Neural representations of time are central to our understanding of the world around us. I review cognitive, neurophysiological and theoretical work that converges on three simple ideas. First, the time of past events is remembered via populations of neurons with a continuum of functional time constants. Second, these time constants evenly tile the log time axis. This results in a neural Weber-Fechner scale for time which can support behavioral Weber-Fechner laws and characteristic behavioral effects in memory experiments. Third, these populations appear as dual pairs---one type of population contains cells that change firing rate monotonically over time and a second type of population that has circumscribed temporal receptive fields. These ideas can be used to build artificial neural networks that have novel properties. Of particular interest, a convolutional neural network built using these principles can generalize to arbitrary rescaling of its inputs. That is, after learning to perform a classification task on a time series presented at one speed, it successfully classifies stimuli presented slowed down or sped up. This result illustrates the point that this confluence of ideas originating in cognitive psychology and measured in the mammalian brain could have wide-reaching impacts on AI research.

Neural circuits exhibit complex activity patterns, both spontaneously and in response to external stimuli. Information encoding and learning in neural circuits depend on the ability of time-varying stimuli to control spontaneous network activity. In particular, variability arising from the sensitivity to initial conditions of recurrent cortical circuits can limit the information conveyed about the sensory input. Spiking and firing rate network models can exhibit such sensitivity to initial conditions that are reflected in their dynamic entropy rate and attractor dimensionality computed from their full Lyapunov spectrum. I will show how chaos in both spiking and rate networks depends on biophysical properties of neurons and the statistics of time-varying stimuli. In spiking networks, increasing the input rate or coupling strength aids in controlling the driven target circuit, which is reflected in both a reduced trial-to-trial variability and a decreased dynamic entropy rate. With sufficiently strong input, a transition towards complete network state control occurs. Surprisingly, this transition does not coincide with the transition from chaos to stability but occurs at even larger values of external input strength. Controllability of spiking activity is facilitated when neurons in the target circuit have a sharp spike onset, thus a high speed by which neurons launch into the action potential. I will also discuss chaos and controllability in firing-rate networks in the balanced state. For these, external control of recurrent dynamics strongly depends on correlations in the input. This phenomenon was studied with a non-stationary dynamic mean-field theory that determines how the activity statistics and the largest Lyapunov exponent depend on frequency and amplitude of the input, recurrent coupling strength, and network size. This shows that uncorrelated inputs facilitate learning in balanced networks. The results highlight the potential of Lyapunov spectrum analysis as a diagnostic for machine learning applications of recurrent networks. They are also relevant in light of recent advances in optogenetics that allow for time-dependent stimulation of a select population of neurons.

Our brains must generate and maintain stable activity patterns over decades of life, despite the dramatic changes in circuit connectivity and function induced by learning and experience-dependent plasticity. How do our brains acheive this balance between opposing need for plasticity and stability? Over the past two decades, we and others have uncovered a family of “homeostatic” negative feedback mechanisms that are theorized to stabilize overall brain activity while allowing specific connections to be reconfigured by experience. Here I discuss recent work in which we demonstrate that individual neocortical neurons in freely behaving animals indeed have a homeostatic activity set-point, to which they return in the face of perturbations. Intriguingly, this firing rate homeostasis is gated by sleep/wake states in a manner that depends on the direction of homeostatic regulation: upward-firing rate homeostasis occurs selectively during periods of active wake, while downward-firing rate homeostasis occurs selectively during periods of sleep, suggesting that an important function of sleep is to temporally segregate bidirectional plasticity. Finally, we show that firing rate homeostasis is compromised in an animal model of autism spectrum disorder. Together our findings suggest that loss of homeostatic plasticity in some neurological disorders may render central circuits unable to compensate for the normal perturbations induced by development and learning.

In behaving rodents, CA1 pyramidal neurons receive spatially-tuned depolarizing synaptic input while traversing a specific location within an environment called its place. Midbrain dopamine neurons participate in reinforcement learning, and bursts of action potentials riding a depolarizing wave of synaptic input signal rewards and reward expectation. Interestingly, slice electrophysiology in vitro shows that both types of cells exhibit a pronounced reduction in firing rate (adaptation) and even cessation of firing during sustained depolarization. We included a five state Markov model of NaV1.6 (for CA1) and NaV1.2 (for dopamine neurons) respectively, in computational models of these two types of neurons. Our simulations suggest that long-term inactivation of this channel is responsible for the adaptation in CA1 pyramidal neurons, in response to triangular depolarizing current ramps. We also show that the differential contribution of slow inactivation in two subpopulations of midbrain dopamine neurons can account for their different dynamic ranges, as assessed by their responses to similar depolarizing ramps. These results suggest long-term inactivation of the sodium channel is a general mechanism for adaptation.

