Coordinating different homeostatic processes

Reliability and robustness of oscillations in some slow-fast chaotic systems

A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or internal conditions. Motivated by the subtle dynamics of cell activity in a crustacean central pattern generator (CPG), this paper proposes a refinement of the notion of chaos that reconciles homeostasis and chaos in systems with multiple timescales. We show that systems displaying relaxation cycles while going through chaotic attractors generate chaotic dynamics that are regular at macroscopic timescales and are, thus, consistent with physiological function. We further show that this relative regularity may break down through global bifurcations of chaotic attractors such as crises, beyond which the system may also generate erratic activity at slow timescales. We analyze these phenomena in detail in the chaotic Rulkov map, a classical neuron model known to exhibit a variety of chaotic spike patterns. This leads us to propose that the passage of slow relaxation cycles through a chaotic attractor crisis is a robust, general mechanism for the transition between such dynamics. We validate this numerically in three other models: a simple model of the crustacean CPG neural network, a discrete cubic map, and a continuous flow.

Degeneracy in the nervous system: from neuronal excitability to neural coding

Degeneracy is ubiquitous across biological systems where structurally different elements can yield a similar outcome. Degeneracy is of particular interest in neuroscience too. On the one hand, degeneracy confers robustness to the nervous system and facilitates evolvability: Different elements provide a backup plan for the system in response to any perturbation or disturbance. On the other, a difficulty in the treatment of some neurological disorders such as chronic pain is explained in light of different elements all of which contribute to the pathological behavior of the system. Under these circumstances, targeting a specific element is ineffective because other elements can compensate for this modulation. Understanding degeneracy in the physiological context explains its beneficial role in the robustness of neural circuits. Likewise, understanding degeneracy in the pathological context opens new avenues of discovery to find more effective therapies.

Homeostatic Plasticity Shapes the Retinal Response to Photoreceptor Degeneration

Homeostatic plasticity stabilizes input and activity levels during neural development, but whether it can restore connectivity and preserve circuit function during neurodegeneration is unknown. Photoreceptor degeneration is the most common cause of blindness in the industrialized world. Visual deficits are dominated by cone loss, which progresses slowly, leaving a window during which rewiring of second-order neurons (i.e., bipolar cells) could preserve function. Here we establish a transgenic model to induce cone degeneration with precise control and analyze bipolar cell responses and their effects on vision through anatomical reconstructions, in vivo electrophysiology, and behavioral assays. In young retinas, we find that three bipolar cell types precisely restore input synapse numbers when 50% of cones degenerate but one does not. Of the three bipolar cell types that rewire, two contact new cones within stable dendritic territories, whereas one expands its dendrite arbors to reach new partners. In mature retinas, only one of four bipolar cell types rewires homeostatically. This steep decline in homeostatic plasticity is accompanied by reduced light responses of bipolar cells and deficits in visual behaviors. By contrast, light responses and behavioral performance are preserved when cones degenerate in young mice. Our results reveal unexpected cell type specificity and a steep maturational decline of homeostatic plasticity. The effect of homeostatic plasticity on functional outcomes identify it as a promising therapeutic target for retinal and other neurodegenerative diseases.

Circuit Stability to Perturbations Reveals Hidden Variability in the Balance of Intrinsic and Synaptic Conductances

Neurons and circuits each with a distinct balance of intrinsic and synaptic conductances can generate similar behavior but sometimes respond very differently to perturbation. Examining a large family of circuit models with non-identical neurons and synapses underlying rhythmic behavior, we analyzed the circuits' response to modifications in single and multiple intrinsic conductances in the individual neurons. To summarize these changes over the entire range of perturbed parameters, we quantified circuit output by defining a global stability measure. Using this measure, we identified specific subsets of conductances that when perturbed generate similar behavior in diverse individuals of the population. Our unbiased clustering analysis enabled us to quantify circuit stability when simultaneously perturbing multiple conductances as a nonlinear combination of single conductance perturbations. This revealed surprising conductance combinations that can predict the response to specific perturbations, even when the remaining intrinsic and synaptic conductances are unknown. Therefore, our approach can expose hidden variability in the balance of intrinsic and synaptic conductances of the same neurons across different versions of the same circuit solely from the circuit response to perturbations. Developed for a specific family of model circuits, our quantitative approach to characterizing high-dimensional degenerate systems provides a conceptual and analytic framework to guide future theoretical and experimental studies on degeneracy and robustness.

