A biophysical perspective on the resilience of neuronal excitability across timescales.

Neuronal membrane excitability must be resilient to perturbations that can take place over timescales from milliseconds to months (or even years in long-lived animals). A great deal of attention has been paid to classes of homeostatic mechanisms that contribute to long-term maintenance of neuronal excitability through processes that alter a key structural parameter: the number of ion channel proteins present at the neuronal membrane. However, less attention has been paid to the self-regulating 'automatic' mechanisms that contribute to neuronal resilience by virtue of the kinetic properties of ion channels themselves. Here, we propose that these two sets of mechanisms are complementary instantiations of feedback control, together enabling resilience on a wide range of temporal scales. We further point to several methodological and conceptual challenges entailed in studying these processes - both of which involve enmeshed feedback control loops - and consider the consequences of these mechanisms of resilience.

Sodium channel slow inactivation normalizes firing in axons with uneven conductance distributions.

The Na+ channels that are important for action potentials show rapid inactivation, a state in which they do not conduct, although the membrane potential remains depolarized.1,2 Rapid inactivation is a determinant of millisecond-scale phenomena, such as spike shape and refractory period. Na+ channels also inactivate orders of magnitude more slowly, and this slow inactivation has impacts on excitability over much longer timescales than those of a single spike or a single inter-spike interval.3,4,5,6,7,8,9,10 Here, we focus on the contribution of slow inactivation to the resilience of axonal excitability11,12 when ion channels are unevenly distributed along the axon. We study models in which the voltage-gated Na+ and K+ channels are unevenly distributed along axons with different variances, capturing the heterogeneity that biological axons display.13,14 In the absence of slow inactivation, many conductance distributions result in spontaneous tonic activity. Faithful axonal propagation is achieved with the introduction of Na+ channel slow inactivation. This "normalization" effect depends on relations between the kinetics of slow inactivation and the firing frequency. Consequently, neurons with characteristically different firing frequencies will need to implement different sets of channel properties to achieve resilience. The results of this study demonstrate the importance of the intrinsic biophysical properties of ion channels in normalizing axonal function.

Identifying regulation with adversarial surrogates.

Homeostasis, the ability to maintain a relatively constant internal environment in the face of perturbations, is a hallmark of biological systems. It is believed that this constancy is achieved through multiple internal regulation and control processes. Given observations of a system, or even a detailed model of one, it is both valuable and extremely challenging to extract the control objectives of the homeostatic mechanisms. In this work, we develop a robust data-driven method to identify these objectives, namely to understand: "what does the system care about?". We propose an algorithm, Identifying Regulation with Adversarial Surrogates (IRAS), that receives an array of temporal measurements of the system and outputs a candidate for the control objective, expressed as a combination of observed variables. IRAS is an iterative algorithm consisting of two competing players. The first player, realized by an artificial deep neural network, aims to minimize a measure of invariance we refer to as the coefficient of regulation. The second player aims to render the task of the first player more difficult by forcing it to extract information about the temporal structure of the data, which is absent from similar "surrogate" data. We test the algorithm on four synthetic and one natural data set, demonstrating excellent empirical results. Interestingly, our approach can also be used to extract conserved quantities, e.g., energy and momentum, in purely physical systems, as we demonstrate empirically.

Lost knowledge.

Eve Marder and Shimon Marom argue that, while we celebrate the remarkable new technologies and their ability to generate new knowledge, we mourn a concurrent loss of knowledge and expertise.

Dialogue Across Chasm: Are Psychology and Neurophysiology Incompatible?

To establish a genuine scientific discourse, we must accept a long due departure from the habit of neatly arranging things in a hierarchy where "macroscopic" psychological mystery awaits explanation in terms of "microscopic" neural objects. Instead, a relational scientific methodology is wanted, accompanied by a dialogic mode of conversation between the disciplines.

Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability.

