Constructive connectomics: How neuronal axons get from here to there using gene-expression maps derived from their family trees.

During brain development, billions of axons must navigate over multiple spatial scales to reach specific neuronal targets, and so build the processing circuits that generate the intelligent behavior of animals. However, the limited information capacity of the zygotic genome puts a strong constraint on how, and which, axonal routes can be encoded. We propose and validate a mechanism of development that can provide an efficient encoding of this global wiring task. The key principle, confirmed through simulation, is that basic constraints on mitoses of neural stem cells-that mitotic daughters have similar gene expression to their parent and do not stray far from one another-induce a global hierarchical map of nested regions, each marked by the expression profile of its common progenitor population. Thus, a traversal of the lineal hierarchy generates a systematic sequence of expression profiles that traces a staged route, which growth cones can follow to their remote targets. We have analyzed gene expression data of developing and adult mouse brains published by the Allen Institute for Brain Science, and found them consistent with our simulations: gene expression indeed partitions the brain into a global spatial hierarchy of nested contiguous regions that is stable at least from embryonic day 11.5 to postnatal day 56. We use this experimental data to demonstrate that our axonal guidance algorithm is able to robustly extend arbors over long distances to specific targets, and that these connections result in a qualitatively plausible connectome. We conclude that, paradoxically, cell division may be the key to uniting the neurons of the brain.

Solving Constraint-Satisfaction Problems with Distributed Neocortical-Like Neuronal Networks.

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of the CSP's planar four-color graph coloring, maximum independent set, and sudoku on this substrate and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. The network is composed of nonsaturating linear threshold neurons. Their lack of right saturation allows the overall network to explore the problem space driven through the unstable dynamics generated by recurrent excitation. The direction of exploration is steered by the constraint neurons. While many problems can be solved using only linear inhibitory constraints, network performance on hard problems benefits significantly when these negative constraints are implemented by nonlinear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation and offer insight into the computational role of dual inhibitory mechanisms in neural circuits.

Unsupervised lineage-based characterization of primate precursors reveals high proliferative and morphological diversity in the OSVZ.

Generation of the primate cortex is characterized by the diversity of cortical precursors and the complexity of their lineage relationships. Recent studies have reported miscellaneous precursor types based on observer classification of cell biology features including morphology, stemness, and proliferative behavior. Here we use an unsupervised machine learning method for Hidden Markov Trees (HMTs), which can be applied to large datasets to classify precursors on the basis of morphology, cell-cycle length, and behavior during mitosis. The unbiased lineage analysis automatically identifies cell types by applying a lineage-based clustering and model-learning algorithm to a macaque corticogenesis dataset. The algorithmic results validate previously reported observer classification of precursor types and show numerous advantages: It predicts a higher diversity of progenitors and numerous potential transitions between precursor types. The HMT model can be initialized to learn a user-defined number of distinct classes of precursors. This makes it possible to 1) reveal as yet undetected precursor types in view of exploring the significant features of precursors with respect to specific cellular processes; and 2) explore specific lineage features. For example, most precursors in the experimental dataset exhibit bidirectional transitions. Constraining the directionality in the HMT model leads to a reduction in precursor diversity following multiple divisions, thereby suggesting that one impact of bidirectionality in corticogenesis is to maintain precursor diversity. In this way we show that unsupervised lineage analysis provides a valuable methodology for investigating fundamental features of corticogenesis.

Developmental self-construction and -configuration of functional neocortical neuronal networks.

The prenatal development of neural circuits must provide sufficient configuration to support at least a set of core postnatal behaviors. Although knowledge of various genetic and cellular aspects of development is accumulating rapidly, there is less systematic understanding of how these various processes play together in order to construct such functional networks. Here we make some steps toward such understanding by demonstrating through detailed simulations how a competitive co-operative ('winner-take-all', WTA) network architecture can arise by development from a single precursor cell. This precursor is granted a simplified gene regulatory network that directs cell mitosis, differentiation, migration, neurite outgrowth and synaptogenesis. Once initial axonal connection patterns are established, their synaptic weights undergo homeostatic unsupervised learning that is shaped by wave-like input patterns. We demonstrate how this autonomous genetically directed developmental sequence can give rise to self-calibrated WTA networks, and compare our simulation results with biological data.

Developmental origin of patchy axonal connectivity in the neocortex: a computational model.

