Stochastic model of central synapses: slow diffusion of transmitter interacting with spatially distributed receptors and transporters.

A detailed mathematical analysis of the diffusion process of neurotransmitter inside the synaptic cleft is presented and the spatio-temporal concentration profile is calculated. Using information about the experimentally observed time course of glutamate in the cleft the effective diffusion coefficient Dnet is estimated as Dnet approximately 20-50 nm(2) microseconds(-1), implying a strong reduction compared with free diffusion in aqueous solution. The tortuosity of the cleft and interactions with transporter molecules are assumed to affect the transmitter motion. We estimate the transporter density to be 5170 to 8900 micrometer(-2) in the synaptic cleft and its vicinity, using the experimentally observed time constant of glutamate. Furthermore a theoretical model of synaptic transmission is presented, taking the spatial distribution of post-synaptic (AMPA-) receptors into account. The transmitter diffusion and receptor dynamics are modeled by Monte Carlo simulations preserving the typically observed noisy character of post-synaptic responses. Distributions of amplitudes, rise and decay times are calculated and shown to agree well with experiments. Average open probabilities are computed from a novel kinetic model and are shown to agree with averages over many Monte Carlo runs. Our results suggest that post-synaptic currents are only weakly potentiated by clustering of post-synaptic receptors, but increase linearly with the total number of receptors. Distributions of amplitudes and rise times are used to discriminate between different morphologies, e.g. simple and perforated synapses. A skew in the miniature amplitude distribution can be caused by multiple release of pre-synaptic vesicles at perforated synapses.     

Spillover of glutamate onto synaptic AMPA receptors enhances fast transmission at a cerebellar synapse

Diffusion of glutamate from the synaptic cleft can activate high-affinity receptors, but is not thought to contribute to fast AMPA receptor-mediated transmission. Here, we show that single AMPA receptor EPSCs at the cerebellar mossy fiber-granule cell connection are mediated by both direct release of glutamate and rapid diffusion of glutamate from neighboring synapses. Immunogold localization revealed that AMPA receptors are located exclusively in postsynaptic densities, indicating that spillover of glutamate occurs between synaptic contacts. Spillover currents contributed half the synaptic charge and exhibited little trial-to-trial variability. We propose that spillover of glutamate improves transmission efficacy by both increasing the amplitude and duration of the EPSP and reducing fluctuations arising from the probabilistic nature of transmitter release.     

Spike timing and reliability in cortical pyramidal neurons: effects of EPSC kinetics, input synchronization and background noise on spike timing

In vivo studies have shown that neurons in the neocortex can generate action potentials at high temporal precision. The mechanisms controlling timing and reliability of action potential generation in neocortical neurons, however, are still poorly understood. Here we investigated the temporal precision and reliability of spike firing in cortical layer V pyramidal cells at near-threshold membrane potentials. Timing and reliability of spike responses were a function of EPSC kinetics, temporal jitter of population excitatory inputs, and of background synaptic noise. We used somatic current injection to mimic population synaptic input events and measured spike probability and spike time precision (STP), the latter defined as the time window (Deltat) holding 80% of response spikes. EPSC rise and decay times were varied over the known physiological spectrum. At spike threshold level, EPSC decay time had a stronger influence on STP than rise time. Generally, STP was highest (6 ms) triggered spikes at lower temporal precision (>or=6.58 ms). We found an overall linear relationship between STP and spike delay. The difference in STP between fast and slow compound EPSCs could be reduced by incrementing the amplitude of slow compound EPSCs. The introduction of a temporal jitter to compound EPSCs had a comparatively small effect on STP, with a tenfold increase in jitter resulting in only a five fold decrease in STP. In the presence of simulated synaptic background activity, precisely timed spikes could still be induced by fast EPSCs, but not by slow EPSCs.     

Variability of neurotransmitter concentration and nonsaturation of postsynaptic AMPA receptors at synapses in hippocampal cultures and slices

To understand the elementary unit of synaptic communication between CNS neurons, one must know what causes the variability of quantal postsynaptic currents and whether unitary packets of transmitter saturate postsynaptic receptors. We studied single excitatory synapses between hippocampal neurons in culture. Focal glutamate application at individual postsynaptic sites evoked currents (I(glu)) with little variability compared with quantal excitatory postsynaptic currents (EPSCs). The maximal I(glu) was >2-fold larger than the median EPSC. Thus, variations in [glu]cleft are the main source of variability in EPSC size, and glutamate receptors are generally far from saturation during quantal transmission. This conclusion was verified by molecular antagonism experiments in hippocampal cultures and slices. The general lack of glutamate receptor saturation leaves room for increases in [glu]cleft as a mechanism for synaptic plasticity.     

