Identifying steady state in the network dynamics of spiking neural networks.

Analysis of the dynamics of complex networks can provide valuable information. For example, the dynamics can be used to characterize and differentiate between different network inputs and configurations. However, without quantitatively delineating the network's dynamic regimes, analysis of the network's dynamics is based on heuristics and qualitative signatures of transient or steady-state regimes. This is not ideal because interesting phenomena can occur during the transient regime, steady-state regime, or at the transition between the two dynamic regimes. Moreover, for simulated and observed systems, precise knowledge of the network's dynamical regime is imperative when considering metrics on minimal mathematical descriptions of the dynamics, otherwise either too much or too little data is analyzed. Here, we develop quantitative methods to ascertain the starting point and period of steady-state network activity. Using the precise knowledge of the network's dynamic regimes, we build minimal representations of the network dynamics that form the basis for future work. We show applications of our techniques on idealized signals and on the dynamics of a biologically inspired spiking neural network.

Super-Selective Reconstruction of Causal and Direct Connectivity With Application to in vitro iPSC Neuronal Networks.

Despite advancements in the development of cell-based in-vitro neuronal network models, the lack of appropriate computational tools limits their analyses. Methods aimed at deciphering the effective connections between neurons from extracellular spike recordings would increase utility of in vitro local neural circuits, especially for studies of human neural development and disease based on induced pluripotent stem cells (hiPSC). Current techniques allow statistical inference of functional couplings in the network but are fundamentally unable to correctly identify indirect and apparent connections between neurons, generating redundant maps with limited ability to model the causal dynamics of the network. In this paper, we describe a novel mathematically rigorous, model-free method to map effective-direct and causal-connectivity of neuronal networks from multi-electrode array data. The inference algorithm uses a combination of statistical and deterministic indicators which, first, enables identification of all existing functional links in the network and then reconstructs the directed and causal connection diagram via a super-selective rule enabling highly accurate classification of direct, indirect, and apparent links. Our method can be generally applied to the functional characterization of any in vitro neuronal networks. Here, we show that, given its accuracy, it can offer important insights into the functional development of in vitro hiPSC-derived neuronal cultures.

All-Optical Electrophysiology in hiPSC-Derived Neurons With Synthetic Voltage Sensors.

Voltage imaging and "all-optical electrophysiology" in human induced pluripotent stem cell (hiPSC)-derived neurons have opened unprecedented opportunities for high-throughput phenotyping of activity in neurons possessing unique genetic backgrounds of individual patients. While prior all-optical electrophysiology studies relied on genetically encoded voltage indicators, here, we demonstrate an alternative protocol using a synthetic voltage sensor and genetically encoded optogenetic actuator that generate robust and reproducible results. We demonstrate the functionality of this method by measuring spontaneous and evoked activity in three independent hiPSC-derived neuronal cell lines with distinct genetic backgrounds.

Generalizable Machine Learning in Neuroscience Using Graph Neural Networks.

Although a number of studies have explored deep learning in neuroscience, the application of these algorithms to neural systems on a microscopic scale, i.e. parameters relevant to lower scales of organization, remains relatively novel. Motivated by advances in whole-brain imaging, we examined the performance of deep learning models on microscopic neural dynamics and resulting emergent behaviors using calcium imaging data from the nematode C. elegans. As one of the only species for which neuron-level dynamics can be recorded, C. elegans serves as the ideal organism for designing and testing models bridging recent advances in deep learning and established concepts in neuroscience. We show that neural networks perform remarkably well on both neuron-level dynamics prediction and behavioral state classification. In addition, we compared the performance of structure agnostic neural networks and graph neural networks to investigate if graph structure can be exploited as a favourable inductive bias. To perform this experiment, we designed a graph neural network which explicitly infers relations between neurons from neural activity and leverages the inferred graph structure during computations. In our experiments, we found that graph neural networks generally outperformed structure agnostic models and excel in generalization on unseen organisms, implying a potential path to generalizable machine learning in neuroscience.

Computing Temporal Sequences Associated With Dynamic Patterns on the C. elegans Connectome.

