A clockwork hypothesis: synaptic release by rod photoreceptors must be regular

We can see at light intensities much lower than an average of one photon per rod photoreceptor, demonstrating that rods must be able to transmit a signal after absorption of a single photon. However, activation of one rhodopsin molecule (Rh*) hyperpolarizes a mammalian rod by just 1 mV. Based on the properties of the voltage-dependent Ca2+ channel and data on [Ca2+] in the rod synaptic terminal, the 1 mV hyperpolarization should reduce the rate of release of quanta of neurotransmitter by only 20%. If quantal release were Poisson, the distributions of quantal count in the dark and in response to one Rh* would overlap greatly. Depending on the threshold quantal count, the overlap would generate too frequent false positives in the dark, too few true positives in response to one Rh*, or both. Therefore, quantal release must be regular, giving narrower distributions of quantal count that overlap less. We model regular release as an Erlang process, essentially a mechanism that counts many Poisson events before release of a quantum of neurotransmitter. The combination of appropriately narrow distributions of quantal count and a suitable threshold can give few false positives and appropriate (e.g., 35%) efficiency for one Rh*.     

A method for testing an extended poisson hypothesis of spontaneous quantal transmitter release at neuromuscular junctions

A statistical method for testing the Poisson hypothesis of spontaneous quantal transmitter release at neuromuscular junctions has been proposed. The notion of the Poisson hypothesis is extended so as to allow for nonstationarity in the data, since nonstationarity is commonly seen in the occurrence of spontaneous miniature potentials. Special emphasis has been put on the nonstationary analysis of the quantal release. A time scaling technique has been introduced and is discussed for the analysis. Artificially generated data, which simulate three types of nonstationary spontaneous quantal release, i.e., Poisson, non-Poisson-clustered, and non-Poisson-ordered types, were analyzed to demonstrate the effectiveness of the method. Some sets of miniature endplate potentials, intracellularly recorded at frog sartorius neuromuscular junctions in low Ca++ and high Mg++ solutions showing apparent nonstationarities, were analyzed as illustrative examples. The proposed method will extend the range of applicable data for the statistical analysis of spontaneous quantal transmitter release.     

Efficiency of synaptic transmission of single-photon events from rod photoreceptor to rod bipolar dendrite

A rod transmits absorption of a single photon by what appears to be a small reduction in the small number of quanta of neurotransmitter (Q(count)) that it releases within the integration period ( approximately 0.1 s) of a rod bipolar dendrite. Due to the quantal and stochastic nature of release, discrete distributions of Q(count) for darkness versus one isomerization of rhodopsin (R*) overlap. We suggested that release must be regular to narrow these distributions, reduce overlap, reduce the rate of false positives, and increase transmission efficiency (the fraction of R* events that are identified as light). Unsurprisingly, higher quantal release rates (Q(rates)) yield higher efficiencies. Focusing here on the effect of small changes in Q(rate), we find that a slightly higher Q(rate) yields greatly reduced efficiency, due to a necessarily fixed quantal-count threshold. To stabilize efficiency in the face of drift in Q(rate), the dendrite needs to regulate the biochemical realization of its quantal-count threshold with respect to its Q(count). These considerations reveal the mathematical role of calcium-based negative feedback and suggest a helpful role for spontaneous R*. In addition, to stabilize efficiency in the face of drift in degree of regularity, efficiency should be approximately 50%, similar to measurements.     

An energetic model of muscle contraction

Initial energy utilization in the twitch is visualized as the result of the activity of two distinct processes. The first is the calcium-pumping activity of the sarcoplasmic reticulum, which has a constant energy requirement under normal conditions. The second is the chemomechanical transduction process consisting of a variable number of quantal contractile events, each with a fixed enthalpy equal to the molecular enthalpy of adenosine triphosphate (ATP) hydrolysis in vivo. This enthalpy appears either as heat or as contractile element work. Total enthalpy varies according to the number of quantal contractile events that occur in the twitch cycle. The basis of the variation is suggested to be velocity-dependent activity of the actomyosin ATPase, allowing more quantal events to occur in a contraction cycle when shortening occurs. The classical designation “activation heat” is held to be appropriate for the first process. The partition of the enthalpy of the second process that is currently in vogue is held to be misleading and a new formulation is suggested in which the properties of the quantal contractile event are reflected in general terms. The formulation of the proposed transduction model represents a conceptual return to the viscoelastic theory, but at a quantal level. The model can explain the results of the preceding paper and is adaptable to different muscles without having to postulate fundamental differences in energy utilization.     

