Role of geometrical cues in neuronal growth

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.

Rich dynamics and functional organization on topographically designed neuronal networks in vitro

Neuronal cultures are a prominent experimental tool to understand complex functional organization in neuronal assemblies. However, neurons grown on flat surfaces exhibit a strongly coherent bursting behavior with limited functionality. To approach the functional richness of naturally formed neuronal circuits, here we studied neuronal networks grown on polydimethylsiloxane (PDMS) topographical patterns shaped as either parallel tracks or square valleys. We followed the evolution of spontaneous activity in these cultures along 20 days in vitro using fluorescence calcium imaging. The networks were characterized by rich spatiotemporal activity patterns that comprised from small regions of the culture to its whole extent. Effective connectivity analysis revealed the emergence of spatially compact functional modules that were associated with both the underpinned topographical features and predominant spatiotemporal activity fronts. Our results show the capacity of spatial constraints to mold activity and functional organization, bringing new opportunities to comprehend the structure-function relationship in living neuronal circuits.

Accelerating Neurite Growth and Directing Neuronal Connections Constrained by 3D Porous Microtubes

Investigation of neural growth and connection is crucial in the field of neural tissue engineering. Here, using a femtosecond laser direct writing (fs-DLW) technique, we propose a directionally aligned porous microtube array as a culture system for accelerating the growth of neurons and directing the connection of neurites. These microtubes exhibited an unprecedented guidance effect toward the outgrowth of primary embryonic rat hippocampal neurons, with a wrap resembling the myelin sheaths of neurons. The speed of neurite growth inside these microtubes was significantly faster than that outside these microtubes. We also achieved selective/directing connection of neural networks inside the magnetic microtubes via precise microtube delivery to a gap between two neural clusters. This work not only proposes a powerful microtube platform for accelerated growth of neurons but also offers a new idea for constructing biological neural circuits by arranging the size, location, and pattern of microtubes.

Feedback-controlled dynamics of neuronal cells on directional surfaces

The formation of neuronal networks is a complex phenomenon of fundamental importance for understanding the development of the nervous system. The basic process underlying the network formation is axonal growth, a process involving the extension of axons from the cell body and axonal navigation toward target neurons. Axonal growth is guided by the interactions between the tip of the axon (growth cone) and its extracellular environmental cues, which include intercellular interactions, the biochemical landscape around the neuron, and the mechanical and geometrical features of the growth substrate. Here, we present a comprehensive experimental and theoretical analysis of axonal growth for neurons cultured on micropatterned polydimethylsiloxane (PDMS) surfaces. We demonstrate that closed-loop feedback is an essential component of axonal dynamics on these surfaces: the growth cone continuously measures environmental cues and adjusts its motion in response to external geometrical features. We show that this model captures all the characteristics of axonal dynamics on PDMS surfaces for both untreated and chemically modified neurons. We combine experimental data with theoretical analysis to measure key parameters that describe axonal dynamics: diffusion (cell motility) coefficients, speed and angular distributions, and cell-substrate interactions. The experiments performed on neurons treated with Taxol (inhibitor of microtubule dynamics) and Y-27632 (disruptor of actin filaments) indicate that the internal dynamics of microtubules and actin filaments plays a critical role for the proper function of the feedback mechanism. Our results demonstrate that axons follow geometrical patterns through a contact-guidance mechanism, in which high-curvature geometrical features impart high traction forces to the growth cone. These results have important implications for our fundamental understanding of axonal growth as well as for bioengineering novel substrate to guide neuronal growth and promote nerve repair.

Axonal growth on surfaces with periodic geometrical patterns

The formation of neuron networks is a complex phenomenon of fundamental importance for understanding the development of the nervous system, and for creating novel bioinspired materials for tissue engineering and neuronal repair. The basic process underlying the network formation is axonal growth, a process involving the extension of axons from the cell body towards target neurons. Axonal growth is guided by environmental stimuli that include intercellular interactions, biochemical cues, and the mechanical and geometrical features of the growth substrate. The dynamics of the growing axon and its biomechanical interactions with the growing substrate remains poorly understood. In this paper, we develop a model of axonal motility which incorporates mechanical interactions between the axon and the growth substrate. We combine experimental data with theoretical analysis to measure the parameters that describe axonal growth on surfaces with micropatterned periodic geometrical features: diffusion (cell motility) coefficients, speed and angular distributions, and axon bending rigidities. Experiments performed on neurons treated Taxol (inhibitor of microtubule dynamics) and Blebbistatin (disruptor of actin filaments) show that the dynamics of the cytoskeleton plays a critical role in the axon steering mechanism. Our results demonstrate that axons follow geometrical patterns through a contact-guidance mechanism, in which high-curvature geometrical features impart high traction forces to the growth cone. These results have important implications for our fundamental understanding of axonal growth as well as for bioengineering novel substrates that promote neuronal growth and nerve repair.

