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.

Melanoma cell invasiveness is regulated by miR-211 suppression of the BRN2 transcription factor

To identify microRNAs potentially involved in melanomagenesis, we compared microRNA expression profiles between melanoma cell lines and cultured melanocytes. The most differentially expressed microRNA between the normal and tumor cell lines was miR-211. We focused on this pigment-cell-enriched miRNA as it is derived from the microphthalmia-associated transcription factor (MITF)-regulated gene, TRPM1 (melastatin). We find that miR-211 expression is greatly decreased in melanoma cells and melanoblasts compared to melanocytes. Bioinformatic analysis identified a large number of potential targets of miR-211, including POU3F2 (BRN2). Inhibition of miR-211 in normal melanocytes resulted in increased BRN2 protein, indicating that endogenous miR-211 represses BRN2 in differentiated cells. Over-expression of miR-211 in melanoma cell lines changed the invasive potential of the cells in vitro through directly targeting BRN2 translation. We propose a model for the apparent non-overlapping expression levels of BRN2 and MITF in melanoma, mediated by miR-211 expression.

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.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

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.

Microbial colonisation of human follicular fluid and adverse in vitro fertilisation outcomes

This study, investigating 263 women undergoing trans-vaginal oocyte retrieval for in vitro fertilisation (IVF) found that microorganisms colonising follicular fluid contributed to adverse IVF (pre-implantation) and pregnancy (post-implantation) outcomes including poor quality embryos, failed pregnancy and early pregnancy loss (< 37 weeks gestation). Some microorganisms also showed in vitro growth patterns in liquid media that appeared to be enhanced by the hormonal stimulation protocol used for oocyte retrieval. Elaborated cytokines within follicular fluid were also associated with adverse IVF outcomes. This study is imperative because infertility affects 16% of the human population and the numbers of couples needing assistance continues to increase. Despite significant improvements in the technical aspects of assisted reproductive technologies (ART), the live birth rate has not increased proportionally. Overt genital tract infection has been associated with both infertility and adverse pregnancy outcomes (including miscarriage and preterm birth) as a direct result of the infection or the host response to it. Importantly, once inflammation had become established, medical treatment often failed to prevent these significant adverse outcomes. Current evaluations of fertility focus on the ovary as a site of steroid hormone production and ovulation. However, infertility as a result of subclinical colonisation of the ovary has not been reported. Furthermore, identification of the microorganisms present in follicular fluid and the local cytokine profile may provide clinicians with an early indication of the prognosis for IVF treatment in infertile couples, thus allowing antimicrobial treatment and/or counselling about possible IVF failure. During an IVF cycle, multiple oocytes undergo maturation in vivo in response to hormonal hyperstimulation. Oocytes for in vitro insemination are collected trans-vaginally. The follicular fluid that bathes the maturing oocyte in vivo, usually is discarded as part of the IVF procedure, but provides a unique opportunity to investigate microbial causes of adverse IVF outcomes. Some previous studies have identified follicular fluid markers that predict IVF pregnancy outcomes. However, there have not been any detailed microbiological studies of follicular fluid. For this current study, paired follicular fluid and vaginal secretion samples were collected from women undergoing IVF cycles to determine whether microorganisms in follicular fluid were associated with adverse IVF outcomes. Microorganisms in follicular fluid were regarded as either "colonisers" or "contaminants"; colonisers, if they were unique to the follicular fluid sample, and contaminants if the same microorganisms were detected in the vaginal and follicular fluid samples indicating that the follicular fluid was merely contaminated during the oocyte retrieval process. Quite unexpectedly, by these criteria, we found that follicular fluid from approximately 30% of all subjects was colonised with bacteria. Fertile and infertile women with colonised follicular fluid had decreased embryo transfer rates and decreased pregnancy rates compared to women with contaminated follicular fluids. The observation that follicular fluid was not always sterile, but contained a diverse range of microorganisms, is novel. Many of the microorganisms we detected in follicular fluid are known opportunistic pathogens that have been detected in upper genital tract infections and are associated with adverse pregnancy outcomes. Bacteria were able to survive for at least 28 weeks in vitro, in cultures of follicular fluid. Within 10 days of establishing these in vitro cultures, several species (Lactobacillus spp., Bifidobacterium spp., Propionibacterium spp., Streptococcus spp. and Salmonella entericus) had formed biofilms. Biofilms play a major role in