NETMORPH: A Framework for the Stochastic Generation of Large Scale Neuronal Networks With Realistic Neuron Morphologies

A biologically inspired repair mechanism for neuronal reconstructions with a focus on human dendrites

Investigating and modelling the functionality of human neurons remains challenging due to the technical limitations, resulting in scarce and incomplete 3D anatomical reconstructions. Here we used a morphological modelling approach based on optimal wiring to repair the parts of a dendritic morphology that were lost due to incomplete tissue samples. In Drosophila, where dendritic regrowth has been studied experimentally using laser ablation, we found that modelling the regrowth reproduced a bimodal distribution between regeneration of cut branches and invasion by neighbouring branches. Interestingly, our repair model followed growth rules similar to those for the generation of a new dendritic tree. To generalise the repair algorithm from Drosophila to mammalian neurons, we artificially sectioned reconstructed dendrites from mouse and human hippocampal pyramidal cell morphologies, and showed that the regrown dendrites were morphologically similar to the original ones. Furthermore, we were able to restore their electrophysiological functionality, as evidenced by the recovery of their firing behaviour. Importantly, we show that such repairs also apply to other neuron types including hippocampal granule cells and cerebellar Purkinje cells. We then extrapolated the repair to incomplete human CA1 pyramidal neurons, where the anatomical boundaries of the particular brain areas innervated by the neurons in question were known. Interestingly, the repair of incomplete human dendrites helped to simulate the recently observed increased synaptic thresholds for dendritic NMDA spikes in human versus mouse dendrites. To make the repair tool available to the neuroscience community, we have developed an intuitive and simple graphical user interface (GUI), which is available in the TREES toolbox (www.treestoolbox.org).

Controlling morpho-electrophysiological variability of neurons with detailed biophysical models

Variability, which is known to be a universal feature among biological units such as neuronal cells, holds significant importance, as, for example, it enables a robust encoding of a high volume of information in neuronal circuits and prevents hypersynchronizations. While most computational studies on electrophysiological variability in neuronal circuits were done with single-compartment neuron models, we instead focus on the variability of detailed biophysical models of neuron multi-compartmental morphologies. We leverage a Markov chain Monte Carlo method to generate populations of electrical models reproducing the variability of experimental recordings while being compatible with a set of morphologies to faithfully represent specifi morpho-electrical type. We demonstrate our approach on layer 5 pyramidal cells and study the morpho-electrical variability and in particular, find that morphological variability alone is insufficient to reproduce electrical variability. Overall, this approach provides a strong statistical basis to create detailed models of neurons with controlled variability.

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.

Tissues as networks of cells: towards generative rules of complex organ development

Network analysis is a well-known and powerful tool in molecular biology. More recently, it has been introduced in developmental biology. Tissues can be readily translated into spatial networks such that cells are represented by nodes and intercellular connections by edges. This discretization of cellular organization enables mathematical approaches rooted in network science to be applied towards the understanding of tissue structure and function. Here, we describe how such tissue abstractions can enable the principles that underpin tissue formation and function to be uncovered. We provide an introduction into biologically relevant network measures, then present an overview of different areas of developmental biology where these approaches have been applied. We then summarize the general developmental rules underpinning tissue topology generation. Finally, we discuss how generative models can help to link the developmental rule back to the tissue topologies. Our collection of results points at general mechanisms as to how local developmental rules can give rise to observed topological properties in multicellular systems.

Models of Purkinje cell dendritic tree selection during early cerebellar development

We investigate the relationship between primary dendrite selection of Purkinje cells and migration of their presynaptic partner granule cells during early cerebellar development. During postnatal development, each Purkinje cell grows more than three dendritic trees, from which a primary tree is selected for development, whereas the others completely retract. Experimental studies suggest that this selection process is coordinated by physical and synaptic interactions with granule cells, which undergo a massive migration at the same time. However, technical limitations hinder continuous experimental observation of multiple cell populations. To explore possible mechanisms underlying this selection process, we constructed a computational model using a new computational framework, NeuroDevSim. The study presents the first computational model that simultaneously simulates Purkinje cell growth and the dynamics of granule cell migrations during the first two postnatal weeks, allowing exploration of the role of physical and synaptic interactions upon dendritic selection. The model suggests that interaction with parallel fibers is important to establish the distinct planar morphology of Purkinje cell dendrites. Specific rules to select which dendritic trees to keep or retract result in larger winner trees with more synaptic contacts than using random selection. A rule based on afferent synaptic activity was less effective than rules based on dendritic size or numbers of synapses.

