Biomedical subjects
Publications and source records attributed to H Parnas.
Classical burster models are based on a fast system that either oscillates or is quiescent, depending on temporarily fixed values of slow variables. In a study of the lobster heart ganglion, we found a new type of burster for which the fast system is globally stable for all relevant fixed values of the slow variables. We describe how this burster works and speculate on its biological significance.
The formation of neuronal networks requires axonal growth towards target neurons. A simple set of grammar rules is introduced to describe axonal growth towards target cells situated both at short and long distances from the growing neuron. Growth for short distances is described by growth following the highest gradient of a chemical compound (which is spread by diffusion from the targets). This approach fails to describe long-distance growth, which is addressed by adopting a graph grammar theory for growing trees. With these rules a flexible tool to draw network of neurons by computer can be developed.
As stated at the beginning of this review, the mechanism of neurotransmitter release is not yet known. Keeping this in mind, we shall, nevertheless, attempt to speculate and outline a possible scenario of events as it emerges from the foregoing discussion. At resting membrane potentials, the release machinery is in a blocked state produced by the constant presence in the synaptic cleft of neurotransmitter at low concentrations. At resting potentials, Ca2+ channels are closed, but this is probably not associated with the presence of low levels of neurotransmitter. Upon arrival of the action potential at the nerve terminal, (as suggested by the Ca-voltage hypothesis) two things happen independently: The release machinery is relieved of its block, being activated and readied to trigger release. Concurrently, Ca2+ enters the presynaptic terminal, and together with specific Ca2+ binding proteins, it abolishes the hydration repulsive forces without which the intimate contact between the vesicle and the plasmatic release machinery is not possible. The biophysical meaning of triggering release is at present not known. There are several suggestions, the one most consistent with the arguments of this review being the mechanism discussed and modeled by Nanavati et al. (1992; see also review: Monck & Fernandez, 1992). According to that hypothesis, an activated scaffold of proteins forms a dimple in the plasma membrane upon stimulation. This dimple, which exhibits high tension--perhaps together with Ca(2+)--overcomes the repulsive forces of hydration, permitting the two membranes to "jump" into intimate contact. As a result, a single hemifused bilayer is formed. In this hemifused bilayer, a lipidic fusion pore opens. In the context of the lipidic fusion pore hypothesis, the role of the depolarization-dependent triggering could be to start those manipulations in the plasmatic membrane that result in increased lateral bilayer tension and formation of the dimple. Ca2+ could then, in view of reduced repulsive forces and increased attractive forces, be responsible for the intimate docking of the vesicle at the release site. Under such conditions, hemifusion could take place with the final formation of the lipidic fusion pore. Finally, once the fusion pore opens, discharge of the vesicular content takes place immediately and lasts for up to 50-70 microseconds. To be so fast, discharge must occur by a mechanism other than diffusion, possibly by ion-exchange (R. Khanin, H. Parnas and L. Segel, in preparation).(ABSTRACT TRUNCATED AT 400 WORDS)
It is now widely accepted that localized high concentrations of Ca2+ (Ca2+ domains) play a major role in controlling the time course of neurotransmitter release. In the present work we calculate the magnitude and the time course of Ca2+ domains that evolve in the vicinity of a Ca2+ channel and an adjacent release site. In the calculations we consider a accurately dimensioned Ca2+ channel. Moreover, the Ca2+ current is continuously adjusted with regard to the accumulated intracellular Ca2+ and, in addition, endogenous buffers are considered. The calculations, carried out by the software FIDAP, based on finite element method, show that the Ca2+ concentrations achieved near the release sites are significantly lower than claimed by other investigators. Furthermore, we present arguments indicating that the Ca2+ domains, regardless of their magnitude, do not play a role in controlling the time course of release of neurotransmitter.
In the present work we show that diffusion cannot provide the observed fast discharge of neurotransmitter from a synaptic vesicle during neurotransmitter release, mainly because it is not sufficiently rapid nor is it sufficiently temperature-dependent. Modeling the discharge from the vesicle into the cleft as a continuous point source, we have determined that discharge should occur in 50-75 microseconds, to provide the observed high concentrations of transmitter at the critical zone.