SIGNIFICANCE STATEMENT Neural circuits can generate nearly identical behavior despite neuronal and synaptic parameters varying several-fold between individual instantiations. Yet, when these parameters are perturbed through channel deletions and mutations or environmental disturbances, seemingly identical circuits can respond very differently. What distinguishes inconsequential perturbations that barely alter circuit behavior from disruptive perturbations that drastically disturb circuit output remains unclear. Focusing on a family of rhythmic circuits, we propose a computational approach to reveal hidden variability in the intrinsic and synaptic conductances in seemingly identical circuits based solely on circuit output to different perturbations. We uncover specific conductance combinations that work similarly to maintain stability and predict the effect of changing multiple conductances simultaneously, which often results from neuromodulation or injury.

Neuronal plasticity: how do neurons know what to do?

A recent study confirms activity-dependent co-regulation of membrane conductances as a mechanism underlying homeostatic regulation of neuronal properties. How multiple cellular and synaptic homeostatic mechanisms interact in a neuronal circuit is best studied with a combination of experimentation and modeling.

Controlling neural network responsiveness: tradeoffs and constraints

In recent years much effort is invested in means to control neural population responses at the whole brain level, within the context of developing advanced medical applications. The tradeoffs and constraints involved, however, remain elusive due to obvious complications entailed by studying whole brain dynamics. Here, we present effective control of response features (probability and latency) of cortical networks in vitro over many hours, and offer this approach as an experimental toy for studying controllability of neural networks in the wider context. Exercising this approach we show that enforcement of stable high activity rates by means of closed loop control may enhance alteration of underlying global input-output relations and activity dependent dispersion of neuronal pair-wise correlations across the network.

Restoration of descending inputs fails to rescue activity following deafferentation of a motor network

Motor networks such as the pyloric network of the stomatogastric ganglion often require descending neuromodulatory inputs to initiate, regulate, and modulate their activity and their synaptic connectivity to manifest physiologically appropriate output. Prolonged removal of these descending inputs often results in a compensatory response that alters the inputs themselves, their targets, or both. Using the pyloric network of the crab, Cancer borealis, we investigated whether isolation of motor networks would result in alterations that change the responses of these networks to restored modulatory input. We used a reversible block with isotonic sucrose to transiently alter descending inputs into the pyloric network of the crab stomatogastric ganglion. Using this method, we found that blocking neuromodulatory inputs caused a reduced ability for subsequently restored modulatory projections to appropriately generate network output. Our results suggest that this could be due to changes in activity of descending projection neurons as well as changes in sensitivity to neuromodulators of the target neurons that develop over the time course of the blockade. These findings suggest that although homeostatic plasticity may play a critical role in recovery of functional output in a deafferented motor network, the results of these compensatory changes may alter the network such that restored inputs no longer function appropriately.

Exome sequencing of ion channel genes reveals complex profiles confounding personal risk assessment in epilepsy

Ion channel mutations are an important cause of rare Mendelian disorders affecting brain, heart, and other tissues. We performed parallel exome sequencing of 237 channel genes in a well-characterized human sample, comparing variant profiles of unaffected individuals to those with the most common neuronal excitability disorder, sporadic idiopathic epilepsy. Rare missense variation in known Mendelian disease genes is prevalent in both groups at similar complexity, revealing that even deleterious ion channel mutations confer uncertain risk to an individual depending on the other variants with which they are combined. Our findings indicate that variant discovery via large scale sequencing efforts is only a first step in illuminating the complex allelic architecture underlying personal disease risk. We propose that in silico modeling of channel variation in realistic cell and network models will be crucial to future strategies assessing mutation profile pathogenicity and drug response in individuals with a broad spectrum of excitability disorders.