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.

An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell

We report on an accurate numerical scheme for the evolution of an inviscid bubble in radial Hele-Shaw flow, where the nonlinear boundary effects of surface tension and kinetic undercooling are included on the bubble-fluid interface. As well as demonstrating the onset of the Saffman-Taylor instability for growing bubbles, the numerical method is used to show the effect of the boundary conditions on the separation (pinch-off) of a contracting bubble into multiple bubbles, and the existence of multiple possible asymptotic bubble shapes in the extinction limit. The numerical scheme also allows for the accurate computation of bubbles which pinch off very close to the theoretical extinction time, raising the possibility of computing solutions for the evolution of bubbles with non-generic extinction behaviour.

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.

SECIS-binding protein 2 promotes cell survival by protecting against oxidative stress

Reactive oxygen species (ROS) are a primary cause of cellular damage that leads to cell death. In cells, protection from ROS-induced damage and maintenance of the redox balance is mediated to a large extent by selenoproteins, a distinct family of proteins that contain selenium in form of selenocysteine (Sec) within their active site. Incorporation of Sec requires the Sec-insertion sequence element (SECIS) in the 3'-untranslated region of selenoproteins mRNAs and the SECIS-binding protein 2 (SBP2). Previous studies have shown that SBP2 is required for the Sec-incorporation mechanism; however, additional roles of SBP2 in the cell have remained undefined. We herein show that depletion of SBP2 by using antisense oligonucleotides (ASOs) causes oxidative stress and induction of caspase- and cytochrome c-dependent apoptosis. Cells depleted of SBP2 have increased levels of ROS, which lead to cellular stress manifested as 8-oxo-7,8-dihydroguanine (8-oxo-dG) DNA lesions, stress granules, and lipid peroxidation. Small-molecule antioxidants N-acetylcysteine, glutathione, and α-tocopherol only marginally reduced ROS and were unable to rescue cells fully from apoptosis, indicating that apoptosis might be directly mediated by selenoproteins. Our results demonstrate that SBP2 is required for protection against ROS-induced cellular damage and cell survival. Antioxid. Redox Signal. 12, 797–808.

Incorporation of exogenous RGD peptide and inter-species blending as strategies for enhancing human corneal limbal epithelial cell growth on Bombyx mori silk fibroin membranes

While fibroin isolated from the cocoons of domesticated silkworm Bombyx mori supports growth of human corneal limbal epithelial (HLE) cells, the mechanism of cell attachment remains unclear. In the present study we sought to enhance the attachment of HLE cells to membranes of Bombyx mori silk fibroin (BMSF) through surface functionalization with an arginine-glycine-aspartic acid (RGD)-containing peptide. Moreover, we have examined the response of HLE cells to BMSF when blended with the fibroin produced by a wild silkworm, Antheraea pernyi, which is known to contain RGD sequences within its primary structure. A procedure to isolate A. pernyi silk fibroin (APSF) from the cocoons was established, and blends of the two fibroins were prepared at five different BMSF/APSF ratios. In another experiment, BMSF surface was modified by binding chemically the GRGDSPC peptide using a water-soluble carbodiimide. Primary HLE were grown in the absence of serum on membranes made of BMSF, APSF, and their blends, as well as on RGD-modified BMSF. There was no statistically significant enhancing effect on the cell attachment due to the RGD presence. This suggests that the adhesion through RGD ligands may have a complex mechanism, and the investigated strategies are of limited value unless the factors contributing to this mechanism become better known.

Numerical solution of an optimal control model of dendritic cell treatment of a growing tumour

A new optimal control model of the interactions between a growing tumour and the host immune system along with an immunotherapy treatment strategy is presented. The model is based on an ordinary differential equation model of interactions between the growing tu- mour and the natural killer, cytotoxic T lymphocyte and dendritic cells of the host immune system, extended through the addition of a control function representing the application of a dendritic cell treat- ment to the system. The numerical solution of this model, obtained from a multi species Runge–Kutta forward-backward sweep scheme, is described. We investigate the effects of varying the maximum al- lowed amount of dendritic cell vaccine administered to the system and find that control of the tumour cell population is best effected via a high initial vaccine level, followed by reduced treatment and finally cessation of treatment. We also found that increasing the strength of the dendritic cell vaccine causes an increase in the number of natural killer cells and lymphocytes, which in turn reduces the growth of the tumour.

Humanised xenograft models of bone metastasis revisited : novel insights into species-specific mechanisms of cancer cell osteotropism

The determinants and key mechanisms of cancer cell osteotropism have not been identified, mainly due to the lack of reproducible animal models representing the biological, genetic and clinical features seen in humans. An ideal model should be capable of recapitulating as many steps of the metastatic cascade as possible, thus facilitating the development of prognostic markers and novel therapeutic strategies. Most animal models of bone metastasis still have to be derived experimentally as most syngeneic and transgeneic approaches do not provide a robust skeletal phenotype and do not recapitulate the biological processes seen in humans. The xenotransplantation of human cancer cells or tumour tissue into immunocompromised murine hosts provides the possibility to simulate early and late stages of the human disease. Human bone or tissue-engineered human bone constructs can be implanted into the animal to recapitulate more subtle, species-specific aspects of the mutual interaction between human cancer cells and the human bone microenvironment. Moreover, the replication of the entire "organ" bone makes it possible to analyse the interaction between cancer cells and the haematopoietic niche and to confer at least a partial human immunity to the murine host. This process of humanisation is facilitated by novel immunocompromised mouse strains that allow a high engraftment rate of human cells or tissue. These humanised xenograft models provide an important research tool to study human biological processes of bone metastasis.

