Figure 4 - available via license: Creative Commons Attribution 4.0 International
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Layer specificity of five different cell-types. ( A ) Real cortical neurons reconstructed from the cat visual cortex; from left to right: a pyramidal cell of layer 2/3, a spiny stellate cell of layer 4, a pyramidal cell of layer 5, a pyramidal cell of layer 6 (axons drawn in black, dendrites in blue) and a basket cell of layer 2/3. Scale bar: 100 m m . (Reconstructed cells are a courtesy of Kevan Martin and colleagues, Institute of Neuroinformatics, Zurich). ( B ) Schematic representation of the axonal branching pattern for encoding in the instruction language G-code. Each color corresponds to a segment of the axonal arbor encoded by a specific G-code machine. doi:10.1371/journal.pcbi.1003173.g004
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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 mod...
Citations
... Conversely, rather little computational modeling of neural development has been published despite its clear importance in forming neural networks. Instead, even morphologically realistic network models are wired randomly using specific rules (Markram et al., 2015) instead of growing connectivity according to their development (Zubler et al., 2013). The most recent textbook on modeling neural development was published in 2003 (van Ooyen, 2003). ...
... Another simulator that explicitly models neural development based on intrinsic and extrinsic contextual factors was CX3D (Zubler and Douglas, 2009). It was used to build an impressive simulation of laminated cortex including a few complete neural morphologies (Zubler et al., 2013). CX3D is no longer supported and its more efficient, parallelized successor BioDynaMo (Breitwieser et al., 2022) is a general agent-based modeling platform that is not specific to neural development. ...
... This paper describes NeuroDevSim, a simulator of neural development that can model the migration of neurons, growth of dendrites and axons, and formation of early synaptic connections. In this regard, NeuroDevSim replicates most of the functionality of the no longer maintained CX3D (Zubler et al., 2013) with the exception of progenitor cell proliferation. Though the birth of new neurons can be made conditional in NeuroDevSim by adding the relevant statements before the add_neurons method (Figure 2), modeling actual neural proliferation is a goal for future NeuroDevSim versions. ...
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 .
... Agent-based modeling (ABM) allows to simulate complex dynamics in a wide range of research fields. ABM has been used to answer research questions in biology [30,43,73], sociology [18], economics [65], technology [50], business [56], and more fields [39]. Agents are individual entities that, among others, can represent subcellular structures to simulate the growth of a neuron, a cell to investigate cancer development, or a person to simulate the spread of infectious diseases [10]. ...
Agent-based modeling plays an essential role in gaining insights into biology, sociology, economics, and other fields. However, many existing agent-based simulation platforms are not suitable for large-scale studies due to the low performance of the underlying simulation engines. To overcome this limitation, we present a novel high-performance simulation engine.
We identify three key challenges for which we present the following solutions. First, to maximize parallelization, we present an optimized grid to search for neighbors and parallelize the merging of thread-local results. Second, we reduce the memory access latency with a NUMA-aware agent iterator, agent sorting with a space-filling curve, and a custom heap memory allocator. Third, we present a mechanism to omit the collision force calculation under certain conditions.
Our evaluation shows an order of magnitude improvement over Biocellion, three orders of magnitude speedup over Cortex3D and NetLogo, and the ability to simulate 1.72 billion agents on a single server.
Supplementary Materials, including instructions to reproduce the results, are available at: https://doi.org/10.5281/zenodo.6463816
... The only simulator that explicitly models neural development based on intrinsic and extrinsic, contextual factors was CX3D (Zubler and Douglas 2009). It was used to build an impressive simulation of laminated cortex including a few complete neural morphologies (Zubler, Hauri et al. 2013). Unfortunately, it no longer seems to be supported. ...
... This paper describes NeuroDevSim, to our knowledge at present the only actively maintained simulator of neural development that can model migration of neurons, growth of dendrites and axons and formation of early synaptic connections. In this regard, NeuroDevSim replicates most of the functionality of the no longer maintained CX3D (Zubler, Hauri et al. 2013) with the exception of progenitor cell proliferation. Though birth of new neurons can be made conditional in NeuroDevSim by adding the relevant statements before the add_neurons method (Figure 2), modeling actual neural proliferation is a goal for future NeuroDevSim versions. ...
The Neural Development Simulator, NeuroDevSim, is a Python module that simulates the most important aspects of development: growth, migration and pruning. It uses an agent-based modeling approach inherited from the NeuroMaC software. Each cycle, agents called fronts execute 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.
NeuroDevSim is a multi-core program that uses an innovative shared memory approach to achieve parallel processing without messaging. We demonstrate close to linear strong scaling for medium size models for up to 32 cores and have run large models successfully on 128 cores. Most of the shared memory parallelism is achieved without memory locking. Instead cores have write privileges to private sections of arrays only, 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 growth of physically overlapping structures. Here a 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 neural development for models ranging from a few complex to thousands of simple neurons or a mixture of both.
... Previous models have described network formation in terms of cellular agents containing a small, but explicit, program consisting of few developmental primitives [17,[51][52][53][54]. These generative cellular programs include physical constraints on development to explain network formation [55]. ...
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.
... Along those lines, other computational studies that model axonal and dendritic trees do not focus on the origins of a layered architecture (Koene et al. 2009;Cuntz et al. 2010). By contrast, Zubler et al. (2013) present a mechanistic computational model for cortical lamination with physical interactions. Using the "Cx3D" software (Zubler 2009), the authors studied cortical layer formation from a conceptual perspective of self-construction (Zubler et al. 2013) and put it into a gene-type coding scheme (Zubler et al. 2011;Hauri 2013). ...
