Bayesian inference for biophysical neuron models enables stimulus optimization for retinal neuroprosthetics

Avoidance of axonal stimulation with sinusoidal epiretinal stimulation

Objective.Neuromodulation, particularly electrical stimulation, necessitates high spatial resolution to achieve artificial vision with high acuity. In epiretinal implants, this is hindered by the undesired activation of distal axons. Here, we investigate focal and axonal activation of retinal ganglion cells (RGCs) in epiretinal configuration for different sinusoidal stimulation frequencies.Approach.RGC responses to epiretinal sinusoidal stimulation at frequencies between 40 and 100 Hz were tested inex-vivophotoreceptor degenerated (rd10) isolated retinae. Experiments were conducted using a high-density CMOS-based microelectrode array, which allows to localize RGC cell bodies and axons at high spatial resolution.Main results.We report current and charge density thresholds for focal and distal axon activation at stimulation frequencies of 40, 60, 80, and 100 Hz for an electrode size with an effective area of 0.01 mm2. Activation of distal axons is avoided up to a stimulation amplitude of 0.23µA (corresponding to 17.3µC cm-2) at 40 Hz and up to a stimulation amplitude of 0.28µA (14.8µC cm-2) at 60 Hz. The threshold ratio between focal and axonal activation increases from 1.1 for 100 Hz up to 1.6 for 60 Hz, while at 40 Hz stimulation frequency, almost no axonal responses were detected in the tested intensity range. With the use of synaptic blockers, we demonstrate the underlying direct activation mechanism of the ganglion cells. Finally, using high-resolution electrical imaging and label-free electrophysiological axon tracking, we demonstrate the extent of activation in axon bundles.Significance.Our results can be exploited to define a spatially selective stimulation strategy avoiding axonal activation in future retinal implants, thereby solving one of the major limitations of artificial vision. The results may be extended to other fields of neuroprosthetics to achieve selective focal electrical stimulation.

Controlling morpho-electrophysiological variability of neurons with detailed biophysical models

Variability, which is known to be a universal feature among biological units such as neuronal cells, holds significant importance, as, for example, it enables a robust encoding of a high volume of information in neuronal circuits and prevents hypersynchronizations. While most computational studies on electrophysiological variability in neuronal circuits were done with single-compartment neuron models, we instead focus on the variability of detailed biophysical models of neuron multi-compartmental morphologies. We leverage a Markov chain Monte Carlo method to generate populations of electrical models reproducing the variability of experimental recordings while being compatible with a set of morphologies to faithfully represent specifi morpho-electrical type. We demonstrate our approach on layer 5 pyramidal cells and study the morpho-electrical variability and in particular, find that morphological variability alone is insufficient to reproduce electrical variability. Overall, this approach provides a strong statistical basis to create detailed models of neurons with controlled variability.

Simulation-based inference for efficient identification of generative models in computational connectomics

Recent advances in connectomics research enable the acquisition of increasing amounts of data about the connectivity patterns of neurons. How can we use this wealth of data to efficiently derive and test hypotheses about the principles underlying these patterns? A common approach is to simulate neuronal networks using a hypothesized wiring rule in a generative model and to compare the resulting synthetic data with empirical data. However, most wiring rules have at least some free parameters, and identifying parameters that reproduce empirical data can be challenging as it often requires manual parameter tuning. Here, we propose to use simulation-based Bayesian inference (SBI) to address this challenge. Rather than optimizing a fixed wiring rule to fit the empirical data, SBI considers many parametrizations of a rule and performs Bayesian inference to identify the parameters that are compatible with the data. It uses simulated data from multiple candidate wiring rule parameters and relies on machine learning methods to estimate a probability distribution (the 'posterior distribution over parameters conditioned on the data') that characterizes all data-compatible parameters. We demonstrate how to apply SBI in computational connectomics by inferring the parameters of wiring rules in an in silico model of the rat barrel cortex, given in vivo connectivity measurements. SBI identifies a wide range of wiring rule parameters that reproduce the measurements. We show how access to the posterior distribution over all data-compatible parameters allows us to analyze their relationship, revealing biologically plausible parameter interactions and enabling experimentally testable predictions. We further show how SBI can be applied to wiring rules at different spatial scales to quantitatively rule out invalid wiring hypotheses. Our approach is applicable to a wide range of generative models used in connectomics, providing a quantitative and efficient way to constrain model parameters with empirical connectivity data.

