Mathematical theory of chemical synaptic transmission

Mathematical theory of chemical synaptic transmission is suggested in which the modes of operation of chemical synapses are given as consequencies of some fundamental theoretical principles presented in the form of systems of quantum and macroscopic postulates. These postulates establish transmitter transfer rules between 3 component parts — cytoplasmic, vesicular and external pools of neurotransmitter. The main features of the transfers are determined by special properties of the dividing membranes (synaptic and vesicle) which show high selectivity towards the direction of the transmitter quantum transfer. The formulation of a previously unknown effect of transmitter quantum transfer from the vesicular pool into the cytoplasmic one is introduced: it is postulated that each arriving presynaptic impulse not only releases a constant fraction of the current contents of the cytoplasmic pool into the synaptic cleft (external pool), but also realizes practically simultaneous transmitter transfer from the vesicular pool into the cytoplasmic one. Zone structure of the vesicular pool is postulated. In accordance with basic equations of the theory a nonlinear control system (dynamic synaptic modulator — DYSYM) of transmitter release from the terminal is constructed.Depending on the parameters relation two types of synapses are classified — those with rapid and slow demobilization. Analytical dependencies of the transmitter pools sizes on the stimulation frequency are introduced. By fitting the frequency dependencies to the empirical data model parameters are determined corresponding to a set of experimentally studied synaptic junctions. Different aspects of the chemical synapse behaviour under the influence of presynaptic stimulation are simulated.     

Nonclassical synaptic functions of transmitters

Nonclassical synaptic functions are considered in two groups, mainly by reference to the models provided by sympathetic ganglia. Slow postsynaptic potentials (PSPs) are compared with classical fast PSPs. Features include loose delivery of transmitter to receptor, very long synaptic delays and durations of PSPs, slow removal of transmitter or of its effects, integration of repetitive inputs, electrogenesis without large increases in ionic conductances. Neuromodulatory actions affect synaptic efficacy without direct excitatory or inhibitory responses to the transmitter. These include a) control of presynaptic release, and b) contingent postsynaptic actions. In b, a modulatory transmitter alters the efficacy of action by another transmitter. The alteration may persist long after exposure to the modulatory transmitter; in mammalian sympathetic ganglia, exposure to dopamine or to a conditioning train of preganglionic volleys induces a long-term enhancement of the muscarinic slow excitatory PSP. Or the alteration may be restricted mostly to the presence of a modulatory transmitter, with examples cited. Nonclassical synaptic functions may be providing revolutionary possibilities for dealing with slow and broadly distributed cerebral functions, manifested electrophysiologically and behaviorally, that have been difficult to analyze successfully in terms restricted to the fast and discretely localized classical synaptic functions.     

A new analytical method of studying post-synaptic currents.

A powerful methodology for analyzing post-synaptic currents recorded from central neurons is presented. An unknown quantity of transmitter molecules released from presynaptic terminals by electrical stimulation of nerve fibers generates a post-synaptic response at the synaptic site. The current induced at the synaptic junction is assumed to rise rapidly and decay slowly with its peak amplitude being proportional to the number of released transmitter molecules. The signal so generated is then distorted by the cable properties of the dendrite, modeled as a time-invariant, linear filter with unknown parameters. The response recorded from the cell body of the neuron following the electrical stimulation is contaminated by zero-mean, white, Gaussian noise. The parameters of the signal are then evaluated from the observation sequence using a quasi-profile likelihood estimation procedure. These parameter values are then employed to deconvolve each measured post-synaptic response to produce an optimal estimate of the transmembrane current flux. From these estimates we derive the amplitude of the synaptic current and the relative amount of transmitter molecules that elicited each response. The underlying amplitude fluctuations in the entire data sequence are investigated using a non-parametric technique based on kernel smoothing procedures. The effectiveness of the new methodology is illustrated in various simulation examples.     

