A Mathematical Model of Tripartite Synapse: Astrocyte Induced Synaptic Plasticity

In this paper we present a biologically detailed mathematical model of tripartite synapses, where astrocytes modulate short-term synaptic plasticity. The model consists of a pre-synaptic bouton, a post-synaptic dendritic spine-head, a synaptic cleft and a peri-synaptic astrocyte controlling Ca2+ dynamics inside the synaptic bouton. This in turn controls glutamate release dynamics in the cleft. As a consequence of this, glutamate concentration in the cleft has been modeled, in which glutamate reuptake by astrocytes has also been incorporated. Finally, dendritic spine-head dynamics has been modeled. As an application, this model clearly shows synaptic potentiation in the hippocampal region, i.e., astrocyte Ca2+ mediates synaptic plasticity, which is in conformity with the majority of the recent findings (Perea & Araque, 2007; Henneberger et al., 2010; Navarrete et al., 2012).Comment: 42 pages, 14 figures, Journal of Biological Physics (to appear

The African pitta, Pitta Angolensis Vieillot

Volume: XXVI

Astrocyte dynamics revisited

A vast amount of experimental evidence hints that astrocytes could be active players in information processing of the brain. It remains unclear nevertheless how these cells could encode synaptic stimuli through variations of their intracellular Ca2+ levels as well as how they could influence the timing of neuronal activity. In this study, we adopt a dynamical system approach and use tools of bifurcation theory and statistics in order to address both these issues. We consider a Li-Rinzel description of astrocyte Ca2+ signalling and we show that thanks to specific choices of biophysical parameters, synaptic activity could be encoded by modulations of Ca2+ oscillations in amplitude (AM), in frequency (FM), or in both (AFM). Interestingly, AM- and FM-encoding pertain to different classes of Ca2+ excitability that are reminiscent of the analogous neuronal ones. In addition, any transition from AM to FM and viceversa is accomplished through a characteristic “Bautin-cusp" bifurcation sequence which could hint the conditions for the coexistence of both these encoding modes. Such a possibility is throughout investigated and eventually formalized in the “CPB rule", a heuristic criterion valid for any system of the Li-Rinzel type that allow us to determine several biophysical conditions under which AFM Ca2+ dynamics could occur in astrocytes. Successively, we demonstrate that different encoding modes could be accomplished not only on the basis of inherent heterogeneities of cellular properties but also thanks to the existence of different (opposite) Ca2+ feedbacks on IP3 production. In this regard we modify the Li-Rinzel system in order to include a third equation for IP3 metabolism which also considers Ca2+ activation of PLC (positive feedback) and Ca2+ activation of IP3 3-kinase (negative feedback). In agreement with experimental data and recent theoretical studies, our analysis hints that Ca2+-dependent activation of PLC could account for a much richer variety of oscillatory regimes and encoding modes with respect to the case of negative feedback. An inspection of the parameter space reveals that this is possible because positive Ca2+ feedback on IP3 production modifies the structure of the system towards the appearance of multistationarity which could also account for Ca2+ dynamics of bursting type. Moreover, we show that the lifetime of IP3 could be a critical limiting factor for the effects of both feedbacks. Meaningfully, IP3 turnover could influence the integrative properties of astrocytic Ca2+ signalling by affecting both the frequency band of Ca2+ oscillations and the threshold stimulus for their onset. In addition, IP3 turnover could regulate the expression of mGlu receptors on the astrocyte plasma membrane. In this regard, we show that the density of mGlu receptors could be proportional to the rate of IP3 turnover and accordingly we provide an estimation of this parameter which otherwise would remain experimentally unknown. In particular, on the basis of our bifurcation data, we estimate that AM-encoding astrocytes could express an average mGluR density between 1-50 receptors/um^2 that is of the same order of AMPA receptor density measured on Bergmann glia somas. We show however that FM-encoding astrocytes could be consistent with an overexpression of mGluRs by a factor of 8 or 10 with respect to AM-encoding cells. In the last part of our study, we finally consider the characterization of the possible integrative properties of astrocyte Ca2+ signalling and the effects of astrocytic Ca2+-dependent glutamate exocytosis on neuronal activity. For this purpose we develop a mathematical description of neuron-glial interactions at the level of a single astrocytic microdomain in which our modified Li-Rinzel model of astrocyte Ca2+/IP3 dynamics is coupled with an ensemble of Tsodyks-Uziel-Markram synapses on the soma a regular spiking Izhikevich neuron. We show that astrocytes of different classes of excitability could respond differently to stimuli of equal intensities and identical interspike-interval (ISI) statistics. On the other hand, stimuli at the same frequency but with different ISI statistics could trigger distinct Ca2+ responses in cells of the same type. All these possibilities are also dependent on the nature of the stimulatory pathway. Astrocyte Ca2+ signalling could therefore result from a complex integration of spatiotemporal features of synaptic stimuli which could represent a form of processing of neuronal activity. Perhaps even more intriguingly, Ca2+ signals could encode information on the past history of synaptic activity which in turn would be transferred back to neuron through Ca2+-dependent glutamate exocytosis with deep consequences on the informational content of postsynaptic neuronal activity. Computation of Fano Factors on simulated time series of postsynaptic action potentials reveal in fact that neuron-astrocyte interactions could substantially affect the rate of neuronal firing by adding long-range correlations to the timing of neuronal spikes. These results are consistent with the possibility that neuron-astrocyte bidirectional signalling could influence information processing of the brain by increasing the information-coding dimension of the neural code