Excitability-a threshold-governed transient in transmembrane voltage-is a fundamental physiological process that controls the function of the heart, endocrine, muscles, and neuronal tissues. The 1950s Hodgkin and Huxley explicit formulation provides a mathematical framework for understanding excitability, as the consequence of the properties of voltage-gated sodium and potassium channels. The Hodgkin-Huxley model is more sensitive to parametric variations of protein densities and kinetics than biological systems whose excitability is apparently more robust. It is generally assumed that the model's sensitivity reflects missing functional relations between its parameters or other components present in biological systems. Here we experimentally assembled excitable membranes using the dynamic clamp and voltage-gated potassium ionic channels (Kv1.3) expressed in Xenopus oocytes. We take advantage of a theoretically derived phase diagram, where the phenomenon of excitability is reduced to two dimensions defined as combinations of the Hodgkin-Huxley model parameters, to examine functional relations in the parameter space. Moreover, we demonstrate activity dependence and hysteretic dynamics over the phase diagram due to the impacts of complex slow inactivation kinetics. The results suggest that maintenance of excitability amid parametric variation is a low-dimensional, physiologically tenable control process. In the context of model construction, the results point to a potentially significant gap between high-dimensional models that capture the full measure of complexity displayed by ion channel function and the lower dimensionality that captures physiological function.

Visual detection of time-varying signals: Opposing biases and their timescales.

Human visual perception is a complex, dynamic and fluctuating process. In addition to the incoming visual stimulus, it is affected by many other factors including temporal context, both external and internal to the observer. In this study we investigate the dynamic properties of psychophysical responses to a continuous stream of visual near-threshold detection tasks. We manipulate the incoming signals to have temporal structures with various characteristic timescales. Responses of human observers to these signals are analyzed using tools that highlight their dynamical features as well. Our experiments show two opposing biases that shape perceptual decision making simultaneously: positive recency, biasing towards repeated response; and adaptation, entailing an increased probability of changed response. While both these effects have been reported in previous work, our results shed new light on the timescales involved in these effects, and on their interplay with varying inputs. We find that positive recency is a short-term bias, inversely correlated with response time, suggesting it can be compensated by afterthought. Adaptation, in contrast, reflects trends over longer times possibly including multiple previous trials. Our entire dataset, which includes different input signal temporal structures, is consistent with a simple model with the two biases characterized by a fixed parameter set. These results suggest that perceptual biases are inherent features which are not flexible to tune to input signals.

A Biohybrid Setup for Coupling Biological and Neuromorphic Neural Networks.

Developing technologies for coupling neural activity and artificial neural components, is key for advancing neural interfaces and neuroprosthetics. We present a biohybrid experimental setting, where the activity of a biological neural network is coupled to a biomimetic hardware network. The implementation of the hardware network (denoted NeuroSoC) exhibits complex dynamics with a multiplicity of time-scales, emulating 2880 neurons and 12.7 M synapses, designed on a VLSI chip. This network is coupled to a neural network in vitro, where the activities of both the biological and the hardware networks can be recorded, processed, and integrated bidirectionally in real-time. This experimental setup enables an adjustable and well-monitored coupling, while providing access to key functional features of neural networks. We demonstrate the feasibility to functionally couple the two networks and to implement control circuits to modify the biohybrid activity. Overall, we provide an experimental model for neuromorphic-neural interfaces, hopefully to advance the capability to interface with neural activity, and with its irregularities in pathology.

Inhibition increases response variability and reduces stimulus discrimination in random networks of cortical neurons.

Much of what is known about the contribution of inhibition to stimulus discrimination is due to extensively studied sensory systems, which are highly structured neural circuits. The effect of inhibition on stimulus representation in less structured networks is not as clear. Here we exercise a biosynthetic approach in order to study the impacts of inhibition on stimulus representation in non-specialized network anatomy. Combining pharmacological manipulation, multisite electrical stimulation and recording from ex-vivo randomly rewired networks of cortical neurons, we quantified the effects of inhibition on response variability and stimulus discrimination at the population and single unit levels. We find that blocking inhibition quenches variability of responses evoked by repeated stimuli and enhances discrimination between stimuli that invade the network from different spatial loci. Enhanced stimulus discrimination is reserved for representation schemes that are based on temporal relation between spikes emitted in groups of neurons. Our data indicate that - under intact inhibition - the response to a given stimulus is a noisy version of the response evoked in the absence of inhibition. Spatial analysis suggests that the dispersion effect of inhibition is due to disruption of an otherwise coherent, wave-like propagation of activity.

Cellular function given parametric variation in the Hodgkin and Huxley model of excitability.

