Neuronal Growth and Formation of Neuron Networks on Directional Surfaces

Stress landscape of folding brain serves as a map for axonal pathfinding

Understanding the mechanics linking cortical folding and brain connectivity is crucial for both healthy and abnormal brain development. Despite the importance of this relationship, existing models fail to explain how growing axon bundles navigate the stress field within a folding brain or how this bidirectional and dynamic interaction shapes the resulting surface morphologies and connectivity patterns. Here, we propose the concept of "axon reorientation" and formulate a mechanical model to uncover the dynamic multiscale mechanics of the linkages between cortical folding and connectivity development. Simulations incorporating axon bundle reorientation and stress-induced growth reveal potential mechanical mechanisms that lead to higher axon bundle density in gyri (ridges) compared to sulci (valleys). In particular, the connectivity patterning resulting from cortical folding exhibits a strong dependence on the growth rate and mechanical properties of the navigating axon bundles. Model predictions are supported by in vivo diffusion tensor imaging of the human brain.

Advances in 3D tissue models for neural engineering: self-assembled versus engineered tissue models

Neural tissue engineering has emerged as a promising field that aims to create functional neural tissue for therapeutic applications, drug screening, and disease modelling. It is becoming evident in the literature that this goal requires development of three-dimensional (3D) constructs that can mimic the complex microenvironment of native neural tissue, including its biochemical, mechanical, physical, and electrical properties. These 3D models can be broadly classified as self-assembled models, which include spheroids, organoids, and assembloids, and engineered models, such as those based on decellularized or polymeric scaffolds. Self-assembled models offer advantages such as the ability to recapitulate neural development and disease processes in vitro, and the capacity to study the behaviour and interactions of different cell types in a more realistic environment. However, self-assembled constructs have limitations such as lack of standardised protocols, inability to control the cellular microenvironment, difficulty in controlling structural characteristics, reproducibility, scalability, and lengthy developmental timeframes. Integrating biomimetic materials and advanced manufacturing approaches to present cells with relevant biochemical, mechanical, physical, and electrical cues in a controlled tissue architecture requires alternate engineering approaches. Engineered scaffolds, and specifically 3D hydrogel-based constructs, have desirable properties, lower cost, higher reproducibility, long-term stability, and they can be rapidly tailored to mimic the native microenvironment and structure. This review explores 3D models in neural tissue engineering, with a particular focus on analysing the benefits and limitations of self-assembled organoids compared with hydrogel-based engineered 3D models. Moreover, this paper will focus on hydrogel based engineered models and probe their biomaterial components, tuneable properties, and fabrication techniques that allow them to mimic native neural tissue structures and environment. Finally, the current challenges and future research prospects of 3D neural models for both self-assembled and engineered models in neural tissue engineering will be discussed.

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.