Search

What are the spatial and temporal scales of brainwide neuronal activity? We used swept, confocally-aligned planar excitation (SCAPE) microscopy to image all cells in a large volume of the brain of adult Drosophila with high spatiotemporal resolution while flies engaged in a variety of spontaneous behaviors. This revealed neural representations of behavior on multiple spatial and temporal scales. The activity of most neurons correlated (or anticorrelated) with running and flailing over timescales that ranged from seconds to a minute. Grooming elicited a weaker global response. Significant residual activity not directly correlated with behavior was high dimensional and reflected the activity of small clusters of spatially organized neurons that may correspond to genetically defined cell types. These clusters participate in the global dynamics, indicating that neural activity reflects a combination of local and broadly distributed components. This suggests that microcircuits with highly specified functions are provided with knowledge of the larger context in which they operate., (© 2023. Springer Nature Limited.)

The cardinal classes are a useful simplification of cortical interneuron diversity, but such broad subgroupings gloss over the molecular, morphological, and circuit specificity of interneuron subtypes, most notably among the somatostatin interneuron class. Although there is evidence that this diversity is functionally relevant, the circuit implications of this diversity are unknown. To address this knowledge gap, we designed a series of genetic strategies to target the breadth of somatostatin interneuron subtypes and found that each subtype possesses a unique laminar organization and stereotyped axonal projection pattern. Using these strategies, we examined the afferent and efferent connectivity of three subtypes (two Martinotti and one non-Martinotti) and demonstrated that they possess selective connectivity with intratelecephalic or pyramidal tract neurons. Even when two subtypes targeted the same pyramidal cell type, their synaptic targeting proved selective for particular dendritic compartments. We thus provide evidence that subtypes of somatostatin interneurons form cell-type-specific cortical circuits., Competing Interests: Declaration of interests G.F. is a founder of Regel Therapeutics, which has no competing interests with the present manuscript. G.F. is an advisor for Neuron and Annual Review of Neuroscience., (Copyright © 2023 Elsevier Inc. All rights reserved.)

In addition to the action potentials used for axonal signaling, many neurons generate dendritic "spikes" associated with synaptic plasticity. However, in order to control both plasticity and signaling, synaptic inputs must be able to differentially modulate the firing of these two spike types. Here, we investigate this issue in the electrosensory lobe (ELL) of weakly electric mormyrid fish, where separate control over axonal and dendritic spikes is essential for the transmission of learned predictive signals from inhibitory interneurons to the output stage of the circuit. Through a combination of experimental and modeling studies, we uncover a novel mechanism by which sensory input selectively modulates the rate of dendritic spiking by adjusting the amplitude of backpropagating axonal action potentials. Interestingly, this mechanism does not require spatially segregated synaptic inputs or dendritic compartmentalization but relies instead on an electrotonically distant spike initiation site in the axon-a common biophysical feature of neurons., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2023 Elsevier Inc. All rights reserved.)

Neural activity is often described in terms of population-level factors extracted from the responses of many neurons. Factors provide a lower-dimensional description with the aim of shedding light on network computations. Yet, mechanistically, computations are performed not by continuously valued factors but by interactions among neurons that spike discretely and variably. Models provide a means of bridging these levels of description. We developed a general method for training model networks of spiking neurons by leveraging factors extracted from either data or firing-rate-based networks. In addition to providing a useful model-building framework, this formalism illustrates how reliable and continuously valued factors can arise from seemingly stochastic spiking. Our framework establishes procedures for embedding this property in network models with different levels of realism. The relationship between spikes and factors in such networks provides a foundation for interpreting (and subtly redefining) commonly used quantities such as firing rates., Competing Interests: Declaration of interests L.F.A. serves on the advisory board of Neuron. D.S. is employed as a research scientist by Meta (Meta Reality Labs); his work there is unrelated to this study., (Copyright © 2022 Elsevier Inc. All rights reserved.)

