Paradoxical self-sustained dynamics emerge from orchestrated excitatory and inhibitory homeostatic plasticity rules.

Self-sustained neural activity maintained through local recurrent connections is of fundamental importance to cortical function. Converging theoretical and experimental evidence indicates that cortical circuits generating self-sustained dynamics operate in an inhibition-stabilized regime. Theoretical work has established that four sets of weights (WE←E, WE←I, WI←E, and WI←I) must obey specific relationships to produce inhibition-stabilized dynamics, but it is not known how the brain can appropriately set the values of all four weight classes in an unsupervised manner to be in the inhibition-stabilized regime. We prove that standard homeostatic plasticity rules are generally unable to generate inhibition-stabilized dynamics and that their instability is caused by a signature property of inhibition-stabilized networks: the paradoxical effect. In contrast, we show that a family of "cross-homeostatic" rules overcome the paradoxical effect and robustly lead to the emergence of stable dynamics. This work provides a model of how-beginning from a silent network-self-sustained inhibition-stabilized dynamics can emerge from learning rules governing all four synaptic weight classes in an orchestrated manner.

Creation of Neuronal Ensembles and Cell-Specific Homeostatic Plasticity through Chronic Sparse Optogenetic Stimulation.

Cortical computations emerge from the dynamics of neurons embedded in complex cortical circuits. Within these circuits, neuronal ensembles, which represent subnetworks with shared functional connectivity, emerge in an experience-dependent manner. Here we induced ensembles in ex vivo cortical circuits from mice of either sex by differentially activating subpopulations through chronic optogenetic stimulation. We observed a decrease in voltage correlation, and importantly a synaptic decoupling between the stimulated and nonstimulated populations. We also observed a decrease in firing rate during Up-states in the stimulated population. These ensemble-specific changes were accompanied by decreases in intrinsic excitability in the stimulated population, and a decrease in connectivity between stimulated and nonstimulated pyramidal neurons. By incorporating the empirically observed changes in intrinsic excitability and connectivity into a spiking neural network model, we were able to demonstrate that changes in both intrinsic excitability and connectivity accounted for the decreased firing rate, but only changes in connectivity accounted for the observed decorrelation. Our findings help ascertain the mechanisms underlying the ability of chronic patterned stimulation to create ensembles within cortical circuits and, importantly, show that while Up-states are a global network-wide phenomenon, functionally distinct ensembles can preserve their identity during Up-states through differential firing rates and correlations.SIGNIFICANCE STATEMENT The connectivity and activity patterns of local cortical circuits are shaped by experience. This experience-dependent reorganization of cortical circuits is driven by complex interactions between different local learning rules, external input, and reciprocal feedback between many distinct brain areas. Here we used an ex vivo approach to demonstrate how simple forms of chronic external stimulation can shape local cortical circuits in terms of their correlated activity and functional connectivity. The absence of feedback between different brain areas and full control of external input allowed for a tractable system to study the underlying mechanisms and development of a computational model. Results show that differential stimulation of subpopulations of neurons significantly reshapes cortical circuits and forms subnetworks referred to as neuronal ensembles.

Time for Memories.

The ability to store information about the past to dynamically predict and prepare for the future is among the most fundamental tasks the brain performs. To date, the problems of understanding how the brain stores and organizes information about the past (memory) and how the brain represents and processes temporal information for adaptive behavior have generally been studied as distinct cognitive functions. This Symposium explores the inherent link between memory and temporal cognition, as well as the potential shared neural mechanisms between them. We suggest that working memory and implicit timing are interconnected and may share overlapping neural mechanisms. Additionally, we explore how temporal structure is encoded in associative and episodic memory and, conversely, the influences of episodic memory on subsequent temporal anticipation and the perception of time. We suggest that neural sequences provide a general computational motif that contributes to timing and working memory, as well as the spatiotemporal coding and recall of episodes.

Neural Sequences and the Encoding of Time.

