Multiple timescale encoding of slowly varying whisker stimulus envelope in cortical and thalamic neurons in vivo

MULTIPLE DISTINCT TIMESCALES OF RAPID SENSORY ADAPATION IN THE THALAMOCORTICAL CIRCUIT

Numerous studies have shown that neuronal representations in sensory pathways are far from static but are instead strongly shaped by the complex properties of the sensory inputs they receive. Adaptation dynamically shapes the neural signaling that underlies our perception of the world, yet remains poorly understood. We investigated rapid adaptation across timescales from hundreds of milliseconds to seconds through simultaneous multi-electrode recordings from the ventro-posteromedial nucleus of the thalamus (VPm) and layer 4 of the primary somatosensory cortex (S1) in anesthetized mice in response to controlled, persistent whisker stimulation. Observations in VPm and S1 reveal a degree of adaptation that progresses through the pathway. Signatures of two distinct timescales of rapid adaptation in the firing rates of both thalamic and cortical neuronal populations were revealed, also reflected in the synchrony of the thalamic population and in the thalamocortical synaptic efficacy that was measured in putatively monosynaptically connected thalamocortical pairs. Controlled optogenetic activation of VPm further demonstrated that the longer timescale adaptation observed in S1 is likely inherited from slow decreases in thalamic firing rate and synchrony. Despite the degraded sensory responses, adaptation resulted in a shift in coding strategy that favors theoretical discrimination over detection across the observed timescales of adaptation. Overall, although multiple mechanisms contribute to rapid adaptation at distinct timescales, they support a unifying framework on the role of adaptation in sensory processing.

Silences, spikes and bursts: Three-part knot of the neural code

When a neuron breaks silence, it can emit action potentials in a number of patterns. Some responses are so sudden and intense that electrophysiologists felt the need to single them out, labelling action potentials emitted at a particularly high frequency with a metonym - bursts. Is there more to bursts than a figure of speech? After all, sudden bouts of high-frequency firing are expected to occur whenever inputs surge. The burst coding hypothesis advances that the neural code has three syllables: silences, spikes and bursts. We review evidence supporting this ternary code in terms of devoted mechanisms for burst generation, synaptic transmission and synaptic plasticity. We also review the learning and attention theories for which such a triad is beneficial.

Descending pathways increase sensory neural response heterogeneity to facilitate decoding and behavior

The functional role of heterogeneous spiking responses of otherwise similarly tuned neurons to stimulation, which has been observed ubiquitously, remains unclear to date. Here, we demonstrate that such response heterogeneity serves a beneficial function that is used by downstream brain areas to generate behavioral responses that follows the detailed timecourse of the stimulus. Multi-unit recordings from sensory pyramidal cells within the electrosensory system of Apteronotus leptorhynchus were performed and revealed highly heterogeneous responses that were similar for all cell types. By comparing the coding properties of a given neural population before and after inactivation of descending pathways, we found that heterogeneities were beneficial as decoding was then more robust to the addition of noise. Taken together, our results not only reveal that descending pathways actively promote response heterogeneity within a given cell type, but also uncover a beneficial function for such heterogeneity that is used by the brain to generate behavior.

Diverse nature of interictal oscillations: EEG-based biomarkers in epilepsy

Interictal electroencephalogram (EEG) patterns, including high-frequency oscillations (HFOs), interictal spikes (ISs), and slow wave activities (SWAs), are defined as specific oscillations between seizure events. These interictal oscillations reflect specific dynamic changes in network excitability and play various roles in epilepsy. In this review, we briefly describe the electrographic characteristics of HFOs, ISs, and SWAs in the interictal state, and discuss the underlying cellular and network mechanisms. We also summarize representative evidence from experimental and clinical epilepsy to address their critical roles in ictogenesis and epileptogenesis, indicating their potential as electrophysiological biomarkers of epilepsy. Importantly, we put forwards some perspectives for further research in the field.

Neural adaptation and fractional dynamics as a window to underlying neural excitability

The relationship between macroscale electrophysiological recordings and the dynamics of underlying neural activity remains unclear. We have previously shown that low frequency EEG activity (<1 Hz) is decreased at the seizure onset zone (SOZ), while higher frequency activity (1-50 Hz) is increased. These changes result in power spectral densities (PSDs) with flattened slopes near the SOZ, which are assumed to be areas of increased excitability. We wanted to understand possible mechanisms underlying PSD changes in brain regions of increased excitability. We hypothesized that these observations are consistent with changes in adaptation within the neural circuit. We developed a theoretical framework and tested the effect of adaptation mechanisms, such as spike frequency adaptation and synaptic depression, on excitability and PSDs using filter-based neural mass models and conductance-based models. We compared the contribution of single timescale adaptation and multiple timescale adaptation. We found that adaptation with multiple timescales alters the PSDs. Multiple timescales of adaptation can approximate fractional dynamics, a form of calculus related to power laws, history dependence, and non-integer order derivatives. Coupled with input changes, these dynamics changed circuit responses in unexpected ways. Increased input without synaptic depression increases broadband power. However, increased input with synaptic depression may decrease power. The effects of adaptation were most pronounced for low frequency activity (< 1Hz). Increased input combined with a loss of adaptation yielded reduced low frequency activity and increased higher frequency activity, consistent with clinical EEG observations from SOZs. Spike frequency adaptation and synaptic depression, two forms of multiple timescale adaptation, affect low frequency EEG and the slope of PSDs. These neural mechanisms may underlie changes in EEG activity near the SOZ and relate to neural hyperexcitability. Neural adaptation may be evident in macroscale electrophysiological recordings and provide a window to understanding neural circuit excitability.

Fractional Spiking Neuron: Fractional Leaky Integrate-and-Fire Circuit Described with Dendritic Fractal Model

As dendrites are essential parts of neurons, they are crucial factors for neuronal activities to follow multiple timescale dynamics, which ultimately affect information processing and cognition. However, in the common SNN (Spiking Neural Networks), the hardware-based LIF (Leaky Integrate-and-Fire) circuit only simulates the single timescale dynamic of soma without relating dendritic morphologies, which may limit the capability of simulating neurons to process information. This study proposes the dendritic fractal model mainly for quantifying dendritic morphological effects containing branch and length. To realize this model, We design multiple analog fractional-order circuits (AFCs) which match their extended structures and parameters with the dendritic features. Then introducing AFC into FLIF (Fractional Leaky Integrate-and-Fire) neuron circuits can demonstrate the same multiple timescale dynamics of spiking patterns as biological neurons, including spiking adaptation, inter-spike variability with power-law distribution, first-spike latency, and intrinsic memory. By contrast, it further enhances the degree of mimicry of neuron models and provides a more accurate model for understanding neural computation and cognition mechanisms.