The molecular mechanisms of quantum mediator secretion in the synapse

The modern condition of knowledge about the molecular mechanisms underlying the quantal transmitter release in the central and the peripheric synapses is analysed. The data about the synaptic vesicles types, their forming, transporting to the sites of release at the nerve endings, exo- and endocytosis processes are presented. Ultrastructural and molecular organization of active zone of nerve ending and transmitter release morphofunctional unit--secretosome, which includes synaptic vesicle, exocytosis protein complex and calcium channels, are described. The basic proteins involved in the exo- and endocytosis and their interactions during transmitter release are examined. The role of the intracellular buffer systems, calcium micro- and macrodomains in the quantal transmitter secretion are considered. The reasons of the active zones functional non-uniformity and plasticity and factors reduced transmitter release in the active zone to the single quantum are analysed.     

Protein synthesis in synaptosomes: a proteomics analysis

A proteomics approach was used to identify the translation products of a unique synaptic model system, squid optic lobe synaptosomes. Unlike its vertebrate counterparts, this preparation is largely free of perikaryal cell fragments and consists predominantly of pre-synaptic terminals derived from retinal photoreceptor neurones. We metabolically labelled synaptosomes with [(35)S] methionine and applied two-dimensional gel electrophoresis to resolve newly synthesized proteins at high resolution. Autoradiographs of blotted two-dimensional gels revealed de novo synthesis of about 80 different proteins, 18 of which could be matched to silver-stained gels that were run in parallel. In-gel digestion of the matched spots and mass spectrometric analyses revealed the identities of various cytosolic enzymes, cytoskeletal proteins, molecular chaperones and nuclear-encoded mitochondrial proteins. A number of novel proteins (i.e. not matching with database sequences) were also detected. In situ hybridization was employed to confirm the presence of mRNA and rRNA in synaptosomes. Together, our data show that pre-synaptic endings of squid photoreceptor neurones actively synthesize a wide variety of proteins involved in synaptic functioning, such as transmitter recycling, energy supply and synaptic architecture.     

Signal processing in the axon initial segment

The axon initial segment (AIS) is a specialized membrane region in the axon of neurons where action potentials are initiated. Crucial to the function of the AIS is the presence of specific voltage-gated channels clustered at high densities, giving the AIS unique electrical properties. Here we review recent data on the physiology of the AIS. These data indicate that the role of the AIS is far richer than originally thought, leading to the idea that it represents a dynamic signal processing unit within neurons, regulating the integration of synaptic inputs, intrinsic excitability, and transmitter release. Furthermore, these observations point to?a critical role of the AIS in disease.     

Vesicular and Plasma Membrane Transporters for Neurotransmitters

The regulated exocytosis that mediates chemical signaling at synapses requires mechanisms to coordinate the immediate response to stimulation with the recycling needed to sustain release. Two general classes of transporter contribute to release, one located on synaptic vesicles that loads them with transmitter, and a second at the plasma membrane that both terminates signaling and serves to recycle transmitter for subsequent rounds of release. Originally identified as the target of psychoactive drugs, these transport systems have important roles in transmitter release, but we are only beginning to understand their contribution to synaptic transmission, plasticity, behavior, and disease. Recent work has started to provide a structural basis for their activity, to characterize their trafficking and potential for regulation. The results indicate that far from the passive target of psychoactive drugs, neurotransmitter transporters undergo regulation that contributes to synaptic plasticity.The speed and potency of synaptic transmission depend on the immediate availability of synaptic vesicles filled with high concentrations of neurotransmitter. In this article, we focus on the mechanisms responsible for packaging transmitter into synaptic vesicles and for reuptake from the extracellular space that both terminates synaptic transmission and recycles transmitter for future rounds of release. Collectively, we refer to this entire process as the neurotransmitter cycle.The recycling of neurotransmitter illustrates a general, conceptual problem for the mechanism of vesicular release. At the plasma membrane, more active reuptake should help to replenish the pool of releasable transmitter, but may also reduce the extent and duration of signaling to the postsynaptic cell. Conversely, loss of reuptake increases the activation of receptors but results in the depletion of stores (Jones et al. 1998). At the vesicle, steeper concentration gradients release more transmitter per vesicle but reduce the cytosolic transmitter available for refilling, whereas more shallow gradients facilitate refilling but reduce the transmitter available for release. The way in which the nerve terminal balances these competing factors thus has profound consequences for synaptic transmission.     