Cortical circuits generate excitatory currents that must be cancelled by strong inhibition to assure stability. The resulting excitatory-inhibitory (E-I) balance can generate spontaneous irregular activity but, in standard balanced E-I models, this requires that an extremely strong feedforward bias current be included along with the recurrent excitation and inhibition. The absence of experimental evidence for such large bias currents inspired us to examine an alternative regime that exhibits asynchronous activity without requiring unrealistically large feedforward input. In these networks, irregular spontaneous activity is supported by a continually changing sparse set of neurons. To support this activity, synaptic strengths must be drawn from high-variance distributions. Unlike standard balanced networks, these sparse balance networks exhibit robust nonlinear responses to uniform inputs and non-Gaussian input statistics. Interestingly, the speed, not the size, of synaptic fluctuations dictates the degree of sparsity in the model. In addition to simulations, we provide a mean-field analysis to illustrate the properties of these networks., Competing Interests: The authors have declared that no competing interests exist.

The representation of odor in olfactory cortex (piriform) is distributive and unstructured and can only be afforded behavioral significance upon learning. We performed 2-photon imaging to examine the representation of odors in piriform and in two downstream areas, the orbitofrontal cortex (OFC) and the medial prefrontal cortex (mPFC), as mice learned olfactory associations. In piriform, we observed that odor responses were largely unchanged during learning. In OFC, 30% of the neurons acquired robust responses to conditioned stimuli (CS+) after learning, and these responses were gated by internal state and task context. Moreover, direct projections from piriform to OFC can be entrained to elicit learned olfactory behavior. CS+ responses in OFC diminished with continued training, whereas persistent representations of both CS+ and CS- odors emerged in mPFC. Optogenetic silencing indicates that these two brain structures function sequentially to consolidate the learning of appetitive associations., Competing Interests: Declaration of Interests The authors declare no competing interests., (Copyright © 2020 Elsevier Inc. All rights reserved.)

The supplementary motor area (SMA) is believed to contribute to higher order aspects of motor control. We considered a key higher order role: tracking progress throughout an action. We propose that doing so requires population activity to display low "trajectory divergence": situations with different future motor outputs should be distinct, even when present motor output is identical. We examined neural activity in SMA and primary motor cortex (M1) as monkeys cycled various distances through a virtual environment. SMA exhibited multiple response features that were absent in M1. At the single-neuron level, these included ramping firing rates and cycle-specific responses. At the population level, they included a helical population-trajectory geometry with shifts in the occupied subspace as movement unfolded. These diverse features all served to reduce trajectory divergence, which was much lower in SMA versus M1. Analogous population-trajectory geometry, also with low divergence, naturally arose in networks trained to internally guide multi-cycle movement., Competing Interests: Declaration of Interests The authors declare no competing interests., (Copyright © 2020 Elsevier Inc. All rights reserved.)

The construction of biologically plausible models of neural circuits is crucial for understanding the computational properties of the nervous system. Constructing functional networks composed of separate excitatory and inhibitory neurons obeying Dale's law presents a number of challenges. We show how a target-based approach, when combined with a fast online constrained optimization technique, is capable of building functional models of rate and spiking recurrent neural networks in which excitation and inhibition are balanced. Balanced networks can be trained to produce complicated temporal patterns and to solve input-output tasks while retaining biologically desirable features such as Dale's law and response variability., Competing Interests: The authors have declared that no competing interests exist.

Neuroscience is experiencing a revolution in which simultaneous recording of thousands of neurons is revealing population dynamics that are not apparent from single-neuron responses. This structure is typically extracted from data averaged across many trials, but deeper understanding requires studying phenomena detected in single trials, which is challenging due to incomplete sampling of the neural population, trial-to-trial variability, and fluctuations in action potential timing. We introduce latent factor analysis via dynamical systems, a deep learning method to infer latent dynamics from single-trial neural spiking data. When applied to a variety of macaque and human motor cortical datasets, latent factor analysis via dynamical systems accurately predicts observed behavioral variables, extracts precise firing rate estimates of neural dynamics on single trials, infers perturbations to those dynamics that correlate with behavioral choices, and combines data from non-overlapping recording sessions spanning months to improve inference of underlying dynamics.