In vivo ephaptic coupling allows memory network formation

It is increasingly clear that memories are distributed across multiple brain areas. Such "engram complexes" are important features of memory formation and consolidation. Here, we test the hypothesis that engram complexes are formed in part by bioelectric fields that sculpt and guide the neural activity and tie together the areas that participate in engram complexes. Like the conductor of an orchestra, the fields influence each musician or neuron and orchestrate the output, the symphony. Our results use the theory of synergetics, machine learning, and data from a spatial delayed saccade task and provide evidence for in vivo ephaptic coupling in memory representations.

A memristive neuron and its adaptability to external electric field

Connecting memristors into any neural circuit can enhance its potential controllability under external physical stimuli. Memristive current along a magnetic flux-controlled memristor can estimate the effect of electromagnetic induction on neural circuits and neurons. Here, a charge-controlled memristor is incorporated into one branch circuit of a simple neural circuit to estimate the effect of an external electric field. The field energy kept in each electric component is respectively calculated, and equivalent dimensionless energy function H is obtained to discern the firing mode dependence on the energy from capacitive, inductive, and memristive channels. The electric field energy H_M in a memristive channel occupies the highest proportion of Hamilton energy H, and neurons can present chaotic/periodic firing modes because of large energy injection from an external electric field, while bursting and spiking behaviors emerge when magnetic field energy H_L holds maximal proportion of Hamilton energy H. The memristive current is modified to control the firing modes in this memristive neuron accompanying with a parameter shift and shape deformation resulting from energy accommodation in the memristive channel. In the presence of noisy disturbance from an external electric field, stochastic resonance is induced in the memristive neuron. Exposed to stronger electromagnetic field, the memristive component can absorb more energy and behave as a signal source for energy shunting, and negative Hamilton energy is obtained for this neuron. The new memristive neuron model can address the main physical properties of biophysical neurons, and it can further be used to explore the collective behaviors and self-organization in networks under energy flow and noisy disturbance.

A theoretical model reveals specialized synaptic depressions and temporal frequency tuning in retinal parallel channels

In the Outer Plexiform Layer of a retina, a cone pedicle provides synaptic inputs for multiple cone bipolar cell (CBC) subtypes so that each subtype formats a parallelized processing channel to filter visual features from the environment. Due to the diversity of short-term depressions among cone-CBC contacts, these channels have different temporal frequency tunings. Here, we propose a theoretical model based on the hierarchy Linear-Nonlinear-Synapse framework to link the synaptic depression and the neural activities of the cone-CBC circuit. The model successfully captures various frequency tunings of subtype-specialized channels and infers synaptic depression recovery time constants inside circuits. Furthermore, the model can predict frequency-tuning behaviors based on synaptic activities. With the prediction of region-specialized UV cone parallel channels, we suggest the acute zone in the zebrafish retina supports detecting light-off events at high temporal frequencies.

Probabilistic solvers enable a straight-forward exploration of numerical uncertainty in neuroscience models

Understanding neural computation on the mechanistic level requires models of neurons and neuronal networks. To analyze such models one typically has to solve coupled ordinary differential equations (ODEs), which describe the dynamics of the underlying neural system. These ODEs are solved numerically with deterministic ODE solvers that yield single solutions with either no, or only a global scalar error indicator on precision. It can therefore be challenging to estimate the effect of numerical uncertainty on quantities of interest, such as spike-times and the number of spikes. To overcome this problem, we propose to use recently developed sampling-based probabilistic solvers, which are able to quantify such numerical uncertainties. They neither require detailed insights into the kinetics of the models, nor are they difficult to implement. We show that numerical uncertainty can affect the outcome of typical neuroscience simulations, e.g. jittering spikes by milliseconds or even adding or removing individual spikes from simulations altogether, and demonstrate that probabilistic solvers reveal these numerical uncertainties with only moderate computational overhead.

