Glucose and lactate as metabolic constraints on presynaptic transmission at an excitatory synapse.

KEY POINTS: Synapses have high energy demands which increase during intense activity. We show that presynaptic terminals can utilise extracellular glucose or lactate to generate energy to maintain synaptic transmission. Reducing energy substrates induces a metabolic stress: presynaptic ATP depletion impaired synaptic transmission through a reduction in the number of functional synaptic vesicle release sites and a slowing of vesicle pool replenishment, without a consistent change in release probability. Metabolic function is compromised in many pathological conditions (e.g. stroke, traumatic brain injury and neurodegeneration). Knowledge of how synaptic transmission is constrained by metabolic stress, especially during intense brain activity, will provide insights to improve cognition following pathological insults. ABSTRACT: The synapse has high energy demands, which increase during intense activity. Presynaptic ATP production depends on substrate availability and usage will increase during activity, which in turn could influence transmitter release and information transmission. We investigated transmitter release at the mouse calyx of Held synapse using glucose or lactate (10, 1 or 0 mm) as the extracellular substrates while inducing metabolic stress. High-frequency stimulation (HFS) and recovery paradigms evoked trains of EPSCs monitored under voltage-clamp. Whilst postsynaptic intracellular ATP was stabilised by diffusion from the patch pipette, depletion of glucose increased EPSC depression during HFS and impaired subsequent recovery. Computational modelling of these data demonstrated a reduction in the number of functional release sites and slowed vesicle pool replenishment during metabolic stress, with little change in release probability. Directly depleting presynaptic terminal ATP impaired transmitter release in an analogous manner to glucose depletion. In the absence of glucose, presynaptic terminal metabolism could utilise lactate from the aCSF and this was blocked by inhibition of monocarboxylate transporters (MCTs). MCT inhibitors significantly suppressed transmission in low glucose, implying that lactate is a presynaptic substrate. Additionally, block of glycogenolysis accelerated synaptic transmission failure in the absence of extracellular glucose, consistent with supplemental supply of lactate by local astrocytes. We conclude that both glucose and lactate support presynaptic metabolism and that limited availability, exacerbated by high-intensity firing, constrains presynaptic ATP, impeding transmission through a reduction in functional presynaptic release sites as vesicle recycling slows when ATP levels are low.

Phase changes in neuronal postsynaptic spiking due to short term plasticity.

In the brain, the postsynaptic response of a neuron to time-varying inputs is determined by the interaction of presynaptic spike times with the short-term dynamics of each synapse. For a neuron driven by stochastic synapses, synaptic depression results in a quite different postsynaptic response to a large population input depending on how correlated in time the spikes across individual synapses are. Here we show using both simulations and mathematical analysis that not only the rate but the phase of the postsynaptic response to a rhythmic population input varies as a function of synaptic dynamics and synaptic configuration. Resultant phase leads may compensate for transmission delays and be predictive of rhythmic changes. This could be particularly important for sensory processing and motor rhythm generation in the nervous system.

A computational study on plasticity during theta cycles at Schaffer collateral synapses on CA1 pyramidal cells in the hippocampus.

Cellular activity in the CA1 area of the hippocampus waxes and wanes at theta frequency (4-8 Hz) during exploratory behavior of rats. Perisomatic inhibition onto pyramidal cells tends to be strongest out of phase with pyramidal cell activity, whereas dendritic inhibition is strongest in phase with pyramidal cell activity. Synaptic plasticity also varies across the theta cycle, from strong long-term potentiation (LTP) to long-term depression (LTD), putatively corresponding to encoding and retrieval phases for information patterns encoded by pyramidal cell activity (Hasselmo et al. (2002a) Neural Comput 14:793-817). The mechanisms underpinning the phasic changes in plasticity are not clear, but it is likely that inhibition plays a role by affecting levels of electrical activity and calcium concentration at synapses. We explore the properties of synaptic plasticity during theta at Schaffer collateral synapses on CA1 pyramidal neurons and the influence of spatially and temporally targeted inhibition using a detailed multicompartmental model of the CA1 pyramidal neuron microcircuit and a phenomenological model of synaptic plasticity. The results suggest CA3-CA1 synapses are potentiated on one phase of theta due to high calcium levels provided by paired weak CA3 and layer III entorhinal cortex (EC) inputs even when somatic spiking is inhibited by perisomatic interneuron activity. Weak CA3 inputs alone induce lower calcium transients and result in depression of the CA3-CA1 synapses. These synapses are depressed if activated in phase with dendritic inhibition as strong CA3 inputs alone are not able to cause high calcium in this theta phase even though the CA1 pyramidal neuron shows somatic spiking. Dendritic inhibition acts as a switch that prevents LTP and promotes LTD during the retrieval phases of the theta rhythm in CA1 pyramidal cell. This may be important for not overly reinforcing recalled memories and in forgetting no longer relevant memories.