Studies of cerebellum-like circuits in fish have demonstrated that synaptic plasticity shapes the motor corollary discharge responses of granule cells into highly-specific predictions of self-generated sensory input. However, the functional significance of such predictions, known as negative images, has not been directly tested. Here we provide evidence for improvements in neural coding and behavioral detection of prey-like stimuli due to negative images. In addition, we find that manipulating synaptic plasticity leads to specific changes in circuit output that disrupt neural coding and detection of prey-like stimuli. These results link synaptic plasticity, neural coding, and behavior and also provide a circuit-level account of how combining external sensory input with internally generated predictions enhances sensory processing., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Neurons in piriform cortex receive input from a random collection of glomeruli, resulting in odor representations that lack the stereotypic organization of the olfactory bulb. We have performed in vivo optical imaging and mathematical modeling to demonstrate that correlations are retained in the transformation from bulb to piriform cortex, a feature essential for generalization across odors. Random connectivity also implies that the piriform representation of a given odor will differ among different individuals and across brain hemispheres in a single individual. We show that these different representations can nevertheless support consistent agreement about odor quality across a range of odors. Our model also demonstrates that, whereas odor discrimination and categorization require far fewer neurons than reside in piriform cortex, consistent generalization may require the full complement of piriform neurons., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Neurons and networks in the cerebral cortex must operate reliably despite multiple sources of noise. To evaluate the impact of both input and output noise, we determine the robustness of single-neuron stimulus selective responses, as well as the robustness of attractor states of networks of neurons performing memory tasks. We find that robustness to output noise requires synaptic connections to be in a balanced regime in which excitation and inhibition are strong and largely cancel each other. We evaluate the conditions required for this regime to exist and determine the properties of networks operating within it. A plausible synaptic plasticity rule for learning that balances weight configurations is presented. Our theory predicts an optimal ratio of the number of excitatory and inhibitory synapses for maximizing the encoding capacity of balanced networks for given statistics of afferent activations. Previous work has shown that balanced networks amplify spatiotemporal variability and account for observed asynchronous irregular states. Here we present a distinct type of balanced network that amplifies small changes in the impinging signals and emerges automatically from learning to perform neuronal and network functions robustly., Competing Interests: The authors declare no conflict of interest., (Published under the PNAS license.)

Spike-timing dependent plasticity (STDP) is a widespread plasticity mechanism in the nervous system. The simplest description of STDP only takes into account pairs of pre- and postsynaptic spikes, with potentiation of the synapse when a presynaptic spike precedes a postsynaptic spike and depression otherwise. In light of experiments that explored a variety of spike patterns, the pair-based STDP model has been augmented to account for multiple pre- and postsynaptic spike interactions. As a result, a number of different "multi-spike" STDP models have been proposed based on different experimental observations. The behavior of these models at the population level is crucial for understanding mechanisms of learning and memory. The challenging balance between the stability of a population of synapses and their competitive modification is well studied for pair-based models, but it has not yet been fully analyzed for multi-spike models. Here, we address this issue through numerical simulations of an integrate-and-fire model neuron with excitatory synapses subject to STDP described by three different proposed multi-spike models. We also analytically calculate average synaptic changes and fluctuations about these averages. Our results indicate that the different multi-spike models behave quite differently at the population level. Although each model can produce synaptic competition in certain parameter regions, none of them induces synaptic competition with its originally fitted parameters. The dichotomy between synaptic stability and Hebbian competition, which is well characterized for pair-based STDP models, persists in multi-spike models. However, anti-Hebbian competition can coexist with synaptic stability in some models. We propose that the collective behavior of synaptic plasticity models at the population level should be used as an additional guideline in applying phenomenological models based on observations of single synapses.

Most of the networks used by computer scientists and many of those studied by modelers in neuroscience represent unit activities as continuous variables. Neurons, however, communicate primarily through discontinuous spiking. We review methods for transferring our ability to construct interesting networks that perform relevant tasks from the artificial continuous domain to more realistic spiking network models. These methods raise a number of issues that warrant further theoretical and experimental study.

Mormyrid electric fish are a model system for understanding how neural circuits predict the sensory consequences of motor acts. Medium ganglion cells in the electrosensory lobe create negative images that predict sensory input resulting from the fish's electric organ discharge (EOD). Previous studies have shown that negative images can be created through plasticity at granule cell-medium ganglion cell synapses, provided that granule cell responses to the brief EOD command are sufficiently varied and prolonged. Here we show that granule cells indeed provide such a temporal basis and that it is well-matched to the temporal structure of self-generated sensory inputs, allowing rapid and accurate sensory cancellation and explaining paradoxical features of negative images. We also demonstrate an unexpected and critical role of unipolar brush cells (UBCs) in generating the required delayed responses. These results provide a mechanistic account of how copies of motor commands are transformed into sensory predictions.

