A Lyapunov theory demonstrating a fundamental limit on the speed of systems consolidation

The nervous system reorganizes memories from an early site to a late site, a commonly observed feature of learning and memory systems known as systems consolidation. Previous work has suggested learning rules by which consolidation may occur. Here, we provide conditions under which such rules are guaranteed to lead to stable convergence of learning and consolidation. We use the theory of Lyapunov functions, which enforces stability by requiring learning rules to decrease an energy-like (Lyapunov) function. We present the theory in the context of a simple circuit architecture motivated by classic models of learning in systems consolidation mediated by the cerebellum. Stability is only guaranteed if the learning rate in the late stage is not faster than the learning rate in the early stage. Further, the slower the learning rate at the late stage, the larger the perturbation the system can tolerate with a guarantee of stability. We provide intuition for this result by mapping the consolidation model to a damped driven oscillator system, and showing that the ratio of early-to late-stage learning rates in the consolidation model can be directly identified with the (square of the) oscillator's damping ratio. This work suggests the power of the Lyapunov approach to provide constraints on nervous system function.

Cyclic structure with cellular precision in a vertebrate sensorimotor neural circuit

Neuronal wiring diagrams reconstructed by electron microscopy1,2,3,4,5 pose new questions about the organization of nervous systems following the time-honored tradition of cross-species comparisons.6,7 The C. elegans connectome has been conceptualized as a sensorimotor circuit that is approximately feedforward,8,9,10,11 starting from sensory neurons proceeding to interneurons and ending with motor neurons. Overrepresentation of a 3-cell motif often known as the "feedforward loop" has provided further evidence for feedforwardness.10,12 Here, we contrast with another sensorimotor wiring diagram that was recently reconstructed from a larval zebrafish brainstem.13 We show that the 3-cycle, another 3-cell motif, is highly overrepresented in the oculomotor module of this wiring diagram. This is a first for any neuronal wiring diagram reconstructed by electron microscopy, whether invertebrate12,14 or mammalian.15,16,17 The 3-cycle of cells is "aligned" with a 3-cycle of neuronal groups in a stochastic block model (SBM)18 of the oculomotor module. However, the cellular cycles exhibit more specificity than can be explained by the group cycles-recurrence to the same neuron is surprisingly common. Cyclic structure could be relevant for theories of oculomotor function that depend on recurrent connectivity. The cyclic structure coexists with the classic vestibulo-ocular reflex arc for horizontal eye movements,19 and could be relevant for recurrent network models of temporal integration by the oculomotor system.20,21.

Oculomotor plant and neural dynamics suggest gaze control requires integration on distributed timescales

A fundamental principle of biological motor control is that the neural commands driving movement must conform to the response properties of the motor plants they control. In the oculomotor system, characterizations of oculomotor plant dynamics traditionally supported models in which the plant responds to neural drive to extraocular muscles on exclusively short, subsecond timescales. These models predict that the stabilization of gaze during fixations between saccades requires neural drive that approximates eye position on longer timescales and is generated through the temporal integration of brief eye velocity-encoding signals that cause saccades. However, recent measurements of oculomotor plant behaviour have revealed responses on longer timescales. Furthermore, measurements of firing patterns in the oculomotor integrator have revealed a more complex encoding of eye movement dynamics. Yet, the link between these observations has remained unclear. Here we use measurements from the larval zebrafish to link dynamics in the oculomotor plant to dynamics in the neural integrator. The oculomotor plant in both anaesthetized and awake larval zebrafish was characterized by a broad distribution of response timescales, including those much longer than 1 s. Analysis of the firing patterns of oculomotor integrator neurons, which exhibited a broadly distributed range of decay time constants, demonstrates the sufficiency of this activity for stabilizing gaze given an oculomotor plant with distributed response timescales. This work suggests that leaky integration on multiple, distributed timescales by the oculomotor integrator reflects an inverse model for generating oculomotor commands, and that multi-timescale dynamics may be a general feature of motor circuitry. KEY POINTS: Recent observations of oculomotor plant response properties and neural activity across the oculomotor system have called into question classical formulations of both the oculomotor plant and the oculomotor integrator. Here we use measurements from new and published experiments in the larval zebrafish together with modelling to reconcile recent oculomotor plant observations with oculomotor integrator function. We developed computational techniques to characterize oculomotor plant responses over several seconds in awake animals, demonstrating that long timescale responses seen in anaesthetized animals extend to the awake state. Analysis of firing patterns of oculomotor integrator neurons demonstrates the sufficiency of this activity for stabilizing gaze given an oculomotor plant with multiple, distributed response timescales. Our results support a formulation of gaze stabilization by the oculomotor system in which commands for stabilizing gaze are generated through integration on multiple, distributed timescales.

