Reliable evaluation of the quantal determinants of synaptic efficacy using Bayesian analysis.

Communication between neurones in the central nervous system depends on synaptic transmission. The efficacy of synapses is determined by pre- and postsynaptic factors that can be characterized using quantal parameters such as the probability of neurotransmitter release, number of release sites, and quantal size. Existing methods of estimating the quantal parameters based on multiple probability fluctuation analysis (MPFA) are limited by their requirement for long recordings to acquire substantial data sets. We therefore devised an algorithm, termed Bayesian Quantal Analysis (BQA), that can yield accurate estimates of the quantal parameters from data sets of as small a size as 60 observations for each of only 2 conditions of release probability. Computer simulations are used to compare its performance in accuracy with that of MPFA, while varying the number of observations and the simulated range in release probability. We challenge BQA with realistic complexities characteristic of complex synapses, such as increases in the intra- or intersite variances, and heterogeneity in release probabilities. Finally, we validate the method using experimental data obtained from electrophysiological recordings to show that the effect of an antagonist on postsynaptic receptors is correctly characterized by BQA by a specific reduction in the estimates of quantal size. Since BQA routinely yields reliable estimates of the quantal parameters from small data sets, it is ideally suited to identify the locus of synaptic plasticity for experiments in which repeated manipulations of the recording environment are unfeasible.

Co-Release of GABA Does Not Occur at Glycinergic Synapses onto Lumbar Motoneurons in Juvenile Mice.

The fast inhibitory neurotransmitters glycine and GABA are co-localized in synaptic terminals of inhibitory interneurons in the spinal cord and co-released onto lumbar motoneurons in neonatal rats. We performed whole-cell voltage-clamp experiments on spinal cord preparations obtained from juvenile (P8-14) mice to determine whether inhibitory currents exhibited GABAergic components in motoneurons of animals of weight-bearing age. Subsequently we established whether or not GABA is co-released at glycinergic synapses onto motoneurons by determining if it conferred modulatory effects on the kinetics of glycinergic currents. Exponential fitting analysis showed that evoked and miniature inhibitory post-synaptic currents (IPSCs) were best-fitted with a single decay time constant. Responses recorded from connected interneuron-motoneuron pairs showed no effect of a benzodiazepine or a GABA(A) receptor antagonist. Similarly IPSCs evoked by extracellular stimulation and miniature IPSCs were not affected by either agent, indicating the absence of co-detection. Experimental manipulation of the relative content of pre-synaptic GABA and glycine conferred no effect on post-synaptic responses. It is thus unlikely that GABA is co-released in biologically relevant amounts at glycinergic synapses onto lumbar motoneurons in mice of this age.

Reading between the spikes of the hypothalamic neural code.

Reading the spike coding of hypothalamic neurones presents a considerable challenge because they exhibit highly irregular firing patterns. Electrophysiologists working in the motor and sensory systems, in which neurones fire more regularly, have devised satisfactory methods to describe the firing of cells, although the statistical assumptions that underlie the methods do not apply to hypothalamic neurones. Measurement of neural activity is nevertheless vital to characterise the activity of neuroendocrine cells. It has thus become necessary to develop methods suitable for the analysis of the highly irregular spike discharge patterns of both spontaneous and stimulus-evoked firing of hypothalamic neurones. We review techniques used to meet this challenge and demonstrate their considerable capacity to address important physiological questions. We also introduce a novel approach for valid statistical estimation of the information conveyed by the response of a single neurone to a periodic stimulus. The approach demonstrated significant diurnal rhythms of synaptic connectivity between hypothalamic nuclei.

Daily rhythms of spike coding in the rat supraoptic nucleus.

Novel measures of coding based on interspike intervals were used to characterise the rhythms of single unit activity in the supraoptic nucleus during the day/night cycle in urethane-anaesthetised rats in vivo. Both continuously firing and phasic cells showed significant (P < 0.001) diurnal rhythms of spike frequency and in the irregularity of firing, as quantified by the log interval entropy (ENT). Comparison of rhythms in log interval ENT showed that the amplitude of the rhythms was greater for the continuously firing cells than for the phasic cells (P = 0.002). Rhythms persisted after hypertonic stimulation or pinealectomy and both treatments reduced the amplitude significantly only for the continuously firing cell group. By contrast, the mesor (i.e. mid-point of the rhythm) was reduced only for the phasic cell group. A similar analysis applied to the activity of cells of the suprachiasmatic nucleus showed that, after pinealectomy, there was a significant rhythm in ENT (P < 0.001) but not firing rate; however, the amplitude of the rhythm in ENT was attenuated (P = 0.047). Diurnal changes in the electrical activity of supraoptic cells are consistent with previously reported circadian changes in magnocellular neuropeptide release. Differences between continuous and phasic cell groups in the effects of osmotic stimulation on rhythmic activity indicate that the two cell types differ in their coding of osmolality and zeitgeber time information. The different effects of pinealectomy on the supraoptic and suprachiasmatic nuclei suggest that removal of endogenous melatonin unmasks a difference in circadian coding between the two nuclei.

