Danny Eytan

Dynamics and effective topology underlying synchronization in networks of cortical neurons

Cognitive processes depend on synchronization and propagation of electrical activity within and between neuronal assemblies. In vivo measurements show that the size of individual assemblies depends on their function and varies considerably, but the timescale of assembly activation is in the range of 0.1–0.2 s and is primarily independent of assembly size. Here we use an in vitro experimental model of cortical assemblies to characterize the process underlying the timescale of synchronization, its relationship to the effective topology of connectivity within an assembly, and its impact on propagation of activity within and between assemblies. We show that the basic mode of assembly activation, “network spike,” is a threshold-governed, synchronized population event of 0.1–0.2 s duration and follows the logistics of neuronal recruitment in an effectively scale-free connected network. Accordingly, the sequence of neuronal activation within a network spike is nonrandom and hierarchical; a small subset of neurons is consistently recruited tens of milliseconds before others. Theory predicts that scale-free topology allows for synchronization time that does not increase markedly with network size; our experiments with networks of different densities support this prediction. The activity of early-to-fire neurons reliably forecasts an upcoming network spike and provides means for expedited propagation between assemblies. We demonstrate this capacity by observing the dynamics of two artificially coupled assemblies in vitro, using neuronal activity of one as a trigger for electrical stimulation of the other.

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.

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.

Neuronal Response Clamp

Responses of individual neurons to ongoing input are highly variable, reflecting complex threshold dynamics. Experimental access to this threshold dynamics is required in order to fully characterize neuronal input–output relationships. The challenge is practically intractable using present day experimental paradigms due to the cumulative, non-linear interactions involved. Here we introduce the Neuronal Response Clamp, a closed-loop technique enabling control over the instantaneous response probability of the neuron. The potential of the technique is demonstrated by showing direct access to threshold dynamics of cortical neuron in vitro using extracellular recording and stimulation, over timescales ranging from seconds to many hours. Moreover, the method allowed us to expose the sensitivity of threshold dynamics to spontaneous input from the network in which the neuron is embedded. The Response-Clamp technique follows the rationale of the voltage-clamp and dynamic-clamp approaches, extending it to the neurons spiking behavior. The general framework offered here is applicable in the study of other neural systems, beyond the single neuron level.

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.

A generic framework for real-time multi-channel neuronal signal analysis, telemetry control, and sub-millisecond latency feedback generation.

Distinct modules of the neural circuitry interact with each other and (through the motor-sensory loop) with the environment, forming a complex dynamic system. Neuro-prosthetic devices seeking to modulate or restore CNS function need to interact with the information flow at the level of neural modules electrically, bi-directionally and in real-time. A set of freely available generic tools is presented that allow computationally demanding multi-channel short-latency bi-directional interactions to be realized in in vivo and in vitro preparations using standard PC data acquisition and processing hardware and software (Mathworks Matlab and Simulink). A commercially available 60-channel extracellular multi-electrode recording and stimulation set-up connected to an ex vivo developing cortical neuronal culture is used as a model system to validate the method. We demonstrate how complex high-bandwidth (>10 MBit/s) neural recording data can be analyzed in real-time while simultaneously generating specific complex electrical stimulation feedback with deterministically timed responses at sub-millisecond resolution.

On the precarious path of reverse neuro-engineering.

In this perspective we provide an example for the limits of reverse engineering in neuroscience. We demonstrate that application of reverse engineering to the study of the design principle of a functional neuro-system with a known mechanism, may result in a perfectly valid but wrong induction of the systems design principle. If in the very simple setup we bring here (static environment, primitive task and practically unlimited access to every piece of relevant information), it is difficult to induce a design principle, what are our chances of exposing biological design principles when more realistic conditions are examined? Implications to the way we do Biology are discussed.

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 systems 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 networks 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.

A generic model for selective adaptation in networks of heterogeneous populations

Adaptation is a biologically ubiquitous process whereby features of the systems responsiveness change as a result of persistent input. Most often, the kinetics of the change are monotonic and depend upon the input frequency. Adaptation in neural systems is inherently selective to the input characteristics; not only between sensory modalities, but even within a given modality, the system is capable of reducing its sensitivity to frequent input while preserving (or even enhancing) its sensitivity to the rare (e.g. [1-4]). In-vivo analyses suggest that a within-modality selective adaptation does not require concrete, precise point-to-point wiring (which would be a trivial yet nonphysiological realization) [5]. Indeed, theoretical considerations indicate that, for the case of a single neuron, selective adaptation can be explained in terms of synaptic population dynamics (e.g. [6]). In-vitro analyses in networks of cortical neurons show that, beyond temporal dynamics, differences between topologies of excitatory and inhibitory sub-networks account for the full range of selective adaptation phenomena, including increased sensitivity to the rare [7]. Formal descriptions of selective adaptation are hindered by the problem of representing these different topologies in an analytically useful manner. In this study we offer a formalism that expresses topologies of connectivity in terms of temporal input gain modulation. Using this technique, we are able to formulate a generic analytic model for selective adaptation, which reconstructs all the major experimentally observed phenomena, offers predictions for further experimental analyses, and caters for a rigorous characterization of adaptation in general, and selective adaptation in particular.

Representation and Learning in Neuronal Networks: A Conceptual Nervous System Approach

The work presented in this review describes the use of large cortical networks developing ex vivo, in a culture dish, to study principles underlying synchronization, adaptation, learning, and representation in neuronal assemblies. The motivation to study neuronal networks ex vivo is outlined together with a short description of recent results in this field. Following a short description of the experimental system, a set of basic results will be presented that concern self-organization of activity, dynamical and functional properties of neurons and networks in response to external stimulation. This short review ends with an outline of future questions and research directions.