Spike timing-dependent plasticity (STDP) modifies synaptic strengths based on timing information available locally at each synapse. Despite this, it induces global structures within a recurrently connected network. We study such structures both through simulations and by analyzing the effects of STDP on pair-wise interactions of neurons. We show how conventional STDP acts as a loop-eliminating mechanism and organizes neurons into in- and out-hubs. Loop-elimination increases when depression dominates and turns into loop-generation when potentiation dominates. STDP with a shifted temporal window such that coincident spikes cause depression enhances recurrent connections and functions as a strict buffering mechanism that maintains a roughly constant average firing rate. STDP with the opposite temporal shift functions as a loop eliminator at low rates and as a potent loop generator at higher rates. In general, studying pairwise interactions of neurons provides important insights about the structures that STDP can produce in large networks.

Randomly connected networks of neurons exhibit a transition from fixed-point to chaotic activity as the variance of their synaptic connection strengths is increased. In this study, we analytically evaluate how well a small external input can be reconstructed from a sparse linear readout of network activity. At the transition point, known as the edge of chaos, networks display a number of desirable features, including large gains and integration times. Away from this edge, in the nonchaotic regime that has been the focus of most models and studies, gains and integration times fall off dramatically, which implies that parameters must be fine tuned with considerable precision if high performance is required. Here we show that, near the edge, decoding performance is characterized by a critical exponent that takes a different value on the two sides. As a result, when the network units have an odd saturating nonlinear response function, the falloff in gains and integration times is much slower on the chaotic side of the transition. This means that, under appropriate conditions, good performance can be achieved with less fine tuning beyond the edge, within the chaotic regime.

Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a "resonant" frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate.

Recent theoretical work has provided a basic understanding of signal propagation in networks of spiking neurons, but mechanisms for gating and controlling these signals have not been investigated previously. Here we introduce an idea for the gating of multiple signals in cortical networks that combines principles of signal propagation with aspects of balanced networks. Specifically, we studied networks in which incoming excitatory signals are normally cancelled by locally evoked inhibition, leaving the targeted layer unresponsive. Transmission can be gated 'on' by modulating excitatory and inhibitory gains to upset this detailed balance. We illustrate gating through detailed balance in large networks of integrate-and-fire neurons. We show successful gating of multiple signals and study failure modes that produce effects reminiscent of clinically observed pathologies. Provided that the individual signals are detectable, detailed balance has a large capacity for gating multiple signals.

Gain modulation, in which the sensitivity of a neural response to one input is modified by a second input, is studied at single-neuron and network levels. At the single neuron level, gain modulation can arise if the two inputs are subject to a direct multiplicative interaction. Alternatively, these inputs can be summed in a linear manner by the neuron and gain modulation can arise, instead, from a nonlinear input-output relationship. We derive a mathematical constraint that can distinguish these two mechanisms even though they can look very similar, provided sufficient data of the appropriate type are available. Previously, it has been shown in coordinate transformation studies that artificial neurons with sigmoid transfer functions can acquire a nonlinear additive form of gain modulation through learning-driven adjustment of synaptic weights. We use the constraint derived for single-neuron studies to compare responses in this network with those of another network model based on a biologically inspired transfer function that can support approximately multiplicative interactions.

We evaluate the capacity and performance of a perceptron discriminator operating in a highly sparse regime where classic perceptron results do not apply. The perceptron is constructed to respond to a specified set of q stimuli, with only statistical information provided about other stimuli to which it is not supposed to respond. We compute the probability of both false-positive and false-negative errors and determine the capacity of the system for not responding to nonselected stimuli and for responding to selected stimuli in the presence of noise. If q is a sublinear function of N, the number of inputs to the perceptron, these capacities are exponential in N/q.

Neurons recorded from electrode arrays show a remarkable scaling property in their bursts of spontaneous activity, referred to as "avalanches" (Beggs and Plenz, 2003, 2004). Such scaling suggests a critical property in the coupling of these circuits. We show that similar scaling laws can arise in a simple model for the growth of neuronal processes. In the model (Van Ooyen and Van Pelt, 1994, 1996), the spatial range of the processes extending from each neuron is represented by a circle that grows or shrinks as a function of the average intracellular calcium concentration. Neurons interact when the circles corresponding to their processes intersect, with a strength proportional to the area of overlap.