Leptin modulates spike coding in the rat suprachiasmatic nucleus.

The mammalian circadian pacemaker, the suprachiasmatic nucleus (SCN), contains receptors to the adipose tissue hormone leptin. In the present study, the effects of leptin on the electrophysiological activity of the SCN cells were characterised in vitro in rat brain slices. During extracellular recording, application of 20 nm leptin (n = 36) decreased mean spike frequency (Wilcoxon signed rank test, z = -3.390, P < 0.001) and increased the irregularity of firing measured by the entropy of the log interspike interval distribution (Student's paired t-test, t = 2.377, P = 0.023), but had no consistent effect on spike patterning as measured by the mutual information between adjacent log interspike intervals (z = 0.745, P = 0.456). Intracellular current-clamp recordings (n = 25) revealed a hyperpolarising effect of 20 nm leptin on SCN neurones (z = -2.290, P = 0.022). The hyperpolarisation largely resulted from the effect of leptin on the subgroup of cells (n = 13) that generated 'rebound' spikes upon termination of a hyperpolarising current pulse (z = -2.697, P = 0.007). Leptin application also increased the group mean duration of the afterhyperpolarisation (n = 25, t = 2.512, P = 0.023). The effects of leptin on extracellularly recorded spike activity were consistent with the changes in membrane potential and spike shape. They suggest that leptin can directly modulate the electrical properties of SCN neurones and, in this way, contribute to the mechanism by which metabolic processes influence the circadian clock.

Osmotic modulation of stimulus-evoked responses in the rat supraoptic nucleus.

Neural information is conveyed by action potentials along axons to downstream synaptic targets. Synapses permit functionally relevant modulation of the information transmitted by converging inputs. Previous studies have measured the amount of information associated with a given stimulus based either on spike counts or on the relative frequencies of spike sequences represented as binary strings. Here we apply information theory to the phase-interval stimulus histogram (PhISH) to measure the extent of the stimulus-evoked response using the statistical relationship between each interspike interval and its phase within the stimulus cycle. We used the PhISH as a novel approach to investigate how different osmotic states affect the flow of information through the osmoreceptor complex of the hypothalamus. The amount of information conveyed from one (afferent) element of the complex, the anteroventral region of the third ventricle (AV3V), to another (an efferent element), the supraoptic nucleus, was increased by hypertonic stimulation (intravenous mannitol, z = 4.39, P < 0.001) and decreased by hypotonic stimulation (intragastric water, z = -3.37, P < 0.001). Supraoptic responses to AV3V stimulation differed from those that follow stimulation of a hypothalamic element outside the osmoreceptor complex, the suprachiasmatic nucleus (SCN), which also projects to the supraoptic nucleus. Thus osmosensitive gain control mechanisms differentially modulate osmotically dependent and osmotically independent inputs, and enhance the osmoresponsiveness of supraoptic cells within a physiological range. The value of the novel approach is that its use is not limited to the osmoreceptor ensemble but it can be used to investigate the flow of information throughout the central nervous system.

Melatonin modulates spike coding in the rat suprachiasmatic nucleus.