Mechanisms underlying activation of retinal bipolar cells through targeted electrical stimulation: a computational study

Objective. Retinal implants have been developed to electrically stimulate healthy retinal neurons in the progressively degenerated retina. Several stimulation approaches have been proposed to improve the visual percept induced in patients with retinal prostheses. We introduce a computational model capable of simulating the effects of electrical stimulation on retinal neurons. Leveraging this computational platform, we delve into the underlying mechanisms influencing the sensitivity of retinal neurons' response to various stimulus waveforms.Approach. We implemented a model of spiking bipolar cells (BCs) in the magnocellular pathway of the primate retina, diffuse BC subtypes (DB4), and utilized our multiscale admittance method (AM)-NEURON computational platform to characterize the response of BCs to epiretinal electrical stimulation with monophasic, symmetric, and asymmetric biphasic pulses.Main results. Our investigations yielded four notable results: (a) the latency of BCs increases as stimulation pulse duration lengthens; conversely, this latency decreases as the current amplitude increases. (b) Stimulation with a long anodic-first symmetric biphasic pulse (duration > 8 ms) results in a significant decrease in spiking threshold compared to stimulation with similar cathodic-first pulses (from 98.2 to 57.5µA). (c) The hyperpolarization-activated cyclic nucleotide-gated channel was a prominent contributor to the reduced threshold of BCs in response to long anodic-first stimulus pulses. (d) Finally, extending the study to asymmetric waveforms, our results predict a lower BCs threshold using asymmetric long anodic-first pulses compared to that of asymmetric short cathodic-first stimulation.Significance. This study predicts the effects of several stimulation parameters on spiking BCs response to electrical stimulation. Of importance, our findings shed light on mechanisms underlying the experimental observations from the literature, thus highlighting the capability of the methodology to predict and guide the development of electrical stimulation protocols to generate a desired biological response, thereby constituting an ideal testbed for the development of electroceutical devices.

Ancestral circuits for vertebrate color vision emerge at the first retinal synapse

For color vision, retinal circuits separate information about intensity and wavelength. In vertebrates that use the full complement of four “ancestral” cone types, the nature and implementation of this computation remain poorly understood. Here, we establish the complete circuit architecture of outer retinal circuits underlying color processing in larval zebrafish. We find that the synaptic outputs of red and green cones efficiently rotate the encoding of natural daylight in a principal components analysis–like manner to yield primary achromatic and spectrally opponent axes, respectively. Blue cones are tuned to capture most remaining variance when opposed to green cones, while UV cone present a UV achromatic axis for prey capture. We note that fruitflies use essentially the same strategy. Therefore, rotating color space into primary achromatic and chromatic axes at the eye’s first synapse may thus be a fundamental principle of color vision when using more than two spectrally well-separated photoreceptor types.

Direction selectivity in retinal bipolar cell axon terminals

The ability to encode the direction of image motion is fundamental to our sense of vision. Direction selectivity along the four cardinal directions is thought to originate in direction-selective ganglion cells (DSGCs) because of directionally tuned GABAergic suppression by starburst cells. Here, by utilizing two-photon glutamate imaging to measure synaptic release, we reveal that direction selectivity along all four directions arises earlier than expected at bipolar cell outputs. Individual bipolar cells contained four distinct populations of axon terminal boutons with different preferred directions. We further show that this bouton-specific tuning relies on cholinergic excitation from starburst cells and GABAergic inhibition from wide-field amacrine cells. DSGCs received both tuned directionally aligned inputs and untuned inputs from among heterogeneously tuned glutamatergic bouton populations. Thus, directional tuning in the excitatory visual pathway is incrementally refined at the bipolar cell axon terminals and their recipient DSGC dendrites by two different neurotransmitters co-released from starburst cells.