REVIEW OF MUSIC AND ITS THERAPEUTICS W.S.R. AYURVEDIC CLASSICS (BRIHATRAYEE

Ayurveda is the science of living being. With the aim of health and procurement of disease it almost covers all facets of life. It includes health of an individual at physical, mental, spiritual, social level. Ayurvedic classics includes brihatrayee samhita like Charak, Sushruta and Ashtanga Hridaya. A review based study of music (geet, sangeet) was done in these classics to explore whether these classics includes any form of music as therapy or not. Based on review of these classics it was found that music in form of geet (vocal or instrument) has been given in contexts like vajikara(aphrodisiac), vata/pitta prakriti (basic consititutional make up), gandharva sattva, madyapana (intake of alcohol), therapy for rajyakshma (immune deficiency diseases), sanyasa (syncope/coma), jivadan (haemetemesis) etc. various swara have been correlated with their pacifying power of three sharirikadoshas viz. vata, pitta and kapha. Also a relationship between various raga of indian classical music have been said to be based on time of its singing which may be used as a therapy to pacify the dearrangement of prevalent doshas. several articles have shown music as therapy in sleep disorder, psychiatric disorders, schizophrenia, cardiovascular, cancer etc. with this paper a perspective of Ayurveda have been explored in music therapeutics

A critical review of fundamental principles of Ayurveda

The fundamental principle holds a strong ground in Ayurveda. Every medical stream has its own science in which its matter is developed, evolved and explained. From creation of living to issues of health, disease and its treatment these fundamental principles are the root. These can be enumerated as Tridosha, Panchamahabhuta, Prakriti, Ojas, Dhatu, Mala, Agni, Manas, Atma etc. They are most unique and original approach to the material creation and it has all scope to incorporate the modern development in the elemental physics. The aim of Ayurveda is to maintain the proper equilibrium of dosa, dhatus, and mala constituent in order to preserve health in a healthy person and cure a disease in a diseased person.The presence of cognition as well as the absence of cognition is an indication of the mind. In the presence of senses with senses object and soul the man does not perceive a thing in the absence of mind that is to say that senses are unable to grasp the object in the absence of Manas. The term Ojas has been used in Ayurveda for the factor which prevents decay and degeneratioif the body and provides strength and support against a disease. Concept of Agni which incorporates all activities and factors responsible for digestion and metabolism in the living organism as known today, knowledge to these fundamental principles is a key to health and diseases .Maintenances of health depend on good and sound knowledge of these. Detail will be given in full paper. Keywords: Ayurveda, health, dosa, Agni, min

conceptual review of Adhyatma in Ayurveda

This adhyatma gyana is also a part of Ayurveda because it is related to human health especially with mental health; A group of diseases is described independently in Sushruta as adhyatmika dukha. Contemporary books also mention adhyatmika dukha and adhyatma has been described in details. The subject matter of adhyatma has been mentioned from different point of view, but in fact the adhyatma is related to atman, as it is knowledge of atman and its related subjects are the knowledgeable materials of adhyatma. Here in thispaper is a brief review of adhyatma ,terminology and its different prospects in ayurveda

Developing student spatial ability with 3D software applications

This paper reports on the design of a library of software applications for the teaching and learning of spatial geometry and visual thinking. The core objective of these applications is the development of a set of dynamic microworlds, which enables (i) students to construct, observe and manipulate configurations in space, (ii) students to study different solids and relates them to their corresponding nets, and (iii) students to promote their visualization skills through the process of constructing dynamic visual images. During the developmental process of software applications the key elements of spatial ability and visualization (mental images, external representations, processes, and abilities of visualization) are carefully taken into consideration

Symbols and the bifurcation between procedural and conceptual thinking

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to d o mathematical problems and to think about mathematical relationships. In this presentation we consider the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and procedural thinking. Evidence will be given from several different contexts in the development of symbols through arithmetic, algebra and calculus, then on to the formalism of axiomatic mathematics. This is taken from a number of research studies recently performed for doctoral dissertations at the University of Warwick by students from the USA, Malaysia, Cyprus and Brazil, with data collected in the USA, Malaysia and the United Kingdom. All the studies form part of a broad investigation into why some students succeed yet others fail