Chemotaxis and chemokinesis of human prostate tumor cell lines in response to human prostate stromal cell secretory proteins containing a nerve growth factor-like protein

The migration of three human prostate tumor epithelial cell lines (TSU-pr1, PC-3, DU-145) in response to secreted protein from a human prostate stromal cell line was investigated by using the modified blind-well Boyden chamber assay. Migrated cells were quantified by spectrophotometrically measuring the concentration of crystal violet stain extracted from their nuclei. Cell number was correlated linearly with the concentration of extracted crystal violet stain. All three tumor cell lines showed intrinsic migratory ability in the absence of chemoattractants, such that approximately 1-7% of plated cells migrated across the filter of the Boyden chambers during a 5-h incubation period. Prostate tumor cell migration was significantly enhanced (3-13-fold) in response to stromal cell secretory protein in a dose-dependent manner, whereas bovine serum albumin had no effect on stimulating tumor cell migration. Immunoprecipitation of the stromal cell secreted protein with a nerve growth factor antibody partially and significantly reduced its stimulatory activity for tumor cell migration. A Zigmond-Hirsch matrix assay of tumor cell migration in response to various concentration gradients of stromal cell secreted protein demonstrated both chemotaxis and chemokinesis by all three cell lines. These results are consistent with the stromal cell secretory protein stimulation of chemokinetic tumor cell migration through the capsule of the prostate. Outside of the prostate gland metastasis of tumor cells may occur by chemotaxis to preferential sites containing chemoattractants similar to or related to maintenance factors that can substitute for components of stromal cell secretory protein.

Supernatants of acquired immunodeficiency syndrome-related Kaposi's sarcoma cells induce endothelial cell chemotaxis and invasiveness

Kaposi's sarcoma (KS) in general, and acquired immunodeficiency syndrome-related KS (AIDS-KS) in particular, is a highly invasive and intensely angiogenic neoplasm of unknown cellular origin. We have recently established AIDS-KS cells in long term culture and reported the development of KS-like lesions in nude mice inoculated with these cells. Here, we have examined the in vitro invasiveness of basement membrane by AIDS-KS cells, as well as the effect(s) of their supernatants on the migration and invasiveness of human vascular endothelial cells. AIDS-KS cells were highly invasive in the Boyden chamber invasion assay and formed invasive, branching colonies in a 3-dimensional gel (Matrigel). Normal endothelial cells form tube-like structures on Matrigel. AIDS-KS cell-conditioned media induced endothelial cells to form invasive clusters in addition to tubes. KS-cell-conditioned media, when placed in the lower compartment of the Boyden chamber, stimulated the migration of human and bovine vascular endothelial cells across filters coated with either small amounts of collagen IV (chemotaxis) or a Matrigel barrier (invasion). Basic fibroblast growth factor could also induce endothelial cell chemotaxis and invasion in these assays. However, when antibodies to basic fibroblast growth factor were used the invasive activity induced by the AIDS-KS-cell-conditioned media was only marginally inhibited, suggesting that the large quantities of basic fibroblast growth factor-like material released by the AIDS-KS cells are not the main mediators of this effect. Specific inhibitors of laminin and collagenase IV action, which represent critical determinants of basement membrane invasion, blocked the invasiveness of the AIDS-KS cell-activated endothelial cells in these assays. These data indicate that KS cells appear to be of smooth muscle origin but secrete a potent inducer of endothelial cell chemotaxis and invasiveness which could be responsible for angiogenesis and the resulting highly vascularized lesions. These assays appear to be a model to study the invasive spread and angiogenic capacity of human AIDS-related KS and should prove useful in the identification of molecular mediators and potential inhibitors of neoplastic neovascularization.

