Integrating EM and Patch-seq data: Synaptic connectivity and target specificity of predicted Sst transcriptomic types.

Neural circuit function is shaped both by the cell types that comprise the circuit and the connections between those cell types 1 . Neural cell types have previously been defined by morphology 2, 3 , electrophysiology 4, 5 , transcriptomic expression 6-8 , connectivity 9-13 , or even a combination of such modalities 14-16 . More recently, the Patch-seq technique has enabled the characterization of morphology (M), electrophysiology (E), and transcriptomic (T) properties from individual cells 17-20 . Using this technique, these properties were integrated to define 28, inhibitory multimodal, MET-types in mouse primary visual cortex 21 . It is unknown how these MET-types connect within the broader cortical circuitry however. Here we show that we can predict the MET-type identity of inhibitory cells within a large-scale electron microscopy (EM) dataset and these MET-types have distinct ultrastructural features and synapse connectivity patterns. We found that EM Martinotti cells, a well defined morphological cell type 22, 23 known to be Somatostatin positive (Sst+) 24, 25 , were successfully predicted to belong to Sst+ MET-types. Each identified MET-type had distinct axon myelination patterns and synapsed onto specific excitatory targets. Our results demonstrate that morphological features can be used to link cell type identities across imaging modalities, which enables further comparison of connectivity in relation to transcriptomic or electrophysiological properties. Furthermore, our results show that MET-types have distinct connectivity patterns, supporting the use of MET-types and connectivity to meaningfully define cell types.

Spontaneous eye movements in goldfish: oculomotor integrator performance, plasticity, and dependence on visual feedback.

To quantify performance of the goldfish oculomotor neural integrator and determine its dependence on visual feedback, we measured the relationship between eye drift-velocity and position during spontaneous gaze fixations in the light and in the dark. In the light, drift-velocities were typically less than 1 deg/s, similar to those observed in humans. During brief periods in darkness, drift-velocities were only slightly larger, but showed greater variance. One hour in darkness degraded fixation-holding performance. These findings suggest that while visual feedback is not essential for online fixation stability, it may be used to tune the mechanism of persistent neural activity in the oculomotor integrator.

Robust persistent neural activity in a model integrator with multiple hysteretic dendrites per neuron.

Short-term memory is often correlated with persistent changes in neuronal firing rates in response to transient inputs. We model the persistent maintenance of an analog eye position signal by an oculomotor neural integrator receiving transient eye movement commands. Previous models of this network rely on precisely tuned positive feedback with <1% tolerance to mistuning, or use neurons that exhibit large discontinuities in firing rate with small changes in eye position. We show analytically how using neurons with multiple bistable dendritic compartments can enhance the robustness of eye fixations to mistuning while reproducing the approximately linear and continuous relationship between neuronal firing rates and eye position, and the dependence of neuron pair firing rate relationships on the direction of the previous saccade. The response of the model to continuously varying inputs makes testable predictions for the performance of the vestibuloocular reflex. Our results suggest that dendritic bistability could stabilize the persistent neural activity observed in working memory systems.

Linear regression of eye velocity on eye position and head velocity suggests a common oculomotor neural integrator.

The oculomotor system produces eye-position signals during fixations and head movements by integrating velocity-coded saccadic and vestibular inputs. A previous analysis of nucleus prepositus hypoglossi (nph) lesions in monkeys found that the integration time constant for maintaining fixations decreased, while that for the vestibulo-ocular reflex (VOR) did not. On this basis, it was concluded that saccadic inputs are integrated by the nph, but that the vestibular inputs are integrated elsewhere. We re-analyze the data from which this conclusion was drawn by performing a linear regression of eye velocity on eye position and head velocity to derive the time constant and velocity bias of an imperfect oculomotor neural integrator. The velocity-position regression procedure reveals that the integration time constants for both VOR and saccades decrease in tandem with consecutive nph lesions, consistent with the hypothesis of a single common integrator. The previous evaluation of the integrator time constant relied upon fitting methods that are prone to error in the presence of velocity bias and saccades. The algorithm used to evaluate imperfect fixations in the dark did not account for the nonzero null position of the eyes associated with velocity bias. The phase-shift analysis used in evaluating the response to sinusoidal vestibular input neglects the effect of saccadic resets of eye position on intersaccadic eye velocity, resulting in gross underestimates of the imperfections in integration during VOR. The linear regression method presented here is valid for both fixation and low head velocity VOR data and is easy to implement.

