimates of D, λ and K for a control assay with estimates of D, λ and K for assays where epidermal growth factor (EGF) is applied in varying concentrations confirms that EGF enhances the rate of scratch closure and that this stimulation is driven by an increase in D and λ, whereas K is relatively unaffected by EGF. Conclusions: Our approach for estimating D, λ and K from an IncuCyte ZOOM™ assay provides more detail about cellular-level behaviour than standard methods for analysing these assays. In particular, our approach can be used to quantify the balance of cell migration and cell proliferation and, as we demonstrate, allow us to quantify how the addition of growth factors affects these processes individually.

Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

A model for mesoscale patterns in motile populations

Experimental observations of cell migration often describe the presence of mesoscale patterns within motile cell populations. These patterns can take the form of cells moving as aggregates or in chain-like formation. Here we present a discrete model capable of producing mesoscale patterns. These patterns are formed by biasing movements to favor a particular configuration of agent–agent attachments using a binding function f(K), where K is the scaled local coordination number. This discrete model is related to a nonlinear diffusion equation, where we relate the nonlinear diffusivity D(C) to the binding function f. The nonlinear diffusion equation supports a range of solutions which can be either smooth or discontinuous. Aggregation patterns can be produced with the discrete model, and we show that there is a transition between the presence and absence of aggregation depending on the sign of D(C). A combination of simulation and analysis shows that both the existence of mesoscale patterns and the validity of the continuum model depend on the form of f. Our results suggest that there may be no formal continuum description of a motile system with strong mesoscale patterns.

Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

The association of single nucleotide polymorphisms with endometrial cancer risk and prognosis

