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

Existence and Stability of a Spike in the Central Component for a Consumer Chain Model

We study a three-component consumer chain model which is based on Schnakenberg type kinetics. In this model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. This means that the first consumer (central component) plays a hybrid role: it acts both as consumer and producer. The model is an extension of the Schnakenberg model suggested in \cite{gm,schn1} for which there is only one producer and one consumer. It is assumed that both the producer and second consumer diffuse much faster than the central component. We construct single spike solutions on an interval for which the profile of the first consumer is that of a spike. The profiles of the producer and the second consumer only vary on a much larger spatial scale due to faster diffusion of these components. It is shown that there exist two different single spike solutions if the feed rates are small enough: a large-amplitude and a small-amplitude spike. We study the stability properties of these solutions in terms of the system parameters. We use a rigorous analysis for the linearized operator around single spike solutions based on nonlocal eigenvalue problems. The following result is established: If the time-relaxation constants for both producer and second consumer vanish, the large-amplitude spike solution is stable and the small-amplitude spike solution is unstable. We also derive results on the stability of solutions when these two time-relaxation constants are small. We show a new effect: if the time-relaxation constant of the second consumer is very small, the large-amplitude spike solution becomes unstable. To the best of our knowledge this phenomenon has not been observed before for the stability of spike patterns. It seems that this behavior is not possible for two-component reaction-diffusion systems but that at least three components are required. Our main motivation to study this system is mathematical since the novel interaction of a spike in the central component with two other components results in new types of conditions for the existence and stability of a spike. This model is realistic if several assumptions are made: (i) cooperation of consumers is prevalent in the system, (ii) the producer and the second consumer diffuse much faster than the first consumer, and (iii) there is practically an unlimited pool of producer. The first assumption has been proven to be correct in many types of consumer groups or populations, the second assumption occurs if the central component has a much smaller mobility than the other two, the third assumption is realistic if the consumers do not feel the impact of the limited amount of producer due to its large quantity. This chain model plays a role in population biology, where consumer and producer are often called predator and prey. This system can also be used as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir

Diagnosis and outcome of oesophageal Crohn's disease

BACKGROUND AND AIMS: Crohn's disease (CD) can involve any part of the gastrointestinal tract. We aimed to characterize clinical, endoscopic, histologic features and treatment outcomes of CD patients with oesophageal involvement. METHODS: We collected cases through a retrospective multicentre European Crohn's and Colitis Organisation CONFER [COllaborative Network For Exceptionally Rare case reports] project. Clinical data were recorded in a standardized case report form. RESULTS: A total of 40 patients were reported [22 males, mean (±SD, range) age at oesophageal CD diagnosis: 25 (±13.3, 10-71) years and mean time of follow-up: 67 (±68.1, 3-240) months]. Oesophageal involvement was established at CD diagnosis in 26 patients (65%) and during follow-up in 14. CD was exclusively located in the oesophagus in 2 patients. Thirteen patients (32.2%) were asymptomatic at oesophageal disease diagnosis. Oesophageal strictures were present in 5 patients and fistulizing oesophageal disease in one. Eight patients exhibited granulomas on biopsies. Proton-pump inhibitors (PPIs) were administered in 37 patients (92.5%). Three patients underwent endoscopic dilation for symptomatic strictures and none oesophageal-related surgery. Diagnosis in pre-established CD resulted in treatment modifications in 9/14 patients. Clinical remission of oesophageal disease was seen in 33/40 patients (82.5%) after a mean time of 7 (±5.6, 1-18) months. Follow-up endoscopy was performed in 29/40 patients and 26/29 (89.7%) achieved mucosal healing. CONCLUSION: In this case series the endoscopic and histologic characteristics of isolated oesophageal CD were similar to those reported in other sites of involvement. Treatment was primarily conservative, with PPIs administered in the majority of patients and modifications in pre-existing IBD-related therapy occurring in two thirds of them. Clinical and endoscopic remission was achieved in more than 80% of the patients.info:eu-repo/semantics/publishedVersio

Measurement delay associated with the Guardian RT continuous glucose monitoring system.