Sensory Adaptation in the Whisker-Mediated Tactile System: Physiology, Theory, and Function

In the natural environment, organisms are constantly exposed to a continuous stream of sensory input. The dynamics of sensory input changes with organism's behaviour and environmental context. The contextual variations may induce >100-fold change in the parameters of the stimulation that an animal experiences. Thus, it is vital for the organism to adapt to the new diet of stimulation. The response properties of neurons, in turn, dynamically adjust to the prevailing properties of sensory stimulation, a process known as "neuronal adaptation." Neuronal adaptation is a ubiquitous phenomenon across all sensory modalities and occurs at different stages of processing from periphery to cortex. In spite of the wealth of research on contextual modulation and neuronal adaptation in visual and auditory systems, the neuronal and computational basis of sensory adaptation in somatosensory system is less understood. Here, we summarise the recent finding and views about the neuronal adaptation in the rodent whisker-mediated tactile system and further summarise the functional effect of neuronal adaptation on the response dynamics and encoding efficiency of neurons at single cell and population levels along the whisker-mediated touch system in rodents. Based on direct and indirect pieces of evidence presented here, we suggest sensory adaptation provides context-dependent functional mechanisms for noise reduction in sensory processing, salience processing and deviant stimulus detection, shift between integration and coincidence detection, band-pass frequency filtering, adjusting neuronal receptive fields, enhancing neural coding and improving discriminability around adapting stimuli, energy conservation, and disambiguating encoding of principal features of tactile stimuli.

The generation of cortical novelty responses through inhibitory plasticity

Animals depend on fast and reliable detection of novel stimuli in their environment. Neurons in multiple sensory areas respond more strongly to novel in comparison to familiar stimuli. Yet, it remains unclear which circuit, cellular, and synaptic mechanisms underlie those responses. Here, we show that spike-timing-dependent plasticity of inhibitory-to-excitatory synapses generates novelty responses in a recurrent spiking network model. Inhibitory plasticity increases the inhibition onto excitatory neurons tuned to familiar stimuli, while inhibition for novel stimuli remains low, leading to a network novelty response. The generation of novelty responses does not depend on the periodicity but rather on the distribution of presented stimuli. By including tuning of inhibitory neurons, the network further captures stimulus-specific adaptation. Finally, we suggest that disinhibition can control the amplification of novelty responses. Therefore, inhibitory plasticity provides a flexible, biologically plausible mechanism to detect the novelty of bottom-up stimuli, enabling us to make experimentally testable predictions.

Low frequency novel interictal EEG biomarker for localizing seizures and predicting outcomes

Localizing hyperexcitable brain tissue to treat focal seizures remains challenging. We want to identify the seizure onset zone from interictal EEG biomarkers. We hypothesize that a combination of interictal EEG biomarkers, including a novel low frequency marker, can predict mesial temporal involvement and can assist in prognosis related to surgical resections. Interictal direct current wide bandwidth invasive EEG recordings from 83 patients implanted with 5111 electrodes were retrospectively studied. Logistic regression was used to classify electrodes and patient outcomes. A feed-forward neural network was implemented to understand putative mechanisms. Interictal infraslow frequency EEG activity was decreased for seizure onset zone electrodes while faster frequencies such as delta (2-4 Hz) and beta-gamma (20-50 Hz) activity were increased. These spectral changes comprised a novel interictal EEG biomarker that was significantly increased for mesial temporal seizure onset zone electrodes compared to non-seizure onset zone electrodes. Interictal EEG biomarkers correctly classified mesial temporal seizure onset zone electrodes with a specificity of 87% and positive predictive value of 80%. These interictal EEG biomarkers also correctly classified patient outcomes after surgical resection with a specificity of 91% and positive predictive value of 87%. Interictal infraslow EEG activity is decreased near the seizure onset zone while higher frequency power is increased, which may suggest distinct underlying physiologic mechanisms. Narrowband interictal EEG power bands provide information about the seizure onset zone and can help predict mesial temporal involvement in seizure onset. Narrowband interictal EEG power bands may be less useful for predictions related to non-mesial temporal electrodes. Together with interictal epileptiform discharges and high-frequency oscillations, these interictal biomarkers may provide prognostic information prior to surgical resection. Computational modelling suggests changes in neural adaptation may be related to the observed low frequency power changes.

The Synaptic Vesicle Priming Protein CAPS-1 Shapes the Adaptation of Sensory Evoked Responses in Mouse Visual Cortex

Short-term plasticity gates information transfer across neuronal synapses and is thought to be involved in fundamental brain processes, such as cortical gain control and sensory adaptation. Neurons employ synaptic vesicle priming proteins of the CAPS and Munc13 families to shape short-term plasticity in vitro, but the relevance of this phenomenon for information processing in the intact brain is unknown. By combining sensory stimulation with in vivo patch-clamp recordings in anesthetized mice, we show that genetic deletion of CAPS-1 in thalamic neurons results in more rapid adaptation of sensory-evoked subthreshold responses in layer 4 neurons of the primary visual cortex. Optogenetic experiments in acute brain slices further reveal that the enhanced adaptation is caused by more pronounced short-term synaptic depression. Our data indicate that neurons engage CAPS-family priming proteins to shape short-term plasticity for optimal sensory information transfer between thalamic and cortical neurons in the intact brain in vivo.

Distinct Structure of Cortical Population Activity on Fast and Infraslow Timescales

Cortical activity is organized across multiple spatial and temporal scales. Most research on the dynamics of neuronal spiking is concerned with timescales of 1 ms–1 s, and little is known about spiking dynamics on timescales of tens of seconds and minutes. Here, we used frequency domain analyses to study the structure of individual neurons’ spiking activity and its coupling to local population rate and to arousal level across 0.01–100 Hz frequency range. In mouse medial prefrontal cortex, the spiking dynamics of individual neurons could be quantitatively captured by a combination of interspike interval and firing rate power spectrum distributions. The relative strength of coherence with local population often differed across timescales: a neuron strongly coupled to population rate on fast timescales could be weakly coupled on slow timescales, and vice versa. On slow but not fast timescales, a substantial proportion of neurons showed firing anticorrelated with the population. Infraslow firing rate changes were largely determined by arousal rather than by local factors, which could explain the timescale dependence of individual neurons’ population coupling strength. These observations demonstrate how neurons simultaneously partake in fast local dynamics, and slow brain-wide dynamics, extending our understanding of infraslow cortical activity beyond the mesoscale resolution of fMRI.

