Role of geometrical cues in neuronal growth

Abstract

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 micro-patterned 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 cross-over from an Ornstein-Uhlenbeck process to a non-linear 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 new insight into the role of curvature sensing proteins and their interactions with geometrical cues.

Neuronal Growth and Formation of Neuron Networks on Directional Surfaces

“…In our previous work, we have shown that axonal growth on surfaces with controlled geometries arises as the result of an interplay between deterministic and stochastic components of growth cone motility [ 10 , 15 , 16 , 19 , 20 ]. Deterministic influences include, for example, the presence of preferred directions of growth along specific geometric patterns on substrates, while stochastic components come from the effects of polymerization of cytoskeletal elements (actin filaments and microtubules), neuron signaling, low concentration biomolecule detection, biochemical reactions within the neuron, and the formation of lamellipodia and filopodia [ 1 , 2 , 7 , 21 ].…”

“…Deterministic influences include, for example, the presence of preferred directions of growth along specific geometric patterns on substrates, while stochastic components come from the effects of polymerization of cytoskeletal elements (actin filaments and microtubules), neuron signaling, low concentration biomolecule detection, biochemical reactions within the neuron, and the formation of lamellipodia and filopodia [ 1 , 2 , 7 , 21 ]. The resultant growth cannot be predicted for individual neurons due to this stochastic-deterministic interplay, however, the growth dynamics for populations of neurons can be modeled by probability functions that satisfy a set of well-defined stochastic differential equations, such as Langevin and Fokker–Planck equations [ 10 , 15 , 19 , 20 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ]. In previous work, we have shown that axonal dynamics on uniform glass surfaces is described by an Ornstein-Uhlenbeck (OU) process, defined by a linear Langevin equation and stochastic white noise [ 19 , 20 ].…”

“…The resultant growth cannot be predicted for individual neurons due to this stochastic-deterministic interplay, however, the growth dynamics for populations of neurons can be modeled by probability functions that satisfy a set of well-defined stochastic differential equations, such as Langevin and Fokker–Planck equations [ 10 , 15 , 19 , 20 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ]. In previous work, we have shown that axonal dynamics on uniform glass surfaces is described by an Ornstein-Uhlenbeck (OU) process, defined by a linear Langevin equation and stochastic white noise [ 19 , 20 ]. We have also reported that neurons cultured on poly-D-lysine coated polydimethylsiloxane (PDMS) substrates with periodic parallel ridge micropatterns of spatial periodicity d (henceforth referred to as the pattern spatial period) grow axons parallel to the surface patterns.…”

“…We have studied axonal growth as a function of time on these micropatterned surfaces and found that axonal alignment increases as a function of time [ 16 ]. The axonal dynamics are described by non-linear Langevin equations, involving quadratic velocity terms and non-zero coefficients for the angular orientation of the growing axon [ 20 ]. In another paper, we have used the Langevin and Fokker–Planck equations to quantify axonal growth on surfaces with ratchet-like topography (asymmetric tilted nanorod: nano-ppx surfaces) [ 10 ].…”

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

“…In addition, devices fabricated at the microscale provide the remarkable advantage of precise experimental validation against analytical models of molecular and convective transport [41,42], viscoelasticity [43][44][45], electrochemical dynamics [46,47] and many others [48][49][50][51][52]. These advantages have pioneered the development of single and multiplexed microfluidic channels [53][54][55], micropatterned substrate surfaces [56][57][58][59], and three-dimensional (3D) microfabricated structures [60,61] to examine localized cell behavior. Moreover, microfluidic "upgrades" of conventional bioassays, such as culture flasks and chambers, have significantly enriched abilities to examine cell behavior on the in vivo microscale.…”