Brain-wide dendrites in a near-optimal performance of dynamic range and information transmission

Dendrites receive and process signals from other neurons. The range of signal intensities that can be robustly distinguished by dendrites is quantified by the dynamic range. We investigate the dynamic range and information transmission efficiency of dendrites in relation to dendritic morphology. We model dendrites in a neuron as multiple excitable binary trees connected to the soma where each node in a tree can be excited by external stimulus or by receiving signals transmitted from adjacent excited nodes. It has been known that larger dendritic trees have a higher dynamic range. We show that for dendritic tress of the same number of nodes, the dynamic range increases with the number of somatic branches and decreases with the asymmetry of dendrites, and the information transmission is more efficient for dendrites with more somatic branches. Moreover, our simulated data suggest that there is an exponential association (decay resp.) of overall relative energy consumption (dynamic range resp.) in relation to the number of somatic branches. This indicates that further increasing the number of somatic branches (e.g. beyond 10 somatic branches) has limited ability to improve the transmission efficiency. With brain-wide neuron digital reconstructions of the pyramidal cells, 90% of neurons have no more than 10 dendrites. These suggest that actual brain-wide dendritic morphology is near optimal in terms of both dynamic range and information transmission.

Computational Models of Typical and Atypical Brain Network Development

Over the last decade, the organization of brain networks at both micro- and macroscales has become a key focus of neuroscientific inquiry. This has revealed fundamental features of brain network organization-small-worldness, modularity, heavy-tailed degree distributions-and has highlighted how these structural features support brain function. However, the driving forces that shape brain networks over the course of development have begun to be explored only recently. Here, we review recent efforts to gain insights into the mechanisms of brain development through generative modeling of both macroscale human brain networks and microscale cellular connectomes in Caenorhabditis elegans and other organisms. We show how these mathematical models can begin to shed light on the biological processes that drive and constrain the development of brain networks. Finally, we show how generative network models can translate genetic and environmental differences into variability in developmental trajectories, leading to diverse cognitive and mental health outcomes in children and young people.

The branching code: A model of actin-driven dendrite arborization

The cytoskeleton is crucial for defining neuronal-type-specific dendrite morphologies. To explore how the complex interplay of actin-modulatory proteins (AMPs) can define neuronal types in vivo, we focused on the class III dendritic arborization (c3da) neuron of Drosophila larvae. Using computational modeling, we reveal that the main branches (MBs) of c3da neurons follow general models based on optimal wiring principles, while the actin-enriched short terminal branches (STBs) require an additional growth program. To clarify the cellular mechanisms that define this second step, we thus concentrated on STBs for an in-depth quantitative description of dendrite morphology and dynamics. Applying these methods systematically to mutants of six known and novel AMPs, we revealed the complementary roles of these individual AMPs in defining STB properties. Our data suggest that diverse dendrite arbors result from a combination of optimal-wiring-related growth and individualized growth programs that are neuron-type specific.

Computational synthesis of cortical dendritic morphologies

Neuronal morphologies provide the foundation for the electrical behavior of neurons, the connectomes they form, and the dynamical properties of the brain. Comprehensive neuron models are essential for defining cell types, discerning their functional roles, and investigating brain-disease-related dendritic alterations. However, a lack of understanding of the principles underlying neuron morphologies has hindered attempts to computationally synthesize morphologies for decades. We introduce a synthesis algorithm based on a topological descriptor of neurons, which enables the rapid digital reconstruction of entire brain regions from few reference cells. This topology-guided synthesis generates dendrites that are statistically similar to biological reconstructions in terms of morpho-electrical and connectivity properties and offers a significant opportunity to investigate the links between neuronal morphology and brain function across different spatiotemporal scales. Synthesized cortical networks based on structurally altered dendrites associated with diverse brain pathologies revealed principles linking branching properties to the structure of large-scale networks.

BioDynaMo: a modular platform for high-performance agent-based simulation

MOTIVATION

Agent-based modeling is an indispensable tool for studying complex biological systems. However, existing simulation platforms do not always take full advantage of modern hardware and often have a field-specific software design.

RESULTS

We present a novel simulation platform called BioDynaMo that alleviates both of these problems. BioDynaMo features a modular and high-performance simulation engine. We demonstrate that BioDynaMo can be used to simulate use cases in: neuroscience, oncology and epidemiology. For each use case, we validate our findings with experimental data or an analytical solution. Our performance results show that BioDynaMo performs up to three orders of magnitude faster than the state-of-the-art baselines. This improvement makes it feasible to simulate each use case with one billion agents on a single server, showcasing the potential BioDynaMo has for computational biology research.

AVAILABILITY AND IMPLEMENTATION

BioDynaMo is an open-source project under the Apache 2.0 license and is available at www.biodynamo.org. Instructions to reproduce the results are available in the supplementary information.

SUPPLEMENTARY INFORMATION

Available at https://doi.org/10.5281/zenodo.5121618.