Neuronal Growth and Formation of Neuron Networks on Directional Surfaces

The formation of neuron networks is a process of fundamental importance for understanding the development of the nervous system and for creating biomimetic devices for tissue engineering and neural repair. The basic process that controls the network formation is the growth of an axon from the cell body and its extension towards target neurons. Axonal growth is directed by environmental stimuli that include intercellular interactions, biochemical cues, and the mechanical and geometrical properties of the growth substrate. Despite significant recent progress, the steering of the growing axon remains poorly understood. In this paper, we develop a model of axonal motility, which incorporates substrate-geometry sensing. We combine experimental data with theoretical analysis to measure the parameters that describe axonal growth on micropatterned surfaces: diffusion (cell motility) coefficients, speed and angular distributions, and cell-substrate interactions. Experiments performed on neurons treated with inhibitors for microtubules (Taxol) and actin filaments (Y-27632) indicate that cytoskeletal dynamics play a critical role in the steering mechanism. Our results demonstrate that axons follow geometrical patterns through a contact-guidance mechanism, in which geometrical patterns impart high traction forces to the growth cone. These results have important implications for bioengineering novel substrates to guide neuronal growth and promote nerve repair.

Multi-curvature micropatterns unveil distinct calcium and mitochondrial dynamics in neuronal networks

Tangential curvatures are a key geometric feature of tissue folds in the human cerebral cortex. In the brain, these smoother and firmer bends are called gyri and sulci and form distinctive curved tissue patterns imposing a mechanical stimulus on neuronal networks. This stimulus is hypothesized to be essential for proper brain cell function but lacks in most standard neuronal cell assays. A variety of soft lithographic micropatterning techniques can be used to integrate round geometries in cell assays. Most microfabricated patterns, however, focus only on a small set of defined curvatures. In contrast, curvatures in the brain span a wide physical range, leaving it unknown which precise role distinct curvatures may play on neuronal cell signaling. Here we report a hydrogel-based multi-curvature design consisting of over twenty bands of distinct parallel curvature ranges to precisely engineer neuronal networks' growth and signaling under patterns of arcs. Monitoring calcium and mitochondrial dynamics in primary rodent neurons grown over two weeks in the multi-curvature patterns, we found that static calcium signaling was locally attenuated under higher curvatures (k > 0.01 μm-1). In contrast, to randomize growth, transient calcium signaling showed higher synchronicity when neurons formed networks in confined multi-curvature patterns. Additionally, we found that mitochondria showed lower motility under high curvatures (k > 0.01 μm-1) than under lower curvatures (k < 0.01 μm-1). Our results demonstrate how sensitive neuronal cell function may be linked and controlled through specific curved geometric features. Furthermore, the hydrogel-based multi-curvature design possesses high compatibility with various surfaces, allowing a flexible integration of geometric features into next-generation neuro devices, cell assays, tissue engineering, and implants.

Microfluidic and Microscale Assays to Examine Regenerative Strategies in the Neuro Retina

Bioengineering systems have transformed scientific knowledge of cellular behaviors in the nervous system (NS) and pioneered innovative, regenerative therapies to treat adult neural disorders. Microscale systems with characteristic lengths of single to hundreds of microns have examined the development and specialized behaviors of numerous neuromuscular and neurosensory components of the NS. The visual system is comprised of the eye sensory organ and its connecting pathways to the visual cortex. Significant vision loss arises from dysfunction in the retina, the photosensitive tissue at the eye posterior that achieves phototransduction of light to form images in the brain. Retinal regenerative medicine has embraced microfluidic technologies to manipulate stem-like cells for transplantation therapies, where de/differentiated cells are introduced within adult tissue to replace dysfunctional or damaged neurons. Microfluidic systems coupled with stem cell biology and biomaterials have produced exciting advances to restore vision. The current article reviews contemporary microfluidic technologies and microfluidics-enhanced bioassays, developed to interrogate cellular responses to adult retinal cues. The focus is on applications of microfluidics and microscale assays within mammalian sensory retina, or neuro retina, comprised of five types of retinal neurons (photoreceptors, horizontal, bipolar, amacrine, retinal ganglion) and one neuroglia (Müller), but excludes the non-sensory, retinal pigmented epithelium.