N-methyl-D-aspartate receptors (NMDARs) are excitatory glutamate-gated ion channels that are expressed throughout the central nervous system. NMDARs mediate calcium entry into cells, and are involved in a host of neurological functions. The GluN2A subunit, encoded by the GRIN2A gene, is expressed by both excitatory and inhibitory neurons, with well described roles in pyramidal cells. By using Grin2a knockout mice, we show that the loss of GluN2A signaling impacts parvalbumin-positive (PV) GABAergic interneuron function in hippocampus. Grin2a knockout mice have 33% more PV cells in CA1 compared to wild type but similar cholecystokinin-positive cell density. Immunohistochemistry and electrophysiological recordings show that excess PV cells do eventually incorporate into the hippocampal network and participate in phasic inhibition. Although the morphology of Grin2a knockout PV cells is unaffected, excitability and action-potential firing properties show age-dependent alterations. Preadolescent (P20-25) PV cells have an increased input resistance, longer membrane time constant, longer action-potential half-width, a lower current threshold for depolarization-induced block of action-potential firing, and a decrease in peak action-potential firing rate. Each of these measures are corrected in adulthood, reaching wild type levels, suggesting a potential delay of electrophysiological maturation. The circuit and behavioral implications of this age-dependent PV interneuron malfunction are unknown. However, neonatal Grin2a knockout mice are more susceptible to lipopolysaccharide and febrile-induced seizures, consistent with a critical role for early GluN2A signaling in development and maintenance of excitatory-inhibitory balance. These results could provide insights into how loss-of-function GRIN2A human variants generate an epileptic phenotypes.

Recent advances in optogenetics allow for stimulation of neurons with sub-millisecond spike jitter and single neuron selectivity. Already this precision has revealed new levels of cortical sensitivity: stimulating tens of neurons can yield changes in the mean firing rate of thousands of similarly tuned neurons. This extreme sensitivity suggests that cortical dynamics are near criticality. Criticality is often studied in neural systems as a non-equilibrium thermodynamic process in which scale-free patterns of activity, called avalanches, emerge between distinct states of spontaneous activity. While criticality is well studied, it is still unclear what these distinct states of spontaneous activity are and what responses we expect from stimulation of this activity. By answering these questions, optogenetic stimulation will become a new avenue for approaching criticality and understanding cortical dynamics. Here, for the first time, we study the effects of optogenetic-like stimulation on a model near criticality. We study a model of Inhibitory/Excitatory (I/E) Leaky Integrate and Fire (LIF) spiking neurons which display a region of high sensitivity as seen in experiments. We find that this region of sensitivity is, indeed, near criticality. We derive the Dynamic Mean Field Theory of this model and find that the distinct states of activity are asynchrony and synchrony. We use our theory to characterize response to various types and strengths of optogenetic stimulation. Our model and theory predict that asynchronous, near-critical dynamics can have two qualitatively different responses to stimulation: one characterized by high sensitivity, discrete event responses, and high trial-to-trial variability, and another characterized by low sensitivity, continuous responses with characteristic frequencies, and low trial-to-trial variability. While both response types may be considered near-critical in model space, networks which are closest to criticality show a hybrid of these response effects.

Neural responses are variable: even under identical experimental conditions, single neuron and population responses typically differ from trial to trial and across time. Recent work has demonstrated that this variability has predictable structure, can be modulated by sensory input and behaviour, and bears critical signatures of the underlying network dynamics and computations. However, current methods for characterising neural variability are primarily geared towards sensory coding in the laboratory: they require trials with repeatable experimental stimuli and behavioural covariates. In addition, they make strong assumptions about the parametric form of variability, rely on assumption-free but data-inefficient histogram-based approaches, or are altogether ill-suited for capturing variability modulation by covariates. Here we present a universal probabilistic spike count model that eliminates these shortcomings. Our method uses scalable Bayesian machine learning techniques to model arbitrary spike count distributions (SCDs) with flexible dependence on observed as well as latent covariates. Without requiring repeatable trials, it can flexibly capture covariate-dependent joint SCDs, and provide interpretable latent causes underlying the statistical dependencies between neurons. We apply the model to recordings from a canonical non-sensory neural population: head direction cells in the mouse. We find that variability in these cells defies a simple parametric relationship with mean spike count as assumed in standard models, its modulation by external covariates can be comparably strong to that of the mean firing rate, and slow low-dimensional latent factors explain away neural correlations. Our approach paves the way to understanding the mechanisms and computations underlying neural variability under naturalistic conditions, beyond the realm of sensory coding with repeatable stimuli.

