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

Efficient simulation of neural development using shared memory parallelization

The Neural Development Simulator, NeuroDevSim, is a Python module that simulates the most important aspects of brain development: morphological growth, migration, and pruning. It uses an agent-based modeling approach inherited from the NeuroMaC software. Each cycle has agents called fronts execute model-specific code. In the case of a growing dendritic or axonal front, this will be a choice between extension, branching, or growth termination. Somatic fronts can migrate to new positions and any front can be retracted to prune parts of neurons. Collision detection prevents new or migrating fronts from overlapping with existing ones. NeuroDevSim is a multi-core program that uses an innovative shared memory approach to achieve parallel processing without messaging. We demonstrate linear strong parallel scaling up to 96 cores for large models and have run these successfully on 128 cores. Most of the shared memory parallelism is achieved without memory locking. Instead, cores have only write privileges to private sections of arrays, while being able to read the entire shared array. Memory conflicts are avoided by a coding rule that allows only active fronts to use methods that need writing access. The exception is collision detection, which is needed to avoid the growth of physically overlapping structures. For collision detection, a memory-locking mechanism was necessary to control access to grid points that register the location of nearby fronts. A custom approach using a serialized lock broker was able to manage both read and write locking. NeuroDevSim allows easy modeling of most aspects of neural development for models simulating a few complex or thousands of simple neurons or a mixture of both.

Code available at

https://github.com/CNS-OIST/NeuroDevSim.

Creative Destruction: A Basic Computational Model of Cortical Layer Formation

One of the most characteristic properties of many vertebrate neural systems is the layered organization of different cell types. This cytoarchitecture exists in the cortex, the retina, the hippocampus, and many other parts of the central nervous system. The developmental mechanisms of neural layer formation have been subject to substantial experimental efforts. Here, we provide a general computational model for cortical layer formation in 3D physical space. We show that this multiscale, agent-based model, comprising two distinct stages of apoptosis, can account for the wide range of neuronal numbers encountered in different cortical areas and species. Our results demonstrate the phenotypic richness of a basic state diagram structure. Importantly, apoptosis allows for changing the thickness of one layer without automatically affecting other layers. Therefore, apoptosis increases the flexibility for evolutionary change in layer architecture. Notably, slightly changed gene regulatory dynamics recapitulate the characteristic properties observed in neurodevelopmental diseases. Overall, we propose a novel computational model using gene-type rules, exhibiting many characteristics of normal and pathological cortical development.

A generative growth model for thalamocortical axonal branching in primary visual cortex

Axonal morphology displays large variability and complexity, yet the canonical regularities of the cortex suggest that such wiring is based on the repeated initiation of a small set of genetically encoded rules. Extracting underlying developmental principles can hence shed light on what genetically encoded instructions must be available during cortical development. Within a generative model, we investigate growth rules for axonal branching patterns in cat area 17, originating from the lateral geniculate nucleus of the thalamus. This target area of synaptic connections is characterized by extensive ramifications and a high bouton density, characteristics thought to preserve the spatial resolution of receptive fields and to enable connections for the ocular dominance columns. We compare individual and global statistics, such as a newly introduced length-weighted asymmetry index and the global segment-length distribution, of generated and biological branching patterns as the benchmark for growth rules. We show that the proposed model surpasses the statistical accuracy of the Galton-Watson model, which is the most commonly employed model for biological growth processes. In contrast to the Galton-Watson model, our model can recreate the log-normal segment-length distribution of the experimental dataset and is considerably more accurate in recreating individual axonal morphologies. To provide a biophysical interpretation for statistical quantifications of the axonal branching patterns, the generative model is ported into the physically accurate simulation framework of Cx3D. In this 3D simulation environment we demonstrate how the proposed growth process can be formulated as an interactive process between genetic growth rules and chemical cues in the local environment.

