Somato-dendritic Synaptic Plasticity and Error-backpropagation in Active Dendrites

In the last decade dendrites of cortical neurons have been shown to nonlinearly combine synaptic inputs by evoking local dendritic spikes. It has been suggested that these nonlinearities raise the computational power of a single neuron, making it comparable to a 2-layer network of point neurons. But how these nonlinearities can be incorporated into the synaptic plasticity to optimally support learning remains unclear. We present a theoretically derived synaptic plasticity rule for supervised and reinforcement learning that depends on the timing of the presynaptic, the dendritic and the postsynaptic spikes. For supervised learning, the rule can be seen as a biological version of the classical error-backpropagation algorithm applied to the dendritic case. When modulated by a delayed reward signal, the same plasticity is shown to maximize the expected reward in reinforcement learning for various coding scenarios. Our framework makes specific experimental predictions and highlights the unique advantage of active dendrites for implementing powerful synaptic plasticity rules that have access to downstream information via backpropagation of action potentials.     

钙依赖性突触的可塑性

突触前和突触后细胞内钙离子（[Ca^2 ]i)在短时程和长时程突触的可塑性中,发挥着重要的住处传递作用。兴奋后残留[Ca^2 ]i,可以激发短时程突触增强。突触前[Ca^2 ]i可以影响被抑制的突触前膜囊泡的更新,并准确编码突前和突触后信息,产生截然相反的长时程突触修（ＬＴＰ或ＬＴＤ）。     

Postsynaptic expression of tetanus toxin light chain blocks synaptogenesis in Drosophila.

During the development of the nervous system embryonic neurons are incorporated into neural networks that underlie behaviour. For example, during embryogenesis in Drosophila, motor neurons in every body segment are wired into the circuitry that drives the simple peristaltic locomotion of the larva. Very little is known about the way in which the necessary central synapses are formed in such a network or how their properties are controlled. One possibility is that presynaptic and postsynaptic elements form relatively independently of each other. Alternatively, there might be an interaction between presynaptic and postsynaptic neurons that allows for adjustment and plasticity in the embryonic network. Here we have addressed this issue by analysing the role of synaptic transmission in the formation of synaptic inputs onto identified motorneurons as the locomotor circuitry is assembled in the Drosophila embryo. We targeted the expression of tetanus toxin light chain (TeTxLC) to single identified neurons using the GAL4 system. TeTxLC prevents the evoked release of neurotransmitter by enzymatically cleaving the synaptic-vesicle-associated protein neuronal-Synaptobrevin (n-Syb) [1]. Unexpectedly, we found that the cells that expressed TeTxLC, which were themselves incapable of evoked release, showed a dramatic reduction in synaptic input. We detected this reduction both electrophysiologically and ultrastructurally.     

Effects of Neural Morphology and Input Distribution on Synaptic Processing by Global and Focal NMDA-Spikes

Cortical neurons can respond to glutamatergic stimulation with regenerative N-Methyl-D-aspartic acid (NMDA)-spikes. NMDA-spikes were initially thought to depend on clustered synaptic activation. Recent work had shown however a new variety of a global NMDA-spike, which can be generated by randomly distributed inputs. Very little is known about the factors that influence the generation of these global NMDA-spikes, as well the potentially distinct rules of synaptic integration and the computational significance conferred by the two types of NMDA-spikes. Here I show that the input resistance (R_IN) plays a major role in influencing spike initiation; while the classical, focal NMDA-spike depended upon the local (dendritic) R_IN, the threshold of global NMDA-spike generation was set by the somatic R_IN. As cellular morphology can exert a large influence on R_IN, morphologically distinct neuron types can have dissimilar rules for NMDA-spikes generation. For example, cortical neurons in superficial layers were found to be generally prone to global NMDA-spike generation. In contrast, electric properties of cortical layer 5b cells clearly favor focal NMDA-spikes. These differences can translate into diverse synaptic integration rules for the different classes of cortical cells; simulated superficial layers neurons were found to exhibit strong synaptic interactions between different dendritic branches, giving rise to a single integrative compartment mediated by the global NMDA-spike. In these cells, efficiency of postsynaptic activation was relatively little dependent on synaptic distribution. By contrast, layer 5b neurons were capable of true multi-unit computation involving independent integrative compartments formed by clustered synaptic input which could trigger focal NMDA-spikes. In a sharp contrast to superficial layers neurons, randomly distributed synaptic inputs were not very effective in driving firing the layer 5b cells, indicating a possibility for different computation performed by these important cortical neurons.     

