Mathematical framework for place coding in the auditory system.

In the auditory system, tonotopy is postulated to be the substrate for a place code, where sound frequency is encoded by the location of the neurons that fire during the stimulus. Though conceptually simple, the computations that allow for the representation of intensity and complex sounds are poorly understood. Here, a mathematical framework is developed in order to define clearly the conditions that support a place code. To accommodate both frequency and intensity information, the neural network is described as a space with elements that represent individual neurons and clusters of neurons. A mapping is then constructed from acoustic space to neural space so that frequency and intensity are encoded, respectively, by the location and size of the clusters. Algebraic operations -addition and multiplication- are derived to elucidate the rules for representing, assembling, and modulating multi-frequency sound in networks. The resulting outcomes of these operations are consistent with network simulations as well as with electrophysiological and psychophysical data. The analyses show how both frequency and intensity can be encoded with a purely place code, without the need for rate or temporal coding schemes. The algebraic operations are used to describe loudness summation and suggest a mechanism for the critical band. The mathematical approach complements experimental and computational approaches and provides a foundation for interpreting data and constructing models.

Voluntary Wheel Running Exercise Evoked by Food-Restriction Stress Exacerbates Weight Loss of Adolescent Female Rats But Also Promotes Resilience by Enhancing GABAergic Inhibition of Pyramidal Neurons in the Dorsal Hippocampus.

Adolescence is marked by increased vulnerability to mental disorders and maladaptive behaviors, including anorexia nervosa. Food-restriction (FR) stress evokes foraging, which translates to increased wheel running exercise (EX) for caged rodents, a maladaptive behavior, since it does not improve food access and exacerbates weight loss. While almost all adolescent rodents increase EX following FR, some then become resilient by suppressing EX by the second-fourth FR day, which minimizes weight loss. We asked whether GABAergic plasticity in the hippocampus may underlie this gain in resilience. In vitro slice physiology revealed doubling of pyramidal neurons' GABA response in the dorsal hippocampus of food-restricted animals with wheel access (FR + EX for 4 days), but without increase of mIPSC amplitudes. mIPSC frequency increased by 46%, but electron microscopy revealed no increase in axosomatic GABAergic synapse number onto pyramidal cells and only a modest increase (26%) of GABAergic synapse lengths. These changes suggest increase of vesicular release probability and extrasynaptic GABAA receptors and unsilencing of GABAergic synapses. GABAergic synapse lengths correlated with individual's suppression of wheel running and weight loss. These analyses indicate that EX can have dual roles-exacerbate weight loss but also promote resilience to some by dampening hippocampal excitability.

Synaptic input correlations leading to membrane potential decorrelation of spontaneous activity in cortex.

Correlations in the spiking activity of neurons have been found in many regions of the cortex under multiple experimental conditions and are postulated to have important consequences for neural population coding. While there is a large body of extracellular data reporting correlations of various strengths, the subthreshold events underlying the origin and magnitude of signal-independent correlations (called noise or spike count correlations) are unknown. Here we investigate, using intracellular recordings, how synaptic input correlations from shared presynaptic neurons translate into membrane potential and spike-output correlations. Using a pharmacologically activated thalamocortical slice preparation, we perform simultaneous recordings from pairs of layer IV neurons in the auditory cortex of mice and measure synaptic potentials/currents, membrane potentials, and spiking outputs. We calculate cross-correlations between excitatory and inhibitory inputs to investigate correlations emerging from the network. We furthermore evaluate membrane potential correlations near resting potential to study how excitation and inhibition combine and affect spike-output correlations. We demonstrate directly that excitation is correlated with inhibition thereby partially canceling each other and resulting in weak membrane potential and spiking correlations between neurons. Our data suggest that cortical networks are set up to partially cancel correlations emerging from the connections between neurons. This active decorrelation is achieved because excitation and inhibition closely track each other. Our results suggest that the numerous shared presynaptic inputs do not automatically lead to increased spiking correlations.

Spatial profile of excitatory and inhibitory synaptic connectivity in mouse primary auditory cortex.