Identification and modelling of fast and slow Ih current components in vestibular ganglion neurons.

Previous experimental data indicates the hyperpolarization-activated cation (Ih) current, in the inner ear, consists of two components [different hyperpolarization-activated cyclic nucleotide-gated (HCN) subunits] which are impossible to pharmacologically isolate. To confirm the presence of these two components in vestibular ganglion neurons we have applied a parameter identification algorithm which is able to discriminate the parameters of the two components from experimental data. Using simulated data we have shown that this algorithm is able to identify the parameters of two populations of non-inactivated ionic channels more accurately than a classical method. Moreover, the algorithm was demonstrated to be insensitive to the key parameter variations. We then applied this algorithm to Ih current recordings from mouse vestibular ganglion neurons. The algorithm revealed the presence of a high-voltage-activated slow component and a low-voltage-activated fast component. Finally, the electrophysiological significance of these two Ih components was tested individually in computational vestibular ganglion neuron models (sustained and transient), in the control case and in the presence of cAMP, an intracellular cyclic nucleotide that modulates HCN channel activity. The results suggest that, first, the fast and slow components modulate differently the action potential excitability and the excitatory postsynaptic potentials in both sustained and transient vestibular neurons and, second, the fast and slow components, in the control case, provide different information about characteristics of the stimulation and this information is significantly modified after modulation by cAMP.

Spine head calcium as a measure of summed postsynaptic activity for driving synaptic plasticity.

We use a computational model of a hippocampal CA1 pyramidal cell to demonstrate that spine head calcium provides an instantaneous readout at each synapse of the postsynaptic weighted sum of all presynaptic activity impinging on the cell. The form of the readout is equivalent to the functions of weighted, summed inputs used in neural network learning rules. Within a dendritic layer, peak spine head calcium levels are either a linear or sigmoidal function of the number of coactive synapses, with nonlinearity depending on the ability of voltage spread in the dendrites to reach calcium spike threshold. This is strongly controlled by the potassium A-type current, with calcium spikes and the consequent sigmoidal increase in peak spine head calcium present only when the A-channel density is low. Other membrane characteristics influence the gain of the relationship between peak calcium and the number of active synapses. In particular, increasing spine neck resistance increases the gain due to increased voltage responses to synaptic input in spine heads. Colocation of stimulated synapses on a single dendritic branch also increases the gain of the response. Input pathways cooperate: CA3 inputs to the proximal apical dendrites can strongly amplify peak calcium levels due to weak EC input to the distal dendrites, but not so strongly vice versa. CA3 inputs to the basal dendrites can boost calcium levels in the proximal apical dendrites, but the relative electrical compactness of the basal dendrites results in the reverse effect being less significant. These results give pointers as to how to better describe the contributions of pre- and postsynaptic activity in the learning "rules" that apply in these cells. The calcium signal is closer in form to the activity measures used in traditional neural network learning rules than to the spike times used in spike-timing-dependent plasticity.

On phasic inhibition during hippocampal theta.