Receptor kinetics pertaining to blockade of nerve-released transmitter at synapses

The question is raised as to whether competitive inhibitors should block responses of tissue to nerve-released neurotransmitter to the same extent as they block equivalent responses to exogenous agonist. From a simple dynamic model of synaptic events, which takes into account non-constancy of transmitter concentration in space and time, it is deduced that equal blockade of responses to nerve-released and exogenous transmitter substance will occur if: (i) there are locally many more receptor molecules than transmitter molecules; (ii) the active agonist-receptor complex, AnR, has n = 1; and (iii) tissue response is insensitive to spatial or temporal inhomogeneity of AR. In such a case there will also be equal sensitivity of responses to other modes of inhibition: irreversible competitive, uncompetitive, and non-competitive. Equal blockade of responses to equi-effective endogenous and exogenous agonist will also occur if nerve stimulation gives rise to a steady uniform concentration of agonist, so that equilibrium kinetics are applicable. When n greater than 1 and/or when tissue responses reflect local peak AnR, response to nerve-released transmitter will be relatively insensitive to receptor blockade by a competitive inhibitor. The same is true for irreversible competitive blockade or for modulation of receptor density. However, an uncompetitive inhibitor (e.g. a 'channel blocker') may be more effective against nerve-released agonist than against exogenous agonist.     

Ultrastructure of synapses with different transmitter-releasing characteristics on motor axon terminals of a crab,Hyas areneas

Synaptic terminals on branches of an excitatory motor axon in a spider crab (Hyas areneas) were examined by electron microscopy to determine whether differences in size, structure, and number of synapses could be correlated with differences in transmitter release. Terminals releasing relatively large amounts of transmitter during low frequencies of nerve impulses ("high-output" terminals) had larger synapses, more prominent presynaptic dense bodies (active zones), and fewer synapses per unit length than terminals releasing relatively small amounts of transmitter ("low-output" terminals). Neither the difference in synaptic area, nor the quantitative differences in the active zones, were sufficient in themselves to explain the difference in synaptic efficacy, and it is postulated that a non-linear relationship may exist between structural features of the synapse and release of transmitter by a nerve impulse, and that differences other than those apparent from the ultrastructure could be involved. Greater facilitation at low-output terminals with high frequencies of nerve impulses may be due to greater reserves of "immediately available" transmitter, and to recruitment or activation of more individual synaptic contacts.     

Analytical description of the activation of multi-state receptors by continuous neurotransmitter signals at brain synapses.

Chemical synaptic transmission is a fundamental component of interneuronal communications in the central nervous system (CNS). Discharge of a presynaptic vesicle containing a few thousand molecules (a quantum) of neurotransmitter into the synaptic cleft generates a transmitter concentration signal that drives postsynaptic ion-channel receptors. These receptors exhibit multiple states, with state transition kinetics dependent on neurotransmitter concentration. Here, a novel and simple analytical approach for describing gating of multi-state receptors by signals with complex continuous time courses is used to describe the generation of glutamate-mediated quantal postsynaptic responses at brain synapses. The neurotransmitter signal, experienced by multi-state N-methyl-D-aspartate (NMDA)- and L-alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionate (AMPA)-type glutamate receptors at specific points in a synaptic cleft, is approximated by a series of step functions of different intensity and duration and used to drive a Markovian, multi-state kinetic scheme that describes receptor gating. Occupancy vectors at any point in time can be computed interatively from the occupancy vectors at the times of steps in transmitter concentration. Multi-state kinetic schemes for both the low-affinity AMPA subtype of glutamate receptor and for the high-affinity NMDA subtype are considered, and expected NMDA and AMPA components of synaptic currents are calculated. The amplitude of quantal responses mediated by postsynaptic receptor clusters having specific spatial distributions relative to foci of quantal neurotransmitter release is then calculated and related to the displacement between the center of the postsynaptic receptor cluster and the focus of synaptic vesicle discharge. Using this approach we show that the spatial relation between the focus of release and the center of the postsynaptic receptor cluster affects synaptic efficacy. We also show how variation in this relation contributes to variation in synaptic current amplitudes.     