microbial pathogenicity and persistence. The propensity of microbial species to form biofilms in follicular fluid suggests that successful treatment of these infections with antimicrobials may be difficult. Bifidobacterium spp. grew, in liquid media, only if concentrations of oestradiol and progesterone were similar to those achieved in vivo during an IVF cycle. In contrast, the growth of Streptococcus agalactiae and Escherichia coli was inhibited or abolished by the addition of these hormones to culture medium. These data suggest that the likelihood of microorganisms colonising follicular fluid and the species of bacteria involved is influenced by the stage of the menstrual cycle and, in the case of IVF, the nature and dose of steroid hormones administered for the maturation of multiple oocytes in vivo. Our findings indicate that the elevated levels of steroid hormones during an IVF cycle may influence the microbial growth within follicular fluid, suggesting that the treatment itself will impact on the microflora present in the female upper genital tract during pre-conception and early post-conception phases of the cycle. The effect of the host immune response on colonising bacteria and on the outcomes of IVF also was investigated. White blood cells reportedly compose between 5% and 15% of the cell population in follicular fluid. The follicular membrane is semi-permeable and cells are actively recruited as part of the normal menstrual cycle and in response to microorganisms. A previous study investigated follicular fluid cytokines from infertile women and fertile oocyte donors undergoing IVF, and concluded that there were no significant differences in the cytokine concentrations between the two groups. However, other studies have reported differences in the follicular fluid cytokine levels associated with infertile women with endometriosis or polycystic ovary syndrome. In this study, elevated levels of interleukin (IL)-1 á, IL-1 â and vascular endothelial growth factor (VEGF) in vaginal fluid were associated with successful fertilisation, which may be useful marker for successful fertilisation outcomes for women trying to conceive naturally or prior to oocyte retrieval for IVF. Elevated levels of IL-6, IL-12p40, granulocyte colony stimulating factor (GCSF) and interferon-gamma (IFN ã) in follicular fluid were associated with successful embryo transfer. Elevated levels of pro-inflammatory IL-18 and decreased levels of anti-inflammatory IL-10 were identified in follicular fluid from women with idiopathic infertility. Successful fertilisation and implantation is dependent on a controlled pro-inflammatory environment, involving active recruitment of pro-inflammatory mediators to the genital tract as part of the menstrual cycle and early pregnancy. However, ongoing pregnancy requires an enhanced anti-inflammatory environment to ensure that the maternal immune system does not reject the semi-allergenic foetus. The pro-inflammatory skew in the follicular fluid of women with idiopathic infertility, correlates with normal rates of fertilisation, embryo discard and embryo transfer, observed for this cohort, which were similar to the outcomes observed for fertile women. However, their pregnancy rate was reduced compared to fertile women. An altered local immune response in follicular fluid may provide a means of explaining infertility in this cohort, previously defined as 'idiopathic'. This study has found that microorganisms colonising follicular fluid may have contributed to adverse IVF and pregnancy outcomes. Follicular fluid bathes the cumulus oocyte complex during the in vivo maturation process, and microorganisms in the fluid, their metabolic products or the local immune response to these microorganisms may result in damage to the oocytes, degradation of the cumulus or contamination of the IVF culture system. Previous studies that have discounted bacterial contamination of follicular fluid as a cause of adverse IVF outcomes failed to distinguish between bacteria that were introduced into the follicular fluid at the time of trans-vaginal oocyte retrieval and those that colonised the follicular fluid. Those bacteria that had colonised the fluid may have had time to form biofilms and to elicit a local immune response. Failure to draw this distinction has previously prevented consideration of bacterial colonisation of follicular fluid as a cause of adverse IVF outcomes. Several observations arising from this study are of significance to IVF programs. Follicular fluid is not always sterile and colonisation of follicular fluid is a cause of adverse IVF and pregnancy outcomes. Hormonal stimulation associated with IVF may influence whether follicular fluid is colonised and enhance the growth of specific species of bacteria within follicular fluid. Bacteria in follicular fluid may form biofilms and literature has reported that this may influence their susceptibility to antibiotics. Monitoring the levels of selected cytokines within vaginal secretions may inform fertilisation outcomes. This study has identified novel factors contributing to adverse IVF outcomes and that are most likely to affect also natural conception outcomes. Early intervention, possibly using antimicrobial or immunological therapies may reduce the need for ART and improve reproductive health outcomes for all women.