Approaching criticality via the zero dissipation limit in the abelian avalanche model

The discrete height abelian sandpile model was introduced by Bak, Tang & Wiesenfeld and Dhar as an example for the concept of self-organized criticality. When the model is modified to allow grains to disappear on each toppling, it is called bulk-dissipative. We provide a detailed study of a continuous height version of the abelian sandpile model, called the abelian avalanche model, which allows an arbitrarily small amount of dissipation to take place on every toppling. We prove that for non-zero dissipation, the infinite volume limit of the stationary measure of the abelian avalanche model exists and can be obtained via a weighted spanning tree measure. We show that in the whole non-zero dissipation regime, the model is not critical, i.e., spatial covariances of local observables decay exponentially. We then study the zero dissipation limit and prove that the self-organized critical model is recovered, both for the stationary measure and for the dynamics. We obtain rigorous bounds on toppling probabilities and introduce an exponent describing their scaling at criticality. We rigorously establish the mean-field value of this exponent for $d > 4$.Comment: 46 pages, substantially revised 4th version, title has been changed. The main new material is Section 6 on toppling probabilities and the toppling probability exponen

Topical and Systemic Cannabidiol Improves Trinitrobenzene Sulfonic Acid Colitis in Mice

Background/Aims: Compounds of Cannabis sativa are known to exert anti-inflammatory properties, some of them without inducing psychotropic side effects. Cannabidiol (CBD) is such a side effect-free phytocannabinoid that improves chemically induced colitis in rodents when given intraperitoneally. Here, we tested the possibility whether rectal and oral application of CBD would also ameliorate colonic inflammation, as these routes of application may represent a more appropriate way for delivering drugs in human colitis. Methods: Colitis was induced in CD1 mice by trinitrobenzene sulfonic acid. Individual groups were either treated with CBD intraperitoneally (10 mg/kg), orally (20 mg/kg) or intrarectally (20 mg/kg). Colitis was evaluated by macroscopic scoring, histopathology and the myeloperoxidase (MPO) assay. Results: Intraperitoneal treatment of mice with CBD led to improvement of colonic inflammation. Intrarectal treatment with CBD also led to a significant improvement of disease parameters and to a decrease in MPO activity while oral treatment, using the same dose as per rectum, had no ameliorating effect on colitis. Conclusion: The data of this study indicate that in addition to intraperitoneal application, intrarectal delivery of cannabinoids may represent a useful therapeutic administration route for the treatment of colonic inflammation. Copyright (C) 2012 S. Karger AG, Base

Role of endocannabinoids and cannabinoid-1 receptors in cerebrocortical blood flow regulation

BACKGROUND: Endocannabinoids are among the most intensively studied lipid mediators of cardiovascular functions. In the present study the effects of decreased and increased activity of the endocannabinoid system (achieved by cannabinoid-1 (CB1) receptor blockade and inhibition of cannabinoid reuptake, respectively) on the systemic and cerebral circulation were analyzed under steady-state physiological conditions and during hypoxia and hypercapnia (H/H). METHODOLOGY/PRINCIPAL FINDINGS: In anesthetized spontaneously ventilating rats the CB1-receptor antagonist/inverse agonist AM-251 (10 mg/kg, i.v.) failed to influence blood pressure (BP), cerebrocortical blood flow (CoBF, measured by laser-Doppler flowmetry) or arterial blood gas levels. In contrast, the putative cannabinoid reuptake inhibitor AM-404 (10 mg/kg, i.v.) induced triphasic responses, some of which could be blocked by AM-251. Hypertension during phase I was resistant to AM-251, whereas the concomitant CoBF-increase was attenuated. In contrast, hypotension during phase III was sensitive to AM-251, whereas the concomitant CoBF-decrease was not. Therefore, CoBF autoregulation appeared to shift towards higher BP levels after CB1-blockade. During phase II H/H developed due to respiratory depression, which could be inhibited by AM-251. Interestingly, however, the concomitant rise in CoBF remained unchanged after AM-251, indicating that CB1-blockade potentially enhanced the reactivity of the CoBF to H/H. In accordance with this hypothesis, AM-251 induced a significant enhancement of the CoBF responses during controlled stepwise H/H. CONCLUSION/SIGNIFICANCE: Under resting physiological conditions CB1-receptor mediated mechanisms appear to have limited influence on systemic or cerebral circulation. Enhancement of endocannabinoid levels, however, induces transient CB1-independent hypertension and sustained CB1-mediated hypotension. Furthermore, enhanced endocannabinoid activity results in respiratory depression in a CB1-dependent manner. Finally, our data indicate for the first time the involvement of the endocannabinoid system and CB1-receptors in the regulation of the cerebral circulation during H/H and also raise the possibility of their contribution to the autoregulation of CoBF

Cannabinoid receptors and endocannabinoids: Evidence for new players

It is now well established that the psychoactive effects ofCannabis sativa are primarily mediated through neuronal CB1 receptors, while its therapeutic immune properties are primarily mediated through CB2 receptors. Two endocannabinoids, arachidonoylethanolamide and 2-arachidonoylglycerol, have been identified, their action on CB1 and CB2 thoroughly characterized, and their production and inactivation elucidated. However, many significant exceptions to these rules exist. Here we review the evidence suggesting that cannabinoids can modulate synaptic transmission, the cardiovascular system, and the immune system through receptors distinct from CB1 and CB2, and that an additional “independent” endocannabinoid signaling system that involves palmitoylethanolamide may exist