Geometric constraints on neuronal connectivity facilitate a concise synaptic adhesive code

Encoding innate ability through a genomic bottleneck

Animals are born with extensive innate behavioral capabilities, which arise from neural circuits encoded in the genome. However, the information capacity of the genome is orders of magnitude smaller than that needed to specify the connectivity of an arbitrary brain circuit, indicating that the rules encoding circuit formation must fit through a "genomic bottleneck" as they pass from one generation to the next. Here, we formulate the problem of innate behavioral capacity in the context of artificial neural networks in terms of lossy compression of the weight matrix. We find that several standard network architectures can be compressed by several orders of magnitude, yielding pretraining performance that can approach that of the fully trained network. Interestingly, for complex but not for simple test problems, the genomic bottleneck algorithm also captures essential features of the circuit, leading to enhanced transfer learning to novel tasks and datasets. Our results suggest that compressing a neural circuit through the genomic bottleneck serves as a regularizer, enabling evolution to select simple circuits that can be readily adapted to important real-world tasks. The genomic bottleneck also suggests how innate priors can complement conventional approaches to learning in designing algorithms for AI.

Wiring the Brain by Clustered Protocadherin Neural Codes

There are more than a thousand trillion specific synaptic connections in the human brain and over a million new specific connections are formed every second during the early years of life. The assembly of these staggeringly complex neuronal circuits requires specific cell-surface molecular tags to endow each neuron with a unique identity code to discriminate self from non-self. The clustered protocadherin (Pcdh) genes, which encode a tremendous diversity of cell-surface assemblies, are candidates for neuronal identity tags. We describe the adaptive evolution, genomic structure, and regulation of expression of the clustered Pcdhs. We specifically focus on the emerging 3-D architectural and biophysical mechanisms that generate an enormous number of diverse cell-surface Pcdhs as neural codes in the brain.

Single-cell RNAseq reveals cell adhesion molecule profiles in electrophysiologically defined neurons

In brain, signaling mediated by cell adhesion molecules defines the identity and functional properties of synapses. The specificity of presynaptic and postsynaptic interactions that is presumably mediated by cell adhesion molecules suggests that there exists a logic that could explain neuronal connectivity at the molecular level. Despite its importance, however, the nature of such logic is poorly understood, and even basic parameters, such as the number, identity, and single-cell expression profiles of candidate synaptic cell adhesion molecules, are not known. Here, we devised a comprehensive list of genes involved in cell adhesion, and used single-cell RNA sequencing (RNAseq) to analyze their expression in electrophysiologically defined interneurons and projection neurons. We compared the cell type-specific expression of these genes with that of genes involved in transmembrane ion conductances (i.e., channels), exocytosis, and rho/rac signaling, which regulates the actin cytoskeleton. Using these data, we identified two independent, developmentally regulated networks of interacting genes encoding molecules involved in cell adhesion, exocytosis, and signal transduction. Our approach provides a framework for a presumed cell adhesion and signaling code in neurons, enables correlating electrophysiological with molecular properties of neurons, and suggests avenues toward understanding synaptic specificity.

Synchronization waves in geometric networks

We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of long-range connections, prevents full synchronization and yields instead the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal that the wave-synchronization state allows detection of the most structurally relevant nodes from a single observation of the dynamics, without any a priori information on the model equations ruling the evolution of the ensemble.

Self-organizing circuit assembly through spatiotemporally coordinated neuronal migration within geometric constraints

BACKGROUND

Neurons are dynamically coupled with each other through neurite-mediated adhesion during development. Understanding the collective behavior of neurons in circuits is important for understanding neural development. While a number of genetic and activity-dependent factors regulating neuronal migration have been discovered on single cell level, systematic study of collective neuronal migration has been lacking. Various biological systems are shown to be self-organized, and it is not known if neural circuit assembly is self-organized. Besides, many of the molecular factors take effect through spatial patterns, and coupled biological systems exhibit emergent property in response to geometric constraints. How geometric constraints of the patterns regulate neuronal migration and circuit assembly of neurons within the patterns remains unexplored.

