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.

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.

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.

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.

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.

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.

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.

Interactions between network synchrony and the dynamics of neuronal threshold.

Synchronous activity impacts on a range of functional brain capacities in health and disease. To address the interrelations between cellular level activity and network-wide synchronous events, we implemented in vitro a recently introduced technique, the response clamp, which enables online monitoring of single neuron threshold dynamics while ongoing network synchronous activity continues uninterrupted. We show that the occurrence of a synchronous network event causes a significant biphasic change in the single neuron threshold. These threshold dynamics are correlated across the neurons constituting the network and are entailed by the input to the neurons rather than by their own spiking (i.e., output) activity. The magnitude of network activity during a synchronous event is correlated with the threshold state of individual neurons at the event's onset. Recovery from the impact of a given synchronous event on the neuronal threshold lasts several seconds and seems to be a key determinant of the time to the next spontaneously occurring synchronous event. Moreover, the neuronal threshold is shown to be correlated with the excitability dynamics of the entire network. We conclude that the relations between the two levels (network activity and the single neuron threshold) should be thought of in terms that emphasize their interactive nature.

Enhancement of neural representation capacity by modular architecture in networks of cortical neurons.

Biological networks are ubiquitously modular, a feature that is believed to be essential for the enhancement of their functional capacities. Here, we have used a simple modular in vitro design to examine the possibility that modularity enhances network functionality in the context of input representation. We cultured networks of cortical neurons obtained from newborn rats in vitro on substrate-integrated multi-electrode arrays, forcing the network to develop two well-defined modules of neural populations that are coupled by a narrow canal. We measured the neural activity, and examined the capacity of each module to individually classify (i.e. represent) spatially distinct electrical stimuli and propagate input-specific activity features to their downstream coupled counterpart. We show that, although each of the coupled modules maintains its autonomous functionality, a significant enhancement of representational capacity is achieved when the system is observed as a whole. We interpret our results in terms of a relative decorrelation effect imposed by weak coupling between modules.

Long-term relationships between synaptic tenacity, synaptic remodeling, and network activity.

Synaptic plasticity is widely believed to constitute a key mechanism for modifying functional properties of neuronal networks. This belief implicitly implies, however, that synapses, when not driven to change their characteristics by physiologically relevant stimuli, will maintain these characteristics over time. How tenacious are synapses over behaviorally relevant time scales? To begin to address this question, we developed a system for continuously imaging the structural dynamics of individual synapses over many days, while recording network activity in the same preparations. We found that in spontaneously active networks, distributions of synaptic sizes were generally stable over days. Following individual synapses revealed, however, that the apparently static distributions were actually steady states of synapses exhibiting continual and extensive remodeling. In active networks, large synapses tended to grow smaller, whereas small synapses tended to grow larger, mainly during periods of particularly synchronous activity. Suppression of network activity only mildly affected the magnitude of synaptic remodeling, but dependence on synaptic size was lost, leading to the broadening of synaptic size distributions and increases in mean synaptic size. From the perspective of individual neurons, activity drove changes in the relative sizes of their excitatory inputs, but such changes continued, albeit at lower rates, even when network activity was blocked. Our findings show that activity strongly drives synaptic remodeling, but they also show that significant remodeling occurs spontaneously. Whereas such spontaneous remodeling provides an explanation for "synaptic homeostasis" like processes, it also raises significant questions concerning the reliability of individual synapses as sites for persistently modifying network function.

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.

Dynamics of excitability over extended timescales in cultured cortical neurons.

Although neuronal excitability is well understood and accurately modeled over timescales of up to hundreds of milliseconds, it is currently unclear whether extrapolating from this limited duration to longer behaviorally relevant timescales is appropriate. Here we used an extracellular recording and stimulation paradigm that extends the duration of single-neuron electrophysiological experiments, exposing the dynamics of excitability in individual cultured cortical neurons over timescales hitherto inaccessible. We show that the long-term neuronal excitability dynamics is unstable and dominated by critical fluctuations, intermittency, scale-invariant rate statistics, and long memory. These intrinsic dynamics bound the firing rate over extended timescales, contrasting observed short-term neuronal response to stimulation onset. Furthermore, the activity of a neuron over extended timescales shows transitions between quasi-stable modes, each characterized by a typical response pattern. Like in the case of rate statistics, the short-term onset response pattern that often serves to functionally define a given neuron is not indicative of its long-term ongoing response. These observations question the validity of describing neuronal excitability based on temporally restricted electrophysiological data, calling for in-depth exploration of activity over wider temporal scales. Such extended experiments will probably entail a different kind of neuronal models, accounting for the unbounded range, from milliseconds up.

