L. Farnell

The probability of quantal secretion near a single calcium channel of an active zone.

A Monte Carlo analysis has been made of calcium dynamics and quantal secretion at microdomains in which the calcium reaches very high concentrations over distances of <50 nm from a channel and for which calcium dynamics are dominated by diffusion. The kinetics of calcium ions in microdomains due to either the spontaneous or evoked opening of a calcium channel, both of which are stochastic events, are described in the presence of endogenous fixed and mobile buffers. Fluctuations in the number of calcium ions within 50 nm of a channel are considerable, with the standard deviation about half the mean. Within 10 nm of a channel these numbers of ions can give rise to calcium concentrations of the order of 100 microM. The temporal changes in free calcium and calcium bound to different affinity indicators in the volume of an entire varicosity or bouton following the opening of a single channel are also determined. A Monte Carlo analysis is also presented of how the dynamics of calcium ions at active zones, after the arrival of an action potential and the stochastic opening of a calcium channel, determine the probability of exocytosis from docked vesicles near the channel. The synaptic vesicles in active zones are found docked in a complex with their calcium-sensor associated proteins and a voltage-sensitive calcium channel, forming a secretory unit. The probability of quantal secretion from an isolated secretory unit has been determined for different distances of an open calcium channel from the calcium sensor within an individual unit: a threefold decrease in the probability of secretion of a quantum occurs with a doubling of the distance from 25 to 50 nm. The Monte Carlo analysis also shows that the probability of secretion of a quantum is most sensitive to the size of the single-channel current compared with its sensitivity to either the binding rates of the sites on the calcium-sensor protein or to the number of these sites that must bind a calcium ion to trigger exocytosis of a vesicle.

The probability of quantal secretion within an array of calcium channels of an active zone.

A Monte Carlo analysis has been made of calcium dynamics in submembranous domains of active zones in which the calcium contributed by the opening of many channels is pooled. The kinetics of calcium ions in these domains has been determined using simulations for channels arranged in different geometries, according to the active zone under consideration: rectangular grids for varicosities and boutons and lines for motor-nerve terminals. The effects of endogenous fixed and mobile buffers on the two-dimensional distribution of free calcium ions at these active zones are then given, together with the extent to which these are perturbed and can be detected with different affinity calcium indicators when the calcium channels open stochastically under an action potential. A Monte Carlo analysis of how the dynamics of calcium ions in the submembranous domains determines the probability of exocytosis from docked vesicles is also presented. The spatial distribution of exocytosis from rectangular arrays of secretory units is such that exocytosis is largely excluded from the edges of the array, due to the effects of endogenous buffers. There is a steeper than linear increase in quantal release with an increase in the number of secretory units in the array, indicating that there is not just a local interaction between secretory units. Conditioning action potentials promote an increase in quantal release by a subsequent action potential primarily by depleting the fixed and mobile buffers in the center of the array. In the case of two parallel lines of secretory units exocytosis is random, and diffusion, together with the endogenous calcium buffers, ensures that the secretory units only interact over relatively short distances. As a consequence of this and in contrast to the case of the rectangular array, there is a linear relationship between the extent of quantal secretion from these zones and their length, for lengths greater than a critical value. This Monte Carlo analysis successfully predicts the relationship between the size and geometry of active zones and the probability of quantal secretion at these, the existence of quantal versus multiquantal release at different active zones, and the origins of the F1 phase of facilitation in synapses possessing different active zone geometries.

Quantal transmission at purinergic junctions: stochastic interaction between ATP and its receptors.

The time course of most quantal currents recorded with a small diameter electrode placed over visualized varicosities of sympathetic nerve terminals that secrete ATP was determined: these had a time to reach 90% of peak of 1.3-1.8 ms and a time constant of decay of 12-18 ms; they were unaffected by blocking ectoenzymes or the uptake of adenosine. Monte Carlo methods were used to analyze the stochastic interaction between ATP, released in a packet from a varicosity, and the underlying patch of purinoceptors, to reconstitute the time course of the quantal current. This leads to certain restrictions on the possible number of ATP molecules in a quantum (about 1000) and the density of purinoceptors at the junctions (about 1000 microns-1), given the known geometry of the junction and the kinetics of ATP action. The observed quantal current has a relatively small variability (coefficient of variation < 0.1), and this stochastic property is reproduced for a given quantum of ATP. Potentiation effects (of about 12%) occur if two quanta are released from the same varicosity because the receptor patch is not saturated even by the release of two quanta. The simulations show that quantal currents have a characteristically distinct shape for varicosities with different junctional cleft widths (50-200 nm). Finally, incorporation of an ectoenzyme with the known kinetics of ATPase into the junctional cleft allows for a quantal current of the observed time course, provided the number of ATP molecules in a quantum is increased over the number in the absence of the ATPase.

Synaptic transmission at visualized sympathetic boutons: stochastic interaction between acetylcholine and its receptors

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.

