A Minimal Model of Burst-Noise Induced Bistability

We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified version of the Schl\"ogl model, which is a chemical reaction system with only one type of molecule. The strength of the intrinsic noise is varied without changing the deterministic description by introducing bursts in the autocatalytic production step. We study the transitions between monostable and bistable behavior in this system by evaluating the number of maxima of the stationary probability distribution. We find that changing the size of bursts can destroy and even induce saddle-node bifurcations. This means that a bursty production of molecules can qualitatively change the dynamics of a chemical reaction system even when the deterministic description remains unchanged.Comment: 7 pages, 9 figure

Microbiome abundance patterns as attractors and the implications for the inference of microbial interaction networks

Inferring microbial interaction networks from abundance patterns is an important approach to advance our understanding of microbial communities in general and the human microbiome in particular. Here we suggest discriminating two levels of information contained in microbial abundance data: (1) the quantitative abundance values and (2) the pattern of presences and absences of microbial organisms. The latter allows for a binary view on microbiome data and a novel interpretation of microbial data as attractors, or more precisely as fixed points, of a Boolean network. Starting from these attractors, our aim is to infer an interaction network between the species present in the microbiome samples. To accomplish this task, we introduce a novel inference method that combines the previously published ESABO (Entropy Shifts of Abundance vectors under Boolean Operations) method with an evolutionary algorithm. The key idea of our approach is that the inferred network should reproduce the original set of (observed) binary abundance patterns as attractors. We study the accuracy and runtime properties of this evolutionary method, as well as its behavior under incomplete knowledge of the attractor sets. Based on this theoretical understanding of the method we then show an application to empirical data

Successful Resuscitation in a Model of Asphyxia and Hemorrhage to Test Different Volume Resuscitation Strategies. A Study in Newborn Piglets After Transition

Background: Evidence for recommendations on the use of volume expansion during cardiopulmonary resuscitation in newborn infants is limited.Objectives: To develop a newborn piglet model with asphyxia, hemorrhage, and cardiac arrest to test different volume resuscitation on return of spontaneous circulation (ROSC). We hypothesized that immediate red cell transfusion reduces time to ROSC as compared to the use of an isotonic crystalloid fluid.Methods: Forty-four anaesthetized and intubated newborn piglets [age 32 h (12–44 h), weight 1,220 g (1,060–1,495g), Median (IQR)] were exposed to hypoxia and blood loss until asystole occurred. At this point they were randomized into two groups: (1) Crystalloid group: receiving isotonic sodium chloride (n = 22). (2) Early transfusion group: receiving blood transfusion (n = 22). In all other ways the piglets were resuscitated according to ILCOR 2015 guidelines [including respiratory support, chest compressions (CC) and epinephrine use]. One hour after ROSC piglets from the crystalloid group were randomized in two sub-groups: late blood transfusion and infusion of isotonic sodium chloride to investigate the effects of a late transfusion on hemodynamic parameters.Results: All animals achieved ROSC. Comparing the crystalloid to early blood transfusion group blood loss was 30.7 ml/kg (22.3–39.6 ml/kg) vs. 34.6 ml/kg (25.2–44.7 ml/kg), Median (IQR). Eleven subjects did not receive volume expansion as ROSC occurred rapidly. Thirty-three animals received volume expansion (16 vs. 17 in the crystalloid vs. early transfusion group). 14.1% vs. 10.5% of previously extracted blood volume in the crystalloid vs. early transfusion group was infused before ROSC. There was no significant difference in time to ROSC between groups [crystalloid group: 164 s (129–198 s), early transfusion group: 163 s (162–199 s), Median (IQR)] with no difference in epinephrine use.Conclusions: Early blood transfusion compared to crystalloid did not reduce time to ROSC, although our model included only a moderate degree of hemorrhage and ROSC occurred early in 11 subjects before any volume resuscitation occurred

Very Low Tidal Volume Ventilation with Associated Hypercapnia - Effects on Lung Injury in a Model for Acute Respiratory Distress Syndrome

