Dynamics of excitability over extended timescales in cultured cortical neurons

Spiking image processing unit based on neural analog of Boolean logic operations

McCulloch and Pitts hypothesized in 1943 that the brain is entirely composed of logic gates, akin to current computers' IP cores, which led to several neural analogs of Boolean logic. The current study proposes a spiking image processing unit (SIPU) based on spiking frequency gates and coordinate logic operations, as a dynamical model of synapses and spiking neurons. SIPU can imitate DSP functions like edge recognition, picture magnification, noise reduction, etc. but can be extended to cater for more advanced computing tasks. The proposed spiking Boolean logic platform can be used to develop advanced applications without relying on learning or specialized datasets. It could aid in gaining a deeper understanding of complex brain functions and spur new forms of neural analogs.

Concurrent TMS/fMRI reveals individual DLPFC dose-response pattern

BACKGROUND

TMS is a valuable tool in both research and clinical settings, playing a crucial role in understanding brain-behavior relationships and providing treatment for various neurological and psychiatric conditions. Importantly, TMS over left DLPFC is an FDA approved treatment for MDD. Despite its potential, response variability to TMS remains a challenge, with stimulation parameters, particularly the stimulation intensity, being a primary contributor to these differences.

OBJECTIVE

The objective of this study was to establish dose-response relationships of TMS stimulation in DLPFC by means of concurrent TMS/fMRI.

METHODS

Here, we stimulated 15 subjects at different stimulation intensities of 80, 90, 100 and 110 % relative to the motor threshold during concurrent TMS/fMRI. The experiment comprised two sessions: one session to collect anatomical data in order to perform neuronavigation and one session dedicated to dose-response mapping. We calculated GLMs for each intensity level and each subject, as well as at a group-level per intensity.

RESULTS

On a group level, we show that the strongest BOLD-response was at 100 % stimulation. However, investigating individual dose response-relationships showed differences in response patterns across the group: subjects that responded to subthreshold stimulation, subjects that required above threshold stimulation in order to show a significant BOLD-response and atypical responders.

CONCLUSIONS

We observed qualitative inter-subject variability in terms of dose-response relationship to TMS over left DLPFC, which hints towards the motor threshold not being directly transferable to the excitability of the DLPFC. Concurrent TMS/fMRI might have the potential to improve response rates to rTMS applications. As such, it may be valuable in the future to consider implementing this approach prior to clinical TMS or validating more cost-effective methods to determine dose and target with respect to changes in clinical symptoms.

Investigation of the input-output relationship of engineered neural networks using high-density microelectrode arrays

Bottom-up neuroscience utilizes small, engineered biological neural networks to study neuronal activity in systems of reduced complexity. We present a platform that establishes up to six independent networks formed by primary rat neurons on planar complementary metal-oxide-semiconductor (CMOS) microelectrode arrays (MEAs). We introduce an approach that allows repetitive stimulation and recording of network activity at any of the over 700 electrodes underlying a network. We demonstrate that the continuous application of a repetitive super-threshold stimulus yields a reproducible network answer within a 15 ms post-stimulus window. This response can be tracked with high spatiotemporal resolution across the whole extent of the network. Moreover, we show that the location of the stimulation plays a significant role in the networks' early response to the stimulus. By applying a stimulation pattern to all network-underlying electrodes in sequence, the sensitivity of the whole network to the stimulus can be visualized. We demonstrate that microchannels reduce the voltage stimulation threshold and induce the strongest network response. By varying the stimulation amplitude and frequency we reveal discrete network transition points. Finally, we introduce vector fields to follow stimulation-induced spike propagation pathways within the network. Overall we show that our defined neural networks on CMOS MEAs enable us to elicit highly reproducible activity patterns that can be precisely modulated by stimulation amplitude, stimulation frequency and the site of stimulation.

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.

Biological complexity facilitates tuning of the neuronal parameter space

The electrical and computational properties of neurons in our brains are determined by a rich repertoire of membrane-spanning ion channels and elaborate dendritic trees. However, the precise reason for this inherent complexity remains unknown, given that simpler models with fewer ion channels are also able to functionally reproduce the behaviour of some neurons. Here, we stochastically varied the ion channel densities of a biophysically detailed dentate gyrus granule cell model to produce a large population of putative granule cells, comparing those with all 15 original ion channels to their reduced but functional counterparts containing only 5 ion channels. Strikingly, valid parameter combinations in the full models were dramatically more frequent at -6% vs. -1% in the simpler model. The full models were also more stable in the face of perturbations to channel expression levels. Scaling up the numbers of ion channels artificially in the reduced models recovered these advantages confirming the key contribution of the actual number of ion channel types. We conclude that the diversity of ion channels gives a neuron greater flexibility and robustness to achieve a target excitability.

Selective inhibition of excitatory synaptic transmission alters the emergent bursting dynamics of in vitro neural networks

Neurons in vitro connect to each other and form neural networks that display emergent electrophysiological activity. This activity begins as spontaneous uncorrelated firing in the early phase of development, and as functional excitatory and inhibitory synapses mature, the activity typically emerges as spontaneous network bursts. Network bursts are events of coordinated global activation among many neurons interspersed with periods of silencing and are important for synaptic plasticity, neural information processing, and network computation. While bursting is the consequence of balanced excitatory-inhibitory (E/I) interactions, the functional mechanisms underlying their evolution from physiological to potentially pathophysiological states, such as decreasing or increasing in synchrony, are still poorly understood. Synaptic activity, especially that related to maturity of E/I synaptic transmission, is known to strongly influence these processes. In this study, we used selective chemogenetic inhibition to target and disrupt excitatory synaptic transmission in in vitro neural networks to study functional response and recovery of spontaneous network bursts over time. We found that over time, inhibition resulted in increases in both network burstiness and synchrony. Our results indicate that the disruption in excitatory synaptic transmission during early network development likely affected inhibitory synaptic maturity which resulted in an overall decrease in network inhibition at later stages. These findings lend support to the importance of E/I balance in maintaining physiological bursting dynamics and, conceivably, information processing capacity in neural networks.