The dynamics of neural networks is influenced strongly by the spectrum of eigenvalues of the matrix describing their synaptic connectivity. In large networks, elements of the synaptic connectivity matrix can be chosen randomly from appropriate distributions, making results from random matrix theory highly relevant. Unfortunately, classic results on the eigenvalue spectra of random matrices do not apply to synaptic connectivity matrices because of the constraint that individual neurons are either excitatory or inhibitory. Therefore, we compute eigenvalue spectra of large random matrices with excitatory and inhibitory columns drawn from distributions with different means and equal or different variances.

Transmission of signals within the brain is essential for cognitive function, but it is not clear how neural circuits support reliable and accurate signal propagation over a sufficiently large dynamic range. Two modes of propagation have been studied: synfire chains, in which synchronous activity travels through feedforward layers of a neuronal network, and the propagation of fluctuations in firing rate across these layers. In both cases, a sufficient amount of noise, which was added to previous models from an external source, had to be included to support stable propagation. Sparse, randomly connected networks of spiking model neurons can generate chaotic patterns of activity. We investigate whether this activity, which is a more realistic noise source, is sufficient to allow for signal transmission. We find that, for rate-coded signals but not for synfire chains, such networks support robust and accurate signal reproduction through up to six layers if appropriate adjustments are made in synaptic strengths. We investigate the factors affecting transmission and show that multiple signals can propagate simultaneously along different pathways. Using this feature, we show how different types of logic gates can arise within the architecture of the random network through the strengthening of specific synapses.

Neural networks that are trained to perform specific tasks must be developed through a supervised learning procedure. This normally takes the form of direct supervision of synaptic plasticity. We explore the idea that supervision takes place instead through the modulation of neuronal excitability. Such supervision can be done using conventional synaptic feedback pathways rather than requiring the hypothetical actions of unknown modulatory agents. During task learning, supervised response modulation guides Hebbian synaptic plasticity indirectly by establishing appropriate patterns of correlated network activity. This results in robust learning of function approximation tasks evenwhenmultiple output units representing different functions share large amounts of common input. Reward-based supervision is also studied, and a number of potential advantages of neuronal response modulation are identified.

In 1998, Sherman and Guillery proposed that there are two types of inputs to cortical neurons; drivers and modulators. These two forms of input are required to explain how, for example, sensory driven responses are controlled and modified by attention and other internally generated gating signals. One might imagine that driver signals are carried by fast ionotropic receptors, whereas modulators correspond to slower metabotropic receptors. Instead, we have proposed a novel mechanism by which both driver and modulator inputs could be carried by transmission through the same types of ionotropic receptors. In this scheme, the distinction between driver and modulator inputs is functional and changeable rather than anatomical and fixed. Driver inputs are carried by excitation and inhibition acting in a push-pull manner. This means that increases in excitation are accompanied by decreases in inhibition and vice versa. Modulators correspond to excitation and inhibition that covary so that they increase or decrease together. Theoretical and experimental work has shown that such an arrangement modulates the gain of a neuron, rather than driving it to respond. Constructing drivers and modulators in this manner allows individual excitatory synaptic inputs to play either role, and indeed to switch between roles, depending on how they are linked with inhibition.

In many neurons, synapses increase in strength as a function of distance from the soma in a manner that appears to compensate for dendritic attenuation. This phenomenon requires a cooperative interaction between local factors that control synaptic strength, such as receptor density and vesicle release probability, and global factors that affect synaptic efficacy, such as attenuation and boosting by active membrane conductances. Anti-spike-timing-dependent plasticity, in combination with nonassociative synaptic potentiation, can accomplish this feat even though it acts locally and independently at individual synapses. Analytic computations and computer simulations show that this combination of synaptic plasticity mechanisms equalizes the efficacy of synapses over an extended dendritic cable by adjusting local synaptic strengths to compensate for global attenuation.

The dynamic clamp uses computer simulation to introduce artificial membrane or synaptic conductances into biological neurons and to create hybrid circuits of real and model neurons. In the ten years since it was first developed, the dynamic clamp has become a widely used tool for the study of neural systems at the cellular and circuit levels. This review describes recent state-of-the-art implementations of the dynamic clamp and summarizes insights gained through its use, ranging from the role of voltage-dependent conductances in shaping neuronal activity to the effects of synaptic dynamics on network behavior and the impact of in vivo-like input on neuronal information processing.

