A general reaction–diffusion model of acidity in cancer invasion

We model the metabolism and behaviour of a developing cancer tumour in the context of its microenvironment, with the aim of elucidating the consequences of altered energy metabolism. Of particular interest is the Warburg Effect, a widespread preference in tumours for cytosolic glycolysis rather than oxidative phosphorylation for glucose breakdown, as yet incompletely understood. We examine a candidate explanation for the prevalence of the Warburg Effect in tumours, the acid-mediated invasion hypothesis, by generalising a canonical non-linear reaction–diffusion model of acid-mediated tumour invasion to consider additional biological features of potential importance. We apply both numerical methods and a non-standard asymptotic analysis in a travelling wave framework to obtain an explicit understanding of the range of tumour behaviours produced by the model and how fundamental parameters govern the speed and shape of invading tumour waves. Comparison with conclusions drawn under the original system—a special case of our generalised system—allows us to comment on the structural stability and predictive power of the modelling framework.     

Cytokines and anti-cytokine biologicals in autoimmunity: present and future

The increasing understanding of the role of cytokines in autoimmunity, and the observation that tumour necrosis factor alpha (TNFalpha) is central to the inflammatory and destructive process common to several human autoimmune diseases, has led to a new generation of therapeutics, the TNFalpha blocking agents. In this article, we review the current knowledge of the role of cytokines in autoimmunity as unravelled by studies both in the laboratory and the clinic. In addition, we discuss future prospects of the anti-TNFalpha therapy that may involve combination therapy with other anti-cytokine or anti-T cell biologicals, or the use of small chemicals targeting molecules involved in TNFalpha production such as NF-kappaB and p38 MAPK. The future developments of anti-TNFalpha and anti-cytokine therapy in general will be interesting.     

Challenges and opportunities of publishing supplements at <Emphasis Type="Italic">Arthritis Research &; Therapy</Emphasis>

Supplements are the cause of much debate in the world of journal publishing. Supplements are criticized for the fact that often they are funded by an external source, and journals have been known to shy away from their publication [1]. But is refusing to publish supplements the only answer? At Arthritis Research & Therapy, we feel that - if subjected to the full rigors of peer review - supplements can provide invaluable educational resources, exploring themes in a detailed and focused way that might not always be possible in the main journal.At Arthritis Research & Therapy, we have decided that the potential risk of a loss of objectivity in industry-sponsored supplements can be managed by scrupulous attention to the peer-review process. Therefore, in our experience, the benefit of publishing supplements greatly outweighs any perception of loss of objectivity. We should note that our colleagues in the pharmaceutical industry have embraced our approach with no efforts to circumvent our rules, as far as we know.We consider proceedings, review collections, and meeting abstracts for inclusion as supplements. Examples of recent supplements are easily accessed on the journal website. It will be apparent that the emphasis is on the molecular and cellular basis of immune and inflammatory mechanisms of disease. The underwriting by the sponsor of the cost of peer review and production ensures that the high-quality publication is freely available. Outlined below is the procedure that we follow when considering any potential supplements for the journal. We recognize the potential for competing interests to influence the content of articles where there is industry involvement, but we believe that by adhering to a stringent publication process we negate this risk with our supplement content.So, what is the procedure? First, in a change from the approach taken by many journals, we appoint an ''internal'' Supplement Editor (usually from the journal''s Editorial Board), whose role is to select peer reviewers and assess the suitability of the supplement articles for publication in the journal. This internal editor is selected by the Editors-in-Chief, and the sponsor''s approval is not sought in making this appointment. Before their appointment, internal editors are asked to declare any potential conflicts of interest, and full disclosures are included in both online and print versions of any supplements. In cases in which internal editors receive a stipend, this is paid for by the publisher - not the sponsor. All conflict of interest disclosures associated with supplement publications follow the National Library of Medicine policy for indexing supplement articles in MEDLINE [2].For some supplements, particularly where articles are commissioned externally, there may be an ''external'' Supplement Editor as well as the internal editor. Before their appointment, external supplement editors must be approved by the Editors-in-Chief. Their role is to identify the subject matter and propose suitable authors for the individual supplement articles, with the proviso that all content must be approved by the Editors-in-Chief. The external editor is not involved in the peer review of any of the articles once submitted. They are also asked for full conflict of interest disclosures, which are included in the supplement publication alongside those of the internal editor.One of the common criticisms levied against supplements is that the articles are not peer-reviewed to the journal''s normal standards. At Arthritis Research & Therapy, supplement articles go through the same thorough peer-review process as articles do in the main journal [3]. The Editors-in-Chief have full editorial control, including the ability to ask authors to make extensive revisions, and reserve the right to reject articles that do not meet the journal''s standards. And in accordance with the guidelines of the International Committee for Medical Journal Editors [4], all contracts clearly include information about editorial control and the role of the internal supplement editor.In addition to disclosures from the individual editors, sources of funding for a supplement are prominently displayed on the supplement title page, and funding is also acknowledged in each individual article. We ensure that supplements can be clearly distinguished as separate from the main journal content on the journal homepage. As with all of our articles, individual authors declare their conflicts of interest. This complies with the good publication practice (GPP2) guidelines [5]. We also adhere to the guidelines of the European Medical Writers Association [6] by ensuring that the involvement of any medical writers is disclosed in an article''s acknowledgments section along with their sources of funding.We hope that by ensuring that there is full transparency of disclosures from everyone involved in supplements and following strictly the peer-review procedure described above, we avoid the potential pitfalls of supplement publishing. The guidelines of the International Committee of Medical Journal Editors themselves state that supplements ''serve useful purposes'' and it is our responsibility as editors to ensure that they continue to be useful without allowing ourselves to be subject to industry influence. By publicly disclosing our policy for supplement review here, we hope that other journals will be more open about their peer-review policies for supplements and that they adopt similarly stringent practices in the future.     

