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.

The Ghrelin axis : does it have an appetite for cancer progression?

Ghrelin, the endogenous ligand for the GH secretagogue receptor (GHSR), is a peptide hormone with diverse physiological roles. Ghrelin regulates GH release, appetite and feeding, gut motility, and energy balance and also has roles in the cardiovascular, immune, and reproductive systems. Ghrelin and the GHSR are expressed in a wide range of normal and tumor tissues, and a fluorescein-labeled, truncated form of ghrelin is showing promise as a biomarker for prostate cancer. Plasma ghrelin levels are generally inversely related to body mass index and are unlikely to be useful as a biomarker for cancer, but may be useful as a marker for cancer cachexia. Some single nucleotide polymorphisms in the ghrelin and GHSR genes have shown associations with cancer risk; however, larger studies are required. Ghrelin regulates processes associated with cancer, including cell proliferation, apoptosis, cell migration, cell invasion, inflammation, and angiogenesis; however, the role of ghrelin in cancer is currently unclear. Ghrelin has predominantly antiinflammatory effects and may play a role in protecting against cancer-related inflammation. Ghrelin and its analogs show promise as treatments for cancer-related cachexia. Further studies using in vivo models are required to determine whether ghrelin has a role in cancer progression.

Irritable bowel syndrome : the role of gut neuroendocrine peptides

Irritable bowel syndrome (IBS) is a common chronic disorder with a prevalence ranging from 5 to 10 % of the world's population. This condition is characterised by abdominal discomfort or pain, altered bowel habits, and often bloating and abdominal distension. IBS reduces quality of life in the same degree of impairment as major chronic diseases such as congestive heart failure and diabetes and the economic burden on the health care system and society is high. Abnormalities have been reported in the neuroendocrine peptides/amines of the stomach, small- and large intestine in patients with IBS. These abnormalities would cause disturbances in digestion, gastrointestinal motility and visceral hypersensitivity, which have been reported in patients with IBS. These abnormalities seem to contribute to the symptom development and appear to play a central role in the pathogenesis of IBS. Neuroendocrine peptides/amines are potential tools in the treatment and diagnosis of IBS. In particular, the cell density of duodenal chromogranin A expressing cells appears to be a good histopathological marker for the diagnosis of IBS with high sensitivity and specificity.

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.

Sensitivity of edge detection methods for quantifying cell migration assays

Quantitative imaging methods to analyze cell migration assays are not standardized. Here we present a suite of two–dimensional barrier assays describing the collective spreading of an initially–confined population of 3T3 fibroblast cells. To quantify the motility rate we apply two different automatic image detection methods to locate the position of the leading edge of the spreading population after 24, 48 and 72 hours. These results are compared with a manual edge detection method where we systematically vary the detection threshold. Our results indicate that the observed spreading rates are very sensitive to the choice of image analysis tools and we show that a standard measure of cell migration can vary by as much as 25% for the same experimental images depending on the details of the image analysis tools. Our results imply that it is very difficult, if not impossible, to meaningfully compare previously published measures of cell migration since previous results have been obtained using different image analysis techniques and the details of these techniques are not always reported. Using a mathematical model, we provide a physical interpretation of our edge detection results. The physical interpretation is important since edge detection algorithms alone do not specify any physical measure, or physical definition, of the leading edge of the spreading population. Our modeling indicates that variations in the image threshold parameter correspond to a consistent variation in the local cell density. This means that varying the threshold parameter is equivalent to varying the location of the leading edge in the range of approximately 1–5% of the maximum cell density.

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.

Design and interpretation of cell trajectory assays

Cell trajectory data is often reported in the experimental cell biology literature to distinguish between different types of cell migration. Unfortunately, there is no accepted protocol for designing or interpreting such experiments and this makes it difficult to quantitatively compare different published data sets and to understand how changes in experimental design influence our ability to interpret different experiments. Here, we use an individual based mathematical model to simulate the key features of a cell trajectory experiment. This shows that our ability to correctly interpret trajectory data is extremely sensitive to the geometry and timing of the experiment, the degree of motility bias and the number of experimental replicates. We show that cell trajectory experiments produce data that is most reliable when the experiment is performed in a quasi 1D geometry with a large number of identically{prepared experiments conducted over a relatively short time interval rather than few trajectories recorded over particularly long time intervals.

