Functional Integration of Neuronal Precursors in the Adult Murine Piriform Cortex.

The extent of functional maturation and integration of nonproliferative neuronal precursors, becoming neurons in the adult murine piriform cortex, is largely unexplored. We thus questioned whether precursors eventually become equivalent to neighboring principal neurons or whether they represent a novel functional network element. Adult brain neuronal precursors and immature neurons (complex cells) were labeled in transgenic mice (DCX-DsRed and DCX-CreERT2 /flox-EGFP), and their cell fate was characterized with patch clamp experiments and morphometric analysis of axon initial segments. Young (DCX+) complex cells in the piriform cortex of 2- to 4-month-old mice received sparse synaptic input and fired action potentials at low maximal frequency, resembling neonatal principal neurons. Following maturation, the synaptic input detected on older (DCX-) complex cells was larger, but predominantly GABAergic, despite evidence of glutamatergic synaptic contacts. Furthermore, the rheobase current of old complex cells was larger and the maximal firing frequency was lower than those measured in neighboring age-matched principal neurons. The striking differences between principal neurons and complex cells suggest that the latter are a novel type of neuron and new coding element in the adult brain rather than simple addition or replacement for preexisting network components.

The divisive normalization model of V1 neurons: a comprehensive comparison of physiological data and model predictions.

The physiological responses of simple and complex cells in the primary visual cortex (V1) have been studied extensively and modeled at different levels. At the functional level, the divisive normalization model (DNM; Heeger DJ. Vis Neurosci 9: 181-197, 1992) has accounted for a wide range of single-cell recordings in terms of a combination of linear filtering, nonlinear rectification, and divisive normalization. We propose standardizing the formulation of the DNM and implementing it in software that takes static grayscale images as inputs and produces firing rate responses as outputs. We also review a comprehensive suite of 30 empirical phenomena and report a series of simulation experiments that qualitatively replicate dozens of key experiments with a standard parameter set consistent with physiological measurements. This systematic approach identifies novel falsifiable predictions of the DNM. We show how the model simultaneously satisfies the conflicting desiderata of flexibility and falsifiability. Our key idea is that, while adjustable parameters are needed to accommodate the diversity across neurons, they must be fixed for a given individual neuron. This requirement introduces falsifiable constraints when this single neuron is probed with multiple stimuli. We also present mathematical analyses and simulation experiments that explicate some of these constraints.

Auditory and visual cortex of primates: a comparison of two sensory systems.

A comparative view of the brain, comparing related functions across species and sensory systems, offers a number of advantages. In particular, it allows separation of the formal purpose of a model structure from its implementation in specific brains. Models of auditory cortical processing can be conceived by analogy to the visual cortex, incorporating neural mechanisms that are found in both the visual and auditory systems. Examples of such canonical features at the columnar level are direction selectivity, size/bandwidth selectivity, and receptive fields with segregated vs. overlapping ON and OFF subregions. On a larger scale, parallel processing pathways have been envisioned that represent the two main facets of sensory perception: (i) identification of objects; and (ii) processing of space. Expanding this model in terms of sensorimotor integration and control offers an overarching view of cortical function independently of sensory modality.

Equation of motion and general solution for the one-dimensional complex cell response in the signal-tuned approach.

A signal-tuned approach has been recently introduced for modeling stimulus-dependent cortical receptive fields. The approach is based on signal-tuned Gabor functions, which are Gaussian-modulated sinusoids whose parameters are obtained from a "tuning" signal. Given a stimulus to a cell, it is taken as the tuning signal for the Gabor function modeling the cell's receptive field, and the inner product of the stimulus and the stimulus-dependent field produces the cell's response. Here, we derive and solve the equation of motion for the signal-tuned complex cell response r(x,τ), where x and τ are receptive-field parameters: its center, and the delay with which it adapts to a change in input. The motion equation can be mapped onto the Schrödinger equation for a system with time-dependent imaginary mass and time-dependent complex potential, and yields a plane-wave solution and an Airy-packet solution. The plane-wave solution replicates responses previously obtained for temporally modulated and translating signals, and yields responses which seem compatible with apparent-motion effects, when the stimulus is a pair of alternating pulses. The Airy-packet solution can lead to long-range propagating responses.