High-Throughput PEDOT:PSS/PtNPs-Modified Microelectrode Array for Simultaneous Recording and Stimulation of Hippocampal Neuronal Networks in Gradual Learning Process

When it comes to mechanisms of brain functions such as learning and memory mediated by neural networks, existing multichannel electrophysiological detection and regulation technology at the cellular level does not suffice. To address this challenge, a 128-channel microelectrode array (MEA) was fabricated for electrical stimulation (ES) training and electrophysiological recording of the hippocampal neurons in vitro. The PEDOT:PSS/PtNPs-coated microelectrodes dramatically promote the recording and electrical stimulation performance. The MEA exhibited low impedance (10.94 ± 0.49 kohm), small phase delay (-12.54 ± 0.51°), high charge storage capacity (14.84 ± 2.72 mC/cm²), and high maximum safe injection charge density (4.37 ± 0.22 mC/cm²), meeting the specific requirements for training neural networks in vitro. A series of ESs at various frequencies was applied to the neuronal cultures in vitro, seeking the optimum training mode that enables the neuron to display the most obvious plasticity, and 1 Hz ES was determined. The network learning process, including three consecutive trainings, affected the original random spontaneous activity. Along with that, the firing pattern gradually changed to burst and the correlation and synchrony of the neuronal activity in the network have progressively improved, increasing by 314% and 240%, respectively. The neurons remembered these changes for at least 4 h. Collectively, ES activates the learning and memory functions of neurons, which is manifested in transformations in the discharge pattern and the improvement of network correlation and synchrony. This study offers a high-performance MEA revealing the underlying learning and memory functions of the brain and therefore serves as a useful tool for the development of brain functions in the future.

Coordination Dynamics: A Foundation for Understanding Social Behavior

Humans' interactions with each other or with socially competent machines exhibit lawful coordination patterns at multiple levels of description. According to Coordination Dynamics, such laws specify the flow of coordination states produced by functional synergies of elements (e.g., cells, body parts, brain areas, people…) that are temporarily organized as single, coherent units. These coordinative structures or synergies may be mathematically characterized as informationally coupled self-organizing dynamical systems (Coordination Dynamics). In this paper, we start from a simple foundation, an elemental model system for social interactions, whose behavior has been captured in the Haken-Kelso-Bunz (HKB) model. We follow a tried and tested scientific method that tightly interweaves experimental neurobehavioral studies and mathematical models. We use this method to further develop a body of empirical research that advances the theory toward more generalized forms. In concordance with this interdisciplinary spirit, the present paper is written both as an overview of relevant advances and as an introduction to its mathematical underpinnings. We demonstrate HKB's evolution in the context of social coordination along several directions, with its applicability growing to increasingly complex scenarios. In particular, we show that accommodating for symmetry breaking in intrinsic dynamics and coupling, multiscale generalization and adaptation are principal evolutions. We conclude that a general framework for social coordination dynamics is on the horizon, in which models support experiments with hypothesis generation and mechanistic insights.

Functional Scaffolding for Brain Implants: Engineered Neuronal Network by Microfabrication and iPSC Technology

Neuroengineering methods can be effectively used in the design of new approaches to treat central nervous system and brain injury caused by neurotrauma, ischemia, or neurodegenerative disorders. During the last decade, significant results were achieved in the field of implant (scaffold) development using various biocompatible and biodegradable materials carrying neuronal cells for implantation into the injury site of the brain to repair its function. Neurons derived from animal or human induced pluripotent stem (iPS) cells are expected to be an ideal cell source, and induction methods for specific cell types have been actively studied to improve efficacy and specificity. A critical goal of neuro-regeneration is structural and functional restoration of the injury site. The target treatment area has heterogeneous and complex network topology with various types of cells that need to be restored with similar neuronal network structure to recover correct functionality. However, current scaffold-based technology for brain implants operates with homogeneous neuronal cell distribution, which limits recovery in the damaged area of the brain and prevents a return to fully functional biological tissue. In this study, we present a neuroengineering concept for designing a neural circuit with a pre-defined unidirectional network architecture that provides a balance of excitation/inhibition in the scaffold to form tissue similar to that in the injured area using various types of iPS cells. Such tissue will mimic the surrounding niche in the injured site and will morphologically and topologically integrate into the brain, recovering lost function.

A hypothesis regarding how sleep can calibrate neuronal excitability in the central nervous system and thereby offer stability, sensitivity and the best possible cognitive function

The function of sleep in mammal and other vertebrates is one of the great mysteries of biology. Many hypotheses have been proposed, but few of these have made even the slightest attempt to explain the essence of sleep - the uncompromising need for reversible unconsciousness. During sleep, epiphenomena - often of a somatic character - occur, but these cannot explain the core function of sleep. One answer could be hidden in the observations made for long periods of time of the function of the central nervous system (CNS). The CNS is faced with conflicting requirements on stability and excitability. A high level of excitability is desirable, and is also a prerequisite for sensitivity and quick reaction times; however, it can also lead to instability and the risk of feedback, with life-threatening epileptic seizures. Activity-dependent negative feedback in neuronal excitability improves stability in the short term, but not to the degree that is required. A hypothesis is presented here demonstrating how calibration of individual neurons - an activity which occurs only during sleep - can establish the balanced and highest possible excitability while also preserving stability in the CNS. One example of a possible mechanism is the observation of slow oscillations in EEGs made on birds and mammals during slow wave sleep. Calibration to a genetically determined level of excitability could take place in individual neurons during the slow oscillation. This is only possible offline, which explains the need for sleep. The hypothesis can explain phenomena such as the need for unconsciousness during sleep, with the disconnection of sensory stimuli, slow EEG oscillations, the relationship of sleep and epilepsy, age, the effects of sleep on neuronal firing rate and the effects of sleep deprivation and sleep homeostasis. This is with regard primarily to mammals, including humans, but also all other vertebrates.

The Energy Homeostasis Principle: Neuronal Energy Regulation Drives Local Network Dynamics Generating Behavior

A major goal of neuroscience is understanding how neurons arrange themselves into neural networks that result in behavior. Most theoretical and experimental efforts have focused on a top-down approach which seeks to identify neuronal correlates of behaviors. This has been accomplished by effectively mapping specific behaviors to distinct neural patterns, or by creating computational models that produce a desired behavioral outcome. Nonetheless, these approaches have only implicitly considered the fact that neural tissue, like any other physical system, is subjected to several restrictions and boundaries of operations. Here, we proposed a new, bottom-up conceptual paradigm: The Energy Homeostasis Principle, where the balance between energy income, expenditure, and availability are the key parameters in determining the dynamics of neuronal phenomena found from molecular to behavioral levels. Neurons display high energy consumption relative to other cells, with metabolic consumption of the brain representing 20% of the whole-body oxygen uptake, contrasting with this organ representing only 2% of the body weight. Also, neurons have specialized surrounding tissue providing the necessary energy which, in the case of the brain, is provided by astrocytes. Moreover, and unlike other cell types with high energy demands such as muscle cells, neurons have strict aerobic metabolism. These facts indicate that neurons are highly sensitive to energy limitations, with Gibb's free energy dictating the direction of all cellular metabolic processes. From this activity, the largest energy, by far, is expended by action potentials and post-synaptic potentials; therefore, plasticity can be reinterpreted in terms of their energy context. Consequently, neurons, through their synapses, impose energy demands over post-synaptic neurons in a close loop-manner, modulating the dynamics of local circuits. Subsequently, the energy dynamics end up impacting the homeostatic mechanisms of neuronal networks. Furthermore, local energy management also emerges as a neural population property, where most of the energy expenses are triggered by sensory or other modulatory inputs. Local energy management in neurons may be sufficient to explain the emergence of behavior, enabling the assessment of which properties arise in neural circuits and how. Essentially, the proposal of the Energy Homeostasis Principle is also readily testable for simple neuronal networks.

