Department of Physics and Astronomy, Center for Nanoscopic Physics, Tufts University, Medford, Massachusetts, United States of America.
PLoS One. 2019 May 6;14(5):e0216181. doi: 10.1371/journal.pone.0216181. eCollection 2019.
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.
几何线索在神经元生长和神经网络形成中起着非常重要的作用。在这里，我们对培养在图案化聚二甲基硅氧烷表面上的神经元的轴突生长和动力学进行了详细分析。我们使用荧光显微镜对神经元进行成像，量化它们的动力学，并证明基底的几何图案导致了轴突的强烈定向排列。我们量化了轴突的生长，并提出了一种通用的随机方法，该方法定量描述了生长锥的运动。生长锥动力学由朗之万和福克-普朗克方程描述，其中包含确定性和随机性贡献。我们表明，确定性项包含轴突生长的角度和速度依赖性，并且可以将这两个贡献分开。生长取向由表面几何形状决定，并通过朗之万方程的确定性部分进行量化。我们将实验数据与理论分析相结合，以测量生长锥运动的关键参数：速度和角度分布、相关函数、扩散系数、特征速度和阻尼系数。我们证明，轴突动力学在早期表现为布朗运动（奥恩斯坦-乌伦贝克过程），在后期表现为异常动力学（超扩散）。超扩散态的特征是速度分布的非高斯性以及轴突均方长度和速度相关函数的幂律依赖性。这些结果表明几何线索在引导轴突生长中的重要性，并可能导致用于控制神经元生长和再生的新型生物工程基底的新方法。
