A Nonlinear Cable Framework for Bidirectional Synaptic Plasticity

Finding the rules underlying how axons of cortical neurons form neural circuits and modify their corresponding synaptic strength is the still subject of intense research. Experiments have shown that internal calcium concentration, and both the precise timing and temporal order of pre and postsynaptic action potentials, are important constituents governing whether the strength of a synapse located on the dendrite is increased or decreased. In particular, previous investigations focusing on spike timing-dependent plasticity (STDP) have typically observed an asymmetric temporal window governing changes in synaptic efficacy. Such a temporal window emphasizes that if a presynaptic spike, arriving at the synaptic terminal, precedes the generation of a postsynaptic action potential, then the synapse is potentiated; however if the temporal order is reversed, then depression occurs. Furthermore, recent experimental studies have now demonstrated that the temporal window also depends on the dendritic location of the synapse. Specifically, it was shown that in distal regions of the apical dendrite, the magnitude of potentiation was smaller and the window for depression was broader, when compared to observations from the proximal region of the dendrite. To date, the underlying mechanism(s) for such a distance-dependent effect is (are) currently unknown. Here, using the ionic cable theory framework in conjunction with the standard calcium based plasticity model, we show for the first time that such distance-dependent inhomogeneities in the temporal learning window for STDP can be largely explained by both the spatial and active properties of the dendrite.     

A Synaptic Mechanism for Temporal Filtering of Visual Signals

The visual system transmits information about fast and slow changes in light intensity through separate neural pathways. We used in vivo imaging to investigate how bipolar cells transmit these signals to the inner retina. We found that the volume of the synaptic terminal is an intrinsic property that contributes to different temporal filters. Individual cells transmit through multiple terminals varying in size, but smaller terminals generate faster and larger calcium transients to trigger vesicle release with higher initial gain, followed by more profound adaptation. Smaller terminals transmitted higher stimulus frequencies more effectively. Modeling global calcium dynamics triggering vesicle release indicated that variations in the volume of presynaptic compartments contribute directly to all these differences in response dynamics. These results indicate how one neuron can transmit different temporal components in the visual signal through synaptic terminals of varying geometries with different adaptational properties.     

Heterogeneous presynaptic release probabilities: functional relevance for short-term plasticity

We discuss a model of presynaptic vesicle dynamics, which allows for heterogeneity in release probability among vesicles. Specifically, we explore the possibility that synaptic activity is carried by two types of vesicles; first, a readily releasable pool and, second, a reluctantly releasable pool. The pools differ regarding their probability of release and time scales on which released vesicles are replaced by new ones. Vesicles of both pools increase their release probability during repetitive stimulation according to the buildup of Ca(2+) concentration in the terminal. These properties are modeled to fit data from the calyx of Held, a giant synapse in the auditory pathway. We demonstrate that this arrangement of two pools of releasable vesicles can account for a variety of experimentally observed patterns of synaptic depression and facilitation at this synapse. We conclude that synaptic transmission cannot be accurately described unless heterogeneity of synaptic release probability is taken into account.     

Transsynaptic Coordination of Synaptic Growth,Function, and Stability by the L1-Type CAM Neuroglian

The precise control of synaptic connectivity is essential for the development and function of neuronal circuits. While there have been significant advances in our understanding how cell adhesion molecules mediate axon guidance and synapse formation, the mechanisms controlling synapse maintenance or plasticity in vivo remain largely uncharacterized. In an unbiased RNAi screen we identified the Drosophila L1-type CAM Neuroglian (Nrg) as a central coordinator of synapse growth, function, and stability. We demonstrate that the extracellular Ig-domains and the intracellular Ankyrin-interaction motif are essential for synapse development and stability. Nrg binds to Ankyrin2 in vivo and mutations reducing the binding affinities to Ankyrin2 cause an increase in Nrg mobility in motoneurons. We then demonstrate that the Nrg–Ank2 interaction controls the balance of synapse growth and stability at the neuromuscular junction. In contrast, at a central synapse, transsynaptic interactions of pre- and postsynaptic Nrg require a dynamic, temporal and spatial, regulation of the intracellular Ankyrin-binding motif to coordinate pre- and postsynaptic development. Our study at two complementary model synapses identifies the regulation of the interaction between the L1-type CAM and Ankyrin as an important novel module enabling local control of synaptic connectivity and function while maintaining general neuronal circuit architecture.     