Sensitivity to Stimulus Irregularity Is Inherent in Neural Networks

Behavior is controlled by complex neural networks in which neurons process thousands of inputs. However, even short spike trains evoked in a single cortical neuron were demonstrated to be sufficient to influence behavior in vivo. Specifically, irregular sequences of interspike intervals (ISIs) had a more reliable influence on behavior despite their resemblance to stochastic activity. Similarly, irregular tactile stimulation led to higher rates of behavioral responses. In this study, we identify the mechanisms enabling this sensitivity to stimulus irregularity (SSI) on the neuronal and network levels using simulated spiking neural networks. Matching in vivo experiments, we find that irregular stimulation elicits more detectable network events (bursts) than regular stimulation. Dissecting the stimuli, we identify short ISIs-occurring more frequently in irregular stimulations-as the main drivers of SSI rather than complex irregularity per se. In addition, we find that short-term plasticity modulates SSI. We subsequently eliminate the different mechanisms in turn to assess their role in generating SSI. Removing inhibitory interneurons, we find that SSI is retained, suggesting that SSI is not dependent on inhibition. Removing recurrency, we find that SSI is retained due to the ability of individual neurons to integrate activity over short timescales ("cell memory"). Removing single-neuron dynamics, we find that SSI is retained based on the short-term retention of activity within the recurrent network structure ("network memory"). Finally, using a further simplified probabilistic model, we find that local network structure is not required for SSI. Hence, SSI is identified as a general property that we hypothesize to be ubiquitous in neural networks with different structures and biophysical properties. Irregular sequences contain shorter ISIs, which are the main drivers underlying SSI. The experimentally observed SSI should thus generalize to other systems, suggesting a functional role for irregular activity in cortex.

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.

Contrasting the effects of adaptation and synaptic filtering on the timescales of dynamics in recurrent networks

Neural activity in awake behaving animals exhibits a vast range of timescales that can be several fold larger than the membrane time constant of individual neurons. Two types of mechanisms have been proposed to explain this conundrum. One possibility is that large timescales are generated by a network mechanism based on positive feedback, but this hypothesis requires fine-tuning of the strength or structure of the synaptic connections. A second possibility is that large timescales in the neural dynamics are inherited from large timescales of underlying biophysical processes, two prominent candidates being intrinsic adaptive ionic currents and synaptic transmission. How the timescales of adaptation or synaptic transmission influence the timescale of the network dynamics has however not been fully explored. To address this question, here we analyze large networks of randomly connected excitatory and inhibitory units with additional degrees of freedom that correspond to adaptation or synaptic filtering. We determine the fixed points of the systems, their stability to perturbations and the corresponding dynamical timescales. Furthermore, we apply dynamical mean field theory to study the temporal statistics of the activity in the fluctuating regime, and examine how the adaptation and synaptic timescales transfer from individual units to the whole population. Our overarching finding is that synaptic filtering and adaptation in single neurons have very different effects at the network level. Unexpectedly, the macroscopic network dynamics do not inherit the large timescale present in adaptive currents. In contrast, the timescales of network activity increase proportionally to the time constant of the synaptic filter. Altogether, our study demonstrates that the timescales of different biophysical processes have different effects on the network level, so that the slow processes within individual neurons do not necessarily induce slow activity in large recurrent neural networks.

Long-Term Activity Dynamics of Single Neurons and Networks

The firing rate of neuronal spiking in vitro and in vivo significantly varies over extended timescales, characterized by long-memory processes and complex statistics, and appears in spontaneous as well as evoked activity upon repeated stimulus presentation. These variations in response features and their statistics, in face of repeated instances of a given physical input, are ubiquitous in all levels of brain-behavior organization. They are expressed in single neuron and network response variability but even appear in variations of subjective percepts or psychophysical choices and have been described as stemming from history-dependent, stochastic, or rate-determined processes.But what are the sources underlying these temporally rich variations in firing rate? Are they determined by interactions of the nervous system as a whole, or do isolated, single neurons or neuronal networks already express these fluctuations independent of higher levels? These questions motivated the application of a method that allows for controlled and specific long-term activation of a single neuron or neuronal network, isolated from higher levels of cortical organization.This chapter highlights the research done in cultured cortical networks to study (1) the inherent non-stationarity of neuronal network activity, (2) single neuron response fluctuations and underlying processes, and (3) the interface layer between network and single cell, the non-stationary efficacy of the ensemble of synapses impinging onto the observed neuron.

Spontaneous activity emerging from an inferred network model captures complex spatio-temporal dynamics of spike data

Inference methods are widely used to recover effective models from observed data. However, few studies attempted to investigate the dynamics of inferred models in neuroscience, and none, to our knowledge, at the network level. We introduce a principled modification of a widely used generalized linear model (GLM), and learn its structural and dynamic parameters from in-vitro spike data. The spontaneous activity of the new model captures prominent features of the non-stationary and non-linear dynamics displayed by the biological network, where the reference GLM largely fails, and also reflects fine-grained spatio-temporal dynamical features. Two ingredients were key for success. The first is a saturating transfer function: beyond its biological plausibility, it limits the neuron's information transfer, improving robustness against endogenous and external noise. The second is a super-Poisson spikes generative mechanism; it accounts for the undersampling of the network, and allows the model neuron to flexibly incorporate the observed activity fluctuations.

