Democratization in a passive dendritic tree : an analytical investigation

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as “dendritic democracy”. Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green’s representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius

Intrinsic Stability of Temporally Shifted Spike-Timing Dependent Plasticity

Spike-timing dependent plasticity (STDP), a widespread synaptic modification mechanism, is sensitive to correlations between presynaptic spike trains and it generates competition among synapses. However, STDP has an inherent instability because strong synapses are more likely to be strengthened than weak ones, causing them to grow in strength until some biophysical limit is reached. Through simulations and analytic calculations, we show that a small temporal shift in the STDP window that causes synchronous, or nearly synchronous, pre- and postsynaptic action potentials to induce long-term depression can stabilize synaptic strengths. Shifted STDP also stabilizes the postsynaptic firing rate and can implement both Hebbian and anti-Hebbian forms of competitive synaptic plasticity. Interestingly, the overall level of inhibition determines whether plasticity is Hebbian or anti-Hebbian. Even a random symmetric jitter of a few milliseconds in the STDP window can stabilize synaptic strengths while retaining these features. The same results hold for a shifted version of the more recent “triplet” model of STDP. Our results indicate that the detailed shape of the STDP window function near the transition from depression to potentiation is of the utmost importance in determining the consequences of STDP, suggesting that this region warrants further experimental study

Spine Calcium Transients Induced by Synaptically-Evoked Action Potentials Can Predict Synapse Location and Establish Synaptic Democracy

CA1 pyramidal neurons receive hundreds of synaptic inputs at different distances from the soma. Distance-dependent synaptic scaling enables distal and proximal synapses to influence the somatic membrane equally, a phenomenon called “synaptic democracy”. How this is established is unclear. The backpropagating action potential (BAP) is hypothesised to provide distance-dependent information to synapses, allowing synaptic strengths to scale accordingly. Experimental measurements show that a BAP evoked by current injection at the soma causes calcium currents in the apical shaft whose amplitudes decay with distance from the soma. However, in vivo action potentials are not induced by somatic current injection but by synaptic inputs along the dendrites, which creates a different excitable state of the dendrites. Due to technical limitations, it is not possible to study experimentally whether distance information can also be provided by synaptically-evoked BAPs. Therefore we adapted a realistic morphological and electrophysiological model to measure BAP-induced voltage and calcium signals in spines after Schaffer collateral synapse stimulation. We show that peak calcium concentration is highly correlated with soma-synapse distance under a number of physiologically-realistic suprathreshold stimulation regimes and for a range of dendritic morphologies. Peak calcium levels also predicted the attenuation of the EPSP across the dendritic tree. Furthermore, we show that peak calcium can be used to set up a synaptic democracy in a homeostatic manner, whereby synapses regulate their synaptic strength on the basis of the difference between peak calcium and a uniform target value. We conclude that information derived from synaptically-generated BAPs can indicate synapse location and can subsequently be utilised to implement a synaptic democracy

GluRδ2 Expression in the Mature Cerebellum of Hotfoot Mice Promotes Parallel Fiber Synaptogenesis and Axonal Competition

Glutamate receptor delta 2 (GluRdelta2) is selectively expressed in the cerebellum, exclusively in the spines of the Purkinje cells (PCs) that are in contact with parallel fibers (PFs). Although its structure is similar to ionotropic glutamate receptors, it has no channel function and its ligand is unknown. The GluRdelta2-null mice, such as knockout and hotfoot have profoundly altered cerebellar circuitry, which causes ataxia and impaired motor learning. Notably, GluRdelta2 in PC-PF synapses regulates their maturation and strengthening and induces long term depression (LTD). In addition, GluRdelta2 participates in the highly territorial competition between the two excitatory inputs to the PC; the climbing fiber (CF), which innervates the proximal dendritic compartment, and the PF, which is connected to spiny distal branchlets. Recently, studies have suggested that GluRdelta2 acts as an adhesion molecule in PF synaptogenesis. Here, we provide in vivo and in vitro evidence that supports this hypothesis. Through lentiviral rescue in hotfoot mice, we noted a recovery of PC-PF contacts in the distal dendritic domain. In the proximal domain, we observed the formation of new spines that were innervated by PFs and a reduction in contact with the CF; ie, the pattern of innervation in the PC shifted to favor the PF input. Moreover, ectopic expression of GluRdelta2 in HEK293 cells that were cocultured with granule cells or in cerebellar Golgi cells in the mature brain induced the formation of new PF contacts. Collectively, our observations show that GluRdelta2 is an adhesion molecule that induces the formation of PF contacts independently of its cellular localization and promotes heterosynaptic competition in the PC proximal dendritic domain