A population genomics overview of the neuronal nitric oxide synthase (nNOS) gene and its relationship to migraine susceptibility

The ubiquitous chemical messenger molecule nitric oxide (NO) has been implicated in a diverse range of biological activities including neurotransmission, smooth muscle motility and mediation of nociception. Endogenous synthesis of NO by the neuronal isoform of the nitric oxide synthase gene family has an essential role within the central and peripheral nervous systems in addition to the autonomic innervation of cerebral blood vessels. To investigate the potential role of NO and more specifically the neuronal nitric oxide synthase (nNOS) gene in migraine susceptibility, we investigated two microsatellite repeat variants residing within the 5′ and 3′ regions of the nNOS gene. Population genomic evaluation of the two nNOS repeat variants indicated significant linkage disequilibrium between the two loci. Z-DNA conformational sequence structures within the 5′ region of the nNOS gene have the potential to enhance or repress gene promoter activity. We suggest that genetic analysis of this 5′ repeat variant is the more functional variant expressing gene wide information that could affect endogenous NO synthesis and potentially result in diseased states. However, no association with migraine (with or without aura) was seen in our extensive case-control cohort (n = 579 affected with matched controls), when both the 5′ and 3′ genetic variants were investigated.

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.

Chemotherapy-induced nausea and vomiting : a review to inform clinical practice

Chemotherapy-induced nausea and vomiting (CINV) is a common sideeffect of cytotoxic treatment and despite the widespread use of anti-emetic medication, it continues to affect a significant proportion of patients with up to 23% and 73% of chemotherapy patients still experiencing vomiting and nausea symptoms, respectively. This is of particular concern in oncology patients as nausea and vomiting may result in malnutrition, decreased quality of life and in extreme cases, treatment stoppage. Therefore, the primary aim of this paper was to inform clinicians on the current literature regarding CINV including its effect on the patient, its pathophysiology, and current treatment options. In addition, this review will also discuss the usage of dietetic interventions as well as less utilised, novel interventions such as oral ginger extracts in the treatment of CINV. In order to address these issues, a systematic literature search was conducted using Pubmed, CINAHL, MEDLINE, Embase, and Health Source (Nursing/Academic Edition). A key finding of this review was that common dietary strategies (e.g. eating slowly, avoiding fatty foods) seem to be solely based on professional opinion as no clinical trials investigating these strategies were identified. In contrast, ginger extracts were found to possess several viable mechanisms that interact with CINV progression including 5-HT3, Substance P and acetylcholine receptor antagonism; anti-inflammatory and antioxidant properties; and gastrointestinal motility and gastric emptying modulation. In conclusion, research investigating dietetic interventions in the management of CINV is sparse and requires further investigation while novel intervention such as ginger, possess multiple mechanisms that may benefit CINV management. This review will discuss the prevalence and significance of CINV, dietetic and novel treatment options, and provide implications for clinical practise and future research.

Ginger - mechanism of action in chemotherapy-induced nausea and vomiting: A review

Despite advances in anti-emetic therapy, chemotherapy-induced nausea and vomiting (CINV) still poses a significant burden to patients undergoing chemotherapy. Nausea, in particular, is still highly prevalent in this population. Ginger has been traditionally used as a folk remedy for gastrointestinal complaints and has been suggested as a viable adjuvant treatment for nausea and vomiting in the cancer context. Substantial research has revealed ginger to possess properties that could exert multiple beneficial effects on chemotherapy patients who experience nausea and vomiting. Bioactive compounds within the rhizome of ginger, particularly the gingerol and shogaol class of compounds, interact with several pathways that are directly implicated in CINV in addition to pathways that could play secondary roles by exacerbating symptoms. These properties include 5-HT3, substance P and acetylcholine receptor antagonism; anti-inflammatory properties; and modulation of cellular redox signalling, vasopressin release, gastrointestinal motility, and gastric emptying rate. This review outlines these proposed mechanisms by discussing the results of clinical, in vitro and animal studies both within the chemotherapy context and in other relevant fields. The evidence presented in this review indicates that ginger possesses multiple properties that could be beneficial in reducing chemotherapy-induced nausea and vomiting.

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.