The effects of the application of melatonin in vitro on the electrophysiological activity of suprachiasmatic neurones were characterised using novel measures of coding based on the analysis of interspike intervals. Perfusion of 1 nM melatonin in vitro (n = 53) had no consistent effect on mean spike frequency (Wilcoxon's sign rank, z = -0.01, P = 0.989), but increased the irregularity of firing (Student's paired t-test, t = -3.02, P = 0.004), as measured by the log interval entropy, and spike patterning (z = -3.43, P < 0.001), as measured by the mutual information between adjacent log intervals. Intracellular recordings in vitro in current clamp mode showed that 1 nM melatonin significantly hyperpolarised (n = 11, z = -2.35, P = 0.019) those cells that showed 'rebound' spikes upon termination of a hyperpolarising current pulse. Grouping all cells together (n = 27), melatonin application decreased the duration of the afterhyperpolarisation (z = -2.49, P = 0.013) and increased the amplitude of the depolarising afterpotential (z = -2.71, P = 0.007). The effects of melatonin seen in vitro from extracellular recordings on interspike interval coding were consistent with the changes in spike shape seen from intracellular recordings. A melatonin-induced increase in the size of the depolarising afterpotential of suprachiasmatic cells might underlie the increased irregularity of spike firing seen during the subjective night time. The method of analysis demonstrated a difference in spike firing that is not revealed by frequency alone and is consistent with the presence of a melatonin-induced depolarising current.

Spike coding during osmotic stimulation of the rat supraoptic nucleus.

Novel measures of coding based on interspike intervals were used to characterize the responses of supraoptic cells to osmotic stimulation. Infusion of hypertonic NaCl in vivo increased the firing rate of continuous (putative oxytocin) cells (Wilcoxon z= 3.84, P= 0.001) and phasic (putative vasopressin) cells (z= 2.14, P= 0.032). The irregularity of activity, quantified by the log interval entropy, was decreased for continuous (Student's t= 3.06, P= 0.003) but not phasic cells (t= 1.34, P= 0.181). For continuous cells, the increase in frequency and decrease in entropy was significantly greater (t= 2.61, P= 0.036 and t= 3.06, P= 0.007, respectively) than for phasic cells. Spike patterning, quantified using the mutual information between intervals, was decreased for phasic (z=-2.64, P= 0.008) but not continuous cells (z=-1.14, P= 0.256). Although continuous cells showed similar osmotic responses to mannitol infusion, phasic cells showed differences: spike frequency decreased (z=-3.70, P < 0.001) and entropy increased (t=-3.41, P < 0.001). Considering both cell types together, osmotic stimulation in vitro using 40 mm NaCl had little effect on firing rate (z=-0.319, P= 0.750), but increased both entropy (t= 2.75, P= 0.010) and mutual information (z=-2.73, P= 0.006) in contrast to the decreases (t= 2.92, P= 0.004 and z=-2.40, P= 0.017) seen in vivo. Responses to less severe osmotic stimulation with NaCl or mannitol were not significant. Potassium-induced depolarization in vitro increased firing rate (r= 0.195, P= 0.034), but the correlation with decreased entropy was not significant (r=-0.097, P= 0.412). Intracellular recordings showed a small depolarization and decrease in input resistance during osmotic stimulation with NaCl or mannitol, and membrane depolarization following addition of potassium. Differences in responses of oxytocin and vasopressin cells in vivo, suggest differences in the balance between the synaptic and membrane properties involved in coding their osmotic responses. The osmotic responses in vivo constrasted with those seen in vitro, which suggests that, in vivo, they depend on extrinsic circuitry. Differences in responses to osmolality and direct depolarization in vitro indicate that the mechanism of osmoresponsiveness within a physiological range is unlikely to be fully explained by depolarization.

Rhythmic changes in spike coding in the rat suprachiasmatic nucleus.

The suprachiasmatic nucleus is regarded as the main mammalian circadian pacemaker but evidence for rhythmic firing of single units in vivo has been obtained only recently. The present study was undertaken to determine if rhythms could be seen using measures of activity in addition to the mean spike frequency. We investigated whether there were changes in the irregularity of cell activity measured by the disorder of the interspike interval distribution for neurones recorded in vivo and in vitro. By plotting the entropy of the log interval histogram that quantifies the coding capacity for each action potential against the respective zeitgeber time, we describe oscillations of spike activity in vivo. Entropy measures have the advantage over variances in that they quantify aspects of the shape of the distribution and not just the dispersion. One hundred and sixty-six cell recordings from the suprachiasmatic nucleus showed a significant rhythm in entropy with an oscillatory trend in the data (P < 0.001) showing a trough towards the end of the light period and a peak in the mid-dark period. There was a similar rhythm for the cells recorded from the peripheral zone (n = 209, P = 0.037). In separate experiments in vitro, to investigate the relationship between mean spike frequency and entropy, potassium-induced depolarization of cells recorded during the subjective night was correlated with a significant increase in mean spike frequency (r = 0.259, P = 0.011) and a decrease in entropy (r = -0.296, P = 0.004). The negative correlation between the entropy and mean spike frequency of cells recorded in vitro was significantly different from that seen in vivo (F = 15.5, P < 0.001), which may reflect differences in the balance between deterministic and stochastic influences on spike occurrence. The study shows that while there is a rhythm of mean spike frequency, parameters based on the variability of interspike interval distributions also display rhythmic changes over the day-night cycle.