Seizures initiate in zones of relative hyperexcitation in a zebrafish epilepsy model

Seizures are thought to arise from an imbalance of excitatory and inhibitory neuronal activity. While most classical studies suggest excessive excitatory neural activity plays a generative role, some recent findings challenge this view and instead argue that excessive activity in inhibitory neurons initiates seizures. We investigated this question of imbalance in a zebrafish seizure model with two-photon imaging of excitatory and inhibitory neuronal activity throughout the brain using a nuclear-localized calcium sensor. We found that seizures consistently initiated in circumscribed zones of the midbrain before propagating to other brain regions. Excitatory neurons were both more prevalent and more likely to be recruited than inhibitory neurons in initiation as compared with propagation zones. These findings support a mechanistic picture whereby seizures initiate in a region of hyper-excitation, then propagate more broadly once inhibitory restraint in the surround is overcome.

Ramp-to-threshold dynamics in a hindbrain population controls the timing of spontaneous saccades

Organisms have the capacity to make decisions based solely on internal drives. However, it is unclear how neural circuits form decisions in the absence of sensory stimuli. Here we provide a comprehensive map of the activity patterns underlying the generation of saccades made in the absence of visual stimuli. We perform calcium imaging in the larval zebrafish to discover a range of responses surrounding spontaneous saccades, from cells that display tonic discharge only during fixations to neurons whose activity rises in advance of saccades by multiple seconds. When we lesion cells in these populations we find that ablation of neurons with pre-saccadic rise delays saccade initiation. We analyze spontaneous saccade initiation using a ramp-to-threshold model and are able to predict the times of upcoming saccades using pre-saccadic activity. These findings suggest that ramping of neuronal activity to a bound is a critical component of self-initiated saccadic movements.

Electron Microscopic Reconstruction of Functionally Identified Cells in a Neural Integrator

Neural integrators are involved in a variety of sensorimotor and cognitive behaviors. The oculomotor system contains a simple example, a hindbrain neural circuit that takes velocity signals as inputs and temporally integrates them to control eye position. Here we investigated the structural underpinnings of temporal integration in the larval zebrafish by first identifying integrator neurons using two-photon calcium imaging and then reconstructing the same neurons through serial electron microscopic analysis. Integrator neurons were identified as those neurons with activities highly correlated with eye position during spontaneous eye movements. Three morphological classes of neurons were observed: ipsilaterally projecting neurons located medially, contralaterally projecting neurons located more laterally, and a population at the extreme lateral edge of the hindbrain for which we were not able to identify axons. Based on their somatic locations, we inferred that neurons with only ipsilaterally projecting axons are glutamatergic, whereas neurons with only contralaterally projecting axons are largely GABAergic. Dendritic and synaptic organization of the ipsilaterally projecting neurons suggests a broad sampling from inputs on the ipsilateral side. We also observed the first conclusive evidence of synapses between integrator neurons, which have long been hypothesized by recurrent network models of integration via positive feedback.

Spatial patterns of persistent neural activity vary with the behavioral context of short-term memory

A short-term memory can be evoked by different inputs and control separate targets in different behavioral contexts. To address the circuit mechanisms underlying context-dependent memory function, we determined through optical imaging how memory is encoded at the whole-network level in two behavioral settings. Persistent neural activity maintaining a memory of desired eye position was imaged throughout the oculomotor integrator after saccadic or optokinetic stimulation. While eye position was encoded by the amplitude of network activity, the spatial patterns of firing were context dependent: cells located caudally generally were most persistent following saccadic input, whereas cells located rostrally were most persistent following optokinetic input. To explain these data, we computationally identified four independent modes of network activity and found these were differentially accessed by saccadic and optokinetic inputs. These results show how a circuit can simultaneously encode memory value and behavioral context, respectively, in its amplitude and spatial pattern of persistent firing.

A modeling framework for deriving the structural and functional architecture of a short-term memory microcircuit

Although many studies have identified neural correlates of memory, relatively little is known about the circuit properties connecting single-neuron physiology to behavior. Here we developed a modeling framework to bridge this gap and identify circuit interactions capable of maintaining short-term memory. Unlike typical studies that construct a phenomenological model and test whether it reproduces select aspects of neuronal data, we directly fit the synaptic connectivity of an oculomotor memory circuit to a broad range of anatomical, electrophysiological, and behavioral data. Simultaneous fits to all data, combined with sensitivity analyses, revealed complementary roles of synaptic and neuronal recruitment thresholds in providing the nonlinear interactions required to generate the observed circuit behavior. This work provides a methodology for identifying the cellular and synaptic mechanisms underlying short-term memory and demonstrates how the anatomical structure of a circuit may belie its functional organization.