Cortical Microcircuit Mechanisms of Mismatch Negativity and Its Underlying Subcomponents

In the neocortex, neuronal processing of sensory events is significantly influenced by context. For instance, responses in sensory cortices are suppressed to repetitive or redundant stimuli, a phenomenon termed “stimulus-specific adaptation” (SSA). However, in a context in which that same stimulus is novel, or deviates from expectations, neuronal responses are augmented. This augmentation is termed “deviance detection” (DD). This contextual modulation of neural responses is fundamental for how the brain efficiently processes the sensory world to guide immediate and future behaviors. Notably, context modulation is deficient in some neuropsychiatric disorders such as schizophrenia (SZ), as quantified by reduced “mismatch negativity” (MMN), an electroencephalography waveform reflecting a combination of SSA and DD in sensory cortex. Although the role of NMDA-receptor function and other neuromodulatory systems on MMN is established, the precise microcircuit mechanisms of MMN and its underlying components, SSA and DD, remain unknown. When coupled with animal models, the development of powerful precision neurotechnologies over the past decade carries significant promise for making new progress into understanding the neurobiology of MMN with previously unreachable spatial resolution. Currently, rodent models represent the best tool for mechanistic study due to the vast genetic tools available. While quantifying human-like MMN waveforms in rodents is not straightforward, the “oddball” paradigms used to study it in humans and its underlying subcomponents (SSA/DD) are highly translatable across species. Here we summarize efforts published so far, with a focus on cortically measured SSA and DD in animals to maintain relevance to the classically measured MMN, which has cortical origins. While mechanistic studies that measure and contrast both components are sparse, we synthesize a potential set of microcircuit mechanisms from the existing rodent, primate, and human literature. While MMN and its subcomponents likely reflect several mechanisms across multiple brain regions, understanding fundamental microcircuit mechanisms is an important step to understand MMN as a whole. We hypothesize that SSA reflects adaptations occurring at synapses along the sensory-thalamocortical pathways, while DD depends on both SSA inherited from afferent inputs and resulting disinhibition of non-adapted neurons arising from the distinct physiology and wiring properties of local interneuronal subpopulations and NMDA-receptor function.

Coding Principles in Adaptation

Adaptation is a common principle that recurs throughout the nervous system at all stages of processing. This principle manifests in a variety of phenomena, from spike frequency adaptation, to apparent changes in receptive fields with changes in stimulus statistics, to enhanced responses to unexpected stimuli. The ubiquity of adaptation leads naturally to the question: What purpose do these different types of adaptation serve? A diverse set of theories, often highly overlapping, has been proposed to explain the functional role of adaptive phenomena. In this review, we discuss several of these theoretical frameworks, highlighting relationships among them and clarifying distinctions. We summarize observations of the varied manifestations of adaptation, particularly as they relate to these theoretical frameworks, focusing throughout on the visual system and making connections to other sensory systems.

Slowing less than 1 Hz is decreased near the seizure onset zone

Focal slowing (<4 Hz) of brain waves is often associated with focal cerebral dysfunction and is assumed to be increased closest to the location of dysfunction. Prior work suggests that slowing may be comprised of at least two distinct neural mechanisms: slow oscillation activity (<1 Hz) may reflect primarily inhibitory cortical mechanisms while power in the delta frequency (1-4 Hz) may correlate with local synaptic strength. In focal epilepsy patients, we examined slow wave activity near and far from the seizure onset zone (SOZ) during wake, sleep, and postictal states using intracranial electroencephalography. We found that slow oscillation (0.3-1 Hz) activity was decreased near the SOZ, while delta activity (2-4 Hz) activity was increased. This finding was most prominent during sleep, and accompanied by a loss of long-range intra-hemispheric synchrony. In contrast to sleep, postictal slowing was characterized by a broadband increase of spectral power, and showed a reduced modulatory effect of slow oscillations on higher frequencies. These results suggest slow oscillation focal slowing is reduced near the seizure onset zone, perhaps reflecting reduced inhibitory activity. Dissociation between slow oscillation and delta slowing could help localize the seizure onset zone from interictal intracranial recordings.

Deviation from the matching law reflects an optimal strategy involving learning over multiple timescales

Behavior deviating from our normative expectations often appears irrational. For example, even though behavior following the so-called matching law can maximize reward in a stationary foraging task, actual behavior commonly deviates from matching. Such behavioral deviations are interpreted as a failure of the subject; however, here we instead suggest that they reflect an adaptive strategy, suitable for uncertain, non-stationary environments. To prove it, we analyzed the behavior of primates that perform a dynamic foraging task. In such nonstationary environment, learning on both fast and slow timescales is beneficial: fast learning allows the animal to react to sudden changes, at the price of large fluctuations (variance) in the estimates of task relevant variables. Slow learning reduces the fluctuations but costs a bias that causes systematic behavioral deviations. Our behavioral analysis shows that the animals solved this bias-variance tradeoff by combining learning on both fast and slow timescales, suggesting that learning on multiple timescales can be a biologically plausible mechanism for optimizing decisions under uncertainty.

Recent experience can only provide limited information to guide decisions in a volatile environment. Here, the authors report that the choices made by a monkey in a dynamic foraging task can be better explained by a model that combines learning on both fast and slow timescales.

Feedback optimizes neural coding and perception of natural stimuli

Growing evidence suggests that sensory neurons achieve optimal encoding by matching their tuning properties to the natural stimulus statistics. However, the underlying mechanisms remain unclear. Here we demonstrate that feedback pathways from higher brain areas mediate optimized encoding of naturalistic stimuli via temporal whitening in the weakly electric fish Apteronotus leptorhynchus. While one source of direct feedback uniformly enhances neural responses, a separate source of indirect feedback selectively attenuates responses to low frequencies, thus creating a high-pass neural tuning curve that opposes the decaying spectral power of natural stimuli. Additionally, we recorded from two populations of higher brain neurons responsible for the direct and indirect descending inputs. While one population displayed broadband tuning, the other displayed high-pass tuning and thus performed temporal whitening. Hence, our results demonstrate a novel function for descending input in optimizing neural responses to sensory input through temporal whitening that is likely to be conserved across systems and species.

Tune it in: mechanisms and computational significance of neuron-autonomous plasticity

The activity of a neural network is a result of synaptic signals that convey the communication between neurons and neuron-based intrinsic currents that determine the neuron’s input-output transfer function. Ample studies have demonstrated that cell-based excitability, and in particular intrinsic excitability, is modulated by learning and that these modifications play a key role in learning-related behavioral changes. The field of cell-based plasticity is largely growing, and it entails numerous experimental findings that demonstrate a large diversity of currents that are affected by learning. The diverse effect of learning on the neuron’s excitability emphasizes the need for a framework under which cell-based plasticity can be categorized to enable the assessment of the computational roles of the intrinsic modifications. We divide the domain of cell-based plasticity into three main categories, where the first category entails the currents that mediate the passive properties and single-spike generation, the second category entails the currents that mediate spike frequency adaptation, and the third category entails a novel learning-induced mechanism where all excitatory and inhibitory synapses double their strength. Curiously, this elementary division enables a natural categorization of the computational roles of these learning-induced plasticities. The computational roles are diverse and include modification of the neuronal mode of action, such as bursting, prolonged, and fast responsive; attention-like effect where the signal detection is improved; transfer of the network into an active state; biasing the competition for memory allocation; and transforming an environmental cue into a dominant cue and enabling a quicker formation of new memories.