Two computational models are used to explore the possible implications of recent experimental data (Royer et al. 2012) on phasic inhibition during theta frequency (4-10 Hz) oscillations in the hippocampi of actively behaving rodents. A working hypothesis from previous experimental and modelling studies is that a theta cycle is divided into encoding (when synaptic plasticity is enhanced) and recall (when plasticity is suppressed) half cycles. Using a compartmental model of a CA1 pyramidal cell, including dendritic spines, we demonstrate that out-of-phase perisomatic and dendritic inhibition, respectively, can promote the necessary conditions for these half cycles. Perisomatic inhibition allows dendritic calcium spikes that promote synaptic LTP, while minimising cell output. Dendritic inhibition, on the other hand, both controls cell output and suppresses dendritic calcium spikes, preventing LTP. The exact phase relationship between these sub-cycles may not be fixed. Using a simple sum-of-sinusoids activity model, we suggest an interpretation of the data of Royer et al. (2012) in which a fixed-phase encoding sub-cycle is surrounded by a flexible-phase recall cycle that follows the peak of excitatory drive and consequent phase precession of activity as an animal passes through a pyramidal cell's place field.

Kv3.3 subunits control presynaptic action potential waveform and neurotransmitter release at a central excitatory synapse.

Kv3 potassium currents mediate rapid repolarisation of action potentials (APs), supporting fast spikes and high repetition rates. Of the four Kv3 gene family members, Kv3.1 and Kv3.3 are highly expressed in the auditory brainstem and we exploited this to test for subunit-specific roles at the calyx of Held presynaptic terminal in the mouse. Deletion of Kv3.3 (but not Kv3.1) reduced presynaptic Kv3 channel immunolabelling, increased presynaptic AP duration and facilitated excitatory transmitter release; which in turn enhanced short-term depression during high-frequency transmission. The response to sound was delayed in the Kv3.3KO, with higher spontaneous and lower evoked firing, thereby reducing signal-to-noise ratio. Computational modelling showed that the enhanced EPSC and short-term depression in the Kv3.3KO reflected increased vesicle release probability and accelerated activity-dependent vesicle replenishment. We conclude that Kv3.3 mediates fast repolarisation for short precise APs, conserving transmission during sustained high-frequency activity at this glutamatergic excitatory synapse.

Encoding and retrieval in a model of the hippocampal CA1 microcircuit.

It has been proposed that the hippocampal theta rhythm (4-7 Hz) can contribute to memory formation by separating encoding (storage) and retrieval of memories into different functional half-cycles (Hasselmo et al. (2002) Neural Comput 14:793-817). We investigate, via computer simulations, the biophysical mechanisms by which storage and recall of spatio-temporal input patterns are achieved by the CA1 microcircuitry. A model of the CA1 microcircuit is presented that uses biophysical representations of the major cell types, including pyramidal (P) cells and four types of inhibitory interneurons: basket (B) cells, axo-axonic (AA) cells, bistratified (BS) cells and oriens lacunosum-moleculare (OLM) cells. Inputs to the network come from the entorhinal cortex (EC), the CA3 Schaffer collaterals and medial septum. The EC input provides the sensory information, whereas all other inputs provide context and timing information. Septal input provides timing information for phasing storage and recall. Storage is accomplished via a local STDP mediated hetero-association of the EC input pattern and the incoming CA3 input pattern on the CA1 pyramidal cell target synapses. The model simulates the timing of firing of different hippocampal cell types relative to the theta rhythm in anesthetized animals and proposes experimentally confirmed functional roles for the different classes of inhibitory interneurons in the storage and recall cycles (Klausberger et al., (2003, 2004) Nature 421:844-848, Nat Neurosci 7:41-47). Measures of recall performance of new and previously stored input patterns in the presence or absence of various inhibitory interneurons are employed to quantitatively test the performance of our model. Finally, the mean recall quality of the CA1 microcircuit is tested as the number of stored patterns is increased.

Interactions between multiple sources of short-term plasticity during evoked and spontaneous activity at the rat calyx of Held.