Understanding how the structural connectivity and spatial geometry of a network constrains the dynamics it is able to support is an active and open area of research. We simulated the plausible dynamics resulting from the known C. elegans connectome using a recent model and theoretical analysis that computes the dynamics of neurobiological networks by focusing on how local interactions among connected neurons give rise to the global dynamics in an emergent way. We studied the dynamics which resulted from stimulating a chemosensory neuron (ASEL) in a known feeding circuit, both in isolation and embedded in the full connectome. We show that contralateral motorneuron activations in ventral (VB) and dorsal (DB) classes of motorneurons emerged from the simulations, which are qualitatively similar to rhythmic motorneuron firing pattern associated with locomotion of the worm. One interpretation of these results is that there is an inherent-and we propose-purposeful structural wiring to the C. elegans connectome that has evolved to serve specific behavioral functions. To study network signaling pathways responsible for the dynamics we developed an analytic framework that constructs Temporal Sequences (TSeq), time-ordered walks of signals on graphs. We found that only 5% of TSeq are preserved between the isolated feeding network relative to its embedded counterpart. The remaining 95% of signaling pathways computed in the isolated network are not present in the embedded network. This suggests a cautionary note for computational studies of isolated neurobiological circuits and networks.

The Effect of Signaling Latencies and Node Refractory States on the Dynamics of Networks.

We describe the construction and theoretical analysis of a framework derived from canonical neurophysiological principles that model the competing dynamics of incident signals into nodes along directed edges in a network. The framework describes the dynamics between the offset in the latencies of propagating signals, which reflect the geometry of the edges and conduction velocities, and the internal refractory dynamics and processing times of the downstream node receiving the signals. This framework naturally extends to the construction of a perceptron model that takes into account such dynamic geometric considerations. We first describe the model in detail, culminating with the model of a geometric dynamic perceptron. We then derive upper and lower bounds for a notion of optimal efficient signaling between vertex pairs based on the structure of the framework. Efficient signaling in the context of the framework we develop here means that there needs to be a temporal match between the arrival time of the signals relative to how quickly nodes can internally process signals. These bounds reflect numerical constraints on the compensation of the timing of signaling events of upstream nodes attempting to activate downstream nodes they connect into that preserve this notion of efficiency. When a mismatch between signal arrival times and the internal states of activated nodes occurs, it can cause a breakdown in the signaling dynamics of the network. In contrast to essentially all of the current state of the art in machine learning, this work provides a theoretical foundation for machine learning and intelligence architectures based on the timing of node activations and their abilities to respond rather than necessary changes in synaptic weights. At the same time, the theoretical ideas we developed are guiding the discovery of experimentally testable new structure-function principles in the biological brain.

A New Frontier: The Convergence of Nanotechnology, Brain Machine Interfaces, and Artificial Intelligence.

A confluence of technological capabilities is creating an opportunity for machine learning and artificial intelligence (AI) to enable "smart" nanoengineered brain machine interfaces (BMI). This new generation of technologies will be able to communicate with the brain in ways that support contextual learning and adaptation to changing functional requirements. This applies to both invasive technologies aimed at restoring neurological function, as in the case of neural prosthesis, as well as non-invasive technologies enabled by signals such as electroencephalograph (EEG). Advances in computation, hardware, and algorithms that learn and adapt in a contextually dependent way will be able to leverage the capabilities that nanoengineering offers the design and functionality of BMI. We explore the enabling capabilities that these devices may exhibit, why they matter, and the state of the technologies necessary to build them. We also discuss a number of open technical challenges and problems that will need to be solved in order to achieve this.

An Optimized Structure-Function Design Principle Underlies Efficient Signaling Dynamics in Neurons.