eBrain: a Three Dimensional Simulation Tool to Study Drug Delivery in the Brain

Neurodegenerative disorders such as Alzheimer’s and Parkinson’s disease are severe disorders with acute symptoms that gradually progress. In the course of developing disease-modifying treatments for neurodegenerative disorders there is a need to develop novel strategies to increase efficacy of drugs and accelerate the development process. We developed a tool for simulating drug delivery in the brain by translating MRI data into an interactive 3D model. This tool, the eBrain, superimposes simulated drug diffusion and tissue uptake by inferring from the MRI data with a seamless display from any angle, magnification, or position. We discuss a representative implementation of eBrain that is inspired by clinical data in which insulin is intranasally administered to Alzheimer patients. Using extensive analysis of multiple eBrain simulations with varying parameters, we show the potential for eBrain to determine the optimal dosage to ensure drug delivery without overdosing the tissue. Specifically, we examined the efficacy of combined drug doses and potential compounds for tissue stimulation. Interestingly, our analysis uncovered that the drug efficacy is inferred from tissue intensity levels. Finally, we discuss the potential of eBrain and possible applications of eBrain to aid both inexperienced and experienced medical professionals as well as patients.

Erratum: Notice of Republication: Simulating Cortical Development as a Self Constructing Process: A Novel Multi-Scale Approach Combining Molecular and Physical Aspects

[This corrects the article DOI: 10.1371/journal.pcbi.1003173.].

Challenges in Reproducibility, Replicability, and Comparability of Computational Models and Tools for Neuronal and Glial Networks, Cells, and Subcellular Structures

The possibility to replicate and reproduce published research results is one of the biggest challenges in all areas of science. In computational neuroscience, there are thousands of models available. However, it is rarely possible to reimplement the models based on the information in the original publication, let alone rerun the models just because the model implementations have not been made publicly available. We evaluate and discuss the comparability of a versatile choice of simulation tools: tools for biochemical reactions and spiking neuronal networks, and relatively new tools for growth in cell cultures. The replicability and reproducibility issues are considered for computational models that are equally diverse, including the models for intracellular signal transduction of neurons and glial cells, in addition to single glial cells, neuron-glia interactions, and selected examples of spiking neuronal networks. We also address the comparability of the simulation results with one another to comprehend if the studied models can be used to answer similar research questions. In addition to presenting the challenges in reproducibility and replicability of published results in computational neuroscience, we highlight the need for developing recommendations and good practices for publishing simulation tools and computational models. Model validation and flexible model description must be an integral part of the tool used to simulate and develop computational models. Constant improvement on experimental techniques and recording protocols leads to increasing knowledge about the biophysical mechanisms in neural systems. This poses new challenges for computational neuroscience: extended or completely new computational methods and models may be required. Careful evaluation and categorization of the existing models and tools provide a foundation for these future needs, for constructing multiscale models or extending the models to incorporate additional or more detailed biophysical mechanisms. Improving the quality of publications in computational neuroscience, enabling progressive building of advanced computational models and tools, can be achieved only through adopting publishing standards which underline replicability and reproducibility of research results.

Framework for efficient synthesis of spatially embedded morphologies

Many problems in science and engineering require the ability to grow tubular or polymeric structures up to large volume fractions within a bounded region of three-dimensional space. Examples range from the construction of fibrous materials and biological cells such as neurons, to the creation of initial configurations for molecular simulations. A common feature of these problems is the need for the growing structures to wind throughout space without intersecting. At any time, the growth of a morphology depends on the current state of all the others, as well as the environment it is growing in, which makes the problem computationally intensive. Neuron synthesis has the additional constraint that the morphologies should reliably resemble biological cells, which possess nonlocal structural correlations, exhibit high packing fractions, and whose growth responds to anatomical boundaries in the synthesis volume. We present a spatial framework for simultaneous growth of an arbitrary number of nonintersecting morphologies that presents the growing structures with information on anisotropic and inhomogeneous properties of the space. The framework is computationally efficient because intersection detection is linear in the mass of growing elements up to high volume fractions and versatile because it provides functionality for environmental growth cues to be accessed by the growing morphologies. We demonstrate the framework by growing morphologies of various complexity.