Sustained activity at most central synapses is accompanied by a number of short-term changes in synaptic strength which act over a range of time scales. Here we examine experimental data and develop a model of synaptic depression at the calyx of Held synaptic terminal that combines many of these mechanisms (acting at differing sites and across a range of time scales). This new model incorporates vesicle recycling, facilitation, activity-dependent vesicle retrieval and multiple mechanisms affecting calcium channel activity and release probability. It can accurately reproduce the time course of experimentally measured short-term depression across different stimulus frequencies and exhibits a slow decay in EPSC amplitude during sustained stimulation. We show that the slow decay is a consequence of vesicle release inhibition by multiple mechanisms and is accompanied by a partial recovery of the releasable vesicle pool. This prediction is supported by patch-clamp data, using long duration repetitive EPSC stimulation at up to 400 Hz. The model also explains the recovery from depression in terms of interaction between these multiple processes, which together generate a stimulus-history-dependent recovery after repetitive stimulation. Given the high rates of spontaneous activity in the auditory pathway, the model also demonstrates how these multiple interactions cause chronic synaptic depression under in vivo conditions. While the magnitude of the depression converges to the same steady state for a given frequency, the time courses of onset and recovery are faster in the presence of spontaneous activity. We conclude that interactions between multiple sources of short-term plasticity can account for the complex kinetics during high frequency stimulation and cause stimulus-history-dependent recovery at this relay synapse.

Mathematical modelling and numerical simulation of the morphological development of neurons.

BACKGROUND: The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other. METHODS: A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described. RESULTS: Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development. CONCLUSION: A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity.

Stability in a mathematical model of neurite elongation.

We have developed a continuum partial differential equation model of tubulin-driven neurite elongation and solved the steady problem. For non-zero values of the decay coefficient, the authors identified three different regimes of steady neurite growth, small, moderate and large, dependent on the strength of the tubulin flux into the neurite at the soma. Solution of the fully time-dependent moving boundary problem is, however, hampered by its analytical intractibility. A linear instability analysis, novel to moving boundary problems in this context, is possible and reduces to finding the zeros of an eigen-condition function. One of the system parameters is small and this permits solutions to the eigen-condition equation in terms of asymptotic series in each growth regime. Linear instability is demonstrated to be absent from the neurite growth model and a Newton-Raphson root-finding algorithm is then shown to corroborate the asymptotic results for some selected examples. By numerically integrating the fully non-linear time-dependent system, we show how the steady solutions are non-linearly stable in each of the three growth regimes with decay and oscillatory behaviour being as predicted by the linear eigenvalue analysis.

Distinguishing between presynaptic and postsynaptic mechanisms of short-term depression during action potential trains.

Short-term facilitation and depression have a profound influence on transmission at many glutamatergic synapses, particularly during trains of stimuli. A major component of these processes is postsynaptic receptor desensitization. Both presynaptic and postsynaptic mechanisms can contribute to synaptic efficacy, but it is often difficult to define their respective contributions. Blockers of desensitization such as cyclothiazide (CTZ) can be used, but many of these drugs have nonspecific effects on transmitter release, complicating attempts to define synaptic effectiveness under physiological conditions. We describe and validate a new method to minimize desensitization during trains of synaptic stimuli that is based on the low-affinity competitive glutamate receptor antagonists gamma-D-glutamylglycine or kynurenic acid. A computational model of AMPA receptor kinetics shows that the mechanism can be accounted for by simple competitive antagonism of AMPA receptors, where the rapid off-rate of the antagonist permits re-equilibration between blocked and unblocked pools during the interstimulus interval. Our results at the calyx of Held show that desensitization makes little contribution to synaptic depression at frequencies below 10 Hz, but at higher frequencies it makes an important contribution, with accumulating desensitization masking short-term facilitation and causing an underestimation of quantal content. This novel method of protection from desensitization is compatible with physiological studies but cannot be used in conjunction with CTZ. Although presynaptic vesicle depletion makes the dominant contribution to short-term depression, our results show that AMPA receptor desensitization contributes to the depression at auditory synapses after hearing onset and in a frequency-dependent manner.

Inhibitory control of site-specific synaptic plasticity in a model CA1 pyramidal neuron.

