Capturing Multiple Timescales of Adaptation to Second-Order Statistics With Generalized Linear Models: Gain Scaling and Fractional Differentiation

MULTIPLE DISTINCT TIMESCALES OF RAPID SENSORY ADAPATION IN THE THALAMOCORTICAL CIRCUIT

Numerous studies have shown that neuronal representations in sensory pathways are far from static but are instead strongly shaped by the complex properties of the sensory inputs they receive. Adaptation dynamically shapes the neural signaling that underlies our perception of the world, yet remains poorly understood. We investigated rapid adaptation across timescales from hundreds of milliseconds to seconds through simultaneous multi-electrode recordings from the ventro-posteromedial nucleus of the thalamus (VPm) and layer 4 of the primary somatosensory cortex (S1) in anesthetized mice in response to controlled, persistent whisker stimulation. Observations in VPm and S1 reveal a degree of adaptation that progresses through the pathway. Signatures of two distinct timescales of rapid adaptation in the firing rates of both thalamic and cortical neuronal populations were revealed, also reflected in the synchrony of the thalamic population and in the thalamocortical synaptic efficacy that was measured in putatively monosynaptically connected thalamocortical pairs. Controlled optogenetic activation of VPm further demonstrated that the longer timescale adaptation observed in S1 is likely inherited from slow decreases in thalamic firing rate and synchrony. Despite the degraded sensory responses, adaptation resulted in a shift in coding strategy that favors theoretical discrimination over detection across the observed timescales of adaptation. Overall, although multiple mechanisms contribute to rapid adaptation at distinct timescales, they support a unifying framework on the role of adaptation in sensory processing.

Dynamic Nonlinear Spatial Integrations on Encoding Contrasting Stimuli of Tectal Neurons

Animals detect targets using a variety of visual cues, with the visual salience of these cues determining which environmental features receive priority attention and further processing. Surround modulation plays a crucial role in generating visual saliency, which has been extensively studied in avian tectal neurons. Recent work has reported that the suppression of tectal neurons induced by motion contrasting stimulus is stronger than that by luminance contrasting stimulus. However, the underlying mechanism remains poorly understood. In this study, we built a computational model (called Generalized Linear-Dynamic Modulation) which incorporates independent nonlinear tuning mechanisms for excitatory and inhibitory inputs. This model aims to describe how tectal neurons encode contrasting stimuli. The results showed that: (1) The dynamic nonlinear integration structure substantially improved the accuracy (significant difference (p < 0.001, paired t-test) in the goodness of fit between the two models) of the predicted responses to contrasting stimuli, verifying the nonlinear processing performed by tectal neurons. (2) The modulation difference between luminance and motion contrasting stimuli emerged from the predicted response by the full model but not by that with only excitatory synaptic input (spatial luminance: 89 ± 2.8% (GL_DM) vs. 87 ± 2.1% (GL_DMexc); motion contrasting stimuli: 87 ± 1.7% (GL_DM) vs. 83 ± 2.2% (GL_DMexc)). These results validate the proposed model and further suggest the role of dynamic nonlinear spatial integrations in contextual visual information processing, especially in spatial integration, which is important for object detection performed by birds.

An advanced approach for the electrical responses of discrete fractional-order biophysical neural network models and their dynamical responses

The multiple activities of neurons frequently generate several spiking-bursting variations observed within the neurological mechanism. We show that a discrete fractional-order activated nerve cell framework incorporating a Caputo-type fractional difference operator can be used to investigate the impacts of complex interactions on the surge-empowering capabilities noticed within our findings. The relevance of this expansion is based on the model's structure as well as the commensurate and incommensurate fractional-orders, which take kernel and inherited characteristics into account. We begin by providing data regarding the fluctuations in electronic operations using the fractional exponent. We investigate two-dimensional Morris-Lecar neuronal cell frameworks via spiked and saturated attributes, as well as mixed-mode oscillations and mixed-mode bursting oscillations of a decoupled fractional-order neuronal cell. The investigation proceeds by using a three-dimensional slow-fast Morris-Lecar simulation within the fractional context. The proposed method determines a method for describing multiple parallels within fractional and integer-order behaviour. We examine distinctive attribute environments where inactive status develops in detached neural networks using stability and bifurcation assessment. We demonstrate features that are in accordance with the analysis's findings. The Erdös-Rényi connection of asynchronization transformed neural networks (periodic and actionable) is subsequently assembled and paired via membranes that are under pressure. It is capable of generating multifaceted launching processes in which dormant neural networks begin to come under scrutiny. Additionally, we demonstrated that boosting connections can cause classification synchronization, allowing network devices to activate in conjunction in the future. We construct a reduced-order simulation constructed around clustering synchronisation that may represent the operations that comprise the whole system. Our findings indicate the influence of fractional-order is dependent on connections between neurons and the system's stored evidence. Moreover, the processes capture the consequences of fractional derivatives on surge regularity modification and enhance delays that happen across numerous time frames in neural processing.

Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems

The diverse excitabilities of cells often produce various spiking-bursting oscillations that are found in the neural system. We establish the ability of a fractional-order excitable neuron model with Caputo's fractional derivative to analyze the effects of its dynamics on the spike train features observed in our results. The significance of this generalization relies on a theoretical framework of the model in which memory and hereditary properties are considered. Employing the fractional exponent, we first provide information about the variations in electrical activities. We deal with the 2D class I and class II excitable Morris-Lecar (M-L) neuron models that show the alternation of spiking and bursting features including MMOs & MMBOs of an uncoupled fractional-order neuron. We then extend the study with the 3D slow-fast M-L model in the fractional domain. The considered approach establishes a way to describe various characteristics similarities between fractional-order and classical integer-order dynamics. Using the stability and bifurcation analysis, we discuss different parameter spaces where the quiescent state emerges in uncoupled neurons. We show the characteristics consistent with the analytical results. Next, the Erdös-Rényi network of desynchronized mixed neurons (oscillatory and excitable) is constructed that is coupled through membrane voltage. It can generate complex firing activities where quiescent neurons start to fire. Furthermore, we have shown that increasing coupling can create cluster synchronization, and eventually it can enable the network to fire in unison. Based on cluster synchronization, we develop a reduced-order model which can capture the activities of the entire network. Our results reveal that the effect of fractional-order depends on the synaptic connectivity and the memory trace of the system. Additionally, the dynamics captures spike frequency adaptation and spike latency that occur over multiple timescales as the effects of fractional derivative, which has been observed in neural computation.

Visual Responses to Moving and Flashed Stimuli of Neurons in Domestic Pigeon (Columba livia domestica) Optic Tectum

Simple Summary

Avian can quickly and accurately detect surrounding objects (especially, moving ones). However, it was unknown how different neurons in the optic tectum (OT) in domestic pigeons (Columba livia domestica) processed moving objects compared to static ones. The electrophysiological results showed that the latency of response to moving stimuli was shorter than that to flashed ones, while the firing rates of response to moving stimulus were higher than that to flashed ones. Furthermore, the modeling study demonstrated that the faster and stronger response to a moving stimulus compared to a flashed stimulus may result from the accumulation process across space and time by tectal neurons. This study also sheds new light on the understanding of motion processing by birds.

Abstract

Birds can rapidly and accurately detect moving objects for better survival in complex environments. This visual ability may be attributed to the response properties of neurons in the optic tectum. However, it is unknown how neurons in the optic tectum respond differently to moving objects compared to static ones. To address this question, neuronal activities were recorded from domestic pigeon (Columba livia domestica) optic tectum, responsible for orienting to moving objects, and the responses to moving and flashed stimuli were compared. An encoding model based on the Generalized Linear Model (GLM) framework was established to explain the difference in neuronal responses. The experimental results showed that the first spike latency to moving stimuli was smaller than that to flashed ones and firing rate was higher. The model further implied the faster and stronger response to a moving target result from spatiotemporal integration process, corresponding to the spatially sequential activation of tectal neurons and the accumulation of information in time. This study provides direct electrophysiological evidence about the different tectal neuron responses to moving objects and flashed ones. The findings of this investigation increase our understanding of the motion detection mechanism of tectal neurons.

Efficient spline regression for neural spiking data

Point process generalized linear models (GLMs) provide a powerful tool for characterizing the coding properties of neural populations. Spline basis functions are often used in point process GLMs, when the relationship between the spiking and driving signals are nonlinear, but common choices for the structure of these spline bases often lead to loss of statistical power and numerical instability when the signals that influence spiking are bounded above or below. In particular, history dependent spike train models often suffer these issues at times immediately following a previous spike. This can make inferences related to refractoriness and bursting activity more challenging. Here, we propose a modified set of spline basis functions that assumes a flat derivative at the endpoints and show that this limits the uncertainty and numerical issues associated with cardinal splines. We illustrate the application of this modified basis to the problem of simultaneously estimating the place field and history dependent properties of a set of neurons from the CA1 region of rat hippocampus, and compare it with the other commonly used basis functions. We have made code available in MATLAB to implement spike train regression using these modified basis functions.