Stability of cluster solutions in a cooperative consumer chain model

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer-Verlag Berlin Heidelberg 2012.We study a cooperative consumer chain model which consists of one producer and two consumers. It is an extension of the Schnakenberg model suggested in Gierer and Meinhardt [Kybernetik (Berlin), 12:30-39, 1972] and Schnakenberg (J Theor Biol, 81:389-400, 1979) for which there is only one producer and one consumer. In this consumer chain model there is a middle component which plays a hybrid role: it acts both as consumer and as producer. It is assumed that the producer diffuses much faster than the first consumer and the first consumer much faster than the second consumer. The system also serves as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir. In the small diffusion limit we construct cluster solutions in an interval which have the following properties: The spatial profile of the third component is a spike. The profile for the middle component is that of two partial spikes connected by a thin transition layer. The first component in leading order is given by a Green's function. In this profile multiple scales are involved: The spikes for the middle component are on the small scale, the spike for the third on the very small scale, the width of the transition layer for the middle component is between the small and the very small scale. The first component acts on the large scale. To the best of our knowledge, this type of spiky pattern has never before been studied rigorously. It is shown that, if the feedrates are small enough, there exist two such patterns which differ by their amplitudes.We also study the stability properties of these cluster solutions. We use a rigorous analysis to investigate the linearized operator around cluster solutions which is based on nonlocal eigenvalue problems and rigorous asymptotic analysis. The following result is established: If the time-relaxation constants are small enough, one cluster solution is stable and the other one is unstable. The instability arises through large eigenvalues of order O(1). Further, there are small eigenvalues of order o(1) which do not cause any instabilities. Our approach requires some new ideas: (i) The analysis of the large eigenvalues of order O(1) leads to a novel system of nonlocal eigenvalue problems with inhomogeneous Robin boundary conditions whose stability properties have been investigated rigorously. (ii) The analysis of the small eigenvalues of order o(1) needs a careful study of the interaction of two small length scales and is based on a suitable inner/outer expansion with rigorous error analysis. It is found that the order of these small eigenvalues is given by the smallest diffusion constant ε22.RGC of Hong Kon

The ErbB2ΔEx16 splice variant is a major oncogenic driver in breast cancer that promotes a pro-metastatic tumor microenvironment.

Amplification and overexpression of erbB2/neu proto-oncogene is observed in 20-30% human breast cancer and is inversely correlated with the survival of the patient. Despite this, somatic activating mutations within erbB2 in human breast cancers are rare. However, we have previously reported that a splice isoform of erbB2, containing an in-frame deletion of exon 16 (herein referred to as ErbB2ΔEx16), results in oncogenic activation of erbB2 because of constitutive dimerization of the ErbB2 receptor. Here, we demonstrate that the ErbB2ΔEx16 is a major oncogenic driver in breast cancer that constitutively signals from the cell surface. We further show that inducible expression of the ErbB2ΔEx16 variant in mammary gland of transgenic mice results in the rapid development of metastatic multifocal mammary tumors. Genetic and biochemical characterization of the ErbB2ΔEx16-derived mammary tumors exhibit several unique features that distinguish this model from the conventional ErbB2 ones expressing the erbB2 proto-oncogene in mammary epithelium. Unlike the wild-type ErbB2-derived tumors that express luminal keratins, ErbB2ΔEx16-derived tumors exhibit high degree of intratumoral heterogeneity co-expressing both basal and luminal keratins. Consistent with these distinct pathological features, the ErbB2ΔEx16 tumors exhibit distinct signaling and gene expression profiles that correlate with activation of number of key transcription factors implicated in breast cancer metastasis and cancer stem cell renewal

Motivating Emotional Intelligence: A Reinforcement Sensitivity Theory (RST) Perspective