Spike-driven adaptation involves intracellular mechanisms that are initiated by spiking and lead to the subsequent reduction of spiking rate. One of its consequences is the temporal patterning of spike trains, as it imparts serial correlations between interspike intervals in baseline activity. Surprisingly the hidden adaptation states that lead to these correlations themselves exhibit quasi-independence. This talk will first discuss recent findings about the role of such adaptation in suppressing noise and extending sensory detection to weak stimuli that leave the firing rate unchanged. Further, a matching of the post-synaptic responses to the pre-synaptic adaptation time scale enables a recovery of the quasi-independence property, and can explain observations of correlations between post-synaptic EPSPs and behavioural detection thresholds. We then consider the involvement of spike-driven adaptation in the representation of intervals between sensory events. We discuss the possible link of this time-stamping mechanism to the conversion of egocentric to allocentric coordinates. The heterogeneity of the population parameters enables the representation and Bayesian decoding of time sequences of events which may be put to good use in path integration and hilus neuron function in hippocampus.

The head direction (HD) system is classically modeled as a ring attractor network which ensures a stable representation of the animal’s head direction. This unidimensional description popularized the view of the HD system as the brain’s internal compass. However, unlike a globally consistent magnetic compass, the orientation of the HD system is dynamic, depends on local cues and exhibits remapping across familiar environments5. Such a system requires mechanisms to remember and align to familiar landmarks, which may not be well described within the classic 1-dimensional framework. To search for these mechanisms, we performed large population recordings of mouse thalamic HD cells using calcium imaging, during controlled manipulations of a visual landmark in a familiar environment. First, we find that realignment of the system was associated with a continuous rotation of the HD network representation. The speed and angular distance of this rotation was predicted by a 2nd dimension to the ring attractor which we refer to as network gain, i.e. the instantaneous population firing rate. Moreover, the 360-degree azimuthal profile of network gain, during darkness, maintained a ‘memory trace’ of a previously displayed visual landmark. In a 2nd experiment, brief presentations of a rotated landmark revealed an attraction of the network back to its initial orientation, suggesting a time-dependent mechanism underlying the formation of these network gain memory traces. Finally, in a 3rd experiment, continuous rotation of a visual landmark induced a similar rotation of the HD representation which persisted following removal of the landmark, demonstrating that HD network orientation is subject to experience-dependent recalibration. Together, these results provide new mechanistic insights into how the neural compass flexibly adapts to environmental cues to maintain a reliable representation of the head direction.

The typical goal of homeostatic mechanisms is to ensure a system operates at or in the vicinity of a stable set point, where a particular measure is relatively constant and stable. Neural firing rate homeostasis is unusual in that a set point of fixed firing rate is at odds with the goal of a neuron to convey information, or produce timed motor responses, which require temporal variations in firing rate. Therefore, for a neuron, a range of firing rates is required for optimal function, which could, for example, be set by a dual system that controls both mean and variance of firing rate. We explore, both via simulations and analysis, how two experimentally measured mechanisms for firing rate homeostasis can cooperate to improve information processing and avoid the pitfall of pulling in different directions when their set points do not appear to match.

Maintaining average activity level within a set-point range constitutes a fundamental property of central neural circuits. Accumulated evidence suggests that firing rate distributions and their means represent physiological variables regulated by homeostatic systems during sleep-wake cycle in central neural circuits. While intracellular Ca2+ has long been hypothesized as a feedback control signal, the source of Ca2+ and the molecular machinery enabling network-wide homeostatic responses remain largely unknown. I will present our hypothesis and framework on identifying homeostatic regulators in neural circuits. Next, I will show our new results on the role of mitochondria in the regulation of activity set-points and feedback responses. Finally, I will provide an evidence on state-dependent dysregulation of activity set-points at the presymptomatic disease stage in familial Alzheimer’s models.

