Distance dependence of neuronal growth on nanopatterned gold surfaces

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.

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.

Graphene-Based Scaffolds for Regenerative Medicine

Leading-edge regenerative medicine can take advantage of improved knowledge of key roles played, both in stem cell fate determination and in cell growth/differentiation, by mechano-transduction and other physicochemical stimuli from the tissue environment. This prompted advanced nanomaterials research to provide tissue engineers with next-generation scaffolds consisting of smart nanocomposites and/or hydrogels with nanofillers, where balanced combinations of specific matrices and nanomaterials can mediate and finely tune such stimuli and cues. In this review, we focus on graphene-based nanomaterials as, in addition to modulating nanotopography, elastic modulus and viscoelastic features of the scaffold, they can also regulate its conductivity. This feature is crucial to the determination and differentiation of some cell lineages and is of special interest to neural regenerative medicine. Hereafter we depict relevant properties of such nanofillers, illustrate how problems related to their eventual cytotoxicity are solved via enhanced synthesis, purification and derivatization protocols, and finally provide examples of successful applications in regenerative medicine on a number of tissues.

A Multiscale Model to Predict Neuronal Cell Deformation with Varying Extracellular Matrix Stiffness and Topography

Introduction

Neuronal cells are sensitive to mechanical properties of extracellular matrix (ECM) such as stiffness and topography. Cells contract and exert a force on ECM to detect the microenvironment, which activates the signaling pathway to influence the cell functions such as differentiation, migration, and proliferation. There are numerous transmembrane proteins that transmit signals; however, integrin and neural cellular adhesion molecules (NCAM) play an important role in sensing the ECM mechanical properties. Mechanotransduction of cell-ECM is the key to understand the influence of ECM stiffness and topography; therefore, in this study, we develop a multiscale computational model to investigate these properties.

Methods

This model couples the molecular behavior of integrin and NCAM to microscale interactions of neuronal cell and the ECM. We analyze the atomistic/molecular behavior of integrin and NCAM due to mechanical stimuli using steered molecular dynamics. The microscale properties of the neuronal cell and the ECM are simulated using non-linear finite element analysis by applying cell contractility.

Results

We predict that by increasing the ECM stiffness, a neuronal cell exerts greater stress on the ECM. However, this stress reaches a saturation value for a threshold stiffness of ECM, and the saturation value is affected by the ECM thickness, topography, and clustering of integrin and NCAMs. Further, the ECM topography leads to asymmetric stress and deformation in the neuronal cell. Predicted stress distribution in neuronal cell and ECM are consistent with experimental results from the literature.

Conclusion

The multiscale computational model will guide in selecting the optimal ECM stiffness and topography range for in vitro studies.

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.

Anomalous diffusion for neuronal growth on surfaces with controlled geometries

Geometrical cues are known to play a very important role in neuronal growth and the formation of neuronal networks. Here, we present a detailed analysis of axonal growth and dynamics for neuronal cells cultured on patterned polydimethylsiloxane surfaces. We use fluorescence microscopy to image neurons, quantify their dynamics, and demonstrate that the substrate geometrical patterns cause strong directional alignment of axons. We quantify axonal growth and report a general stochastic approach that quantitatively describes the motion of growth cones. The growth cone dynamics is described by Langevin and Fokker-Planck equations with both deterministic and stochastic contributions. We show that the deterministic terms contain both the angular and speed dependence of axonal growth, and that these two contributions can be separated. Growth alignment is determined by surface geometry, and it is quantified by the deterministic part of the Langevin equation. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: speed and angular distributions, correlation functions, diffusion coefficients, characteristics speeds and damping coefficients. We demonstrate that axonal dynamics displays a cross-over from Brownian motion (Ornstein-Uhlenbeck process) at earlier times to anomalous dynamics (superdiffusion) at later times. The superdiffusive regime is characterized by non-Gaussian speed distributions and power law dependence of the axonal mean square length and the velocity correlation functions. These results demonstrate the importance of geometrical cues in guiding axonal growth, and could lead to new methods for bioengineering novel substrates for controlling neuronal growth and regeneration.