The role of local cortical activity in shaping neuronal responses is controversial. Among other questions, it is unknown how the diverse response patterns reported in vivo-lateral inhibition in some cases, approximately balanced excitation and inhibition (co-tuning) in others-compare to the local spread of synaptic connectivity. Excitatory and inhibitory activity might cancel each other out, or, whether one outweighs the other, receptive field properties might be substantially affected. As a step toward addressing this question, we used multiple intracellular recording in mouse primary auditory cortical slices to map synaptic connectivity among excitatory pyramidal cells and the two broad classes of inhibitory cells, fast-spiking (FS) and non-FS cells in the principal input layer. Connection probability was distance-dependent; the spread of connectivity, parameterized by Gaussian fits to the data, was comparable for all cell types, ranging from 85 to 114 µm. With brief stimulus trains, unitary synapses formed by FS interneurons were stronger than other classes of synapses; synapse strength did not correlate with distance between cells. The physiological data were qualitatively consistent with predictions derived from anatomical reconstruction. We also analyzed the truncation of neuronal processes due to slicing; overall connectivity was reduced but the spatial pattern was unaffected. The comparable spatial patterns of connectivity and relatively strong excitatory-inhibitory interconnectivity are consistent with a theoretical model where either lateral inhibition or co-tuning can predominate, depending on the structure of the input.

Characterization of thalamocortical responses of regular-spiking and fast-spiking neurons of the mouse auditory cortex in vitro and in silico.

We use a combination of in vitro whole cell recordings and computer simulations to characterize the cellular and synaptic properties that contribute to processing of auditory stimuli. Using a mouse thalamocortical slice preparation, we record the intrinsic membrane properties and synaptic properties of layer 3/4 regular-spiking (RS) pyramidal neurons and fast-spiking (FS) interneurons in primary auditory cortex (AI). We find that postsynaptic potentials (PSPs) evoked in FS cells are significantly larger and depress more than those evoked in RS cells after thalamic stimulation. We use these data to construct a simple computational model of the auditory thalamocortical circuit and find that the differences between FS and RS cells observed in vitro generate model behavior similar to that observed in vivo. We examine how feedforward inhibition and synaptic depression affect cortical responses to time-varying inputs that mimic sinusoidal amplitude-modulated tones. In the model, the balance of cortical inhibition and thalamic excitation evolves in a manner that depends on modulation frequency (MF) of the stimulus and determines cortical response tuning.

Coexistence of lateral and co-tuned inhibitory configurations in cortical networks.

The responses of neurons in sensory cortex depend on the summation of excitatory and inhibitory synaptic inputs. How the excitatory and inhibitory inputs scale with stimulus depends on the network architecture, which ranges from the lateral inhibitory configuration where excitatory inputs are more narrowly tuned than inhibitory inputs, to the co-tuned configuration where both are tuned equally. The underlying circuitry that gives rise to lateral inhibition and co-tuning is yet unclear. Using large-scale network simulations with experimentally determined connectivity patterns and simulations with rate models, we show that the spatial extent of the input determined the configuration: there was a smooth transition from lateral inhibition with narrow input to co-tuning with broad input. The transition from lateral inhibition to co-tuning was accompanied by shifts in overall gain (reduced), output firing pattern (from tonic to phasic) and rate-level functions (from non-monotonic to monotonically increasing). The results suggest that a single cortical network architecture could account for the extended range of experimentally observed response types between the extremes of lateral inhibitory versus co-tuned configurations.

Development of inhibitory timescales in auditory cortex.

The time course of inhibition plays an important role in cortical sensitivity, tuning, and temporal response properties. We investigated the development of L2/3 inhibitory circuitry between fast-spiking (FS) interneurons and pyramidal cells (PCs) in auditory thalamocortical slices from mice between postnatal day 10 (P10) and P29. We found that the maturation of the intrinsic and synaptic properties of both FS cells and their connected PCs influence the timescales of inhibition. FS cell firing rates increased with age owing to decreased membrane time constants, shorter afterhyperpolarizations, and narrower action potentials. Between FS-PC pairs, excitatory postsynaptic potentials (EPSPs) and inhibitory postsynaptic potentials (IPSPs) changed with age. The latencies, rise, and peak times of the IPSPs, as well as the decay constants of both EPSPs and IPSPs decreased between P10 and P29. In addition, decreases in short-term depression at excitatory PC-FS synapses resulted in more sustained synaptic responses during repetitive stimulation. Finally, we show that during early development, the temporal properties that influence the recruitment of inhibition lag those of excitation. Taken together, our results suggest that the changes in the timescales of inhibitory recruitment coincide with the development of the tuning and temporal response properties of auditory cortical networks.