Rod sensitivity and visual pigment concentration in Xenopus

Xenopus larvae were raised on a vitamin A-free diet under constant illumination until their visual pigment content had decreased to between 8% of normal and an undetectably low level. After the intramuscular injection of 2.1 X 10(13-2.1 X 10(16) molecules of [3H]vitamin A, ocular tissue showed a rapid rate of uptake of label which reached a maximum level of incorporation by 48 h. Light- microscopic autoradiography revealed that the retinal uptake of label was concentrated within the receptor outer segments. Spectral transmissivity measurements at various times after injection were made upon intact retinas and upon digitonin extracts. They showed that visual pigment with a lambdamax of 504 nm was formed in the retina and that the amount formed was a function of incubation time and the magnitude of the dose administered. Electrophysiological measures of photoreceptor light responses were obtained from the PIII component of the electroretinogram, isolated with aspartate. The quantal flux required to elicit a criterion response was determined and related to the fraction of visual pigment present. The results showed that rod sensitivity varied linearly with the probability of quantal absorption.     

Probabilistic secretion of quanta from nerve terminals at synaptic sites on muscle cells: non-uniformity, autoinhibition and the binomial hypothesis

A model of the secretion of a quantum at a release site is proposed in which, following the influx of calcium ions, synaptic vesicles are made available for release by the activation of kappa phosphorylation steps with rate alpha. At any time during this process the vesicles may become unavailable for secretion at rate gamma. On completion of the kappa phosphorylation steps the vesicles participate in the formation of a fusion pore with the terminal membrane to give exocytosis at rate delta. Changes in alpha, delta and kappa are shown to produce characteristic changes in the number and timecourse of quantal secretions following a nerve impulse, which are similar to those observed following drug treatments that are thought to act selectively on each of these processes. The number of quanta secreted from nerve terminals that consist of many release sites does not fluctuate much during a low frequency train of impulses: the variance is small compared with the mean level, so secretion follows binomial rather than Poisson statistics. A theory is derived that shows that variations in the probability of secretion amongst these release sites of any particular kind fails to reduce the variance of the total secretion from the terminal; Poisson rather than binomial statistics then still apply. The theory shows that an interaction between release sites is required to reduce this variance and such an effect is provided if secretion at a site inhibits secretion at nearby sites. Simulations show that incorporating this process of autoinhibition into the model reproduces the experimental observations on the effects of calcium ions on the binomial parameters p and n as well as on the relative constancy of p during facilitation and depression of quantal secretion. Methods for estimating the timecourse of changes in the probability of secretion at release sites following an impulse, by using either the time of occurrence of first, second, third or later quantal latencies, are given. These procedures show that current methods for estimating the time-dependent probability changes are inadequate for detecting interaction between release sites, such as autoinhibition, unless this is relatively large. Therefore, estimates from third quantal latencies are used.     

Down-regulation of quantal size at frog neuromuscular junctions: possible roles for elevated intracellular calcium and for protein kinase C

Previous work showed that quantal size can be at least doubled at the frog neuromuscular junction by pretreatment with hormones or hypertonic solutions, primarily by the release of more acetylcholine (ACh) per quantum. Once increased, quantal size slowly declined over hours. Quantal size was measured from miniature end-plate potentials (MEPPs) or currents (MEPCs). In the present experiments, preparations in which quantal size had been increased were exposed to 17-25 mM [K+], quantal size decreased within minutes. Release of comparable numbers of quanta by nerve stimulation did not decrease size. K(+)-solutions did not decrease size if Ca2+ was omitted or replaced with Sr2+. The phosphokinase C (PKC) activators phorbol 12,13-diacetate (PDA) and 1-oleoyl-2-acetyl-rac-glycerol (OAG) also decreased quantal size within minutes when applied in a hypertonic solution that increased the rate of spontaneous release. Phorbol 12,13-dideconate, which does not activate PKC, did not decrease quantal size. The size decrease triggered by K(+)-solutions or PKC activators was blocked by 100 microM 1-(5-isoquinolinyl-sulfonyl)-2-methyl-piperazine (H7), a protein kinase inhibitor. Apparently, increasing [K+] elevated intracellular [Ca2+], which activates PKC, and which leads to the down-regulation of quantal size. During the period in which size is decreasing, there appears to be large and normal subpopulations of MEPP sizes, with normal gradually replacing large. This suggests that large quanta are formed by adding additional ACh to preformed quanta shortly before they are available for release.     