Injections of neural tracers into many mammalian neocortical areas reveal a common patchy motif of clustered axonal projections. We studied in simulation a mathematical model for neuronal development in order to investigate how this patchy connectivity could arise in layer II/III of the neocortex. In our model, individual neurons of this layer expressed the activator-inhibitor components of a Gierer-Meinhardt reaction-diffusion system. The resultant steady-state reaction-diffusion pattern across the neuronal population was approximately hexagonal. Growth cones at the tips of extending axons used the various morphogens secreted by intrapatch neurons as guidance cues to direct their growth and invoke axonal arborization, so yielding a patchy distribution of arborization across the entire layer II/III. We found that adjustment of a single parameter yields the intriguing linear relationship between average patch diameter and interpatch spacing that has been observed experimentally over many cortical areas and species. We conclude that a simple Gierer-Meinhardt system expressed by the neurons of the developing neocortex is sufficient to explain the patterns of clustered connectivity observed experimentally.

Precursor diversity and complexity of lineage relationships in the outer subventricular zone of the primate.

Long-term ex vivo live imaging combined with unbiased sampling of cycling precursors shows that macaque outer subventricular zone (OSVZ) includes four distinct basal radial glial (bRG) cell morphotypes, bearing apical and/or basal processes in addition to nonpolar intermediate progenitors (IPs). Each of the five precursor types exhibits extensive self-renewal and proliferative capacities as well as the ability to directly generate neurons, albeit with different frequencies. Cell-cycle parameters exhibited an unusual stage-specific regulation with short cell-cycle duration and increased rates of proliferative divisions during supragranular layer production at late corticogenesis. State transition analysis of an extensive clonal database reveals bidirectional transitions between OSVZ precursor types as well as stage-specific differences in their progeny and topology of the lineage relationships. These results explore rodent-primate differences and show that primate cortical neurons are generated through complex lineages by a mosaic of precursors, thereby providing an innovative framework for understanding specific features of primate corticogenesis.

Simulating cortical development as a self constructing process: a novel multi-scale approach combining molecular and physical aspects.

Current models of embryological development focus on intracellular processes such as gene expression and protein networks, rather than on the complex relationship between subcellular processes and the collective cellular organization these processes support. We have explored this collective behavior in the context of neocortical development, by modeling the expansion of a small number of progenitor cells into a laminated cortex with layer and cell type specific projections. The developmental process is steered by a formal language analogous to genomic instructions, and takes place in a physically realistic three-dimensional environment. A common genome inserted into individual cells control their individual behaviors, and thereby gives rise to collective developmental sequences in a biologically plausible manner. The simulation begins with a single progenitor cell containing the artificial genome. This progenitor then gives rise through a lineage of offspring to distinct populations of neuronal precursors that migrate to form the cortical laminae. The precursors differentiate by extending dendrites and axons, which reproduce the experimentally determined branching patterns of a number of different neuronal cell types observed in the cat visual cortex. This result is the first comprehensive demonstration of the principles of self-construction whereby the cortical architecture develops. In addition, our model makes several testable predictions concerning cell migration and branching mechanisms.

Synthesizing cognition in neuromorphic electronic systems.

The quest to implement intelligent processing in electronic neuromorphic systems lacks methods for achieving reliable behavioral dynamics on substrates of inherently imprecise and noisy neurons. Here we report a solution to this problem that involves first mapping an unreliable hardware layer of spiking silicon neurons into an abstract computational layer composed of generic reliable subnetworks of model neurons and then composing the target behavioral dynamics as a "soft state machine" running on these reliable subnets. In the first step, the neural networks of the abstract layer are realized on the hardware substrate by mapping the neuron circuit bias voltages to the model parameters. This mapping is obtained by an automatic method in which the electronic circuit biases are calibrated against the model parameters by a series of population activity measurements. The abstract computational layer is formed by configuring neural networks as generic soft winner-take-all subnetworks that provide reliable processing by virtue of their active gain, signal restoration, and multistability. The necessary states and transitions of the desired high-level behavior are then easily embedded in the computational layer by introducing only sparse connections between some neurons of the various subnets. We demonstrate this synthesis method for a neuromorphic sensory agent that performs real-time context-dependent classification of motion patterns observed by a silicon retina.

TrakEM2 software for neural circuit reconstruction.

A key challenge in neuroscience is the expeditious reconstruction of neuronal circuits. For model systems such as Drosophila and C. elegans, the limiting step is no longer the acquisition of imagery but the extraction of the circuit from images. For this purpose, we designed a software application, TrakEM2, that addresses the systematic reconstruction of neuronal circuits from large electron microscopical and optical image volumes. We address the challenges of image volume composition from individual, deformed images; of the reconstruction of neuronal arbors and annotation of synapses with fast manual and semi-automatic methods; and the management of large collections of both images and annotations. The output is a neural circuit of 3d arbors and synapses, encoded in NeuroML and other formats, ready for analysis.

Competition through selective inhibitory synchrony.