Circuit Polarity Effect of Cortical Connectivity, Activity, and Memory

Experimental constraints have traditionally implied separate studies of different cortical functions, such as memory and sensory-motor control. Yet certain cortical modalities, while repeatedly observed and reported, have not been clearly identified with one cortical function or another. Specifically, while neuronal membrane and synapse polarities with respect to a certain potential value have been attracting considerable interest in recent years, the purposes of such polarities have largely remained a subject for speculation and debate. Formally identifying these polarities as on-off neuronal polarity gates, we analytically show that cortical circuit structure, behavior, and memory are all governed by the combined potent effect of these gates, which we collectively term circuit polarity. Employing widely accepted and biologically validated firing rate and plasticity paradigms, we show that circuit polarity is mathematically embedded in the corresponding models. Moreover, we show that the firing rate dynamics implied by these models are driven by ongoing circuit polarity gating dynamics. Furthermore, circuit polarity is shown to segregate cortical circuits into internally synchronous, externally asynchronous subcircuits, defining their firing rate modes in accordance with different cortical tasks. In contrast to the Hebbian paradigm, which is shown to be susceptible to mutual neuronal interference in the face of asynchrony, circuit polarity is shown to block such interference. Noting convergence of synaptic weights, we show that circuit polarity holds the key to cortical memory, having a segregated capacity linear in the number of neurons. While memory concealment is implied by complete neuronal silencing, memory is restored by reactivating the original circuit polarity. Finally, we show that incomplete deterioration or restoration of circuit polarity results in memory modification, which may be associated with partial or false recall, or novel innovation.

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.

Principles of Temporal Processing Across the Cortical Hierarchy

The world is richly structured on multiple spatiotemporal scales. In order to represent spatial structure, many machine-learning models repeat a set of basic operations at each layer of a hierarchical architecture. These iterated spatial operations - including pooling, normalization and pattern completion - enable these systems to recognize and predict spatial structure, while robust to changes in the spatial scale, contrast and noisiness of the input signal. Because our brains also process temporal information that is rich and occurs across multiple time scales, might the brain employ an analogous set of operations for temporal information processing? Here we define a candidate set of temporal operations, and we review evidence that they are implemented in the mammalian cerebral cortex in a hierarchical manner. We conclude that multiple consecutive stages of cortical processing can be understood to perform temporal pooling, temporal normalization and temporal pattern completion.

Investigating the impact of electrical stimulation temporal distribution on cortical network responses

Background

The brain is continuously targeted by a wealth of stimuli with complex spatio-temporal patterns and has presumably evolved in order to cope with those inputs in an optimal way. Previous studies investigating the response capabilities of either single neurons or intact sensory systems to external stimulation demonstrated that stimuli temporal distribution is an important, if often overlooked, parameter.

Results

In this study we investigated how cortical networks plated over micro-electrode arrays respond to different stimulation sequences in which inter-pulse intervals followed a 1/f^β distribution, for different values of β ranging from 0 to ∞. Cross-correlation analysis revealed that network activity preferentially synchronizes with external input sequences featuring β closer to 1 and, in any case, never for regular (i.e. fixed-frequency) stimulation sequences. We then tested the interplay between different average stimulation frequencies (based on the intrinsic firing/bursting frequency of the network) for two selected values of β, i.e. 1 (scale free) and ∞ (regular). In general, we observed no preference for stimulation frequencies matching the endogenous rhythms of the network. Moreover, we found that in case of regular stimulation the capability of the network to follow the stimulation sequence was negatively correlated to the absolute stimulation frequency, whereas using scale-free stimulation cross-correlation between input and output sequences was independent from average input frequency.

Conclusions

Our results point out that the preference for a scale-free distribution of the stimuli is observed also at network level and should be taken into account in designing more efficient protocols for neuromodulation purposes.

Electronic supplementary material

The online version of this article (doi:10.1186/s12868-017-0366-z) contains supplementary material, which is available to authorized users.

Combination of High-density Microelectrode Array and Patch Clamp Recordings to Enable Studies of Multisynaptic Integration

We present a novel, all-electric approach to record and to precisely control the activity of tens of individual presynaptic neurons. The method allows for parallel mapping of the efficacy of multiple synapses and of the resulting dynamics of postsynaptic neurons in a cortical culture. For the measurements, we combine an extracellular high-density microelectrode array, featuring 11’000 electrodes for extracellular recording and stimulation, with intracellular patch-clamp recording. We are able to identify the contributions of individual presynaptic neurons - including inhibitory and excitatory synaptic inputs - to postsynaptic potentials, which enables us to study dendritic integration. Since the electrical stimuli can be controlled at microsecond resolution, our method enables to evoke action potentials at tens of presynaptic cells in precisely orchestrated sequences of high reliability and minimum jitter. We demonstrate the potential of this method by evoking short- and long-term synaptic plasticity through manipulation of multiple synaptic inputs to a specific neuron.

Dynamical Timescale Explains Marginal Stability in Excitability Dynamics

Action potentials, taking place over milliseconds, are the basis of neural computation. However, the dynamics of excitability over longer, behaviorally relevant timescales remain underexplored. A recent experiment used long-term recordings from single neurons to reveal multiple timescale fluctuations in response to constant stimuli, along with more reliable responses to variable stimuli. Here, we demonstrate that this apparent paradox is resolved if neurons operate in a marginally stable dynamic regime, which we reveal using a novel inference method. Excitability in this regime is characterized by large fluctuations while retaining high sensitivity to external varying stimuli. A new model with a dynamic recovery timescale that interacts with excitability captures this dynamic regime and predicts the neurons' response with high accuracy. The model explains most experimental observations under several stimulus statistics. The compact structure of our model permits further exploration on the network level.SIGNIFICANCE STATEMENT Excitability is the basis for all neural computations and its long-term dynamics reveal a complex combination of many timescales. We discovered that neural excitability operates under a marginally stable regime in which the system is dominated by internal fluctuation while retaining high sensitivity to externally varying stimuli. We offer a novel approach to modeling excitability dynamics by assuming that the recovery timescale is itself a dynamic variable. Our model is able to capture a wide range of experimental phenomena using few parameters with significantly higher predictive power than previous models.

Multichannel activity propagation across an engineered axon network

OBJECTIVE

Although substantial progress has been made in mapping the connections of the brain, less is known about how this organization translates into brain function. In particular, the massive interconnectivity of the brain has made it difficult to specifically examine data transmission between two nodes of the connectome, a central component of the 'neural code.' Here, we investigated the propagation of multiple streams of asynchronous neuronal activity across an isolated in vitro 'connectome unit.'

APPROACH

We used the novel technique of axon stretch growth to create a model of a long-range cortico-cortical network, a modular system consisting of paired nodes of cortical neurons connected by axon tracts. Using optical stimulation and multi-electrode array recording techniques, we explored how input patterns are represented by cortical networks, how these representations shift as they are transmitted between cortical nodes and perturbed by external conditions, and how well the downstream node distinguishes different patterns.