3D Free-Standing Ordered Graphene Network Geometrically Regulates Neuronal Growth and Network Formation

The control of cell-microenvironment interactions plays a pivotal role in constructing specific scaffolds for tissue engineering. Here, we fabricated a 3D free-standing ordered graphene (3D-OG) network with a precisely defined pattern. When primary cortical cells are cultured on 3D-OG scaffolds, they form well-defined 3D connections. Astrocytes have a more ramified shape similar to that seen in vivo because of the nanosized ripples and wrinkles on the surface of graphene skeleton. Neurons have axons and dendrites aligned along the graphene skeleton, allowing the formation of neuronal networks with highly controlled connections. Neuronal networks have higher electrical activity with functional signaling over a long distance along the graphene skeleton. Our study, for the first time, investigated the geometrical cues on ordered neuronal growth and network formation with the support of graphene in 3D, which therefore advanced the development of customized scaffolds for brain-machine interfaces or neuroprosthetic devices.

Toward guiding principles for the design of biologically-integrated electrodes for the central nervous system

Innovation in electrode design has produced a myriad of new and creative strategies for interfacing the nervous system with softer, less invasive, more broadly distributed sites with high spatial resolution. However, despite rapid growth in the use of implanted electrode arrays in research and clinical applications, there are no broadly accepted guiding principles for the design of biocompatible chronic recording interfaces in the central nervous system (CNS). Studies suggest that the architecture and flexibility of devices play important roles in determining effective tissue integration: device feature dimensions (varying from 'sub'- to 'supra'-cellular scales, <10 µm to  >100 µm), Young's modulus, and bending modulus have all been identified as key features of design. However, critical knowledge gaps remain in the field with respect to the underlying motivation for these designs: (1) a systematic study of the relationship between device design features (materials, architecture, flexibility), biointegration, and signal quality needs to be performed, including controls for interaction effects between design features, (2) benchmarks for success need to be determined (biological integration, recording performance, longevity, stability), and (3) user results, particularly those that champion a specific design or electrode modification, need to be replicated across laboratories. Finally, the ancillary effects of factors such as tethering, site impedance and insertion method need to be considered. Here, we briefly review observations to-date of device design effects on tissue integration and performance, and then highlight the need for comprehensive and systematic testing of these effects moving forward.

Neuron dynamics on directional surfaces

Geometrical features play a very important role in neuronal growth and the formation of functional connections between neuronal cells. Here, we analyze the dynamics of axonal growth for neuronal cells cultured on micro-patterned polydimethylsiloxane surfaces. We utilize fluorescence microscopy to image axons, quantify their dynamics, and demonstrate that periodic geometrical patterns impart strong directional bias to neuronal growth. We quantify axonal alignment and present a general stochastic approach that quantitatively describes the dynamics of the growth cones. Neuronal growth is described by a general phenomenological model, based on a simple automatic controller with a closed-loop feedback system. We demonstrate that axonal alignment on these substrates is determined by the surface geometry, and it is quantified by the deterministic part of the stochastic (Langevin and Fokker-Planck) equations. We also show that the axonal alignment with the surface patterns is greatly suppressed by the neuron treatment with Blebbistatin, a chemical compound that inhibits the activity of myosin II. These results give new insight into the role played by the molecular motors and external geometrical cues in guiding axonal growth, and could lead to novel approaches for bioengineering neuronal regeneration platforms.

Variations of Elastic Modulus and Cell Volume with Temperature for Cortical Neurons

Neurons change their growth dynamics and mechanical properties in response to external stimuli such as stiffness of the local microenvironment, ambient temperature, and biochemical or geometrical guidance cues. Here we use combined atomic force microscopy (AFM) and fluorescence microscopy experiments to investigate the relationship between external temperature, soma volume, and elastic modulus for cortical neurons. We measure how changes in ambient temperature affect the volume and the mechanical properties of neuronal cells at both the bulk (elastic modulus) and local (elasticity maps) levels. The experimental data demonstrate that both the volume and the elastic modulus of the neuron soma vary with changes in temperature. Our results show a decrease by a factor of 2 in the soma elastic modulus as the ambient temperature increases from room (25 °C) to physiological (37 °C) temperature, while the volume of the soma increases by a factor of 1.3 during the same temperature sweep. Using high-resolution AFM force mapping, we measure the temperature-induced variations within different regions of the elasticity maps (low and high values of elastic modulus) and correlate these variations with the dynamics of cytoskeleton components and molecular motors. We quantify the change in soma volume with temperature and propose a simple theoretical model that relates this change with variations in soma elastic modulus. These results have significant implications for understanding neuronal development and functions, as ambient temperature, cytoskeletal dynamics, and cellular volume may change with variations in physiological conditions, for example, during tissue compression and infections in vivo as well as during cell manipulation and tissue regeneration ex vivo.