Spatial profile and differential recruitment of GABAB modulate oscillatory activity in auditory cortex.

The interplay between inhibition and excitation is at the core of cortical network activity. In many cortices, including auditory cortex (ACx), interactions between excitatory and inhibitory neurons generate synchronous network gamma oscillations (30-70 Hz). Here, we show that differences in the connection patterns and synaptic properties of excitatory-inhibitory microcircuits permit the spatial extent of network inputs to modulate the magnitude of gamma oscillations. Simultaneous multiple whole-cell recordings from connected fast-spiking interneurons and pyramidal cells in L2/3 of mouse ACx slices revealed that for intersomatic distances <50 microm, most inhibitory connections occurred in reciprocally connected (RC) pairs; at greater distances, inhibitory connections were equally likely in RC and nonreciprocally connected (nRC) pairs. Furthermore, the GABA(B)-mediated inhibition in RC pairs was weaker than in nRC pairs. Simulations with a network model that incorporated these features showed strong, gamma band oscillations only when the network inputs were confined to a small area. These findings suggest a novel mechanism by which oscillatory activity can be modulated by adjusting the spatial distribution of afferent input.

Linking the response properties of cells in auditory cortex with network architecture: cotuning versus lateral inhibition.

The frequency-intensity receptive fields (RF) of neurons in primary auditory cortex (AI) are heterogeneous. Some neurons have V-shaped RFs, whereas others have enclosed ovoid RFs. Moreover, there is a wide range of temporal response profiles ranging from phasic to tonic firing. The mechanisms underlying this diversity of receptive field properties are yet unknown. Here we study the characteristics of thalamocortical (TC) and intracortical connectivity that give rise to the individual cell responses. Using a mouse auditory TC slice preparation, we found that the amplitude of synaptic responses in AI varies non-monotonically with the intensity of the stimulation in the medial geniculate nucleus (MGv). We constructed a network model of MGv and AI that was simulated using either rate model cells or in vitro neurons through an iterative procedure that used the recorded neural responses to reconstruct network activity. We compared the receptive fields and firing profiles obtained with networks configured to have either cotuned excitatory and inhibitory inputs or relatively broad, lateral inhibitory inputs. Each of these networks yielded distinct response properties consistent with those documented in vivo with natural stimuli. The cotuned network produced V-shaped RFs, phasic-tonic firing profiles, and predominantly monotonic rate-level functions. The lateral inhibitory network produced enclosed RFs with narrow frequency tuning, a variety of firing profiles, and robust non-monotonic rate-level functions. We conclude that both types of circuits must be present to account for the wide variety of responses observed in vivo.

Propagation of temporal and rate signals in cultured multilayer networks.

Analyses of idealized feedforward networks suggest that several conditions have to be satisfied in order for activity to propagate faithfully across layers. Verifying these concepts experimentally has been difficult owing to the vast number of variables that must be controlled. Here, we cultured cortical neurons in a chamber with sequentially connected compartments, optogenetically stimulated individual neurons in the first layer with high spatiotemporal resolution, and then monitored the subthreshold and suprathreshold potentials in subsequent layers. Brief stimuli delivered to the first layer evoked a short-latency transient response followed by sustained activity. Rate signals, carried by the sustained component, propagated reliably through 4 layers, unlike idealized feedforward networks, which tended strongly towards synchrony. Moreover, temporal jitter in the stimulus was transformed into a rate code and transmitted to the last layer. This novel mode of propagation occurred in the balanced excitatory-inhibitory regime and is mediated by NMDA-mediated receptors and recurrent activity.

Gain modulation from background synaptic input.

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.

Synaptic mechanisms underlying auditory processing.