A computational framework for cortical learning

Recent physiological findings have revealed that long-term adaptation of the synaptic strengths between cortical pyramidal neurons depends on the temporal order of presynaptic and postsynaptic spikes, which is called spike-timing-dependent plasticity (STDP) or temporally asymmetric Hebbian (TAH) learning. Here I prove by analytical means that a physiologically plausible variant of STDP adapts synaptic strengths such that the presynaptic spikes predict the postsynaptic spikes with minimal error. This prediction error model of STDP implies a mechanism for cortical memory: cortical tissue learns temporal spike patterns if these spike patterns are repeatedly elicited in a set of pyramidal neurons. The trained network finishes these patterns if their beginnings are presented, thereby recalling the memory. Implementations of the proposed algorithms may be useful for applications in voice recognition and computer vision.     

Maturation of GABAergic Inhibition Promotes Strengthening of Temporally Coherent Inputs among Convergent Pathways

Spike-timing-dependent plasticity (STDP), a form of Hebbian plasticity, is inherently stabilizing. Whether and how GABAergic inhibition influences STDP is not well understood. Using a model neuron driven by converging inputs modifiable by STDP, we determined that a sufficient level of inhibition was critical to ensure that temporal coherence (correlation among presynaptic spike times) of synaptic inputs, rather than initial strength or number of inputs within a pathway, controlled postsynaptic spike timing. Inhibition exerted this effect by preferentially reducing synaptic efficacy, the ability of inputs to evoke postsynaptic action potentials, of the less coherent inputs. In visual cortical slices, inhibition potently reduced synaptic efficacy at ages during but not before the critical period of ocular dominance (OD) plasticity. Whole-cell recordings revealed that the amplitude of unitary IPSCs from parvalbumin positive (Pv+) interneurons to pyramidal neurons increased during the critical period, while the synaptic decay time-constant decreased. In addition, intrinsic properties of Pv+ interneurons matured, resulting in an increase in instantaneous firing rate. Our results suggest that maturation of inhibition in visual cortex ensures that the temporally coherent inputs (e.g. those from the open eye during monocular deprivation) control postsynaptic spike times of binocular neurons, a prerequisite for Hebbian mechanisms to induce OD plasticity.     

Activity-dependent remodeling of presynaptic inputs by postsynaptic expression of activated CaMKII

Competitive synaptic remodeling is an important feature of developmental plasticity, but the molecular mechanisms remain largely unknown. Calcium/calmodulin-dependent protein kinase II (CaMKII) can induce postsynaptic changes in synaptic strength. We show that postsynaptic CaMKII also generates structural synaptic rearrangements between cultured cortical neurons. Postsynaptic expression of activated CaMKII (T286D) increased the strength of transmission between pairs of pyramidal neuron by a factor of 4, through a modest increase in quantal amplitude and a larger increase in the number of synaptic contacts. Concurrently, T286D reduced overall excitatory synaptic density and increased the proportion of unconnected pairs. This suggests that connectivity from some synaptic partners was increased while other partners were eliminated. The enhancement of connectivity required activity and NMDA receptor activation, while the elimination did not. These data suggest that postsynaptic activation of CaMKII induces a structural remodeling of presynaptic inputs that favors the retention of active presynaptic partners.     

Sonic hedgehog expression in corticofugal projection neurons directs cortical microcircuit formation

The precise connectivity of inputs and outputs is critical for cerebral cortex function; however, the cellular mechanisms that establish these connections are poorly understood. Here, we show that the secreted molecule Sonic Hedgehog (Shh) is involved in synapse formation of a specific cortical circuit. Shh is expressed in layer V corticofugal projection neurons and the Shh receptor, Brother of CDO (Boc), is expressed in local and callosal projection neurons of layer II/III that synapse onto the subcortical projection neurons. Layer V neurons of mice lacking functional Shh exhibit decreased synapses. Conversely, the loss of functional Boc leads to a reduction in the strength of synaptic connections onto layer Vb, but not layer II/III, pyramidal neurons. These results demonstrate that Shh is expressed in postsynaptic target cells while Boc is expressed in a complementary population of presynaptic input neurons, and they function to guide the formation of cortical microcircuitry. VIDEO ABSTRACT:     

Contralateral input modulates the excitability of dorsal horn neurons involved in noxious signal processes. Potential role in neuronal sensitization