Efficient metadata mining of web-accessible neural morphologies

Advancements in neuroscience research have led to steadily accelerating data production and sharing. The online community repository of neural reconstructions NeuroMorpho.Org grew from fewer than 1000 digitally traced neurons in 2006 to more than 140,000 cells today, including glia that now constitute 10.1% of the content. Every reconstruction consists of a detailed 3D representation of branch geometry and connectivity in a standardized format, from which a collection of morphometric features is extracted and stored. Moreover, each entry in the database is accompanied by rich metadata annotation describing the animal subject, anatomy, and experimental details. The rapid expansion of this resource in the past decade was accompanied by a parallel rise in the complexity of the available information, creating both opportunities and challenges for knowledge mining. Here, we introduce a new summary reporting functionality, allowing NeuroMorpho.Org users to efficiently download digests of metadata and morphometrics from multiple groups of similar cells for further analysis. We demonstrate the capabilities of the tool for both glia and neurons and present an illustrative statistical analysis of the resulting data.

Active Dendrites and Local Field Potentials: Biophysical Mechanisms and Computational Explorations

Neurons and glial cells are endowed with membranes that express a rich repertoire of ion channels, transporters, and receptors. The constant flux of ions across the neuronal and glial membranes results in voltage fluctuations that can be recorded from the extracellular matrix. The high frequency components of this voltage signal contain information about the spiking activity, reflecting the output from the neurons surrounding the recording location. The low frequency components of the signal, referred to as the local field potential (LFP), have been traditionally thought to provide information about the synaptic inputs that impinge on the large dendritic trees of various neurons. In this review, we discuss recent computational and experimental studies pointing to a critical role of several active dendritic mechanisms that can influence the genesis and the location-dependent spectro-temporal dynamics of LFPs, spanning different brain regions. We strongly emphasize the need to account for the several fast and slow dendritic events and associated active mechanisms - including gradients in their expression profiles, inter- and intra-cellular spatio-temporal interactions spanning neurons and glia, heterogeneities and degeneracy across scales, neuromodulatory influences, and activitydependent plasticity - towards gaining important insights about the origins of LFP under different behavioral states in health and disease. We provide simple but essential guidelines on how to model LFPs taking into account these dendritic mechanisms, with detailed methodology on how to account for various heterogeneities and electrophysiological properties of neurons and synapses while studying LFPs.

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.

Prediction of Neural Diameter From Morphology to Enable Accurate Simulation

Accurate neuron morphologies are paramount for computational model simulations of realistic neural responses. Over the last decade, the online repository NeuroMorpho.Org has collected over 140,000 available neuron morphologies to understand brain function and promote interaction between experimental and computational research. Neuron morphologies describe spatial aspects of neural structure; however, many of the available morphologies do not contain accurate diameters that are essential for computational simulations of electrical activity. To best utilize available neuron morphologies, we present a set of equations that predict dendritic diameter from other morphological features. To derive the equations, we used a set of NeuroMorpho.org archives with realistic neuron diameters, representing hippocampal pyramidal, cerebellar Purkinje, and striatal spiny projection neurons. Each morphology is separated into initial, branching children, and continuing nodes. Our analysis reveals that the diameter of preceding nodes, Parent Diameter, is correlated to diameter of subsequent nodes for all cell types. Branching children and initial nodes each required additional morphological features to predict diameter, such as path length to soma, total dendritic length, and longest path to terminal end. Model simulations reveal that membrane potential response with predicted diameters is similar to the original response for several tested morphologies. We provide our open source software to extend the utility of available NeuroMorpho.org morphologies, and suggest predictive equations may supplement morphologies that lack dendritic diameter and improve model simulations with realistic dendritic diameter.

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful techniques for computing topological descriptors, the inverse problem, i.e., recovering the input data from topological descriptors, has proved to be challenging. In this article, we study in detail the Topological Morphology Descriptor (TMD), which assigns a persistence diagram to any tree embedded in Euclidean space, and a sort of stochastic inverse to the TMD, the Topological Neuron Synthesis (TNS) algorithm, gaining both theoretical and computational insights into the relation between the two. We propose a new approach to classify barcodes using symmetric groups, which provides a concrete language to formulate our results. We investigate to what extent the TNS recovers a geometric tree from its TMD and describe the effect of different types of noise on the process of tree generation from persistence diagrams. We prove moreover that the TNS algorithm is stable with respect to specific types of noise.

Achieving functional neuronal dendrite structure through sequential stochastic growth and retraction

Class I ventral posterior dendritic arborisation (c1vpda) proprioceptive sensory neurons respond to contractions in the Drosophila larval body wall during crawling. Their dendritic branches run along the direction of contraction, possibly a functional requirement to maximise membrane curvature during crawling contractions. Although the molecular machinery of dendritic patterning in c1vpda has been extensively studied, the process leading to the precise elaboration of their comb-like shapes remains elusive. Here, to link dendrite shape with its proprioceptive role, we performed long-term, non-invasive, in vivo time-lapse imaging of c1vpda embryonic and larval morphogenesis to reveal a sequence of differentiation stages. We combined computer models and dendritic branch dynamics tracking to propose that distinct sequential phases of stochastic growth and retraction achieve efficient dendritic trees both in terms of wire and function. Our study shows how dendrite growth balances structure-function requirements, shedding new light on general principles of self-organisation in functionally specialised dendrites.