MAIN RESULTS

Stimulus representations included direct, synaptic, and multiplexed responses that grew in complexity as the distance between the stimulation source and recorded neuron increased. These representations collapsed into patterns with lower information content at higher stimulation frequencies. With internodal activity propagation, a hierarchy of network pathways, including latent circuits, was revealed using glutamatergic blockade. As stimulus channels were added, divergent, non-linear effects were observed in local versus distant network layers. Pairwise difference analysis of neuronal responses suggested that neuronal ensembles generally outperformed individual cells in discriminating input patterns.

SIGNIFICANCE

Our data illuminate the complexity of spiking activity propagation in cortical networks in vitro, which is characterized by the transformation of an input into myriad outputs over several network layers. These results provide insight into how the brain potentially processes information and generates the neural code and could guide the development of clinical therapies based on multichannel brain stimulation.

Autonomous Optimization of Targeted Stimulation of Neuronal Networks

Driven by clinical needs and progress in neurotechnology, targeted interaction with neuronal networks is of increasing importance. Yet, the dynamics of interaction between intrinsic ongoing activity in neuronal networks and their response to stimulation is unknown. Nonetheless, electrical stimulation of the brain is increasingly explored as a therapeutic strategy and as a means to artificially inject information into neural circuits. Strategies using regular or event-triggered fixed stimuli discount the influence of ongoing neuronal activity on the stimulation outcome and are therefore not optimal to induce specific responses reliably. Yet, without suitable mechanistic models, it is hardly possible to optimize such interactions, in particular when desired response features are network-dependent and are initially unknown. In this proof-of-principle study, we present an experimental paradigm using reinforcement-learning (RL) to optimize stimulus settings autonomously and evaluate the learned control strategy using phenomenological models. We asked how to (1) capture the interaction of ongoing network activity, electrical stimulation and evoked responses in a quantifiable ‘state’ to formulate a well-posed control problem, (2) find the optimal state for stimulation, and (3) evaluate the quality of the solution found. Electrical stimulation of generic neuronal networks grown from rat cortical tissue in vitro evoked bursts of action potentials (responses). We show that the dynamic interplay of their magnitudes and the probability to be intercepted by spontaneous events defines a trade-off scenario with a network-specific unique optimal latency maximizing stimulus efficacy. An RL controller was set to find this optimum autonomously. Across networks, stimulation efficacy increased in 90% of the sessions after learning and learned latencies strongly agreed with those predicted from open-loop experiments. Our results show that autonomous techniques can exploit quantitative relationships underlying activity-response interaction in biological neuronal networks to choose optimal actions. Simple phenomenological models can be useful to validate the quality of the resulting controllers.

Electrical stimulation of the brain is increasingly used to alleviate the symptoms of a range of neurological disorders and as a means to artificially inject information into neural circuits in neuroprosthetic applications. Machine learning has been proposed to find optimal stimulation settings autonomously. However, this approach is impeded by the complexity of the interaction between the stimulus and the activity of the network, which makes it difficult to test how good the result actually is. We used phenomenological models of the interaction between stimulus and spontaneous activity in a neuronal network to design a testable machine learning challenge and evaluate the quality of the solution found by the algorithm. In this task, the learning algorithm had to find a solution that balances competing interdependencies of ongoing neuronal activity with opposing effects on the efficacy of stimulation. We show that machine learning can successfully solve this task and that the solutions found are close to the optimal settings to maximize the efficacy of stimulation. Since the paradigm involves several typical problems found in other settings, such concepts could help to formalize machine learning problems in more complex biological networks and to test the quality of their performance.

Modelling and Analysis of Electrical Potentials Recorded in Microelectrode Arrays (MEAs)

Microelectrode arrays (MEAs), substrate-integrated planar arrays of up to thousands of closely spaced metal electrode contacts, have long been used to record neuronal activity in in vitro brain slices with high spatial and temporal resolution. However, the analysis of the MEA potentials has generally been mainly qualitative. Here we use a biophysical forward-modelling formalism based on the finite element method (FEM) to establish quantitatively accurate links between neural activity in the slice and potentials recorded in the MEA set-up. Then we develop a simpler approach based on the method of images (MoI) from electrostatics, which allows for computation of MEA potentials by simple formulas similar to what is used for homogeneous volume conductors. As we find MoI to give accurate results in most situations of practical interest, including anisotropic slices covered with highly conductive saline and MEA-electrode contacts of sizable physical extensions, a Python software package (ViMEAPy) has been developed to facilitate forward-modelling of MEA potentials generated by biophysically detailed multicompartmental neurons. We apply our scheme to investigate the influence of the MEA set-up on single-neuron spikes as well as on potentials generated by a cortical network comprising more than 3000 model neurons. The generated MEA potentials are substantially affected by both the saline bath covering the brain slice and a (putative) inadvertent saline layer at the interface between the MEA chip and the brain slice. We further explore methods for estimation of current-source density (CSD) from MEA potentials, and find the results to be much less sensitive to the experimental set-up.

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.

The mechanics of state-dependent neural correlations

Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of population activity is the trial-to-trial correlated fluctuation of spike train outputs from recorded neuron pairs. Similar to the firing rate of single neurons, correlated activity can be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. However, the physiological mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations and the transfer function of single neurons. We first examine these mechanisms in feedforward pathways and then show how the same approach can explain the modulation of correlations in recurrent networks. Such mechanistic constraints on the modulation of population activity will be important in statistical analyses of high-dimensional neural data.

Combined Exposure to Simulated Microgravity and Acute or Chronic Radiation Reduces Neuronal Network Integrity and Survival

During orbital or interplanetary space flights, astronauts are exposed to cosmic radiations and microgravity. However, most earth-based studies on the potential health risks of space conditions have investigated the effects of these two conditions separately. This study aimed at assessing the combined effect of radiation exposure and microgravity on neuronal morphology and survival in vitro. In particular, we investigated the effects of simulated microgravity after acute (X-rays) or during chronic (Californium-252) exposure to ionizing radiation using mouse mature neuron cultures. Acute exposure to low (0.1 Gy) doses of X-rays caused a delay in neurite outgrowth and a reduction in soma size, while only the high dose impaired neuronal survival. Of interest, the strongest effect on neuronal morphology and survival was evident in cells exposed to microgravity and in particular in cells exposed to both microgravity and radiation. Removal of neurons from simulated microgravity for a period of 24 h was not sufficient to recover neurite length, whereas the soma size showed a clear re-adaptation to normal ground conditions. Genome-wide gene expression analysis confirmed a modulation of genes involved in neurite extension, cell survival and synaptic communication, suggesting that these changes might be responsible for the observed morphological effects. In general, the observed synergistic changes in neuronal network integrity and cell survival induced by simulated space conditions might help to better evaluate the astronaut's health risks and underline the importance of investigating the central nervous system and long-term cognition during and after a space flight.