In vivo voltage clamp recordings have provided new insights into the synaptic mechanisms that underlie processing in the primary auditory cortex. Of particular importance are the discoveries that excitatory and inhibitory inputs have similar frequency and intensity tuning, that excitation is followed by inhibition with a short delay, and that the duration of inhibition is briefer than expected. These findings challenge existing models of auditory processing in which broadly tuned lateral inhibition is used to limit excitatory receptive fields and suggest new mechanisms by which inhibition and short term plasticity shape neural responses.

Cholinergic modulation of local pyramid-interneuron synapses exhibiting divergent short-term dynamics in rat sensory cortex.

Acetylcholine (ACh) influences attention, short-term memory, and sleep/waking transitions, through its modulatory influence on cortical neurons. It has been proposed that behavioral state changes mediated by ACh result from its selective effects on the intrinsic membrane properties of diverse cortical inhibitory interneuron classes. ACh has been widely shown to reduce the strength of excitatory (glutamatergic) synapses. But past studies using extracellular stimulation have not been able to examine the effects of ACh on local cortical connections important for shaping sensory processing. Here, using dual intracellular recording in slices of rat somatosensory cortex, we show that reduction of local excitatory input to inhibitory neurons by ACh is coupled to differences in the underlying short-term synaptic plasticity (STP). In synapses with short-term depression, where successive evoked excitatory postsynaptic potentials (EPSPs; >5 Hz) usually diminish in strength (short-term depression), cholinergic agonist (5-10 microM carbachol (CCh)) reduced the amplitude of the first EPSP in an evoked train, but CCh's net effect on subsequent EPSPs rapidly diminished. In synapses where successive EPSPs increased in strength (facilitation), the effect of CCh on later EPSPs in an evoked train became progressively greater. The effect of CCh on both depressing and facilitating synapses was blocked by the muscarinic antagonist, 1-5 microM atropine. It is suggested that selective influence on STP contributes fundamentally to cholinergic "switching" between cortical rhythms that underlie different behavioral states.

Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro.

The precise role of synchronous neuronal firing in signal encoding remains unclear. To examine what kinds of signals can be carried by synchrony, I reproduced a multilayer feedforward network of neurons in an in vitro slice preparation of rat cortex using an iterative procedure. When constant and time-varying frequency signals were delivered to the network, the firing of neurons in successive layers became progressively more synchronous. Notably, synchrony in the in vitro network developed even with uncorrelated input, persisted under a wide range of physiological conditions and was crucial for the stable propagation of rate signals. The firing rate was represented by a classical rate code in the initial layers, but switched to a synchrony-based code in the deeper layers.

Boosting of neuronal firing evoked with asynchronous and synchronous inputs to the dendrite.

Dendritic conductances have previously been shown to boost excitatory postsynaptic potentials (EPSPs). To determine whether this boosting translates to an increase in the efficacy for evoking action potentials, we injected barrages of EPSPs that simulate the inputs generated by a population of presynaptic cells into either the dendrite or the soma of pyramidal neurons in vitro. Although the individual dendritic and somatic EPSPs were identical, barrages delivered to the dendrite generated much higher firing rates. Boosting occurred when the simulated cells fired asynchronously and synchronously. This Na+-mediated boosting, which was manifested during repetitive firing, may compensate functionally for electrotonic attenuation of EPSPs.

Optogenetic Stimulation and Recording of Primary Cultured Neurons with Spatiotemporal Control.

We studied a network of cortical neurons in culture and developed an innovative optical device to stimulate optogenetically a large neuronal population with both spatial and temporal precision. We first describe how to culture primary neurons expressing channelrhodopsin. We then detail the optogenetic setup based on the workings of a fast Digital Light Processing (DLP) projector. The setup is able to stimulate tens to hundreds neurons with independent trains of light pulses that evoked action potentials with high temporal resolution. During photostimulation, network activity was monitored using patch-clamp recordings of up to 4 neurons. The experiment is ideally suited to study recurrent network dynamics or biological processes such as plasticity or homeostasis in a network of neurons when a sub-population is activated by distinct stimuli whose characteristics (correlation, rate, and, size) were finely controlled.