Synapse-specific contribution of the variation of transmitter concentration to the decay of inhibitory postsynaptic currents

Synaptic transmission is characterized by a remarkable trial-to-trial variability in the postsynaptic response, influencing the way in which information is processed in neuronal networks. This variability may originate from the probabilistic nature of quantal transmitter release, from the stochastic behavior of the receptors, or from the fluctuation of the transmitter concentration in the cleft. We combined nonstationary noise analysis and modeling techniques to estimate the contribution of transmitter fluctuation to miniature inhibitory postsynaptic current (mIPSC) variability. A substantial variability (approximately 30%) in mIPSC decay was found in all cell types studied (neocortical layer2/3 pyramidal cells, granule cells of the olfactory bulb, and interneurons of the cerebellar molecular layer). This large variability was not solely the consequence of the expression of multiple types of GABA(A) receptors, as a similar mIPSC decay variability was observed in cerebellar interneurons that express only a single type (alpha(1)beta(2)gamma(2)) of GABA(A) receptor. At large synapses on these cells, all variance in mIPSC decay could be accounted for by the stochastic behavior of approximately 36 pS channels, consistent with the conductance of alpha(1)beta(2)gamma(2) GABA(A) receptors at physiological temperatures. In contrast, at small synapses, a significant amount of variability in the synaptic cleft GABA transient had to be present to account for the additional variance in IPSC decay over that produced by stochastic channel openings. Thus, our results suggest a synapse-specific contribution of the variation of the spatiotemporal profile of GABA to the decay of IPSCs.     

Recordings from neuron–HEK cell cocultures reveal the determinants of miniature excitatory postsynaptic currents

Spontaneous exocytosis of single synaptic vesicles generates miniature synaptic currents, which provide a window into the dynamic control of synaptic transmission. To resolve the impact of different factors on the dynamics and variability of synaptic transmission, we recorded miniature excitatory postsynaptic currents (mEPSCs) from cocultures of mouse hippocampal neurons with HEK cells expressing the postsynaptic proteins GluA2, neuroligin 1, PSD-95, and stargazin. Synapses between neurons and these heterologous cells have a molecularly defined postsynaptic apparatus, while the compact morphology of HEK cells eliminates the distorting effect of dendritic filtering. HEK cells in coculture produced mEPSCs with a higher frequency, larger amplitude, and more rapid rise and decay than neurons from the same culture. However, mEPSC area indicated that nerve terminals in synapses with both neurons and HEK cells release similar populations of vesicles. Modulation by the glutamate receptor ligand aniracetam revealed receptor contributions to mEPSC shape. Dendritic cable effects account for the slower mEPSC rise in neurons, whereas the slower decay also depends on other factors. Lastly, expression of synaptobrevin transmembrane domain mutants in neurons slowed the rise of HEK cell mEPSCs, thus revealing the impact of synaptic fusion pores. In summary, we show that cocultures of neurons with heterologous cells provide a geometrically simplified and molecularly defined system to investigate the time course of synaptic transmission and to resolve the contribution of vesicles, fusion pores, dendrites, and receptors to this process.     

Triheteromeric NR1/NR2A/NR2B receptors constitute the major N-methyl-D-aspartate receptor population in adult hippocampal synapses

