Neural Interactome: Interactive Simulation of a Neuronal System

Fibration symmetries and cluster synchronization in the Caenorhabditis elegans connectome

Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differential equations simulations admissible to these graphs are used to validate the predictions of these fiber symmetries and are compared to the more restrictive orbit symmetries. Additionally fibration symmetries are used to decompose these graphs into their fundamental building blocks which reveal units formed by nested loops or multilayered fibers. It is found that fiber symmetries of the connectome can accurately predict neuronal synchronization even under not idealized connectivity as long as the dynamics are within stable regimes of simulations.

Fibration symmetries and cluster synchronization in the Caenorhabditis elegans connectome

Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differential equations simulations admissible to these graphs are used to validate the predictions of these fiber symmetries and are compared to the more restrictive orbit symmetries. Additionally fibration symmetries are used to decompose these graphs into their fundamental building blocks which reveal units formed by nested loops or multilayered fibers. It is found that fiber symmetries of the connectome can accurately predict neuronal synchronization even under not idealized connectivity as long as the dynamics are within stable regimes of simulations.

Biophysical modeling of the whole-cell dynamics of C. elegans motor and interneurons families

The nematode Caenorhabditis elegans is a widely used model organism for neuroscience. Although its nervous system has been fully reconstructed, the physiological bases of single-neuron functioning are still poorly explored. Recently, many efforts have been dedicated to measuring signals from C. elegans neurons, revealing a rich repertoire of dynamics, including bistable responses, graded responses, and action potentials. Still, biophysical models able to reproduce such a broad range of electrical responses lack. Realistic electrophysiological descriptions started to be developed only recently, merging gene expression data with electrophysiological recordings, but with a large variety of cells yet to be modeled. In this work, we contribute to filling this gap by providing biophysically accurate models of six classes of C. elegans neurons, the AIY, RIM, and AVA interneurons, and the VA, VB, and VD motor neurons. We test our models by comparing computational and experimental time series and simulate knockout neurons, to identify the biophysical mechanisms at the basis of inter and motor neuron functioning. Our models represent a step forward toward the modeling of C. elegans neuronal networks and virtual experiments on the nematode nervous system.

Learning the dynamics of realistic models of C. elegans nervous system with recurrent neural networks

Given the inherent complexity of the human nervous system, insight into the dynamics of brain activity can be gained from studying smaller and simpler organisms. While some of the potential target organisms are simple enough that their behavioural and structural biology might be well-known and understood, others might still lead to computationally intractable models that require extensive resources to simulate. Since such organisms are frequently only acting as proxies to further our understanding of underlying phenomena or functionality, often one is not interested in the detailed evolution of every single neuron in the system. Instead, it is sufficient to observe the subset of neurons that capture the effect that the profound nonlinearities of the neuronal system have in response to different stimuli. In this paper, we consider the well-known nematode Caenorhabditis elegans and seek to investigate the possibility of generating lower complexity models that capture the system's dynamics with low error using only measured or simulated input-output information. Such models are often termed black-box models. We show how the nervous system of C. elegans can be modelled and simulated with data-driven models using different neural network architectures. Specifically, we target the use of state-of-the-art recurrent neural network architectures such as Long Short-Term Memory and Gated Recurrent Units and compare these architectures in terms of their properties and their accuracy (Root Mean Square Error), as well as the complexity of the resulting models. We show that Gated Recurrent Unit models with a hidden layer size of 4 are able to accurately reproduce the system response to very different stimuli. We furthermore explore the relative importance of their inputs as well as scalability to more scenarios.

Dissection of a sensorimotor circuit underlying pathogen aversion in C. elegans

BACKGROUND

Altering animal behavior to reduce pathogen exposure is a key line of defense against pathogen attack. In Caenorhabditis elegans, alterations in intestinal physiology caused by pathogen colonization and sensation of microbial metabolites may lead to activation of pathogen aversive behaviors ranging from aversive reflexes to learned avoidance. However, the neural circuitry between chemosensory neurons that sense pathogenic bacterial cues and the motor neurons responsible for avoidance-associated locomotion remains unknown.