Epileptiform activity in a neocortical network: a mathematical model

 A simple mathematical model describing the generation and propagation of epileptiform activity in a cerebral cortical network is presented. The model consists of a system of nonlinear delay differential equations. Physiological properties are taken into account as nonlinear transmission of signals at the synapse, temporal and spatial summation of incoming signals at the soma, active membrane characteristics, and dendritic and axonal propagation times. The influence of the connectivity and the temporal parameters on the oscillatory properties of the model is studied. The computer simulations are in agreement with experimental observations in cortical networks: whereas a weak excitatory or strong inhibitory synaptic connection strength produces a stationary status with short-lasting responses to external stimuli, increases in excitation or decreases in inhibition induce spontaneous and stimulus-evoked rhythmic discharges. Synaptic burst-like activity is observed only for an intermediate range of excitatory and inhibitory connection strengths and external inputs. The form and duration of the bursts can also be controlled by the temporal parameters. The results demonstrate that relatively simple mathematical equations are sufficient to model some of the network properties underlying the generation and propagation of epileptiform activity. Received: 2 October 2000 / Accepted in revised form: 4 March 2001     

Neuromodulatory changes in short-term synaptic dynamics may be mediated by two distinct mechanisms of presynaptic calcium entry

Although synaptic output is known to be modulated by changes in presynaptic calcium channels, additional pathways for calcium entry into the presynaptic terminal, such as non-selective channels, could contribute to modulation of short term synaptic dynamics. We address this issue using computational modeling. The neuropeptide proctolin modulates the inhibitory synapse from the lateral pyloric (LP) to the pyloric dilator (PD) neuron, two slow-wave bursting neurons in the pyloric network of the crab Cancer borealis. Proctolin enhances the strength of this synapse and also changes its dynamics. Whereas in control saline the synapse shows depression independent of the amplitude of the presynaptic LP signal, in proctolin, with high-amplitude presynaptic LP stimulation the synapse remains depressing while low-amplitude stimulation causes facilitation. We use simple calcium-dependent release models to explore two alternative mechanisms underlying these modulatory effects. In the first model, proctolin directly targets calcium channels by changing their activation kinetics which results in gradual accumulation of calcium with low-amplitude presynaptic stimulation, leading to facilitation. The second model uses the fact that proctolin is known to activate a non-specific cation current I _MI . In this model, we assume that the MI channels have some permeability to calcium, modeled to be a result of slow conformation change after binding calcium. This generates a gradual increase in calcium influx into the presynaptic terminals through the modulatory channel similar to that described in the first model. Each of these models can explain the modulation of the synapse by proctolin but with different consequences for network activity.     

Electron microscope observations on synaptic vesicles in synapses of the retinal rods and cones

The submicroscopic organization of the rod and cone synapses of the albino rabbit has been investigated with the use of the electron microscope. The most common rod synapse consists of an enlarged expansion of the rod fiber (the so called spherule) into which the dendritic postsynaptic fiber of the bipolar cell penetrates and digitates. The membrane surrounding the terminal consists of a double layer, the external of which is interpreted as belonging to the intervening glial cells. The synaptic membrane has a pre- and a postsynaptic layer with a total thickness of 180 to 300 A. The presynaptic layer is frequently denser and is intimately associated with the adjacent synaptic vesicles. The synaptic membrane shows processes constituted by foldings of the presynaptic layer. The entire spherule is filled with synaptic vesicles varying in diameter between 200 and 650 A with a mean of 386 A. In addition, the spherule contains a few large vacuoles near the rod fiber, interpreted as endoplasmic reticulum, and a matrix in which with high resolution a fine filamentous material can be observed. The postsynaptic fiber is homogeneous and usually does not show synaptic vesicles. In animals maintained in complete darkness for 24 hours vesicles appear to accumulate near the synaptic membrane and its processes. After 9 days there is a sharp decrease in size of the synaptic vesicles. A special rod synapse in which the dendritic postsynaptic expansion penetrates directly into the rod cell body has been identified. In line with Cajal's classification this type of synapse could be considered as a somatodendritic one. The cone synapse has a much larger terminal with a more complex relationship with the postsynaptic fiber. However, the same components recognized in the rod synapse can be observed. In animals maintained for 9 days in complete darkness there is also a considerable diminution in size of the synaptic vesicles.     