Neuronal variability is a reflection of recurrent circuitry and cellular physiology. The modulation of neuronal variability is a reliable signature of cognitive and processing state. A pervasive yet puzzling feature of cortical circuits is that despite their complex wiring, population-wide shared spiking variability is low dimensional with all neurons fluctuating en masse. We show that the spatiotemporal dynamics in a spatially structured network produce large population-wide shared variability. When the spatial and temporal scales of inhibitory coupling match known physiology, model spiking neurons naturally generate low dimensional shared variability that captures in vivo population recordings along the visual pathway. Further, we show that firing rate models with spatial coupling can also generate chaotic and low-dimensional rate dynamics. The chaotic parameter region expands when the network is driven by correlated noisy inputs, while being insensitive to the intensity of independent noise.

Working memory (WM) is a fundamental human cognitive capacity that allows us to maintain and manipulate information stored for a short period of time in an active form. Thanks to a unique opportunity to record activity of neurons in humans during epilepsy monitoring we could test neuronal mechanisms of this cognitive capacity. We showed that firing rate of image selective neurons in Medial Temporal Lobe persists through maintenance periods of working memory task. This activity was behaviorally relevant and formed attractors in its state-space. Furthermore, we showed that firing rate of those neurons phase lock to ongoing slow-frequency oscillations. The properties of phase locking are dependent on memory content and load. During high memory loads, the phase of the oscillatory activity to which neurons phase lock provides information about memory content not available in the firing rate of the neurons.

Neural circuit functions are stabilized by homeostatic mechanisms at long timescales in response to changes in experience and learning. However, we still do not know which specific physiological variables are being stabilized, nor which cellular or neural-network components comprise the homeostatic machinery. At this point, most evidence suggests that the distribution of firing rates amongst neurons in a brain circuit is the key variable that is maintained around a circuit-specific set-point value in a process called firing rate homeostasis. Here, I will discuss our recent findings that implicate mitochondria as a central player in mediating firing rate homeostasis and its impairments. While mitochondria are known to regulate neuronal variables such as synaptic vesicle release or intracellular calcium concentration, we searched for the mitochondrial signaling pathways that are essential for homeostatic regulation of firing rates. We utilize basic concepts of control theory to build a framework for classifying possible components of the homeostatic machinery in neural networks. This framework may facilitate the identification of new homeostatic pathways whose malfunctions drive instability of neural circuits in distinct brain disorders.

Medium-spiny neurons (MSNs) in the striatum are required for interval timing, or the estimation of the time over several seconds via a motor response. We and others have shown that striatal MSNs can encode the duration of temporal intervals via time-dependent ramping activity, progressive monotonic changes in firing rate preceding behaviorally salient points in time. Here, we investigated how timing-related activity within striatal ensembles changes with experience. We leveraged a rodent-optimized interval timing task in which mice ‘switch’ response ports after an amount of time has passed without reward. We report three main results. First, we found that the proportion of MSNs exhibiting time-dependent modulations of firing rate increased after 10 days of task overtraining. Second, temporal decoding by MSN ensembles increased with experience and was largely driven by time-related ramping activity. Finally, we found that time-related ramping activity generalized across both correct and error trials. These results enhance our understanding of striatal temporal processing by demonstrating that time-dependent activity within MSN ensembles evolves with experience and is dissociable from motor- and reward-related processes.

A wealth of experimental studies show that the trial-to-trial variability of neuronal activity is quenched during stimulus evoked responses. This fact has helped ground a popular view that the variability of spiking activity can be decomposed into two components. The first is due to irregular spike timing conditioned on the firing rate of a neuron (i.e. a Poisson process), and the second is the trial-to-trial variability of the firing rate itself. Quenching of the variability of the overall response is assumed to be a reflection of a suppression of firing rate variability. Network models have explained this phenomenon through a variety of circuit mechanisms. However, in all cases, from the vantage of a neuron embedded within the network, quenching of its response variability is inherited from its synaptic input. We analyze in vivo whole cell recordings from principal cells in layer (L) 2/3 of mouse visual cortex. While the variability of the membrane potential is quenched upon stimulation, the variability of excitatory and inhibitory currents afferent to the neuron are amplified. This discord complicates the simple inheritance assumption that underpins network models of neuronal variability. We propose and validate an alternative (yet not mutually exclusive) mechanism for the quenching of neuronal variability. We show how an increase in synaptic conductance in the evoked state shunts the transfer of current to the membrane potential, formally decoupling changes in their trial-to-trial variability. The ubiquity of conductance based neuronal transfer combined with the simplicity of our model, provides an appealing framework. In particular, it shows how the dependence of cellular properties upon neuronal state is a critical, yet often ignored, factor. Further, our mechanism does not require a decomposition of variability into spiking and firing rate components, thereby challenging a long held view of neuronal activity.