Biological network growth in complex environments: A computational framework

Spatial biological networks are abundant on all scales of life, from single cells to ecosystems, and perform various important functions including signal transmission and nutrient transport. These biological functions depend on the architecture of the network, which emerges as the result of a dynamic, feedback-driven developmental process. While cell behavior during growth can be genetically encoded, the resulting network structure depends on spatial constraints and tissue architecture. Since network growth is often difficult to observe experimentally, computer simulations can help to understand how local cell behavior determines the resulting network architecture. We present here a computational framework based on directional statistics to model network formation in space and time under arbitrary spatial constraints. Growth is described as a biased correlated random walk where direction and branching depend on the local environmental conditions and constraints, which are presented as 3D multilayer grid. To demonstrate the application of our tool, we perform growth simulations of a dense network between cells and compare the results to experimental data from osteocyte networks in bone. Our generic framework might help to better understand how network patterns depend on spatial constraints, or to identify the biological cause of deviations from healthy network function.

Local CPG Self Growing Network Model with Multiple Physical Properties

Compared with traditional control methods, the advantage of CPG (Central Pattern Generator) network control is that it can significantly reduce the size of the control variable without losing the complexity of its motion mode output. Therefore, it has been widely used in the motion control of robots. To date, the research into CPG network has been polarized: one direction has focused on the function of CPG control rather than biological rationality, which leads to the poor functional adaptability of the control network and means that the control network can only be used under fixed conditions and cannot adapt to new control requirements. This is because, when there are new control requirements, it is difficult to develop a control network with poor biological rationality into a new, qualified network based on previous research; instead, it must be explored again from the basic link. The other direction has focused on the rationality of biology instead of the function of CPG control, which means that the form of the control network is only similar to a real neural network, without practical use. In this paper, we propose some physical characteristics (including axon resistance, capacitance, length and diameter, etc.) that can determine the corresponding parameters of the control model to combine the growth process and the function of the CPG control network. Universal gravitation is used to achieve the targeted guidance of axon growth, Brownian random motion is used to simulate the random turning of axon self-growth, and the signal of a single neuron is established by the Rall Cable Model that simplifies the axon membrane potential distribution. The transfer model, which makes the key parameters of the CPG control network—the delay time constant and the connection weight between the synapses—correspond to the axon length and axon diameter in the growth model and the growth and development of the neuron processes and control functions are combined. By coordinating the growth and development process and control function of neurons, we aim to realize the control function of the CPG network as much as possible under the conditions of biological reality. In this way, the complexity of the control model we develop will be close to that of a biological neural network, and the control network will have more control functions. Finally, the effectiveness of the established CPG self-growth control network is verified through the experiments of the simulation prototype and experimental prototype.

Dissecting Sholl Analysis into Its Functional Components

Sholl analysis has been an important technique in dendritic anatomy for more than 60 years. The Sholl intersection profile is obtained by counting the number of dendritic branches at a given distance from the soma and is a key measure of dendritic complexity; it has applications from evaluating the changes in structure induced by pathologies to estimating the expected number of anatomical synaptic contacts. We find that the Sholl intersection profiles of most neurons can be reproduced from three basic, functional measures: the domain spanned by the dendritic arbor, the total length of the dendrite, and the angular distribution of how far dendritic segments deviate from a direct path to the soma (i.e., the root angle distribution). The first two measures are determined by axon location and hence microcircuit structure; the third arises from optimal wiring and represents a branching statistic estimating the need for conduction speed in a neuron.

Generation of Granule Cell Dendritic Morphologies by Estimating the Spatial Heterogeneity of Dendritic Branching

Biological realism of dendritic morphologies is important for simulating electrical stimulation of brain tissue. By adding point process modeling and conditional sampling to existing generation strategies, we provide a novel means of reproducing the nuanced branching behavior that occurs in different layers of granule cell dendritic morphologies. In this study, a heterogeneous Poisson point process was used to simulate branching events. Conditional distributions were then used to select branch angles depending on the orthogonal distance to the somatic plane. The proposed method was compared to an existing generation tool and a control version of the proposed method that used a homogeneous Poisson point process. Morphologies were generated with each method and then compared to a set of digitally reconstructed neurons. The introduction of a conditionally dependent branching rate resulted in the generation of morphologies that more accurately reproduced the emergent properties of dendritic material per layer, Sholl intersections, and proximal passive current flow. Conditional dependence was critically important for the generation of realistic granule cell dendritic morphologies.