BACKGROUND: Ventilation using low tidal volumes with permission of hypercapnia is recommended to protect the lung in acute respiratory distress syndrome. However, the most lung protective tidal volume in association with hypercapnia is unknown. The aim of this study was to assess the effects of different tidal volumes with associated hypercapnia on lung injury and gas exchange in a model for acute respiratory distress syndrome. METHODOLOGY/PRINCIPAL FINDINGS: In this randomized controlled experiment sixty-four surfactant-depleted rabbits were exposed to 6 hours of mechanical ventilation with the following targets: Group 1: tidal volume = 8-10 ml/kg/PaCO(2) = 40 mm Hg; Group 2: tidal volume = 4-5 ml/kg/PaCO(2) = 80 mm Hg; Group 3: tidal volume = 3-4 ml/kg/PaCO(2) = 120 mm Hg; Group 4: tidal volume = 2-3 ml/kg/PaCO(2) = 160 mm Hg. Decreased wet-dry weight ratios of the lungs, lower histological lung injury scores and higher PaO(2) were found in all low tidal volume/hypercapnia groups (group 2, 3, 4) as compared to the group with conventional tidal volume/normocapnia (group 1). The reduction of the tidal volume below 4-5 ml/kg did not enhance lung protection. However, oxygenation and lung protection were maintained at extremely low tidal volumes in association with very severe hypercapnia and no adverse hemodynamic effects were observed with this strategy. CONCLUSION: Ventilation with low tidal volumes and associated hypercapnia was lung protective. A tidal volume below 4-5 ml/kg/PaCO(2) 80 mm Hg with concomitant more severe hypercapnic acidosis did not increase lung protection in this surfactant deficiency model. However, even at extremely low tidal volumes in association with severe hypercapnia lung protection and oxygenation were maintained

Relation between the convective field and the stationary probability distribution of chemical reaction networks

We investigate the relation between the stationary probability distribution of chemical reaction systems and the convective field derived from the chemical Fokker–Planck equation (CFPE) by comparing predictions of the convective field to the results of stochastic simulations based on Gillespie's algorithm. The convective field takes into account the drift term of the CFPE and the reaction bias introduced by the diffusion term. For one-dimensional systems, fixed points and bifurcations of the convective field correspond to extrema and phenomenological bifurcations of the stationary probability distribution whenever the CFPE is a good approximation to the stochastic dynamics. This provides an efficient way to calculate the effect of system size on the number and location of probability maxima and their phenomenological bifurcations in parameter space. For two-dimensional systems, we study models that have saddle-node and Hopf bifurcations in the macroscopic limit. Here, the existence of two stable fixed points of the convective field correlates either with two peaks of the stationary probability distribution, or with a peak and a shoulder. In contrast, a Hopf bifurcation that occurs in the convective field for decreasing system size is not accompanied by the onset of a crater-shaped probability distribution; decreasing system size rather destroys craters and replaces them by local maxima

Analyse stochastischer Reaktionssysteme anhand der Extrema der stationären Fokker-Planck-Gleichung

Die Analyse stochastischer Reaktionsnetzwerke anhand einer Master- oder Fokker-Planck-Gleichung ist in der Regel deutlich komplexer und weniger anschaulich als eine Beschreibung als deterministisches dynamisches System und meist nur numerisch möglich. Dennoch lassen sich viele interessante Phänomene, wie beispielsweise der Einfluss intrinsischen Rauschens, nur in stochastischen Modellen untersuchen. In dieser Arbeit wird daher ein Formalismus entwickelt, der – ausgehend von den Maxima und Minima der Fokker-Planck-Gleichung – eine Analyse stochastischer Reaktionsnetzwerke ermöglicht, die ebenso leicht zu handhaben ist wie die deterministische Beschreibung. Hierzu führen wir zunächst das sogenannte Konvektionsfeld α ein, dessen Nullstellen mit den Extrema der eindimensionalen, stationären Fokker-Planck-Gleichung übereinstimmen. Mithilfe dieser Größe analysieren wir rauschinduzierte stochastische Bifurkationen im Schlögl-Modell. Hierbei zeigt sich, dass sowohl stabile Systemzustände, die durch eine Erhöhung des intrinsischen Rauschens zerstört werden, als auch rauschinduzierte Bistabilität durch das Konvektionsfeld korrekt vorhergesagt werden. Bei der anschließenden Erweiterung des Formalismus auf mehrdimensionale Systeme ist jedoch der einfache Zusammenhang zwischen den Nullstellen von α und den Extrema der Fokker-Planck-Gleichung im Allgemeinen nicht mehr gegeben. Wir entwickeln daher eine Näherung für große Systemgrößen N, die eine Übertragung des Konvektionsfelds zumindest auf Systeme mit ausreichend großer Teilchenzahl ermöglicht. Anhand verschiedener Beispielsysteme lässt sich feststellen, dass diese Näherung für die meisten relevanten Reaktionsnetzwerke in weiten Teilen des Zustandsraum erfüllt ist. Mithilfe des Konvektionsfelds lassen sich zudem Phasenportraits des stochastischen Systems definieren, die in weiten Teilen die gleichen Eigenschaften aufweisen wie ihre deterministischen Pendants. Mit ihrer Hilfe analysieren wir unter anderem ein Modell nahrungssuchender Ameisen ohne Lösen der Fokker-Planck-Gleichung und unter Anwendung der gleichen mathematischen Methoden wie im deterministischen Fall. Für die hierbei erzielten Ergebnisse war ein Lösen der Fokker-Planck-Gleichung bislang unumgänglich. Anhand einesweiteren Beispiels aus der Populationsdynamik, dem sogenannten Rosenzweig-MacArthur-Modell, können wir außerdem eine neue Art von Bifurkation identifizieren, die nur in stochastischen Systemen auftreten kann: die Nullklinen-Lücken-Bifurkation. Diese lässt sich direkt aus den stochastischen Phasenportraits ablesen. Zuletzt erweitern wir unseren Formalismus um eine Methode zur Vorhersage stationärer Wahrscheinlichkeitsströme, die ebenfalls ohne Lösen der Fokker-Planck-Gleichung auskommt. Mit ihrer Hilfe stellen wir fest, dass an Orten, an denen unsere Näherung für kleine Systemgrößen versagt, in der Regel Dipolströme auftreten. Durch Anwendung auf verschiedene Beispielsysteme validieren wir die Vorhersagen dieser Methode. Hierbei analysieren wir unter anderem die unphysikalischen Ströme, die in der Fokker-Planck-Gleichung auftreten, wenn die zugrunde liegende Mastergleichung detailliertes Gleichgewicht aufweist