Modeling the Cerebellar Microcircuit: New Strategies for a Long-Standing Issue

The cerebellar microcircuit has been the work bench for theoretical and computational modeling since the beginning of neuroscientific research. The regular neural architecture of the cerebellum inspired different solutions to the long-standing issue of how its circuitry could control motor learning and coordination. Originally, the cerebellar network was modeled using a statistical-topological approach that was later extended by considering the geometrical organization of local microcircuits. However, with the advancement in anatomical and physiological investigations, new discoveries have revealed an unexpected richness of connections, neuronal dynamics and plasticity, calling for a change in modeling strategies, so as to include the multitude of elementary aspects of the network into an integrated and easily updatable computational framework. Recently, biophysically accurate “realistic” models using a bottom-up strategy accounted for both detailed connectivity and neuronal non-linear membrane dynamics. In this perspective review, we will consider the state of the art and discuss how these initial efforts could be further improved. Moreover, we will consider how embodied neurorobotic models including spiking cerebellar networks could help explaining the role and interplay of distributed forms of plasticity. We envisage that realistic modeling, combined with closed-loop simulations, will help to capture the essence of cerebellar computations and could eventually be applied to neurological diseases and neurorobotic control systems.

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.

Dendrite and Axon Specific Geometrical Transformation in Neurite Development

We propose a model of neurite growth to explain the differences in dendrite and axon specific neurite development. The model implements basic molecular kinetics, e.g., building protein synthesis and transport to the growth cone, and includes explicit dependence of the building kinetics on the geometry of the neurite. The basic assumption was that the radius of the neurite decreases with length. We found that the neurite dynamics crucially depended on the relationship between the rate of active transport and the rate of morphological changes. If these rates were in the balance, then the neurite displayed axon specific development with a constant elongation speed. For dendrite specific growth, the maximal length was rapidly saturated by degradation of building protein structures or limited by proximal part expansion reaching the characteristic cell size.

REMOD: A Tool for Analyzing and Remodeling the Dendritic Architecture of Neural Cells

Dendritic morphology is a key determinant of how individual neurons acquire a unique signal processing profile. The highly branched dendritic structure that originates from the cell body, explores the surrounding 3D space in a fractal-like manner, until it reaches a certain amount of complexity. Its shape undergoes significant alterations under various physiological or neuropathological conditions. Yet, despite the profound effect that these alterations can have on neuronal function, the causal relationship between the two remains largely elusive. The lack of a systematic approach for remodeling neural cells and their dendritic trees is a key limitation that contributes to this problem. Such causal relationships can be inferred via the use of large-scale neuronal models whereby the anatomical plasticity of neurons is accounted for, in order to enhance their biological relevance and hence their predictive performance. To facilitate this effort, we developed a computational tool named REMOD that allows the structural remodeling of any type of virtual neuron. REMOD is written in Python and can be accessed through a dedicated web interface that guides the user through various options to manipulate selected neuronal morphologies. REMOD can also be used to extract meaningful morphology statistics for one or multiple reconstructions, including features such as sholl analysis, total dendritic length and area, path length to the soma, centrifugal branch order, diameter tapering and more. As such, the tool can be used both for the analysis and/or the remodeling of neuronal morphologies of any type.

Beyond boundaries--Eph:ephrin signaling in neurogenesis

Eph:ephrin signaling plays an important role in embryonic development as well as tissue homeostasis in the adult. At the cellular level, this transduction pathway is best known for its role in the control of cell adhesion and repulsion, cell migration and morphogenesis. Yet, a number of publications have also implicated Eph:ephrin signaling in the control of adult and embryonic neurogenesis. As is the case for other biological processes, these studies have reported conflicting and sometimes opposite roles for Eph:ephrin signaling in neurogenesis. Herein, we review these studies and we discuss existing mathematical models of stem cell dynamics and neurogenesis that provide a coherent framework and may help reconcile conflicting results.

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.

Models of learning in artificial neural networks generally assume that the neurons and approximate network are given, and then learning tunes the synaptic weights. By contrast, we address the question of how an entire functional neuronal network containing many differentiated neurons and connections can develop from only a single progenitor cell. We chose a winner-take-all network as the developmental target, because it is a computationally powerful circuit, and a candidate motif of neocortical networks. The key aspect of this challenge is that the developmental mechanisms must be locally autonomous as in Biology: They cannot depend on global knowledge or supervision. We have explored this developmental process by simulating in physical detail the fundamental biological behaviors, such as cell proliferation, neurite growth and synapse formation that give rise to the structural connectivity observed in the superficial layers of the neocortex. These differentiated, approximately connected neurons then adapt their synaptic weights homeostatically to obtain a uniform electrical signaling activity before going on to organize themselves according to the fundamental correlations embedded in a noisy wave-like input signal. In this way the precursor expands itself through development and unsupervised learning into winner-take-all functionality and orientation selectivity in a biologically plausible manner.