Image-derived models of cell organization changes during differentiation and drug treatments

PC12 cells are a popular model system to study changes driving and accompanying neuronal differentiation. While attention has been paid to changes in transcriptional regulation and protein signaling, much less is known about the changes in organization that accompany PC12 differentiation. Fluorescence microscopy can provide extensive information about these changes, although it is difficult to continuously observe changes over many days of differentiation. We describe a generative model of differentiation-associated changes in cell and nuclear shape and their relationship to mitochondrial distribution constructed from images of different cells at discrete time points. We show that the model accurately represents complex cell and nuclear shapes and learn a regression model that relates cell and nuclear shape to mitochondrial distribution; the predictive accuracy of the model increases during differentiation. Most importantly, we propose a method, based on cell matching and interpolation, to produce realistic simulations of the dynamics of cell differentiation from only static images. We also found that the distribution of cell shapes is hollow: most shapes are very different from the average shape. Finally, we show how the method can be used to model nuclear shape changes of human-induced pluripotent stem cells resulting from drug treatments.

Decay of connection probabilities with distance in 2D and 3D neuronal networks

We study connectivity in a model of a growing neuronal network in dimensions 2 and 3. Although the axon-to-dendrite proximity is an insufficient condition for establishing a functional synapse, it is still a necessary one. Therefore we study connection probabilities at short distances between the randomly grown axon trees and somas as probabilities of potential connections between the corresponding neurons. Our results show that, contrary to a common belief, these probabilities do not necessarily decay polynomially or exponentially in distance, but there are regimes of parameter values when the probability of proximity is not sensitive to the distance. In particular, in 3 dimensions the Euclidean distance between the neuronal cell body centers of neurons seems to play a very subtle role, as the probabilities of connections are practically constant within a certain finite range of distance. The model has a sufficient number of parameters to assess networks of neurons of different types. Our results give a firm basis for further modelling of the neuronal connectivity taking into account some realistic bouton distributions for establishing synaptic connections.

Networks of random trees as a model of neuronal connectivity

We provide an analysis of a randomly grown 2-d network which models the morphological growth of dendritic and axonal arbors. From the stochastic geometry of this model we derive a dynamic graph of potential synaptic connections. We estimate standard network parameters such as degree distribution, average shortest path length and clustering coefficient, considering all these parameters as functions of time. Our results show that even a simple model with just a few parameters is capable of representing a wide spectra of architecture, capturing properties of well-known models, such as random graphs or small world networks, depending on the time of the network development. The introduced model allows not only rather straightforward simulations but it is also amenable to a rigorous analysis. This provides a base for further study of formation of synaptic connections on such networks and their dynamics due to plasticity.

Theoretical Models of Neural Development

Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.

Modelling brain-wide neuronal morphology via rooted Cayley trees

Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide neuron topology. Based on estimated order-dependent branching probability from actual axonal and dendritic trees, our inhomogeneous model quantitatively captures a number of topological features including size and shape of both axons and dendrites. This sheds lights on a universal mechanism behind the topological formation of brain-wide axonal and dendritic trees.

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.

Stochastic Modeling of Radiation-induced Dendritic Damage on in silico Mouse Hippocampal Neurons

Cognitive dysfunction associated with radiotherapy for cancer treatment has been correlated to several factors, one of which is changes to the dendritic morphology of neuronal cells. Alterations in dendritic geometry and branching patterns are often accompanied by deficits that impact learning and memory. The purpose of this study is to develop a novel predictive model of neuronal dendritic damages caused by exposure to low linear energy transfer (LET) radiation, such as X-rays, γ-rays and high-energy protons. We established in silico representations of mouse hippocampal dentate granule cell layer (GCL) and CA1 pyramidal neurons, which are frequently examined in radiation-induced cognitive decrements. The in silico representations are used in a stochastic model that describes time dependent dendritic damage induced by exposure to low LET radiation. Changes in morphometric parameters, such as total dendritic length, number of branch points and branch number, including the Sholl analysis for single neurons are described by the model. Our model based predictions for different patterns of morphological changes based on energy deposition in dendritic segments (EDDS) will serve as a useful basis to compare specific patterns of morphological alterations caused by EDDS mechanisms.

Design and implementation of multi-signal and time-varying neural reconstructions

Several efficient procedures exist to digitally trace neuronal structure from light microscopy, and mature community resources have emerged to store, share, and analyze these datasets. In contrast, the quantification of intracellular distributions and morphological dynamics is not yet standardized. Current widespread descriptions of neuron morphology are static and inadequate for subcellular characterizations. We introduce a new file format to represent multichannel information as well as an open-source Vaa3D plugin to acquire this type of data. Next we define a novel data structure to capture morphological dynamics, and demonstrate its application to different time-lapse experiments. Importantly, we designed both innovations as judicious extensions of the classic SWC format, thus ensuring full back-compatibility with popular visualization and modeling tools. We then deploy the combined multichannel/time-varying reconstruction system on developing neurons in live Drosophila larvae by digitally tracing fluorescently labeled cytoskeletal components along with overall dendritic morphology as they changed over time. This same design is also suitable for quantifying dendritic calcium dynamics and tracking arbor-wide movement of any subcellular substrate of interest.