... By contrast, Zubler et al. (2013) present a mechanistic computational model for cortical lamination with physical interactions. Using the "Cx3D" software (Zubler 2009), the authors studied cortical layer formation from a conceptual perspective of self-construction (Zubler et al. 2013) and put it into a gene-type coding scheme (Zubler et al. 2011;Hauri 2013). Importantly, this approach relies solely on modeling local information exchange; hence, it maintains the biologically realistic condition that cells can only experience their local 3D environment. ...
... While the studies of Zubler et al. (2013) and Hauri (2013) propose working agent-based models for cortical layer formation, they do not demonstrate the generation of appropriate layer-specific cell numbers. Hence, it is currently unclear how a core gene regulatory network (GRN) can produce various different layer architectures. ...
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.
... Cortex3D (Cx3D) is a computational modeling tool for simulating neurodevelopmental processes 8 and has been used to define generative models of cortical circuits 44 . We integrate Cx3D with SNT through the sciview visualization package by rewriting Cx3D to grow neuronal processes with sciview's data structures. ...
Quantification of neuronal morphology is essential for understanding neuronal connectivity and many software tools have been developed for neuronal reconstruction and morphometry. However, such tools remain domain-specific, tethered to specific imaging modalities, and were not designed to accommodate the rich metadata generated by recent whole-brain cellular connectomics. To address these limitations, we created SNT : a unifying framework for neuronal morphometry and analysis of single-cell connectomics for the widely used Fiji and ImageJ platforms.
We demonstrate that SNT —that replaces the popular Simple Neurite Tracer software— can be used to tackle important problems in contemporary neuroscience, validate its utility, and illustrate how it establishes an end-to-end platform for tracing, proof-editing, visualization, quantification, and modeling of neuroanatomy.
With an open and scriptable architecture, a large user base, and thorough community-based documentation, SNT is an accessible and scalable resource for the broad neuroscience community that synergizes well with existing software.
... used to develop large-scale models of branching neurons [23] or leaf vascular 34 networks [24]. Another type of approach is based on growth processes emanating from 35 predefined seed points with branching and merging and has been used to model neural 36 network development [25,26], fibrous materials [27] or the development of branching organ 37 structures [28]. Most of these existing models are targeted towards a specific domain such 38 as neural networks and synapse formation, or include only simplified interactions with the 39 environment. ...
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.
Author summary
We present a novel modeling approach and computational implementation to better understand the development of spatial biological networks under the influence of external signals. Our tool allows us to study the relationship between local biological growth parameters and the emerging macroscopic network function using simulations. This computational approach can generate plausible network graphs that take local feedback into account and provide a basis for comparative studies using graph-based methods.
... Thalamocortical arborizations in the primary visual cortex must be organized with high precision to enable dense synaptic connections for the ocular dominance columns [1,2] and to preserve the spatial resolution of the associated receptive fields [3]. Arborizations of these thalamocortical axons in cat area 17 are characterized by a high bouton density and extensive and highly variable ramifications, ranging from structures consisting of only a single branch to elaborate morphologies with tens of segments of highly diverse lengths [4]. What developmental rules give rise to such morphological variability while enabling simultaneously the precise wiring required for accurate functionality? ...
... Due to their morphological difference, we distinguish here between the long-range axonal projections with a relatively low bifurcation ratio which constitute the axonal trunk [4], and the self-similar ramifications in the target area of axonal projections, which we call here florets. Fig 1 panel A visualizes the two different parts of the axonal arbor. ...
... All axonal structures inside these clusters whose initial segment has come from side-branching are then defined as florets. A side-branch is defined as a branch that grows approximately perpendicular to the original direction of the axon, thereby distinguishing it from other bifurcations, which exhibit smaller branching angles between 20-80˚ [4,38]. and longrange axonal projections (blue). ...
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.
... Along those lines, other computational studies that model axonal and dendritic trees do not focus on the origins of a layered architecture (Koene et al. 2009;Cuntz et al. 2010). In contrast, Zubler et al. present an agent-based computational model for cortical lamination with mechanical interactions (Zubler et al. 2013). Based on this approach and software (Zubler 2009), cortical development has been studied from a conceptual perspective of selfconstruction and put in correspondence with genetic data (Zubler et al. 2013). ...
... In contrast, Zubler et al. present an agent-based computational model for cortical lamination with mechanical interactions (Zubler et al. 2013). Based on this approach and software (Zubler 2009), cortical development has been studied from a conceptual perspective of selfconstruction and put in correspondence with genetic data (Zubler et al. 2013). Importantly, this approach relies solely on modelling local information exchange, hence it is maintained the biologically realistic condition that cells can only experience their local 3D environment. ...
... Here, we build upon the approach of Zubler et al. (2013). Going beyond a qualitative assessment, we here provide a computational model that reproduces quantitative measurements of the cortical layer architecture. ...
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 multi-scale, 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, and suggest a novel function for apoptosis. Moreover, slightly changed gene regulatory dynamics recapitulate 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.
... Notably, eBrain can be personalized to each patient by processing data specific to each individual. eBrain is built on previous simulation strategies that have successfully predicted experimental results in various biological systems, some of which gained support by subsequent experimental study [17][18][19][20][21][22] . Several reviews have highlighted the potential of simulation in aspects related to neuroscience, e.g., migration, and symptom profiles 23,24 . ...
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.
