Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularisation

We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.

Cell death control : the interplay of apoptosis and autophagy in the pathogenicity of sclerotinia sclerotiorum

Programmed cell death is characterized by a cascade of tightly controlled events that culminate in the orchestrated death of the cell. In multicellular organisms autophagy and apoptosis are recognized as two principal means by which these genetically determined cell deaths occur. During plant-microbe interactions cell death programs can mediate both resistant and susceptible events. Via oxalic acid (OA), the necrotrophic phytopathogen Sclerotinia sclerotiorum hijacks host pathways and induces cell death in host plant tissue resulting in hallmark apoptotic features in a time and dose dependent manner. OA-deficient mutants are non-pathogenic and trigger a restricted cell death phenotype in the host that unexpectedly exhibits markers associated with the plant hypersensitive response including callose deposition and a pronounced oxidative burst, suggesting the plant can recognize and in this case respond, defensively. The details of this plant directed restrictive cell death associated with OA deficient mutants is the focus of this work. Using a combination of electron and fluorescence microscopy, chemical effectors and reverse genetics, we show that this restricted cell death is autophagic. Inhibition of autophagy rescued the non-pathogenic mutant phenotype. These findings indicate that autophagy is a defense response in this necrotrophic fungus/plant interaction and suggest a novel function associated with OA; namely, the suppression of autophagy. These data suggest that not all cell deaths are equivalent, and though programmed cell death occurs in both situations, the outcome is predicated on who is in control of the cell death machinery. Based on our data, we suggest that it is not cell death per se that dictates the outcome of certain plant-microbe interactions, but the manner by which cell death occurs that is crucial.

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.

Steps toward the validation of the Trendelenburg Test : the effect of experimentally reduced hip abductor muscle function on frontal plane mechanics

Objective: To investigate the validity of the Trendelenburg test (TT) using an ultrasound-guided nerve block (UNB) of the superior gluteal nerve and determine whether the reduction in hip abductor muscle (HABD) strength would result in the theorized mechanical compensatory strategies measured during the TT. Design: Quasi-experimental. Setting: Hospital. Participants: Convenience sample of 9 healthy men. Only participants with no current or previous injury to the lumbar spine, pelvis, or lower extremities, and no previous surgeries were included. Interventions: Ultrasound-guided nerve block. Main Outcome Measures: Hip abductor muscle strength (percent body weight [%BW]), contralateral pelvic drop (cPD), change in contralateral pelvic drop (Delta cPD), ipsilateral hip adduction, and ipsilateral trunk sway (TRUNK) measured in degrees. Results: The median age and weight of the participants were 31 years (interquartile range [IQR], 22-32 years) and 73 kg (IQR, 67-81 kg), respectively. An average 52% reduction of HABD strength (z = 2.36, P = 0.02) resulted after the UNB. No differences were found in cPD or Delta cPD (z = 0.01, P = 0.99, z = 20.67, P = 0.49, respectively). Individual changes in biomechanics showed no consistency between participants and nonsystematic changes across the group. One participant demonstrated the mechanical compensations described by Trendelenburg. Conclusions: The TT should not be used as a screening measure for HABD strength in populations demonstrating strength greater than 30% BW but should be reserved for use with populations with marked HABD weakness. Clinical Relevance: This study presents data regarding a critical level of HABD strength required to support the pelvis during the TT.

Steps towards the validation of the Trendelenburg test : The effect of experimentally reduced hip abductor muscle function on frontal plane mechanics

Introduction: The Trendelenburg Test (TT) is used to assess the functional strength of the hip abductor muscles (HABD), their ability to control frontal plane motion of the pelvis, and the ability of the lumbopelvic complex to transfer load into single leg stance. Rationale: Although a standard method to perform the test has been described for use within clinical populations, no study has directly investigated Trendelenburg’s hypotheses. Purpose: To investigate the validity of the TT using an ultrasound guided nerve block (UNB) of the superior gluteal nerve and determine whether the reduction in HABD strength would result in the theorized mechanical compensatory strategies measured during the TT. Methods: Quasi-experimental design using a convenience sample of nine healthy males. Only subjects with no current or previous injury to the lumbar spine, pelvis, or lower extremities, and no previous surgeries were included. Force dynamometry was used to evaluation HABD strength (%BW). 2D mechanics were used to evaluate contralateral pelvic drop (cMPD), change in contralateral pelvic drop (∆cMPD), ipsilateral hip adduction (iHADD) and ipsilateral trunk sway (TRUNK) measured in degrees (°). All measures were collected prior to and following a UNB on the superior gluteal nerve performed by an interventional radiologist. Results: Subjects’ age was median 31yrs (IQR:22-32yrs); and weight was median 73kg (IQR:67-81kg). An average 52% reduction of HABD strength (z=2.36,p=0.02) resulted following the UNB. No differences were found in cMPD or ∆cMPD (z=0.01,p= 0.99, z=-0.67,p=0.49). Individual changes in biomechanics show no consistency between subjects and non-systematic changes across the group. One subject demonstrated the mechanical compensations described by Trendelenburg. Discussion: The TT should not be used as screening measure for HABD strength in populations demonstrating strength greater than 30%BW but reserved for use with populations with marked HABD weakness. Importance: This study presents data regarding a critical level of HABD strength required to support the pelvis during the TT.

Anisotropic damage mechanics as a novel approach to improve pre-and post-failure borehole stability analysis

Anisotropic damage distribution and evolution have a profound effect on borehole stress concentrations. Damage evolution is an irreversible process that is not adequately described within classical equilibrium thermodynamics. Therefore, we propose a constitutive model, based on non-equilibrium thermodynamics, that accounts for anisotropic damage distribution, anisotropic damage threshold and anisotropic damage evolution. We implemented this constitutive model numerically, using the finite element method, to calculate stress–strain curves and borehole stresses. The resulting stress–strain curves are distinctively different from linear elastic-brittle and linear elastic-ideal plastic constitutive models and realistically model experimental responses of brittle rocks. We show that the onset of damage evolution leads to an inhomogeneous redistribution of material properties and stresses along the borehole wall. The classical linear elastic-brittle approach to borehole stability analysis systematically overestimates the stress concentrations on the borehole wall, because dissipative strain-softening is underestimated. The proposed damage mechanics approach explicitly models dissipative behaviour and leads to non-conservative mud window estimations. Furthermore, anisotropic rocks with preferential planes of failure, like shales, can be addressed with our model.

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.

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.