Weakly electric fish distinguish between envelope stimuli arising from different behavioral contexts

Understanding how sensory information is processed by the brain in order to give rise to behavior remains poorly understood in general. Here, we investigated the behavioral responses of the weakly electric fish Apteronotus albifrons to stimuli arising from different contexts, by measuring changes in the electric organ discharge (EOD) frequency. Specifically, we focused on envelopes, which can arise either because of movement (i.e. motion envelopes) or because of interactions between the electric fields of three of more fish (i.e. social envelopes). Overall, we found that the animal's EOD frequency effectively tracked the detailed time course of both motion and social envelopes. In general, behavioral sensitivity (i.e. gain) decreased while phase lag increased with increasing envelope and carrier frequency. However, changes in gain and phase lag as a function of changes in carrier frequency were more prominent for motion than for social envelopes in general. Importantly, we compared behavioral responses to motion and social envelopes with similar characteristics. Although behavioral sensitivities were similar, we observed an increased response lag for social envelopes, primarily for low carrier frequencies. Thus, our results imply that the organism can, based on behavioral responses, distinguish envelope stimuli resulting from movement from those that instead result from social interactions. We discuss the implications of our results for neural coding of envelopes and propose that behavioral responses to motion and social envelopes are mediated by different neural circuits in the brain.

Descending pathways generate perception of and neural responses to weak sensory input

Natural sensory stimuli frequently consist of a fast time-varying waveform whose amplitude or contrast varies more slowly. While changes in contrast carry behaviorally relevant information necessary for sensory perception, their processing by the brain remains poorly understood to this day. Here, we investigated the mechanisms that enable neural responses to and perception of low-contrast stimuli in the electrosensory system of the weakly electric fish Apteronotus leptorhynchus. We found that fish reliably detected such stimuli via robust behavioral responses. Recordings from peripheral electrosensory neurons revealed stimulus-induced changes in firing activity (i.e., phase locking) but not in their overall firing rate. However, central electrosensory neurons receiving input from the periphery responded robustly via both phase locking and increases in firing rate. Pharmacological inactivation of feedback input onto central electrosensory neurons eliminated increases in firing rate but did not affect phase locking for central electrosensory neurons in response to low-contrast stimuli. As feedback inactivation eliminated behavioral responses to these stimuli as well, our results show that it is changes in central electrosensory neuron firing rate that are relevant for behavior, rather than phase locking. Finally, recordings from neurons projecting directly via feedback to central electrosensory neurons revealed that they provide the necessary input to cause increases in firing rate. Our results thus provide the first experimental evidence that feedback generates both neural and behavioral responses to low-contrast stimuli that are commonly found in the natural environment.

Feedback input from more central to more peripheral brain areas is found ubiquitously in the central nervous system of vertebrates. In this study, we used a combination of electrophysiological, behavioral, and pharmacological approaches to reveal a novel function for feedback pathways in generating neural and behavioral responses to weak sensory input in the weakly electric fish. We first determined that weak sensory input gives rise to responses that are phase locked in both peripheral sensory neurons and in the central neurons that are their downstream targets. However, central neurons also responded to weak sensory inputs that were not relayed via a feedforward input from the periphery, because complete inactivation of the feedback pathway abolished increases in firing rate but not the phase locking in response to weak sensory input. Because such inactivation also abolished the behavioral responses, our results show that the increases in firing rate in central neurons, and not the phase locking, are decoded downstream to give rise to perception. Finally, we discovered that the neurons providing feedback input were also activated by weak sensory input, thereby offering further evidence that feedback is necessary to elicit increases in firing rate that are needed for perception.

On stability of fixed points and chaos in fractional systems

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0<α<2. The method is tested on various forms of fractional generalizations of the standard and logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.

Olfactory coding in the turbulent realm

Long-distance olfactory search behaviors depend on odor detection dynamics. Due to turbulence, olfactory signals travel as bursts of variable concentration and spacing and are characterized by long-tail distributions of odor/no-odor events, challenging the computing capacities of olfactory systems. How animals encode complex olfactory scenes to track the plume far from the source remains unclear. Here we focus on the coding of the plume temporal dynamics in moths. We compare responses of olfactory receptor neurons (ORNs) and antennal lobe projection neurons (PNs) to sequences of pheromone stimuli either with white-noise patterns or with realistic turbulent temporal structures simulating a large range of distances (8 to 64 m) from the odor source. For the first time, we analyze what information is extracted by the olfactory system at large distances from the source. Neuronal responses are analyzed using linear-nonlinear models fitted with white-noise stimuli and used for predicting responses to turbulent stimuli. We found that neuronal firing rate is less correlated with the dynamic odor time course when distance to the source increases because of improper coding during long odor and no-odor events that characterize large distances. Rapid adaptation during long puffs does not preclude however the detection of puff transitions in PNs. Individual PNs but not individual ORNs encode the onset and offset of odor puffs for any temporal structure of stimuli. A higher spontaneous firing rate coupled to an inhibition phase at the end of PN responses contributes to this coding property. This allows PNs to decode the temporal structure of the odor plume at any distance to the source, an essential piece of information moths can use in their tracking behavior.

Variable Temporal Integration of Stimulus Patterns in the Mouse Barrel Cortex

Making sense of the world requires distinguishing temporal patterns and sequences lasting hundreds of milliseconds or more. How cortical circuits integrate over time to represent specific sensory sequences remains elusive. Here we assessed whether neurons in the barrel cortex (BC) integrate information about temporal patterns of whisker movements. We performed cell-attached recordings in anesthetized mice while delivering whisker deflections at variable intervals and compared the information carried by neurons about the latest interstimulus interval (reflecting sensitivity to instantaneous frequency) and earlier intervals (reflecting integration over timescales up to several hundred milliseconds). Neurons carried more information about the latest interval than earlier ones. The amount of temporal integration varied with neuronal responsiveness and with the cortical depth of the recording site, that is, with laminar location. A subset of neurons in the upper layers displayed the strongest integration. Highly responsive neurons in the deeper layers encoded the latest interval but integrated particularly weakly. Under these conditions, BC neurons act primarily as encoders of current stimulation parameters; however, our results suggest that temporal integration over hundreds of milliseconds can emerge in some neurons within BC.

Dynamical Timescale Explains Marginal Stability in Excitability Dynamics

Action potentials, taking place over milliseconds, are the basis of neural computation. However, the dynamics of excitability over longer, behaviorally relevant timescales remain underexplored. A recent experiment used long-term recordings from single neurons to reveal multiple timescale fluctuations in response to constant stimuli, along with more reliable responses to variable stimuli. Here, we demonstrate that this apparent paradox is resolved if neurons operate in a marginally stable dynamic regime, which we reveal using a novel inference method. Excitability in this regime is characterized by large fluctuations while retaining high sensitivity to external varying stimuli. A new model with a dynamic recovery timescale that interacts with excitability captures this dynamic regime and predicts the neurons' response with high accuracy. The model explains most experimental observations under several stimulus statistics. The compact structure of our model permits further exploration on the network level.SIGNIFICANCE STATEMENT Excitability is the basis for all neural computations and its long-term dynamics reveal a complex combination of many timescales. We discovered that neural excitability operates under a marginally stable regime in which the system is dominated by internal fluctuation while retaining high sensitivity to externally varying stimuli. We offer a novel approach to modeling excitability dynamics by assuming that the recovery timescale is itself a dynamic variable. Our model is able to capture a wide range of experimental phenomena using few parameters with significantly higher predictive power than previous models.

