How does electrical activity in neuronal circuits give rise to intelligent behavior? We believe that this question is impossible to answer without a comprehensive description of the connectivity in neuronal networks. Such a description may be a wiring diagram, which catalogs all neurons and synaptic connections between them. In collaboration with several laboratories, we are reconstructing vertebrate and invertebrate wiring diagrams from electrophysiological, light, and electron microscopical data. To gain insight into brain function from the wiring diagrams, we formulate engineering principles of brain design and test them experimentally. By focusing initially on explaining the function of simpler organisms, we are assembling a theoretical framework and accumulating experience necessary to understand more complex systems, such as the mammalian neocortex.
Statistical Circuit Reconstructions from Light Microscopy and Electrophysiology
We have developed the necessary theoretical framework to estimate, or reconstruct statistically, wiring diagrams from the shapes of axonal and dendritic arbors visualized with light microscopy. Such reconstructions are based on the principle that physical proximity between the axons of one neuron and the dendrites of another predicts probabilistically synaptic connections between the two. This principle is not new. However, only with recent developments in cell labeling, imaging, and computing infrastructure has the comprehensive geometric description of neuronal connectivity become an attainable goal. As a demonstration, we have statistically reconstructed the cortical column from three-dimensional shapes of dozens of neurons labeled in vivo (Figure 1).
To determine how well geometric connectivity maps correspond to functional connectivity we compared maps calculated from neuronal shapes with those obtained electrophysiologically in collaboration with Karel Svoboda's laboratory (HHMI, Janelia Farm Research Campus). In many cases our maps accurately predicted connectivity on the level of populations of neurons, i.e., projections between cortical layers.
A geometric connectivity map is a particularly appropriate description of cortical circuits in the face of ongoing changes in connectivity. Previously, we proposed that the growth and retraction of dendritic spines could alter connectivity, and Svoboda's laboratory has observed such experience-dependent plasticity in adult animals. As geometric connectivity maps rely on the mostly stable layout of axons and dendrites rather than on the more volatile spines, they provide an invariant description of cortical circuits.
Geometric maps have their limitations: they yield the probability of connections but cannot predict for certain whether a given pair of neurons is connected. The maps also do not capture the strong correlations we found in synaptic connections in pairs and triplets of neurons when we analyzed electrophysiological recordings by collaborators.
Complete Circuit Reconstructions from Electron Microscopy
Electron microscopy is currently the only technique capable of reconstructing wiring diagrams in their entirety. By detecting synapses on electron micrographs of serial sections and tracing axons and dendrites to their somas, one can identify synaptically connected neurons. The largest such reconstruction, the Caenorhabditis elegans nervous system, was carried out manually at the Medical Research Council (MRC), Cambridge, England, and finalized by us (Figure 2).
Complete electron microscopic circuit reconstruction is a painstakingly slow process because of the sheer amount of data involved. Axons and dendrites spanning millimeters must be traced with a resolution of a few nanometers. The reconstruction of the C. elegans nervous system (Figure 2), containing only 279 neurons, took the equivalent of several decades of work to complete!
To reconstruct more complex circuits, we are using techniques from image processing and machine learning to develop automated tracing algorithms. So far, we have reconstructed a neuropil volume of a thousand cubic microns. We intend to scale up our automated algorithms to fully reconstruct circuits of wide interest among neurobiologists, such as the fly brain, the vertebrate retina, and the cortical column.
From Wiring Diagrams to Behavior
Armed with wiring diagrams, we are starting to understand how electrical activity in neuronal circuits generates behavior. Our initial strategy is to focus on relatively simple circuits and behaviors. Once those are well understood, our experience will serve as a foundation for reverse engineering more complex systems.
One such simple system is the neuronal control of undulatory locomotion in C. elegans. Many species rely on a central pattern generator for undulatory locomotion. The C. elegans wiring diagram by itself does not support required oscillations. This implies that undulatory locomotion likely relies on propriosensory feedback. To understand how locomotion arises, we combine measurements of body muscle activity using a calcium indicator (see Movie 1), a method pioneered by Rex Kerr (HHMI, Janelia Farm Research Campus),and a simple model based on the known wiring diagram.
This simple system demonstrates that even the complete wiring diagram is not sufficient to understand how a circuit works. Modeling circuit function requires knowing certain dynamic parameters of neurons and synapsesmost of which are missing from the wiring diagrams. The problem goes even deeper: not only are most of the parameters missing, but we do not even know which of them are essential and which are not.
Design Principles Based on Optimization Theory
For models of brain function to have predictive power, an appropriate level of abstraction must be chosen and the essential parameters must be identified and measured. When we look to disciplines where modeling is well established, such as physics or engineering, we find that model building must be based on fundamental principles, or physical laws, such as the laws of conservation. Identifying similar fundamental principles in biology would help constrain the choice of possible models and focus our efforts.
As biological systems have evolved over hundreds of millions of years, their design has been optimized under various physical constraints. It is thus natural that a theoretical approach to biology must incorporate aspects of constrained optimization. We quantitatively formulate principles of brain design and rely on optimization theory to answer why questions.
A particularly successful example of optimization in biology is the wiring economy principle proposed by Ramón y Cajal more than 100 years ago. By quantitatively formulating and applying this principle, we were able to make unexpected, experimentally testable predictions and explain many aspects of brain design, such as the existence and structure of cortical maps, the spatial arrangement of neurons, the existence of dendritic spines, the dimensions of axons and dendrites, and the segregation of the neocortex into the gray and white matter. In addition to the many successes of our theoretical predictions, experiments have revealed several discrepancies. These discrepancies led to the discovery of another important principle of brain design: maximization of entropy (or information capacity). This principle in turn explains several key properties of synapses and the shapes of neurons.
Our research continues to focus on mapping the brain's structure and establishing its relationship with function. We have reconstructed both statistical and deterministic wiring diagrams and explained many structural observations as outcomes of constrained optimization. We plan to reconstruct wiring diagrams of more complex circuits and understand their function by combining anatomical, physiological, and theoretical approaches.
Parts of this work were supported by a grant from the National Institutes of Health and awards from the Swartz Foundation, the David and Lucile Packard Foundation, and the Klingenstein Foundation.