In vivo intracellular recording and perturbation of persistent activity in a neural integrator.

To investigate the mechanisms of persistent neural activity, we obtained in vivo intracellular recordings from neurons in an oculomotor neural integrator of the goldfish during spontaneous saccades and fixations. Persistent changes in firing rate following saccades were associated with step changes in interspike membrane potential that were correlated with changes in eye position. Perturbation of persistent activity with brief intracellular current pulses designed to mimic saccadic input only induced transient changes of firing rate and membrane potential. When neurons were hyperpolarized below action potential threshold, position-correlated step changes in membrane potential remained. Membrane potential fluctuations were greater during more depolarized steps. These results suggest that sustained changes in firing rate are supported not by either membrane multistability or changes in pacemaker currents, but rather by persistent changes in the rate or amplitude of synaptic inputs.

The autapse: a simple illustration of short-term analog memory storage by tuned synaptic feedback.

According to a popular hypothesis, short-term memories are stored as persistent neural activity maintained by synaptic feedback loops. This hypothesis has been formulated mathematically in a number of recurrent network models. Here we study an abstraction of these models, a single neuron with a synapse onto itself, or autapse. This abstraction cannot simulate the way in which persistent activity patterns are distributed over neural populations in the brain. However, with proper tuning of parameters, it does reproduce the continuously graded, or analog, nature of many examples of persistent activity. The conditions for tuning are derived for the dynamics of a conductance-based model neuron with a slow excitatory autapse. The derivation uses the method of averaging to approximate the spiking model with a nonspiking, reduced model. Short-term analog memory storage is possible if the reduced model is approximately linear and if its feedforward bias and autapse strength are precisely tuned.

Anatomy and discharge properties of pre-motor neurons in the goldfish medulla that have eye-position signals during fixations.

Previous work in goldfish has suggested that the oculomotor velocity-to-position neural integrator for horizontal eye movements may be confined bilaterally to a distinct group of medullary neurons that show an eye-position signal. To establish this localization, the anatomy and discharge properties of these position neurons were characterized with single-cell Neurobiotin labeling and extracellular recording in awake goldfish while monitoring eye movements with the scleral search-coil method. All labeled somata (n = 9) were identified within a region of a medially located column of the inferior reticular formation that was approximately 350 microm in length, approximately 250 microm in depth, and approximately 125 microm in width. The dendrites of position neurons arborized over a wide extent of the ventral half of the medulla with especially heavy ramification in the initial 500 microm rostral of cell somata (n = 9). The axons either followed a well-defined ventral pathway toward the ipsilateral abducens (n = 4) or crossed the midline (n = 2) and projected toward the contralateral group of position neurons and the contralateral abducens. A mapping of the somatic region using extracellular single unit recording revealed that position neurons (n > 120) were the dominant eye-movement-related cell type in this area. Position neurons did not discharge below a threshold value of horizontal fixation position of the ipsilateral eye. Above this threshold, firing rates increased linearly with increasing temporal position [mean position sensitivity = 2.8 (spikes/s)/ degrees, n = 44]. For a given fixation position, average rates of firing were higher after a temporal saccade than a nasal one (n = 19/19); the magnitude of this hysteresis increased with increasing position sensitivity. Transitions in firing rate accompanying temporal saccades were overshooting (n = 43/44), beginning, on average, 17.2 ms before saccade onset (n = 17). Peak firing rate change accompanying temporal saccades was correlated with eye velocity (n = 36/41). The anatomical findings demonstrate that goldfish medullary position neurons have somata that are isolated from other parts of the oculomotor system, have dendritic fields overlapping with axonal terminations of neurons with velocity signals, and have axons that are capable of relaying commands to the abducens. The physiological findings demonstrate that the signals carried by position neurons could be used by motoneurons to set the fixation position of the eye. These results are consistent with a role for position neurons as elements of the velocity-to-position neural integrator for horizontal eye movements.

Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit.