SK channel subtypes enable parallel optimized coding of behaviorally relevant stimulus attributes: A review

Ion channels play essential roles toward determining how neurons respond to sensory input to mediate perception and behavior. Small conductance calcium-activated potassium (SK) channels are found ubiquitously throughout the brain and have been extensively characterized both molecularly and physiologically in terms of structure and function. It is clear that SK channels are key determinants of neural excitability as they mediate important neuronal response properties such as spike frequency adaptation. However, the functional roles of the different known SK channel subtypes are not well understood. Here we review recent evidence from the electrosensory system of weakly electric fish suggesting that the function of different SK channel subtypes is to optimize the processing of independent but behaviorally relevant stimulus attributes. Indeed, natural sensory stimuli frequently consist of a fast time-varying waveform (i.e., the carrier) whose amplitude (i.e., the envelope) varies slowly and independently. We first review evidence showing how somatic SK2 channels mediate tuning and responses to carrier waveforms. We then review evidence showing how dendritic SK1 channels instead determine tuning and optimize responses to envelope waveforms based on their statistics as found in the organism's natural environment in an independent fashion. The high degree of functional homology between SK channels in electric fish and their mammalian orthologs, as well as the many important parallels between the electrosensory system and the mammalian visual, auditory, and vestibular systems, suggest that these functional roles are conserved across systems and species.

Functional roles of short-term synaptic plasticity with an emphasis on inhibition

Almost all synapses show activity-dependent dynamic changes in efficacy. Numerous studies have explored the mechanisms underlying different forms of short-term synaptic plasticity (STP), but the functional role of STP for circuit output and animal behavior is less understood. This is particularly true for inhibitory synapses that can play widely varied roles in circuit activity. We review recent findings on the role of synaptic STP in sensory, pattern generating, thalamocortical, and hippocampal networks, with a focus on synaptic inhibition. These studies show a variety of functions including sensory adaptation and gating, dynamic gain control and rhythm generation. Because experimental manipulations of STP are difficult and nonspecific, a clear demonstration of STP function often requires a combination of experimental and computational techniques.

Rapid Sensory Adaptation Redux: A Circuit Perspective

Adaptation is fundamental to life. All organisms adapt over timescales that span from evolution to generations and lifetimes to moment-by-moment interactions. The nervous system is particularly adept at rapidly adapting to change, and this in fact may be one of its fundamental principles of organization and function. Rapid forms of sensory adaptation have been well documented across all sensory modalities in a wide range of organisms, yet we do not have a comprehensive understanding of the adaptive cellular mechanisms that ultimately give rise to the corresponding percepts, due in part to the complexity of the circuitry. In this Perspective, we aim to build links between adaptation at multiple scales of neural circuitry by investigating the differential adaptation across brain regions and sub-regions and across specific cell types, for which the explosion of modern tools has just begun to enable. This investigation points to a set of challenges for the field to link functional observations to adaptive properties of the neural circuit that ultimately underlie percepts.

Efficient sensory cortical coding optimizes pursuit eye movements

In the natural world, the statistics of sensory stimuli fluctuate across a wide range. In theory, the brain could maximize information recovery if sensory neurons adaptively rescale their sensitivity to the current range of inputs. Such adaptive coding has been observed in a variety of systems, but the premise that adaptation optimizes behaviour has not been tested. Here we show that adaptation in cortical sensory neurons maximizes information about visual motion in pursuit eye movements guided by that cortical activity. We find that gain adaptation drives a rapid (<100 ms) recovery of information after shifts in motion variance, because the neurons and behaviour rescale their sensitivity to motion fluctuations. Both neurons and pursuit rapidly adopt a response gain that maximizes motion information and minimizes tracking errors. Thus, efficient sensory coding is not simply an ideal standard but a description of real sensory computation that manifests in improved behavioural performance.

Adaptation to second order stimulus features by electrosensory neurons causes ambiguity

Understanding the coding strategies used to process sensory input remains a central problem in neuroscience. Growing evidence suggests that sensory systems process natural stimuli efficiently by ensuring a close match between neural tuning and stimulus statistics through adaptation. However, adaptation causes ambiguity as the same response can be elicited by different stimuli. The mechanisms by which the brain resolves ambiguity remain poorly understood. Here we investigated adaptation in electrosensory pyramidal neurons within different parallel maps in the weakly electric fish Apteronotus leptorhynchus. In response to step increases in stimulus variance, we found that pyramidal neurons within the lateral segment (LS) displayed strong scale invariant adaptation whereas those within the centromedial segment (CMS) instead displayed weaker degrees of scale invariant adaptation. Signal detection analysis revealed that strong adaptation in LS neurons significantly reduced stimulus discriminability. In contrast, weaker adaptation displayed by CMS neurons led to significantly lesser impairment of discriminability. Thus, while LS neurons display adaptation that is matched to natural scene statistics, thereby optimizing information transmission, CMS neurons instead display weaker adaptation and would instead provide information about the context in which these statistics occur. We propose that such a scheme is necessary for decoding by higher brain structures.

Temporal decorrelation by SK channels enables efficient neural coding and perception of natural stimuli

It is commonly assumed that neural systems efficiently process natural sensory input. However, the mechanisms by which such efficient processing is achieved, and the consequences for perception and behaviour remain poorly understood. Here we show that small conductance calcium-activated potassium (SK) channels enable efficient neural processing and perception of natural stimuli. Specifically, these channels allow for the high-pass filtering of sensory input, thereby removing temporal correlations or, equivalently, whitening frequency response power. Varying the degree of adaptation through pharmacological manipulation of SK channels reduced efficiency of coding of natural stimuli, which in turn gave rise to predictable changes in behavioural responses that were no longer matched to natural stimulus statistics. Our results thus demonstrate a novel mechanism by which the nervous system can implement efficient processing and perception of natural sensory input that is likely to be shared across systems and species.

Adaptive learning and decision-making under uncertainty by metaplastic synapses guided by a surprise detection system

Recent experiments have shown that animals and humans have a remarkable ability to adapt their learning rate according to the volatility of the environment. Yet the neural mechanism responsible for such adaptive learning has remained unclear. To fill this gap, we investigated a biophysically inspired, metaplastic synaptic model within the context of a well-studied decision-making network, in which synapses can change their rate of plasticity in addition to their efficacy according to a reward-based learning rule. We found that our model, which assumes that synaptic plasticity is guided by a novel surprise detection system, captures a wide range of key experimental findings and performs as well as a Bayes optimal model, with remarkably little parameter tuning. Our results further demonstrate the computational power of synaptic plasticity, and provide insights into the circuit-level computation which underlies adaptive decision-making.

