A principal means of transmitting intracellular calcium (Ca2+) waves at junctions between astrocytes involves the release of the chemical transmitter adenosine triphosphate (ATP). A model of this process is presented in which activation of purinergic P2Y receptors by ATP triggers the release of ATP, in an autocrine manner, as well as concomitantly increasing intracellular Ca2+. The dependence of the temporal characteristics of the Ca2+ wave are shown to critically depend on the dissociation constant (K(R)) for ATP binding to the P2Y receptor type. Incorporating this model astrocyte into networks of these cells successfully accounts for many of the properties of propagating Ca2+ waves, such as the dependence of velocity on the type of P2Y receptor and the time-lag of the Ca2+ wave behind the ATP wave. In addition, the conditions under which Ca2+ waves may jump from one set of astrocytes across an astrocyte-free lane to another set of astrocytes are quantitatively accounted for by the model. The properties of purinergic transmission at astrocyte junctions may determine many of the characteristics of Ca2+ propagation in networks of these cells.

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Excitatory postsynaptic currents (EPSCs) were recorded with loose patch electrodes placed over visualized boutons on the surface of rat pelvic ganglion cells. At 34 degrees C the time to peak of the EPSC was about 0.7 ms, and a single exponential described the declining phase with a time constant of about 4.0 ms; these times were not correlated with changes in the amplitude of the EPSC. The amplitude-frequency histogram of the EPSC at individual boutons was well described by a single Gaussian-distribution that possessed a variance similar to that of the electrical noise. Nonstationary fluctuation analysis of the EPSCs at a bouton indicated that about 120 ACh receptor channels were available beneath boutons for interaction with a quantum of ACh. The characteristics of these EPSCs were compared with the results of Monte Carlo simulations of the quantal release of 9000 acetylcholine (ACh) molecules onto receptor patches of density 1400 microns-2 and 0.41 micron diameter, using a kinetic scheme of interaction between ACh and the receptors similar to that observed at the neuromuscular junction. The simulated EPSC generated in this way had temporal characteristics similar to those of the experimental EPSC when either the diffusion of the ACh is slowed or allowance is made for a finite period of transmitter release from the bouton. The amplitude of the simulated EPSC then exhibited stochastic fluctuations similar to those of the experimental EPSC.

Micro-photolithographic methods have been employed to form discrete patterns of spinal cord astrocytes that allow quantitative measurements of Ca(2+) wave propagation. Astrocytes were confined to lanes 20-100 microm wide and Ca(2+) waves propagated from a point of mechanical stimulation or of application of adenosine triphosphate; all Ca(2+) wave propagation was blocked by simultaneous application of purinergic P2Y(1) and P2Y(2) antagonists. Stimulation of an astrocyte at one end of a lane, followed by further stimulation of this astrocyte, gave rise to Ca(2+) transients in the same astrocytes; however, if the second stimulation was applied to an astrocyte at the other end of the lane, then this gave rise to a different but overlapping set of astrocytes generating a Ca(2+) signal. Both the amplitude and velocity of the Ca(2+) wave decreased over 270 microm from the point of initiation, and thereafter remained, on average, constant with random variations for at least a further 350 microm. Also, the percentage of astrocytes that gave a Ca(2+) transient decreased with distance along lanes. All the above observations were quantitatively predicted by our recent theoretical model of purinergic junctional transmission, as was the Ca(2+) wave propagation along and between parallel lanes of astrocytes different distances apart. These observations show that a model in which the main determinants are the diffusion of adenosine triphosphates regeneratively released from a stimulated astrocyte, together with differences in the properties and density of the purinergic P2Y receptors on astrocytes, is adequate to predict a wide range of Ca(2+) wave transmission and propagation phenomena.

Spreading depression (SD), a propagating wave of electrical silence in the cortex and archicortex, involves depolarization of neurons and astrocytes for approximately 1 min, due principally to a large increase in extracellular K+. SD is accompanied by large increases in extracellular ATP and is blocked by glutamate N-methyl-D-aspartate receptor antagonists. As a principal means of transmission between astrocytes is through their release of ATP, we have investigated if a model in which SD is driven by the effects of astrocyte waves of ATP interacting with waves of glutamate release from neurons and astrocytes can give a quantitative account of experimental observations on SD. We show that the characteristics of SD and the accompanying extracellular ionic changes can be accommodated by such a model-whether astrocyte transmission is principally through the release of ATP, as in archicortex (hippocampus) and spinal cord, or via gap junctions, as in the neocortex. Furthermore, these models give quantitative accounts of the effects on the characteristics of SD of agents toxic for astrocytes and of gap-junction blockers. Finally, an additional series of critical tests of the model is suggested.

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A comparison is made of structural predictions for open-shell systems resulting from a variety of ab initio molecular orbital procedures. Calculations have been performed with the minimal STO-3G, split-valence 3-21G, and split-valence plus d-polarization 6-31G* basis sets; with restricted (RHF) and unrestricted (UHF) Hartree-Fock procedures; and with valence-electron correlation incorporated by means of Moller-Plesset perturbation theory terminated at second (MP2) or third (MP3) order. It is found that spin contamination in UHF wave functions is associated with poor geometry predictions. However, the degree of spin contamination decreases with increasing size of basis set with the result that UHF/6-31G* and RHF/6-31G* geometries are generally very similar. Enforcement of symmetry on the molecular wave function of homonuclear diatomics reduces the UHF spin contamination to near zero and leads to markedly improved geometry predictions. In general, UMP3/6-31G* geometry predictions for open-shell systems are of comparable accuracy to those for closed-shell systems, with mean absolute deviations of approximately 0.01 Á in bond lengths and 2°in bond angles.