Trait emotional intelligence (trait EI) is generally associated with positive outcomes and can inform clinical and social interventions. We investigated the sub-factors of trait EI: Wellbeing, Self-control, Emotionality, and Sociability, in the context of the Reinforcement Sensitivity Theory (RST) of motivation. In Study 1, participants (N = 247) completed Carver and White’s (1994) BIS/BAS scales and a measure of trait EI. All EI sub-factors were positively associated with BAS Drive and negatively with BIS. Study 2 (N = 382) employed a new questionnaire based on revised RST (Corr & Cooper, 2016). All trait EI factors were positively associated with BAS Goal-Drive Persistence and Reward Interest, and negatively with the BIS. Self-control showed negative associations with BAS Impulsivity and was the only factor not to correlate with BAS Reward Reactivity. Results suggest that high trait EI individuals are goal driven, sensitive to reward and lower in avoidance motivation and negative emotion. This motivational basis to trait EI further explicates its structure

Using Rasch analysis to form plausible health states amenable to valuation: the development of CORE-6D from CORE-OM in order to elicit preferences for common mental health problems

Purpose: To describe a new approach for deriving a preference-based index from a condition specific measure that uses Rasch analysis to develop health states. Methods: CORE-OM is a 34-item instrument monitoring clinical outcomes of people with common mental health problems. CORE-OM is characterised by high correlation across its domains. Rasch analysis was used to reduce the number of items and response levels in order to produce a set of unidimensionally-behaving items, and to generate a credible set of health states corresponding to different levels of symptom severity using the Rasch item threshold map. Results: The proposed methodology resulted in the development of CORE-6D, a 2-dimensional health state description system consisting of a unidimensionally-behaving 5-item emotional component and a physical symptom item. Inspection of the Rasch item threshold map of the emotional component helped identify a set of 11 plausible health states, which, combined with the physical symptom item levels, will be used for the valuation of the instrument, resulting in the development of a preference-based index. Conclusions: This is a useful new approach to develop preference-based measures where the domains of a measure are characterised by high correlation. The CORE-6D preference-based index will enable calculation of Quality Adjusted Life Years in people with common mental health problems

The effects of climatic fluctuations and extreme events on running water ecosystems

Most research on the effects of environmental change in freshwaters has focused on incremental changes in average conditions, rather than fluctuations or extreme events such as heatwaves, cold snaps, droughts, floods or wildfires, which may have even more profound consequences. Such events are commonly predicted to increase in frequency, intensity and duration with global climate change, with many systems being exposed to conditions with no recent historical precedent. We propose a mechanistic framework for predicting potential impacts of environmental fluctuations on running water ecosystems by scaling up effects of fluctuations from individuals to entire ecosystems. This framework requires integration of four key components: effects of the environment on individual metabolism, metabolic and biomechanical constraints on fluctuating species interactions, assembly dynamics of local food webs and mapping the dynamics of the meta-community onto ecosystem function. We illustrate the framework by developing a mathematical model of environmental fluctuations on dynamically assembling food webs. We highlight (currently limited) empirical evidence for emerging insights and theoretical predictions. For example, widely supported predictions about the effects of environmental fluctuations are: high vulnerability of species with high per capita metabolic demands such as large-bodied ones at the top of food webs; simplification of food web network structure and impaired energetic transfer efficiency; reduced resilience and top-down relative to bottom-up regulation of food web and ecosystem processes. We conclude by identifying key questions and challenges that need to be addressed to develop more accurate and predictive bio-assessments of the effects of fluctuations, and implications of fluctuations for management practices in an increasingly uncertain world

Eosinophils Are Important for Protection, Immunoregulation and Pathology during Infection with Nematode Microfilariae