Mapping entrained brain oscillations during transcranial alternating current stimulation (tACS)

Transcranial alternating current stimulation (tACS), a non-invasive and well-tolerated form of electric brain stimulation, can influence perception, memory, as well as motor and cognitive function. While the exact underlying neurophysiological mechanisms are unknown, the effects of tACS are mainly attributed to frequency-specific entrainment of endogenous brain oscillations in brain areas close to the stimulation electrodes, and modulation of spike timing dependent plasticity reflected in gamma band oscillatory responses. tACS-related electromagnetic stimulator artifacts, however, impede investigation of these neurophysiological mechanisms. Here we introduce a novel approach combining amplitude-modulated tACS during whole-head magnetoencephalography (MEG) allowing for artifact-free source reconstruction and precise mapping of entrained brain oscillations underneath the stimulator electrodes. Using this approach, we show that reliable reconstruction of neuromagnetic low- and high-frequency oscillations including high gamma band activity in stimulated cortical areas is feasible opening a new window to unveil the mechanisms underlying the effects of stimulation protocols that entrain brain oscillatory activity.

On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations

In this paper, we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is a total (a convolution) of the generating functions of all previous values of the variable with weights, which are powers of the time passed. In discrete cases, these systems can be described by difference equations in which a fractional difference on the left hand side is equal to a total (also a convolution) of the generating functions of all previous values of the system's variable with the fractional Eulerian number weights on the right hand side. In the continuous limit, the considered systems can be described by the Grünvald-Letnikov fractional differential equations, which are equivalent to the Volterra integral equations of the second kind. New properties of the fractional Eulerian numbers and possible applications of the results are discussed.

Wideband phase locking to modulated whisker vibration point to a temporal code for texture in the rat's barrel cortex

Rats probe objects with their whiskers and make decisions about sizes, shapes, textures and distances within a few tens of milliseconds. This perceptual analysis requires the processing of tactile high-frequency object components reflecting surface roughness. We have shown that neurons in the barrel cortex of rats encode high-frequency sinusoidal vibrations of whiskers for sustained periods when presented with constant amplitudes and frequencies. In a natural situation, however, stimulus parameters change rapidly when whiskers are brushing across objects. In this study, we therefore analysed cortical responses to vibratory movements of single whiskers with rapidly changing amplitudes and frequencies. The results show that different neural codes are employed for a processing of stimulus parameters. The frequency of whisker vibration is encoded by the temporal pattern of spike discharges, i.e., the phase-locked responses of barrel cortex neurons. In addition, oscillatory gamma band activity was induced during high-frequency stimulation. The pivotal descriptor of the amplitude of whisker displacement, the velocity, is reflected in the rate of spike discharges. While phase-locked discharges occurred over the entire range of frequencies tested (10-600 Hz), the discharge rate increased with stimulus velocity only up to about 60 µm/ms, saturating at a mean rate of ~117 spikes/s. In addition, the results show that whisker movements of more than 500 Hz bandwidth may be encoded by phase-locked responses of small groups of cortical neurons. Thus, even single whiskers may transmit information about wide ranges of textural components owing to their set of different types of hair follicle mechanoreceptors.

Neural heterogeneities determine response characteristics to second-, but not first-order stimulus features

Neural heterogeneities are seen ubiquitously, but how they determine neural response properties remains unclear. Here we show that heterogeneities can either strongly, or not at all, influence neural responses to a given stimulus feature. Specifically, we recorded from peripheral electroreceptor neurons, which display strong heterogeneities in their resting discharge activity, in response to naturalistic stimuli consisting of a fast time-varying waveform (i.e., first-order) whose amplitude (i.e., second-order or envelope) varied slowly in the weakly electric fish Apteronotus leptorhynchus. Although electroreceptors displayed relatively homogeneous responses to first-order stimulus features, further analysis revealed two subpopulations with similar sensitivities that were excited or inhibited by increases in the envelope, respectively, for stimuli whose frequency content spanned the natural range. We further found that a linear-nonlinear cascade model incorporating the known linear response characteristics to first-order features and a static nonlinearity accurately reproduced experimentally observed responses to both first- and second-order features for all stimuli tested. Importantly, this model correctly predicted that the response magnitude is independent of either the stimulus waveform's or the envelope's frequency content. Further analysis of our model led to the surprising prediction that the mean discharge activity can be used to determine whether a given neuron is excited or inhibited by increases in the envelope. This prediction was validated by our experimental data. Thus, our results provide key insight as to how neural heterogeneities can determine response characteristics to some, but not other, behaviorally relevant stimulus features.

Coding of envelopes by correlated but not single-neuron activity requires neural variability

Understanding how the brain processes sensory information is often complicated by the fact that neurons exhibit trial-to-trial variability in their responses to stimuli. Indeed, the role of variability in sensory coding is still highly debated. Here, we examined how variability influences neural responses to naturalistic stimuli consisting of a fast time-varying waveform (i.e., carrier or first order) whose amplitude (i.e., envelope or second order) varies more slowly. Recordings were made from fish electrosensory and monkey vestibular sensory neurons. In both systems, we show that correlated but not single-neuron activity can provide detailed information about second-order stimulus features. Using a simple mathematical model, we made the strong prediction that such correlation-based coding of envelopes requires neural variability. Strikingly, the performance of correlated activity at predicting the envelope was similarly optimally tuned to a nonzero level of variability in both systems, thereby confirming this prediction. Finally, we show that second-order sensory information can only be decoded if one takes into account joint statistics when combining neural activities. Our results thus show that correlated but not single-neural activity can transmit information about the envelope, that such transmission requires neural variability, and that this information can be decoded. We suggest that envelope coding by correlated activity is a general feature of sensory processing that will be found across species and systems.

Intrinsic neuronal properties switch the mode of information transmission in networks

Diverse ion channels and their dynamics endow single neurons with complex biophysical properties. These properties determine the heterogeneity of cell types that make up the brain, as constituents of neural circuits tuned to perform highly specific computations. How do biophysical properties of single neurons impact network function? We study a set of biophysical properties that emerge in cortical neurons during the first week of development, eventually allowing these neurons to adaptively scale the gain of their response to the amplitude of the fluctuations they encounter. During the same time period, these same neurons participate in large-scale waves of spontaneously generated electrical activity. We investigate the potential role of experimentally observed changes in intrinsic neuronal properties in determining the ability of cortical networks to propagate waves of activity. We show that such changes can strongly affect the ability of multi-layered feedforward networks to represent and transmit information on multiple timescales. With properties modeled on those observed at early stages of development, neurons are relatively insensitive to rapid fluctuations and tend to fire synchronously in response to wave-like events of large amplitude. Following developmental changes in voltage-dependent conductances, these same neurons become efficient encoders of fast input fluctuations over few layers, but lose the ability to transmit slower, population-wide input variations across many layers. Depending on the neurons' intrinsic properties, noise plays different roles in modulating neuronal input-output curves, which can dramatically impact network transmission. The developmental change in intrinsic properties supports a transformation of a networks function from the propagation of network-wide information to one in which computations are scaled to local activity. This work underscores the significance of simple changes in conductance parameters in governing how neurons represent and propagate information, and suggests a role for background synaptic noise in switching the mode of information transmission.

