A computational study on the role of gap junctions and rod Ih conductance in the enhancement of the dynamic range of the retina

Virtual human retina: Simulating neural signalling, degeneration, and responses to electrical stimulation

INTRODUCTION

Current brain-based visual prostheses pose significant challenges impeding adoption such as the necessarily complex surgeries and occurrence of more substantial side effects due to the sensitivity of the brain. This has led to much effort toward vision restoration being focused on the more approachable part of the brain - the retina. Here we introduce a novel, parameterised simulation platform that enables study of human retinal degeneration and optimization of stimulation strategies. The platform bears immense potential for patient-specific tailoring and serves to enhance artificial vision solutions for individuals with visual impairments.

MATERIAL AND METHOD

Our virtual retina is developed using the software package, NEURON. This virtual retina platform supports large-scale simulations of over 10,000 neurons whilst upholding strong biological plausibility with multiple important visual pathways and detailed network properties. The comprehensive three-dimensional model includes photoreceptors, horizontal cells, bipolar cells, amacrine cells, and midget and parasol retinal ganglion cells, with comprehensive network connectivity across various eccentricities (1 mm-5 mm from the fovea) in the human retina. The model is constructed using electrophysiology, immunohistology, and optical coherence tomography imaging data from healthy and degenerate human retinas. We validated our model by replicating numerous experimental observations from human and primate retina, with a particular focus on retinal degeneration.

RESULT

We simulated interactions between diseased retinas and state-of-the-art retinal implants, shedding light on the limitations of commercial retinal prostheses. Our results suggested that appropriate stimulation settings with intraretinal prototype devices could leverage network-mediated activation to achieve activation mosaics more alike that of the retina's response to natural light, promoting the prospect of more naturalistic vision. Our study additionally highlights the importance of controlling inhibitory circuits in the retinal network to induce functionally relevant retinal activity.

CONCLUSION

This study demonstrates the potential of this software package and highlights its utility as a valuable tool for engineers, scientists, and clinicians in the design and optimization of retinal stimulation devices for both research and educational applications.

Simulating the impact of photoreceptor loss and inner retinal network changes on electrical activity of the retina

Objective.A major reason for poor visual outcomes provided by existing retinal prostheses is the limited knowledge of the impact of photoreceptor loss on retinal remodelling and its subsequent impact on neural responses to electrical stimulation. Computational network models of the neural retina assist in the understanding of normal retinal function but can be also useful for investigating diseased retinal responses to electrical stimulation.Approach.We developed and validated a biophysically detailed discrete neuronal network model of the retina in the software package NEURON. The model includes rod and cone photoreceptors, ON and OFF bipolar cell pathways, amacrine and horizontal cells and finally, ON and OFF retinal ganglion cells with detailed network connectivity and neural intrinsic properties. By accurately controlling the network parameters, we simulated the impact of varying levels of degeneration on retinal electrical function.Main results.Our model was able to reproduce characteristic monophasic and biphasic oscillatory patterns seen in ON and OFF neurons during retinal degeneration (RD). Oscillatory activity occurred at 3 Hz with partial photoreceptor loss and at 6 Hz when all photoreceptor input to the retina was removed. Oscillations were found to gradually weaken, then disappear when synapses and gap junctions were destroyed in the inner retina. Without requiring any changes to intrinsic cellular properties of individual inner retinal neurons, our results suggest that changes in connectivity alone were sufficient to give rise to neural oscillations during photoreceptor degeneration, and significant network connectivity destruction in the inner retina terminated the oscillations.Significance.Our results provide a platform for further understanding physiological retinal changes with progressive photoreceptor and inner RD. Furthermore, our model can be used to guide future stimulation strategies for retinal prostheses to benefit patients at different stages of disease progression, particularly in the early and mid-stages of RD.