Converging experimental and computational evidence indicate that on the scale of seconds the brain encodes time through changing patterns of neural activity. Experimentally, two general forms of neural dynamic regimes that can encode time have been observed: neural population clocks and ramping activity. Neural population clocks provide a high-dimensional code to generate complex spatiotemporal output patterns, in which each neuron exhibits a nonlinear temporal profile. A prototypical example of neural population clocks are neural sequences, which have been observed across species, brain areas, and behavioral paradigms. Additionally, neural sequences emerge in artificial neural networks trained to solve time-dependent tasks. Here, we examine the role of neural sequences in the encoding of time, and how they may emerge in a biologically plausible manner. We conclude that neural sequences may represent a canonical computational regime to perform temporal computations.

Encoding time in neural dynamic regimes with distinct computational tradeoffs.

Converging evidence suggests the brain encodes time in dynamic patterns of neural activity, including neural sequences, ramping activity, and complex dynamics. Most temporal tasks, however, require more than just encoding time, and can have distinct computational requirements including the need to exhibit temporal scaling, generalize to novel contexts, or robustness to noise. It is not known how neural circuits can encode time and satisfy distinct computational requirements, nor is it known whether similar patterns of neural activity at the population level can exhibit dramatically different computational or generalization properties. To begin to answer these questions, we trained RNNs on two timing tasks based on behavioral studies. The tasks had different input structures but required producing identically timed output patterns. Using a novel framework we quantified whether RNNs encoded two intervals using either of three different timing strategies: scaling, absolute, or stimulus-specific dynamics. We found that similar neural dynamic patterns at the level of single intervals, could exhibit fundamentally different properties, including, generalization, the connectivity structure of the trained networks, and the contribution of excitatory and inhibitory neurons. Critically, depending on the task structure RNNs were better suited for generalization or robustness to noise. Further analysis revealed different connection patterns underlying the different regimes. Our results predict that apparently similar neural dynamic patterns at the population level (e.g., neural sequences) can exhibit fundamentally different computational properties in regards to their ability to generalize to novel stimuli and their robustness to noise-and that these differences are associated with differences in network connectivity and distinct contributions of excitatory and inhibitory neurons. We also predict that the task structure used in different experimental studies accounts for some of the experimentally observed variability in how networks encode time.

Differential Excitability of PV and SST Neurons Results in Distinct Functional Roles in Inhibition Stabilization of Up States.

Up states are the best studied example of an emergent neural dynamic regime. Computational models based on a single class of inhibitory neurons indicate that Up states reflect bistable dynamic systems in which positive feedback is stabilized by strong inhibition and predict a paradoxical effect in which increased drive to inhibitory neurons results in decreased inhibitory activity. To date, however, computational models have not incorporated empirically defined properties of parvalbumin (PV) and somatostatin (SST) neurons. Here we first experimentally characterized the frequency-current (F-I) curves of pyramidal (Pyr), PV, and SST neurons from mice of either sex, and confirmed a sharp difference between the threshold and slopes of PV and SST neurons. The empirically defined F-I curves were incorporated into a three-population computational model that simulated the empirically derived firing rates of pyramidal, PV, and SST neurons. Simulations revealed that the intrinsic properties were sufficient to predict that PV neurons are primarily responsible for generating the nontrivial fixed points representing Up states. Simulations and analytical methods demonstrated that while the paradoxical effect is not obligatory in a model with two classes of inhibitory neurons, it is present in most regimes. Finally, experimental tests validated predictions of the model that the Pyr ↔ PV inhibitory loop is stronger than the Pyr ↔ SST loop.SIGNIFICANCE STATEMENT Many cortical computations, such as working memory, rely on the local recurrent excitatory connections that define cortical circuit motifs. Up states are among the best studied examples of neural dynamic regimes that rely on recurrent excitatory excitation. However, this positive feedback must be held in check by inhibition. To address the relative contribution of PV and SST neurons, we characterized the intrinsic input-output differences between these classes of inhibitory neurons and, using experimental and theoretical methods, show that the higher threshold and gain of PV leads to a dominant role in network stabilization.

Differential Short-Term Plasticity of PV and SST Neurons Accounts for Adaptation and Facilitation of Cortical Neurons to Auditory Tones.

