Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold

In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.     

Multiscale modelling of vascular tumour growth in 3D: the roles of domain size and boundary conditions

We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour.     

Origin of the prolactin-releasing hormone (PRLH) receptors: evidence of coevolution between PRLH and a redundant neuropeptide Y receptor during vertebrate evolution

We present seven new vertebrate homologs of the prolactin-releasing hormone receptor (PRLHR) and show that these are found as two separate subtypes, PRLHR1 and PRLHR2. Analysis of a number of vertebrate sequences using phylogeny, pharmacology, and paralogon analysis indicates that the PRLHRs are likely to share a common ancestry with the neuropeptide Y (NPY) receptors. Moreover, a micromolar level of NPY was able to bind and inhibit completely the PRLH-evoked response in PRLHR1-expressing cells. We suggest that an ancestral PRLH peptide started coevolving with a redundant NPY binding receptor, which then became PRLHR, approximately 500 million years ago. The PRLHR1 subtype was shown to have a relatively high evolutionary rate compared to receptors with fixed peptide preference, which could indicate a drastic change in binding preference, thus supporting this hypothesis. This report suggests how gene duplication events can lead to novel peptide ligand/receptor interactions and hence spur the evolution of new physiological functions.     

Cutting edge: back to "one-way" germinal centers

The present status of germinal center (GC) research is revisited using in silico simulations based on recent lymphocyte motility data in mice. The generally adopted view of several rounds of somatic hypermutations and positive selection is analyzed with special emphasis on the spatial organization of the GC reaction. We claim that the development of dark zones is not necessary for successful GC reactions to develop. We find that a recirculation of positively selected centrocytes to the dark zone is rather unlikely. Instead we propose a scenario that combines a multiple-step mutation and selection concept with a "one-way" GC in the sense of cell migration.     

On the proportion of cancer stem cells in a tumour

It is now generally accepted that cancers contain a sub-population, the cancer stem cells (CSCs), which initiate and drive a tumour’s growth. At least until recently it has been widely assumed that only a small proportion of the cells in a tumour are CSCs. Here we use a mathematical model, supported by experimental evidence, to show that such an assumption is unwarranted. We show that CSCs may comprise any possible proportion of the tumour, and that the higher the proportion the more aggressive the tumour is likely to be.     

Mode Transitions in a Model Reaction–Diffusion System Driven by Domain Growth and Noise

Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction-diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns.     

Interleukin-6: a new therapeutic target

The therapeutic success of biological agents, especially the tumour necrosis factor (TNF) inhibitors, has opened a new chapter in the book of therapies for rheumatoid arthritis. Nevertheless, more than 50% of patients may not respond by > 50% improvement. New compounds have recently entered the treatment arena. One of these is rituximab, which depletes B cells, and another, abatacept, interferes with T-cell co-stimulation. However, although these agents may be effective in a number of patients who fail to respond to TNF blockade, they only rarely induce remission and overall 50% response rates do not exceed those with the TNF inhibitors. Among the major proinflammatory cytokines, IL-6 plays a pleiotropic role both in terms of activating the inflammatory response and osteoclastogenesis. Here, we review recent phase II trials of tocilizumab, a humanized anti-IL-6 receptor antibody that achieves a significant therapeutic response rate.     

Upregulation of the Tim-3/Galectin-9 Pathway of T Cell Exhaustion in Chronic Hepatitis B Virus Infection

The S-type lectin galectin-9 binds to the negative regulatory molecule Tim-3 on T cells and induces their apoptotic deletion or functional inactivation. We investigated whether galectin-9/Tim-3 interactions contribute to the deletion and exhaustion of the antiviral T cell response in chronic hepatitis B virus infection (CHB). We found Tim-3 to be expressed on a higher percentage of CD4 and CD8 T cells from patients with CHB than healthy controls (p<0.0001) and to be enriched on activated T cells and those infiltrating the HBV-infected liver. Direct ex vivo examination of virus-specific CD8 T cells binding HLA-A2/peptide multimers revealed that Tim-3 was more highly upregulated on HBV-specific CD8 T cells than CMV-specific CD8 T cells or the global CD8 T cell population in patients with CHB (p<0.001) or than on HBV-specific CD8 after resolution of infection. T cells expressing Tim-3 had an impaired ability to produce IFN-γ and TNF-α upon recognition of HBV-peptides and were susceptible to galectin-9-triggered cell death in vitro. Galectin-9 was detectable at increased concentrations in the sera of patients with active CHB-related liver inflammation (p = 0.02) and was strongly expressed by Kupffer cells within the liver sinusoidal network. Tim-3 blockade resulted in enhanced expansion of HBV-specific CD8 T cells able to produce cytokines and mediate cytotoxicity in vitro. Blocking PD-1 in combination with Tim-3 enhanced the number of patients from whom functional antiviral responses could be recovered and/or the strength of responses, indicating that these co-inhibitory molecules play a non-redundant role in driving T cell exhaustion in CHB. Patients taking antivirals able to potently suppress HBV viraemia continued to express Tim-3 on their T cells and respond to Tim-3 blockade. In summary, both Tim-3 and galectin-9 are increased in CHB and may contribute to the inhibition and deletion of T cells as they infiltrate the HBV-infected liver.     

A simple mechanistic model of sprout spacing in tumour-associated angiogenesis

This paper develops a simple mathematical model of the sitting of capillary sprouts on an existing blood vessel during the initiation of tumour-induced angiogenesis. The model represents an inceptive attempt to address the question of how unchecked sprouting of the parent vessel is avoided at the initiation of angiogenesis, based on the idea that feedback regulation processes play the dominant role. No chemical interaction between the proangiogenic and antiangiogenic factors is assumed. The model is based on corneal pocket experiments, and provides a mathematical analysis of the initial spacing of angiogenic sprouts.     

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis II: Bacterial Populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.