Role of geometrical cues in neuronal growth

Geometrical cues play an essential role in neuronal growth. Here, we quantify axonal growth on surfaces with controlled geometries and report a general stochastic approach that quantitatively describes the motion of growth cones. We show that axons display a strong directional alignment on micropatterned surfaces when the periodicity of the patterns matches the dimension of the growth cone. The growth cone dynamics on surfaces with uniform geometry is described by a linear Langevin equation with both deterministic and stochastic contributions. In contrast, axonal growth on surfaces with periodic patterns is characterized by a system of two generalized Langevin equations with both linear and quadratic velocity dependence and stochastic noise. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: angular distributions, correlation functions, diffusion coefficients, characteristics speeds, and damping coefficients. We demonstrate that axonal dynamics displays a crossover from an Ornstein-Uhlenbeck process to a nonlinear stochastic regime when the geometrical periodicity of the pattern approaches the linear dimension of the growth cone. Growth alignment is determined by surface geometry, which is fully quantified by the deterministic part of the Langevin equation. These results provide insight into the role of curvature sensing proteins and their interactions with geometrical cues.

Easy to Apply Polyoxazoline-Based Coating for Precise and Long-Term Control of Neural Patterns

Arranging cultured cells in patterns via surface modification is a tool used by biologists to answer questions in a specific and controlled manner. In the past decade, bottom-up neuroscience emerged as a new application, which aims to get a better understanding of the brain via reverse engineering and analyzing elementary circuitry in vitro. Building well-defined neural networks is the ultimate goal. Antifouling coatings are often used to control neurite outgrowth. Because erroneous connectivity alters the entire topology and functionality of minicircuits, the requirements are demanding. Current state-of-the-art coating solutions such as widely used poly(l-lysine)-g-poly(ethylene glycol) (PLL-g-PEG) fail to prevent primary neurons from making undesired connections in long-term cultures. In this study, a new copolymer with greatly enhanced antifouling properties is developed, characterized, and evaluated for its reliability, stability, and versatility. To this end, the following components are grafted to a poly(acrylamide) (PAcrAm) backbone: hexaneamine, to support spontaneous electrostatic adsorption in buffered aqueous solutions, and propyldimethylethoxysilane, to increase the durability via covalent bonding to hydroxylated culture surfaces and antifouling polymer poly(2-methyl-2-oxazoline) (PMOXA). In an assay for neural connectivity control, the new copolymer's ability to effectively prevent unwanted neurite outgrowth is compared to the gold standard, PLL-g-PEG. Additionally, its versatility is evaluated on polystyrene, glass, and poly(dimethylsiloxane) using primary hippocampal and cortical rat neurons as well as C2C12 myoblasts, and human fibroblasts. PAcrAm-g-(PMOXA, NH₂, Si) consistently outperforms PLL-g-PEG with all tested culture surfaces and cell types, and it is the first surface coating which reliably prevents arranged nodes of primary neurons from forming undesired connections over the long term. Whereas the presented work focuses on the proof of concept for the new antifouling coating to successfully and sustainably prevent unwanted connectivity, it is an important milestone for in vitro neuroscience, enabling follow-up studies to engineer neurologically relevant networks. Furthermore, because PAcrAm-g-(PMOXA, NH₂, Si) can be quickly applied and used with various surfaces and cell types, it is an attractive extension to the toolbox for in vitro biology and biomedical engineering.