On the relation between receptive field structure and stimulus selectivity in the tree shrew primary visual cortex.

There are notable differences in functional properties of primary visual cortex (V1) neurons among mammalian species, particularly those concerning the occurrence of simple and complex cells and the generation of orientation selectivity. Here, we present quantitative data on receptive field (RF) structure, response modulation, and orientation tuning for single neurons in V1 of the tree shrew, a close relative of primates. We find that spatial RF subfield segregation, a criterion for identifying simple cells, was exceedingly small in the tree shrew V1. In contrast, many neurons exhibited elevated F1/F0 modulation that is often used as a simple cell marker. This apparent discrepancy can be explained by the robust stimulus polarity preference in tree shrew V1, which inflates F1/F0 ratio values. RF structure mapped with sparse-noise-which is spatially restricted and emphasizes thalamo-cortical feed-forward inputs-appeared unrelated to orientation selectivity. However, RF structure mapped using the Hartley subspace stimulus-which covers a large area of the visual field and recruits considerable intracortical processing-did predict orientation preference. Our findings reveal a number of striking similarities in V1 functional organization between tree shrews and primates, emphasizing the important role of intracortical recurrent processing in shaping V1 response properties in these species.

Optimal disparity estimation in natural stereo images.

A great challenge of systems neuroscience is to understand the computations that underlie perceptual constancies, the ability to represent behaviorally relevant stimulus properties as constant even when irrelevant stimulus properties vary. As signals proceed through the visual system, neural states become more selective for properties of the environment, and more invariant to irrelevant features of the retinal images. Here, we describe a method for determining the computations that perform these transformations optimally, and apply it to the specific computational task of estimating a powerful depth cue: binocular disparity. We simultaneously determine the optimal receptive field population for encoding natural stereo images of locally planar surfaces and the optimal nonlinear units for decoding the population responses into estimates of disparity. The optimal processing predicts well-established properties of neurons in cortex. Estimation performance parallels important aspects of human performance. Thus, by analyzing the photoreceptor responses to natural images, we provide a normative account of the neurophysiology and psychophysics of absolute disparity processing. Critically, the optimal processing rules are not arbitrarily chosen to match the properties of neurophysiological processing, nor are they fit to match behavioral performance. Rather, they are dictated by the task-relevant statistical properties of complex natural stimuli. Our approach reveals how selective invariant tuning-especially for properties not trivially available in the retinal images-could be implemented in neural systems to maximize performance in particular tasks.

Simple and complex cells revisited: toward a selectivity-invariance model of object recognition.

This paper presents a theoretical perspective on modeling ventral stream processing by revisiting the computational abstraction of simple and complex cells. In parallel to David Marr's vision theory, we organize the new perspective into three levels. At the computational level, we abstract simple and complex cells into space partitioning and composition in a topological space based on the redundancy exploitation hypothesis of Horace Barlow. At the algorithmic level, we present a hierarchical extension of sparse coding by exploiting the manifold constraint in high-dimensional space (i.e., the blessing of dimensionality). The resulting over-parameterized models for object recognition differ from existing hierarchical models by disentangling the objectives of selectivity and invariance computation. It is possible to interpret our hierarchical construction as a computational implementation of cortically local subspace untangling for object recognition and face representation, which are closely related to exemplar-based and axis-based coding in the medial temporal lobe. At the implementation level, we briefly discuss two possible implementations based on asymmetric sparse autoencoders and divergent spiking neural networks.

The neurons in mouse V1 show different degrees of spatial clustering.