NMDA receptors (NMDARs), fundamental to learning and memory and implicated in certain neurological disorders, are heterotetrameric complexes composed of two NR1 and two NR2 subunits. The function of synaptic NMDARs in postnatal principal forebrain neurons is typically attributed to diheteromeric NR1/NR2A and NR1/NR2B receptors, despite compelling evidence for triheteromeric NR1/NR2A/NR2B receptors. In synapses, the properties of triheteromeric NMDARs could thus far not be distinguished from those of mixtures of diheteromeric NMDARs. To find a signature of NR1/NR2A/NR2B receptors, we have employed two gene-targeted mouse lines, expressing either NR1/NR2A or NR1/NR2B receptors without NR1/NR2A/NR2B receptors, and compared their synaptic properties with those of wild type. In acute hippocampal slices of mutants older than 4 weeks we found a distinct voltage dependence of NMDA R-mediated excitatory postsynaptic current (NMDA EPSC) decay time for the two diheteromeric NMDARs. In wild-type mice, NMDA EPSCs unveiled the NR1/NR2A characteristic for this voltage-dependent deactivation exclusively, indicating that the contribution of NR1/NR2B receptors to evoked NMDA EPSCs is negligible in adult CA3-to-CA1 synapses. The presence of NR1/NR2A/NR2B receptors was obvious from properties that could not be explained by a mixture of diheteromeric NR1/NR2A and NR1/NR2B receptors or by the presence of NR1/NR2A receptors alone. The decay time for NMDA EPSCs in wild type was slower than that for NR1/NR2A receptors, and the sensitivity of NMDA EPSCs to NR2B-directed NMDAR antagonists was 50%. Thus, NR2B is prominent in adult hippocampal synapses as an integral part of NR1/NR2A/NR2B receptors.     

Fast, automated implementation of temporally precise blind deconvolution of multiphasic excitatory postsynaptic currents

Records of excitatory postsynaptic currents (EPSCs) are often complex, with overlapping signals that display a large range of amplitudes. Statistical analysis of the kinetics and amplitudes of such complex EPSCs is nonetheless essential to the understanding of transmitter release. We therefore developed a maximum-likelihood blind deconvolution algorithm to detect exocytotic events in complex EPSC records. The algorithm is capable of characterizing the kinetics of the prototypical EPSC as well as delineating individual release events at higher temporal resolution than other extant methods. The approach also accommodates data with low signal-to-noise ratios and those with substantial overlaps between events. We demonstrated the algorithm's efficacy on paired whole-cell electrode recordings and synthetic data of high complexity. Using the algorithm to align EPSCs, we characterized their kinetics in a parameter-free way. Combining this approach with maximum-entropy deconvolution, we were able to identify independent release events in complex records at a temporal resolution of less than 250 μs. We determined that the increase in total postsynaptic current associated with depolarization of the presynaptic cell stems primarily from an increase in the rate of EPSCs rather than an increase in their amplitude. Finally, we found that fluctuations owing to postsynaptic receptor kinetics and experimental noise, as well as the model dependence of the deconvolution process, explain our inability to observe quantized peaks in histograms of EPSC amplitudes from physiological recordings.     

Statistical models of synaptic transmission evaluated using the expectation-maximization algorithm.

Amplitude fluctuations of evoked synaptic responses can be used to extract information on the probabilities of release at the active sites, and on the amplitudes of the synaptic responses generated by transmission at each active site. The parameters that describe this process must be obtained from an incomplete data set represented by the probability density of the evoked synaptic response. In this paper, the equations required to calculate these parameters using the Expectation-Maximization algorithm and the maximum likelihood criterion have been derived for a variety of statistical models of synaptic transmission. These models are ones where the probabilities associated with the different discrete amplitudes in the evoked responses are a) unconstrained, b) binomial, and c) compound binomial. The discrete amplitudes may be separated by equal (quantal) or unequal amounts, with or without quantal variance. Alternative models have been considered where the variance associated with the discrete amplitudes is sufficiently large such that no quantal amplitudes can be detected. These models involve the sum of a normal distribution (to represent failures) and a unimodal distribution (to represent the evoked responses). The implementation of the algorithm is described in each case, and its accuracy and convergence have been demonstrated.     

From the stochasticity of molecular processes to the variability of synaptic transmission

The variability of the postsynaptic response following a single action potential arises from two sources: the neurotransmitter release is probabilistic, and the postsynaptic response to neurotransmitter release has variable timing and amplitude. At individual synapses, the number of molecules of a given type that are involved in these processes is small enough that the stochastic (random) properties of molecular events cannot be neglected. How the stochasticity of molecular processes contributes to the variability of synaptic transmission, its sensitivity and its robustness to molecular fluctuations has important implications for our understanding of the mechanistic basis of synaptic transmission and of synaptic plasticity.     