Dynamic signaling on branching axons is critical for rapid and efficient communication between neurons in the brain. Efficient signaling in axon arbors depends on a trade-off between the time it takes action potentials to reach synaptic terminals (temporal cost) and the amount of cellular material associated with the wiring path length of the neuron's morphology (material cost). However, where the balance between structural and dynamical considerations for achieving signaling efficiency is, and the design principle that neurons optimize to preserve this balance, is still elusive. In this work, we introduce a novel analysis that compares morphology and signaling dynamics in axonal networks to address this open problem. We show that in Basket cell neurons the design principle being optimized is the ratio between the refractory period of the membrane, and action potential latencies between the initial segment and the synaptic terminals. Our results suggest that the convoluted paths taken by axons reflect a design compensation by the neuron to slow down signaling latencies in order to optimize this ratio. Deviations in this ratio may result in a breakdown of signaling efficiency in the cell. These results pave the way to new approaches for investigating more complex neurophysiological phenomena that involve considerations of neuronal structure-function relationships.

Towards high-resolution retinal prostheses with direct optical addressing and inductive telemetry.

OBJECTIVE: Despite considerable advances in retinal prostheses over the last two decades, the resolution of restored vision has remained severely limited, well below the 20/200 acuity threshold of blindness. Towards drastic improvements in spatial resolution, we present a scalable architecture for retinal prostheses in which each stimulation electrode is directly activated by incident light and powered by a common voltage pulse transferred over a single wireless inductive link. APPROACH: The hybrid optical addressability and electronic powering scheme provides separate spatial and temporal control over stimulation, and further provides optoelectronic gain for substantially lower light intensity thresholds than other optically addressed retinal prostheses using passive microphotodiode arrays. The architecture permits the use of high-density electrode arrays with ultra-high photosensitive silicon nanowires, obviating the need for excessive wiring and high-throughput data telemetry. Instead, the single inductive link drives the entire array of electrodes through two wires and provides external control over waveform parameters for common voltage stimulation. MAIN RESULTS: A complete system comprising inductive telemetry link, stimulation pulse demodulator, charge-balancing series capacitor, and nanowire-based electrode device is integrated and validated ex vivo on rat retina tissue. SIGNIFICANCE: Measurements demonstrate control over retinal neural activity both by light and electrical bias, validating the feasibility of the proposed architecture and its system components as an important first step towards a high-resolution optically addressed retinal prosthesis.

The roadmap for estimation of cell-type-specific neuronal activity from non-invasive measurements.

The computational properties of the human brain arise from an intricate interplay between billions of neurons connected in complex networks. However, our ability to study these networks in healthy human brain is limited by the necessity to use non-invasive technologies. This is in contrast to animal models where a rich, detailed view of cellular-level brain function with cell-type-specific molecular identity has become available due to recent advances in microscopic optical imaging and genetics. Thus, a central challenge facing neuroscience today is leveraging these mechanistic insights from animal studies to accurately draw physiological inferences from non-invasive signals in humans. On the essential path towards this goal is the development of a detailed 'bottom-up' forward model bridging neuronal activity at the level of cell-type-specific populations to non-invasive imaging signals. The general idea is that specific neuronal cell types have identifiable signatures in the way they drive changes in cerebral blood flow, cerebral metabolic rate of O2 (measurable with quantitative functional Magnetic Resonance Imaging), and electrical currents/potentials (measurable with magneto/electroencephalography). This forward model would then provide the 'ground truth' for the development of new tools for tackling the inverse problem-estimation of neuronal activity from multimodal non-invasive imaging data.This article is part of the themed issue 'Interpreting BOLD: a dialogue between cognitive and cellular neuroscience'.

Assembly and Calcium Binding Properties of Quantum Dot-Calmodulin Calcium Sensor.

We have developed the first nanoengineered quantum dot molecular complex designed to measure changes of calcium ion (Ca2+) concentration at high spatial and temporal resolutions in real time. The sensor is ratiometric and composed of three components: a quantum dot (QD) emitting at 620 nm as a fluorescence donor, an organic dye (Alexa Fluor 647) as a fluorescence acceptor, and a calmodulin-M13 (CaM-M13) protein part as a calcium sensing component. In this work, we have determined the maximal number of CaM-M13 required for saturating a single QD particle to be approximately 16. The dissociation constant, Kd of the QD-based calcium ion sensor was also estimated to be around 30 microM.