Brief wide-field photostimuli evoke and modulate oscillatory reverberating activity in cortical networks

Cell assemblies manipulation by optogenetics is pivotal to advance neuroscience and neuroengineering. In in vivo applications, photostimulation often broadly addresses a population of cells simultaneously, leading to feed-forward and to reverberating responses in recurrent microcircuits. The former arise from direct activation of targets downstream, and are straightforward to interpret. The latter are consequence of feedback connectivity and may reflect a variety of time-scales and complex dynamical properties. We investigated wide-field photostimulation in cortical networks in vitro, employing substrate-integrated microelectrode arrays and long-term cultured neuronal networks. We characterized the effect of brief light pulses, while restricting the expression of channelrhodopsin to principal neurons. We evoked robust reverberating responses, oscillating in the physiological gamma frequency range, and found that such a frequency could be reliably manipulated varying the light pulse duration, not its intensity. By pharmacology, mathematical modelling, and intracellular recordings, we conclude that gamma oscillations likely emerge as in vivo from the excitatory-inhibitory interplay and that, unexpectedly, the light stimuli transiently facilitate excitatory synaptic transmission. Of relevance for in vitro models of (dys)functional cortical microcircuitry and in vivo manipulations of cell assemblies, we give for the first time evidence of network-level consequences of the alteration of synaptic physiology by optogenetics.

Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model

We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron.

There is increasing evidence that the activity of individual membrane ion channels, conductances, and the firing rate of neurons are history dependent. In this work we studied how history dependent activation of membrane conductances affect the action potential activity of the Hodgkin-Huxley model, a widely used model of action potential generation. In order to implement history dependent activation, we made use of fractional order differential equations. This type of history dependent differential equations are increasingly being used in biomedical sciences to simulate complex phenomena. We use fractional order derivatives to model the kinetic dynamics of the gate variables for the potassium and sodium conductances of the Hodgkin-Huxley model. Our results show that power-law dynamics of the different gate variables result in a wide range of action potential shapes and spiking patterns, even in the case where the model was stimulated with constant current. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron.

Time-Dependent Increase in Network Response to Stimulation

In vitro neuronal cultures have become a popular method with which to probe network-level neuronal dynamics and phenomena in controlled laboratory settings. One of the key dynamics of interest in these in vitro studies has been the extent to which cultured networks display properties indicative of learning. Here we demonstrate the effects of a high frequency electrical stimulation signal in training cultured networks of cortical neurons. Networks receiving this training signal displayed a time-dependent increase in the response to a low frequency probing stimulation, particularly in the time window of 20–50 ms after stimulation. This increase was found to be statistically significant as compared to control networks that did not receive training. The timing of this increase suggests potentiation of synaptic mechanisms. To further investigate this possibility, we leveraged the powerful Cox statistical connectivity method as previously investigated by our group. This method was used to identify and track changes in network connectivity strength.

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.

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.

Can mechanistic explanation be reconciled with scale-free constitution and dynamics?

This paper considers two objections to explanations that appeal to mechanisms to explain biological phenomena. Marom argues that the time-scale on which many phenomena occur is scale-free. There is also reason to suspect that the network of interacting entities is scale-free. The result is that mechanisms do not have well-delineated boundaries in nature. I argue that bounded mechanisms should be viewed as entities scientists posit in advancing scientific hypotheses. In positing such entities, scientists idealize. Such idealizations can be highly productive in developing and improving scientific explanations even if the hypothesized mechanisms never precisely correspond to bounded entities in nature. Mechanistic explanations can be reconciled with scale-free constitution and dynamics even if mechanisms as bounded entities don't exist.

Interaction of electrically evoked activity with intrinsic dynamics of cultured cortical networks with and without functional fast GABAergic synaptic transmission

The modulation of neuronal activity by means of electrical stimulation is a successful therapeutic approach for patients suffering from a variety of central nervous system disorders. Prototypic networks formed by cultured cortical neurons represent an important model system to gain general insights in the input–output relationships of neuronal tissue. These networks undergo a multitude of developmental changes during their maturation, such as the excitatory–inhibitory shift of the neurotransmitter GABA. Very few studies have addressed how the output properties to a given stimulus change with ongoing development. Here, we investigate input–output relationships of cultured cortical networks by probing cultures with and without functional GABA_Aergic synaptic transmission with a set of stimulation paradigms at various stages of maturation. On the cellular level, low stimulation rates (<15 Hz) led to reliable neuronal responses; higher rates were increasingly ineffective. Similarly, on the network level, lowest stimulation rates (<0.1 Hz) lead to maximal output rates at all ages, indicating a network wide refractory period after each stimulus. In cultures aged 3 weeks and older, a gradual recovery of the network excitability within tens of milliseconds was in contrast to an abrupt recovery after about 5 s in cultures with absent GABA_Aergic synaptic transmission. In these GABA deficient cultures evoked responses were prolonged and had multiple discharges. Furthermore, the network excitability changed periodically, with a very slow spontaneous change of the overall network activity in the minute range, which was not observed in cultures with absent GABA_Aergic synaptic transmission. The electrically evoked activity of cultured cortical networks, therefore, is governed by at least two potentially interacting mechanisms: A refractory period in the order of a few seconds and a very slow GABA dependent oscillation of the network excitability.

Stability of Neuronal Networks with Homeostatic Regulation

Neurons are equipped with homeostatic mechanisms that counteract long-term perturbations of their average activity and thereby keep neurons in a healthy and information-rich operating regime. While homeostasis is believed to be crucial for neural function, a systematic analysis of homeostatic control has largely been lacking. The analysis presented here analyses the necessary conditions for stable homeostatic control. We consider networks of neurons with homeostasis and show that homeostatic control that is stable for single neurons, can destabilize activity in otherwise stable recurrent networks leading to strong non-abating oscillations in the activity. This instability can be prevented by slowing down the homeostatic control. The stronger the network recurrence, the slower the homeostasis has to be. Next, we consider how non-linearities in the neural activation function affect these constraints. Finally, we consider the case that homeostatic feedback is mediated via a cascade of multiple intermediate stages. Counter-intuitively, the addition of extra stages in the homeostatic control loop further destabilizes activity in single neurons and networks. Our theoretical framework for homeostasis thus reveals previously unconsidered constraints on homeostasis in biological networks, and identifies conditions that require the slow time-constants of homeostatic regulation observed experimentally.