Eosinophil responses typify both allergic and parasitic helminth disease. In helminthic disease, the role of eosinophils can be both protective in immune responses and destructive in pathological responses. To investigate whether eosinophils are involved in both protection and pathology during filarial nematode infection, we explored the role of eosinophils and their granule proteins, eosinophil peroxidase (EPO) and major basic protein-1 (MBP-1), during infection with Brugia malayi microfilariae. Using eosinophil-deficient mice (PHIL), we further clarify the role of eosinophils in clearance of microfilariae during primary, but not challenge infection in vivo. Deletion of EPO or MBP-1 alone was insufficient to abrogate parasite clearance suggesting that either these molecules are redundant or eosinophils act indirectly in parasite clearance via augmentation of other protective responses. Absence of eosinophils increased mast cell recruitment, but not other cell types, into the broncho-alveolar lavage fluid during challenge infection. In addition absence of eosinophils or EPO alone, augmented parasite-induced IgE responses, as measured by ELISA, demonstrating that eosinophils are involved in regulation of IgE. Whole body plethysmography indicated that nematode-induced changes in airway physiology were reduced in challenge infection in the absence of eosinophils and also during primary infection in the absence of EPO alone. However lack of eosinophils or MBP-1 actually increased goblet cell mucus production. We did not find any major differences in cytokine responses in the absence of eosinophils, EPO or MBP-1. These results reveal that eosinophils actively participate in regulation of IgE and goblet cell mucus production via granule secretion during nematode-induced pathology and highlight their importance both as effector cells, as damage-inducing cells and as supervisory cells that shape both innate and adaptive immunity

Appointing Women to Boards: Is There a Cultural Bias?

Companies that are serious about corporate governance and business ethics are turning their attention to gender diversity at the most senior levels of business (Institute of Business Ethics, Business Ethics Briefing 21:1, 2011). Board gender diversity has been the subject of several studies carried out by international organizations such as Catalyst (Increasing gender diversity on boards: Current index of formal approaches, 2012), the World Economic Forum (Hausmann et al., The global gender gap report, 2010), and the European Board Diversity Analysis (Is it getting easier to find women on European boards? 2010). They all lead to reports confirming the overall relatively low proportion of women on boards and the slow pace at which more women are being appointed. Furthermore, the proportion of women on corporate boards varies much across countries. Based on institutional theory, this study hypothesizes and tests whether this variation can be attributed to differences in cultural settings across countries. Our analysis of the representation of women on boards for 32 countries during 2010 reveals that two cultural characteristics are indeed associated with the observed differences. We use the cultural dimensions proposed by Hofstede (Culture’s consequences: International differences in work-related values, 1980) to measure this construct. Results show that countries which have the greatest tolerance for inequalities in the distribution of power and those that tend to value the role of men generally exhibit lower representations of women on boards

Mutual information rate and bounds for it

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two data sets (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators

You turn me cold: evidence for temperature contagion

Introduction During social interactions, our own physiological responses influence those of others. Synchronization of physiological (and behavioural) responses can facilitate emotional understanding and group coherence through inter-subjectivity. Here we investigate if observing cues indicating a change in another's body temperature results in a corresponding temperature change in the observer. Methods Thirty-six healthy participants (age; 22.9±3.1 yrs) each observed, then rated, eight purpose-made videos (3 min duration) that depicted actors with either their right or left hand in visibly warm (warm videos) or cold water (cold videos). Four control videos with the actors' hand in front of the water were also shown. Temperature of participant observers' right and left hands was concurrently measured using a thermistor within a Wheatstone bridge with a theoretical temperature sensitivity of <0.0001°C. Temperature data were analysed in a repeated measures ANOVA (temperature × actor's hand × observer's hand). Results Participants rated the videos showing hands immersed in cold water as being significantly cooler than hands immersed in warm water, F(1,34) = 256.67, p0.1). There was however no evidence of left-right mirroring of these temperature effects p>0.1). Sensitivity to temperature contagion was also predicted by inter-individual differences in self-report empathy. Conclusions We illustrate physiological contagion of temperature in healthy individuals, suggesting that empathetic understanding for primary low-level physiological challenges (as well as more complex emotions) are grounded in somatic simulation

Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue.Comment: 26 pages, 13 figures, appendix and 2 movies, as accepted to PLoS ONE 2011/08/0