Cortical responses to sensory stimuli are strongly modulated by temporal context. One of the best studied examples of such modulation is sensory adaptation. We first show that in response to repeated tones pyramidal (Pyr) neurons in male mouse auditory cortex (A1) exhibit facilitating and stable responses, in addition to adapting responses. To examine the potential mechanisms underlying these distinct temporal profiles, we developed a reduced spiking model of sensory cortical circuits that incorporated the signature short-term synaptic plasticity (STP) profiles of the inhibitory parvalbumin (PV) and somatostatin (SST) interneurons. The model accounted for all three temporal response profiles as the result of dynamic changes in excitatory/inhibitory balance produced by STP, primarily through shifts in the relative latency of Pyr and inhibitory neurons. Transition between the three response profiles was possible by changing the strength of the inhibitory PV→Pyr and SST→Pyr synapses. The model predicted that a unit's latency would be related to its temporal profile. Consistent with this prediction, the latency of stable units was significantly shorter than that of adapting and facilitating units. Furthermore, because of the history-dependence of STP the model generated a paradoxical prediction: that inactivation of inhibitory neurons during one tone would decrease the response of A1 neurons to a subsequent tone. Indeed, we observed that optogenetic inactivation of PV neurons during one tone counterintuitively decreased the spiking of Pyr neurons to a subsequent tone 400 ms later. These results provide evidence that STP is critical to temporal context-dependent responses in the sensory cortex.SIGNIFICANCE STATEMENT Our perception of speech and music depends strongly on temporal context, i.e., the significance of a stimulus depends on the preceding stimuli. Complementary neural mechanisms are needed to sometimes ignore repetitive stimuli (e.g., the tic of a clock) or detect meaningful repetition (e.g., consecutive tones in Morse code). We modeled a neural circuit that accounts for diverse experimentally-observed response profiles in auditory cortex (A1) neurons, based on known forms of short-term synaptic plasticity (STP). Whether the simulated circuit reduced, maintained, or enhanced its response to repeated tones depended on the relative dominance of two different types of inhibitory cells. The model made novel predictions that were experimentally validated. Results define an important role for STP in temporal context-dependent perception.

Differential Encoding of Time by Prefrontal and Striatal Network Dynamics.

Telling time is fundamental to many forms of learning and behavior, including the anticipation of rewarding events. Although the neural mechanisms underlying timing remain unknown, computational models have proposed that the brain represents time in the dynamics of neural networks. Consistent with this hypothesis, changing patterns of neural activity dynamically in a number of brain areas-including the striatum and cortex-has been shown to encode elapsed time. To date, however, no studies have explicitly quantified and contrasted how well different areas encode time by recording large numbers of units simultaneously from more than one area. Here, we performed large-scale extracellular recordings in the striatum and orbitofrontal cortex of mice that learned the temporal relationship between a stimulus and a reward and reported their response with anticipatory licking. We used a machine-learning algorithm to quantify how well populations of neurons encoded elapsed time from stimulus onset. Both the striatal and cortical networks encoded time, but the striatal network outperformed the orbitofrontal cortex, a finding replicated both in simultaneously and nonsimultaneously recorded corticostriatal datasets. The striatal network was also more reliable in predicting when the animals would lick up to ∼1 s before the actual lick occurred. Our results are consistent with the hypothesis that temporal information is encoded in a widely distributed manner throughout multiple brain areas, but that the striatum may have a privileged role in timing because it has a more accurate "clock" as it integrates information across multiple cortical areas. SIGNIFICANCE STATEMENT: The neural representation of time is thought to be distributed across multiple functionally specialized brain structures, including the striatum and cortex. However, until now, the neural code for time has not been compared quantitatively between these areas. Here, we performed large-scale recordings in the striatum and orbitofrontal cortex of mice trained on a stimulus-reward association task involving a delay period and used a machine-learning algorithm to quantify how well populations of simultaneously recorded neurons encoded elapsed time from stimulus onset. We found that, although both areas encoded time, the striatum consistently outperformed the orbitofrontal cortex. These results suggest that the striatum may refine the code for time by integrating information from multiple inputs.

Encoding Time in Feedforward Trajectories of a Recurrent Neural Network Model.