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.

Improved earthwork allocation planning for fuel consumption and emissions reduction in linear infrastructure construction – case study data

This document provides data for the case study presented in our recent earthwork planning papers. Some results are also provided in a graphical format using Excel.

Cutaneous markers of photo-damage and risk of basal cell carcinoma of the skin : a meta-analysis

BACKGROUND: Epidemiologic research has demonstrated that cutaneous markers of photo-damage are associated with risk of basal cell carcinoma (BCC). However there has been no previous attempt to calculate pooled risk estimates. METHODS: We conducted a systematic review and meta-analysis after extracting relevant studies published up to January 2013 from five electronic databases. Eligible studies were those that permitted quantitative assessment of the association between histologically-confirmed BCC and actinic keratoses, solar elastosis, solar lentigines, or telangiectasia. RESULTS: Seven eligible studies were identified and summary odds ratios (OR) were calculated using both random and quality effects models. Having more than ten actinic keratoses was most strongly associated with BCC, conferring up to a 5-fold increase in risk (OR: 4.97; 95% CI: 3.26, 7.58). Other factors, including solar elastosis, solar lentigines, and telangiectasia had weaker but positive associations with BCC with ORs around 1.5. CONCLUSIONS: Markers of chronic photo-damage are positively associated with BCC. The presence of actinic keratoses was the most strongly associated with BCC of the markers examined. IMPACT: This work highlights the relatively modest association between markers of chronic ultraviolet exposure and BCC.

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.

Development of an ultra-thin fibroin membrane for RPE cell transplantation

Purpose: One of the challenges associated with cell-based therapies for repairing the retina is the development of suitable materials on which to grow and transplant retinal cells. Using the ARPE-19 cell line, we have previously demonstrated the feasibility of growing RPE-derived cells on membranes prepared from the silk protein fibroin. The present study was aimed at developing a porous, ultra-thin fibroin membrane that might better support development of apical-basal polarity in culture, and to extend this work to primary cultures of human RPE cells. Methods: Ultra-thin fibroin membranes were prepared using a highly polished casting table coated with Topas® (a cyclic olefin copolymer) and a 1:0.03 aqueous solution of fibroin and PEO (Mv 900 000 g/mol). Following drying, the membranes were water annealed to make them water-stable, washed in water to remove PEO, sterilised by treatment with 95% ethanol, and washed extensively in saline. Primary cultures containing human RPE cells were established from donor posterior eye cups and maintained in DMEM/F12 medium supplemented with 10% fetal bovine serum and antibiotics. First passage cultures were seeded onto fibroin membranes pre-coated with vitronectin and grown for 6 weeks in medium supplemented with 1% serum. Comparative cultures were established on porous 1.0 µm pore PET membrane (Millipore) and using ARPE-19 cells. Results: The fibroin membranes displayed an average thickness of 3 µm and contained numerous dimples/pore-like structures of up to 3-5 µm in diameter. The primary cultures predominantly contained pigmented epithelial cells, but mesenchymal cells (presumed fibroblasts) were also often present. Passaged cultures appeared to attach equally well to either fibroin or PET membranes. Over time cells on either material adopted a more cobblestoned morphology. Conclusions: Progress has been made towards developing a porous ultra-thin fibroin membrane that supports cultivation of RPE cells. Further studies are required to determine the degree of membrane permeability and RPE polarity.

Serine protease inhibition and mitochondrial dysfunction associated with cisplatin resistance in human tumor cell lines: targets for therapy

Indicators of mitochondrial function were studied in two different cell culture models of cis-diamminedichloroplatinum-II (CDDP) resistance: the intrinsically resistant human ovarian cancer cell line CI-80-13S, and resistant clones (HeLa-S1a and HeLa-S1b) generated by stable expression of the serine protease inhibitor—plasminogen activator inhibitor type-2 (PAI-2), in the human cervical cancer cell line HeLa. In both models, CDDP resistance was associated with sensitivity to killing by adriamycin, etoposide, auranofin, bis[1,2-bis(diphenylphosphino)ethane]gold(I) chloride {[Au(DPPE)2]Cl}, CdCl2 and the mitochondrial inhibitors rhodamine-123 (Rhl23), dequalinium chloride (DeCH), tetraphenylphosphonium (TPP), and ethidium bromide (EtBr) and with lower constitutive levels of ATP. Unlike the HeLa clones, CI-80-13S cells were additionally sensitive to chloramphenicol, 1-methyl-4-phenylpyridinium ion (MPP+), rotenone, thenoyltrifluoroacetone (TTFA), and antimycin A, and showed poor reduction of 1-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide (MTT), suggesting a deficiency in NADH dehydrogenase and/or succinate dehydrogenase activities. Total platinum uptake and DNA-bound platinum were slightly lower in CI-80-13S than in sensitive cells. The HeLa-S1a and HeLa-S1b clones, on the other hand, showed poor reduction of triphenyltetrazolium chloride (TTC), indicative of low cytochrome c oxidase activity. Total platinum uptake by HeLa-S1a was similar to HeLa, but DNA-bound platinum was much lower than for the parent cell line. The mitochondria of CI-80-13S and HeLa-S1a showed altered morphology and were fewer in number than those of JAM and HeLa. In both models, CDDP resistance was associated with less platinum accumulation and with mitochondrial and membrane defects, brought about one case with expression of a protease inhibitor which is implicated in tumor progression. Such markers may identify tumors suitable for treatment with gold phosphine complexes or other mitochondrial inhibitors.