Retrograde regualtion of presynaptic development during synaptogenesis

Major advances are occurring in our understanding of the events leading to synapse formation. Contact between the growth cone and target tissu leads to intercellular signaling which controls both pre- and postsynaptic development of the synapse. The identity of retrograde signals that regualte presynaptic development are beginning to emerge, and the signal transduction cascades that are activated presynaptically are being characterized. Recent studies have shown that both the resting calcium level and activation of presynatptic protein kinase A are critical in the development of the presynaptic terminal. An understanding of these regulatory mechanisms is be ginning to provide insight into the molecular control of synaptic specificity. 1994 John Wiley & Sons, Inc.     

Self-influencing synaptic plasticity: Recurrent changes of synaptic weights can lead to specific functional properties

Recent experimental results suggest that dendritic and back-propagating spikes can influence synaptic plasticity in different ways (Holthoff, 2004; Holthoff et al., 2005). In this study we investigate how these signals could interact at dendrites in space and time leading to changing plasticity properties at local synapse clusters. Similar to a previous study (Saudargiene et al., 2004) we employ a differential Hebbian learning rule to emulate spike-timing dependent plasticity and investigate how the interaction of dendritic and back-propagating spikes, as the post-synaptic signals, could influence plasticity. Specifically, we will show that local synaptic plasticity driven by spatially confined dendritic spikes can lead to the emergence of synaptic clusters with different properties. If one of these clusters can drive the neuron into spiking, plasticity may change and the now arising global influence of a back-propagating spike can lead to a further segregation of the clusters and possibly the dying-off of some of them leading to more functional specificity. These results suggest that through plasticity being a spatial and temporal local process, the computational properties of dendrites or complete neurons can be substantially augmented. Action Editor: Wulfram Gerstner     

Short term synaptic depression imposes a frequency dependent filter on synaptic information transfer

Depletion of synaptic neurotransmitter vesicles induces a form of short term depression in synapses throughout the nervous system. This plasticity affects how synapses filter presynaptic spike trains. The filtering properties of short term depression are often studied using a deterministic synapse model that predicts the mean synaptic response to a presynaptic spike train, but ignores variability introduced by the probabilistic nature of vesicle release and stochasticity in synaptic recovery time. We show that this additional variability has important consequences for the synaptic filtering of presynaptic information. In particular, a synapse model with stochastic vesicle dynamics suppresses information encoded at lower frequencies more than information encoded at higher frequencies, while a model that ignores this stochasticity transfers information encoded at any frequency equally well. This distinction between the two models persists even when large numbers of synaptic contacts are considered. Our study provides strong evidence that the stochastic nature neurotransmitter vesicle dynamics must be considered when analyzing the information flow across a synapse.     

Activity-dependent elimination of neuromuscular synapses

At developing neuromuscular synapses in vertebrates, different motor axon inputs to muscle fibers compete for maintenance of their synapses. Competition results in progressive changes in synaptic structure and strength that lead to the weakening and loss of some inputs, a process that has been called synapse elimination. At the same time, a single input is strengthened and maintained throughout adult life, consistently recruiting muscle fibers to contract even at rapid firing rates. Work over the last decade has led to an understanding of some of the cell biological mechanisms that underlie competition and how these culminate in synapse elimination. We discuss current ideas about how activity modulates neuromuscular synaptic competition, how competition leads to synapse loss, and how these processes are modulated by cell-cell signaling. A common feature of competition at neuromuscular as well as CNS synapses is that temporally correlated activity seems to slow or prevent competition, while uncorrelated activity seems to trigger or enhance competition. Important questions that remain to be addressed include how patterns of motor neuron activity affect synaptic strength, what is the temporal relationship between changes in synaptic strength and structure, and what cellular signals mediate synapse loss. Answers to these questions will expand our understanding of the mechanisms by which activity edits synaptic structure and function, writing permanent changes in neural circuitry.     