METHODOLOGY/PRINCIPAL FINDINGS

We established a two-dimensional model for studying collective neuronal migration of a circuit, with hippocampal neurons from embryonic rats on Matrigel-coated self-assembled monolayers (SAMs). When the neural circuit is subject to geometric constraints of a critical scale, we found that the collective behavior of neuronal migration is spatiotemporally coordinated. Neuronal somata that are evenly distributed upon adhesion tend to aggregate at the geometric center of the circuit, forming mono-clusters. Clustering formation is geometry-dependent, within a critical scale from 200 µm to approximately 500 µm. Finally, somata clustering is neuron-type specific, and glutamatergic and GABAergic neurons tend to aggregate homo-philically.

CONCLUSIONS/SIGNIFICANCE

We demonstrate self-organization of neural circuits in response to geometric constraints through spatiotemporally coordinated neuronal migration, possibly via mechanical coupling. We found that such collective neuronal migration leads to somata clustering, and mono-cluster appears when the geometric constraints fall within a critical scale. The discovery of geometry-dependent collective neuronal migration and the formation of somata clustering in vitro shed light on neural development in vivo.

Geometric effects on complex network structure in the cortex

It is shown that homogeneous, short-range, two-dimensional (2D) cortical connectivity, without modularity, hierarchy, or other specialized structure, reproduces key observed properties of cortical networks, including low path length, high clustering and modularity index, and apparent hierarchical block-diagonal structure in connection matrices. Geometry strongly influences connection matrices, implying that simple interpretations of connectivity measures as reflecting specialized structure can be misleading: Such apparent structure is seen in strictly uniform, locally connected architectures in 2D. Geometry is thus a proxy for function, modularity, and hierarchy and must be accounted for when structural inferences are made.

Mesoscopic organization reveals the constraints governing Caenorhabditis elegans nervous system

One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental stimuli. Investigating the intermediate or mesoscopic level of organization in the nervous system is a vital step towards understanding how the integration of micro-level dynamics results in macro-level functioning. The coordination of many different co-occurring processes at this level underlies the command and control of overall network activity. In this paper, we have considered the somatic nervous system of the nematode Caenorhabditis elegans, for which the entire neuronal connectivity diagram is known. We focus on the organization of the system into modules, i.e., neuronal groups having relatively higher connection density compared to that of the overall network. We show that this mesoscopic feature cannot be explained exclusively in terms of considerations such as, optimizing for resource constraints (viz., total wiring cost) and communication efficiency (i.e., network path length). Even including information about the genetic relatedness of the cells cannot account for the observed modular structure. Comparison with other complex networks designed for efficient transport (of signals or resources) implies that neuronal networks form a distinct class. This suggests that the principal function of the network, viz., processing of sensory information resulting in appropriate motor response, may be playing a vital role in determining the connection topology. Using modular spectral analysis we make explicit the intimate relation between function and structure in the nervous system. This is further brought out by identifying functionally critical neurons purely on the basis of patterns of intra- and inter-modular connections. Our study reveals how the design of the nervous system reflects several constraints, including its key functional role as a processor of information.

Random distance dependent attachment as a model for neural network generation in the Caenorhabditis elegans

MOTIVATION

The topology of the network induced by the neurons connectivity's in the Caenorhabditis elegans differs from most common random networks. The neurons positions of the C.elegans have been previously explained as being optimal to induce the required network wiring. We here propose a complementary explanation that the network wiring is the direct result of a local stochastic synapse formation process.

RESULTS

We show that a model based on the physical distance between neurons can explain the C.elegans neural network structure, specifically, we demonstrate that a simple model based on a geometrical synapse formation probability and the inhibition of short coherent cycles can explain the properties of the C.elegans' neural network. We suggest this model as an initial framework to discuss neural network generation and as a first step toward the development of models for more advanced creatures. In order to measure the circle frequency in the network, a novel graph-theory circle length measurement algorithm is proposed.