Systematic generation of biophysically detailed models with generalization capability for non-spiking neurons

Unlike spiking neurons which compress continuous inputs into digital signals for transmitting information via action potentials, non-spiking neurons modulate analog signals through graded potential responses. Such neurons have been found in a large variety of nervous tissues in both vertebrate and invertebrate species, and have been proven to play a central role in neuronal information processing. If general and vast efforts have been made for many years to model spiking neurons using conductance-based models (CBMs), very few methods have been developed for non-spiking neurons. When a CBM is built to characterize the neuron behavior, it should be endowed with generalization capabilities (i.e. the ability to predict acceptable neuronal responses to different novel stimuli not used during the model’s building). Yet, since CBMs contain a large number of parameters, they may typically suffer from a lack of such a capability. In this paper, we propose a new systematic approach based on multi-objective optimization which builds general non-spiking models with generalization capabilities. The proposed approach only requires macroscopic experimental data from which all the model parameters are simultaneously determined without compromise. Such an approach is applied on three non-spiking neurons of the nematode Caenorhabditis elegans (C. elegans), a well-known model organism in neuroscience that predominantly transmits information through non-spiking signals. These three neurons, arbitrarily labeled by convention as RIM, AIY and AFD, represent, to date, the three possible forms of non-spiking neuronal responses of C. elegans.

A Computational Model Simulates Light-Evoked Responses in the Retinal Cone Pathway

Partial vision restoration on degenerated retina can be achieved by electrically stimulating the surviving retinal ganglion cells via implanted electrodes to elicit a signal corresponding to the natural response of the cells. Realistic computational models of electrical stimulation of the retina can prove useful to test different stimulation strategies and improve the performance of retinal implants. Simulation of healthy retinal networks and their dynamical response to natural light stimulation may also help us understand how retinal processing takes place via a series of electrical signals flowing through different stages of retinal processing, ultimately giving rise to visual percepts. Such models may provide further insights on retinal network processing and thus guide the design of retinal prostheses and their stimulation protocols to generate more natural percepts. This work aims to characterize the photocurrent generated by healthy cone photoreceptors in response to a light flash stimulation and the resulting membrane potential for the photoreceptors and its postsynaptic cone bipolar cells. A simple network of ten cone photoreceptors synapsing with a cone bipolar cell is simulated using the NEURON environment and validated against patch-clamp recordings of cone photoreceptors and ON-type bipolar cells (ON-BC). The results presented will be valuable in modeling light-evoked or electrically stimulated retinal networks that comprise cone pathways. The computational models and methods developed in this work will serve as an integral building block in the development of large and realistic retinal networks.Clinical Relevance- Accurate computational model of a retinal neural network can help in predicting cell responses to electrical stimulation in vision restoration therapies using prostheses. It can be leveraged to optimize the stimulation parameters to match the natural light response of the network as closely as possible.

Modeling ON Cone Bipolar Cells for Electrical Stimulation

Retinal prosthetic systems have been developed to help blind patients suffering from retinal degenerative diseases gain some useful form of vision. Various experimental and computational studies have been performed to test electrical stimulation strategies that can improve the performance of these devices. Detailed computational models of retinal neurons, such as retinal ganglion cells (RGCs) and bipolar cells (BCs), allow us to explore the mechanisms underlying the response of cells to electrical stimulation. While electrophysiological studies have shown the presence of voltage-gated ionic channels in different regions of BCs, many of the existing cone BCs models are assumed to be passive or only contain calcium channels at the synaptic terminals. We have utilized our Admittance Method (AM)-NEURON computational platform to implement a more realistic model of ON-BCs. Our model closely replicates the recent patch-clamp experiments directly measuring the response of ON-BCs to epiretinal electrical stimulation and thereby predicts the regional distributions of the ionic channels. Our computational results further indicate that outward potassium current strongly contributes to the depolarizing voltage transient of ON-BCs in response to electrical stimulation.

Model-based comparison of current flow in rod bipolar cells of healthy and early-stage degenerated retina