Effects of surface asymmetry on neuronal growth

Detailed knowledge of how the surface physical properties, such as mechanics, topography and texture influence axonal outgrowth and guidance is essential for understanding the processes that control neuron development, the formation of functional neuronal connections and nerve regeneration. Here we synthesize asymmetric surfaces with well-controlled topography and texture and perform a systematic experimental and theoretical investigation of axonal outgrowth on these substrates. We demonstrate unidirectional axonal bias imparted by the surface ratchet-based topography and quantify the topographical guidance cues that control neuronal growth. We describe the growth cone dynamics using a general stochastic model (Fokker-Planck formalism) and use this model to extract two key dynamical parameters: diffusion (cell motility) coefficient and asymmetric drift coefficient. The drift coefficient is identified with the torque caused by the asymmetric ratchet topography. We relate the observed directional bias in axonal outgrowth to cellular contact guidance behavior, which results in an increase in the cell-surface coupling with increased surface anisotropy. We also demonstrate that the disruption of cytoskeletal dynamics through application of Taxol (stabilizer of microtubules) and Blebbistatin (inhibitor of myosin II activity) greatly reduces the directional bias imparted by these asymmetric surfaces. These results provide new insight into the role played by topographical cues in neuronal growth and could lead to new methods for stimulating neuronal regeneration and the engineering of artificial neuronal tissue.

Local polymer replacement for neuron patterning and in situ neurite guidance

By locally dispensing poly-L-lysine (PLL) molecules with a FluidFM onto a protein and cell resistant poly-L-lysine-graft-polyethylene glycol (PLL-g-PEG) coated substrate, the antifouling layer can be replaced under the tip aperture by the cell adhesive PLL. We used this approach for guiding the adhesion and axonal outgrowth of embryonic hippocampal neurons in situ. Cultures of hippocampal neurons were chosen because they mostly contain pyramidal neurons. The hippocampus is known to be involved in memory formation, and the stages of network development are well characterized, which is an asset to fundamental research. After fabricating diffuse PLL spots with 10-250 μm diameter, seeded hippocampal cells stick preferentially onto the spots migrating toward the spot center along the PLL gradient. Cell clusters were formed depending on the lateral size of the PLL dots and the density of seeded cells. In a second step of this protocol, the FluidFM is used to connect in situ the obtained clusters. The outgrowth of neurites, which are known to grow preferentially on adhesive substrates, is tailored by writing PLL lines. Antibody staining confirms that the outgrowing neurites are mostly axons, while the activity of the neurons is assessed by a calcium indicator, proving cell viability. The calcium signal intensity of two actively interconnected clusters showed to be correlated, corroborating the formation of vectored and polarized interconnections.

Neuronal growth as diffusion in an effective potential

Current understanding of neuronal growth is mostly qualitative, as the staggering number of physical and chemical guidance cues involved prohibit a fully quantitative description of axonal dynamics. We report on a general approach that describes axonal growth in vitro, on poly-D-lysine-coated glass substrates, as diffusion in an effective external potential, representing the collective contribution of all causal influences on the growth cone. We use this approach to obtain effective growth rules that reveal an emergent regulatory mechanism for axonal pathfinding on these substrates.

Neuron biomechanics probed by atomic force microscopy

Mechanical interactions play a key role in many processes associated with neuronal growth and development. Over the last few years there has been significant progress in our understanding of the role played by the substrate stiffness in neuronal growth, of the cell-substrate adhesion forces, of the generation of traction forces during axonal elongation, and of the relationships between the neuron soma elastic properties and its health. The particular capabilities of the Atomic Force Microscope (AFM), such as high spatial resolution, high degree of control over the magnitude and orientation of the applied forces, minimal sample damage, and the ability to image and interact with cells in physiologically relevant conditions make this technique particularly suitable for measuring mechanical properties of living neuronal cells. This article reviews recent advances on using the AFM for studying neuronal biomechanics, provides an overview about the state-of-the-art measurements, and suggests directions for future applications.