Digital circuits such as the flip-flop use feedback to achieve multistability and nonlinearity to restore signals to logical levels, for example 0 and 1. Analogue feedback circuits are generally designed to operate linearly, so that signals are over a range, and the response is unique. By contrast, the response of cortical circuits to sensory stimulation can be both multistable and graded. We propose that the neocortex combines digital selection of an active set of neurons with analogue response by dynamically varying the positive feedback inherent in its recurrent connections. Strong positive feedback causes differential instabilities that drive the selection of a set of active neurons under the constraints embedded in the synaptic weights. Once selected, the active neurons generate weaker, stable feedback that provides analogue amplification of the input. Here we present our model of cortical processing as an electronic circuit that emulates this hybrid operation, and so is able to perform computations that are similar to stimulus selection, gain modulation and spatiotemporal pattern generation in the neocortex.

Stability of the memory of eye position in a recurrent network of conductance-based model neurons.

Studies of the neural correlates of short-term memory in a wide variety of brain areas have found that transient inputs can cause persistent changes in rates of action potential firing, through a mechanism that remains unknown. In a premotor area that is responsible for holding the eyes still during fixation, persistent neural firing encodes the angular position of the eyes in a characteristic manner: below a threshold position the neuron is silent, and above it the firing rate is linearly related to position. Both the threshold and linear slope vary from neuron to neuron. We have reproduced this behavior in a biophysically plausible network model. Persistence depends on precise tuning of the strength of synaptic feedback, and a relatively long synaptic time constant improves the robustness to mistuning.

Cognition. The manifold ways of perception.

One of the great puzzles of visual perception is how an image that is in perpetual flux can still be seen by the observer as the same object. In an informative Perspective, Seung and Lee explain the mathematical intricacies of two new algorithms for modeling the variability of perceptual stimuli and other types of high-dimensional data (Tenenbaum et al., and Roweis and Saul).

Learning the parts of objects by non-negative matrix factorization.

Is perception of the whole based on perception of its parts? There is psychological and physiological evidence for parts-based representations in the brain, and certain computational theories of object recognition rely on such representations. But little is known about how brains or computers might learn the parts of objects. Here we demonstrate an algorithm for non-negative matrix factorization that is able to learn parts of faces and semantic features of text. This is in contrast to other methods, such as principal components analysis and vector quantization, that learn holistic, not parts-based, representations. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. When non-negative matrix factorization is implemented as a neural network, parts-based representations emerge by virtue of two properties: the firing rates of neurons are never negative and synaptic strengths do not change sign.

How the brain keeps the eyes still.

The brain can hold the eyes still because it stores a memory of eye position. The brain's memory of horizontal eye position appears to be represented by persistent neural activity in a network known as the neural integrator, which is localized in the brainstem and cerebellum. Existing experimental data are reinterpreted as evidence for an "attractor hypothesis" that the persistent patterns of activity observed in this network form an attractive line of fixed points in its state space. Line attractor dynamics can be produced in linear or nonlinear neural networks by learning mechanisms that precisely tune positive feedback.

Simple models for reading neuronal population codes.

In many neural systems, sensory information is distributed throughout a population of neurons. We study simple neural network models for extracting this information. The inputs to the networks are the stochastic responses of a population of sensory neurons tuned to directional stimuli. The performance of each network model in psychophysical tasks is compared with that of the optimal maximum likelihood procedure. As a model of direction estimation in two dimensions, we consider a linear network that computes a population vector. Its performance depends on the width of the population tuning curves and is maximal for width, which increases with the level of background activity. Although for narrowly tuned neurons the performance of the population vector is significantly inferior to that of maximum likelihood estimation, the difference between the two is small when the tuning is broad. For direction discrimination, we consider two models: a perceptron with fully adaptive weights and a network made by adding an adaptive second layer to the population vector network. We calculate the error rates of these networks after exhaustive training to a particular direction. By testing on the full range of possible directions, the extent of transfer of training to novel stimuli can be calculated. It is found that for threshold linear networks the transfer of perceptual learning is nonmonotonic. Although performance deteriorates away from the training stimulus, it peaks again at an intermediate angle. This nonmonotonicity provides an important psychophysical test of these models.