A reaction-diffusion model of cholinergic retinal waves

Unsupervised learning on spontaneous retinal activity leads to efficient neural representation geometry

Prior to the onset of vision, neurons in the developing mammalian retina spontaneously fire in correlated activity patterns known as retinal waves. Experimental evidence suggests that retinal waves strongly influence the emergence of sensory representations before visual experience. We aim to model this early stage of functional development by using movies of neurally active developing retinas as pre-training data for neural networks. Specifically, we pre-train a ResNet-18 with an unsupervised contrastive learning objective (SimCLR) on both simulated and experimentally-obtained movies of retinal waves, then evaluate its performance on image classification tasks. We find that pre-training on retinal waves significantly improves performance on tasks that test object invariance to spatial translation, while slightly improving performance on more complex tasks like image classification. Notably, these performance boosts are realized on held-out natural images even though the pre-training procedure does not include any natural image data. We then propose a geometrical explanation for the increase in network performance, namely that the spatiotemporal characteristics of retinal waves facilitate the formation of separable feature representations. In particular, we demonstrate that networks pre-trained on retinal waves are more effective at separating image manifolds than randomly initialized networks, especially for manifolds defined by sets of spatial translations. These findings indicate that the broad spatiotemporal properties of retinal waves prepare networks for higher order feature extraction.

Neural field models for latent state inference: Application to large-scale neuronal recordings

Large-scale neural recording methods now allow us to observe large populations of identified single neurons simultaneously, opening a window into neural population dynamics in living organisms. However, distilling such large-scale recordings to build theories of emergent collective dynamics remains a fundamental statistical challenge. The neural field models of Wilson, Cowan, and colleagues remain the mainstay of mathematical population modeling owing to their interpretable, mechanistic parameters and amenability to mathematical analysis. Inspired by recent advances in biochemical modeling, we develop a method based on moment closure to interpret neural field models as latent state-space point-process models, making them amenable to statistical inference. With this approach we can infer the intrinsic states of neurons, such as active and refractory, solely from spiking activity in large populations. After validating this approach with synthetic data, we apply it to high-density recordings of spiking activity in the developing mouse retina. This confirms the essential role of a long lasting refractory state in shaping spatiotemporal properties of neonatal retinal waves. This conceptual and methodological advance opens up new theoretical connections between mathematical theory and point-process state-space models in neural data analysis.

Developing statistical tools to connect single-neuron activity to emergent collective dynamics is vital for building interpretable models of neural activity. Neural field models relate single-neuron activity to emergent collective dynamics in neural populations, but integrating them with data remains challenging. Recently, latent state-space models have emerged as a powerful tool for constructing phenomenological models of neural population activity. The advent of high-density multi-electrode array recordings now enables us to examine large-scale collective neural activity. We show that classical neural field approaches can yield latent state-space equations and demonstrate that this enables inference of the intrinsic states of neurons from recorded spike trains in large populations.

Gap junctions set the speed and nucleation rate of stage I retinal waves

Spontaneous waves in the developing retina are essential in the formation of the retinotopic mapping in the visual system. From experiments in rabbits, it is known that the earliest type of retinal waves (stage I) is nucleated spontaneously, propagates at a speed of 451±91 μm/sec and relies on gap junction coupling between ganglion cells. Because gap junctions (electrical synapses) have short integration times, it has been argued that they cannot set the low speed of stage I retinal waves. Here, we present a theoretical study of a two-dimensional neural network of the ganglion cell layer with gap junction coupling and intrinsic noise. We demonstrate that this model can explain observed nucleation rates as well as the comparatively slow propagation speed of the waves. From the interaction between two coupled neurons, we estimate the wave speed in the model network. Furthermore, using simulations of small networks of neurons (N≤260), we estimate the nucleation rate in the form of an Arrhenius escape rate. These results allow for informed simulations of a realistically sized network, yielding values of the gap junction coupling and the intrinsic noise level that are in a physiologically plausible range.

A biophysical model explains the spontaneous bursting behavior in the developing retina

During early development, waves of activity propagate across the retina and play a key role in the proper wiring of the early visual system. During a particular phase of the retina development (stage II) these waves are triggered by a transient network of neurons, called Starburst Amacrine Cells (SACs), showing a bursting activity which disappears upon further maturation. The underlying mechanisms of the spontaneous bursting and the transient excitability of immature SACs are not completely clear yet. While several models have attempted to reproduce retinal waves, none of them is able to mimic the rhythmic autonomous bursting of individual SACs and reveal how these cells change their intrinsic properties during development. Here, we introduce a mathematical model, grounded on biophysics, which enables us to reproduce the bursting activity of SACs and to propose a plausible, generic and robust, mechanism that generates it. The core parameters controlling repetitive firing are fast depolarizing V-gated calcium channels and hyperpolarizing V-gated potassium channels. The quiescent phase of bursting is controlled by a slow after hyperpolarization (sAHP), mediated by calcium-dependent potassium channels. Based on a bifurcation analysis we show how biophysical parameters, regulating calcium and potassium activity, control the spontaneously occurring fast oscillatory activity followed by long refractory periods in individual SACs. We make a testable experimental prediction on the role of voltage-dependent potassium channels on the excitability properties of SACs and on the evolution of this excitability along development. We also propose an explanation on how SACs can exhibit a large variability in their bursting periods, as observed experimentally within a SACs network as well as across different species, yet based on a simple, unique, mechanism. As we discuss, these observations at the cellular level have a deep impact on the retinal waves description.

Theoretical Models of Neural Development

Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.

The use of in vivo, ex vivo, in vitro, computational models and volunteer studies in vision research and therapy, and their contribution to the Three Rs

Much is known about mammalian vision, and considerable progress has been achieved in treating many vision disorders, especially those due to changes in the eye, by using various therapeutic methods, including stem cell and gene therapy. While cells and tissues from the main parts of the eye and the visual cortex (VC) can be maintained in culture, and many computer models exist, the current non-animal approaches are severely limiting in the study of visual perception and retinotopic imaging. Some of the early studies with cats and non-human primates (NHPs) are controversial for animal welfare reasons and are of questionable clinical relevance, particularly with respect to the treatment of amblyopia. More recently, the UK Home Office records have shown that attention is now more focused on rodents, especially the mouse. This is likely to be due to the perceived need for genetically-altered animals, rather than to knowledge of the similarities and differences of vision in cats, NHPs and rodents, and the fact that the same techniques can be used for all of the species. We discuss the advantages and limitations of animal and non-animal methods for vision research, and assess their relative contributions to basic knowledge and clinical practice, as well as outlining the opportunities they offer for implementing the principles of the Three Rs (Replacement, Reduction and Refinement).