Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.

Phenomenological modeling of cell-to-cell and beat-to-beat variability in isolated Guinea Pig ventricular myocytes

Experimental action potential (AP) recordings in isolated ventricular myoctes display significant temporal beat-to-beat variability in morphology and duration. Furthermore, significant cell-to-cell differences in AP also exist even for isolated cells originating from the same region of the same heart. However, current mathematical models of ventricular AP fail to replicate the temporal and cell-to-cell variability in AP observed experimentally. In this study, we propose a novel mathematical framework for the development of phenomenological AP models capable of capturing cell-to-cell and temporal variabilty in cardiac APs. A novel stochastic phenomenological model of the AP is developed, based on the deterministic Bueno-Orovio/Fentonmodel. Experimental recordings of AP are fit to the model to produce AP models of individual cells from the apex and the base of the guinea-pig ventricles. Our results show that the phenomenological model is able to capture the considerable differences in AP recorded from isolated cells originating from the location. We demonstrate the closeness of fit to the available experimental data which may be achieved using a phenomenological model, and also demonstrate the ability of the stochastic form of the model to capture the observed beat-to-beat variablity in action potential duration.

An ultraviolet selective photodetector based on a nanocrystalline TiO2 photoelectrochemical cell

Solar ultraviolet (UV) radiation causes a range of skin disorders as well as affecting vision and the immune system. It also inhibits development of plants and animals. UV radiation monitoring is used routinely in some locations in order to alert the population to harmful solar radiation levels. There is ongoing research to develop UV-selective-sensors [1–3]. A personal, inexpensive and simple UV-selective-sensor would be desirable to measure UV intensity exposure. A prototype of such a detector has been developed and evaluated in our laboratory. It comprises a sealed two-electrode photoelectrochemical cell (PEC) based on nanocrystalline TiO2. This abundant semiconducting oxide, which is innocuous and very sta-ble, is the subject of intense study at present due to its application in dye sensitized solar cells (DSSC) [4]. Since TiO2 has a wide band gap (EG = 3.0 eV for rutile and EG = 3.2 eV for anatase), it is inher-ently UV-selective, so that UV filters are not required. This further reduces the cost of the proposed photodetector in comparison with conventional silicon detectors. The PEC is a semiconductor–electrolyte device that generates a photovoltage when it is illuminated and a corresponding photocur-rent if the external circuit is closed. The device does not require external bias, and the short circuit current is generally a linear function of illumination intensity. This greatly simplifies the elec-trical circuit needed when using the PEC as a photodetector. DSSC technology, which is based on a PEC containing nanocrystalline TiO2 sensitized with a ruthenium dye, holds out the promise of solar cells that are significantly cheaper than traditional silicon solar cells. The UV-sensor proposed in this paper relies on the cre-ation of electron–hole pairs in the TiO2 by UV radiation, so that it would be even cheaper than a DSSC since no sensitizer dye is needed. Although TiO2 has been reported as a suitable material for UV sensing [3], to the best of our knowledge, the PEC configuration described in the present paper is a new approach. In the present study, a novel double-layer TiO2 structure has been investigated. Fabrication is based on a simple and inexpensive technique for nanostructured TiO2 deposition using microwave-activated chemical bath deposition (MW-CBD) that has been reported recently [5]. The highly transparent TiO2 (anatase) films obtained are densely packed, and they adhere very well to the transparent oxide (TCO) substrate [6]. These compact layers have been studied as contacting layers in double-layer TiO2 structures for DSSC since improvement of electron extraction at the TiO2–TCO interface is expected [7]. Here we compare devices incorporating a single mesoporous nanocrystalline TiO2 structure with devices based on a double structure in which a MW-CBD film is situated between the TCO and the mesoporous nanocrystalline TiO2 layer. Besides improving electron extraction, this film could also help to block recombination of electrons transferred to the TCO with oxidized species in the electrolyte, as has been reported in the case of DSSC for compact TiO2 films obtained by other deposition tech-niques [8,9]. The two types of UV-selective sensors were characterized in detail. The current voltage characteristics, spectral response, inten-sity dependence of short circuit current and response times were measured and analyzed in order to evaluate the potential of sealed mesoporous TiO2-based photoelectrochemical cells (PEC) as low cost personal UV-photodetectors.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Velocity-jump models with crowding effects