Directional persistence and the optimality of run-and-tumble chemotaxis

E. coli does chemotaxis by performing a biased random walk composed of alternating periods of swimming (runs) and reorientations (tumbles). Tumbles are typically modelled as complete directional randomisations but it is known that in wild type E. coli, successive run directions are actually weakly correlated, with a mean directional difference of ∼63°. We recently presented a model of the evolution of chemotactic swimming strategies in bacteria which is able to quantitatively reproduce the emergence of this correlation. The agreement between model and experiments suggests that directional persistence may serve some function, a hypothesis supported by the results of an earlier model. Here we investigate the effect of persistence on chemotactic efficiency, using a spatial Monte Carlo model of bacterial swimming in a gradient, combined with simulations of natural selection based on chemotactic efficiency. A direct search of the parameter space reveals two attractant gradient regimes, (a) a low-gradient regime, in which efficiency is unaffected by directional persistence and (b) a high-gradient regime, in which persistence can improve chemotactic efficiency. The value of the persistence parameter that maximises this effect corresponds very closely with the value observed experimentally. This result is matched by independent simulations of the evolution of directional memory in a population of model bacteria, which also predict the emergence of persistence in high-gradient conditions. The relationship between optimality and persistence in different environments may reflect a universal property of random-walk foraging algorithms, which must strike a compromise between two competing aims: exploration and exploitation. We also present a new graphical way to generally illustrate the evolution of a particular trait in a population, in terms of variations in an evolvable parameter.

Relaxin stimulates leukocyte adhesion and migration through a relaxin receptor LGR7-dependent mechanism

Leukocytes are critical effectors of inflammation and tumor biology. Chemokine-like factors produced by such inflammatory sites are key mediators of tumor growth that activate leukocytic recruitment and tumor infiltration and suppress immune surveillance. Here we report that the endocrine peptide hormone, relaxin, is a regulator of leukocyte biology with properties important in recruitment to sites of inflammation. This study uses the human monocytic cell line THP-1 and normal human peripheral blood mononuclear cells to define a novel role for relaxin in regulation of leukocyte adhesion and migration. Our studies indicate that relaxin promotes adenylate cyclase activation, substrate adhesion, and migratory capacity of mononuclear leukocytes through a relaxin receptor LGR7-dependent mechanism. Relaxin-stimulated cAMP accumulation was observed to occur primarily in non-adherent cells. Relaxin stimulation results in increased substrate adhesion and increased migratory activity of leukocytes. In addition, relaxin-stimulated substrate adhesion resulted in enhanced chemotaxis to monocyte chemoattractant protein-1. These responses in THP-1 and peripheral blood mononuclear cells are relaxin dose-dependent and proportional to cAMP accumulation. We further demonstrate that LGR7 is critical for mediating these biological responses by use of RNA interference lentiviral short hairpin constructs. In summary, we provide evidence that relaxin is a novel leukocyte stimulatory agent with properties affecting adhesion and chemomigration

A Bayesian model predicts the response of axons to molecular gradients

Axon guidance by molecular gradients plays a crucial role in wiring up the nervous system. However, the mechanisms axons use to detect gradients are largely unknown. We first develop a Bayesian “ideal observer” analysis of gradient detection by axons, based on the hypothesis that a principal constraint on gradient detection is intrinsic receptor binding noise. Second, from this model, we derive an equation predicting how the degree of response of an axon to a gradient should vary with gradient steepness and absolute concentration. Third, we confirm this prediction quantitatively by performing the first systematic experimental analysis of how axonal response varies with both these quantities. These experiments demonstrate a degree of sensitivity much higher than previously reported for any chemotacting system. Together, these results reveal both the quantitative constraints that must be satisfied for effective axonal guidance and the computational principles that may be used by the underlying signal transduction pathways, and allow predictions for the degree of response of axons to gradients in a wide variety of in vivo and in vitro settings.