Endometrial cancer is one of the most common female diseases in developed nations and is the most commonly diagnosed gynaecological cancer in Australia. The disease is commonly classified by histology: endometrioid or non-endometrioid endometrial cancer. While non-endometrioid endometrial cancers are accepted to be high-grade, aggressive cancers, endometrioid cancers (comprising 80% of all endometrial cancers diagnosed) generally carry a favourable patient prognosis. However, endometrioid endometrial cancer patients endure significant morbidity due to surgery and radiotherapy used for disease treatment, and patients with recurrent disease have a 5-year survival rate of less than 50%. Genetic analysis of women with endometrial cancer could uncover novel markers associated with disease risk and/or prognosis, which could then be used to identify women at high risk and for the use of specialised treatments. Proteases are widely accepted to play an important role in the development and progression of cancer. This PhD project hypothesised that SNPs from two protease gene families, the matrix metalloproteases (MMPs, including their tissue inhibitors, TIMPs) and the tissue kallikrein-related peptidases (KLKs) would be associated with endometrial cancer susceptibility and/or prognosis. In the first part of this study, optimisation of the genotyping techniques was performed. Results from previously published endometrial cancer genetic association studies were attempted to be validated in a large, multicentre replication set (maximum cases n = 2,888, controls n = 4,483, 3 studies). The rs11224561 progesterone receptor SNP (PGR, A/G) was observed to be associated with increased endometrial cancer risk (per A allele OR 1.31, 95% CI 1.12-1.53; p-trend = 0.001), a result which was initially reported among a Chinese sample set. Previously reported associations for the remaining 8 SNPs investigated for this section of the PhD study were not confirmed, thereby reinforcing the importance of validation of genetic association studies. To examine the effect of SNPs from the MMP and KLK families on endometrial cancer risk, we selected the most significantly associated MMP and KLK SNPs from genome-wide association study analysis (GWAS) to be genotyped in the GWAS replication set (cases n = 4,725, controls n = 9,803, 13 studies). The significance of the MMP24 rs932562 SNP was unchanged after incorporation of the stage 2 samples (Stage 1 per allele OR 1.18, p = 0.002; Combined Stage 1 and 2 OR 1.09, p = 0.002). The rs10426 SNP, located 3' to KLK10 was predicted by bioinformatic analysis to effect miRNA binding. This SNP was observed in the GWAS stage 1 result to exhibit a recessive effect on endometrial cancer risk, a result which was not validated in the stage 2 sample set (Stage 1 OR 1.44, p = 0.007; Combined Stage 1 and 2 OR 1.14, p = 0.08). Investigation of the regions imputed surrounding the MMP, TIMP and KLK genes did not reveal any significant targets for further analysis. Analysis of the case data from the endometrial cancer GWAS to identify genetic variation associated with cancer grade did not reveal SNPs from the MMP, TIMP or KLK genes to be statistically significant. However, the representation of SNPs from the MMP, TIMP and KLK families by the GWAS genotyping platform used in this PhD project was examined and observed to be very low, with the genetic variation of four genes (MMP23A, MMP23B, MMP28 and TIMP1) not captured at all by this technique. This suggests that comprehensive candidate gene association studies will be required to assess the role of SNPs from these genes with endometrial cancer risk and prognosis. Meta-analysis of gene expression microarray datasets curated as part of this PhD study identified a number of MMP, TIMP and KLK genes to display differential expression by endometrial cancer status (MMP2, MMP10, MMP11, MMP13, MMP19, MMP25 and KLK1) and histology (MMP2, MMP11, MMP12, MMP26, MMP28, TIMP2, TIMP3, KLK6, KLK7, KLK11 and KLK12). In light of these findings these genes should be prioritised for future targeted genetic association studies. Two SNPs located 43.5 Mb apart on chromosome 15 were observed from the GWAS analysis to be associated with increased endometrial cancer grade, results that were validated in silico in two independent datasets. One of these SNPs, rs8035725 is located in the 5' untranslated region of a MYC promoter binding protein DENND4A (Stage 1 OR 1.15, p = 9.85 x 10P -5 P, combined Stage 1 and in silico validation OR 1.13, p = 5.24 x 10P -6 P). This SNP has previously been reported to alter the expression of PTPLAD1, a gene involved in the synthesis of very long fatty acid chains and in the Rac1 signaling pathway. Meta-analysis of gene expression microarray data found PTPLAD1 to display increased expression in the aggressive non-endometrioid histology compared with endometrioid endometrial cancer, suggesting that the causal SNP underlying the observed genetic association may influence expression of this gene. Neither rs8035725 nor significant SNPs identified by imputation were predicted bioinformatically to affect transcription factor binding sites, indicating that further studies are required to assess their potential effect on other regulatory elements. The other grade- associated SNP, rs6606792, is located upstream of an inferred pseudogene, ELMO2P1 (Stage 1 OR 1.12, p = 5 x 10P -5 P; combined Stage 1 and in silico validation OR 1.09, p = 3.56 x 10P -5 P). Imputation of the ±1 Mb region surrounding this SNP revealed a cluster of significantly associated variants which are predicted to abolish various transcription factor binding sites, and would be expected to decrease gene expression. ELMO2P1 was not included on the microarray platforms collected for this PhD, and so its expression could not be investigated. However, the high sequence homology of ELMO2P1 with ELMO2, a gene important to cell motility, indicates that ELMO2 could be the parent gene for ELMO2P1 and as such, ELMO2P1 could function to regulate the expression of ELMO2. Increased expression of ELMO2 was seen to be associated with increasing endometrial cancer grade, as well as with aggressive endometrial cancer histological subtypes by microarray meta-analysis. Thus, it is hypothesised that SNPs in linkage disequilibrium with rs6606792 decrease the transcription of ELMO2P1, reducing the regulatory effect of ELMO2P1 on ELMO2 expression. Consequently, ELMO2 expression is increased, cell motility is enhanced leading to an aggressive endometrial cancer phenotype. In summary, these findings have identified several areas of research for further study. The results presented in this thesis provide evidence that a SNP in PGR is associated with risk of developing endometrial cancer. This PhD study also reports two independent loci on chromosome 15 to be associated with increased endometrial cancer grade, and furthermore, genes associated with these SNPs to be differentially expressed according in aggressive subtypes and/or by grade. The studies reported in this thesis support the need for comprehensive SNP association studies on prioritised MMP, TIMP and KLK genes in large sample sets. Until these studies are performed, the role of MMP, TIMP and KLK genetic variation remains unclear. Overall, this PhD study has contributed to the understanding of genetic variation involvement in endometrial cancer susceptibility and prognosis. Importantly, the genetic regions highlighted in this study could lead to the identification of novel gene targets to better understand the biology of endometrial cancer and also aid in the development of therapeutics directed at treating this disease.

Do pioneer cells exist?

Most mathematical models of collective cell spreading make the standard assumption that the cell diffusivity and cell proliferation rate are constants that do not vary across the cell population. Here we present a combined experimental and mathematical modeling study which aims to investigate how differences in the cell diffusivity and cell proliferation rate amongst a population of cells can impact the collective behavior of the population. We present data from a three–dimensional transwell migration assay which suggests that the cell diffusivity of some groups of cells within the population can be as much as three times higher than the cell diffusivity of other groups of cells within the population. Using this information, we explore the consequences of explicitly representing this variability in a mathematical model of a scratch assay where we treat the total population of cells as two, possibly distinct, subpopulations. Our results show that when we make the standard assumption that all cells within the population behave identically we observe the formation of moving fronts of cells where both subpopulations are well–mixed and indistinguishable. In contrast, when we consider the same system where the two subpopulations are distinct, we observe a very different outcome where the spreading population becomes spatially organized with the more motile subpopulation dominating at the leading edge while the less motile subpopulation is practically absent from the leading edge. These modeling predictions are consistent with previous experimental observations and suggest that standard mathematical approaches, where we treat the cell diffusivity and cell proliferation rate as constants, might not be appropriate.