An in silico agent-based model demonstrates Reelin function in directing lamination of neurons during cortical development

The characteristic six-layered appearance of the neocortex arises from the correct positioning of pyramidal neurons during development and alterations in this process can cause intellectual disabilities and developmental delay. Malformations in cortical development arise when neurons either fail to migrate properly from the germinal zones or fail to cease migration in the correct laminar position within the cortical plate. The Reelin signalling pathway is vital for correct neuronal positioning as loss of Reelin leads to a partially inverted cortex. The precise biological function of Reelin remains controversial and debate surrounds its role as a chemoattractant or stop signal for migrating neurons. To investigate this further we developed an in silico agent-based model of cortical layer formation. Using this model we tested four biologically plausible hypotheses for neuron motility and four biologically plausible hypotheses for the loss of neuron motility (conversion from migration). A matrix of 16 combinations of motility and conversion rules was applied against the known structure of mouse cortical layers in the wild-type cortex, the Reelin-null mutant, the Dab1-null mutant and a conditional Dab1 mutant. Using this approach, many combinations of motility and conversion mechanisms can be rejected. For example, the model does not support Reelin acting as a repelling or as a stopping signal. In contrast, the study lends very strong support to the notion that the glycoprotein Reelin acts as a chemoattractant for neurons. Furthermore, the most viable proposition for the conversion mechanism is one in which conversion is affected by a motile neuron sensing in the near vicinity neurons that have already converted. Therefore, this model helps elucidate the function of Reelin during neuronal migration and cortical development.

Context-aware modeling of neuronal morphologies

Neuronal morphologies are pivotal for brain functioning: physical overlap between dendrites and axons constrain the circuit topology, and the precise shape and composition of dendrites determine the integration of inputs to produce an output signal. At the same time, morphologies are highly diverse and variant. The variance, presumably, originates from neurons developing in a densely packed brain substrate where they interact (e.g., repulsion or attraction) with other actors in this substrate. However, when studying neurons their context is never part of the analysis and they are treated as if they existed in isolation. Here we argue that to fully understand neuronal morphology and its variance it is important to consider neurons in relation to each other and to other actors in the surrounding brain substrate, i.e., their context. We propose a context-aware computational framework, NeuroMaC, in which large numbers of neurons can be grown simultaneously according to growth rules expressed in terms of interactions between the developing neuron and the surrounding brain substrate. As a proof of principle, we demonstrate that by using NeuroMaC we can generate accurate virtual morphologies of distinct classes both in isolation and as part of neuronal forests. Accuracy is validated against population statistics of experimentally reconstructed morphologies. We show that context-aware generation of neurons can explain characteristics of variation. Indeed, plausible variation is an inherent property of the morphologies generated by context-aware rules. We speculate about the applicability of this framework to investigate morphologies and circuits, to classify healthy and pathological morphologies, and to generate large quantities of morphologies for large-scale modeling.

Learning and stabilization of winner-take-all dynamics through interacting excitatory and inhibitory plasticity

Winner-Take-All (WTA) networks are recurrently connected populations of excitatory and inhibitory neurons that represent promising candidate microcircuits for implementing cortical computation. WTAs can perform powerful computations, ranging from signal-restoration to state-dependent processing. However, such networks require fine-tuned connectivity parameters to keep the network dynamics within stable operating regimes. In this article, we show how such stability can emerge autonomously through an interaction of biologically plausible plasticity mechanisms that operate simultaneously on all excitatory and inhibitory synapses of the network. A weight-dependent plasticity rule is derived from the triplet spike-timing dependent plasticity model, and its stabilization properties in the mean-field case are analyzed using contraction theory. Our main result provides simple constraints on the plasticity rule parameters, rather than on the weights themselves, which guarantee stable WTA behavior. The plastic network we present is able to adapt to changing input conditions, and to dynamically adjust its gain, therefore exhibiting self-stabilization mechanisms that are crucial for maintaining stable operation in large networks of interconnected subunits. We show how distributed neural assemblies can adjust their parameters for stable WTA function autonomously while respecting anatomical constraints on neural wiring.