T2N as a new tool for robust electrophysiological modeling demonstrated for mature and adult-born dentate granule cells

Compartmental models are the theoretical tool of choice for understanding single neuron computations. However, many models are incomplete, built ad hoc and require tuning for each novel condition rendering them of limited usability. Here, we present T2N, a powerful interface to control NEURON with Matlab and TREES toolbox, which supports generating models stable over a broad range of reconstructed and synthetic morphologies. We illustrate this for a novel, highly detailed active model of dentate granule cells (GCs) replicating a wide palette of experiments from various labs. By implementing known differences in ion channel composition and morphology, our model reproduces data from mouse or rat, mature or adult-born GCs as well as pharmacological interventions and epileptic conditions. This work sets a new benchmark for detailed compartmental modeling. T2N is suitable for creating robust models useful for large-scale networks that could lead to novel predictions. We discuss possible T2N application in degeneracy studies.

Morphological determinants of dendritic arborization neurons in Drosophila larva

Pairing in vivo imaging and computational modeling of dendritic arborization (da) neurons from the fruit fly larva provides a unique window into neuronal growth and underlying molecular processes. We image, reconstruct, and analyze the morphology of wild-type, RNAi-silenced, and mutant da neurons. We then use local and global rule-based stochastic simulations to generate artificial arbors, and identify the parameters that statistically best approximate the real data. We observe structural homeostasis in all da classes, where an increase in size of one dendritic stem is compensated by a reduction in the other stems of the same neuron. Local rule models show that bifurcation probability is determined by branch order, while branch length depends on path distance from the soma. Global rule simulations suggest that most complex morphologies tend to be constrained by resource optimization, while simpler neuron classes privilege path distance conservation. Genetic manipulations affect both the local and global optimal parameters, demonstrating functional perturbations in growth mechanisms.

Reconstruction and visualization of large-scale volumetric models of neocortical circuits for physically-plausible in silico optical studies

BACKGROUND

We present a software workflow capable of building large scale, highly detailed and realistic volumetric models of neocortical circuits from the morphological skeletons of their digitally reconstructed neurons. The limitations of the existing approaches for creating those models are explained, and then, a multi-stage pipeline is discussed to overcome those limitations. Starting from the neuronal morphologies, we create smooth piecewise watertight polygonal models that can be efficiently utilized to synthesize continuous and plausible volumetric models of the neurons with solid voxelization. The somata of the neurons are reconstructed on a physically-plausible basis relying on the physics engine in Blender.

RESULTS

Our pipeline is applied to create 55 exemplar neurons representing the various morphological types that are reconstructed from the somatsensory cortex of a juvenile rat. The pipeline is then used to reconstruct a volumetric slice of a cortical circuit model that contains ∼210,000 neurons. The applicability of our pipeline to create highly realistic volumetric models of neocortical circuits is demonstrated with an in silico imaging experiment that simulates tissue visualization with brightfield microscopy. The results were evaluated with a group of domain experts to address their demands and also to extend the workflow based on their feedback.

CONCLUSION

A systematic workflow is presented to create large scale synthetic tissue models of the neocortical circuitry. This workflow is fundamental to enlarge the scale of in silico neuroscientific optical experiments from several tens of cubic micrometers to a few cubic millimeters.

AMS SUBJECT CLASSIFICATION

Modelling and Simulation.

An Algorithm for Motif-Based Network Design

A determinant property of the structure of a biological network is the distribution of local connectivity patterns, i.e., network motifs. In this work, a method for creating directed, unweighted networks while promoting a certain combination of motifs is presented. This motif-based network algorithm starts with an empty graph and randomly connects the nodes by advancing or discouraging the formation of chosen motifs. The in- or out-degree distribution of the generated networks can be explicitly chosen. The algorithm is shown to perform well in producing networks with high occurrences of the targeted motifs, both ones consisting of three nodes as well as ones consisting of four nodes. Moreover, the algorithm can also be tuned to bring about global network characteristics found in many natural networks, such as small-worldness and modularity.

Mechanisms of Connectome Development

At the centenary of D'Arcy Thompson's seminal work 'On Growth and Form', pioneering the description of principles of morphological changes during development and evolution, recent experimental advances allow us to study change in anatomical brain networks. Here, we outline potential principles for connectome development. We will describe recent results on how spatial and temporal factors shape connectome development in health and disease. Understanding the developmental origins of brain diseases in individuals will be crucial for deciding on personalized treatment options. We argue that longitudinal studies, experimentally derived parameters for connection formation, and biologically realistic computational models are needed to better understand the link between brain network development, network structure, and network function.