Retinal degenerative diseases, such as retinitis pigmentosa, are generally thought to initiate with the loss of photoreceptors, though recent work suggests that plasticity and remodeling occurs prior to photoreceptor cell loss. This degeneration subsequently leads to death of other retinal neurons, creating functional alterations and extensive remodeling of retinal networks. Retinal prosthetic devices stimulate the surviving retinal cells by applying external current using implanted electrodes. Although these devices restore partial vision, the quality of restored vision is limited. Further knowledge about the precise changes in degenerated retina as the disease progresses is essential to understand how current flows in retinas undergoing degenerative disease and to improve the performance of retinal prostheses. We developed computational models that describe current flow from rod photoreceptors to rod bipolar cells (RodBCs) in the healthy and early-stage degenerated retina. Morphologically accurate models of retinal cells with their synapses are constructed based on retinal connectome datasets, created using serial section transmission electron microscopy (TEM) images of 70 nm-thick slices of either healthy (RC1) or early-stage degenerated (RPC1) rabbit retina. The passive membrane and active ion currents of each cell are implemented using conductance-based models in the Neuron simulation environment. In response to photocurrent input at rod photoreceptors, the simulated membrane potential at RodBCs in early degenerate tissue is approximately 10-20 mV lower than that of RodBCs of that observed in wild type retina. Results presented here suggest that although RodBCs in RPC1 show early, altered morphology compared to RC1, the lower membrane potential is primarily a consequence of reduced rod photoreceptor input to RodBCs in the degenerated retina. Frequency response and step input analyses suggest that individual cell responses of RodBCs in either healthy or early-degenerated retina, prior to substantial photoreceptor cell loss, do not differ significantly.

Response to coincident inputs in electrically coupled primary afferents is heterogeneous and is enhanced by H-current (IH) modulation

Electrical synapses represent a widespread modality of interneuronal communication in the mammalian brain. These contacts, by lowering the effectiveness of random or temporally uncorrelated inputs, endow circuits of coupled neurons with the ability to selectively respond to simultaneous depolarizations. This mechanism may support coincidence detection, a property involved in sensory perception, organization of motor outputs, and improvement signal-to-noise ratio. While the role of electrical coupling is well established, little is known about the contribution of the cellular excitability and its modulations to the susceptibility of groups of neurons to coincident inputs. Here, we obtained dual whole cell patch-clamp recordings of pairs of mesencephalic trigeminal (MesV) neurons in brainstem slices from rats to evaluate coincidence detection and its determinants. MesV neurons are primary afferents involved in the organization of orofacial behaviors whose cell bodies are electrically coupled mainly in pairs through soma-somatic gap junctions. We found that coincidence detection is highly heterogeneous across the population of coupled neurons. Furthermore, combined electrophysiological and modeling approaches reveal that this heterogeneity arises from the diversity of MesV neuron intrinsic excitability. Consistently, increasing these cells' excitability by upregulating the hyperpolarization-activated cationic current (I_H) triggered by cGMP results in a dramatic enhancement of the susceptibility of coupled neurons to coincident inputs. In conclusion, the ability of coupled neurons to detect coincident inputs is critically shaped by their intrinsic electrophysiological properties, emphasizing the relevance of neuronal excitability for the many functional operations supported by electrical transmission in mammals. NEW & NOTEWORTHY We show that the susceptibility of pairs of coupled mesencephalic trigeminal (MesV) neurons to coincident inputs is highly heterogenous and depends on the interaction between electrical coupling and neuronal excitability. Additionally, upregulating the hyperpolarization-activated cationic current (I_H) by cGMP results in a dramatic increase of this susceptibility. The I_H and electrical synapses have been shown to coexist in many neuronal populations, suggesting that modulation of this conductance could represent a common strategy to regulate circuit operation supported by electrical coupling.

Compartment models for the electrical stimulation of retinal bipolar cells

Bipolar cells of the retina are among the smallest neurons of the nervous system. For this reason, compared to other neurons, their delay in signaling is minimal. Additionally, the small bipolar cell surface combined with the low membrane conductance causes very little attenuation in the signal from synaptic input to the terminal. The existence of spiking bipolar cells was proven over the last two decades, but until now no complete model including all important ion channel types was published. The present study amends this and analyzes the impact of the number of model compartments on simulation accuracy. Characteristic features like membrane voltages and spike generation were tested and compared for one-, two-, four- and 117-compartment models of a macaque bipolar cell. Although results were independent of the compartment number for low membrane conductances (passive membranes), nonlinear regimes such as spiking required at least a separate axon compartment. At least a four compartment model containing the functionally different segments dendrite, soma, axon and terminal was needed for understanding signaling in spiking bipolar cells. Whereas for intracellular current application models with small numbers of compartments showed quantitatively correct results in many cases, the cell response to extracellular stimulation is sensitive to spatial variation of the electric field and accurate modeling therefore demands for a large number of short compartments even for passive membranes.

