Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations

Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatio-temporal interactions between the protein and its mRNA in a 1-dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behaviour and this is the case for our model, shown initially via computational simulations. In order to investigate this behaviour more deeply, we next solve our system using Greens functions and then undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. This has implications for transcription factors such as p53, NF-$kappa$B and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer

Multiscale modelling of cancer progression and treatment control : the role of intracellular heterogeneities in chemotherapy treatment

Cancer is a complex, multiscale process involving interactions at intracellular, intercellular and tissue scales that are in turn susceptible to microenvironmental changes. Each individual cancer cell within a cancer cell mass is unique, with its own internal cellular pathways and biochemical interactions. These interactions contribute to the functional changes at the cellular and tissue scale, creating a heterogenous cancer cell population. Anticancer drugs are effective in controlling cancer growth by inflicting damage to various target molecules and thereby triggering multiple cellular and intracellular pathways, leading to cell death or cell-cycle arrest. One of the major impediments in the chemotherapy treatment of cancer is drug resistance driven by multiple mechanisms, including multi-drug and cell-cycle mediated resistance to chemotherapy drugs. In this article, we discuss two hybrid multiscale modelling approaches, incorporating multiple interactions involved in the sub-cellular, cellular and microenvironmental levels to study the effects of cell-cycle, phase-specific chemotherapy on the growth and progression of cancer cells.PostprintPeer reviewe

Quantitative Predictive Modelling Approaches to Understanding Rheumatoid Arthritis:A Brief Review

Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion, which lead to chronic pain, poor life quality and, in some cases, mortality. Understanding the biological mechanisms behind the progression of the disease, as well as developing new methods for quantitative predictions of disease progression in the presence/absence of various therapies is important for the success of therapeutic approaches. The aim of this study is to review various quantitative predictive modelling approaches for understanding rheumatoid arthritis. To this end, we start by briefly discussing the biology of this disease and some current treatment approaches, as well as emphasising some of the open problems in the field. Then, we review various mathematical mechanistic models derived to address some of these open problems. We discuss models that investigate the biological mechanisms behind the progression of the disease, as well as pharmacokinetic and pharmacodynamic models for various drug therapies. Furthermore, we highlight models aimed at optimising the costs of the treatments while taking into consideration the evolution of the disease and potential complications.Publisher PDFPeer reviewe

Altruism and volunteering among high school students: a mixed methods study

2017 Spring.Includes bibliographical references.Twenty- first century skills require that students leave high school prepared for leadership by exhibiting selflessness and acting with larger community interests at heart. The role of altruism and volunteering among high school students who volunteered for a local Special Olympics event is examined with a mixed methods approach. An exploratory factor analysis of the Rushton Self-Rater Altruism scale (SRAS) was is conducted to evaluate the existence of underlying factors present in the altruism scale. All questions of the SRAS loaded onto three factors, which were are also verified by a scree plot analysis. Further analysis was is conducted to determine if sex differences, grade level differences, and grade point average correlations among the total SRAS score and summated factor scores are were significant. Sex differences were are statistically significant for females in total altruism, low risk, and high-risk summated factor scores. There were are no statistically significant differences between grade levels total altruism, or summated factor scores. Grade point averages (GPAs) were are also not found to correlate with altruism scores, indicating that students with higher GPAs are not more altruistic than their peers with lower GPAs . Qualitative coding and thematic analysis of written responses related to student motivations and benefits from volunteering are is conducted. Eleven motivational codes and eight benefit codes are developed. These codes were are then analyzed with quantitative analysis methods to determine if there were are statistically significant sex and grade level differences in the reported motivations and benefits of the volunteer experiences. Sex differences were are statistically significant for females on the motivation code of volunteering for a social/friend connection, and were are statistically significant for males on the motivation code of volunteering to fulfill a senior service/community service requirement. Grade level differences were are statistically significant for sophomore students on the motivation code of volunteering for career exploration, and for senior students on the motivation code of completing a senior service/community service project. While there are/were no sex differences amongst volunteers in relation to the benefits from volunteering, there were are statistically significant differences for sophomores on the benefit codes of gaining skills/experience and a community connection. Junior students have statistically significant differences for the benefit code of a social/friend connection

Editorial

The last year has been a very busy one for the BMB. We have published 140 articles online, which is over twice the publication rate of the previous year. This reflects the increase in the submission rates and Springer's view that papers should be published online as quickly as possible. In addition, the entire archive of the Bulletin of Mathematical Biology is now available on the Springer website for the journal, digitized back to Vol. 1, No. 1, published in 1939

Inefficacy of the Crisis Intervention Team Model

Following the murder of Joseph Dewayne Robinson in 1987 by Memphis, Tennessee police, community and civil organizers collaborated with the Universities of Memphis and Tennessee and the Memphis Police Department to organize Memphis PD’s Crisis Intervention Team (CIT). Similar modes of the CIT model have been deployed nationally as a law enforcement-based crisis intervention strategy aiming to reduce lethality in police response to mental health crises. At least 2,700 communities around the United States utilize CIT methodology to provide mental health education and training for police officers, yet statistical evidence of police-related response, injury, and use of force with individuals experiencing mental illness crises undermines the CIT mission and goals. While systematic analyses of CIT training support officer-level outcomes, national police incident data confirms parallels between use of force and injury and individuals experiencing a mental health crisis. As a nationally deployed and largely unstandardized methodology, the CIT model seeks to reduce the risk of injury or death for people experiencing mental illness during emergency police interactions, yet its objective improvements in arrests, officer and citizen injury, and use of force during de-escalations remain unclear