Two families of TARP isoforms that have distinct effects on the kinetic properties of AMPA receptors and synaptic currents

Transmembrane AMPA receptor regulatory proteins (TARPs) are auxiliary AMPA receptor subunits that regulate both the trafficking and gating properties of AMPA receptors, and different TARP isoforms display distinct expression patterns in brain. Here, we compared the effects of four TARP isoforms on the kinetics of AMPA receptor currents. Each isoform slowed the deactivation of GluR1 currents, but the slowing was greatest with gamma-4 and gamma-8. Isoform-specific differences in desensitization were also observed that correlated with effects on deactivation. TARP isoforms also differentially modulated responses to trains of glutamate applications designed to mimic high-frequency presynaptic firing. Importantly, whereas both stargazin and gamma-4 rescued excitatory synaptic transmission in cerebellar granule cells from stargazer mice, the decay of miniature EPSCs was 2-fold slower in neurons expressing gamma-4. The results show that heterogeneity in the composition of AMPA receptor/TARP complexes contributes to synapse-specific differences in EPSC decays and frequency-dependent modulation of neurotransmission.     

Axonal Noise as a Source of Synaptic Variability

Post-synaptic potential (PSP) variability is typically attributed to mechanisms inside synapses, yet recent advances in experimental methods and biophysical understanding have led us to reconsider the role of axons as highly reliable transmission channels. We show that in many thin axons of our brain, the action potential (AP) waveform and thus the Ca⁺⁺ signal controlling vesicle release at synapses will be significantly affected by the inherent variability of ion channel gating. We investigate how and to what extent fluctuations in the AP waveform explain observed PSP variability. Using both biophysical theory and stochastic simulations of central and peripheral nervous system axons from vertebrates and invertebrates, we show that channel noise in thin axons (<1 µm diameter) causes random fluctuations in AP waveforms. AP height and width, both experimentally characterised parameters of post-synaptic response amplitude, vary e.g. by up to 20 mV and 0.5 ms while a single AP propagates in C-fibre axons. We show how AP height and width variabilities increase with a ¾ power-law as diameter decreases and translate these fluctuations into post-synaptic response variability using biophysical data and models of synaptic transmission. We find for example that for mammalian unmyelinated axons with 0.2 µm diameter (matching cerebellar parallel fibres) axonal noise alone can explain half of the PSP variability in cerebellar synapses. We conclude that axonal variability may have considerable impact on synaptic response variability. Thus, in many experimental frameworks investigating synaptic transmission through paired-cell recordings or extracellular stimulation of presynaptic neurons, causes of variability may have been confounded. We thereby show how bottom-up aggregation of molecular noise sources contributes to our understanding of variability observed at higher levels of biological organisation.     

Chronic pregabalin inhibits synaptic transmission between rat dorsal root ganglion and dorsal horn neurons in culture

In this study, we have examined the properties of synaptic transmission between dorsal root ganglion (DRG) and dorsal horn (DH) neurons, placed in co-culture. We also examined the effect of the anti-hyperalgesic gabapentinoid drug pregabalin (PGB) at this pharmacologically relevant synapse. The main method used was electrophysiological recording of excitatory post synaptic currents (EPSCs) in DH neurons. Synaptic transmission between DRG and DH neurons was stimulated by capsaicin, which activates transient receptor potential vanilloid-1 (TRPV1) receptors on small diameter DRG neurons. Capsaicin (1 μM) application increased the frequency of EPSCs recorded in DH neurons in DRG-DH co-cultures, by about 3-fold, but had no effect on other measured properties of the EPSCs. There was also no effect of capsaicin in the absence of co-cultured DRGs. Application of PGB (100 μM) for 40–48 h caused a reduction in the capsaicin-induced increase in EPSC frequency by 57%. In contrast, brief preincubation of PGB had no significant effect on the capsaicin-induced increase in EPSC frequency. In conclusion, this study shows that PGB applied for 40–48 h, but not acute application inhibits excitatory synaptic transmission at DRG-DH synapses, in response to nociceptive stimulation, most likely by a presynaptic effect on neurotransmitter release from DRG presynaptic terminals.     