A Quantitative Model of Cortical Spreading Depression Due to Purinergic and Gap-Junction Transmission in Astrocyte Networks

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.

Solution of poisson equations on a nonuniform grid

Abstract The solution of a Poisson equation expressed in finite-difference form on a nonuniform multidimensional mesh of gridpoints in an orthogonal coordinate system is discussed. The discussion is specifically directed toward problems which require the solution of many such equations with the gridpoint distribution and boundary conditions fixed, which implies that in comparing different techniques the task of generating required constants may be neglected. Extension of the matrix decomposition technique to cover the case of smoothly varying grid-intervals is considered when zero-gradient, zero-value, or (under certain conditions) periodic boundary conditions are incorporated. This method is compared in particular with the widely used Alternating Direction Implicit procedure, and it is concluded that for sufficiently small meshes, not exceeding about 40 points in any direction, it is both faster and more precise than ADI.

P2X7 regenerative-loop potentiation of glutamate synaptic transmission by microglia and astrocytes.

P2X7 purinergic receptors have been implicated in chronic neuropathic and neuroinflammatory pain as well as in depression. These receptors are predominantly found in the central nervous system on microglial cells and on glutamatergic nerve terminals. Here, we develop hypotheses concerning mechanisms by which transient high-frequency impulse firing in glutamatergic terminals, such as occurs in nociceptor terminals accompanying neuropathic/neuroinflammatory pain, can lead to long-lasting changes in neural network function that is mediated by surrounding glial cells. The hypothesis consists of two parts. In the first, glutamate released by low-frequency (2Hz) terminal action potentials is insufficient to generate postsynaptic action potentials, but these are generated by brief high-frequency input bursts. Glutamate released by these bursts is partly removed by transporters on the enveloping astrocyte processes and also excites AMPA receptors on these processes, which then release ATP. This ATP is partly metabolised to adenosine, which acts on presynaptic A1 receptors to inhibit glutamate release. The remaining ATP acts on the presynaptic P2X7 receptors to facilitate glutamate release by both the high-frequency burst of action potentials as well as by a continuous low-frequency (2Hz) action potential firing that occurs in the absence of a neuropathic/neuroinflammatory insult. The positive feedback of terminal glutamate release, triggering astrocyte ATP release and leading to further glutamate release through activation of P2X7 receptors, is then sufficient to allow the normal low-frequency (2Hz) action potentials to now elicit postsynaptic action potentials after the insult is removed. In the second part of this model, the high concentration of ATP derived from astrocytes at the terminal attracts microglia by chemotaxis. The P2X7 receptors on these microglia are then engaged, resulting in microglia secreting the cytokine TNFalpha. This acts on postsynaptic TNF-R1 receptors to increase the number of AMPA receptors there, thus enhancing the efficacy of synaptic transmission. The TNFalpha also acts on presynaptic TNF-R1 to increase the amount of glutamate released by each nerve terminal impulse. Experimental tests can be made of this hypothesis that P2X7 receptors on the presynaptic terminal and those on the microglia synergistically act to ensure feedback pathways that reset to a high level the efficacy of synaptic transmission, thus ensuring chronic neuropathic/neuroinflammatory pain even when the initial insult has subsided.

The structure of propadienone (CH2CCO)

Abstract A complete r o structure has been obtained for propadienone (CH 2 CCCO) with the aid of ab initio molecular-orbital calculations. The effect of electron correlation has been investigated using third order Moller-Plesset perturbation theory. The molecule is found to be planar bent (CCC145°) and the calculated structure yields rotational constants which are in good agreemant with experimental values.

The geometric and electronic structures of oxocarbons. An ab initio molecular orbital study

Ab initio molecular orbital calculations with the STO-3G and 4-31G basis sets have been carried out for the neutral oxocarbons CnOn (n = 3, 4, 5, 6 and 7), the dianions CnOn2- (n = 3, 4, 5, 6 and 7), the monoanions CnOnH− (n = 3 and 4) and the related acids CnOnH2 (n = 3 and 4). Fully optimised geometries have been obtained for all species. The geometries, stabilities and acidities are discussed.

A theoretical consideration of the quasi-bent nature of the HCNO molecule

Abstract Ab initio molecular orbital calculations with large basis sets and with incorporation of electron correlation have been used to study the structure of the HCNO molecule with particular emphasis on its quasi-bent nature. The potential function for HCN bending is found to be extremely flat and, in agreement with previous theoretical calculations and a recent experimental analysis, the equilibrium structure of HCNO is found to be linear. Again in agreement with experiment, it is found that ground-state vibrational effects modify the potential function so as to favor bent structures. However, these effects are not sufficiently large so as to lead to a theoretical prediction of a bent ground-state vibrational structure. On the other hand, because of the flatness of the potential function, the theoretical results do not rule out the possibility (as found experimentally) that a slight barrier to linearity may be produced.