Velocity jump processes are discrete random walk models that have many applications including the study of biological and ecological collective motion. In particular, velocity jump models are often used to represent a type of persistent motion, known as a “run and tumble”, which is exhibited by some isolated bacteria cells. All previous velocity jump processes are non-interacting, which means that crowding effects and agent-to-agent interactions are neglected. By neglecting these agent-to-agent interactions, traditional velocity jump models are only applicable to very dilute systems. Our work is motivated by the fact that many applications in cell biology, such as wound healing, cancer invasion and development, often involve tissues that are densely packed with cells where cell-to-cell contact and crowding effects can be important. To describe these kinds of high cell density problems using a velocity jump process we introduce three different classes of crowding interactions into a one-dimensional model. Simulation data and averaging arguments lead to a suite of continuum descriptions of the interacting velocity jump processes. We show that the resulting systems of hyperbolic partial differential equations predict the mean behavior of the stochastic simulations very well.

Inverse expression states of the BRN2 and MITF transcription factors in melanoma spheres and tumour xenografts regulate the NOTCH pathway

The use of adherent monolayer cultures have produced many insights into melanoma cell growth and differentiation, but often novel therapeutics demonstrated to act on these cells are not active in vivo. It is imperative that new methods of growing melanoma cells that reflect growth in vivo are investigated. To this end, a range of human melanoma cell lines passaged as adherent cultures or induced to form melanoma spheres (melanospheres) in stem cell media have been studied to compare cellular characteristics and protein expression. Melanoma spheres and tumours grown from cell lines as mouse xenografts had increased heterogeneity when compared with adherent cells and 3D-spheroids in agar (aggregates). Furthermore, cells within the melanoma spheres and mouse xenografts each displayed a high level of reciprocal BRN2 or MITF expression, which matched more closely the pattern seen in human melanoma tumours in situ, rather than the propensity for co-expression of these important melanocytic transcription factors seen in adherent cells and 3D-spheroids. Notably, when the levels of the BRN2 and MITF proteins were each independently repressed using siRNA treatment of adherent melanoma cells, members of the NOTCH pathway responded by decreasing or increasing expression, respectively. This links BRN2 as an activator, and conversely, MITF as a repressor of the NOTCH pathway in melanoma cells. Loss of the BRN2-MITF axis in antisense-ablated cell lines decreased the melanoma sphere-forming capability, cell adhesion during 3D-spheroid formation and invasion through a collagen matrix. Combined, this evidence suggests that the melanoma sphere-culture system induces subpopulations of cells that may more accurately portray the in vivo disease, than the growth as adherent melanoma cells.

Human neural cell interactions with orientated electrospun nanofibers in vitro

Aim: Electrospun nanofibers represent potent guidance substrates for nervous tissue repair. Development of nanofiber-based scaffolds for CNS repair requires, as a first step, an understanding of appropriate neural cell type-substrate interactions. Materials & methods: Astrocyte–nanofiber interactions (e.g., adhesion, proliferation, process extension and migration) were studied by comparing human neural progenitor-derived astrocytes (hNP-ACs) and a human astrocytoma cell line (U373) with aligned polycaprolactone (PCL) nanofibers or blended (25% type I collagen/75% PCL) nanofibers. Neuron–nanofiber interactions were assessed using a differentiated human neuroblastoma cell line (SH-SY5Y). Results & discussion: U373 cells and hNP-AC showed similar process alignment and length when associated with PCL or Type I collagen/PCL nanofibers. Cell adhesion and migration by hNP-AC were clearly improved by functionalization of nanofiber surfaces with type I collagen. Functionalized nanofibers had no such effect on U373 cells. Another clear difference between the U373 cells and hNP-AC interactions with the nanofiber substrate was proliferation; the cell line demonstrating strong proliferation, whereas the hNP-AC line showed no proliferation on either type of nanofiber. Long axonal growth (up to 600 µm in length) of SH-SY5Y neurons followed the orientation of both types of nanofibers even though adhesion of the processes to the fibers was poor. Conclusion: The use of cell lines is of only limited predictive value when studying cell–substrate interactions but both morphology and alignment of human astrocytes were affected profoundly by nanofibers. Nanofiber surface functionalization with collagen significantly improved hNP-AC adhesion and migration. Alternative forms of functionalization may be required for optimal axon–nanofiber interactions.