Variation of input-output properties along the somatodendritic axis of pyramidal neurons.

The firing evoked by injection of simulated barrages of EPSCs into the proximal dendrite of layer 5 pyramidal neurons is greater than when comparable inputs are injected into the soma. This boosting is mediated by dendritic Na+ conductances. However, the presence of other active conductances in the dendrites, some of which are nonuniformly distributed, suggests that the degree of boosting may differ along the somatodendritic axis. Here, we injected EPSC barrages at the soma and at the proximal, middle, and distal segments of the apical dendrite and measured boosting of subthreshold and suprathreshold responses. We found that although boosting was maintained throughout the apical dendrite, the degree of boosting changed nonmonotonically with distance from the soma. Boosting dipped in the middle dendritic segments as a result of the deactivation of the hyperpolarization-activated cation current, Ih, but increased in the distal dendrites as a result of the activation of Ca2+ conductances. In the distal dendrites, EPSC barrages evoked repetitive bursts of action potentials, and the bursting pattern changed systematically with the magnitude of the input barrages. The quantitative changes in boosting along the somatodendritic axis suggest that inputs from different classes of presynaptic cells are weighted differently, depending on the location of the synaptic contacts. Moreover, the tight coupling between burst characteristics and stimulus parameters indicate that the distal dendrites can support a coding scheme that is different from that at sites closer to the soma, consistent with the notion of a separate dendritic integration site.

Integration of subthreshold and suprathreshold excitatory barrages along the somatodendritic axis of pyramidal neurons.

Neurons integrate inputs arriving in different cellular compartments to produce action potentials that are transmitted to other neurons. Because of the voltage- and time-dependent conductances in the dendrites and soma, summation of synaptic inputs is complex. To examine summation of membrane potentials and firing rates, we performed whole-cell recordings from layer 5 cortical pyramidal neurons in acute slices of the rat's somatosensory cortex. We delivered subthreshold and suprathreshold stimuli at the soma and several sites on the apical dendrite, and injected inputs that mimic synaptic barrages at individual or distributed sites. We found that summation of subthreshold potentials differed from that of firing rates. Subthreshold summation was linear when barrages were small but became supralinear as barrages increased. When neurons were discharging repetitively the rules were more diverse. At the soma and proximal apical dendrite summation of the evoked firing rates was predominantly sublinear whereas in the distal dendrite summation ranged from supralinear to sublinear. In addition, the integration of inputs delivered at a single location differed from that of distributed inputs only for suprathreshold responses. These results indicate that convergent inputs onto the apical dendrite and soma do not simply summate linearly, as suggested previously, and that distinct presynaptic afferents that target specific sites on the dendritic tree may perform unique sets of computations.

Synaptic short-term plasticity in auditory cortical circuits.

The auditory system must be able to adapt to changing acoustic environment and still maintain accurate representation of signals. Mechanistically, this is a difficult task because the responsiveness of a large heterogeneous population of interconnected neurons must be adjusted properly and precisely. Synaptic short-term plasticity (STP) is widely regarded as a viable mechanism for adaptive processes. Although the cellular mechanism for STP is well characterized, the overall effect on information processing at the network level is poorly understood. The main challenge is that there are many cell types in auditory cortex, each of which exhibit different forms and degrees of STP. In this article, I will review the basic properties of STP in auditory cortical circuits and discuss the possible impact on signal processing.

Flexible traffic control of the synfire-mode transmission by inhibitory modulation: nonlinear noise reduction.

Intermingled neural connections apparent in the brain make us wonder what controls the traffic of propagating activity in the brain to secure signal transmission without harmful crosstalk. Here, we reveal that inhibitory input but not excitatory input works as a particularly useful traffic controller because it controls the degree of synchrony of population firing of neurons as well as controlling the size of the population firing bidirectionally. Our dynamical system analysis reveals that the synchrony enhancement depends crucially on the nonlinear membrane potential dynamics and a hidden slow dynamical variable. Our electrophysiological study with rodent slice preparations show that the phenomenon happens in real neurons. Furthermore, our analysis with the Fokker-Planck equations demonstrates the phenomenon in a semianalytical manner.