Lattice-free descriptions of collective motion with crowding and adhesion

Cell-to-cell adhesion is an important aspect of malignant spreading that is often observed in images from the experimental cell biology literature. Since cell-to-cell adhesion plays an important role in controlling the movement of individual malignant cells, it is likely that cell-to-cell adhesion also influences the spatial spreading of populations of such cells. Therefore, it is important for us to develop biologically realistic simulation tools that can mimic the key features of such collective spreading processes to improve our understanding of how cell-to-cell adhesion influences the spreading of cell populations. Previous models of collective cell spreading with adhesion have used lattice-based random walk frameworks which may lead to unrealistic results, since the agents in the random walk simulations always move across an artificial underlying lattice structure. This is particularly problematic in high-density regions where it is clear that agents in the random walk align along the underlying lattice, whereas no such regular alignment is ever observed experimentally. To address these limitations, we present a lattice-free model of collective cell migration that explicitly incorporates crowding and adhesion. We derive a partial differential equation description of the discrete process and show that averaged simulation results compare very well with numerical solutions of the partial differential equation.

PITX2 and non-canonical Wnt pathway interaction in metastatic prostate cancer

The non-canonical Wnt pathway, a regulator of cellular motility and morphology, is increasingly implicated in cancer metastasis. In a quantitative PCR array analysis of 84 Wnt pathway associated genes, both non-canonical and canonical pathways were activated in primary and metastatic tumors relative to normal prostate. Expression of the Wnt target gene PITX2 in a prostate cancer (PCa) bone metastasis was strikingly elevated over normal prostate (over 2,000-fold) and primary prostate cancer (over 200-fold). The elevation of PITX2 protein was also evident on tissue microarrays, with strong PITX2 immunostaining in PCa skeletal and, to a lesser degree, soft tissue metastases. PITX2 is associated with cell migration during normal tissue morphogenesis. In our studies, overexpression of individual PITX2A/B/C isoforms stimulated PC-3 PCa cell motility, with the PITX2A isoform imparting a specific motility advantage in the presence of non-canonical Wnt5a stimulation. Furthermore, PITX2 specific shRNA inhibited PC-3 cell migration toward bone cell derived chemoattractant. These experimental results support a pivotal role of PITX2A and non-canonical Wnt signaling in enhancement of PCa cell motility, suggest PITX2 involvement in homing of PCa to the skeleton, and are consistent with a role for PITX2 in PCa metastasis to soft and bone tissues. Our findings, which significantly expand previous evidence that PITX2 is associated with risk of PCa biochemical recurrence, indicate that variation in PITX2 expression accompanies and may promote prostate tumor progression and metastasis.

How much information can be obtained from tracking the position of the leading edge in a scratch assay?

Moving cell fronts are an essential feature of wound healing, development and disease. The rate at which a cell front moves is driven, in part, by the cell motility, quantified in terms of the cell diffusivity $D$, and the cell proliferation rate �$\lambda$. Scratch assays are a commonly-reported procedure used to investigate the motion of cell fronts where an initial cell monolayer is scratched and the motion of the front is monitored over a short period of time, often less than 24 hours. The simplest way of quantifying a scratch assay is to monitor the progression of the leading edge. Leading edge data is very convenient since, unlike other methods, it is nondestructive and does not require labeling, tracking or counting individual cells amongst the population. In this work we study short time leading edge data in a scratch assay using a discrete mathematical model and automated image analysis with the aim of investigating whether such data allows us to reliably identify $D$ and $\lambda$�. Using a naıve calibration approach where we simply scan the relevant region of the ($D$;$\lambda$�) parameter space, we show that there are many choices of $D$ and $\lambda$� for which our model produces indistinguishable short time leading edge data. Therefore, without due care, it is impossible to estimate $D$ and $\lambda$� from this kind of data. To address this, we present a modified approach accounting for the fact that cell motility occurs over a much shorter time scale than proliferation. Using this information we divide the duration of the experiment into two periods, and we estimate $D$ using data from the first period, while we estimate �$\lambda$ using data from the second period. We confirm the accuracy of our approach using in silico data and a new set of in vitro data, which shows that our method recovers estimates of $D$ and $\lamdba$� that are consistent with previously-reported values except that that our approach is fast, inexpensive, nondestructive and avoids the need for cell labeling and cell counting.