Higher mammals' primary visual cortex exhibits columnar organization, where neurons with similar response preferences are clustered. In contrast, rodents are presumed to lack this fine-scale organization; their neurons appear to be randomly arranged, described as a salt-and-pepper map. However, recent studies suggested a weak but significant spatial clustering of tuning in the salt-and-pepper map, similar to columnar organization. Thus, the salt-and-pepper map possesses the characteristics of both columnar organization and random arrangement. This raises the question about whether this mixed organization is attributed to different types of neurons. Here, we examined the tuning of primary visual cortical neurons in awake mice with a two-photon calcium imaging dataset, which were released by Allen Institute MindScope Program. First, we demonstrated that neurons with similar response preferences were clustered by showing that neighboring neurons tended to have similar orientation and temporal frequency preferences. Then, we compared the clustering of tuning between simple cells and complex cells and found the clustering of tuning among simple cells was significantly more prominent than that among complex cells. Furthermore, the simple/complex cell classification correlated with the stability of neuronal response. Neurons with stable responses were arranged independent of their tuning similarity, whereas unstable neurons were clustered according to their tuning similarity. These findings might represent a balance between efficiency and robustness: relatively independent tuning among stable neurons represents visual information efficiently, whereas unstable neurons with similar response preferences are clustered to obtain a robust representation with population codes.

Sparse Functional Identification of Complex Cells from Spike Times and the Decoding of Visual Stimuli.

We investigate the sparse functional identification of complex cells and the decoding of spatio-temporal visual stimuli encoded by an ensemble of complex cells. The reconstruction algorithm is formulated as a rank minimization problem that significantly reduces the number of sampling measurements (spikes) required for decoding. We also establish the duality between sparse decoding and functional identification and provide algorithms for identification of low-rank dendritic stimulus processors. The duality enables us to efficiently evaluate our functional identification algorithms by reconstructing novel stimuli in the input space. Finally, we demonstrate that our identification algorithms substantially outperform the generalized quadratic model, the nonlinear input model, and the widely used spike-triggered covariance algorithm.

The spatial summation characteristics of three categories of V1 neurons differing in non-classical receptive field modulation properties.

The spatial summation of excitation and inhibition determines the final output of neurons in the cat V1. To characterize the spatial extent of the excitatory classical receptive field (CRF) and inhibitory non-classical receptive field (nCRF) areas, we examined the spatial summation properties of 169 neurons in cat V1 at high (20-90%) and low (5-15%) stimulus contrasts. Three categories were classified based on the difference in the contrast dependency of the surround suppression. We discovered that the three categories significantly differed in CRF size, peak firing rate, and the proportion of simple/complex cell number. The classification of simple and complex cells was determined at both high and low contrasts. While the majority of V1 neurons had stable modulation ratios in their responses, 10 cells (6.2%) in our sample crossed the classification boundary under different stimulus contrasts. No significant difference was found in the size of the CRF between simple and complex cells. Further comparisons in each category determined that the CRFs for complex cells were significantly larger than those for simple cells in category type I neurons, with no significant differences between simple and complex cells in category type II and type III neurons. In addition, complex cells have higher peak firing rates than simple cells.

Development of maps of simple and complex cells in the primary visual cortex.

Hubel and Wiesel (1962) classified primary visual cortex (V1) neurons as either simple, with responses modulated by the spatial phase of a sine grating, or complex, i.e., largely phase invariant. Much progress has been made in understanding how simple-cells develop, and there are now detailed computational models establishing how they can form topographic maps ordered by orientation preference. There are also models of how complex cells can develop using outputs from simple cells with different phase preferences, but no model of how a topographic orientation map of complex cells could be formed based on the actual connectivity patterns found in V1. Addressing this question is important, because the majority of existing developmental models of simple-cell maps group neurons selective to similar spatial phases together, which is contrary to experimental evidence, and makes it difficult to construct complex cells. Overcoming this limitation is not trivial, because mechanisms responsible for map development drive receptive fields (RF) of nearby neurons to be highly correlated, while co-oriented RFs of opposite phases are anti-correlated. In this work, we model V1 as two topographically organized sheets representing cortical layer 4 and 2/3. Only layer 4 receives direct thalamic input. Both sheets are connected with narrow feed-forward and feedback connectivity. Only layer 2/3 contains strong long-range lateral connectivity, in line with current anatomical findings. Initially all weights in the model are random, and each is modified via a Hebbian learning rule. The model develops smooth, matching, orientation preference maps in both sheets. Layer 4 units become simple cells, with phase preference arranged randomly, while those in layer 2/3 are primarily complex cells. To our knowledge this model is the first explaining how simple cells can develop with random phase preference, and how maps of complex cells can develop, using only realistic patterns of connectivity.