Nanotopography-guided tissue engineering and regenerative medicine

Human tissues are intricate ensembles of multiple cell types embedded in complex and well-defined structures of the extracellular matrix (ECM). The organization of ECM is frequently hierarchical from nano to macro, with many proteins forming large scale structures with feature sizes up to several hundred microns. Inspired from these natural designs of ECM, nanotopography-guided approaches have been increasingly investigated for the last several decades. Results demonstrate that the nanotopography itself can activate tissue-specific function in vitro as well as promote tissue regeneration in vivo upon transplantation. In this review, we provide an extensive analysis of recent efforts to mimic functional nanostructures in vitro for improved tissue engineering and regeneration of injured and damaged tissues. We first characterize the role of various nanostructures in human tissues with respect to each tissue-specific function. Then, we describe various fabrication methods in terms of patterning principles and material characteristics. Finally, we summarize the applications of nanotopography to various tissues, which are classified into four types depending on their functions: protective, mechano-sensitive, electro-active, and shear stress-sensitive tissues. Some limitations and future challenges are briefly discussed at the end.

Neuronal alignment on asymmetric textured surfaces

Axonal growth and the formation of synaptic connections are key steps in the development of the nervous system. Here, we present experimental and theoretical results on axonal growth and interconnectivity in order to elucidate some of the basic rules that neuronal cells use for functional connections with one another. We demonstrate that a unidirectional nanotextured surface can bias axonal growth. We perform a systematic investigation of neuronal processes on asymmetric surfaces and quantify the role that biomechanical surface cues play in neuronal growth. These results represent an important step towards engineering directed axonal growth for neuro-regeneration studies.

Elasticity maps of living neurons measured by combined fluorescence and atomic force microscopy

Detailed knowledge of mechanical parameters such as cell elasticity, stiffness of the growth substrate, or traction stresses generated during axonal extensions is essential for understanding the mechanisms that control neuronal growth. Here, we combine atomic force microscopy-based force spectroscopy with fluorescence microscopy to produce systematic, high-resolution elasticity maps for three different types of live neuronal cells: cortical (embryonic rat), embryonic chick dorsal root ganglion, and P-19 (mouse embryonic carcinoma stem cells) neurons. We measure how the stiffness of neurons changes both during neurite outgrowth and upon disruption of microtubules of the cell. We find reversible local stiffening of the cell during growth, and show that the increase in local elastic modulus is primarily due to the formation of microtubules. We also report that cortical and P-19 neurons have similar elasticity maps, with elastic moduli in the range 0.1-2 kPa, with typical average values of 0.4 kPa (P-19) and 0.2 kPa (cortical). In contrast, dorsal root ganglion neurons are stiffer than P-19 and cortical cells, yielding elastic moduli in the range 0.1-8 kPa, with typical average values of 0.9 kPa. Finally, we report no measurable influence of substrate protein coating on cell body elasticity for the three types of neurons.

Young’s Modulus of Cortical and P19 Derived Neurons Measured by Atomic Force Microscopy

In this paper we use the Atomic Force Microscope to measure the Young’s modulus for two types of neuronal cell bodies: cortical neurons obtained from rat embryos and neurons derived from P19 mouse embryonic carcinoma stem cells. The neurons are plated on different substrates coated with two types of protein growth factors, poly-D-lysine and laminin. We report on the Young’s modulus of each type of neuron as well as the variation of modulus between cells plated on different protein substrates. We compare these results to various individual cell and bulk tissue measurements reported in literature. We additionally report on an observed change in the Young’s modulus of cortical neurons when subjected to a short-term reduction in ambient temperature.

Atomic force microscopy and its contribution to understanding the development of the nervous system

While our understanding of the influence of biochemical signaling on cell functioning is increasing rapidly, the consequences of mechanical signaling are currently poorly understood. However, cells of the nervous system respond to their mechanical environment; their mechanosensitivity has important implications for development and disease. Atomic force microscopy provides a powerful technique to investigate the mechanical interaction of cells with their environment with high resolution. This method can be used to obtain high-resolution surface topographies, stiffness maps, and apply well-defined forces to samples at different length scales. This review summarizes recent advances of atomic force microscopy, provides an overview about state-of-the-art measurements, and suggests directions for future applications to investigate the involvement of mechanics in the development of the nervous system.