Wide Dynamic Range (WDR) neurons in the spinal cord receive inputs from the contralateral side that, under normal conditions, are ineffective in generating an active response. These inputs are effective when the target WDRs change their excitability conditions. To further reveal the mechanisms supporting this effectiveness shift, we investigated the weight of the excitation of the contralateral neurons on the target WDR responses. In the circuit of presynaptic (sending) and postsynaptic (receiving) neurons in crossed spinal connections the fibres that form the presynaptic neurons impinge on postsynaptic neurons can be considered the final relay of this contralateral pathway. The enhancement of the presynaptic neuron excitability may thus modify the efficacy of the contralateral input. Pairs of neurons each on a side of the spinal cord, at the L5-L6 lumbar level were simultaneously recorded in intact, anaesthetized, paralysed rats. The excitatory aminoacid NMDA and strychnine, the antagonist of the inhibitory aminoacid glycine, were iontophoretically administrated to presynaptic neurons to increase their excitability. Before and during the drug administration, spontaneous and noxious-evoked activities of the neurons were analysed. During the iontophoresis of the two substances we found that noxious stimuli applied to the receptive field of presynaptic neurons activated up to 50% of the previously unresponsive postsynaptic neurons on the opposite side. Furthermore, the neurons on both sides of the spinal cord showed significantly increased spontaneous activity and amplified responses to ipsilateral noxious stimulation. These findings indicate that the contralateral input participates in the circuit dynamics of spinal nociceptive transmission, by modulating the excitability of the postsynaptic neurons. A possible functional role of such a nociceptive transmission circuit in neuronal sensitization following unilateral nerve injury is hypothesized.     

Contralateral input modulates the excitability of dorsal horn neurons involved in noxious signal processes. Potential role in neuronal sensitization

Wide Dynamic Range (WDR) neurons in the spinal cord receive inputs from the contralateral side that, under normal conditions, are ineffective in generating an active response. These inputs are effective when the target WDRs change their excitability conditions. To further reveal the mechanisms supporting this effectiveness shift, we investigated the weight of the excitation of the contralateral neurons on the target WDR responses. In the circuit of presynaptic (sending) and postsynaptic (receiving) neurons in crossed spinal connections the fibres that form the presynaptic neurons impinge on postsynaptic neurons can be considered the final relay of this contralateral pathway. The enhancement of the presynaptic neuron excitability may thus modify the efficacy of the contralateral input. Pairs of neurons each on a side of the spinal cord, at the L5–L6 lumbar level were simultaneously recorded in intact, anaesthetized, paralysed rats. The excitatory aminoacid NMDA and strychnine, the antagonist of the inhibitory aminoacid glycine, were iontophoretically administrated to presynaptic neurons to increase their excitability. Before and during the drug administration, spontaneous and noxious-evoked activities of the neurons were analysed. During the iontophoresis of the two substances we found that noxious stimuli applied to the receptive field of presynaptic neurons activated up to 50% of the previously unresponsive postsynaptic neurons on the opposite side. Furthermore, the neurons on both sides of the spinal cord showed significantly increased spontaneous activity and amplified responses to ipsilateral noxious stimulation. These findings indicate that the contralateral input participates in the circuit dynamics of spinal nociceptive transmission, by modulating the excitability of the postsynaptic neurons. A possible functional role of such a nociceptive transmission circuit in neuronal sensitization following unilateral nerve injury is hypothesized.     

Phase-response curves and synchronized neural networks

We review the principal assumptions underlying the application of phase-response curves (PRCs) to synchronization in neuronal networks. The PRC measures how much a given synaptic input perturbs spike timing in a neural oscillator. Among other applications, PRCs make explicit predictions about whether a given network of interconnected neurons will synchronize, as is often observed in cortical structures. Regarding the assumptions of the PRC theory, we conclude: (i) The assumption of noise-tolerant cellular oscillations at or near the network frequency holds in some but not all cases. (ii) Reduced models for PRC-based analysis can be formally related to more realistic models. (iii) Spike-rate adaptation limits PRC-based analysis but does not invalidate it. (iv) The dependence of PRCs on synaptic location emphasizes the importance of improving methods of synaptic stimulation. (v) New methods can distinguish between oscillations that derive from mutual connections and those arising from common drive. (vi) It is helpful to assume linear summation of effects of synaptic inputs; experiments with trains of inputs call this assumption into question. (vii) Relatively subtle changes in network structure can invalidate PRC-based predictions. (viii) Heterogeneity in the preferred frequencies of component neurons does not invalidate PRC analysis, but can annihilate synchronous activity.     