The Effects of NR2 Subunit-Dependent NMDA Receptor Kinetics on Synaptic Transmission and CaMKII Activation

N-Methyl-d-aspartic acid (NMDA) receptors are widely expressed in the brain and are critical for many forms of synaptic plasticity. Subtypes of the NMDA receptor NR2 subunit are differentially expressed during development; in the forebrain, the NR2B receptor is dominant early in development, and later both NR2A and NR2B are expressed. In heterologous expression systems, NR2A-containing receptors open more reliably and show much faster opening and closing kinetics than do NR2B-containing receptors. However, conflicting data, showing similar open probabilities, exist for receptors expressed in neurons. Similarly, studies of synaptic plasticity have produced divergent results, with some showing that only NR2A-containing receptors can drive long-term potentiation and others showing that either subtype is capable of driving potentiation. In order to address these conflicting results as well as open questions about the number and location of functional receptors in the synapse, we constructed a Monte Carlo model of glutamate release, diffusion, and binding to NMDA receptors and of receptor opening and closing as well as a model of the activation of calcium-calmodulin kinase II, an enzyme critical for induction of synaptic plasticity, by NMDA receptor-mediated calcium influx. Our results suggest that the conflicting data concerning receptor open probabilities can be resolved, with NR2A- and NR2B-containing receptors having very different opening probabilities. They also support the conclusion that receptors containing either subtype can drive long-term potentiation. We also are able to estimate the number of functional receptors at a synapse from experimental data. Finally, in our models, the opening of NR2B-containing receptors is highly dependent on the location of the receptor relative to the site of glutamate release whereas the opening of NR2A-containing receptors is not. These results help to clarify the previous findings and suggest future experiments to address open questions concerning NMDA receptor function

Two-photon single-cell optogenetic control of neuronal activity by sculpted light

Recent advances in optogenetic techniques have generated new tools for controlling neuronal activity, with a wide range of neuroscience applications. The most commonly used approach has been the optical activation of the light-gated ion channel channelrhodopsin-2 (ChR2). However, targeted single-cell-level optogenetic activation with temporal precessions comparable to the spike timing remained challenging. Here we report fast (≤1 ms), selective, and targeted control of neuronal activity with single-cell resolution in hippocampal slices. Using temporally focused laser pulses (TEFO) for which the axial beam profile can be controlled independently of its lateral distribution, large numbers of channels on individual neurons can be excited simultaneously, leading to strong (up to 15 mV) and fast (≤1 ms) depolarizations. Furthermore, we demonstrated selective activation of cellular compartments, such as dendrites and large presynaptic terminals, at depths up to 150 μm. The demonstrated spatiotemporal resolution and the selectivity provided by TEFO allow manipulation of neuronal activity, with a large number of applications in studies of neuronal microcircuit function in vitro and in vivo

Surface Mobility of Postsynaptic AMPARs Tunes Synaptic Transmission

AMPA glutamate receptors (AMPARs) mediate fast excitatory synaptic transmission. Upon fast consecutive synaptic stimulation, transmission can be depressed. Recuperation from fast synaptic depression has been attributed solely to recovery of transmitter release and/or AMPAR desensitization. We show that AMPAR lateral diffusion, observed in both intact hippocampi and cultured neurons, allows fast exchange of desensitized receptors with naive functional ones within or near the postsynaptic density. Recovery from depression in the tens of millisecond time range can be explained in part by this fast receptor exchange. Preventing AMPAR surface movements through cross-linking, endogenous clustering, or calcium rise all slow recovery from depression. Physiological regulation of postsynaptic receptor mobility affects the fidelity of synaptic transmission by shaping the frequency dependence of synaptic responses

Cocaine triggered AMPA receptor redistribution is reversed in vivo by mGluR-dependent long-term depression

Drugs of abuse induce long-lasting changes in neural circuits that may underlie core components of addiction. Here we focus on glutamatergic synapses onto dopamine (DA) neurons of the ventral tegmental area (VTA). Using an 'ex vivo' approach in mice, we show that a single injection of cocaine caused strong rectification and conferred sensitivity to the polyamine Joro spider toxin (JST) of AMPAR-mediated excitatory postsynaptic currents (AMPAR EPSCs), indicating the recruitment of receptors that lack GluR2. This qualitative change in transmission was paralleled by an increase in the AMPAR:NMDAR ratio and was prevented by interfering with the protein interacting with C kinase-1 (PICK1) in vivo. Activation of metabotropic glutamate receptors (mGluR1s) by intraperitoneal injection of a positive modulator depotentiated synapses and abolished rectification in slices of cocaine-treated mice, revealing a mechanism to reverse cocaine-induced synaptic plasticity in vivo