Presynaptic mitochondria and the temporal pattern of neurotransmitter release

Mitochondria are critical for the function of nerve terminals as the cycling of synaptic vesicle membrane requires an efficient supply of ATP. In addition, the presynaptic mitochondria take part in functions such as Ca2+ buffering and neurotransmitter synthesis. To learn more about presynaptic mitochondria, we have examined their organization in two types of synapse in the lamprey, both of which are glutamatergic but are adapted to different temporal patterns of activity. The first is the giant lamprey reticulospinal synapse, which is specialized to transmit phasic signals (i.e. bursts of impulses). The second is the synapse established by sensory dorsal column axons, which is adapted to tonic activity. In both cases, the presynaptic axons were found to contain two distinct types of mitochondria; small 'synaptic' mitochondria, located near release sites, and larger mitochondria located in more central parts of the axon. The size of the synapse-associated mitochondria was similar in both types of synapse. However, their number differed considerably. Whereas the reticulospinal synapses contained only single mitochondria within 1 micron distance from the edge of the active zone (on average 1.2 per active zone, range of 1-3), the tonic dorsal column synapses were surrounded by clusters of mitochondria (4.5 per active zone, range of 3-6), with individual mitochondria sometimes apparently connected by intermitochondrial contacts. In conjunction with studies of crustacean neuromuscular junctions, these observations indicate that the temporal pattern of transmitter release is an important determinant of the organization of presynaptic mitochondria.     

Targeting of the Synaptic Vesicle Protein Synaptobrevin in the Axon of Cultured Hippocampal Neurons: Evidence for Two Distinct Sorting Steps

Synaptic vesicles are concentrated in the distal axon, far from the site of protein synthesis. Integral membrane proteins destined for this organelle must therefore make complex targeting decisions. Short amino acid sequences have been shown to act as targeting signals directing proteins to a variety of intracellular locations. To identify synaptic vesicle targeting sequences and to follow the path that proteins travel en route to the synaptic vesicle, we have used a defective herpes virus amplicon expression system to study the targeting of a synaptobrevin-transferrin receptor (SB-TfR) chimera in cultured hippocampal neurons. Addition of the cytoplasmic domain of synaptobrevin onto human transferrin receptor was sufficient to retarget the transferrin receptor from the dendrites to presynaptic sites in the axon. At the synapse, the SB-TfR chimera did not localize to synaptic vesicles, but was instead found in an organelle with biochemical and functional characteristics of an endosome. The chimera recycled in parallel with synaptic vesicle proteins demonstrating that the nerve terminal efficiently sorts transmembrane proteins into different pathways. The synaptobrevin sequence that controls targeting to the presynaptic endosome was not localized to a single, 10– amino acid region of the molecule, indicating that this targeting signal may be encoded by a more distributed structural conformation. However, the chimera could be shifted to synaptic vesicles by deletion of amino acids 61–70 in synaptobrevin, suggesting that separate signals encode the localization of synaptobrevin to the synapse and to the synaptic vesicle.     

Presynaptic CK2 promotes synapse organization and stability by targeting Ankyrin2

The precise regulation of synapse maintenance is critical to the development and function of neuronal circuits. Using an in vivo RNAi screen targeting the Drosophila kinome and phosphatome, we identify 11 kinases and phosphatases controlling synapse stability by regulating cytoskeletal, phospholipid, or metabolic signaling. We focus on casein kinase 2 (CK2) and demonstrate that the regulatory (β) and catalytic (α) subunits of CK2 are essential for synapse maintenance. CK2α kinase activity is required in the presynaptic motoneuron, and its interaction with CK2β, mediated cooperatively by two N-terminal residues of CK2α, is essential for CK2 holoenzyme complex stability and function in vivo. Using genetic and biochemical approaches we identify Ankyrin2 as a key presynaptic target of CK2 to maintain synapse stability. In addition, CK2 activity controls the subcellular organization of individual synaptic release sites within the presynaptic nerve terminal. Our study identifies phosphorylation of structural synaptic components as a compelling mechanism to actively control the development and longevity of synaptic connections.     