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In outside-out patches of mouse-muscle membrane, embryonic-like channels were activated by pulses of acetylcholine (ACh). On increasing the ACh concentration, the rate of desensitization, 1/tau d, increased linearly with the peak open probability, indicating desensitization from the open state. Desensitization had only one time constant tau d at each ACh concentration. Recovery from desensitization was only approximately 10 times slower than desensitization, whereas the probability of steady-state channel opening, declined to < 0.01 with > 10(-6) M ACh. The peak probability of opening in > 10(-4) M ACh pulse was close to 1. A linear reaction scheme was not compatible with these results. The scheme had to be expanded resulting in a circular scheme with two additional ACh binding steps to desensitized channel states. The approximate rate constants of all reaction steps in the circular scheme could be determined using computer simulations. The model predicted that clusters of channel opening had the average duration tau d at the respective ACh concentration. In cell-attached patches on intact muscle fibers, similar average cluster durations were observed at the respective ACh concentration. This indicates that tau d in the intact muscle fibers has similar values as in outside-out patches.
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Pulses of acetylcholine (ACh) applied to outside-out patches of embryonic-like muscle membrane elicited channel currents which declined rapidly (tau d = 10-60 ms) due to desensitization. Recovery from desensitization was determined by pulse pairs, varying the pulse interval. When the pulse interval was about 300 ms, the response to the second pulse was about half that to the first pulse, i.e. about half of the channels had recovered from desensitization. The results are discussed in the frame of a cyclic reaction scheme. If this scheme includes high affinity binding of ACh to desensitized receptors, it can also explain the finding that low ACh concentrations (less than or equal to 1 microM) largely desensitize the receptors, but elicit very little channel opening.
In order to account for the time courses of both evoked release and facilitation, in the framework of the Ca2+ hypothesis, Fogelson and Zucker (1985, Biophys. J. 48, 1003-1017) suggested treating diffusion of Ca2+, once it enters through the Ca2+ channels, as a three-dimensional process (three-dimensional diffusion model). This model is examined here as a refined version of the "Ca(2+)-theory" for neurotransmitter release. The three-dimensional model was suggested to account for both the time course of release and that of facilitation. As such, it has been examined here as to its ability to predict the dependence of the amplitude and time course of facilitation under various experimental conditions. It is demonstrated that the three-dimensional diffusion model predicts the time course of facilitation to be insensitive to temperature. It also predicts the amplitude and time course of facilitation to be independent of extracellular Ca2+ concentration. Moreover, it predicts that inhibition of the [Na+]o in equilibrium with [Ca2+]i exchange does not alter facilitation. These predictions are not upheld by the experimental results. Facilitation is prolonged upon reduction in temperature. The amplitude of facilitation declines and its duration is prolonged upon increase in extracellular Ca2+ concentration. Finally, inhibition of the [Na+]o in equilibrium with [Ca2+]i exchange prolongs facilitation but does not alter the time course of evoked release after an impulse.
Ca2+ buffers were injected into the excitatory axon of the crayfish opener muscle. The magnitude and time course of evoked release and of facilitation were measured. EGTA (on-rate about 10(6) M-1S-1) had no effect on evoked release but reduced facilitation. BAPTA and nitr-5, buffers with similar Kd's but faster on-rates, reduced both evoked release and facilitation. However, these buffers had no effect on the time course of evoked release. These results show that fast Ca2+ buffers reduce the Ca2+ transient associated with evoked release and also the level of residual Ca2+ involved in facilitation. However, Ca2+ buffering is not the mechanism which controls the time course of release.
Presented here is a minimal biophysical cell model, based on work by Hodgkin and Huxley and by Rinzel, that can exhibit both excitable and oscillatory behavior. Two versions of the model are studied, which conform to data for squid and lobster giant axons.