Models of cortical neuronal circuits commonly depend on inhibitory feedback to control gain, provide signal normalization, and selectively amplify signals using winner-take-all (WTA) dynamics. Such models generally assume that excitatory and inhibitory neurons are able to interact easily because their axons and dendrites are colocalized in the same small volume. However, quantitative neuroanatomical studies of the dimensions of axonal and dendritic trees of neurons in the neocortex show that this colocalization assumption is not valid. In this letter, we describe a simple modification to the WTA circuit design that permits the effects of distributed inhibitory neurons to be coupled through synchronization, and so allows a single WTA to be distributed widely in cortical space, well beyond the arborization of any single inhibitory neuron and even across different cortical areas. We prove by nonlinear contraction analysis and demonstrate by simulation that distributed WTA subsystems combined by such inhibitory synchrony are inherently stable. We show analytically that synchronization is substantially faster than winner selection. This circuit mechanism allows networks of independent WTAs to fully or partially compete with other.

Embedding of cortical representations by the superficial patch system.

Pyramidal cells in layers 2 and 3 of the neocortex of many species collectively form a clustered system of lateral axonal projections (the superficial patch system--Lund JS, Angelucci A, Bressloff PC. 2003. Anatomical substrates for functional columns in macaque monkey primary visual cortex. Cereb Cortex. 13:15-24. or daisy architecture--Douglas RJ, Martin KAC. 2004. Neuronal circuits of the neocortex. Annu Rev Neurosci. 27:419-451.), but the function performed by this general feature of the cortical architecture remains obscure. By comparing the spatial configuration of labeled patches with the configuration of responses to drifting grating stimuli, we found the spatial organizations both of the patch system and of the cortical response to be highly conserved between cat and monkey primary visual cortex. More importantly, the configuration of the superficial patch system is directly reflected in the arrangement of function across monkey primary visual cortex. Our results indicate a close relationship between the structure of the superficial patch system and cortical responses encoding a single value across the surface of visual cortex (self-consistent states). This relationship is consistent with the spontaneous emergence of orientation response-like activity patterns during ongoing cortical activity (Kenet T, Bibitchkov D, Tsodyks M, Grinvald A, Arieli A. 2003. Spontaneously emerging cortical representations of visual attributes. Nature. 425:954-956.). We conclude that the superficial patch system is the physical encoding of self-consistent cortical states, and that a set of concurrently labeled patches participate in a network of mutually consistent representations of cortical input.

What's black and white about the grey matter?

In 1873 Camillo Golgi discovered his eponymous stain, which he called la reazione nera. By adding to it the concepts of the Neuron Doctrine and the Law of Dynamic Polarisation, Santiago Ramon y Cajal was able to link the individual Golgi-stained neurons he saw down his microscope into circuits. This was revolutionary and we have all followed Cajal's winning strategy for over a century. We are now on the verge of a new revolution, which offers the prize of a far more comprehensive description of neural circuits and their operation. The hope is that we will exploit the power of computer vision algorithms and modern molecular biological techniques to acquire rapidly reconstructions of single neurons and synaptic circuits, and to control the function of selected types of neurons. Only one item is now conspicuous by its absence: the 21st century equivalent of the concepts of the Neuron Doctrine and the Law of Dynamic Polarisation. Without their equivalent we will inevitably struggle to make sense of our 21st century observations within the 19th and 20th century conceptual framework we have inherited.

From neural arbors to daisies.

Pyramidal neurons in layers 2 and 3 of the neocortex collectively form an horizontal lattice of long-range, periodic axonal projections, known as the superficial patch system. The precise pattern of projections varies between cortical areas, but the patch system has nevertheless been observed in every area of cortex in which it has been sought, in many higher mammals. Although the clustered axonal arbors of single pyramidal cells have been examined in detail, the precise rules by which these neurons collectively merge their arbors remain unknown. To discover these rules, we generated models of clustered axonal arbors following simple geometric patterns. We found that models assuming spatially aligned but independent formation of each axonal arbor do not produce patchy labeling patterns for large simulated injections into populations of generated axonal arbors. In contrast, a model that used information distributed across the cortical sheet to generate axonal projections reproduced every observed quality of cortical labeling patterns. We conclude that the patch system cannot be built during development using only information intrinsic to single neurons. Information shared across the population of patch-projecting neurons is required for the patch system to reach its adult state.

Collective stability of networks of winner-take-all circuits.