Potential of a quantal response as a mechanism for oscillatory behavior: implications for our concepts of hormonal control mechanisms

This article describes the potential of a quantal (i.e., all-or-none) response as a model for understanding the interactions between endocrine, paracrine and autocrine hormones. We review the general features of continuous and discontinuous (i.e., oscillating) quantal models including the role of a threshold. In addition, we also describe a few of the many different biochemical mechanisms which may give rise to quantal behavior. One of the more attractive schemes involves the coordinate regulation of opposing biochemical pathways resulting from phosphorylation of hormone receptors and/or rate-limiting enzymes. At least one hormone receptor (i.e., that for insulin) and many rate-limiting enzymes which control the flow of metabolites through a variety of metabolic pathways can be phosphorylated at multiple sites by one or more protein kinases. Phosphorylation may enhance or inhibit the activities of these proteins depending on which sites are modified. Furthermore, since phosphorylation of some sites on a protein may enhance the ability of phosphoprotein phosphatases to dephosphorylate other sites responsible for biological activity of the protein, phosphorylation also has the potential to produce a discontinuous quantal response. Quantal response mechanisms may alter our notions of endocrine regulation. When a quantal response mechanism is applied to a simple negative feedback model similar to that which was originally postulated to explain the interactions between gonadotropin and steroid hormonal levels, the model can account for the oscillations in hormone levels even when the input is constant. Conversely, when a graded mechanism is applied to the same negative feedback model, the model will almost certainly result in constant hormone levels. Further, the model illustrates that small changes in rate constants and thresholds of response, amplification of hormonal signals, and degradation of intermediate regulators can produce large shifts in the output of the system. These may account for the variability in hormonal levels observed in some endocrine systems. Finally, the high sensitivity of the quantal response mechanism accounts for the data which suggest that gonadotropins may play permissive rather than causal roles in regulation of gonadal function. Since increasing evidence suggests that all cells of a given type may not be equal in terms of hormonal responsiveness, measurements of response in single cells over short time periods will be needed before the role of a quantal response can be determined and endocrine regulation will be fully understood.     

Maximum likelihood estimation of non-uniform transmitter release probabilities at the crayfish neuromuscular junction

The classical model of quantal release of neurotransmitter assumes that a fixed number of quantal units are available for release in the presynaptic terminal, and that each unit has the same probability of being released. This model also assumes that different units are released independently of one another. We consider two variations of the classical model. In the first case we assume that release is independent, but with potentially different release probabilities at different sites. In the second case we allow for dependence among the release units. A maximum likelihood procedure for the estimation of model parameters is developed, and an estimator of the number of quantal units is proposed. The performance of the method is assessed through a simulation study, and the procedures are applied to the analysis of a sequence of post-synaptic potentials recorded intracellularly at the crayfish neuromuscular junction. Goodness of fit and hypothesis test procedures reject the classical model in favor of an independent release mechanism with differing release probabilities. A more general release mechanism, allowing for dependence in the release process, also provides a good fit to the data analyzed.     

Radiation Resistance of Spores of Some Clostridium perfringens Strains

Clostridium perfringens spores (eight strains) were irradiated in a model system with 60Co gamma rays at -30 C. The quantal response data obtained were analyzed with extreme value statistics. It was found (at the 95% confidence level) that all eight strains followed the same rate of death and that this rate was probably (at the 95% level) not exponential. The statistics did not exclude, however, a normal, lognormal, Weibull, or related rate of spore kill. A more definitive study would be required to distinguish between the latter distributions.     

Inhibition of packing of acetylcholine into quanta by ammonium

Soaking frog motor nerve terminals in a hypertonic solution produces an increase in the size of miniature end plate potentials (mepp's) and miniature end plate currents (mepc's) after the preparations are returned to normal Ringer's solution. There is substantial evidence that the size increase occurs because additional acetylcholine (ACh+) is incorporated into the quanta. It has been proposed that ACh+ loading into synaptic vesicles requires a proton gradient. As a step in testing this hypothesis the effects of millimolar concentrations of NH4+, methylamine+, or trimethylamine+ in the extracellular solution on the increase in quantal size were measured. These substances would be expected to accumulate in acid intracellular compartments, which would diminish the acidity. The increase in quantal size was blocked by these substances, in agreement with the idea that the proton gradient is involved in ACh+ accumulation. Tetanic stimulation in solutions containing 5 mM NH4Cl also produces a decrease in quantal size, not seen in controls in NH4+-free solution. The inhibition of transmitter packaging by ammonia may play a role in the neural sequelae of hepatic failure.     