Modular topology emerges from plasticity in a minimalistic excitable network model

Topological features play a major role in the emergence of complex brain network dynamics underlying brain function. Specific topological properties of brain networks, such as their modular organization, have been widely studied in recent years and shown to be ubiquitous across spatial scales and species. However, the mechanisms underlying the generation and maintenance of such features are still unclear. Using a minimalistic network model with excitable nodes and discrete deterministic dynamics, we studied the effects of a local Hebbian plasticity rule on global network topology. We found that, despite the simple model set-up, the plasticity rule was able to reorganize the global network topology into a modular structure. The structural reorganization was accompanied by enhanced correlations between structural and functional connectivity, and the final network organization reflected features of the dynamical model. These findings demonstrate the potential of simple plasticity rules for structuring the topology of brain connectivity.

Biomaterials and computation: a strategic alliance to investigate emergent responses of neural cells

Synergistic use of biomaterials and computation allows to identify and unravel neural cell responses.

Fuzzy-Logic Based Detection and Characterization of Junctions and Terminations in Fluorescence Microscopy Images of Neurons

Digital reconstruction of neuronal cell morphology is an important step toward understanding the functionality of neuronal networks. Neurons are tree-like structures whose description depends critically on the junctions and terminations, collectively called critical points, making the correct localization and identification of these points a crucial task in the reconstruction process. Here we present a fully automatic method for the integrated detection and characterization of both types of critical points in fluorescence microscopy images of neurons. In view of the majority of our current studies, which are based on cultured neurons, we describe and evaluate the method for application to two-dimensional (2D) images. The method relies on directional filtering and angular profile analysis to extract essential features about the main streamlines at any location in an image, and employs fuzzy logic with carefully designed rules to reason about the feature values in order to make well-informed decisions about the presence of a critical point and its type. Experiments on simulated as well as real images of neurons demonstrate the detection performance of our method. A comparison with the output of two existing neuron reconstruction methods reveals that our method achieves substantially higher detection rates and could provide beneficial information to the reconstruction process.

BlastNeuron for Automated Comparison, Retrieval and Clustering of 3D Neuron Morphologies

Characterizing the identity and types of neurons in the brain, as well as their associated function, requires a means of quantifying and comparing 3D neuron morphology. Presently, neuron comparison methods are based on statistics from neuronal morphology such as size and number of branches, which are not fully suitable for detecting local similarities and differences in the detailed structure. We developed BlastNeuron to compare neurons in terms of their global appearance, detailed arborization patterns, and topological similarity. BlastNeuron first compares and clusters 3D neuron reconstructions based on global morphology features and moment invariants, independent of their orientations, sizes, level of reconstruction and other variations. Subsequently, BlastNeuron performs local alignment between any pair of retrieved neurons via a tree-topology driven dynamic programming method. A 3D correspondence map can thus be generated at the resolution of single reconstruction nodes. We applied BlastNeuron to three datasets: (1) 10,000+ neuron reconstructions from a public morphology database, (2) 681 newly and manually reconstructed neurons, and (3) neurons reconstructions produced using several independent reconstruction methods. Our approach was able to accurately and efficiently retrieve morphologically and functionally similar neuron structures from large morphology database, identify the local common structures, and find clusters of neurons that share similarities in both morphology and molecular profiles.

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.

Reconstructing the brain: from image stacks to neuron synthesis

Large-scale brain initiatives such as the US BRAIN initiative and the European Human Brain Project aim to marshall a vast amount of data and tools for the purpose of furthering our understanding of brains. Fundamental to this goal is that neuronal morphologies must be seamlessly reconstructed and aggregated on scales up to the whole rodent brain. The experimental labor needed to manually produce this number of digital morphologies is prohibitively large. The BigNeuron initiative is assembling community-generated, open-source, automated reconstruction algorithms into an open platform, and is beginning to generate an increasing flow of high-quality reconstructed neurons. We propose a novel extension of this workflow to use this data stream to generate an unlimited number of statistically equivalent, yet distinct, digital morphologies. This will bring automated processing of reconstructed cells into digital neurons to the wider neuroscience community, and enable a range of morphologically accurate computational models.

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.

Structure of a randomly grown 2-d network

We introduce a growing random network on a plane as a model of a growing neuronal network. The properties of the structure of the induced graph are derived. We compare our results with available data. In particular, it is shown that depending on the parameters of the model the system undergoes in time different phases of the structure. We conclude with a possible explanation of some empirical data on the connections between neurons.

Tree Topology Estimation

Tree-like structures are fundamental in nature, and it is often useful to reconstruct the topology of a tree - what connects to what - from a two-dimensional image of it. However, the projected branches often cross in the image: the tree projects to a planar graph, and the inverse problem of reconstructing the topology of the tree from that of the graph is ill-posed. We regularize this problem with a generative, parametric tree-growth model. Under this model, reconstruction is possible in linear time if one knows the direction of each edge in the graph - which edge endpoint is closer to the root of the tree - but becomes NP-hard if the directions are not known. For the latter case, we present a heuristic search algorithm to estimate the most likely topology of a rooted, three-dimensional tree from a single two-dimensional image. Experimental results on retinal vessel, plant root, and synthetic tree data sets show that our methodology is both accurate and efficient.