Increasing Electrical Stimulation Efficacy in Degenerated Retina: Stimulus Waveform Design in a Multiscale Computational Model

A computational model of electrical stimulation of the retina is proposed for investigating current waveforms used in prosthetic devices for restoring partial vision lost to retinal degenerative diseases. The model framework combines a connectome-based neural network model characterized by accurate morphological and synaptic properties with an admittance method model of bulk tissue and prosthetic electronics. In this model, the retina was computationally "degenerated," considering cellular death and anatomical changes that occur early in disease, as well as altered neural behavior that develops throughout the neurodegeneration and is likely interfering with current attempts at restoring vision. A resulting analysis of stimulation range and threshold of ON ganglion cells within the retina that are either healthy or in beginning stages of degeneration is presented for currently used stimulation waveforms, and an asymmetric biphasic current stimulation for subduing spontaneous firing to allow increased control over ganglion cell firing patterns in degenerated retina is proposed. Results show that stimulation thresholds of retinal ganglion cells do not notably vary after beginning stages of retina degeneration. In addition, simulation of proposed asymmetric waveforms showed the ability to enhance the control of ganglion cell firing via electrical stimulation.

[A Potential Mechanism for Spontaneous Oscillation in the Abnormal Retina]

　Rhythmic neural activities are observed in many brain regions, and these are considered to play an important role in neural information processing. On the other hand, distinct rhythmic neural activities emerge under several pathological conditions, suggesting that rhythmic neural activity has a close relation to brain function and dysfunction. In many pathological cases, the intrinsic property of unusual rhythm generation in a neuron or a neuronal network is prevented under normal conditions, but released by the pathological condition. Therefore, it may be useful to explore which conditions determine rhythm generation in order to understand the mechanisms of brain function/dysfunction. The pathological retina in retinal degeneration exhibits rhythmic neural activity not observed in the healthy retina. In this review, we first provide a brief introduction to the possible mechanisms of rhythm generation in a neural system. Then we introduce experimental evidence of rhythm generation in the pathological retina, as well as two hypotheses regarding this mechanism. Finally, we raise several issues to be solved for the further understanding of pathological rhythm generation.

Formulation and Implementation of Nonlinear Integral Equations to Model Neural Dynamics Within the Vertebrate Retina

Existing computational models of the retina often compromise between the biophysical accuracy and a hardware-adaptable methodology of implementation. When compared to the current modes of vision restoration, algorithmic models often contain a greater correlation between stimuli and the affected neural network, but lack physical hardware practicality. Thus, if the present processing methods are adapted to complement very-large-scale circuit design techniques, it is anticipated that it will engender a more feasible approach to the physical construction of the artificial retina. The computational model presented in this research serves to provide a fast and accurate predictive model of the retina, a deeper understanding of neural responses to visual stimulation, and an architecture that can realistically be transformed into a hardware device. Traditionally, implicit (or semi-implicit) ordinary differential equations (OES) have been used for optimal speed and accuracy. We present a novel approach that requires the effective integration of different dynamical time scales within a unified framework of neural responses, where the rod, cone, amacrine, bipolar, and ganglion cells correspond to the implemented pathways. Furthermore, we show that adopting numerical integration can both accelerate retinal pathway simulations by more than 50% when compared with traditional ODE solvers in some cases, and prove to be a more realizable solution for the hardware implementation of predictive retinal models.

Survey of electrically evoked responses in the retina - stimulus preferences and oscillation among neurons

Electrical stimulation is an important tool in neuroscience research and clinically. In the retina, extensive work has revealed how the retinal ganglion cells respond to extracellular electrical stimulation. But little is known about the responses of other neuronal types, and more generally, how the network responds to stimulation. We conducted a survey of electrically evoked responses, over a range of pulse amplitudes and pulse widths, for 21 cell types spanning the inner two layers of the rabbit retina. It revealed: (i) the evoked responses of some neurons were charge insensitive; (ii) pulse-width sensitivity varied between cell types, allowing preferential recruitment of cell types; and (iii) 10-20 Hz damped oscillations across retinal layers. These oscillations were generated by reciprocal excitatory / inhibitory synapses, at locations as early as the cone-horizontal-cell synapses. These results illustrate at cellular resolution how a network responds to extracellular stimulation, and could inform the development of bioelectronic implants for treating blindness.

Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding

The vicinity of phase transitions selectively amplifies weak stimuli, yielding optimal sensitivity to distinguish external input. Along with this enhanced sensitivity, enhanced levels of fluctuations at criticality reduce the specificity of the response. Given that the specificity of the response is largely compromised when the sensitivity is maximal, the overall benefit of criticality for signal processing remains questionable. Here, it is shown that this impasse can be solved by heterogeneous systems incorporating functional diversity, in which critical and subcritical components coexist. The subnetwork of critical elements has optimal sensitivity, and the subnetwork of subcritical elements has enhanced specificity. Combining segregated features extracted from the different subgroups, the resulting collective response can maximize the trade-off between sensitivity and specificity measured by the dynamic-range-to-noise ratio. Although numerous benefits can be observed when the entire system is critical, our results highlight that optimal performance is obtained when only a small subset of the system is at criticality.

Modulation of neuronal dynamic range using two different adaptation mechanisms

The capability of neurons to discriminate between intensity of external stimulus is measured by its dynamic range. A larger dynamic range indicates a greater probability of neuronal survival. In this study, the potential roles of adaptation mechanisms (ion currents) in modulating neuronal dynamic range were numerically investigated. Based on the adaptive exponential integrate-and-fire model, which includes two different adaptation mechanisms, i.e. subthreshold and suprathreshold (spike-triggered) adaptation, our results reveal that the two adaptation mechanisms exhibit rather different roles in regulating neuronal dynamic range. Specifically, subthreshold adaptation acts as a negative factor that observably decreases the neuronal dynamic range, while suprathreshold adaptation has little influence on the neuronal dynamic range. Moreover, when stochastic noise was introduced into the adaptation mechanisms, the dynamic range was apparently enhanced, regardless of what state the neuron was in, e.g. adaptive or non-adaptive. Our model results suggested that the neuronal dynamic range can be differentially modulated by different adaptation mechanisms. Additionally, noise was a non-ignorable factor, which could effectively modulate the neuronal dynamic range.

Computational Modeling of Single Neuron Extracellular Electric Potentials and Network Local Field Potentials using LFPsim

Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interaction of current sources and dipoles. Mathematical computations of LFPs allow the study of circuit functions and dysfunctions via simulations. This paper introduces LFPsim, a NEURON-based tool for computing population LFP activity and single neuron extracellular potentials. LFPsim was developed to be used on existing cable compartmental neuron and network models. Point source, line source, and RC based filter approximations can be used to compute extracellular activity. As a demonstration of efficient implementation, we showcase LFPs from mathematical models of electrotonically compact cerebellum granule neurons and morphologically complex neurons of the neocortical column. LFPsim reproduced neocortical LFP at 8, 32, and 56 Hz via current injection, in vitro post-synaptic N_2a, N_2b waves and in vivo T-C waves in cerebellum granular layer. LFPsim also includes a simulation of multi-electrode array of LFPs in network populations to aid computational inference between biophysical activity in neural networks and corresponding multi-unit activity resulting in extracellular and evoked LFP signals.

On the computation of a retina resistivity profile for applications in multi-scale modeling of electrical stimulation and absorption

This study proposes a methodology for computationally estimating resistive properties of tissue in multi-scale computational models, used for studying the interaction of electromagnetic fields with neural tissue, with applications to both dosimetry and neuroprosthetics. Traditionally, models at bulk tissue- and cellular-level scales are solved independently, linking resulting voltage from existing resistive tissue-scale models as extracellular sources to cellular models. This allows for solving the effects that external electric fields have on cellular activity. There are two major limitations to this approach: first, the resistive properties of the tissue need to be chosen, of which there are contradicting measurements in literature; second, the measurements of resistivity themselves may be inaccurate, leading to the mentioned contradicting results found across different studies. Our proposed methodology allows for constructing computed resistivity profiles using knowledge of only the neural morphology within the multi-scale model, resulting in a practical implementation of the effective medium theory; this bypasses concerns regarding the choice of resistive properties and accuracy of measurement setups. A multi-scale model of retina is constructed with an external electrode to serve as a test bench for analyzing existing and resulting resistivity profiles, and validation is presented through the reconstruction of a published resistivity profile of retina tissue. Results include a computed resistivity profile of retina tissue for use with a retina multi-scale model used to analyze effects of external electric fields on neural activity.