Cutaneous pectoris muscles of frogs were isolated, mounted in a chamber and superfused with Ringer's solution. With a macro-patch-clamp electrode placed on a section of a motor nerve terminal, quantal synaptic currents were elicited by depolarizing pulses and recorded. The electrode tip and the section of the terminal recorded from were perfused rapidly by Ringer's solution alone or containing 20-500 microM Cd2+ to block Ca2+ inflow. Separate superfusion of the muscle and the rest of the terminal with normal or elevated Ca2+ Ringer's solution provided a sufficiently high resting Ca2+ concentration in the terminal even when Ca2+ was blocked by Cd2+. The depolarization level of maximal Ca2+ inflow into the terminal was found by measuring maximal test pulse facilitation, Fc. In control solution as well as in the case of Cd2+ block, the rate of phasic release after depolarizing pulses rose further when depolarization was increased past the level of Fc, and reached a saturation level which was maintained at estimated depolarizations up to +200 mV. Block of Ca2+ inflow by Cd2+ decreased release substantially, but did not suppress it. The depression of release was greater in the range of large Ca2+ inflow (around Fc) than for very large depolarizations. The time course of phasic release was unaltered by blockage of Ca2+ inflow. It is concluded that Ca2+ inflow contributes to the promotion of evoked release only in the depolarization range in which Ca2+ inward current is large.(ABSTRACT TRUNCATED AT 250 WORDS)
A method for obtaining delay histograms for the time course of neurotransmitter release is presented. The delay histogram is derived from the measured psc (or the sum of several psc's) and the mpsc (obtained experimentally or otherwise) by means of a simple, quick, mathematical procedure. The procedure may be automated for the greater part. No approximation of the mpsc shape is performed, and the method is applicable to all quantal contents. For low and medium quantal contents, the delay histograms obtained by the method are compared to those obtained by direct analysis. A reasonable agreement is achieved. An experiment of high quantal content, for which direct analysis is impossible, is then analysed using the new method. Difficulties which may arise when applying the procedure and methods to overcome them are discussed at length. Other methods are set forth in the Discussion.
Outside-out patches of enzymatically dissociated adult and denervated mouse muscle fibers were superfused repetitively by pulses of acetylcholine (ACh) containing solution. Up to 300 channels opened simultaneously 300 microseconds after the beginning of a 1,000 microM ACh pulse corresponding to a peak current i of almost -1 nA. Single responses to ACh were averaged and the concentration dependence of i and of the rise time tr from 0.1 i to 0.9 i was measured. In adult receptors, i increased proportional to the second to third power of ACh concentration, whereas in embryonic-type receptors it was proportional to the first to the second power. tr increased from approximately 0.3 ms at 1,000 microM ACh to a plateau value of approximately 5 ms for adult and of approximately 10 ms for embryoniclike receptors at concentrations less than 10 microM ACh. The concentration dependence of i and tr was simulated using the standard model of ACh binding with different combinations of rate constants and two and three binding sites for ACh. The calculated curves were compared to the measurements and a set of well fitting rate constants was determined for adult and embryoniclike receptors. Three binding sites for ACh were necessary to fit the dose response for i for adult receptors. A method for deriving rate constants in a model of ACh-receptor interaction is described that avoids analysis of open-closed kinetics of single channels, which in rapid systems, as the ones studied here, are at the limit of the frequency response of the current measurement.
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A procedure is developed wherein the time course of neurotransmitter release is used to discern the mechanism of effects of drugs on the release process. It is shown, in agreement with experiments, that the time course of release is insensitive to the temporal distribution of intracellular Ca2+ concentration. The time course is also invariant to the steps in the release process that are Ca2+ dependent. The most influential events in determining the time course of release are shown to be the steps associated with the slowest forward rate constant and all the backward steps. The procedure was examined for its ability to explain the effects on release of the poison curare and those of temperature. It appears that curare probably blocks release by lowering the rate constant associated with the rate limiting step in release. Increasing temperature is predicted to increase both the forward and the backward rate constants, but not to the same extent.
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