Gain modulation is a prominent feature of neuronal activity recorded in behaving animals, but the mechanism by which it occurs is unknown. By introducing a barrage of excitatory and inhibitory synaptic conductances that mimics conditions encountered in vivo into pyramidal neurons in slices of rat somatosensory cortex, we show that the gain of a neuronal response to excitatory drive can be modulated by varying the level of "background" synaptic input. Simultaneously increasing both excitatory and inhibitory background firing rates in a balanced manner results in a divisive gain modulation of the neuronal response without appreciable signal-independent increases in firing rate or spike-train variability. These results suggest that, within active cortical circuits, the overall level of synaptic input to a neuron acts as a gain control signal that modulates responsiveness to excitatory drive.

Parameters for models of biological systems are often obtained by averaging over experimental results from a number of different preparations. To explore the validity of this procedure, we studied the behavior of a conductance-based model neuron with five voltage-dependent conductances. We randomly varied the maximal conductance of each of the active currents in the model and identified sets of maximal conductances that generate bursting neurons that fire a single action potential at the peak of a slow membrane potential depolarization. A model constructed using the means of the maximal conductances of this population is not itself a one-spike burster, but rather fires three action potentials per burst. Averaging fails because the maximal conductances of the population of one-spike bursters lie in a highly concave region of parameter space that does not contain its mean. This demonstrates that averages over multiple samples can fail to characterize a system whose behavior depends on interactions involving a number of highly variable components.

The electrical characteristics of many neurons are remarkably robust in the face of changing internal and external conditions. At the same time, neurons can be highly sensitive to neuromodulators. We find correlates of this dual robustness and sensitivity in a global analysis of the structure of a conductance-based model neuron. We vary the maximal conductance parameters of the model neuron and, for each set of parameters tested, characterize the activity pattern generated by the cell as silent, tonically firing, or bursting. Within the parameter space of the five maximal conductances of the model, we find directions, representing concerted changes in multiple conductances, along which the basic pattern of neural activity does not change. In other directions, relatively small concurrent changes in a few conductances can induce transitions between these activity patterns. The global structure of the conductance-space maps implies that neuromodulators that alter a sensitive set of conductances will have powerful, and possibly state-dependent, effects. Other modulators that may have no direct impact on the activity of the neuron may nevertheless change the effects of such direct modulators via this state dependence. Some of the results and predictions arising from the model studies are replicated and verified in recordings of stomatogastric ganglion neurons using the dynamic clamp.

Noise can have a significant impact on the response dynamics of a nonlinear system. For neurons, the primary source of noise comes from background synaptic input activity. If this is approximated as white noise, the amplitude of the modulation of the firing rate in response to an input current oscillating at frequency omega decreases as 1/square root[omega] and lags the input by 45 degrees in phase. However, if filtering due to realistic synaptic dynamics is included, the firing rate is modulated by a finite amount even in the limit omega-->infinity and the phase lag is eliminated. Thus, through its effect on noise inputs, realistic synaptic dynamics can ensure unlagged neuronal responses to high-frequency inputs.

Synaptic plasticity provides the basis for most models of learning, memory and development in neural circuits. To generate realistic results, synapse-specific Hebbian forms of plasticity, such as long-term potentiation and depression, must be augmented by global processes that regulate overall levels of neuronal and network activity. Regulatory processes are often as important as the more intensively studied Hebbian processes in determining the consequences of synaptic plasticity for network function. Recent experimental results suggest several novel mechanisms for regulating levels of activity in conjunction with Hebbian synaptic modification. We review three of them-synaptic scaling, spike-timing dependent plasticity and synaptic redistribution-and discuss their functional implications.

Hebbian models of development and learning require both activity-dependent synaptic plasticity and a mechanism that induces competition between different synapses. One form of experimentally observed long-term synaptic plasticity, which we call spike-timing-dependent plasticity (STDP), depends on the relative timing of pre- and postsynaptic action potentials. In modeling studies, we find that this form of synaptic modification can automatically balance synaptic strengths to make postsynaptic firing irregular but more sensitive to presynaptic spike timing. It has been argued that neurons in vivo operate in such a balanced regime. Synapses modifiable by STDP compete for control of the timing of postsynaptic action potentials. Inputs that fire the postsynaptic neuron with short latency or that act in correlated groups are able to compete most successfully and develop strong synapses, while synapses of longer-latency or less-effective inputs are weakened.