The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual cortex are consistent with the recurrent excitation and inhibitory feedback required for cooperative-competitive circuits such as the soft winner-take-all (WTA). WTA circuits offer interesting computational properties such as selective amplification, signal restoration, and decision making. But these properties depend on the signal gain derived from positive feedback, and so there is a critical trade-off between providing feedback strong enough to support the sophisticated computations while maintaining overall circuit stability. The issue of stability is all the more intriguing when one considers that the WTAs are expected to be densely distributed through the superficial layers and that they are at least partially interconnected. We consider how to reason about stability in very large distributed networks of such circuits. We approach this problem by approximating the regular cortical architecture as many interconnected cooperative-competitive modules. We demonstrate that by properly understanding the behavior of this small computational module, one can reason over the stability and convergence of very large networks composed of these modules. We obtain parameter ranges in which the WTA circuit operates in a high-gain regime, is stable, and can be aggregated arbitrarily to form large, stable networks. We use nonlinear contraction theory to establish conditions for stability in the fully nonlinear case and verify these solutions using numerical simulations. The derived bounds allow modes of operation in which the WTA network is multistable and exhibits state-dependent persistent activities. Our approach is sufficiently general to reason systematically about the stability of any network, biological or technological, composed of networks of small modules that express competition through shared inhibition.

Reward-modulated Hebbian learning of decision making.

We introduce a framework for decision making in which the learning of decision making is reduced to its simplest and biologically most plausible form: Hebbian learning on a linear neuron. We cast our Bayesian-Hebb learning rule as reinforcement learning in which certain decisions are rewarded and prove that each synaptic weight will on average converge exponentially fast to the log-odd of receiving a reward when its pre- and postsynaptic neurons are active. In our simple architecture, a particular action is selected from the set of candidate actions by a winner-take-all operation. The global reward assigned to this action then modulates the update of each synapse. Apart from this global reward signal, our reward-modulated Bayesian Hebb rule is a pure Hebb update that depends only on the coactivation of the pre- and postsynaptic neurons, not on the weighted sum of all presynaptic inputs to the postsynaptic neuron as in the perceptron learning rule or the Rescorla-Wagner rule. This simple approach to action-selection learning requires that information about sensory inputs be presented to the Bayesian decision stage in a suitably preprocessed form resulting from other adaptive processes (acting on a larger timescale) that detect salient dependencies among input features. Hence our proposed framework for fast learning of decisions also provides interesting new hypotheses regarding neural nodes and computational goals of cortical areas that provide input to the final decision stage.

Forced G1-phase reduction alters mode of division, neuron number, and laminar phenotype in the cerebral cortex.

The link between cortical precursors G1 duration (TG1) and their mode of division remains a major unresolved issue of potential importance for regulating corticogenesis. Here, we induced a 25% reduction in TG1 in mouse cortical precursors via forced expression of cyclin D1 and cyclin E1. We found that in utero electroporation-mediated gene transfer transfects a cohort of synchronously cycling precursors, necessitating alternative methods of measuring cell-cycle phases to those classical used. TG1 reduction promotes cell-cycle reentry at the expense of differentiation and increases the self-renewal capacities of Pax6 precursors as well as of Tbr2 basal precursors (BPs). A population level analysis reveals sequential and lineage-specific effects, showing that TG1 reduction: (i) promotes Pax6 self-renewing proliferative divisions before promoting divisions wherein Pax6 precursors generate Tbr2 BPs and (ii) promotes self-renewing proliferative divisions of Tbr2 precursors at the expense of neurogenesis, thus leading to an amplification of the BPs pool in the subventricular zone and the dispersed mitotic compartment of the intermediate zone. These results point to the G1 mode of division relationship as an essential control mechanism of corticogenesis. This is further supported by long-term studies showing that TG1 reduction results in cytoarchitectural modifications including supernumerary supragranular neuron production. Modeling confirms that the TG1-induced changes in neuron production and laminar fate are mediated via the changes in the mode of division. These findings also have implications for understanding the mechanisms that have contributed to brain enlargement and complexity during evolution.

State-dependent computation using coupled recurrent networks.

Although conditional branching between possible behavioral states is a hallmark of intelligent behavior, very little is known about the neuronal mechanisms that support this processing. In a step toward solving this problem, we demonstrate by theoretical analysis and simulation how networks of richly interconnected neurons, such as those observed in the superficial layers of the neocortex, can embed reliable, robust finite state machines. We show how a multistable neuronal network containing a number of states can be created very simply by coupling two recurrent networks whose synaptic weights have been configured for soft winner-take-all (sWTA) performance. These two sWTAs have simple, homogeneous, locally recurrent connectivity except for a small fraction of recurrent cross-connections between them, which are used to embed the required states. This coupling between the maps allows the network to continue to express the current state even after the input that elicited that state is withdrawn. In addition, a small number of transition neurons implement the necessary input-driven transitions between the embedded states. We provide simple rules to systematically design and construct neuronal state machines of this kind. The significance of our finding is that it offers a method whereby the cortex could construct networks supporting a broad range of sophisticated processing by applying only small specializations to the same generic neuronal circuit.