Cabergoline Decreases Alcohol Drinking and Seeking Behaviors Via Glial Cell Line-Derived Neurotrophic Factor

Background: Cabergoline is an ergotamine derivative that increases the expression of glial cell line-derived neurotrophic factor (GDNF) in vitro. We recently showed that GDNF in the ventral tegmental area (VTA) reduces the motivation to consume alcohol. We therefore set out to determine whether cabergoline administration decreases alcohol-drinking and -seeking behaviors via GDNF. Methods: Reverse transcription polymerase chain reaction (RT-PCR) and Enzyme-Linked ImmunoSorbent Assay (ELISA) were used to measure GDNF levels. Western blot analysis was used for phosphorylation experiments. Operant self-administration in rats and a two-bottle choice procedure in mice were used to assess alcohol-drinking behaviors. Instrumental performance tested during extinction was used to measure alcohol-seeking behavior. The [35S]GTPγS binding assay was used to assess the expression and function of the dopamine D2 receptor (D2R). Results: We found that treatment of the dopaminergic-like cell line SH-SY5Y with cabergoline and systemic administration of cabergoline in rats resulted in an increase in GDNF level and in the activation of the GDNF pathway. Cabergoline treatment decreased alcohol-drinking and -seeking behaviors including relapse, and its action to reduce alcohol consumption was localized to the VTA. Finally, the increase in GDNF expression and the decrease in alcohol consumption by cabergoline were abolished in GDNF heterozygous knockout mice. Conclusions: Together, these findings suggest that cabergoline-mediated upregulation of the GDNF pathway attenuates alcohol-drinking behaviors and relapse. Alcohol abuse and addiction are devastating and costly problems worldwide. This study puts forward the possibility that cabergoline might be an effective treatment for these disorders. © 2009 Society of Biological Psychiatry.

A brief history of haemotopoietic stem cell Ex vivo expansion

Haematopoiesis is the process by which a hierarchy of mature and progenitor blood cells are formed. These cell populations are all derived from multipotent haematopoietic stem cells (HSC), which reside in the bone marrow ‘niche’ of adult humans. Over the lifetime of a healthy individual, this HSC population replenishes between 1010-1011 blood cells on a daily basis. Dysregulation of this system can lead to a number of haematopoietic diseases, including aplastic anaemias and leukaemias, which result in, or require for disease resolution, bone marrow cell depletion. In 1956, E. Donnall Thomas demonstrated that haematopoiesis could be restored by transplanting bone marrow-derived cells from one man into his identical twin brother, who was suffering from advanced leukaemia. His success drew significant interest in academic research and medicine communities, and 12 years later, the first successful allogeneic transplant was performed. To this day, HSCs remain the most studied and characterised stem cell population. In fact, HSCs are the only stem cell population routinely utilised in the clinic. As such, HSCs function as a model system both for the biological investigation of stem cells, as well as for their clinical application. Herein, we briefly review HSC transplantation, strategies for the ex vivo cultivation of HSCs, recent clinical outcomes, and their impact on the future direction of HSC transplantation therapy.

Plant programmed cell death : Can't live with it; Can't live without it

The decision of whether a cell should live or die is fundamental for the wellbeing of all organisms. Despite intense investigation into cell growth and proliferation, only recently has the essential and equally important idea that cells control/programme their own demise for proper maintenance of cellular homeostasis gained recognition. Furthermore, even though research into programmed cell death (PCD) has been an extremely active area of research there are significant gaps in our understanding of the process in plants. In this review, we discuss PCD during plant development and pathogenesis, and compare/contrast this with mammalian apoptosis. © 2008 Blackwell Publishing Ltd.

Controlling cell-material interactions with polymer nanocomposites by use of surface modifying additives

Polymer nanocomposites (NC) are fabricated by incorporating well dispersed nanoscale particles within a polymer matrix. This study focuses on elastomeric polyurethane (PU) based nanocomposites, containing organically modified silicates (OMS), as bioactive materials. Nanocomposites incorporating chlorhexidine diacetate as an organic modifier (OM) were demonstrated to be antibacterial with a dose dependence related to both the silicate loading and the loading of OM. When the non-antibacterial OM dodecylamine was used, both cell and platelet adhesion were decreased on the nanocomposite surface. These results suggest that OM is released from the polymer and can impact on cell behaviour at the interface. Nanocomposites have potential use as bioactive materials in a range of biomedical applications.