The quantal theory of how the immune system discriminates between "self and non-self"

In the past 50 years, immunologists have accumulated an amazing amount of information as to how the immune system functions. However, one of the most fundamental aspects of immunity, how the immune system discriminates between self vs. non-self, still remains an enigma. Any attempt to explain this most intriguing and fundamental characteristic must account for this decision at the level of the whole immune system, but as well, at the level of the individual cells making up the immune system. Moreover, it must provide for a molecular explanation as to how and why the cells behave as they do. The "Quantal Theory", proposed herein, is based upon the "Clonal Selection Theory", first proposed by Sir McFarland Burnet in 1955, in which he explained the remarkable specificity as well as diversity of recognition of everything foreign in the environment. The "Quantal Theory" is built upon Burnet's premise that after antigen selection of cell clones, a proliferative expansion of the selected cells ensues. Furthermore, it is derived from experiments which indicate that the proliferation of antigen-selected cell clones is determined by a quantal, "all-or-none", decision promulgated by a critical number of cellular receptors triggered by the T Cell Growth Factor (TCGF), interleukin 2 (IL2). An extraordinary number of experiments reported especially in the past 20 years, and detailed herein, indicate that the T cell Antigen Receptor (TCR) behaves similarly, and also that there are several critical numbers of triggered TCRs that determine different fates of the T cells. Moreover, the fates of the cells appear ultimately to be determined by the TCR triggering of the IL2 and IL2 receptor (IL2R) genes, which are also expressed in a very quantal fashion. The "Quantal Theory" states that the fundamental decisions of the T cell immune system are dependent upon the cells receiving a critical number of triggered TCRs and IL2Rs and that the cells respond in an all-or-none fashion. The "Quantal Theory" accounts fully for the development of T cells in the thymus, and such fundamental cellular fates as both "positive" and "negative" selection, as well as the decision to differentiate into a "Regulatory T cell" (T-Reg). In the periphery, the "Quantal Theory" accounts for the decision to proliferate or not in response to the presence of an antigen, either non-self or self, or to differentiate into a T-Reg. Since the immune system discriminates between self and non-self antigens by the accumulated number of triggered TCRs and IL2Rs, therapeutic manipulation of the determinants of these quantal decisions should permit new approaches to either enhance or dampen antigen-specific immune responses.     

Analysis of quantal response data from bacterial destruction studies in sterilization: the Stumbo estimate is biased.

Real and simulated experimental data and theoretical data from quantal response experiments were used to make a comparison between the analysis of data from a quantal response experiment and data from a direct enumeration experiment. The method of analysis for each is differentiated, thereby enhancing the utility of the quantal response experiment in sterilization studies. From this comparison it appears that the Stumbo estimate of the D value is biased. Furthermore, the Stumbo estimate depends upon the spore load per replicate in quantal response type experiments, which makes experimental comparisons difficult. Another estimate of D is demonstrated which overcomes some of these shortcomings.     

Analysis of quantal response data from bacterial destruction studies in sterilization: the Stumbo estimate is biased

J. HACHIGIAN AND R.J. SCHLESINGER. 1991. Real and simulated experimental data and theoretical data from quantal response experiments were used to make a comparison between the analysis of data from a quantal response experiment and data from a direct enumeration experiment. The method of analysis for each is differentiated, thereby enhancing the utility of the quantal response experiment in sterilization studies. From this comparison it appears that the Stumbo estimate of the D value is biased. Furthermore, the Stumbo estimate depends upon the spore load per replicate in quantal response type experiments, which makes experimental comparisons difficult. Another estimate of D is demonstrated which overcomes some of these shortcomings.     

Use of Quantal Method for Estimation of Agricultural Production

The usual analysis of quantal response data occurring in diverse fields such as economics, medicine, psychology and toxicology use probit and logit models or their extensions with generalised least squares or the principle of likelihood as the method of statistical inference. The quantal method was first used for estimation of agricultural production by S. M. Vidwans (1991). He has collected the data on yield rate of rabi jowar from the farmers for year 1981 in four villages in Shirur taluka and three villages in Daund taluka of Pune district of Maharashtra in India. The probit regression line is fitted. The fit is not good. The estimation is done using truncation of data. Here we observed that a second degree polynomial is a good fit to the data. This will give correct prediction of agricultural production with smaller standard error.     