How is reliable physiological function maintained in cells despite considerable variability in the values of key parameters of multiple interacting processes that govern that function? Here, we use the classic Hodgkin-Huxley formulation of the squid giant axon action potential to propose a possible approach to this problem. Although the full Hodgkin-Huxley model is very sensitive to fluctuations that independently occur in its many parameters, the outcome is in fact determined by simple combinations of these parameters along two physiological dimensions: structural and kinetic (denoted S and K, respectively). Structural parameters describe the properties of the cell, including its capacitance and the densities of its ion channels. Kinetic parameters are those that describe the opening and closing of the voltage-dependent conductances. The impacts of parametric fluctuations on the dynamics of the system-seemingly complex in the high-dimensional representation of the Hodgkin-Huxley model-are tractable when examined within the S-K plane. We demonstrate that slow inactivation, a ubiquitous activity-dependent feature of ionic channels, is a powerful local homeostatic control mechanism that stabilizes excitability amid changes in structural and kinetic parameters.

Long-range synchrony and emergence of neural reentry.

Neural synchronization across long distances is a functionally important phenomenon in health and disease. In order to access the basis of different modes of long-range synchrony, we monitor spiking activities over centimetre scale in cortical networks and show that the mode of synchrony depends upon a length scale, λ, which is the minimal path that activity should propagate through to find its point of origin ready for reactivation. When λ is larger than the physical dimension of the network, distant neuronal populations operate synchronously, giving rise to irregularly occurring network-wide events that last hundreds of milliseconds to several seconds. In contrast, when λ approaches the dimension of the network, a continuous self-sustained reentry propagation emerges, a regular seizure-like mode that is marked by precise spatiotemporal patterns ('synfire chains') and may last many minutes. Termination of a reentry phase is preceded by a decrease of propagation speed to a halt. Stimulation decreases both propagation speed and λ values, which modifies the synchrony mode respectively. The results contribute to the understanding of the origin and termination of different modes of neural synchrony as well as their long-range spatial patterns, while hopefully catering to manipulation of the phenomena in pathological conditions.

Emergence and maintenance of excitability: kinetics over structure.

The capacity to generate action potentials in neurons and other excitable cells requires tuning of both ionic channel expression and kinetics in a large parameter space. Alongside studies that extend traditional focus on control-based regulation of structural parameters (channel densities), there is a budding interest in self-organization of kinetic parameters. In this picture, ionic channels are continually forced by activity in-and-out of a pool of states not available for the mechanism of excitability. The process, acting on expressed structure, provides a bed for generation of a spectrum of excitability modes. Driven by microscopic fluctuations over a broad range of temporal scales, self-organization of kinetic parameters enriches the concepts and tools used in the study of development of excitability.

Network Events on Multiple Space and Time Scales in Cultured Neural Networks and in a Stochastic Rate Model.

Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them has been variously recognized in previous works as expression of the excitability of the cortical tissue and the associated nonlinear dynamics, a unified picture of the determinant factors (dynamical and architectural) is desirable and not yet available. Progress has also been partially hindered by the use of a variety of statistical measures to define the network events of interest. We propose here a common probabilistic definition of network events that, applied to the firing activity of cultured neural networks, highlights the co-occurrence of network spikes, power-law distributed avalanches, and exponentially distributed 'quasi-orbits', which offer a third type of collective behavior. A rate model, including synaptic excitation and inhibition with no imposed topology, synaptic short-term depression, and finite-size noise, accounts for all these different, coexisting phenomena. We find that their emergence is largely regulated by the proximity to an oscillatory instability of the dynamics, where the non-linear excitable behavior leads to a self-amplification of activity fluctuations over a wide range of scales in space and time. In this sense, the cultured network dynamics is compatible with an excitation-inhibition balance corresponding to a slightly sub-critical regime. Finally, we propose and test a method to infer the characteristic time of the fatigue process, from the observed time course of the network's firing rate. Unlike the model, possessing a single fatigue mechanism, the cultured network appears to show multiple time scales, signalling the possible coexistence of different fatigue mechanisms.

Slow dynamics in features of synchronized neural network responses.

In this report trial-to-trial variations in the synchronized responses of neural networks are explored over time scales of minutes, in ex-vivo large scale cortical networks. We show that sub-second measures of the individual synchronous response, namely-its latency and decay duration, are related to minutes-scale network response dynamics. Network responsiveness is reflected as residency in, or shifting amongst, areas of the latency-decay plane. The different sensitivities of latency and decay durations to synaptic blockers imply that these two measures reflect aspects of inhibitory and excitatory activities. Taken together, the data suggest that trial-to-trial variations in the synchronized responses of neural networks might be related to effective excitation-inhibition ratio being a dynamic variable over time scales of minutes.