Electrical activity of ON and OFF retinal ganglion cells: a modelling study

OBJECTIVE

Retinal ganglion cells (RGCs) demonstrate a large range of variation in their ionic channel properties and morphologies. Cell-specific properties are responsible for the unique way RGCs process synaptic inputs, as well as artificial electrical signals such as that from a visual prosthesis. A cell-specific computational modelling approach allows us to examine the functional significance of regional membrane channel expression and cell morphology.

APPROACH

In this study, an existing RGC ionic model was extended by including a hyperpolarization activated non-selective cationic current as well as a T-type calcium current identified in recent experimental findings. Biophysically-defined model parameters were simultaneously optimized against multiple experimental recordings from ON and OFF RGCs.

MAIN RESULTS

With well-defined cell-specific model parameters and the incorporation of detailed cell morphologies, these models were able to closely reconstruct and predict ON and OFF RGC response properties recorded experimentally.

SIGNIFICANCE

The resulting models were used to study the contribution of different ion channel properties and spatial structure of neurons to RGC activation. The techniques of this study are generally applicable to other excitable cell models, increasing the utility of theoretical models in accurately predicting the response of real biological neurons.

A model of electrical stimulation of a retinal cell population using a multi-electrode array

A novel computational modelling approach is employed to investigate the response of a population of retinal ganglion cells (RGCs) to external electrical stimulation. Current is delivered via a multi-electrode array design that would be employed in a future retinal prosthesis device being developed by our group. The RGCs are morphologically realistic and allow examination of the biophysical responses of intracellular compartments to externally applied currents. A number of stimulation paradigms are simulated including the use of monopolar, hexapolar and quasi-monopolar return paths. The model provides a powerful simulation tool to test and optimize electrical stimulation strategies for future retinal prosthesis devices.

Rod electrical coupling is controlled by a circadian clock and dopamine in mouse retina

Rod single-photon responses are critical for vision in dim light. Electrical coupling via gap junction channels shapes the light response properties of vertebrate photoreceptors, but the regulation of rod coupling and its impact on the single-photon response have remained unclear. To directly address these questions, we developed a perforated patch-clamp recording technique and recorded from single rod inner segments in isolated intact neural mouse retinae, maintained by superfusion. Experiments were conducted at different times of the day or under constant environmental conditions, at different times across the circadian cycle. We show that rod electrical coupling is regulated by a circadian clock and dopamine, so that coupling is weak during the day and strong at night. Altogether, patch-clamp recordings of single-photon responses in mouse rods, tracer coupling, receptive field measurements and pharmacological manipulations of gap junction and dopamine receptor activity provide compelling evidence that rod coupling is modulated in a circadian manner. These data are consistent with computer modelling. At night, single-photon responses are smaller due to coupling, but the signal-to-noise ratio for a dim (multiphoton) light response is increased at night because of signal averaging between coupled rods.

Functional regulation of neuronal nitric oxide synthase expression and activity in the rat retina

In the nervous system within physiological conditions, nitric oxide (NO) production depends on the activity of nitric oxide synthases (NOSs), and particularly on the expression of the neuronal isoform (nNOS). In the sensory systems, the role of NO is poorly understood. In this study, we identified nNOS-positive cells in the inner nuclear layer (INL) of the rat retina, with distinct characteristics such as somata size, immunolabeling level and location. Employing mathematical cluster analysis, we determined that nNOS amacrine cells are formed by two distinct populations. We next investigated the molecular identity of these cells, which did not show colocalization with calbindin (CB), choline acetyltransferase (ChAT), parvalbumin (PV) or protein kinase C (PKC), and only partial colocalization with calretinin (CR), revealing the accumulation of nNOS in specific amacrine cell populations. To access the functional, circuitry-related roles of these cells, we performed experiments after adaptation to different ambient light conditions. After 24h of dark-adaptation, we detected a subtle, yet statistically significant decrease in nNOS transcript levels, which returned to steady-state levels after 24h of normal light-dark cycle, revealing that nNOS expression is governed by ambient light conditions. Employing electron paramagnetic resonance (EPR), we demonstrated that dark-adaptation decreases NO production in the retina. Furthermore, nNOS accumulation changed in the dark-adapted retinas, with a general reduction in the inner plexiform layer. Finally, computational analysis based on clustering techniques revealed that dark-adaptation differently affected both types of nNOS-positive amacrine cells. Taken together, our data disclosed functional regulation of nNOS expression and activity, disclosing new circuitry-related roles of nNOS-positive cells. More importantly, this study indicated unsuspected roles for NO in the sensory systems, particularly related to adaptation to ambient demands.