Cell type specificity of neurovascular coupling in cerebral cortex.

Identification of the cellular players and molecular messengers that communicate neuronal activity to the vasculature driving cerebral hemodynamics is important for (1) the basic understanding of cerebrovascular regulation and (2) interpretation of functional Magnetic Resonance Imaging (fMRI) signals. Using a combination of optogenetic stimulation and 2-photon imaging in mice, we demonstrate that selective activation of cortical excitation and inhibition elicits distinct vascular responses and identify the vasoconstrictive mechanism as Neuropeptide Y (NPY) acting on Y1 receptors. The latter implies that task-related negative Blood Oxygenation Level Dependent (BOLD) fMRI signals in the cerebral cortex under normal physiological conditions may be mainly driven by the NPY-positive inhibitory neurons. Further, the NPY-Y1 pathway may offer a potential therapeutic target in cerebrovascular disease.

Bidirectional neural interface: Closed-loop feedback control for hybrid neural systems.

Closed-loop neural prostheses enable bidirectional communication between the biological and artificial components of a hybrid system. However, a major challenge in this field is the limited understanding of how these components, the two separate neural networks, interact with each other. In this paper, we propose an in vitro model of a closed-loop system that allows for easy experimental testing and modification of both biological and artificial network parameters. The interface closes the system loop in real time by stimulating each network based on recorded activity of the other network, within preset parameters. As a proof of concept we demonstrate that the bidirectional interface is able to establish and control network properties, such as synchrony, in a hybrid system of two neural networks more significantly more effectively than the same system without the interface or with unidirectional alternatives. This success holds promise for the application of closed-loop systems in neural prostheses, brain-machine interfaces, and drug testing.

The challenge of connecting the dots in the B.R.A.I.N.

The Brain Research through Advancing Innovative Neurotechnologies (BRAIN) Initiative has focused scientific attention on the necessary tools to understand the human brain and mind. Here, we outline our collective vision for what we can achieve within a decade with properly targeted efforts and discuss likely technological deliverables and neuroscience progress.

Visual evoked potential characterization of rabbit animal model for retinal prosthesis research.

Visual evoked potentials (VEP) are used to confirm the function of prosthetic devices designed to stimulate retinas with damaged photoreceptors in vivo. In this work, we focus on methods and experimental consideration for recording visual evoked potential in rabbit models and assesses the use for retinal prosthesis research. We compare both invasive and noninvasive methods for recording VEPs, the response of the rabbit retina to various light wavelengths and intensities, focal vs. full field stimulation, and the effect of light bleaching on the retinal response.

Nanotechnologies for stimulating and recording excitable events in neurons and cardiomyocytes.

Nanotechnologies are engineered materials and devices that have a functional organization in at least one dimension on the nanometer scale, ranging from a few to about 100 nanometers. Functionally, nanotechnologies can display physical, chemical, and engineering properties that go beyond the component building block molecules or structures that make them up. Given such properties and the physical scale involved, these technologies are capable of interacting and interfacing with target cells and tissues in unique ways. One particular emerging application of wide spread interest is the development of nanotechnologies for stimulating and recording excitable cells such as neurons and cardiomyocytes. Such approaches offer the possibility of achieving high density stimulation and recording at sub-cellular resolutions in large populations of cells. This would provide a scale of electrophysiological interactions with excitable cells beyond anything achievable by current existing methods. In this review we introduce the reader to the key concepts and methods associated with nanotechnology and nanoengineering, and discuss the work of some of the key groups developing nanoscale stimulation and recording technologies.

A positive feedback cell signaling nucleation model of astrocyte dynamics.