Spike coding from the perspective of a neurone.

In this paper, we compare existing methods for quantifying the coding capacity of a spike train, and review recent developments in the application of information theory to neural coding. We present novel methods for characterising single-unit activity based on the perspective of a downstream neurone and propose a simple yet universally applicable framework to characterise the order of complexity of neural coding by single units. We establish four orders of complexity in the capacity for neural coding. First-order coding, quantified by firing rates, is conveyed by frequencies and is thus entirely described by first moment processes. Second-order coding, represented by the variability of interspike intervals, is quantified by the log interval entropy. Third-order coding is the result of spike motifs that associate adjacent inter-spike intervals beyond chance levels; it is described by the joint interval histogram, and is measured by the mutual information between adjacent log intervals. Finally, nonstationarities in activity represent coding of the fourth-order that arise from the effects of a known or unknown stimulus.

Assessment of spike activity in the supraoptic nucleus.

Novel approaches to the characterization of coding carried by spike trains are discussed. Measuring firing frequency alone may only partially reflect spike patterning, and can only quantify changes of the most obvious kind. We have devised a method that combines probabilistic and information approaches to quantify the variability of the interspike intervals in a way that is independent of spike frequency. To illustrate the technique, the firing of an oxytocin cell and a vasopressin cell were compared before and after osmotic stimulation. A bimodal lognormal function was fitted to the interspike interval histograms. The entropy of the log interval histogram was used to measure the variability of intervals and to reflect the coding capacity of the cell per spike. A perfect metronome shows no variability in interval and thus has no greater coding capacity than is conveyed by its frequency, whereas the variability of intervals of magnocellular neurones means that their irregular activity has greater potential for coding. While the mean spike frequency increased in both the oxytocin and vasopressin cells in response to osmotic stimulation, the changes in their irregularity showed differences. Osmotic stimulation reduced the entropy of the oxytocin cell, reflecting an increase in the regularity of its spike activity. Conversely, osmotic stimulation had little effect on the entropy of the vasopressin cell. Such differences are not evident from a simple inspection of ratemeter activity. The comparison highlights the limitations of mean spike frequency as a measure of spike coding. Parameters based on the interspike intervals constitute informative measures of spike activity that allow objective comparisons to be made between the activity under different physiological conditions.

Measuring spike coding in the rat supraoptic nucleus.

Measuring spike coding objectively is essential to establish whether activity recorded under one set of conditions is truly different from that recorded under another set of conditions. However, there is no generally accepted method for making such comparisons. Measuring firing frequency alone only partially reflects spike patterning. In this paper, novel quantities based on the logarithmic interspike intervals are proposed as useful measures of spontaneous activity. We illustrate the methods by comparing extracellular recordings from magnocellular cells of the rat supraoptic nucleus in vivo and in vitro and between oxytocin and vasopressin cells in vivo. A bimodal Gaussian function fitted to the log interspike interval histogram accurately described the distribution profile for very different types of activity. We introduce the entropy of the log interval distribution as a novel quantity that measures the capacity of a cell to encode information other than a constant instantaneous frequency. Unlike existing entropy measures that are based on spike counts, it quantifies the variability in the interval distribution. In addition, the mutual information between adjacent log intervals is proposed as an objective measure of patterned activity. For cells recorded in vivo and in vitro, there was no significant difference in mean spike frequencies but there were differences in the log interval entropy (t = -4.97, P < 0.001) and the mutual information (z = -2.64, P < 0.01). The differences may result from the disruption of connections in the slice preparation. When a comparison was made between the spike activity of oxytocin and vasopressin cells recorded in vivo, there was a difference in mutual information (z = 5.15, P < 0.001) but not in mean spike frequency. Both comparisons highlight the potential limitations of using mean spike frequency alone as a measure of spike coding. We propose that our novel parameters based on interval analysis constitute informative measures of spontaneous activity under different physiological conditions.