Tradeoffs and constraints on neural representation in networks of cortical neurons.

Neural representation is pivotal in neuroscience. Yet, the large number and variance of underlying determinants make it difficult to distinguish general physiologic constraints on representation. Here we offer a general approach to the issue, enabling a systematic and well controlled experimental analysis of constraints and tradeoffs, imposed by the physiology of neuronal populations, on plausible representation schemes. Using in vitro networks of rat cortical neurons as a model system, we compared the efficacy of different kinds of "neural codes" to represent both spatial and temporal input features. Two rate-based representation schemes and two time-based representation schemes were considered. Our results indicate that, by large, all representation schemes perform well in the various discrimination tasks tested, indicating the inherent redundancy in neural population activity; Nevertheless, differences in representation efficacy are identified when unique aspects of input features are considered. We discuss these differences in the context of neural population dynamics.

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.

Cell therapy for modification of the myocardial electrophysiological substrate.

BACKGROUND: Traditional antiarrhythmic pharmacological therapies are limited by their global cardiac action, low efficacy, and significant proarrhythmic effects. We present a novel approach for the modification of the myocardial electrophysiological substrate using cell grafts genetically engineered to express specific ionic channels. METHODS AND RESULTS: To test the aforementioned concept, we performed ex vivo, in vivo, and computer simulation studies to determine the ability of fibroblasts transfected to express the voltage-sensitive potassium channel Kv1.3 to modify the local myocardial excitable properties. Coculturing of the transfected fibroblasts with neonatal rat ventricular myocyte cultures resulted in a significant reduction (68%) in the spontaneous beating frequency of the cultures compared with baseline values and cocultures seeded with naive fibroblasts. In vivo grafting of the transfected fibroblasts in the rat ventricular myocardium significantly prolonged the local effective refractory period from an initial value of 84+/-8 ms (cycle length, 200 ms) to 154+/-13 ms (P<0.01). Margatoxin partially reversed this effect (effective refractory period, 117+/-8 ms; P<0.01). In contrast, effective refractory period did not change in nontransplanted sites (86+/-7 ms) and was only mildly increased in the animals injected with wild-type fibroblasts (73+/-5 to 88+/-4 ms; P<0.05). Similar effective refractory period prolongation also was found during slower pacing drives (cycle length, 350 to 500 ms) after transplantation of the potassium channels expressing fibroblasts (Kv1.3 and Kir2.1) in pigs. Computer modeling studies confirmed the in vivo results. CONCLUSIONS: Genetically engineered cell grafts, transfected to express potassium channels, can couple with host cardiomyocytes and alter the local myocardial electrophysiological properties by reducing cardiac automaticity and prolonging refractoriness.

Selective adaptation in networks of heterogeneous populations: model, simulation, and experiment.

Biological systems often change their responsiveness when subject to persistent stimulation, a phenomenon termed adaptation. In neural systems, this process is often selective, allowing the system to adapt to one stimulus while preserving its sensitivity to another. In some studies, it has been shown that adaptation to a frequent stimulus increases the system's sensitivity to rare stimuli. These phenomena were explained in previous work as a result of complex interactions between the various subpopulations of the network. A formal description and analysis of neuronal systems, however, is hindered by the network's heterogeneity and by the multitude of processes taking place at different time-scales. Viewing neural networks as populations of interacting elements, we develop a framework that facilitates a formal analysis of complex, structured, heterogeneous networks. The formulation developed is based on an analysis of the availability of activity dependent resources, and their effects on network responsiveness. This approach offers a simple mechanistic explanation for selective adaptation, and leads to several predictions that were corroborated in both computer simulations and in cultures of cortical neurons developing in vitro. The framework is sufficiently general to apply to different biological systems, and was demonstrated in two different cases.

Order-based representation in random networks of cortical neurons.

The wide range of time scales involved in neural excitability and synaptic transmission might lead to ongoing change in the temporal structure of responses to recurring stimulus presentations on a trial-to-trial basis. This is probably the most severe biophysical constraint on putative time-based primitives of stimulus representation in neuronal networks. Here we show that in spontaneously developing large-scale random networks of cortical neurons in vitro the order in which neurons are recruited following each stimulus is a naturally emerging representation primitive that is invariant to significant temporal changes in spike times. With a relatively small number of randomly sampled neurons, the information about stimulus position is fully retrievable from the recruitment order. The effective connectivity that makes order-based representation invariant to time warping is characterized by the existence of stations through which activity is required to pass in order to propagate further into the network. This study uncovers a simple invariant in a noisy biological network in vitro; its applicability under in vivo constraints remains to be seen.

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.

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.