Predicting properties of the stationary probability currents for two-species reaction systems without solving the Fokker-Planck equation

We derive methods for estimating the topology of the stationary probability current $\vec{j}_s$ of the two-species Fokker-Planck equation (FPE) without the need to solve the FPE. These methods are chosen such that they become exact in certain limits, such as infinite system size or vanishing coupling between species in the diffusion matrix. The methods make predictions about the fixed points of $\vec{j}_s$ and their relation to extrema of the stationary probability distribution and to fixed points of the convective field, which is related to the deterministic drift of the system. Furthermore, they predict the rotation sense of $\vec{j}_s$ around extrema of the stationary probability distribution. Even though these methods cannot be proven to be valid away from extrema, the boundary lines between regions with different rotation sense are obtained with surprising accuracy. We illustrate and test these method using simple reaction systems with only one coupling term between the two species as well as a few generic reaction networks taken from literature. We use it also to investigate the shape of non-physical probability currents occurring in reaction systems with detailed balance due to the approximations involved in deriving the Fokker-Planck equation

Einfluss von permissiver Hyperkapnie auf den Gasaustausch, die Lungenschädigung und die Hämodynamik am Versuchstier mit schwerem "Acute Respiratory Distress Syndrome (ARDS)"

Background: Ventilation using low tidal volumes with permission of hypercapnia is recommended to protect the lung in acute respiratory distress syndrome. However, the most lung protective tidal volume in association with hypercapnia is unknown. The aim of this study was to assess the effects of different tidal volumes with associated hypercapnia on lung injury and gas exchange in a model for acute respiratory distress syndrome. Methodology/Principal findings: In this randomized controlled experiment sixty-four surfactant-depleted rabbits were exposed to 6 hours of mechanical ventilation with the following targets: Group 1: tidal volume = 8 - 10 ml/kg/PaCO2 = 40 mm Hg; Group 2: tidal volume = 4 - 5 ml/kg/PaCO2 = 80 mm Hg; Group 3: tidal volume = 3 - 4 ml/kg/PaCO2 = 120 mm Hg; Group 4: tidal volume = 2 - 3 ml/kg/PaCO2 = 160 mm Hg. Decreased wet-dry weight ratios of the lungs, lower histological lung injury scores and higher PaO2 were found in all low tidal volume/hypercapnia groups (group 2, 3, 4) as compared to the group with conventional tidal volume/normocapnia (group 1). The reduction of the tidal volume below 4 - 5 ml/kg did not enhance lung protection. However, oxygenation and lung protection were maintained at extremely low tidal volumes in association with very severe hypercapnia and no adverse hemodynamic effects were observed with this strategy. Conclusion: Ventilation with low tidal volumes and associated hypercapnia was lung protective. A tidal volume below 4 - 5 ml/kg/PaCO2 80 mm Hg with concomitant more severe hypercapnic acidosis did not increase lung protection in this surfactant deficiency model. However, even at extremely low tidal volumes in association with severe hypercapnia lung protection and oxygenation were maintained

Review of advice services in Leicester

SIGLEAvailable from British Library Document Supply Centre-DSC:q97/12256 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Analysis of stochastic bifurcations with phase portraits

We propose a method to obtain phase portraits for stochastic systems. Starting from the Fokker-Planck equation, we separate the dynamics into a convective and a diffusive part. We show that stable and unstable fixed points of the convective field correspond to maxima and minima of the stationary probability distribution if the probability current vanishes at these points. Stochastic phase portraits, which are vector plots of the convective field, therefore indicate the extrema of the stationary distribution and can be used to identify stochastic bifurcations that change the number and stability of these extrema. We show that limit cycles in stochastic phase portraits can indicate ridges of the probability distribution, and we identify a novel type of stochastic bifurcation, where the probability maximum moves to the edge of the system through a gap between the two nullclines of the convective field