Nonlinear signal transmission between second- and third-order neurons of cockroach ocelli

Transfer characteristics of the synapse made from second- to third-order neurons of cockroach ocelli were studied using simultaneous microelectrode penetrations and the application of tetrodotoxin. Potential changes were evoked in second-order neurons by either an extrinsic current or a sinusoidally modulated light. The synapse had a low-pass filter characteristic with a cutoff frequency of 25-30 Hz, which passed most presynaptic signals. The synapse operated at an exponentially rising part of the overall sigmoidal input/output curve relating pre- and postsynaptic voltages. Although the response of the second-order neuron to sinusoidal light was essentially linear, the response of the third-order neuron contained an accelerating nonlinearity: the response amplitude was a positively accelerated function of the stimulus contrast, reflecting nonlinear synaptic transmission. The response of the third-order neuron exhibited a half-wave rectification: the depolarizing response to light decrement was much larger than the hyperpolarizing response to light increment. Nonlinear synaptic transmission also enhanced the transient response to step-like intensity changes. I conclude that (a) the major function of synaptic transmission between second- and third-order neurons of cockroach ocelli is to convert linear presynaptic signals into nonlinear ones and that (b) signal transmission at the synapse between second- and third-order neurons of cockroach ocelli fundamentally differs from that at the synapse between photoreceptors and second-order neurons of visual systems so far studied, where the synapse operates in the midregion of the characteristic curve and the transmission is essentially linear.     

Memory Maintenance in Synapses with Calcium-Based Plasticity in the Presence of Background Activity

Most models of learning and memory assume that memories are maintained in neuronal circuits by persistent synaptic modifications induced by specific patterns of pre- and postsynaptic activity. For this scenario to be viable, synaptic modifications must survive the ubiquitous ongoing activity present in neural circuits in vivo. In this paper, we investigate the time scales of memory maintenance in a calcium-based synaptic plasticity model that has been shown recently to be able to fit different experimental data-sets from hippocampal and neocortical preparations. We find that in the presence of background activity on the order of 1 Hz parameters that fit pyramidal layer 5 neocortical data lead to a very fast decay of synaptic efficacy, with time scales of minutes. We then identify two ways in which this memory time scale can be extended: (i) the extracellular calcium concentration in the experiments used to fit the model are larger than estimated concentrations in vivo. Lowering extracellular calcium concentration to in vivo levels leads to an increase in memory time scales of several orders of magnitude; (ii) adding a bistability mechanism so that each synapse has two stable states at sufficiently low background activity leads to a further boost in memory time scale, since memory decay is no longer described by an exponential decay from an initial state, but by an escape from a potential well. We argue that both features are expected to be present in synapses in vivo. These results are obtained first in a single synapse connecting two independent Poisson neurons, and then in simulations of a large network of excitatory and inhibitory integrate-and-fire neurons. Our results emphasise the need for studying plasticity at physiological extracellular calcium concentration, and highlight the role of synaptic bi- or multistability in the stability of learned synaptic structures.     

Dissecting tripartite synapses with STED microscopy

The concept of the tripartite synapse reflects the important role that astrocytic processes are thought to play in the function and regulation of neuronal synapses in the mammalian nervous system. However, many basic aspects regarding the dynamic interplay between pre- and postsynaptic neuronal structures and their astrocytic partners remain to be explored. A major experimental hurdle has been the small physical size of the relevant glial and synaptic structures, leaving them largely out of reach for conventional light microscopic approaches such as confocal and two-photon microscopy. Hence, most of what we know about the organization of the tripartite synapse is based on electron microscopy, which does not lend itself to investigating dynamic events and which cannot be carried out in parallel with functional assays. The development and application of superresolution microscopy for neuron–glia research is opening up exciting experimental opportunities in this regard. In this paper, we provide a basic explanation of the theory and operation of stimulated emission depletion (STED) microscopy, outlining the potential of this recent superresolution imaging modality for advancing our understanding of the morpho-functional interactions between astrocytes and neurons that regulate synaptic physiology.