Neuronal Graphs: A Graph Theory Primer for Microscopic, Functional Networks of Neurons Recorded by Calcium Imaging

From calcium imaging to graph topology

Systems neuroscience is facing an ever-growing mountain of data. Recent advances in protein engineering and microscopy have together led to a paradigm shift in neuroscience; using fluorescence, we can now image the activity of every neuron through the whole brain of behaving animals. Even in larger organisms, the number of neurons that we can record simultaneously is increasing exponentially with time. This increase in the dimensionality of the data is being met with an explosion of computational and mathematical methods, each using disparate terminology, distinct approaches, and diverse mathematical concepts. Here we collect, organize, and explain multiple data analysis techniques that have been, or could be, applied to whole-brain imaging, using larval zebrafish as an example model. We begin with methods such as linear regression that are designed to detect relations between two variables. Next, we progress through network science and applied topological methods, which focus on the patterns of relations among many variables. Finally, we highlight the potential of generative models that could provide testable hypotheses on wiring rules and network progression through time, or disease progression. While we use examples of imaging from larval zebrafish, these approaches are suitable for any population-scale neural network modeling, and indeed, to applications beyond systems neuroscience. Computational approaches from network science and applied topology are not limited to larval zebrafish, or even to systems neuroscience, and we therefore conclude with a discussion of how such methods can be applied to diverse problems across the biological sciences.

Data-Driven Network Dynamical Model of Rat Brains During Acute Ictogenesis

Epilepsy is one of the most common neurological disorders worldwide. Recent findings suggest that the brain is a complex system composed of a network of neurons, and seizure is considered an emergent property resulting from its interactions. Based on this perspective, network physiology has emerged as a promising approach to explore how brain areas coordinate, synchronize and integrate their dynamics, both under perfect health and critical illness conditions. Therefore, the objective of this paper is to present an application of (Dynamic) Bayesian Networks (DBN) to model Local Field Potentials (LFP) data on rats induced to epileptic seizures based on the number of arcs found using threshold analytics. Results showed that DBN analysis captured the dynamic nature of brain connectivity across ictogenesis and a significant correlation with neurobiology derived from pioneering studies employing techniques of pharmacological manipulation, lesion, and modern optogenetics. The arcs evaluated under the proposed approach achieved consistent results based on previous literature, in addition to demonstrating robustness regarding functional connectivity analysis. Moreover, it provided fascinating and novel insights, such as discontinuity between forelimb clonus and generalized tonic-clonic seizure (GTCS) dynamics. Thus, DBN coupled with threshold analytics may be an excellent tool for investigating brain circuitry and their dynamical interplay, both in homeostasis and dysfunction conditions.

A Graph Network Model for Neural Connection Prediction and Connection Strength Estimation

Objective. Reconstruction of connectomes at the cellular scale is a prerequisite for understanding the principles of neural circuits. However, due to methodological limits, scientists have reconstructed the connectomes of only a few organisms such as C. elegans, and estimated synaptic strength indirectly according to their size and number. Approach. Here, we propose a graph network model to predict synaptic connections and estimate synaptic strength by using the calcium activity data from C. elegans. Main results. The results show that this model can reliably predict synaptic connections in the neural circuits of C. elegans, and estimate their synaptic strength, which is an intricate and comprehensive reflection of multiple factors such as synaptic type and size, neurotransmitter and receptor type, and even activity dependence. In addition, the excitability or inhibition of synapses can be identified by this model. We also found that chemical synaptic strength is almost linearly positively correlated to electrical synaptic strength, and the influence of one neuron on another is non-linearly correlated with the number between them. This reflects the intrinsic interaction between electrical and chemical synapses. Significance. Our model is expected to provide a more accessible quantitative and data-driven approach for the reconstruction of connectomes in more complex nervous systems, as well as a promising method for accurately estimating synaptic strength.

A 3D in vitro model of the device-tissue interface: Functional and structural symptoms of innate neuroinflammation are mitigated by antioxidant ceria nanoparticles

OBJECTIVE

The recording instability of neural implants due to neuroinflammation at the device-tissue interface is a primary roadblock to broad adoption of brain-machine interfaces. While a multiphasic immune response, marked by glial scaring, oxidative stress (OS), and neurodegeneration, is well-characterized, the independent contributions of systemic and local "innate" immune responses are not well-understood. We aimed to understand and mitigate the isolated the innate neuroinflammatory response to devices.

APPROACH

Three-dimensional primary neural cultures provide a unique environment for studying the drivers of neuroinflammation by decoupling the innate and systemic immune systems, while conserving an endogenous extracellular matrix and structural and functional network complexity. We created a three-dimensional in vitro model of the DTI by seeding primary cortical cells around microwires. Live imaging of both dye and AAV-mediated functional, structural, and lipid peroxidation fluorescence was employed to characterize the neuroinflammatory response.

MAIN RESULTS

Live imaging of microtissues over time revealed independent innate neuroinflammation, marked by increased OS, decreased neuronal density, and increased functional connectivity. We demonstrated the use of this model for therapeutic screening by directly applying drugs to neural tissue, bypassing low bioavailability through the in vivo blood brain barrier. As there is growing interest in long-acting antioxidant therapies, we tested efficacy of "perpetual" antioxidant ceria nanoparticles, which reduced OS, increased neuronal density, and protected functional connectivity.

SIGNIFICANCE

Our 3D in vitro model of the device-tissue interface exhibited symptoms of OS-mediated innate neuroinflammation, indicating a significant local immune response to devices. The dysregulation of functional connectivity of microcircuits surround implants suggests the presence of an observer effect, in which the process of recording neural activity may fundamentally change the neural signal. Finally, the demonstration of antioxidant ceria nanoparticle treatment exhibited substantial promise as a neuroprotective and anti-inflammatory treatment strategy.

Lipopolysaccharide-induced neuroinflammation disrupts functional connectivity and community structure in primary cortical microtissues

Three-dimensional (3D) neural microtissues are a powerful in vitro paradigm for studying brain development and disease under controlled conditions, while maintaining many key attributes of the in vivo environment. Here, we used primary cortical microtissues to study the effects of neuroinflammation on neural microcircuits. We demonstrated the use of a genetically encoded calcium indicator combined with a novel live-imaging platform to record spontaneous calcium transients in microtissues from day 14-34 in vitro. We implemented graph theory analysis of calcium activity to characterize underlying functional connectivity and community structure of microcircuits, which are capable of capturing subtle changes in network dynamics during early disease states. We found that microtissues cultured for 34 days displayed functional remodeling of microcircuits and that community structure strengthened over time. Lipopolysaccharide, a neuroinflammatory agent, significantly increased functional connectivity and disrupted community structure 5-9 days after exposure. These microcircuit-level changes have broad implications for the role of neuroinflammation in functional dysregulation of neural networks.