RESULTS

Using C. elegans, we found that backward locomotion was a component of learned pathogen avoidance, as animals pre-exposed to Pseudomonas aeruginosa or Enterococcus faecalis showed reflexive aversion to drops of the bacteria driven by chemosensory neurons, including the olfactory AWB neurons. This response also involved intestinal distention and, for E. faecalis, required expression of TRPM channels in the intestine and excretory system. Additionally, we uncovered a circuit composed of olfactory neurons, interneurons, and motor neurons that controls the backward locomotion crucial for learned reflexive aversion to pathogenic bacteria, learned avoidance, and the repulsive odor 2-nonanone.

CONCLUSIONS

Using whole-brain simulation and functional assays, we uncovered a novel sensorimotor circuit governing learned reflexive aversion. The discovery of a complete sensorimotor circuit for reflexive aversion demonstrates the utility of using the C. elegans connectome and computational modeling in uncovering new neuronal regulators of behavior.

Systematic generation of biophysically detailed models with generalization capability for non-spiking neurons

Unlike spiking neurons which compress continuous inputs into digital signals for transmitting information via action potentials, non-spiking neurons modulate analog signals through graded potential responses. Such neurons have been found in a large variety of nervous tissues in both vertebrate and invertebrate species, and have been proven to play a central role in neuronal information processing. If general and vast efforts have been made for many years to model spiking neurons using conductance-based models (CBMs), very few methods have been developed for non-spiking neurons. When a CBM is built to characterize the neuron behavior, it should be endowed with generalization capabilities (i.e. the ability to predict acceptable neuronal responses to different novel stimuli not used during the model’s building). Yet, since CBMs contain a large number of parameters, they may typically suffer from a lack of such a capability. In this paper, we propose a new systematic approach based on multi-objective optimization which builds general non-spiking models with generalization capabilities. The proposed approach only requires macroscopic experimental data from which all the model parameters are simultaneously determined without compromise. Such an approach is applied on three non-spiking neurons of the nematode Caenorhabditis elegans (C. elegans), a well-known model organism in neuroscience that predominantly transmits information through non-spiking signals. These three neurons, arbitrarily labeled by convention as RIM, AIY and AFD, represent, to date, the three possible forms of non-spiking neuronal responses of C. elegans.

Statistical Perspective on Functional and Causal Neural Connectomics: A Comparative Study

Representation of brain network interactions is fundamental to the translation of neural structure to brain function. As such, methodologies for mapping neural interactions into structural models, i.e., inference of functional connectome from neural recordings, are key for the study of brain networks. While multiple approaches have been proposed for functional connectomics based on statistical associations between neural activity, association does not necessarily incorporate causation. Additional approaches have been proposed to incorporate aspects of causality to turn functional connectomes into causal functional connectomes, however, these methodologies typically focus on specific aspects of causality. This warrants a systematic statistical framework for causal functional connectomics that defines the foundations of common aspects of causality. Such a framework can assist in contrasting existing approaches and to guide development of further causal methodologies. In this work, we develop such a statistical guide. In particular, we consolidate the notions of associations and representations of neural interaction, i.e., types of neural connectomics, and then describe causal modeling in the statistics literature. We particularly focus on the introduction of directed Markov graphical models as a framework through which we define the Directed Markov Property—an essential criterion for examining the causality of proposed functional connectomes. We demonstrate how based on these notions, a comparative study of several existing approaches for finding causal functional connectivity from neural activity can be conducted. We proceed by providing an outlook ahead regarding the additional properties that future approaches could include to thoroughly address causality.