Despite their apparent robustness many biological system work best in controlled environments, the tightly regulated mammalian body temperature being a good example. Biological homeostatic control systems, not unlike those used in engineering, ensure that the right operating conditions are met. Similarly, neurons appear to adjust the amount of activity they produce to be neither too high nor too low by, among other ways, regulating their excitability. However, for no apparent reason the neural homeostatic processes are very slow, taking hours or even days to regulate the neuron. Here we use results from mathematical control theory to examine under which conditions such slow control is necessary to prevent instabilities that lead to strong, sustained oscillations in the activity. Our results lead to a deeper understanding of neural homeostasis and can help the design of artificial neural systems.

Irregular spiking of pyramidal neurons organizes as scale-invariant neuronal avalanches in the awake state

Spontaneous fluctuations in neuronal activity emerge at many spatial and temporal scales in cortex. Population measures found these fluctuations to organize as scale-invariant neuronal avalanches, suggesting cortical dynamics to be critical. Macroscopic dynamics, though, depend on physiological states and are ambiguous as to their cellular composition, spatiotemporal origin, and contributions from synaptic input or action potential (AP) output. Here, we study spontaneous firing in pyramidal neurons (PNs) from rat superficial cortical layers in vivo and in vitro using 2-photon imaging. As the animal transitions from the anesthetized to awake state, spontaneous single neuron firing increases in irregularity and assembles into scale-invariant avalanches at the group level. In vitro spike avalanches emerged naturally yet required balanced excitation and inhibition. This demonstrates that neuronal avalanches are linked to the global physiological state of wakefulness and that cortical resting activity organizes as avalanches from firing of local PN groups to global population activity.

DOI:http://dx.doi.org/10.7554/eLife.07224.001

Even when we are not engaged in any specific task, the brain shows coordinated patterns of spontaneous activity that can be monitored using electrodes placed on the scalp. This resting activity shapes the way that the brain responds to subsequent stimuli. Changes in resting activity patterns are seen in various neurological and psychiatric disorders, as well as in healthy individuals following sleep deprivation.

The brain's outer layer is known as the cortex. On a large scale, when monitoring many thousands of neurons, resting activity in the cortex demonstrates propagation in the brain in an organized manner. Specifically, resting activity was found to organize as so-called neuronal avalanches, in which large bursts of neuronal activity are grouped with medium-sized and smaller bursts in a very characteristic order. In fact, the sizes of these bursts—that is, the number of neurons that fire—are found to be scale-invariant, that is, the ratio of large bursts to medium-sized bursts is the same as that of medium-sized to small bursts. Such scale-invariance suggests that neuronal bursts are not independent of one another. However, it is largely unclear how neuronal avalanches arise from individual neurons, which fire simply in a noisy, irregular manner.

Bellay, Klaus et al. have now provided insights into this process by examining patterns of firing of a particular type of neuron—known as a pyramidal cell—in the cortex of rats as they recover from anesthesia. As the animals awaken, the firing of individual pyramidal cells in the cortex becomes even more irregular than under anesthesia. However, by considering the activity of a group of these neurons, Bellay, Klaus et al. realized that it is this more irregular firing that gives rise to neuronal avalanches, and that this occurs only when the animals are awake. Further experiments on individual pyramidal cells grown in the laboratory confirmed that neuronal avalanches emerge spontaneously from the irregular firing of individual neurons. These avalanches depend on there being a balance between two types of activity among the cells: ‘excitatory’ activity that causes other neurons to fire, and ‘inhibitory’ activity that prevents neuronal firing.

Given that resting activity influences the brain's responses to the outside world, the origins of neuronal avalanches are likely to provide clues about the way the brain processes information. Future experiments should also examine the possibility that the emergence of neuronal avalanches marks the transition from unconsciousness to wakefulness within the brain.

DOI:http://dx.doi.org/10.7554/eLife.07224.002

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond

Experimental neuroscience is witnessing an increased interest in the development and application of novel and often complex, closed-loop protocols, where the stimulus applied depends in real-time on the response of the system. Recent applications range from the implementation of virtual reality systems for studying motor responses both in mice and in zebrafish, to control of seizures following cortical stroke using optogenetics. A key advantage of closed-loop techniques resides in the capability of probing higher dimensional properties that are not directly accessible or that depend on multiple variables, such as neuronal excitability and reliability, while at the same time maximizing the experimental throughput. In this contribution and in the context of cellular electrophysiology, we describe how to apply a variety of closed-loop protocols to the study of the response properties of pyramidal cortical neurons, recorded intracellularly with the patch clamp technique in acute brain slices from the somatosensory cortex of juvenile rats. As no commercially available or open source software provides all the features required for efficiently performing the experiments described here, a new software toolbox called LCG was developed, whose modular structure maximizes reuse of computer code and facilitates the implementation of novel experimental paradigms. Stimulation waveforms are specified using a compact meta-description and full experimental protocols are described in text-based configuration files. Additionally, LCG has a command-line interface that is suited for repetition of trials and automation of experimental protocols.

Neuronal response impedance mechanism implementing cooperative networks with low firing rates and μs precision

Realizations of low firing rates in neural networks usually require globally balanced distributions among excitatory and inhibitory links, while feasibility of temporal coding is limited by neuronal millisecond precision. We show that cooperation, governing global network features, emerges through nodal properties, as opposed to link distributions. Using in vitro and in vivo experiments we demonstrate microsecond precision of neuronal response timings under low stimulation frequencies, whereas moderate frequencies result in a chaotic neuronal phase characterized by degraded precision. Above a critical stimulation frequency, which varies among neurons, response failures were found to emerge stochastically such that the neuron functions as a low pass filter, saturating the average inter-spike-interval. This intrinsic neuronal response impedance mechanism leads to cooperation on a network level, such that firing rates are suppressed toward the lowest neuronal critical frequency simultaneously with neuronal microsecond precision. Our findings open up opportunities of controlling global features of network dynamics through few nodes with extreme properties.

Incubator-independent cell-culture perfusion platform for continuous long-term microelectrode array electrophysiology and time-lapse imaging

Most in vitro electrophysiology studies extract information and draw conclusions from representative, temporally limited snapshot experiments. This approach bears the risk of missing decisive moments that may make a difference in our understanding of physiological events. This feasibility study presents a simple benchtop cell-culture perfusion system adapted to commercial microelectrode arrays (MEAs), multichannel electrophysiology equipment and common inverted microscopy stages for simultaneous and uninterrupted extracellular electrophysiology and time-lapse imaging at ambient CO2 levels. The concept relies on a transparent, replica-casted polydimethylsiloxane perfusion cap, gravity- or syringe-pump-driven perfusion and preconditioning of pH-buffered serum-free cell-culture medium to ambient CO2 levels at physiological temperatures. The low-cost microfluidic in vitro enabling platform, which allows us to image cultures immediately after cell plating, is easy to reproduce and is adaptable to the geometries of different cell-culture containers. It permits the continuous and simultaneous multimodal long-term acquisition or manipulation of optical and electrophysiological parameter sets, thereby considerably widening the range of experimental possibilities. Two exemplary proof-of-concept long-term MEA studies on hippocampal networks illustrate system performance. Continuous extracellular recordings over a period of up to 70 days revealed details on both sudden and gradual neural activity changes in maturing cell ensembles with large intra-day fluctuations. Correlated time-lapse imaging unveiled rather static macroscopic network architectures with previously unreported local morphological oscillations on the timescale of minutes.