Brain activity evolves through time, creating trajectories of activity that underlie sensorimotor processing, behavior, and learning and memory. Therefore, understanding the temporal nature of neural dynamics is essential to understanding brain function and behavior. In vivo studies have demonstrated that sequential transient activation of neurons can encode time. However, it remains unclear whether these patterns emerge from feedforward network architectures or from recurrent networks and, furthermore, what role network structure plays in timing. We address these issues using a recurrent neural network (RNN) model with distinct populations of excitatory and inhibitory units. Consistent with experimental data, a single RNN could autonomously produce multiple functionally feedforward trajectories, thus potentially encoding multiple timed motor patterns lasting up to several seconds. Importantly, the model accounted for Weber's law, a hallmark of timing behavior. Analysis of network connectivity revealed that efficiency-a measure of network interconnectedness-decreased as the number of stored trajectories increased. Additionally, the balance of excitation (E) and inhibition (I) shifted toward excitation during each unit's activation time, generating the prediction that observed sequential activity relies on dynamic control of the E/I balance. Our results establish for the first time that the same RNN can generate multiple functionally feedforward patterns of activity as a result of dynamic shifts in the E/I balance imposed by the connectome of the RNN. We conclude that recurrent network architectures account for sequential neural activity, as well as for a fundamental signature of timing behavior: Weber's law.

Time in Cortical Circuits.

Time is central to cognition. However, the neural basis for time-dependent cognition remains poorly understood. We explore how the temporal features of neural activity in cortical circuits and their capacity for plasticity can contribute to time-dependent cognition over short time scales. This neural activity is linked to cognition that operates in the present or anticipates events or stimuli in the near future. We focus on deliberation and planning in the context of decision making as a cognitive process that integrates information across time. We progress to consider how temporal expectations of the future modulate perception. We propose that understanding the neural basis for how the brain tells time and operates in time will be necessary to develop general models of cognition. SIGNIFICANCE STATEMENT: Time is central to cognition. However, the neural basis for time-dependent cognition remains poorly understood. We explore how the temporal features of neural activity in cortical circuits and their capacity for plasticity can contribute to time-dependent cognition over short time scales. We propose that understanding the neural basis for how the brain tells time and operates in time will be necessary to develop general models of cognition.

Multifocal fluorescence microscope for fast optical recordings of neuronal action potentials.

In recent years, optical sensors for tracking neural activity have been developed and offer great utility. However, developing microscopy techniques that have several kHz bandwidth necessary to reliably capture optically reported action potentials (APs) at multiple locations in parallel remains a significant challenge. To our knowledge, we describe a novel microscope optimized to measure spatially distributed optical signals with submillisecond and near diffraction-limit resolution. Our design uses a spatial light modulator to generate patterned illumination to simultaneously excite multiple user-defined targets. A galvanometer driven mirror in the emission path streaks the fluorescence emanating from each excitation point during the camera exposure, using unused camera pixels to capture time varying fluorescence at rates that are ∼1000 times faster than the camera's native frame rate. We demonstrate that this approach is capable of recording Ca(2+) transients resulting from APs in neurons labeled with the Ca(2+) sensor Oregon Green Bapta-1 (OGB-1), and can localize the timing of these events with millisecond resolution. Furthermore, optically reported APs can be detected with the voltage sensitive dye DiO-DPA in multiple locations within a neuron with a signal/noise ratio up to ∼40, resolving delays in arrival time along dendrites. Thus, the microscope provides a powerful tool for photometric measurements of dynamics requiring submillisecond sampling at multiple locations.

A model of order-selectivity based on dynamic changes in the balance of excitation and inhibition produced by short-term synaptic plasticity.

Determining the order of sensory events separated by a few hundred milliseconds is critical to many forms of sensory processing, including vocalization and speech discrimination. Although many experimental studies have recorded from auditory order-sensitive and order-selective neurons, the underlying mechanisms are poorly understood. Here we demonstrate that universal properties of cortical synapses-short-term synaptic plasticity of excitatory and inhibitory synapses-are well suited for the generation of order-selective neural responses. Using computational models of canonical disynaptic circuits, we show that the dynamic changes in the balance of excitation and inhibition imposed by short-term plasticity lead to the generation of order-selective responses. Parametric analyses predict that among the forms of short-term plasticity expressed at excitatory-to-excitatory, excitatory-to-inhibitory, and inhibitory-to-excitatory synapses, the single most important contributor to order-selectivity is the paired-pulse depression of inhibitory postsynaptic potentials (IPSPs). A topographic model of the auditory cortex that incorporates short-term plasticity accounts for both context-dependent suppression and enhancement in response to paired tones. Together these results provide a framework to account for an important computational problem based on ubiquitous synaptic properties that did not yet have a clearly established computational function. Additionally, these studies suggest that disynaptic circuits represent a fundamental computational unit that is capable of processing both spatial and temporal information.