The principal neurons of the medial nucleus of the trapezoid body and NG2+ glial cells receive coordinated excitatory synaptic input

Glial cell processes are part of the synaptic structure and sense spillover of transmitter, while some glial cells can even receive direct synaptic input. Here, we report that a defined type of glial cell in the medial nucleus of the trapezoid body (MNTB) receives excitatory glutamatergic synaptic input from the calyx of Held (CoH). This giant glutamatergic terminal forms an axosomatic synapse with a single principal neuron located in the MNTB. The NG2 glia, as postsynaptic principal neurons, establish synapse-like structures with the CoH terminal. In contrast to the principal neurons, which are known to receive excitatory as well as inhibitory inputs, the NG2 glia receive mostly, if not exclusively, α-amino-3-hydroxy-5-methyl-isoxazole-4-propionic acid receptor–mediated evoked and spontaneous synaptic input. Simultaneous recordings from neurons and NG2 glia indicate that they partially receive synchronized spontaneous input. This shows that an NG2⁺ glial cell and a postsynaptic neuron share presynaptic terminals.     

Modelling Feedback Excitation,Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.     

Natural patterns of activity and long-term synaptic plasticity

Long-term potentiation (LTP) of synaptic transmission is traditionally elicited by massively synchronous, high-frequency inputs, which rarely occur naturally. Recent in vitro experiments have revealed that both LTP and long-term depression (LTD) can arise by appropriately pairing weak synaptic inputs with action potentials in the postsynaptic cell. This discovery has generated new insights into the conditions under which synaptic modification may occur in pyramidal neurons in vivo. First, it has been shown that the temporal order of the synaptic input and the postsynaptic spike within a narrow temporal window determines whether LTP or LTD is elicited, according to a temporally asymmetric Hebbian learning rule. Second, backpropagating action potentials are able to serve as a global signal for synaptic plasticity in a neuron compared with local associative interactions between synaptic inputs on dendrites. Third, a specific temporal pattern of activity--postsynaptic bursting--accompanies synaptic potentiation in adults.     

Long-term modifications in the strength of excitatory associative inputs in the piriform cortex

Afferent olfactory information, in vivo and in vitro, can be rapidly adapted to through a metabotropic glutamate receptor (mGluR)-mediated attenuation of synaptic strength. Specific cellular and synaptic mechanisms underlying olfactory learning and habituation at the cortical level remain unclear. Through whole-cell recording, excitatory postsynaptic currents (EPSCs) were obtained from piriform cortex (PC) principal cells. Using a coincidental, pre- and postsynaptic stimulation protocol, long-term depression (LTD) in synaptic strength was induced at associative, excitatory synapses onto layer II pyramidal neurons of the mouse (P15-27) PC. LTD was mimicked and occluded by mGluR agonists and blocked by nonselective mGluR antagonist (RS)-alpha-methyl-4-sulfonophenylglycine (MSPG) but not by N-methyl-D-aspartic acid (NMDA) receptor antagonist 2-amino-5-phosphonovaleric acid (APV). Analysis of the paired-pulse ratio, alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)/NMDA current ratio, and spontaneous EPSCs indicate that electrically induced LTD was mediated predominantly by postsynaptic mechanisms. Additionally, presynaptic mGluRs were involved in agonist-mediated synaptic depression. Immunohistochemical analysis supports the presence of multiple subclasses of mGluRs throughout the PC, with large concentrations of several receptors present in layer II. These observations provide further evidence of activity-dependent, long-term modification of associative inputs and its underlying mechanisms. Cortical adaptation at associative synapses provides an additional link between cortical olfactory processing and subcortical centers that influence behavior.     

Pre- and postsynaptic mechanisms in Hebbian activity-dependent synapse modification

We have used a three compartment tissue culture system that involved two separate populations of cholinergic neurons in the side compartments that converged on a common target population of myotubes in the center compartment. Activation of the axons from one population of neurons produced selective down-regulation of the synaptic inputs from the other neuronal population (when the two inputs innervated the same myotubes). The decrease in heterosynaptic inputs was mediated by protein kinase C (PKC). An activity-dependent action of protein kinase A (PKA) was associated with the stimulated input and this served to selectively stabilize this input. These changes associated with PKA and PKC activation were mediated by alterations in the number of acetylcholine receptors at the neuromuscular junction. These results suggest that neuromuscular electrical activity produces postsynaptic activation of both PKA and PKC, with the latter producing generalized synapse weakening and the former a selective synapse stabilization. Treatment of the neuronal cell body and axon to increase PKC activity by putting phorbal ester (PMA) in the side chamber did not affect synaptic transmission (with or without stimulation). By contrast, PKA blockade in the side compartment did produce an activity-dependent decrease in synaptic efficacy, which was due to a decrease in quantal release of neurotransmitter. Thus, when the synapse is activated, it appears that presynaptic PKA action is necessary to maintain transmitter output.     