Critical slowing down governs the transition to neuron spiking

Many complex systems have been found to exhibit critical transitions, or so-called tipping points, which are sudden changes to a qualitatively different system state. These changes can profoundly impact the functioning of a system ranging from controlled state switching to a catastrophic break-down; signals that predict critical transitions are therefore highly desirable. To this end, research efforts have focused on utilizing qualitative changes in markers related to a system’s tendency to recover more slowly from a perturbation the closer it gets to the transition—a phenomenon called critical slowing down. The recently studied scaling of critical slowing down offers a refined path to understand critical transitions: to identify the transition mechanism and improve transition prediction using scaling laws.

Here, we outline and apply this strategy for the first time in a real-world system by studying the transition to spiking in neurons of the mammalian cortex. The dynamical system approach has identified two robust mechanisms for the transition from subthreshold activity to spiking, saddle-node and Hopf bifurcation. Although theory provides precise predictions on signatures of critical slowing down near the bifurcation to spiking, quantitative experimental evidence has been lacking. Using whole-cell patch-clamp recordings from pyramidal neurons and fast-spiking interneurons, we show that 1) the transition to spiking dynamically corresponds to a critical transition exhibiting slowing down, 2) the scaling laws suggest a saddle-node bifurcation governing slowing down, and 3) these precise scaling laws can be used to predict the bifurcation point from a limited window of observation. To our knowledge this is the first report of scaling laws of critical slowing down in an experiment. They present a missing link for a broad class of neuroscience modeling and suggest improved estimation of tipping points by incorporating scaling laws of critical slowing down as a strategy applicable to other complex systems.

Neurons efficiently convey information by being able to switch rapidly between two different states: quiescence and spiking. Such sudden shifts to a qualitatively different state are observed in many complex systems; the often dramatic consequences of these tipping points for diverse fields such as economics, ecology, and the brain have spurred interest to better understand their transition mechanisms and predict their sudden occurrences. By studying the transition from neuronal quiescence to spiking, we show that the quantitative scaling laws for critical slowing down, i.e., a system’s tendency to recover more slowly from perturbations upon approaching its transition point, inform about the underlying bifurcation mechanism and can be used to improve the prediction of a system’s tipping point.

Interplay between population firing stability and single neuron dynamics in hippocampal networks

Neuronal circuits' ability to maintain the delicate balance between stability and flexibility in changing environments is critical for normal neuronal functioning. However, to what extent individual neurons and neuronal populations maintain internal firing properties remains largely unknown. In this study, we show that distributions of spontaneous population firing rates and synchrony are subject to accurate homeostatic control following increase of synaptic inhibition in cultured hippocampal networks. Reduction in firing rate triggered synaptic and intrinsic adaptive responses operating as global homeostatic mechanisms to maintain firing macro-stability, without achieving local homeostasis at the single-neuron level. Adaptive mechanisms, while stabilizing population firing properties, reduced short-term facilitation essential for synaptic discrimination of input patterns. Thus, invariant ongoing population dynamics emerge from intrinsically unstable activity patterns of individual neurons and synapses. The observed differences in the precision of homeostatic control at different spatial scales challenge cell-autonomous theory of network homeostasis and suggest the existence of network-wide regulation rules.

DOI:http://dx.doi.org/10.7554/eLife.04378.001

The human brain contains more than 80 billion neurons, which are organised into extensive networks. Changes in the strength of connections between neurons are thought to underlie learning and memory: neuronal networks must therefore be sufficiently stable to allow existing memories to be stored, while remaining flexible enough to enable the brain to form new memories.

Evidence suggests that the stability of neuronal networks is maintained by a process called homeostasis. If properties of the network—such as the average firing rate of all the neurons—deviate from a set point, changes occur to return the network the original set point. However, much less is known about the effects of homeostasis at the level of individual neurons within networks: do their firing rates also remain stable over time?

Slomowitz, Styr et al. have now addressed this question by recording the activity of neuronal networks grown on an array of electrodes. Applying a drug that inhibits neuronal firing caused the average firing rate of the networks to decrease initially, as expected. However, after 2 days, homeostasis had restored the average firing rate to its original value, despite the continued presence of the drug. By contrast, the individual neurons within the networks behaved differently: on day 2 almost 90% of neurons had a firing rate that was different from their original firing rate.

Similar behavior was seen when Slomowitz, Styr et al. studied the degree of synchronization between neurons as they fire: the average value for the network returned to its original value, but this did not happen at the level of individual neurons. Surprisingly, however, the ability of the network to undergo short-lived changes in average strength of the connections between neurons—which is thought to support short-term memory—was not subject to homeostasis. This suggests that the loss of short-term memory that occurs in many brain diseases may be an unfortunate consequence of the efforts of neuronal networks to keep their average responses stable.

DOI:http://dx.doi.org/10.7554/eLife.04378.002

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.

Network dynamics of 3D engineered neuronal cultures: a new experimental model for in-vitro electrophysiology

Despite the extensive use of in-vitro models for neuroscientific investigations and notwithstanding the growing field of network electrophysiology, all studies on cultured cells devoted to elucidate neurophysiological mechanisms and computational properties, are based on 2D neuronal networks. These networks are usually grown onto specific rigid substrates (also with embedded electrodes) and lack of most of the constituents of the in-vivo like environment: cell morphology, cell-to-cell interaction and neuritic outgrowth in all directions. Cells in a brain region develop in a 3D space and interact with a complex multi-cellular environment and extracellular matrix. Under this perspective, 3D networks coupled to micro-transducer arrays, represent a new and powerful in-vitro model capable of better emulating in-vivo physiology. In this work, we present a new experimental paradigm constituted by 3D hippocampal networks coupled to Micro-Electrode-Arrays (MEAs) and we show how the features of the recorded network dynamics differ from the corresponding 2D network model. Further development of the proposed 3D in-vitro model by adding embedded functionalized scaffolds might open new prospects for manipulating, stimulating and recording the neuronal activity to elucidate neurophysiological mechanisms and to design bio-hybrid microsystems.