Testing the fit of a quantal model of neurotransmission

Many studies of synaptic transmission have assumed a parametric model to estimate the mean quantal content and size or the effect upon them of manipulations such as the induction of long-term potentiation. Classical tests of fit usually assume that model parameters have been selected independently of the data. Therefore, their use is problematic after parameters have been estimated. We hypothesized that Monte Carlo (MC) simulations of a quantal model could provide a table of parameter-independent critical values with which to test the fit after parameter estimation, emulating Lilliefors's tests. However, when we tested this hypothesis within a conventional quantal model, the empirical distributions of two conventional goodness-of-fit statistics were affected by the values of the quantal parameters, falsifying the hypothesis. Notably, the tests' critical values increased when the combined variances of the noise and quantal-size distributions were reduced, increasing the distinctness of quantal peaks. Our results support two conclusions. First, tests that use a predetermined critical value to assess the fit of a quantal model after parameter estimation may operate at a differing unknown level of significance for each experiment. Second, a MC test enables a valid assessment of the fit of a quantal model after parameter estimation.     

A computer system for real-time data acquisition and analysis of biopotentials and quantal content at the neuromuscular junction

A computerized data acquisition system for on-line analysis of the parameters of neuromuscular transmission is described. Both hardware usage and software methodologies are discussed with regard to sampling in real-time and analyzing miniature end-plate potentials (MEPPs), end-plate potentials (EPPs) and quantal content of the evoked transmitter release. Significant features of the program include: (1) automatic threshold determination for MEPP detection; (2) the use of a circular buffer to give pre-trigger information; (3) real-time noise spike rejection; (4) an automatic procedure for EPP failure detection; (5) rapid quantal content determinations by several methods as well as complete MEPP and EPP waveform analysis. The system has proven both accurate and reliable during more than two years of use. Advantages of the system over conventional methods include: (1) increased accuracy and efficiency in data analysis; (2) immediate availability of results; (3) conventional data storage; (4) flexibility to meet changing requirements.     

Calcium modulation of the release kinetics of the acetylcholine quanta generating multiquantal postsynaptic response

The effects of calcium on the quantal content of nerve-evoked endplate currents (EPC) and on the temporal parameters of quantal release were studied in the frog neuromuscular synapse using the method of "subtractions". It was shown that under physiological conditions quanta generating multiquantal postsynaptic responses were released nonsynchronously because of a considerable variability of latencies of the uniquantal responses forming multiquantal EPC. Different calcium dependences for EPCs quantal content and time course of the quantal release were revealed. The average quantal content grew exponentially with the increase in calcium concentration from 0.4 to 1.8 mmol/L, whereas the release synchronicity reached the maximum at 1 mmol/L calcium. It was suggested that the changes in the synchronicity of the evoked release were one of the mechanisms of the synaptic plasticity.     

Analysis and implications of equivalent uniform approximations of nonuniform unitary synaptic systems

Real synaptic systems consist of a nonuniform population of synapses with a broad spectrum of probability and response distributions varying between synapses, and broad amplitude distributions of postsynaptic unitary responses within a given synapse. A common approach to such systems has been to assume identical synapses and recover apparent quantal parameters by deconvolution procedures from measured evoked (ePSC) and unitary evoked postsynaptic current (uePSC) distributions. Here we explicitly consider nonuniform synaptic systems with both intra (type I) and intersynaptic (type II) response variability and formally define an equivalent system of uniform synapses in which both uePSC and ePSC amplitude distributions best approximate those of the actual nonuniform synaptic system. This equivalent system has the advantage of being fully defined by just four quantal parameters: ?, the number of equivalent synapses;p, the mean probability of quantal release; mu, mean; and sigma(2), variance of the uePSC distribution. We show that these equivalent parameters are weighted averages of intrinsic parameters and can be approximated by apparent quantal parameters, therefore establishing a useful analytical link between the apparent and intrinsic parameters. The present study extends previous work on compound binomial analysis of synaptic transmission by highlighting the importance of the product of p and mu, and the variance of that product. Conditions for a unique deconvolution of apparent uniform synaptic parameters have been derived and justified. Our approach does not require independence of synaptic parameters, such as p and mu from each other, therefore the approach will hold even if feedback (i.e., via retrograde transmission) exists between pre and postsynaptic signals. Using numerical simulations we demonstrate how equivalent parameters are meaningful even when there is considerable variation in intrinsic parameters, including systems where subpopulations of high- and low-release probability synapses are present, therefore even under such conditions the apparent parameters estimated from experiments would be informative.