Coding with spike shapes and graded potentials in cortical networks

In cortical neurones, analogue dendritic potentials are thought to be encoded into patterns of digital spikes. According to this view, neuronal codes and computations are based on the temporal patterns of spikes: spike times, bursts or spike rates. Recently, we proposed an 'action potential waveform code' for cortical pyramidal neurones in which the spike shape carries information. Broader somatic action potentials are reliably produced in response to higher conductance input, allowing for four times more information transfer than spike times alone. This information is preserved during synaptic integration in a single neurone, as back-propagating action potentials of diverse shapes differentially shunt incoming postsynaptic potentials and so participate in the next round of spike generation. An open question has been whether the information in action potential waveforms can also survive axonal conduction and directly influence synaptic transmission to neighbouring neurones. Several new findings have now brought new light to this subject, showing cortical information processing that transcends the classical models.     

Substance P and spinal neurones.

When applied by microiontophoresis, substance P (sP) had a strong, but slow and prolonged excitatory action on nearly half the neurones tested in the lumbar spinal cord of cats. Motoneuronal antidromic field potentials only occasionally showed a significant effect of sP. Cerebral cortical neurones in cats and rats were much less readily excited than spinal interneurones. Some unresponsive units showed evidence of a depressant effect of sP. Although sP may have a significant function in central afferent pathways, it is not likely to be a quickly-acting synaptic transmitter.     

Geometric and many-particle aspects of transmitter binding.

We investigate the various reactivity patterns possible when several transmitter molecules, released at one side of a synaptic gap, diffuse and bind reversibly to a single receptor at the other end. In the framework of a one-dimensional approximation, the complete time, reactivity, concentration and gap-width dependence are determined, using a rigorous theoretical and computational approach to the many-body aspects of this problem. The time dependence of the survival probability is found to consist of up to four phases. These include a short delay followed by gaussian, power-law, and exponential decay phases. A rigorous expression is derived for the long-time exponent and approximate expressions are obtained for describing the short-time gaussian phase.     

Synaptic transmission in suprasylvian visual cortex is reduced by excitatory amino acid antagonists

The activities of cortical neurones lying in the Clare-Bishop area of the suprasylvian visual region in anaesthetized cats were monitored during the application of cholinergic and amino acid agonists and antagonists, as well as during sequences of light and electrical stimulation. Of those Clare-Bishop cells which could be activated at short latencies by electrical stimuli applied to the contralateral, homologous cortical zone, D-alpha-aminoadipate and 2-amino-5-phosphonovalerate antagonized neuronal responses elicited by electrically evoked synaptic activation and by the presentation of light stimuli. Acetylcholine as well as the excitatory amino acids increased the firing of many of these neurones; however only the amino acid antagonists blocked the commissurally evoked excitations although both types of antagonist reduced the magnitudes of the visually evoked responses. It therefore appears as though the same synaptic transmitter is utilized by cortical commissural afferents as is employed by the cortical ipsilateral projection to the Clare-Bishop area, and furthermore this transmitter is likely to be an excitatory amino acid.     

The isolation, from electromotor neurone perikarya, of messenger RNAs coding for synaptic proteins

Poly(A)-containing mRNA was isolated from the electric lobe, cerebellum and forebrain of Torpedo marmorata and from cholinergic electromotor perikarya isolated from the electric lobe. All the mRNA preparations were translated by a cell-free protein-synthesizing system from rabbit reticulocytes; no brain-specific factors were required. The highest stimulation rate was found with the perikaryal mRNA suggesting that this purely neuronal mRNA is a preferred template in the protein-synthesis system; the molecular basis of this phenomenon remains to be elucidated. The translation products of the perikaryal mRNA were analysed by two-dimensional gel electrophoresis and compared with the proteins of synaptosomes derived from the electromotor nerve terminals. The majority of the synaptosomal proteins comigrated with synthesized products. More than 100 synthesized proteins were detected as individual spots in the gel pattern, among them actin, subunits of neurofilamentous proteins and a protein considered to be a specific component of electromotor synaptic vesicles. Identities were confirmed in some cases by immunochemical methods. The results suggest that protein synthesis in the perikaryon of the electromotor neurone is largely directed to the production of proteins needed to maintain synaptic integrity. A comparison of the translation products of mRNA derived from the highly cholinergic electric lobe and a brain region, the cerebellum, which is non-cholinergic, revealed, as expected, some common translation products and others which appeared to be specific for the brain regions concerned. This approach may lead to the identification of protein specific for neurones of different transmitter types.     