Sets of neuronal tuning curves, which describe the responses of neurons as functions of a stimulus, can serve as a basis for approximating other functions of stimulus parameters. In a function-approximating network, synaptic weights determined by a correlation-based Hebbian rule are closely related to the coefficients that result when a function is expanded in an orthogonal basis. Although neuronal tuning curves typically are not orthogonal functions, the relationship between function approximation and correlation-based synaptic weights can be retained if the tuning curves satisfy the conditions of a tight frame. We examine whether the spatial receptive fields of simple cells in cat and monkey primary visual cortex (V1) form a tight frame, allowing them to serve as a basis for constructing more complicated extrastriate receptive fields using correlation-based synaptic weights. Our calculations show that the set of V1 simple cell receptive fields is not tight enough to account for the acuity observed psychophysically.

Identified neurons of the stomatogastric ganglion of the crab Cancer borealis were voltage-clamped, and the current densities of three K+ currents were measured. The current densities of each of the three K+ currents varied twofold to fivefold in inferior cardiac (IC) neurons from different animals. Conventionally, this degree of variability has been attributed to experimental artifacts. Instead, we suggest that it reflects a natural variability that may be related to an underlying process of plasticity. First, we found that there is no fixed ratio among the three K+ currents. Second, we found that several hours of stimulation with depolarizing current pulses (0.5 sec duration at 1 Hz) altered the current density of the Ca2+-dependent outward current, IK(Ca), and the transient outward current, IA. This stimulation paradigm mimics the normal pattern of activity for these neurons. The effect of stimulation on the IA current density was eliminated when Ca2+ influx was blocked by extracellular Cd2+. In contrast, the K+ current densities of the lateral pyloric (LP) neuron were unaffected by the same pattern of stimulation, and the currents expressed by both the IC and the LP neurons were insensitive to hyperpolarizing pulses at the same frequency. We conclude that the conductance densities expressed by neurons may vary continually depending on the recent history of electrical activity in the preparation, and that intracellular Ca2+ may play a role in the processes by which activity influences the regulation of current densities in neurons.

The majority of synapses in primary visual cortex mediate excitation between nearby neurons, yet the role of local recurrent connections in visual processing remains unclear. We propose that these connections are responsible for the spatial-phase invariance of complex-cell responses. In a network model with selective cortical amplification, neurons exhibit simple-cell responses when recurrent connections are weak and complex-cell responses when they are strong, suggesting that simple and complex cells are the low- and high-gain limits of the same basic cortical circuit. Given the ubiquity of invariant responses in cognitive processing, the recurrent mechanism we propose for complex cells may be widely applicable.

We study the impact of correlated neuronal firing rate variability on the accuracy with which an encoded quantity can be extracted from a population of neurons. Contrary to widespread belief, correlations in the variabilities of neuronal firing rates do not, in general, limit the increase in coding accuracy provided by using large populations of encoding neurons. Furthermore, in some cases, but not all, correlations improve the accuracy of a population code.

We explore the effects of short-term synaptic depression on the temporal dynamics of V1 responses to visual images by constructing a model simple cell. Synaptic depression is modeled on the basis of previous detailed fits to experimental data. A component of synaptic depression operating in the range of hundreds of milliseconds can account for a number of the unique temporal characteristics of cortical neurons, including the bandpass nature of frequency-response curves, increases in response amplitude and in cutoff frequency for transient stimuli, nonlinear temporal summation, and contrast-dependent shifts in response phase. Synaptic depression also provides a mechanism for generating the temporal phase shifts needed to produce direction selectivity, and a model constructed along these lines matches both extracellular and intracellular data. A slower component of depression can reproduce the effects of contrast adaptation.

