The Edge of Stability: Response Times and Delta Oscillations in Balanced Networks

On the physiological and structural contributors to the overall balance of excitation and inhibition in local cortical networks

Overall balance of excitation and inhibition in cortical networks is central to their functionality and normal operation. Such orchestrated co-evolution of excitation and inhibition is established through convoluted local interactions between neurons, which are organized by specific network connectivity structures and are dynamically controlled by modulating synaptic activities. Therefore, identifying how such structural and physiological factors contribute to establishment of overall balance of excitation and inhibition is crucial in understanding the homeostatic plasticity mechanisms that regulate the balance. We use biologically plausible mathematical models to extensively study the effects of multiple key factors on overall balance of a network. We characterize a network's baseline balanced state by certain functional properties, and demonstrate how variations in physiological and structural parameters of the network deviate this balance and, in particular, result in transitions in spontaneous activity of the network to high-amplitude slow oscillatory regimes. We show that deviations from the reference balanced state can be continuously quantified by measuring the ratio of mean excitatory to mean inhibitory synaptic conductances in the network. Our results suggest that the commonly observed ratio of the number of inhibitory to the number of excitatory neurons in local cortical networks is almost optimal for their stability and excitability. Moreover, the values of inhibitory synaptic decay time constants and density of inhibitory-to-inhibitory network connectivity are critical to overall balance and stability of cortical networks. However, network stability in our results is sufficiently robust against modulations of synaptic quantal conductances, as required by their role in learning and memory. Our study based on extensive bifurcation analyses thus reveal the functional optimality and criticality of structural and physiological parameters in establishing the baseline operating state of local cortical networks.

Comparing therapeutic modulators of the SOD1 G93A Amyotrophic Lateral Sclerosis mouse pathophysiology

Introduction

Amyotrophic Lateral Sclerosis (ALS) is a paralyzing, multifactorial neurodegenerative disease with limited therapeutics and no known cure. The study goal was to determine which pathophysiological treatment targets appear most beneficial.

Methods

A big data approach was used to analyze high copy SOD1 G93A experimental data. The secondary data set comprised 227 published studies and 4,296 data points. Treatments were classified by pathophysiological target: apoptosis, axonal transport, cellular chemistry, energetics, neuron excitability, inflammation, oxidative stress, proteomics, or systemic function. Outcome assessment modalities included onset delay, health status (rotarod performance, body weight, grip strength), and survival duration. Pairwise statistical analysis (two-tailed t-test with Bonferroni correction) of normalized fold change (treatment/control) assessed significant differences in treatment efficacy. Cohen's d quantified pathophysiological treatment category effect size compared to "all" (e.g., all pathophysiological treatment categories combined).

Results

Inflammation treatments were best at delaying onset (d = 0.42, p > 0.05). Oxidative stress treatments were significantly better for prolonging survival duration (d = 0.18, p < 0.05). Excitability treatments were significantly better for prolonging overall health status (d = 0.22, p < 0.05). However, the absolute best pathophysiological treatment category for prolonging health status varied with disease progression: oxidative stress was best for pre-onset health (d = 0.18, p > 0.05); excitability was best for prolonging function near onset (d = 0.34, p < 0.05); inflammation was best for prolonging post-onset function (d = 0.24, p > 0.05); and apoptosis was best for prolonging end-stage function (d = 0.49, p > 0.05). Finally, combination treatments simultaneously targeting multiple pathophysiological categories (e.g., polytherapy) performed significantly (p < 0.05) better than monotherapies at end-stage.

Discussion

In summary, the most effective pathophysiological treatments change as function of assessment modality and disease progression. Shifting pathophysiological treatment category efficacy with disease progression supports the homeostatic instability theory of ALS disease progression.

Machine Learning Selection of Most Predictive Brain Proteins Suggests Role of Sugar Metabolism in Alzheimer's Disease

BACKGROUND

The complex and not yet fully understood etiology of Alzheimer's disease (AD) shows important proteopathic signs which are unlikely to be linked to a single protein. However, protein subsets from deep proteomic datasets can be useful in stratifying patient risk, identifying stage dependent disease markers, and suggesting possible disease mechanisms.

OBJECTIVE

The objective was to identify protein subsets that best classify subjects into control, asymptomatic Alzheimer's disease (AsymAD), and AD.

METHODS

Data comprised 6 cohorts; 620 subjects; 3,334 proteins. Brain tissue-derived predictive protein subsets for classifying AD, AsymAD, or control were identified and validated with label-free quantification and machine learning.

RESULTS

A 29-protein subset accurately classified AD (AUC = 0.94). However, an 88-protein subset best predicted AsymAD (AUC = 0.92) or Control (AUC = 0.92) from AD (AUC = 0.98). AD versus Control: APP, DHX15, NRXN1, PBXIP1, RABEP1, STOM, and VGF. AD versus AsymAD: ALDH1A1, BDH2, C4A, FABP7, GABBR2, GNAI3, PBXIP1, and PRKAR1B. AsymAD versus Control: APP, C4A, DMXL1, EXOC2, PITPNB, RABEP1, and VGF. Additional predictors: DNAJA3, PTBP2, SLC30A9, VAT1L, CROCC, PNP, SNCB, ENPP6, HAPLN2, PSMD4, and CMAS.

CONCLUSION

Biomarkers were dynamically separable across disease stages. Predictive proteins were significantly enriched to sugar metabolism.

Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method

Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive functions. Jansen's neural mass model (NMM) was initially proposed to study the origin of alpha oscillations. Most of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical methods. In this study, we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the NMM. First, the sigmoid nonlinear function in the NMM is approximated by its describing function, allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear part. Second, by conducting a theoretical analysis, we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and, furthermore, accurately determine its amplitude and frequency. The results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha oscillations. Furthermore, strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.

Short-term depression and transient memory in sensory cortex

Persistent neuronal activity is usually studied in the context of short-term memory localized in central cortical areas. Recent studies show that early sensory areas also can have persistent representations of stimuli which emerge quickly (over tens of milliseconds) and decay slowly (over seconds). Traditional positive feedback models cannot explain sensory persistence for at least two reasons: (i) They show attractor dynamics, with transient perturbations resulting in a quasi-permanent change of system state, whereas sensory systems return to the original state after a transient. (ii) As we show, those positive feedback models which decay to baseline lose their persistence when their recurrent connections are subject to short-term depression, a common property of excitatory connections in early sensory areas. Dual time constant network behavior has also been implemented by nonlinear afferents producing a large transient input followed by much smaller steady state input. We show that such networks require unphysiologically large onset transients to produce the rise and decay observed in sensory areas. Our study explores how memory and persistence can be implemented in another model class, derivative feedback networks. We show that these networks can operate with two vastly different time courses, changing their state quickly when new information is coming in but retaining it for a long time, and that these capabilities are robust to short-term depression. Specifically, derivative feedback networks with short-term depression that acts differentially on positive and negative feedback projections are capable of dynamically changing their time constant, thus allowing fast onset and slow decay of responses without requiring unrealistically large input transients.