Differences in ion channel composition endow different neuronal types with distinct computational properties. Understanding how these biophysical differences affect network-level computation is an important frontier. We focus on a set of biophysical properties, experimentally observed in developing cortical neurons, that allow these neurons to efficiently encode their inputs despite time-varying changes in the statistical context. Large-scale propagating waves are autonomously generated by the developing brain even before the onset of sensory experience. Using multi-layered feedforward networks, we examine how changes in intrinsic properties can lead to changes in the network's ability to represent and transmit information on multiple timescales. We demonstrate that measured changes in the computational properties of immature single neurons enable the propagation of slow-varying wave-like inputs. In contrast, neurons with more mature properties are more sensitive to fast fluctuations, which modulate the slow-varying information. While slow events are transmitted with high fidelity in initial network layers, noise degrades transmission in downstream network layers. Our results show how short-term adaptation and modulation of the neurons' input-output firing curves by background synaptic noise determine the ability of neural networks to transmit information on multiple timescales.

Modeling multiple time scale firing rate adaptation in a neural network of local field potentials

In response to stimulus changes, the firing rates of many neurons adapt, such that stimulus change is emphasized. Previous work has emphasized that rate adaptation can span a wide range of time scales and produce time scale invariant power law adaptation. However, neuronal rate adaptation is typically modeled using single time scale dynamics, and constructing a conductance-based model with arbitrary adaptation dynamics is nontrivial. Here, a modeling approach is developed in which firing rate adaptation, or spike frequency adaptation, can be understood as a filtering of slow stimulus statistics. Adaptation dynamics are modeled by a stimulus filter, and quantified by measuring the phase leads of the firing rate in response to varying input frequencies. Arbitrary adaptation dynamics are approximated by a set of weighted exponentials with parameters obtained by fitting to a desired filter. With this approach it is straightforward to assess the effect of multiple time scale adaptation dynamics on neural networks. To demonstrate this, single time scale and power law adaptation were added to a network model of local field potentials. Rate adaptation enhanced the slow oscillations of the network and flattened the output power spectrum, dampening intrinsic network frequencies. Thus, rate adaptation may play an important role in network dynamics.

Caputo standard α-family of maps: fractional difference vs. fractional

In this paper, the author compares behaviors of systems which can be described by fractional differential and fractional difference equations using the fractional and fractional difference Caputo standard α-Families of maps as examples. The author shows that properties of fractional difference maps (systems with falling factorial-law memory) are similar to the properties of fractional maps (systems with power-law memory). The similarities (types of attractors, power-law convergence of trajectories, existence of cascade of bifurcations and intermittent cascade of bifurcations type trajectories, and dependence of properties on the memory parameter α) and differences in properties of falling factorial- and power-law memory maps are investigated.

The neuronal response at extended timescales: long-term correlations without long-term memory

Long term temporal correlations frequently appear at many levels of neural activity. We show that when such correlations appear in isolated neurons, they indicate the existence of slow underlying processes and lead to explicit conditions on the dynamics of these processes. Moreover, although these slow processes can potentially store information for long times, we demonstrate that this does not imply that the neuron possesses a long memory of its input, even if these processes are bidirectionally coupled with neuronal response. We derive these results for a broad class of biophysical neuron models, and then fit a specific model to recent experiments. The model reproduces the experimental results, exhibiting long term (days-long) correlations due to the interaction between slow variables and internal fluctuations. However, its memory of the input decays on a timescale of minutes. We suggest experiments to test these predictions directly.

Algorithms of whisker-mediated touch perception

Comparison of the functional organization of sensory modalities can reveal the specialized mechanisms unique to each modality as well as processing algorithms that are common across modalities. Here we examine the rodent whisker system. The whisker's mechanical properties shape the forces transmitted to specialized receptors. The sensory and motor systems are intimately interconnected, giving rise to two forms of sensation: generative and receptive. The sensory pathway is a test bed for fundamental concepts in computation and coding: hierarchical feature detection, sparseness, adaptive representations, and population coding. The central processing of signals can be considered a sequence of filters. At the level of cortex, neurons represent object features by a coordinated population code which encompasses cells with heterogeneous properties.

Perception and coding of envelopes in weakly electric fishes

Natural sensory stimuli have a rich spatiotemporal structure and can often be characterized as a high frequency signal that is independently modulated at lower frequencies. This lower frequency modulation is known as the envelope. Envelopes are commonly found in a variety of sensory signals, such as contrast modulations of visual stimuli and amplitude modulations of auditory stimuli. While psychophysical studies have shown that envelopes can carry information that is essential for perception, how envelope information is processed in the brain is poorly understood. Here we review the behavioral salience and neural mechanisms for the processing of envelopes in the electrosensory system of wave-type gymnotiform weakly electric fishes. These fish can generate envelope signals through movement, interactions of their electric fields in social groups or communication signals. The envelopes that result from the first two behavioral contexts differ in their frequency content, with movement envelopes typically being of lower frequency. Recent behavioral evidence has shown that weakly electric fish respond in robust and stereotypical ways to social envelopes to increase the envelope frequency. Finally, neurophysiological results show how envelopes are processed by peripheral and central electrosensory neurons. Peripheral electrosensory neurons respond to both stimulus and envelope signals. Neurons in the primary hindbrain recipient of these afferents, the electrosensory lateral line lobe (ELL), exhibit heterogeneities in their responses to stimulus and envelope signals. Complete segregation of stimulus and envelope information is achieved in neurons in the target of ELL efferents, the midbrain torus semicircularis (Ts).

Transformation of adaptation and gain rescaling along the whisker sensory pathway

Neurons in all sensory systems have a remarkable ability to adapt their sensitivity to the statistical structure of the sensory signals to which they are tuned. In the barrel cortex, firing rate adapts to the variance of a whisker stimulus and neuronal sensitivity (gain) adjusts in inverse proportion to the stimulus standard deviation. To determine how adaptation might be transformed across the ascending lemniscal pathway, we measured the responses of single units in the first and last subcortical stages, the trigeminal ganglion (TRG) and ventral posterior medial thalamic nucleus (VPM), to controlled whisker stimulation in urethane-anesthetized rats. We probed adaptation using a filtered white noise stimulus that switched between low- and high-variance epochs. We found that the firing rate of both TRG and VPM neurons adapted to stimulus variance. By fitting the responses of each unit to a Linear-Nonlinear-Poisson model, we tested whether adaptation changed feature selectivity and/or sensitivity. We found that, whereas feature selectivity was unaffected by stimulus variance, units often exhibited a marked change in sensitivity. The extent of these sensitivity changes increased systematically along the pathway from TRG to barrel cortex. However, there was marked variability across units, especially in VPM. In sum, in the whisker system, the adaptation properties of subcortical neurons are surprisingly diverse. The significance of this diversity may be that it contributes to a rich population representation of whisker dynamics.