The expression, regulation and function of kallikrein 4 in prostate cancer

Prostate cancer is a significant health problem faced by aging men. Currently, diagnostic strategies for the detection of prostate cancer are either unreliable, yielding high numbers of false positive results, or too invasive to be used widely as screening tests. Furthermore, the current therapeutic strategies for the treatment of the disease carry considerable side effects. Although organ confined prostate cancer can be curable, most detectable clinical symptoms occur in advanced disease when primary tumour cells have metastasised to distant sites - usually lymph nodes and bone. Many growth factors and steroids assist the continued growth and maintenance of prostatic tumour cells. Of these mitogens, androgens are important in the development of the normal prostate but are also required to sustain the growth of prostate cancer cells in the early stage of the disease. Not only are androgens required in the early stage of disease, but also many other growth factors and hormones interact to cause uncontrolled proliferation of malignant cells. The early, androgen sensitive phase of disease is followed by an androgen insensitive phase, whereby androgens are no longer required to stimulate the growth of the tumour cells. Growth factors such as transforming growth factor  and  (TGF/), epidermal growth factor (EGF), basic fibroblast growth factor (bFGF), insulin-like growth factors (IGFs), Vitamin D and thyroid hormone have been suggested to be important at this stage of disease. Interestingly, some of the kallikrein family of genes, including prostate specific antigen (PSA), the current serum diagnostic marker for prostate cancer, are regulated by androgens and many of the aforementioned growth factors. The kallikrein gene family is a group of serine proteases that are involved in a diverse range of physiological processes: regulation of local blood flow, angiogenesis, tissue invasion and mitogenesis. The earliest members of the kallikrein gene family (KLK1-KLK3) have been strongly associated with general disease states, such as hypertension, inflammation, pancreatitis and renal disease, but are also linked to various cancers. Recently, this family was extended to include 15 genes (KLK1-15). Several newer members of the kallikrein family have been implicated in the carcinogenesis and tumour metastasis of hormone-dependent cancers such as prostate, breast, endometrial and ovarian cancer. The aims of this project were to investigate the expression of the newly identified kallikrein, KLK4, in benign and malignant prostate tissues, and prostate cancer cell lines. This thesis has demonstrated the elevated expression of KLK4 mRNA transcripts in malignant prostate tissue compared to benign prostates. Additionally, expression of the full length KLK4 transcript was detected in the androgen dependent prostate cancer cell line, LNCaP. Based on the above finding, the LNCaP cell line was chosen to assess the potential regulation of full length KLK4 by androgen, thyroid hormone and epidermal growth factor. KLK4 mRNA and protein was found to be up-regulated by androgen and a combination of androgen and thyroid hormone. Thyroid hormone alone produced no significant change in KLK4 mRNA or protein over the control. Epidermal growth factor treatment also resulted in elevated expression levels of KLK4 mRNA and protein. To assess the potential functional role(s) of KLK4/hK4 in processes associated with tumour progression, full length KLK4 was transfected into PC-3 cells - a prostate cancer cell line originally derived from a secondary bone lesion. The KLK4/hK4 over-expressing cells were assessed for their proliferation, migration, invasion and attachment properties. The KLK4 over-expressing clones exhibited a marked change in morphology, indicative of a more aggressive phenotype. The KLK4 clones were irregularly shaped with compromised adhesion to the growth surface. In contrast, the control cell lines (parent PC-3 and empty vector clones) retained a rounded morphology with obvious cell to cell adhesion, as well as significant adhesion to their growth surface. The KLK4 clones exhibited significantly greater attachment to Collagen I and IV than native PC-3s and empty vector controls. Over a 12 hour period, in comparison to the control cells, the KLK4 clones displayed an increase in migration towards PC-3 native conditioned media, a 3 fold increase towards conditioned media from an osteoblastic cell line (Saos-2) and no change in migration towards conditioned media from neonatal foreskin fibroblast cells or 20% foetal bovine serum. Furthermore, the increase in migration exhibited by the KLK4 clones was partially blocked by the serine protease inhibitor, aprotinin. The data presented in this thesis suggests that KLK4/hK4 is important in prostate carcinogenesis due to its over-expression in malignant prostate tissues, its regulation by hormones and growth factors associated with prostate disease and the functional consequences of over-expression of KLK4/hK4 in the PC-3 cell line. These results indicate that KLK4/hK4 may play an important role in tumour invasion and bone metastasis via increased attachment to the bone matrix protein, Collagen I, and enhanced migration due to soluble factors produced by osteoblast cells. This suggestion is further supported by the morphological changes displayed by the KLK4 over-expressing cells. Overall, this data suggests that KLK4/hK4 should be further studied to more fully investigate the potential value of KLK4/hK4 as a diagnostic/prognostic biomarker or in therapeutic applications.