Neuronal Growth and Formation of Neuron Networks on Directional Surfaces

Nonlinear Growth Dynamics of Neuronal Cells Cultured on Directional Surfaces

During the development of the nervous system, neuronal cells extend axons and dendrites that form complex neuronal networks, which are essential for transmitting and processing information. Understanding the physical processes that underlie the formation of neuronal networks is essential for gaining a deeper insight into higher-order brain functions such as sensory processing, learning, and memory. In the process of creating networks, axons travel towards other recipient neurons, directed by a combination of internal and external cues that include genetic instructions, biochemical signals, as well as external mechanical and geometrical stimuli. Although there have been significant recent advances, the basic principles governing axonal growth, collective dynamics, and the development of neuronal networks remain poorly understood. In this paper, we present a detailed analysis of nonlinear dynamics for axonal growth on surfaces with periodic geometrical patterns. We show that axonal growth on these surfaces is described by nonlinear Langevin equations with speed-dependent deterministic terms and gaussian stochastic noise. This theoretical model yields a comprehensive description of axonal growth at both intermediate and long time scales (tens of hours after cell plating), and predicts key dynamical parameters, such as speed and angular correlation functions, axonal mean squared lengths, and diffusion (cell motility) coefficients. We use this model to perform simulations of axonal trajectories on the growth surfaces, in turn demonstrating very good agreement between simulated growth and the experimental results. These results provide important insights into the current understanding of the dynamical behavior of neurons, the self-wiring of the nervous system, as well as for designing innovative biomimetic neural network models.

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

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.

Unidirectional diphenylalanine nanotubes for dynamically guiding neurite outgrowth

Neural networks have been culturedin vitroto investigate brain functions and diseases, clinical treatments for brain damage, and device development. However, it remains challenging to form complex neural network structures with desired orientations and connectionsin vitro. Here, we introduce a dynamic strategy by using diphenylalanine (FF) nanotubes for controlling physical patterns on a substrate to regulate neurite-growth orientation in cultivating neural networks. Parallel FF nanotube patterns guide neurons to develop neurites through the unidirectional FF nanotubes while restricting their polarization direction. Subsequently, the FF nanotubes disassemble and the restriction of neurites disappear, and secondary neurite development of the neural network occurs in other direction. Experiments were conducted that use the hippocampal neurons, and the results demonstrated that the cultured neural networks by using the proposed dynamic approach can form a significant cross-connected structure with substantially more lateral neural connections than static substrates. The proposed dynamic approach for neurite outgrowing enables the construction of oriented innervation and cross-connected neural networksin vitroand may explore the way for the bio-fabrication of highly complex structures in tissue engineering.

Engineering Tissues of the Central Nervous System: Interfacing Conductive Biomaterials with Neural Stem/Progenitor Cells

Conductive biomaterials provide an important control for engineering neural tissues, where electrical stimulation can potentially direct neural stem/progenitor cell (NS/PC) maturation into functional neuronal networks. It is anticipated that stem cell-based therapies to repair damaged central nervous system (CNS) tissues and ex vivo, "tissue chip" models of the CNS and its pathologies will each benefit from the development of biocompatible, biodegradable, and conductive biomaterials. Here, technological advances in conductive biomaterials are reviewed over the past two decades that may facilitate the development of engineered tissues with integrated physiological and electrical functionalities. First, one briefly introduces NS/PCs of the CNS. Then, the significance of incorporating microenvironmental cues, to which NS/PCs are naturally programmed to respond, into biomaterial scaffolds is discussed with a focus on electrical cues. Next, practical design considerations for conductive biomaterials are discussed followed by a review of studies evaluating how conductive biomaterials can be engineered to control NS/PC behavior by mimicking specific functionalities in the CNS microenvironment. Finally, steps researchers can take to move NS/PC-interfacing, conductive materials closer to clinical translation are discussed.

Mathematical models of neuronal growth

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites—axons and dendrites—to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.