Universality, complexity and the praxis of biology: Two case studies.

The phenomenon of biology provides a prime example for a naturally occurring complex system. The approach to this complexity reflects the tension between a reductionist, reverse-engineering stance, and more abstract, systemic ones. Both of us are reductionists, but our observations challenge reductionism, at least the naive version of it. Here we describe the challenge, focusing on two universal characteristics of biological complexity: two-way microscopic-macroscopic degeneracy, and lack of time scale separation within and between levels of organization. These two features and their consequences for the praxis of experimental biology, reflect inherent difficulties in separating the dynamics of any given level of organization from the coupled dynamics of all other levels, including the environment within which the system is embedded. Where these difficulties are not deeply acknowledged, the impacts of fallacies that are inherent to naive reductionism are significant. In an era where technology enables experimental high-resolution access to numerous observables, the challenge faced by the mature reductionist-identification of relevant microscopic variables-becomes more demanding than ever. The demonstrations provided here are taken from two very different biological realizations: populations of microorganisms and populations of neurons, thus making the lesson potentially general.

Synaptic dynamics contribute to long-term single neuron response fluctuations.

Firing rate variability at the single neuron level is characterized by long-memory processes and complex statistics over a wide range of time scales (from milliseconds up to several hours). Here, we focus on the contribution of non-stationary efficacy of the ensemble of synapses-activated in response to a given stimulus-on single neuron response variability. We present and validate a method tailored for controlled and specific long-term activation of a single cortical neuron in vitro via synaptic or antidromic stimulation, enabling a clear separation between two determinants of neuronal response variability: membrane excitability dynamics vs. synaptic dynamics. Applying this method we show that, within the range of physiological activation frequencies, the synaptic ensemble of a given neuron is a key contributor to the neuronal response variability, long-memory processes and complex statistics observed over extended time scales. Synaptic transmission dynamics impact on response variability in stimulation rates that are substantially lower compared to stimulation rates that drive excitability resources to fluctuate. Implications to network embedded neurons are discussed.

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.

Entrainment of the intrinsic dynamics of single isolated neurons by natural-like input.

Neuronal dynamics is intrinsically unstable, producing activity fluctuations that are essentially scale free. Here we study single cortical neurons of newborn rats in vitro, and show that while these scale-free fluctuations are independent of temporal input statistics, they can be entrained by input variation. Joint input-output statistics and spike train reproducibility in synaptically isolated cortical neurons were measured in response to various input regimes over extended timescales (many minutes). Response entrainment was found to be maximal when the input itself possesses natural-like, scale-free statistics. We conclude that preference for natural stimuli, often observed at the system level, exists already at the elementary, single neuron level.

Synchronization by elastic neuronal latencies.

Psychological and physiological considerations entail that formation and functionality of neuronal cell assemblies depend upon synchronized repeated activation such as zero-lag synchronization. Several mechanisms for the emergence of this phenomenon have been suggested, including the global network quantity, the greatest common divisor of neuronal circuit delay loops. However, they require strict biological prerequisites such as precisely matched delays and connectivity, and synchronization is represented as a stationary mode of activity instead of a transient phenomenon. Here we show that the unavoidable increase in neuronal response latency to ongoing stimulation serves as a nonuniform gradual stretching of neuronal circuit delay loops. This apparent nuisance is revealed to be an essential mechanism in various types of neuronal time controllers, where synchronization emerges as a transient phenomenon and without predefined precisely matched synaptic delays. These findings are described in an experimental procedure where conditioned stimulations were enforced on a circuit of neurons embedded within a large-scale network of cortical cells in vitro, and are corroborated and extended by simulations of circuits composed of Hodgkin-Huxley neurons with time-dependent latencies. These findings announce a cortical time scale for time controllers based on tens of microseconds stretching of neuronal circuit delay loops per spike. They call for a reexamination of the role of the temporal periodic mode in brain functionality using advanced in vitro and in vivo experiments.

Self-organized criticality in single-neuron excitability.

We present experimental and theoretical arguments, at the single-neuron level, suggesting that neuronal response fluctuations reflect a process that positions the neuron near a transition point that separates excitable and unexcitable phases. This view is supported by the dynamical properties of the system as observed in experiments on isolated cultured cortical neurons, as well as by a theoretical mapping between the constructs of self-organized criticality and membrane excitability biophysics.