A computational model of a biochemical network underlying synaptic plasticity is combined with simulated on-going electrical activity in a model of a hippocampal pyramidal neuron to study the impact of synapse location and inhibition on synaptic plasticity. The simulated pyramidal neuron is activated by the realistic stimulation protocol of causal and anticausal spike pairings of presynaptic and postsynaptic action potentials in the presence and absence of spatially targeted inhibition provided by basket, bistratified and oriens-lacunosum moleculare (OLM) interneurons. The resulting Spike-timing-dependent plasticity (STDP) curves depend strongly on the number of pairing repetitions, the synapse location and the timing and strength of inhibition.

Wide-band information transmission at the calyx of Held.

We use a mathematical model of the calyx of Held to explore information transmission at this giant glutamatergic synapse. The significant depression of the postsynaptic response to repeated stimulation in vitro is a result of various activity-dependent processes in multiple timescales, which can be reproduced by multiexponential functions in this model. When the postsynaptic current is stimulated by Poisson-distributed spike trains, its amplitude varies considerably with the preceding interspike intervals. Here we quantify the information contained in the postsynaptic current amplitude about preceding interspike intervals and determine the impact of different pre- and postsynaptic factors on information transmission. The mutual information between presynaptic spike times and the amplitude of the postsynaptic response in general decreases as the mean stimulation rate increases, but remains high even at frequencies greater than 100 Hz, unlike at many neocortical synapses. The maintenance of information transmission is attributable largely to vesicle recycling rates at low frequencies of stimulation, shifting to vesicle release probability at high frequencies. Also, at higher frequencies, the synapse operates largely in a release-ready mode in which most release sites contain a release-ready vesicle and release probabilities are low.

Implications of noise and neural heterogeneity for vestibulo-ocular reflex fidelity.

The vestibulo-ocular reflex (VOR) is characterized by a short-latency, high-fidelity eye movement response to head rotations at frequencies up to 20 Hz. Electrophysiological studies of medial vestibular nucleus (MVN) neurons, however, show that their response to sinusoidal currents above 10 to 12 Hz is highly nonlinear and distorted by aliasing for all but very small current amplitudes. How can this system function in vivo when single cell response cannot explain its operation? Here we show that the necessary wide VOR frequency response may be achieved not by firing rate encoding of head velocity in single neurons, but in the integrated population response of asynchronously firing, intrinsically active neurons. Diffusive synaptic noise and the pacemaker-driven, intrinsic firing of MVN cells synergistically maintain asynchronous, spontaneous spiking in a population of model MVN neurons over a wide range of input signal amplitudes and frequencies. Response fidelity is further improved by a reciprocal inhibitory link between two MVN populations, mimicking the vestibular commissural system in vivo, but only if asynchrony is maintained by noise and pacemaker inputs. These results provide a previously missing explanation for the full range of VOR function and a novel account of the role of the intrinsic pacemaker conductances in MVN cells. The values of diffusive noise and pacemaker currents that give optimal response fidelity yield firing statistics similar to those in vivo, suggesting that the in vivo network is tuned to optimal performance. While theoretical studies have argued that noise and population heterogeneity can improve coding, to our knowledge this is the first evidence indicating that these parameters are indeed tuned to optimize coding fidelity in a neural control system in vivo.

Nitric oxide is a volume transmitter regulating postsynaptic excitability at a glutamatergic synapse.

Neuronal nitric oxide synthase (nNOS) is broadly expressed in the brain and associated with synaptic plasticity through NMDAR-mediated calcium influx. However, its physiological activation and the mechanisms by which nitric oxide (NO) influences synaptic transmission have proved elusive. Here, we exploit the unique input-specificity of the calyx of Held to characterize NO modulation at this glutamatergic synapse in the auditory pathway. NO is generated in an activity-dependent manner by MNTB principal neurons receiving a calyceal synaptic input. It acts in the target neuron and adjacent inactive neurons to modulate excitability and synaptic efficacy, inhibiting postsynaptic Kv3 potassium currents (via phosphorylation), reducing EPSCs and so increasing action potential duration and reducing transmission fidelity. We conclude that NO serves as a volume transmitter and slow dynamic modulator, integrating spontaneous and evoked neuronal firing, thereby providing an index of global activity and regulating information transmission across a population of active and inactive neurons.