Computation of the electroencephalogram (EEG) from network models of point neurons

The electroencephalogram (EEG) is a major tool for non-invasively studying brain function and dysfunction. Comparing experimentally recorded EEGs with neural network models is important to better interpret EEGs in terms of neural mechanisms. Most current neural network models use networks of simple point neurons. They capture important properties of cortical dynamics, and are numerically or analytically tractable. However, point neurons cannot generate an EEG, as EEG generation requires spatially separated transmembrane currents. Here, we explored how to compute an accurate approximation of a rodent’s EEG with quantities defined in point-neuron network models. We constructed different approximations (or proxies) of the EEG signal that can be computed from networks of leaky integrate-and-fire (LIF) point neurons, such as firing rates, membrane potentials, and combinations of synaptic currents. We then evaluated how well each proxy reconstructed a ground-truth EEG obtained when the synaptic currents of the LIF model network were fed into a three-dimensional network model of multicompartmental neurons with realistic morphologies. Proxies based on linear combinations of AMPA and GABA currents performed better than proxies based on firing rates or membrane potentials. A new class of proxies, based on an optimized linear combination of time-shifted AMPA and GABA currents, provided the most accurate estimate of the EEG over a wide range of network states. The new linear proxies explained 85–95% of the variance of the ground-truth EEG for a wide range of network configurations including different cell morphologies, distributions of presynaptic inputs, positions of the recording electrode, and spatial extensions of the network. Non-linear EEG proxies using a convolutional neural network (CNN) on synaptic currents increased proxy performance by a further 2–8%. Our proxies can be used to easily calculate a biologically realistic EEG signal directly from point-neuron simulations thus facilitating a quantitative comparison between computational models and experimental EEG recordings.     

The influence of limited presynaptic growth and synapse removal on adaptive synaptogenesis

This report continues our research into the effectiveness of adaptive synaptogenesis in constructing feed-forward networks which perform good transformations on their inputs. Good transformations are characterized by the maintenance of input information and the removal of statistical dependence. Adaptive synaptogenesis stochastically builds and sculpts a synaptic connectivity in initially unconnected networks using two mechanisms. The first, synaptogenesis, creates new, excitatory, feed-forward connections. The second, associative modification, adjusts the strength of existing synapses. Our previous implementations of synaptogenesis only incorporated a postsynaptic regulatory process, receptivity to new innervation (Adelsberger-Mangan and Levy 1993a, b). In the present study, a presynaptic regulatory process, presynaptic avidity, which regulates the tendency of a presynaptic neuron to participate in a new synaptic connection as a function of its total synaptic weight, is incorporated into the synaptogenesis process. In addition, we investigate a third mechanism, selective synapse removal. This process removes synapses between neurons whose firing is poorly correlated. Networks that are constructed with the presynaptic regulatory process maintain more information and remove more statistical dependence than networks constructed with postsynaptic receptivity and associative modification alone. Selective synapse removal also improves network performance, but only when implemented in conjunction with the presynaptic regulatory process. Received: 20 August 1993/Accepted in revised form: 16 April 1994     

Imperfect space clamp permits electrotonic interactions between inhibitory and excitatory synaptic conductances, distorting voltage clamp recordings

The voltage clamp technique is frequently used to examine the strength and composition of synaptic input to neurons. Even accounting for imperfect voltage control of the entire cell membrane ("space clamp"), it is often assumed that currents measured at the soma are a proportional indicator of the postsynaptic conductance. Here, using NEURON simulation software to model somatic recordings from morphologically realistic neurons, we show that excitatory conductances recorded in voltage clamp mode are distorted significantly by neighboring inhibitory conductances, even when the postsynaptic membrane potential starts at the reversal potential of the inhibitory conductance. Analogous effects are observed when inhibitory postsynaptic currents are recorded at the reversal potential of the excitatory conductance. Escape potentials in poorly clamped dendrites reduce the amplitude of excitatory or inhibitory postsynaptic currents recorded at the reversal potential of the other conductance. In addition, unclamped postsynaptic inhibitory conductances linearize the recorded current-voltage relationship of excitatory inputs comprising AMPAR and NMDAR-mediated components, leading to significant underestimation of the relative contribution by NMDARs, which are particularly sensitive to small perturbations in membrane potential. Voltage clamp accuracy varies substantially between neurons and dendritic arbors of different morphology; as expected, more reliable recordings are obtained from dendrites near the soma, but up to 80% of the synaptic signal on thin, distant dendrites may be lost when postsynaptic interactions are present. These limitations of the voltage clamp technique may explain how postsynaptic effects on synaptic transmission could, in some cases, be attributed incorrectly to presynaptic mechanisms.