Mathematical modelling and computational study of two-dimensional and three-dimensional dynamics of receptor–ligand interactions in signalling response mechanisms

Cell signalling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signalling pathways. But the binding process still presents many enigmas and, by analogy with surface catalytic reactions, two different mechanisms can be conceived: the first mechanism is related to the Eley–Rideal (ER) mechanism, i.e. the bulk-dissolved ligand interacts directly by pure three-dimensional (3D) diffusion with the specific surface receptor; the second mechanism is similar to the Langmuir–Hinshelwood (LH) process, i.e. 3D diffusion of the ligand to the cell surface followed by reversible ligand adsorption and subsequent two-dimensional (2D) surface diffusion to the receptor. A situation where both mechanisms simultaneously contribute to the signalling process could also occur. The aim of this paper is to perform a computational study of the behavior of the signalling response when these different mechanisms for ligand-receptor interactions are integrated into a model for signal transduction and ligand transport. To this end, partial differential equations have been used to develop spatio-temporal models that show trafficking dynamics of ligands, cell surface components, and intracellular signalling molecules through the different domains of the system. The mathematical modeling developed for these mechanisms has been applied to the study of two situations frequently found in cell systems: (a) dependence of the signal response on cell density; and (b) enhancement of the signalling response in a synaptic environment.     

A single packet of transmitter does not saturate postsynaptic glutamate receptors

Neurotransmitter is stored in synaptic vesicles and released by exocytosis into the synaptic cleft. One of the fundamental questions in central synaptic transmission is whether a quantal packet of transmitter saturates postsynaptic receptors. To address this question, we loaded the excitatory transmitter L-glutamate via whole-cell recording pipettes into the giant nerve terminal, the calyx of Held, in rat brainstem slices. This caused marked potentiations of both quantal and action potential-evoked EPSCs mediated by alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) or N-methyl-D-aspartate (NMDA) receptors. These results directly demonstrate that neither AMPA nor NMDA receptors are saturated by a single packet of transmitter, and indicate that vesicular transmitter content is an important determinant of synaptic efficacy.     

Glutamate may be an efferent transmitter that elicits inhibition in mouse taste buds

Recent studies suggest that l-glutamate may be an efferent transmitter released from axons innervating taste buds. In this report, we determined the types of ionotropic synaptic glutamate receptors present on taste cells and that underlie this postulated efferent transmission. We also studied what effect glutamate exerts on taste bud function. We isolated mouse taste buds and taste cells, conducted functional imaging using Fura 2, and used cellular biosensors to monitor taste-evoked transmitter release. The findings show that a large fraction of Presynaptic (Type III) taste bud cells (～50%) respond to 100 μM glutamate, NMDA, or kainic acid (KA) with an increase in intracellular Ca(2+). In contrast, Receptor (Type II) taste cells rarely (4%) responded to 100 μM glutamate. At this concentration and with these compounds, these agonists activate glutamatergic synaptic receptors, not glutamate taste (umami) receptors. Moreover, applying glutamate, NMDA, or KA caused taste buds to secrete 5-HT, a Presynaptic taste cell transmitter, but not ATP, a Receptor cell transmitter. Indeed, glutamate-evoked 5-HT release inhibited taste-evoked ATP secretion. The findings are consistent with a role for glutamate in taste buds as an inhibitory efferent transmitter that acts via ionotropic synaptic glutamate receptors.