Mathematical models of neuronal growth

Oliveri, Hadrien; Goriely, Alain

doi:10.1007/s10237-021-01539-0

Cited by 19 publications

(11 citation statements)

References 257 publications

(576 reference statements)

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“…Several mechanical models takes into account the interplay of GC pushing and pulling forces, shaft viscoelasticity and contractility, and adhesions to describe axonal elongation (see, e.g. the detailed review of Olivery and Goriely [28]). Lastly, a complete picture of the mechanical link between the soma and the GC should include GC-like, anterogradely propagative structures produced in extending mammalian neurons [29,30].…”

mentioning

confidence: 99%

Spatial confinement: A spur for axonal growth

Villard

2023

Seminars in Cell & Developmental Biology

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mentioning

confidence: 99%

Spatial confinement: A spur for axonal growth

Villard

2023

Seminars in Cell & Developmental Biology

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“…A distinguishing feature of the model is dynamic axonal growth, echoing in vitro and in vivo evidence suggesting that axons actively modify growth pathways in response to local molecular and mechanical cues (Dickson, 2002; Oliveri & Goriely, 2022). The simulated axons grow progressively in a step-by-step manner, based on the attractive forces described by (Fig.…”

Section: Resultsmentioning

confidence: 99%

A generative model of the connectome with dynamic axon growth

Liu,

Seguin,

Betzel

et al. 2024

Preprint

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Connectome generative models, otherwise known as generative network models, provide insight into the wiring principles underpinning brain network organization. While these models can approximate numerous statistical properties of empirical networks, they typically fail to explicitly characterize an important contributor to brain organization - axonal growth. Emulating the chemoaffinity guided axonal growth, we provide a novel generative model in which axons dynamically steer the direction of propagation based on distance-dependent chemoattractive forces acting on their growth cones. This simple dynamic growth mechanism, despite being solely geometry-dependent, is shown to generate axonal fiber bundles with brain-like geometry and features of complex network architecture consistent with the human brain, including lognormally distributed connectivity weights, scale-free nodal degrees, small-worldness, and modularity. We demonstrate that our model parameters can be fitted to individual connectomes, enabling connectome dimensionality reduction and comparison of parameters between groups. Our work offers an opportunity to bridge studies of axon guidance and connectome development, providing new avenues for understanding neural development from a computational perspective.

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“…Stochastic processes arise from a variety of sources, including fluctuations in the signaling molecules detected by the growth cone, polymerization of actin filaments, formation of lamellipodia and filopodia, and intercellular interactions. By explicitly deriving probability distributions for the ensemble of axons as a solution to a Fokker–Planck equation, it is possible to generate predictions about the formation of neuronal networks under different conditions and to test different growth mechanisms from experimentally observed results [ 38 ]. For instance, Hentschel and van Ooyen [ 39 ] demonstrated that a combination of chemoattractant and chemorepellent factors could account for the bundling, guidance, and subsequent de-bundling of axons towards specific target regions.…”

Section: Theoretical Models Of Neuronal Growthmentioning

confidence: 99%

Biased Random Walk Model of Neuronal Dynamics on Substrates with Periodic Geometrical Patterns

Staii

2023

Biomimetics

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Neuronal networks are complex systems of interconnected neurons responsible for transmitting and processing information throughout the nervous system. The building blocks of neuronal networks consist of individual neurons, specialized cells that receive, process, and transmit electrical and chemical signals throughout the body. The formation of neuronal networks in the developing nervous system is a process of fundamental importance for understanding brain activity, including perception, memory, and cognition. To form networks, neuronal cells extend long processes called axons, which navigate toward other target neurons guided by both intrinsic and extrinsic factors, including genetic programming, chemical signaling, intercellular interactions, and mechanical and geometrical cues. Despite important recent advances, the basic mechanisms underlying collective neuron behavior and the formation of functional neuronal networks are not entirely understood. In this paper, we present a combined experimental and theoretical analysis of neuronal growth on surfaces with micropatterned periodic geometrical features. We demonstrate that the extension of axons on these surfaces is described by a biased random walk model, in which the surface geometry imparts a constant drift term to the axon, and the stochastic cues produce a random walk around the average growth direction. We show that the model predicts key parameters that describe axonal dynamics: diffusion (cell motility) coefficient, average growth velocity, and axonal mean squared length, and we compare these parameters with the results of experimental measurements. Our findings indicate that neuronal growth is governed by a contact-guidance mechanism, in which the axons respond to external geometrical cues by aligning their motion along the surface micropatterns. These results have a significant impact on developing novel neural network models, as well as biomimetic substrates, to stimulate nerve regeneration and repair after injury.

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Mathematical models of neuronal growth

Cited by 19 publications

References 257 publications

Spatial confinement: A spur for axonal growth

Spatial confinement: A spur for axonal growth

A generative model of the connectome with dynamic axon growth

Biased Random Walk Model of Neuronal Dynamics on Substrates with Periodic Geometrical Patterns

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