Mathematical modelling of tumour-induced angiogenesis

The growth of solid tumours beyond a critical size is dependent upon angiogenesis, the formation of new blood vessels from an existing vasculature. Tumours may remain dormant at microscopic sizes for some years before switching to a mode in which growth of a supportive vasculature is initiated. The new blood vessels supply nutrients, oxygen, and access to routes by which tumour cells may travel to other sites within the host (metastasize). In recent decades an abundance of biological research has focused on tumour-induced angiogenesis in the hope that treatments targeted at the vasculature may result in a stabilisation or regression of the disease: a tantalizing prospect. The complex and fascinating process of angiogenesis has also attracted the interest of researchers in the field of mathematical biology, a discipline that is, for mathematics, relatively new. The challenge in mathematical biology is to produce a model that captures the essential elements and critical dependencies of a biological system. Such a model may ultimately be used as a predictive tool. In this thesis we examine a number of aspects of tumour-induced angiogenesis, focusing on growth of the neovasculature external to the tumour. Firstly we present a one-dimensional continuum model of tumour-induced angiogenesis in which elements of the immune system or other tumour-cytotoxins are delivered via the newly formed vessels. This model, based on observations from experiments by Judah Folkman et al., is able to show regression of the tumour for some parameter regimes. The modelling highlights a number of interesting aspects of the process that may be characterised further in the laboratory. The next model we present examines the initiation positions of blood vessel sprouts on an existing vessel, in a two-dimensional domain. This model hypothesises that a simple feedback inhibition mechanism may be used to describe the spacing of these sprouts with the inhibitor being produced by breakdown of the existing vessel's basement membrane. Finally, we have developed a stochastic model of blood vessel growth and anastomosis in three dimensions. The model has been implemented in C++, includes an openGL interface, and uses a novel algorithm for calculating proximity of the line segments representing a growing vessel. This choice of programming language and graphics interface allows for near-simultaneous calculation and visualisation of blood vessel networks using a contemporary personal computer. In addition the visualised results may be transformed interactively, and drop-down menus facilitate changes in the parameter values. Visualisation of results is of vital importance in the communication of mathematical information to a wide audience, and we aim to incorporate this philosophy in the thesis. As biological research further uncovers the intriguing processes involved in tumourinduced angiogenesis, we conclude with a comment from mathematical biologist Jim Murray, Mathematical biology is : : : the most exciting modern application of mathematics.

Tactically-driven nonmonotone travelling waves

Models of cell invasion incorporating directed cell movement up a gradient of an external substance and carrying capacity-limited proliferation give rise to travelling wave solutions. Travelling wave profiles with various shapes, including smooth monotonically decreasing, shock-fronted monotonically decreasing and shock-fronted nonmonotone shapes, have been reported previously in the literature. The existence of tacticallydriven shock-fronted nonmonotone travelling wave solutions is analysed for the first time. We develop a necessary condition for nonmonotone shock-fronted solutions. This condition shows that some of the previously reported shock-fronted nonmonotone solutions are genuine while others are a consequence of numerical error. Our results demonstrate that, for certain conditions, travelling wave solutions can be either smooth and monotone, smooth and nonmonotone or discontinuous and nonmonotone. These different shapes correspond to different invasion speeds. A necessary and sufficient condition for the travelling wave with minimum wave speed to be nonmonotone is presented. Several common forms of the tactic sensitivity function have the potential to satisfy the newly developed condition for nonmonotone shock-fronted solutions developed in this work.

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.

Mathematical modelling of soft callus formation in early murine bone repair

Fracture healing is a complicated coupling of many processes. Yet despite the apparent complexity, fracture repair is usually effective. There is, however, no comprehensive mathematical model addressing the multiple interactions of cells, cytokines and oxygen that includes extra-cellular matrix production and that results in the formation of the early stage soft callus. This thesis develops a one dimensional continuum transport model in the context of early fracture healing. Although fracture healing is a complex interplay of many local factors, critical components are identified and used to construct an hypothesis about regulation of the evolution of early callus formation. Multiple cell lines, cellular differentiation, oxygen levels and cytokine concentrations are examined as factors affecting this model of early bone repair. The model presumes diffusive and chemotactic cell migration mechanisms. It is proposed that the initial signalling regime and oxygen availability arising as consequences of bone fracture, are sufficient to determine the quantity and quality of early soft callus formation. Readily available software and purpose written algorithms have been used to obtain numerical solutions representative of various initial conditions. These numerical distributions of cellular populations reflect available histology obtained from murine osteotomies. The behaviour of the numerical system in response to differing initial conditions can be described by alternative in vivo healing pathways. An experimental basis, as illustrated in murine fracture histology, has been utilised to validate the mathematical model outcomes. The model developed in this thesis has potential for future extension, to incorporate processes leading to woven bone deposition, while maintaining the characteristics that regulate early callus formation.