State-dependent computations: spatiotemporal processing in cortical networks.

A conspicuous ability of the brain is to seamlessly assimilate and process spatial and temporal features of sensory stimuli. This ability is indispensable for the recognition of natural stimuli. Yet, a general computational framework for processing spatiotemporal stimuli remains elusive. Recent theoretical and experimental work suggests that spatiotemporal processing emerges from the interaction between incoming stimuli and the internal dynamic state of neural networks, including not only their ongoing spiking activity but also their 'hidden' neuronal states, such as short-term synaptic plasticity.

Neural dynamics based timing in the subsecond to seconds range.

The brain must solve a wide range of different temporal problems, each of which can be defined by a relevant time scale and specific functional requirements. Experimental and theoretical studies suggest that some forms of timing reflect general and inherent properties of local neural networks. Like the ripples on a pond, neural networks represent rich dynamical systems that can produce time-varying patterns of activity in response to a stimulus. State-dependent network models propose that sensory timing arises from the interaction between incoming stimuli and the internal dynamics of recurrent neural circuits. A wide-variety of time-dependent neural properties, such as short-term synaptic plasticity, are important contributors to the internal dynamics of neural circuits. In contrast to sensory timing, motor timing requires that network actively generate appropriately timed spikes even in the absence of sensory stimuli. Population clock models propose that motor timing arises from internal dynamics of recurrent network capable of self-perpetuating activity.

Ex Vivo Cortical Circuits Learn to Predict and Spontaneously Replay Temporal Patterns.

It has been proposed that prediction and timing are computational primitives of neocortical microcircuits, specifically, that neural mechanisms are in place to allow neocortical circuits to autonomously learn the temporal structure of external stimuli and generate internal predictions. To test this hypothesis, we trained cortical organotypic slices on two specific temporal patterns using dual-optical stimulation. After 24-hours of training, whole-cell recordings revealed network dynamics consistent with training-specific timed prediction. Unexpectedly, there was replay of the learned temporal structure during spontaneous activity. Furthermore, some neurons exhibited timed prediction errors. Mechanistically our results indicate that learning relied in part on asymmetric connectivity between distinct neuronal ensembles with temporally-ordered activation. These findings further suggest that local cortical microcircuits are intrinsically capable of learning temporal information and generating predictions, and that the learning rules underlying temporal learning and spontaneous replay can be intrinsic to local cortical microcircuits and not necessarily dependent on top-down interactions.

Unified control of temporal and spatial scales of sensorimotor behavior through neuromodulation of short-term synaptic plasticity.

Neuromodulators have been shown to alter the temporal profile of short-term synaptic plasticity (STP); however, the computational function of this neuromodulation remains unexplored. Here, we propose that the neuromodulation of STP provides a general mechanism to scale neural dynamics and motor outputs in time and space. We trained recurrent neural networks that incorporated STP to produce complex motor trajectories-handwritten digits-with different temporal (speed) and spatial (size) scales. Neuromodulation of STP produced temporal and spatial scaling of the learned dynamics and enhanced temporal or spatial generalization compared to standard training of the synaptic weights in the absence of STP. The model also accounted for the results of two experimental studies involving flexible sensorimotor timing. Neuromodulation of STP provides a unified and biologically plausible mechanism to control the temporal and spatial scales of neural dynamics and sensorimotor behaviors.

Adapting and facilitating responses in mouse somatosensory cortex are dynamic and shaped by experience.