Dynamics of outgrowth in a continuum model of neurite elongation.

Neurite outgrowth (dendrites and axons) should be a stable, but easily regulated process to enable a neuron to make its appropriate network connections during development. We explore the dynamics of outgrowth in a mathematical continuum model of neurite elongation. The model describes the construction of the internal microtubule cytoskeleton, which results from the production and transport of tubulin dimers and their assembly into microtubules at the growing neurite tip. Tubulin is assumed to be largely synthesised in the cell body from where it is transported by active mechanisms and by diffusion along the neurite. It is argued that this construction process is a fundamental limiting factor in neurite elongation. In the model, elongation is highly stable when tubulin transport is dominated by either active transport or diffusion, but oscillations in length may occur when both active transport and diffusion contribute. Autoregulation of tubulin production can eliminate these oscillations. In all cases a stable steady-state length is reached, provided there is intrinsic decay of tubulin. Small changes in growth parameters, such as the tubulin production rate, can lead to large changes in length. Thus cytoskeleton construction can be both stable and easily regulated, as seems necessary for neurite outgrowth during nervous system development.

Unmasking group III metabotropic glutamate autoreceptor function at excitatory synapses in the rat CNS.

Presynaptic group III metabotropic glutamate receptor (mGluR) activation by exogenous agonists (such as L-2-amino-4-phosphonobutyrate (L-AP4)) potently inhibit transmitter release, but their autoreceptor function has been questioned because endogenous activation during high-frequency stimulation appears to have little impact on synaptic amplitude. We resolve this ambiguity by studying endogenous activation of mGluRs during trains of high-frequency synaptic stimuli at the calyx of Held. In vitro whole-cell patch recordings were made from medial nucleus of the trapezoid body (MNTB) neurones during 1 s excitatory postsynaptic current (EPSC) trains delivered at 200 Hz and at 37 degrees C. The group III mGluR antagonist (R,S)-cyclopropyl-4-phosphonophenylglycine (CPPG, 300 microm) had no effect on EPSC short-term depression, but accelerated subsequent recovery time course (tau: 4.6 +/- 0.8 s to 2.4 +/- 0.4 s, P = 0.02), and decreased paired pulse ratio from 1.18 +/- 0.06 to 0.97 +/- 0.03 (P = 0.01), indicating that mGluR activation reduced release probability (P). Modelling autoreceptor activation during repetitive stimulation revealed that as P declines, the readily releasable pool size (N) increases so that the net EPSC (NP) is unchanged and short-term depression proceeds with the same overall time course as in the absence of autoreceptor activation. Thus, autoreceptor action on the synaptic response is masked but the synapse is now in a different state (lower P, higher N). While vesicle replenishment clearly underlies much of the recovery from short-term depression, our results show that the recovery time course of P also contributes to the reduced response amplitude for 1-2 s. The results show that passive equilibration between N and P masks autoreceptor modulation of the EPSC and suggests that mGluR autoreceptors function to change the synaptic state and distribute metabolic demand, rather than to depress synaptic amplitude.

Transport limited effects in a model of dendritic branching.

A variety of stochastic models of dendritic growth in developing neurons have been formulated previously. Such models indicate that the probability of a new branch forming in a growing tree may be modulated by factors such as the number of terminals in the tree and their centrifugal order. However, these models cannot identify any underlying biophysical mechanisms that may cause such dependencies. Here, we explore a new model in which branching depends on the concentration of a branch-determining substance in each terminal segment. The substance is produced in the cell body and is transported by active transport and diffusion to the terminals. The model reveals that transport-limited effects may give rise to the same modulation of branching as indicated by the stochastic models. Different limitations arise if transport is dominated by active transport or by diffusion.