Mixed-mode pattern in Doublefoot mutant mouse limb--Turing reaction-diffusion model on a growing domain during limb development

It has been suggested that the Turing reaction-diffusion model on a growing domain is applicable during limb development, but experimental evidence for this hypothesis has been lacking. In the present study, we found that in Doublefoot mutant mice, which have supernumerary digits due to overexpansion of the limb bud, thin digits exist in the proximal part of the hand or foot, which sometimes become normal abruptly at the distal part. We found that exactly the same behaviour can be reproduced by numerical simulation of the simplest possible Turing reaction-diffusion model on a growing domain. We analytically showed that this pattern is related to the saturation of activator kinetics in the model. Furthermore, we showed that a number of experimentally observed phenomena in this system can be explained within the context of a Turing reaction-diffusion model. Finally, we make some experimentally testable predictions.     

Leaky vessels as a potential source of stromal acidification in tumours

Malignant tumours are characterised by higher rates of acid production and a lower extracellular pH than normal tissues. Previous mathematical modelling has indicated that the tumour-derived production of acid leads to a gradient of low pH in the interior of the tumour extending to a normal pH in the peritumoural tissue. This paper uses mathematical modelling to examine the potential of leaky vessels as an additional source of stromal acidification in tumours. We explore whether and to what extent increasing vascular permeability in vessels can lead to the breakdown of the acid gradient from the core of the tumour to the normal tissue, and a progressive acidification of the peritumoural stroma. We compare our mathematical simulations to experimental results found in vivo with a tumour implanted in the mammary fat pad of a mouse in a window chamber construct. We find that leaky vasculature can cause a net acidification of the normal tissue away from the tumour boundary, though not a progressive acidification over time as seen in the experiments. Only through progressively increasing the leakiness can the model qualitatively reproduce the experimental results. Furthermore, the extent of the acidification predicted by the mathematical model is less than as seen in the window chamber, indicating that although vessel leakiness might be acting as a source of acid, it is not the only factor contributing to this phenomenon. Nevertheless, tumour destruction of vasculature could result in enhanced stromal acidification and invasion, hence current therapies aimed at buffering tumour pH should also examine the possibility of preventing vessel disruption.     

Implementing vertex dynamics models of cell populations in biology within a consistent computational framework

The dynamic behaviour of epithelial cell sheets plays a central role during development, growth, disease and wound healing. These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes acting at the cellular and molecular level. Computational models offer a useful means by which to investigate and test hypotheses about these processes, and have played a key role in the study of cell–cell interactions. However, the necessarily complex nature of such models means that it is difficult to make accurate comparison between different models, since it is often impossible to distinguish between differences in behaviour that are due to the underlying model assumptions, and those due to differences in the in silico implementation of the model. In this work, an approach is described for the implementation of vertex dynamics models, a discrete approach that represents each cell by a polygon (or polyhedron) whose vertices may move in response to forces. The implementation is undertaken in a consistent manner within a single open source computational framework, Chaste, which comprises fully tested, industrial-grade software that has been developed using an agile approach. This framework allows one to easily change assumptions regarding force generation and cell rearrangement processes within these models. The versatility and generality of this framework is illustrated using a number of biological examples. In each case we provide full details of all technical aspects of our model implementations, and in some cases provide extensions to make the models more generally applicable.     

A mathematical model of tumour and blood pHe regulation: The HCO3-/CO2 buffering system

Malignant tumours are characterised by a low, acidic extracellular pH (pHe) which facilitates invasion and metastasis. Previous research has proposed the potential benefits of manipulating systemic pHe, and recent experiments have highlighted the potential for buffer therapy to raise tumour pHe, prevent metastases, and prolong survival in laboratory mice. To examine the physiological regulation of tumour buffering and investigate how perturbations of the buffering system (via metabolic/respiratory disorders or changes in parameters) can alter tumour and blood pHe, we develop a simple compartmentalised ordinary differential equation model of pHe regulation by the HCO3-/CO2 buffering system. An approximate analytical solution is constructed and used to carry out a sensitivity analysis, where we identify key parameters that regulate tumour pHe in both humans and mice. From this analysis, we suggest promising alternative and combination therapies, and identify specific patient groups which may show an enhanced response to buffer therapy. In addition, numerical simulations are performed, validating the model against well-known metabolic/respiratory disorders and predicting how these disorders could change tumour pHe.