Membrane channels are subject to a wide variety of regulatory mechanisms that can be affected by activity. We present a model of a stomatogastric ganglion (STG) neuron in which several Ca2+-dependent pathways are used to regulate the maximal conductances of membrane currents in an activity-dependent manner. Unlike previous models of this type, the regulation and modification of maximal conductances by electrical activity is unconstrained. The model has seven voltage-dependent membrane currents and uses three Ca2+ sensors acting on different time scales. Starting from random initial conditions over a given range, the model sets the maximal conductances for its active membrane currents to values that produce a predefined target pattern of activity approximately 90% of the time. In these models, the same pattern of electrical activity can be produced by a range of maximal conductances, and this range is compared with voltage-clamp data from the lateral pyloric neuron of the STG. If the electrical activity of the model neuron is perturbed, the maximal conductances adjust to restore the original pattern of activity. When the perturbation is removed, the activity pattern is again restored after a transient adjustment period, but the conductances may not return to their initial values. The model suggests that neurons may regulate their conductances to maintain fixed patterns of electrical activity, rather than fixed maximal conductances, and that the regulation process requires feedback systems capable of reacting to changes of electrical activity on a number of different time scales.

The primary visual cortex (V1) is the first cortical area to receive visual input, and inferior temporal (IT) areas are among the last along the ventral visual pathway. We recorded, in area V1 of anaesthetized cats and area IT of awake macaque monkeys, responses of neurons to videos of natural scenes. Responses were analysed to test various hypotheses concerning the nature of neural coding in these two regions. A variety of spike-train statistics were measured including spike-count distributions, interspike interval distributions, coefficients of variation, power spectra, Fano factors and different sparseness measures. All statistics showed non-Poisson characteristics and several revealed self-similarity of the spike trains. Spike-count distributions were approximately exponential in both visual areas for eight different videos and for counting windows ranging from 50 ms to 5 seconds. The results suggest that the neurons maximize their information carrying capacity while maintaining a fixed long-term-average firing rate, or equivalently, minimize their average firing rate for a fixed information carrying capacity.

Cortical neurons receive synaptic inputs from thousands of afferents that fire action potentials at rates ranging from less than 1 hertz to more than 200 hertz. Both the number of afferents and their large dynamic range can mask changes in the spatial and temporal pattern of synaptic activity, limiting the ability of a cortical neuron to respond to its inputs. Modeling work based on experimental measurements indicates that short-term depression of intracortical synapses provides a dynamic gain-control mechanism that allows equal percentage rate changes on rapidly and slowly firing afferents to produce equal postsynaptic responses. Unlike inhibitory and adaptive mechanisms that reduce responsiveness to all inputs, synaptic depression is input-specific, leading to a dramatic increase in the sensitivity of a neuron to subtle changes in the firing patterns of its afferents.

We analyze a model of navigational map formation based on correlation-based, temporally asymmetric potentiation and depression of synapses between hippocampal place cells. We show that synaptic modification during random exploration of an environment shifts the location encoded by place cell activity in such a way that it indicates the direction from any location to a fixed target avoiding walls and other obstacles. Multiple maps to different targets can be simultaneously stored if we introduce target-dependent modulation of place cell activity. Once maps to a number of target locations in a given environment have been stored, novel maps to previously unknown target locations are automatically constructed by interpolation between existing maps.

Almost all theoretical and experimental studies of the mechanisms underlying learning and memory focus on synaptic efficacy and make the implicit assumption that changes in synaptic efficacy are both necessary and sufficient to account for learning and memory. However, network dynamics depends on the complex interaction between intrinsic membrane properties and synaptic strengths and time courses. Furthermore, neuronal activity itself modifies not only synaptic efficacy but also the intrinsic membrane properties of neurons. This paper presents examples demonstrating that neurons with complex temporal dynamics can provide short-term "memory" mechanisms that rely solely on intrinsic neuronal properties. Additionally, we discuss the potential role that activity may play in long-term modification of intrinsic neuronal properties. While not replacing synaptic plasticity as a powerful learning mechanism, these examples suggest that memory in networks results from an ongoing interplay between changes in synaptic efficacy and intrinsic membrane properties.

Visual responses of neurons in parietal area 7a are modulated by a combined eye and head position signal in a multiplicative manner. Neurons with multiplicative responses can act as powerful computational elements in neural networks. In the case of parietal cortex, multiplicative gain modulation appears to play a crucial role in the transformation of object locations from retinal to body-centered coordinates. It has proven difficult to uncover single-neuron mechanisms that account for neuronal multiplication. Here we show that multiplicative responses can arise in a network model through population effects. Specifically, neurons in a recurrently connected network with excitatory connections between similarly tuned neurons and inhibitory connections between differently tuned neurons can perform a product operation on additive synaptic inputs. The results suggest that parietal responses may be based on this architecture.