Sensory adaptation is the process whereby brain circuits adjust neuronal activity in response to redundant sensory stimuli. Although sensory adaptation has been extensively studied for individual neurons on timescales of tens of milliseconds to a few seconds, little is known about it over longer timescales or at the population level. We investigated population-level adaptation in the barrel field of the mouse somatosensory cortex (S1BF) using in vivo two-photon calcium imaging and Neuropixels recordings in awake mice. Among stimulus-responsive neurons, we found both adapting and facilitating neurons, which decreased or increased their firing, respectively, with repetitive whisker stimulation. The former outnumbered the latter by 2:1 in layers 2/3 and 4; hence, the overall population response of mouse S1BF was slightly adapting. We also discovered that population adaptation to one stimulus frequency (5 Hz) does not necessarily generalize to a different frequency (12.5 Hz). Moreover, responses of individual neurons to repeated rounds of stimulation over tens of minutes were strikingly heterogeneous and stochastic, such that their adapting or facilitating response profiles were not stable across time. Such representational drift was particularly striking when recording longitudinally across 8-9 days, as adaptation profiles of most whisker-responsive neurons changed drastically from one day to the next. Remarkably, repeated exposure to a familiar stimulus paradoxically shifted the population away from strong adaptation and toward facilitation. Thus, the adapting vs. facilitating response profile of S1BF neurons is not a fixed property of neurons but rather a highly dynamic feature that is shaped by sensory experience across days.

Chronic electrical stimulation homeostatically decreases spontaneous activity, but paradoxically increases evoked network activity.

Neural dynamics generated within cortical networks play a fundamental role in brain function. However, the learning rules that allow recurrent networks to generate functional dynamic regimes, and the degree to which these regimes are themselves plastic, are not known. In this study we examined plasticity of network dynamics in cortical organotypic slices in response to chronic changes in activity. Studies have typically manipulated network activity pharmacologically; we used chronic electrical stimulation to increase activity in in vitro cortical circuits in a more physiological manner. Slices were stimulated with "implanted" electrodes for 4 days. Chronic electrical stimulation or treatment with bicuculline decreased spontaneous activity as predicted by homeostatic learning rules. Paradoxically, however, whereas bicuculline decreased evoked network activity, chronic stimulation actually increased the likelihood that evoked stimulation elicited polysynaptic activity, despite a decrease in evoked monosynaptic strength. Furthermore, there was an inverse correlation between spontaneous and evoked activity, suggesting a homeostatic tradeoff between spontaneous and evoked activity. Within-slice experiments revealed that cells close to the stimulated electrode exhibited more evoked polysynaptic activity and less spontaneous activity than cells close to a control electrode. Collectively, our results establish that chronic stimulation changes the dynamic regimes of networks. In vitro studies of homeostatic plasticity typically lack any external input, and thus neurons must rely on "spontaneous" activity to reach homeostatic "set points." However, in the presence of external input we propose that homeostatic learning rules seem to shift networks from spontaneous to evoked regimes.

Multiplexing working memory and time in the trajectories of neural networks.

Working memory (WM) and timing are generally considered distinct cognitive functions, but similar neural signatures have been implicated in both. To explore the hypothesis that WM and timing may rely on shared neural mechanisms, we used psychophysical tasks that contained either task-irrelevant timing or WM components. In both cases, the task-irrelevant component influenced performance. We then developed recurrent neural network (RNN) simulations that revealed that cue-specific neural sequences, which multiplexed WM and time, emerged as the dominant regime that captured the behavioural findings. During training, RNN dynamics transitioned from low-dimensional ramps to high-dimensional neural sequences, and depending on task requirements, steady-state or ramping activity was also observed. Analysis of RNN structure revealed that neural sequences relied primarily on inhibitory connections, and could survive the deletion of all excitatory-to-excitatory connections. Our results indicate that in some instances WM is encoded in time-varying neural activity because of the importance of predicting when WM will be used.

Improvement of sensory deficits in fragile X mice by increasing cortical interneuron activity after the critical period.

Changes in the function of inhibitory interneurons (INs) during cortical development could contribute to the pathophysiology of neurodevelopmental disorders. Using all-optical in vivo approaches, we find that parvalbumin (PV) INs and their immature precursors are hypoactive and transiently decoupled from excitatory neurons in postnatal mouse somatosensory cortex (S1) of Fmr1 KO mice, a model of fragile X syndrome (FXS). This leads to a loss of parvalbumin INs (PV-INs) in both mice and humans with FXS. Increasing the activity of future PV-INs in neonatal Fmr1 KO mice restores PV-IN density and ameliorates transcriptional dysregulation in S1, but not circuit dysfunction. Critically, administering an allosteric modulator of Kv3.1 channels after the S1 critical period does rescue circuit dynamics and tactile defensiveness. Symptoms in FXS and related disorders could be mitigated by targeting PV-INs.