The effects of neuron morphology on graph theoretic measures of network connectivity: the analysis of a two-level statistical model

We developed a two-level statistical model that addresses the question of how properties of neurite morphology shape the large-scale network connectivity. We adopted a low-dimensional statistical description of neurites. From the neurite model description we derived the expected number of synapses, node degree, and the effective radius, the maximal distance between two neurons expected to form at least one synapse. We related these quantities to the network connectivity described using standard measures from graph theory, such as motif counts, clustering coefficient, minimal path length, and small-world coefficient. These measures are used in a neuroscience context to study phenomena from synaptic connectivity in the small neuronal networks to large scale functional connectivity in the cortex. For these measures we provide analytical solutions that clearly relate different model properties. Neurites that sparsely cover space lead to a small effective radius. If the effective radius is small compared to the overall neuron size the obtained networks share similarities with the uniform random networks as each neuron connects to a small number of distant neurons. Large neurites with densely packed branches lead to a large effective radius. If this effective radius is large compared to the neuron size, the obtained networks have many local connections. In between these extremes, the networks maximize the variability of connection repertoires. The presented approach connects the properties of neuron morphology with large scale network properties without requiring heavy simulations with many model parameters. The two-steps procedure provides an easier interpretation of the role of each modeled parameter. The model is flexible and each of its components can be further expanded. We identified a range of model parameters that maximizes variability in network connectivity, the property that might affect network capacity to exhibit different dynamical regimes.

Developmental time windows for axon growth influence neuronal network topology

Early brain connectivity development consists of multiple stages: birth of neurons, their migration and the subsequent growth of axons and dendrites. Each stage occurs within a certain period of time depending on types of neurons and cortical layers. Forming synapses between neurons either by growing axons starting at similar times for all neurons (much-overlapped time windows) or at different time points (less-overlapped) may affect the topological and spatial properties of neuronal networks. Here, we explore the extreme cases of axon formation during early development, either starting at the same time for all neurons (parallel, i.e., maximally overlapped time windows) or occurring for each neuron separately one neuron after another (serial, i.e., no overlaps in time windows). For both cases, the number of potential and established synapses remained comparable. Topological and spatial properties, however, differed: Neurons that started axon growth early on in serial growth achieved higher out-degrees, higher local efficiency and longer axon lengths while neurons demonstrated more homogeneous connectivity patterns for parallel growth. Second, connection probability decreased more rapidly with distance between neurons for parallel growth than for serial growth. Third, bidirectional connections were more numerous for parallel growth. Finally, we tested our predictions with C. elegans data. Together, this indicates that time windows for axon growth influence the topological and spatial properties of neuronal networks opening up the possibility to a posteriori estimate developmental mechanisms based on network properties of a developed network.

Discrete stochastic model for the generation of axonal trees

In this work we propose a 2D discrete stochastic model for the simulation of axonal biogenesis. The model is defined by a third order Markov Chain. The model considers two main processes: the growth process that models the elongation and shape of the neurites and the bifurcation process that models the generation of branches. The growth process depends, among other variables, on the external attraction field generated by a chemoattractant molecule secreted by the target area. We propose an estimation scheme of the involved parameters from real fluorescent confocal microscopy images of single neurons within intact adult Drosophila fly brains. Both normal neurons and neurons in which certain genes were inactivated have been considered (two mutations). In total, 53 images (18 normal, 21 type 1 mutant and 14 type 2 mutant) were used. The model parameters allow us to describe pathological characteristics of the mutated populations.

Statistical analysis and data mining of digital reconstructions of dendritic morphologies

Neuronal morphology is diverse among animal species, developmental stages, brain regions, and cell types. The geometry of individual neurons also varies substantially even within the same cell class. Moreover, specific histological, imaging, and reconstruction methodologies can differentially affect morphometric measures. The quantitative characterization of neuronal arbors is necessary for in-depth understanding of the structure-function relationship in nervous systems. The large collection of community-contributed digitally reconstructed neurons available at NeuroMorpho.Org constitutes a “big data” research opportunity for neuroscience discovery beyond the approaches typically pursued in single laboratories. To illustrate these potential and related challenges, we present a database-wide statistical analysis of dendritic arbors enabling the quantification of major morphological similarities and differences across broadly adopted metadata categories. Furthermore, we adopt a complementary unsupervised approach based on clustering and dimensionality reduction to identify the main morphological parameters leading to the most statistically informative structural classification. We find that specific combinations of measures related to branching density, overall size, tortuosity, bifurcation angles, arbor flatness, and topological asymmetry can capture anatomically and functionally relevant features of dendritic trees. The reported results only represent a small fraction of the relationships available for data exploration and hypothesis testing enabled by sharing of digital morphological reconstructions.