AIMS: Using compartment modelling, we assessed the time delay between blood glucose and sensor glucose measured by the Guardian RT continuous glucose monitoring system in young subjects with Type 1 diabetes (T1D). METHODS: Twelve children and adolescents with T1D treated by continuous subcutaneous insulin infusion (male/female 7/5; age 13.1 +/- 4.2 years; body mass index 21.9 +/- 4.3 kg/m(2); mean +/- sd) were studied over 19 h in a Clinical Research Facility. Guardian RT was calibrated every 6 h and sensor glucose measured every 5 min. Reference blood glucose was measured every 15 min using a YSI 2300 STAT Plus Analyser. A population compartment model of sensor glucose-blood glucose kinetics was adopted to estimate the time delay, the calibration scale and the calibration shift. RESULTS: The population median of the time delay was 15.8 (interquartile range 15.2, 16.5) min, which was corroborated by correlation analysis between blood glucose and 15-min delayed sensor glucose. The delay has a relatively low intersubject variability, with 95% of individuals predicted to have delays between 10.4 and 24.3 min. Population medians (interquartile range) for the scale and shift are 0.800 (0.777, 0.823) (unitless) and 1.66 (1.47, 1.84) mmol/l, respectively. CONCLUSIONS: In young subjects with T1D, the total time delay associated with the Guardian RT system was approximately 15 min. This is twice that expected on physiological grounds, suggesting a 5- to 10-min delay because of data processing. Delays above 25 min are rarely to be observed

A Stochastic Approach to Shortcut Bridging in Programmable Matter

In a self-organizing particle system, an abstraction of programmable matter, simple computational elements called particles with limited memory and communication self-organize to solve system-wide problems of movement, coordination, and configuration. In this paper, we consider a stochastic, distributed, local, asynchronous algorithm for "shortcut bridging", in which particles self-assemble bridges over gaps that simultaneously balance minimizing the length and cost of the bridge. Army ants of the genus Eciton have been observed exhibiting a similar behavior in their foraging trails, dynamically adjusting their bridges to satisfy an efficiency trade-off using local interactions. Using techniques from Markov chain analysis, we rigorously analyze our algorithm, show it achieves a near-optimal balance between the competing factors of path length and bridge cost, and prove that it exhibits a dependence on the angle of the gap being "shortcut" similar to that of the ant bridges. We also present simulation results that qualitatively compare our algorithm with the army ant bridging behavior. Our work gives a plausible explanation of how convergence to globally optimal configurations can be achieved via local interactions by simple organisms (e.g., ants) with some limited computational power and access to random bits. The proposed algorithm also demonstrates the robustness of the stochastic approach to algorithms for programmable matter, as it is a surprisingly simple extension of our previous stochastic algorithm for compression.Comment: Published in Proc. of DNA23: DNA Computing and Molecular Programming - 23rd International Conference, 2017. An updated journal version will appear in the DNA23 Special Issue of Natural Computin

Self Injection length in La0.7 Ca0.3 Mno3-YBa 2Cu3O7-d ferromagnet- superconductor multi layer thin films

We have carried out extensive studies on the self-injection problem in barrierless heterojunctions between La0.7Ca0.3MnO3 (LCMO) and YBa2Cu3O7-d (YBCO). The heterojunctions were grown in situ by sequentially growing LCMO and YBCO films on LaAlO3 (LAO) substrate using a pulsed laser deposition (PLD) system. YBCO micro-bridges with 64 microns width were patterned both on the LAO (control) and LCMO side of the substrate. Critical current, Ic, was measured at 77K on both the control side as well as the LCMO side for different YBCO film thickness. It was observed that while the control side showed a Jc of ~2 x 10E6 A/ cm2 the LCMO side showed about half the value for the same thickness (1800 A). The difference in Jc indicates that a certain thickness of YBCO has become 'effectively' normal due to self-injection. From the measurement of Jc at two different thickness' (1800 A and 1500 A) of YBCO both on the LAO as well as the LCMO side, the value of self-injection length (at 77K) was estimated to be ~900 A self-injection length has been quantified. A control experiment carried out with LaNiO3 deposited by PLD on YBCO did not show any evidence of self-injection.Comment: 6 pages, one figure in .ps forma

A Compensatory Mutation Provides Resistance to Disparate HIV Fusion Inhibitor Peptides and Enhances Membrane Fusion