Neurons in the primary visual cortex (V1) encode the orientation and contrast of visual stimuli through changes in firing rate (Hubel and Wiesel, 1962). Their activity typically peaks at a preferred orientation and decays to zero at the orientations that are orthogonal to the preferred. This activity pattern is re-scaled by contrast but its shape is preserved, a phenomenon known as contrast invariance. Contrast-invariant selectivity is also observed at the population level in V1 (Carandini and Sengpiel, 2004). The mechanisms supporting the emergence of contrast-invariance at the population level remain unclear. How does the activity of different neurons with diverse orientation selectivity and non-linear contrast sensitivity combine to give rise to contrast-invariant population selectivity? Theoretical studies have shown that in the balance limit, the properties of single-neurons do not determine the population activity (van Vreeswijk and Sompolinsky, 1996). Instead, the synaptic dynamics (Mongillo et al., 2012) as well as the intracortical connectivity (Rosenbaum and Doiron, 2014) shape the population activity in balanced networks. We report that short-term plasticity can change the synaptic strength between neurons as a function of the presynaptic activity, which in turns modifies the population response to a stimulus. Thus, the same circuit can process a stimulus in different ways –linearly, sublinearly, supralinearly – depending on the properties of the synapses. We found that balanced networks with excitatory to excitatory short-term synaptic plasticity cannot be contrast-invariant. Instead, short-term plasticity modifies the network selectivity such that the tuning curves are narrower (broader) for increasing contrast if synapses are facilitating (depressing). Based on these results, we wondered whether balanced networks with plastic synapses (other than short-term) can support the emergence of contrast-invariant selectivity. Mathematically, we found that the only synaptic transformation that supports perfect contrast invariance in balanced networks is a power-law release of neurotransmitter as a function of the presynaptic firing rate (in the excitatory to excitatory and in the excitatory to inhibitory neurons). We validate this finding using spiking network simulations, where we report contrast-invariant tuning curves when synapses release the neurotransmitter following a power- law function of the presynaptic firing rate. In summary, we show that synaptic plasticity controls the type of non-linear network response to stimulus contrast and that it can be a potential mechanism mediating the emergence of contrast invariance in balanced networks with orientation-dependent connectivity. Our results therefore connect the physiology of individual synapses to the network level and may help understand the establishment of contrast-invariant selectivity.

Mammalian babies are “sensory traps” for parents. Various sensory cues from the newborn are tremendously efficient in triggering parental responses in caregivers. We recently showed that core aspects of maternal behavior such as pup retrieval in response to infant vocalizations rely on active learning of auditory cues from pups facilitated by the neurohormone oxytocin (OT). Release of OT from the hypothalamus might thus help induce recognition of different infant cues but it is unknown what sensory stimuli can activate OT neurons. I performed unprecedented in vivo whole-cell and cell-attached recordings from optically-identified OT neurons in awake dams. I found that OT neurons, but not other hypothalamic cells, increased their firing rate after playback of pup distress vocalizations. Using anatomical tracing approaches and channelrhodopsin-assisted circuit mapping, I identified the projections and brain areas (including inferior colliculus, auditory cortex, and posterior intralaminar thalamus) relaying auditory information about social sounds to OT neurons. In hypothalamic brain slices, when optogenetically stimulating thalamic afferences to mimic high-frequency thalamic discharge, observed in vivo during pup calls playback, I found that thalamic activity led to long-term depression of synaptic inhibition in OT neurons. This was mediated by postsynaptic NMDARs-induced internalization of GABAARs. Therefore, persistent activation of OT neurons following pup calls in vivo is likely mediated by disinhibition. This gain modulation of OT neurons by infant cries, may be important for sustaining motivation. Using a genetically-encoded OT sensor, I demonstrated that pup calls were efficient in triggering OT release in downstream motivational areas. When thalamus projections to hypothalamus were inhibited with chemogenetics, dams exhibited longer latencies to retrieve crying pups, suggesting that the thalamus-hypothalamus noncanonical auditory pathway may be a specific circuit for the detection of social sounds, important for disinhibiting OT neurons, gating OT release in downstream brain areas, and speeding up maternal behavior.