Undersampled critical branching processes on small-world and random networks fail to reproduce the statistics of spike avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent . Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Single-neuron criticality optimizes analog dendritic computation

Active dendritic branchlets enable the propagation of dendritic spikes, whose computational functions remain an open question. Here we propose a concrete function to the active channels in large dendritic trees. Modelling the input-output response of large active dendritic arbors subjected to complex spatio-temporal inputs and exhibiting non-stereotyped dendritic spikes, we find that the dendritic arbor can undergo a continuous phase transition from a quiescent to an active state, thereby exhibiting spontaneous and self-sustained localized activity as suggested by experiments. Analogously to the critical brain hypothesis, which states that neuronal networks self-organize near criticality to take advantage of its specific properties, here we propose that neurons with large dendritic arbors optimize their capacity to distinguish incoming stimuli at the critical state. We suggest that "computation at the edge of a phase transition" is more compatible with the view that dendritic arbors perform an analog rather than a digital dendritic computation.

Developmental and functional expression of miRNA-stability related genes in the nervous system

In the nervous system, control of gene expression by microRNAs (miRNAs) has been investigated in fundamental processes, such as development and adaptation to ambient demands. The action of these short nucleotide sequences on specific genes depends on intracellular concentration, which in turn reflects the balance of biosynthesis and degradation. Whereas mechanisms underlying miRNA biogenesis has been investigated in recent studies, little is known about miRNA-stability related proteins. We first detected two genes in the retina that have been associated to miRNA stability, XRN2 and PAPD4. These genes are highly expressed during retinal development, however with distinct subcellular localization. We investigated whether these proteins are regulated during specific phases of the cell cycle. Combined analyses of nuclei position in neuroblastic layer and labeling using anti-cyclin D1 revealed that both proteins do not accumulate in S or M phases of the cell cycle, being poorly expressed in progenitor cells. Indeed, XRN2 and PAPD4 were observed mainly after neuronal differentiation, since low expression was also observed in astrocytes, endothelial and microglial cells. XRN2 and PAPD4 are expressed in a wide variety of neurons, including horizontal, amacrine and ganglion cells. To evaluate the functional role of both genes, we carried out experiments addressed to the retinal adaptation in response to different ambient light conditions. PAPD4 is upregulated after 3 and 24 hours of dark- adaptation, revealing that accumulation of this protein is governed by ambient light levels. Indeed, the fast and functional regulation of PAPD4 was not related to changes in gene expression, disclosing that control of protein levels occurs by post-transcriptional mechanisms. Furthermore, we were able to quantify changes in PAPD4 in specific amacrine cells after dark -adaptation, suggesting for circuitry-related roles in visual perception. In summary, in this study we first described the ontogenesis and functional expression of these two miRNA-stability related proteins in the retina.

Role of Ih in the firing pattern of mammalian cold thermoreceptor endings

Mammalian peripheral cold thermoreceptors respond to cooling of their sensory endings with an increase in firing rate and modification of their discharge pattern. We recently showed that cultured trigeminal cold-sensitive (CS) neurons express a prominent hyperpolarization-activated current ( Ih), mainly carried by HCN1 channels, supporting subthreshold resonance in the soma without participating in the response to acute cooling. However, peripheral pharmacological blockade of Ih, or characterization of HCN1−/− mice, reveals a deficit in acute cold detection. Here we investigated the role of Ih in CS nerve endings, where cold sensory transduction actually takes place. Corneal CS nerve endings in mice show a rhythmic spiking activity at neutral skin temperature that switches to bursting mode when the temperature is lowered. Ih blockers ZD7288 and ivabradine alter firing patterns of CS nerve endings, lengthening interspike intervals and inducing bursts at neutral skin temperature. We characterized the CS nerve endings from HCN1−/− mouse corneas and found that they behave similar to wild type, although with a lower slope in the firing frequency vs. temperature relationship, thus explaining the deficit in cold perception of HCN1−/− mice. The firing pattern of nerve endings from HCN1−/− mice was also affected by ZD7288, which we attribute to the presence of HCN2 channels in the place of HCN1. Mathematical modeling shows that the firing phenotype of CS nerve endings from HCN1−/− mice can be reproduced by replacing HCN1 channels with the slower HCN2 channels rather than by abolishing Ih. We propose that Ih carried by HCN1 channels helps tune the frequency of the oscillation and the length of bursts underlying regular spiking in cold thermoreceptors, having important implications for neural coding of cold sensation.