Statistics of the electrosensory input in the freely swimming weakly electric fish Apteronotus leptorhynchus

The neural computations underlying sensory-guided behaviors can best be understood in view of the sensory stimuli to be processed under natural conditions. This input is often actively shaped by the movements of the animal and its sensory receptors. Little is known about natural sensory scene statistics taking into account the concomitant movement of sensory receptors in freely moving animals. South American weakly electric fish use a self-generated quasi-sinusoidal electric field for electrolocation and electrocommunication. Thousands of cutaneous electroreceptors detect changes in the transdermal potential (TDP) as the fish interact with conspecifics and the environment. Despite substantial knowledge about the circuitry and physiology of the electrosensory system, the statistical properties of the electrosensory input evoked by natural swimming movements have never been measured directly. Using underwater wireless telemetry, we recorded the TDP of Apteronotus leptorhynchus as they swam freely by themselves and during interaction with a conspecific. Swimming movements caused low-frequency TDP amplitude modulations (AMs). Interacting with a conspecific caused additional AMs around the difference frequency of their electric fields, with the amplitude of the AMs (envelope) varying at low frequencies due to mutual movements. Both AMs and envelopes showed a power-law relationship with frequency, indicating spectral scale invariance. Combining a computational model of the electric field with video tracking of movements, we show that specific swimming patterns cause characteristic spatiotemporal sensory input correlations that contain information that may be used by the brain to guide behavior.

Emergence of adaptive computation by single neurons in the developing cortex

Adaptation is a fundamental computational motif in neural processing. To maintain stable perception in the face of rapidly shifting input, neural systems must extract relevant information from background fluctuations under many different contexts. Many neural systems are able to adjust their input-output properties such that an input's ability to trigger a response depends on the size of that input relative to its local statistical context. This "gain-scaling" strategy has been shown to be an efficient coding strategy. We report here that this property emerges during early development as an intrinsic property of single neurons in mouse sensorimotor cortex, coinciding with the disappearance of spontaneous waves of network activity, and can be modulated by changing the balance of spike-generating currents. Simultaneously, developing neurons move toward a common intrinsic operating point and a stable ratio of spike-generating currents. This developmental trajectory occurs in the absence of sensory input or spontaneous network activity. Through a combination of electrophysiology and modeling, we demonstrate that developing cortical neurons develop the ability to perform nearly perfect gain scaling by virtue of the maturing spike-generating currents alone. We use reduced single neuron models to identify the conditions for this property to hold.

Low-dimensional sensory feature representation by trigeminal primary afferents

In any sensory system, the primary afferents constitute the first level of sensory representation and fundamentally constrain all subsequent information processing. Here, we show that the spike timing, reliability, and stimulus selectivity of primary afferents in the whisker system can be accurately described by a simple model consisting of linear stimulus filtering combined with spike feedback. We fitted the parameters of the model by recording the responses of primary afferents to filtered, white noise whisker motion in anesthetized rats. The model accurately predicted not only the response of primary afferents to white noise whisker motion (median correlation coefficient 0.92) but also to naturalistic, texture-induced whisker motion. The model accounted both for submillisecond spike-timing precision and for non-Poisson spike train structure. We found substantial diversity in the responses of the afferent population, but this diversity was accurately captured by the model: a 2D filter subspace, corresponding to different mixtures of position and velocity sensitivity, captured 94% of the variance in the stimulus selectivity. Our results suggest that the first stage of the whisker system can be well approximated as a bank of linear filters, forming an overcomplete representation of a low-dimensional feature space.

Universal fractional map and cascade of bifurcations type attractors

We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal α-Family of Maps depending on a single parameter α>0, which is the order of the fractional derivative in the nonlinear fractional differential equation describing a system experiencing periodic kicks. We consider two particular α-families corresponding to the Standard and Logistic Maps. For fractional α<2 in the area of parameter values of the transition through the period doubling cascade of bifurcations from regular to chaotic motion in regular dynamics corresponding fractional systems demonstrate a new type of attractors--cascade of bifurcations type trajectories.

Imbalance between excitation and inhibition in the somatosensory cortex produces postadaptation facilitation

Adaptation is typically associated with attenuation of the neuronal response during sustained or repetitive sensory stimulation, followed by a gradual recovery of the response to its baseline level thereafter. Here, we examined the process of recovery from sensory adaptation in layer IV cells of the rat barrel cortex using in vivo intracellular recordings. Surprisingly, in approximately one-third of the cells, the response to a test stimulus delivered a few hundred milliseconds after the adapting stimulation was significantly facilitated. Recordings under different holding potentials revealed that the enhanced response was the result of an imbalance between excitation and inhibition, where a faster recovery of excitation compared with inhibition facilitated the response. Hence, our data provide the first mechanistic explanation of sensory facilitation after adaptation and suggest that adaptation increases the sensitivity of cortical neurons to sensory stimulation by altering the balance between excitation and inhibition.

Speed-invariant encoding of looming object distance requires power law spike rate adaptation

Neural representations of a moving object's distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent's response to "looming" object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent's response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent's firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli.

Parallel coding of first- and second-order stimulus attributes by midbrain electrosensory neurons

Natural stimuli often have time-varying first-order (i.e., mean) and second-order (i.e., variance) attributes that each carry critical information for perception and can vary independently over orders of magnitude. Experiments have shown that sensory systems continuously adapt their responses based on changes in each of these attributes. This adaptation creates ambiguity in the neural code as multiple stimuli may elicit the same neural response. While parallel processing of first- and second-order attributes by separate neural pathways is sufficient to remove this ambiguity, the existence of such pathways and the neural circuits that mediate their emergence have not been uncovered to date. We recorded the responses of midbrain electrosensory neurons in the weakly electric fish Apteronotus leptorhynchus to stimuli with first- and second-order attributes that varied independently in time. We found three distinct groups of midbrain neurons: the first group responded to both first- and second-order attributes, the second group responded selectively to first-order attributes, and the last group responded selectively to second-order attributes. In contrast, all afferent hindbrain neurons responded to both first- and second-order attributes. Using computational analyses, we show how inputs from a heterogeneous population of ON- and OFF-type afferent neurons are combined to give rise to response selectivity to either first- or second-order stimulus attributes in midbrain neurons. Our study thus uncovers, for the first time, generic and widely applicable mechanisms by which parallel processing of first- and second-order stimulus attributes emerges in the brain.