Fusion inhibitors are a class of antiretroviral drugs used to prevent entry of HIV into host cells. Many of the fusion inhibitors being developed, including the drug enfuvirtide, are peptides designed to competitively inhibit the viral fusion protein gp41. With the emergence of drug resistance, there is an increased need for effective and unique alternatives within this class of antivirals. One such alternative is a class of cyclic, cationic, antimicrobial peptides known as θ-defensins, which are produced by many non-human primates and exhibit broad-spectrum antiviral and antibacterial activity. Currently, the θ-defensin analog RC-101 is being developed as a microbicide due to its specific antiviral activity, lack of toxicity to cells and tissues, and safety in animals. Understanding potential RC-101 resistance, and how resistance to other fusion inhibitors affects RC-101 susceptibility, is critical for future development. In previous studies, we identified a mutant, R5-tropic virus that had evolved partial resistance to RC-101 during in vitro selection. Here, we report that a secondary mutation in gp41 was found to restore replicative fitness, membrane fusion, and the rate of viral entry, which were compromised by an initial mutation providing partial RC-101 resistance. Interestingly, we show that RC-101 is effective against two enfuvirtide-resistant mutants, demonstrating the clinical importance of RC-101 as a unique fusion inhibitor. These findings both expand our understanding of HIV drug-resistance to diverse peptide fusion inhibitors and emphasize the significance of compensatory gp41 mutations. © 2013 Wood et al

Can intravenous oxytocin infusion counteract hyperinflammation in COVID-19 infected patients?

Objectives Based on its well-documented anti-inflammatory and restorative properties we propose trials with the natural hormone oxytocin for treatment of hospitalised Covid-19 patients. Methods We searched for, retrieved, and commented on specific literature regarding multiple functions of oxytocin with a special focus on its modulation of inflammatory, immune, and restorative functions. Results Available data gathered in animals and humans support the anti-inflammatory properties of oxytocin. The multiple anti-inflammatory effects of oxytocin have been demonstrated in vitro and in vivo in various animal models and also in humans in response to intravenous infusion of oxytocin. Furthermore, oxytocin has been documented to activate several types of protective and restorative mechanisms and to exert positive effects on the immune system. Conclusions In addition, to being anti-inflammatory, it may be hypothesised, that oxytocin may be less suppressive on adaptive immune systems, as compared with glucocorticoids. Finally, by its restorative effects coupled with its anti-stress and healing properties, oxytocin may shorten the recovery period of the Covid-19 patients

Use of B-natriuretic peptide as a diagnostic marker in the differential diagnosis of transfusion-associated circulatory overload

Transfusion-associated circulatory overload (TACO) occurs when the transfusion rate or volume exceeds the capacity of a compromised cardiovascular system. Characteristic symptoms and signs associated with TACO are neither sensitive nor specific. B-natriuretic peptide (BNP) is a 32-amino-acid polypeptide secreted from the cardiac ventricles in response to ventricular volume expansion and pressure overload. This study was performed to explore the usage of BNP in the differential diagnosis of TACO. STUDY DESIGN AND METHODS: Pre- and posttransfusion BNP levels were determined in 21 patients with suspected TACO and 19 control patients. The BNP was considered significant if the posttransfusion-to-pretransfusion ratio was at least 1.5 and the posttransfusion BNP level was at least 100 pg per mL. RESULTS: The BNP test has a sensitivity and specificity of 81 and 89 percent, respectively, in diagnosis of TACO. It has a positive predictive value of 89 percent, a negative predictive value of 81 percent, and an accuracy of 87 percent. In logistic regression analysis, BNP was found to have significant predictive power independent of other clinical variables in models predicting which patients had TACO. CONCLUSIONS: Our study suggests that in patients who present symptoms suggestive of TACO, BNP can be a useful adjunct marker in confirming volume overload as the cause of acute dyspnea and symptoms related to cardiovascular compromise.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75697/1/j.1537-2995.2005.04326.x.pd

Using geographically weighted regression to explore the spatially heterogeneous spread of bovine tuberculosis in England and Wales

An understanding of the factors that affect the spread of endemic bovine tuberculosis (bTB) is critical for the development of measures to stop and reverse this spread. Analyses of spatial data need to account for the inherent spatial heterogeneity within the data, or else spatial autocorrelation can lead to an overestimate of the significance of variables. This study used three methods of analysis—least-squares linear regression with a spatial autocorrelation term, geographically weighted regression (GWR) and boosted regression tree (BRT) analysis—to identify the factors that influence the spread of endemic bTB at a local level in England and Wales. The linear regression and GWR methods demonstrated the importance of accounting for spatial differences in risk factors for bTB, and showed some consistency in the identification of certain factors related to flooding, disease history and the presence of multiple genotypes of bTB. This is the first attempt to explore the factors associated with the spread of endemic bTB in England and Wales using GWR. This technique improves on least-squares linear regression approaches by identifying regional differences in the factors associated with bTB spread. However, interpretation of these complex regional differences is difficult and the approach does not lend itself to predictive models which are likely to be of more value to policy makers. Methods such as BRT may be more suited to such a task. Here we have demonstrated that GWR and BRT can produce comparable outputs