Chronic pregabalin inhibits synaptic transmission between rat dorsal root ganglion and dorsal horn neurons in culture

In this study, we have examined the properties of synaptic transmission between dorsal root ganglion (DRG) and dorsal horn (DH) neurons, placed in co-culture. We also examined the effect of the anti-hyperalgesic gabapentinoid drug pregabalin (PGB) at this pharmacologically relevant synapse. The main method used was electrophysiological recording of excitatory post synaptic currents (EPSCs) in DH neurons. Synaptic transmission between DRG and DH neurons was stimulated by capsaicin, which activates transient receptor potential vanilloid-1 (TRPV1) receptors on small diameter DRG neurons. Capsaicin (1 μM) application increased the frequency of EPSCs recorded in DH neurons in DRG-DH co-cultures, by about 3-fold, but had no effect on other measured properties of the EPSCs. There was also no effect of capsaicin in the absence of co-cultured DRGs. Application of PGB (100 μM) for 40-48 h caused a reduction in the capsaicin-induced increase in EPSC frequency by 57%. In contrast, brief preincubation of PGB had no significant effect on the capsaicin-induced increase in EPSC frequency. In conclusion, this study shows that PGB applied for 40-48 h, but not acute application inhibits excitatory synaptic transmission at DRG-DH synapses, in response to nociceptive stimulation, most likely by a presynaptic effect on neurotransmitter release from DRG presynaptic terminals.     

Excitotoxicity induced by enhanced excitatory neurotransmission in cultured hippocampal pyramidal neurons.

Cultures of rat hippocampal pyramidal neurons were used to examine the roles of excitatory synaptic transmission, NMDA receptors, and elevated [Ca2+]i in the production of excitotoxicity. In integral of 70% of the cells observed, perfusion with Mg2(+)-free, glycine-supplemented medium induced large spontaneous fluctuations or maintained plateaus of [Ca2+]i. [Ca2+]i fluctuations could be blocked by tetrodotoxin, NMDA receptor antagonists, dihydropyridines, or compounds that inhibit synaptic transmission in the hippocampus, but not by the non-NMDA receptor antagonist 6-cyano-7-nitroquinoxaline-2,3-dione. When cells were treated with Mg2(+)-free, glycine-supplemented medium and examined 24 hr later, integral of 30% of the neurons were found to have died. Cell death could be inhibited by the same agents that reduced [Ca2+]i fluctuations. These results support a role for direct excitatory synaptic transmission, as opposed to the general release of glutamate, in excitotoxicity. A major role for synaptically activated NMDA receptors, rather than kainate/quisqualate receptors, is also indicated. Neuronal death may be produced by abnormal changes in neuronal [Ca2+]i.     

Local anesthetic alteration of miniature endplate currents and endplate current fluctuations.

The effect of the local anesthetic QX222 on the kinetics of miniature endplate currents and acetylcholine induced endplate current fluctuations was studied in voltage clamped cutaneous pectoris muscle of Rana pipiens. Both the endplate current fluctuation spectra and the miniature endplate current decay consisted of two or three components depending upon the holding potential and local anesthetic concentration. The cutoff frequency of each spectral component was equal to the decay rate of its corresponding constituent of the miniature endplate current. Comparison of the relative amplitudes of the spectral and miniature endplate components indicated that QX222 did not act by creating two kinetically distinct populations of acetylcholine receptors. QX222 action could be explained by alteration of the acetylcholine receptors such that they sequentially change conformation form one open state to another. A specific case in which QX222 binds to the open state of the acetyl-choline receptor creating a blocked state, was found to account for the observed relationship between the relative amplitudes of the miniature endplate current and spectral components, as well as the previously observed voltage and concentration sensitivity of the decay rates of endplate current components.     

Dependence of Miniature Endplate Current on Kinetic Parameters of Acetylcholine Receptors Activation: A Model Study

Mathematical modeling was applied to study the dependence of miniature endplate current (MEPC) amplitude and temporal parameters on the values of the rate constants of acetylcholine binding to receptors (k₊) when cholinesterase was either active or inactive. The simulation was performed under two different sets of parameters describing acetylcholine receptor activation–one with high and another with low probability (Po_high and Po_low) of receptor transition into the open state after double ligand binding. The dependence of model MEPC amplitudes, rise times, and decay times on k₊ differs for set Po_low and set Po_high. The main outcome is that for set Po_high, the rise time is significantly longer at low values of k₊ because of the prolongation of ACh diffusion time to the receptor. For the set Polow, the rise time is shorter at low values of k1, which can be explained by the small probability of AChR forward isomerization after ACh binding and faster MEPC's peak formation.