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Cardinal direction selectivity emerges at types 7 and 2 bipolar cell axon terminals

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Starburst amacrine cells are necessary for direction selectivity in bipolar cells

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Cholinergic excitation and GABAergic inhibition are integrated at axon terminals

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Direction-selective ganglion cells receive directionally aligned glutamate inputs

Distinct synaptic transfer functions in same-type photoreceptors

Many sensory systems use ribbon-type synapses to transmit their signals to downstream circuits. The properties of this synaptic transfer fundamentally dictate which aspects in the original stimulus will be accentuated or suppressed, thereby partially defining the detection limits of the circuit. Accordingly, sensory neurons have evolved a wide variety of ribbon geometries and vesicle pool properties to best support their diverse functional requirements. However, the need for diverse synaptic functions does not only arise across neuron types, but also within. Here we show that UV-cones, a single type of photoreceptor of the larval zebrafish eye, exhibit striking differences in their synaptic ultrastructure and consequent calcium to glutamate transfer function depending on their location in the eye. We arrive at this conclusion by combining serial section electron microscopy and simultaneous 'dual-colour' two-photon imaging of calcium and glutamate signals from the same synapse in vivo. We further use the functional dataset to fit a cascade-like model of the ribbon synapse with different vesicle pool sizes, transfer rates, and other synaptic properties. Exploiting recent developments in simulation-based inference, we obtain full posterior estimates for the parameters and compare these across different retinal regions. The model enables us to extrapolate to new stimuli and to systematically investigate different response behaviours of various ribbon configurations. We also provide an interactive, easy-to-use version of this model as an online tool. Overall, we show that already on the synaptic level of single-neuron types there exist highly specialised mechanisms which are advantageous for the encoding of different visual features.

Discrimination of simple objects decoded from the output of retinal ganglion cells upon sinusoidal electrical stimulation

Objective. Most neuroprosthetic implants employ pulsatile square-wave electrical stimuli, which are significantly different from physiological inter-neuronal communication. In case of retinal neuroprosthetics, which use a certain type of pulsatile stimuli, reliable object and contrast discrimination by implanted blind patients remained challenging. Here we investigated to what extent simple objects can be discriminated from the output of retinal ganglion cells (RGCs) upon sinusoidal stimulation.Approach. Spatially confined objects were formed by different combinations of 1024 stimulating microelectrodes. The RGC activity in theex vivoretina of photoreceptor-degenerated mouse, of healthy mouse or of primate was recorded simultaneously using an interleaved recording microelectrode array implemented in a CMOS-based chip.Main results. We report that application of sinusoidal electrical stimuli (40 Hz) in epiretinal configuration instantaneously and reliably modulates the RGC activity in spatially confined areas at low stimulation threshold charge densities (40 nC mm^-2). Classification of overlapping but spatially displaced objects (1° separation) was achieved by distinct spiking activity of selected RGCs. A classifier (regularized logistic regression) discriminated spatially displaced objects (size: 5.5° or 3.5°) with high accuracy (90% or 62%). Stimulation with low artificial contrast (10%) encoded by different stimulus amplitudes generated RGC activity, which was classified with an accuracy of 80% for large objects (5.5°).Significance. We conclude that time-continuous smooth-wave stimulation provides robust, localized neuronal activation in photoreceptor-degenerated retina, which may enable future artificial vision at high temporal, spatial and contrast resolution.

The impact of synchronous versus asynchronous electrical stimulation in artificial vision

Visual prosthesis devices designed to restore sight to the blind have been under development in the laboratory for several decades. Clinical translation continues to be challenging, due in part to gaps in our understanding of critical parameters such as how phosphenes, the electrically-generated pixels of artificial vision, can be combined to form images. In this review we explore the effects that synchronous and asynchronous electrical stimulation across multiple electrodes have in evoking phosphenes. Understanding how electrical patterns influence phosphene generation to control object binding and perception of visual form is fundamental to creation of a clinically successful prosthesis.

Bayesian inference for biophysical neuron models enables stimulus optimization for retinal neuroprosthetics

While multicompartment models have long been used to study the biophysics of neurons, it is still challenging to infer the parameters of such models from data including uncertainty estimates. Here, we performed Bayesian inference for the parameters of detailed neuron models of a photoreceptor and an OFF- and an ON-cone bipolar cell from the mouse retina based on two-photon imaging data. We obtained multivariate posterior distributions specifying plausible parameter ranges consistent with the data and allowing to identify parameters poorly constrained by the data. To demonstrate the potential of such mechanistic data-driven neuron models, we created a simulation environment for external electrical stimulation of the retina and optimized stimulus waveforms to target OFF- and ON-cone bipolar cells, a current major problem of retinal neuroprosthetics.