Black-box model reduction of the C. Elegans nervous system. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2021;2021:4174-4179. [PMID: 34892144 DOI: 10.1109/embc46164.2021.9630241]

In recent years, modeling neurons and neuronal collections with high accuracy have become central issues of neuroscience. The development of efficient algorithms for their simulation as well as the increase in computational power and parallelization need to keep up with the quantity and complexity of novel recordings and reconstructions reported by the experimental neuroscientists. The extraction of low-order equivalents that capture the essential aspects of the high-accuracy models is an essential part of the simulation process. The complexity of these models require the use of black-box data-oriented reduction approaches. We create a detailed model of the nervous system of a very known organism, C. Elegans, and show that it can be reduced using a modified data-driven model reduction method up to the order of 4 with very little loss in accuracy. The reduced model is able to predict the behaviour of the original for time ranges beyond the data used for the reduction.

Visual explanations from spiking neural networks using inter-spike intervals

By emulating biological features in brain, Spiking Neural Networks (SNNs) offer an energy-efficient alternative to conventional deep learning. To make SNNs ubiquitous, a 'visual explanation' technique for analysing and explaining the internal spike behavior of such temporal deep SNNs is crucial. Explaining SNNs visually will make the network more transparent giving the end-user a tool to understand how SNNs make temporal predictions and why they make a certain decision. In this paper, we propose a bio-plausible visual explanation tool for SNNs, called Spike Activation Map (SAM). SAM yields a heatmap (i.e., localization map) corresponding to each time-step of input data by highlighting neurons with short inter-spike interval activity. Interestingly, without the use of gradients and ground truth, SAM produces a temporal localization map highlighting the region of interest in an image attributed to an SNN's prediction at each time-step. Overall, SAM outsets the beginning of a new research area 'explainable neuromorphic computing' that will ultimately allow end-users to establish appropriate trust in predictions from SNNs.

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.

Synthetic ablations in the C. elegans nervous system

Synthetic lethality, the finding that the simultaneous knockout of two or more individually nonessential genes leads to cell or organism death, has offered a systematic framework to explore cellular function, and also offered therapeutic applications. Yet the concept lacks its parallel in neuroscience—a systematic knowledge base on the role of double or higher order ablations in the functioning of a neural system. Here, we use the framework of network control to systematically predict the effects of ablating neuron pairs and triplets on the gentle touch response. We find that surprisingly small sets of 58 pairs and 46 triplets can reduce muscle controllability in this context, and that these sets are localized in the nervous system in distinct groups. Further, they lead to highly specific experimentally testable predictions about mechanisms of loss of control, and which muscle cells are expected to experience this loss.

“Synthetic lethality” in cell biology is an extreme example of the effects of higher order genetic interactions: The simultaneous knockout of two or more individually nonessential genes leads to cell death. We define a neural analog to this concept in relation to the locomotor response to gentle touch in C. elegans. Two or more neurons are synthetic essential if individually they are not required for this behavior, yet their combination is. We employ a network control approach to systematically assess all pairs and triplets of neurons by their effect on body wall muscle controllability, and find that only surprisingly small sets of neurons are synthetic essential. They are highly localized in the nervous system and predicted to affect control over specific sets of muscles.

Novel Technological Advances in Functional Connectomics in C. elegans

The complete structure and connectivity of the Caenorhabditis elegans nervous system ("mind of a worm") was first published in 1986, representing a critical milestone in the field of connectomics. The reconstruction of the nervous system (connectome) at the level of synapses provided a unique perspective of understanding how behavior can be coded within the nervous system. The following decades have seen the development of technologies that help understand how neural activity patterns are connected to behavior and modulated by sensory input. Investigations on the developmental origins of the connectome highlight the importance of role of neuronal cell lineages in the final connectivity matrix of the nervous system. Computational modeling of neuronal dynamics not only helps reconstruct the biophysical properties of individual neurons but also allows for subsequent reconstruction of whole-organism neuronal network models. Hence, combining experimental datasets with theoretical modeling of neurons generates a better understanding of organismal behavior. This review discusses some recent technological advances used to analyze and perturb whole-organism neuronal function along with developments in computational modeling, which allows for interrogation of both local and global neural circuits, leading to different behaviors. Combining these approaches will shed light into how neural networks process sensory information to generate the appropriate behavioral output, providing a complete understanding of the worm nervous system.