Dynamic range of vertebrate retina ganglion cells: importance of active dendrites and coupling by electrical synapses

The vertebrate retina has a very high dynamic range. This is due to the concerted action of its diverse cell types. Ganglion cells, which are the output cells of the retina, have to preserve this high dynamic range to convey it to higher brain areas. Experimental evidence shows that the firing response of ganglion cells is strongly correlated with their total dendritic area and only weakly correlated with their dendritic branching complexity. On the other hand, theoretical studies with simple neuron models claim that active and large dendritic trees enhance the dynamic range of single neurons. Theoretical models also claim that electrical coupling between ganglion cells via gap junctions enhances their collective dynamic range. In this work we use morphologically reconstructed multi-compartmental ganglion cell models to perform two studies. In the first study we investigate the relationship between single ganglion cell dynamic range and number of dendritic branches/total dendritic area for both active and passive dendrites. Our results support the claim that large and active dendrites enhance the dynamic range of a single ganglion cell and show that total dendritic area has stronger correlation with dynamic range than with number of dendritic branches. In the second study we investigate the dynamic range of a square array of ganglion cells with passive or active dendritic trees coupled with each other via dendrodendritic gap junctions. Our results suggest that electrical coupling between active dendritic trees enhances the dynamic range of the ganglion cell array in comparison with both the uncoupled case and the coupled case with cells with passive dendrites. The results from our detailed computational modeling studies suggest that the key properties of the ganglion cells that endow them with a large dynamic range are large and active dendritic trees and electrical coupling via gap junctions.

Statistical physics approach to dendritic computation: the excitable-wave mean-field approximation

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a nonequilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5, e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

Spike avalanches exhibit universal dynamics across the sleep-wake cycle

BACKGROUND

Scale-invariant neuronal avalanches have been observed in cell cultures and slices as well as anesthetized and awake brains, suggesting that the brain operates near criticality, i.e. within a narrow margin between avalanche propagation and extinction. In theory, criticality provides many desirable features for the behaving brain, optimizing computational capabilities, information transmission, sensitivity to sensory stimuli and size of memory repertoires. However, a thorough characterization of neuronal avalanches in freely-behaving (FB) animals is still missing, thus raising doubts about their relevance for brain function.

METHODOLOGY/PRINCIPAL FINDINGS

To address this issue, we employed chronically implanted multielectrode arrays (MEA) to record avalanches of action potentials (spikes) from the cerebral cortex and hippocampus of 14 rats, as they spontaneously traversed the wake-sleep cycle, explored novel objects or were subjected to anesthesia (AN). We then modeled spike avalanches to evaluate the impact of sparse MEA sampling on their statistics. We found that the size distribution of spike avalanches are well fit by lognormal distributions in FB animals, and by truncated power laws in the AN group. FB data surrogation markedly decreases the tail of the distribution, i.e. spike shuffling destroys the largest avalanches. The FB data are also characterized by multiple key features compatible with criticality in the temporal domain, such as 1/f spectra and long-term correlations as measured by detrended fluctuation analysis. These signatures are very stable across waking, slow-wave sleep and rapid-eye-movement sleep, but collapse during anesthesia. Likewise, waiting time distributions obey a single scaling function during all natural behavioral states, but not during anesthesia. Results are equivalent for neuronal ensembles recorded from visual and tactile areas of the cerebral cortex, as well as the hippocampus.

CONCLUSIONS/SIGNIFICANCE

Altogether, the data provide a comprehensive link between behavior and brain criticality, revealing a unique scale-invariant regime of spike avalanches across all major behaviors.