We constructed a model of calcium signaling in astrocyte neural glial cells that incorporates a positive feedback nucleation mechanism, whereby small microdomain increases in local calcium can stochastically produce global cellular and intercellular network scale dynamics. The model is able to simultaneously capture dynamic spatial and temporal heterogeneities associated with intracellular calcium transients in individual cells and intercellular calcium waves (ICW) in spatially realistic networks of astrocytes, i.e., networks where the positions of cells were taken from real in vitro experimental data of spontaneously forming sparse networks, as opposed to artificially constructed grid networks or other non-realistic geometries. This is the first work we are aware of where an intracellular model of calcium signaling that reproduces intracellular dynamics inherently accounts for intercellular network dynamics. These results suggest that a nucleation type mechanism should be further investigated experimentally in order to test its contribution to calcium signaling in astrocytes and in other cells more broadly. It may also be of interest in engineered neuromimetic network systems that attempt to emulate biological signaling and information processing properties in synthetic hardwired neuromorphometric circuits or coded algorithms.

In vivo stimulus-induced vasodilation occurs without IP3 receptor activation and may precede astrocytic calcium increase.

Calcium-dependent release of vasoactive gliotransmitters is widely assumed to trigger vasodilation associated with rapid increases in neuronal activity. Inconsistent with this hypothesis, intact stimulus-induced vasodilation was observed in inositol 1,4,5-triphosphate (IP3) type-2 receptor (R2) knock-out (KO) mice, in which the primary mechanism of astrocytic calcium increase-the release of calcium from intracellular stores following activation of an IP3-dependent pathway-is lacking. Further, our results in wild-type (WT) mice indicate that in vivo onset of astrocytic calcium increase in response to sensory stimulus could be considerably delayed relative to the simultaneously measured onset of arteriolar dilation. Delayed calcium increases in WT mice were observed in both astrocytic cell bodies and perivascular endfeet. Thus, astrocytes may not play a role in the initiation of blood flow response, at least not via calcium-dependent mechanisms. Moreover, an increase in astrocytic intracellular calcium was not required for normal vasodilation in the IP3R2-KO animals.

Neuromodulation: selected approaches and challenges.

The brain operates through complex interactions in the flow of information and signal processing within neural networks. The 'wiring' of such networks, being neuronal or glial, can physically and/or functionally go rogue in various pathological states. Neuromodulation, as a multidisciplinary venture, attempts to correct such faulty nets. In this review, selected approaches and challenges in neuromodulation are discussed. The use of water-dispersible carbon nanotubes has been proven effective in the modulation of neurite outgrowth in culture and in aiding regeneration after spinal cord injury in vivo. Studying neural circuits using computational biology and analytical engineering approaches brings to light geometrical mapping of dynamics within neural networks, much needed information for stimulation interventions in medical practice. Indeed, sophisticated desynchronization approaches used for brain stimulation have been successful in coaxing 'misfiring' neuronal circuits to resume productive firing patterns in various human disorders. Devices have been developed for the real-time measurement of various neurotransmitters as well as electrical activity in the human brain during electrical deep brain stimulation. Such devices can establish the dynamics of electrochemical changes in the brain during stimulation. With increasing application of nanomaterials in devices for electrical and chemical recording and stimulating in the brain, the era of cellular, and even intracellular, precision neuromodulation will soon be upon us.

Targeting the brain: advances in drug delivery.

The blood-brain barrier (BBB) represents a significant obstacle for drug delivery to the brain. Many therapeutics with potential for treating neurological conditions prove incompatible with intravenous delivery simply because of this barrier. Rather than modifying drugs to penetrate the BBB directly, it has proven more efficacious to either physically bypass the barrier or to use specialized delivery vehicles that circumvent BBB regulatory mechanisms. Controlled-release intracranial polymer implants and particle injections are the clinical state of the art with regard to localized delivery, although these approaches can impose significant surgical risks. Focused ultrasound provides a non-invasive alternative that may prove more desirable for acute treatment of brain tumors and other conditions requiring local tissue necrosis. For targeting the brain as a whole, cell-penetrating peptides (CPPs) and molecular trojan horses (MTHs) have demonstrated particular ability as delivery molecules and will likely see increased application. CPPs are not brain specific but offer the potential for efficient traversal of the BBB, and tandem systems with targeting molecules may produce extremely effective brain drug delivery tools. Molecular trojan horses utilize receptor-mediated transcytosis to transport cargo and are thus limited by the quantity of relevant receptors; however, they can be very selective for the BBB endothelium and have shown promise in gene therapy.