考虑细胞外基质刚度的神经轴突力学模型

A mechanical model of neuron axons considering extracellular matrix stiffness

细胞外基质在神经系统发育和再生过程中起到关键作用,其力学特性的非正常变化与神经系统疾病的发生发展密切相关.神经元利用其轴突末端生长锥感知细胞外基质力学特性,进而产生定向迁移行为.本文通过建立细胞黏附依赖的神经轴突力学模型,探究了细胞外基质刚度影响神经元定向迁移行为的分子机制.通过描述细胞黏附分子结合-解离过程、肌动蛋白激活-收缩及轴突生长等动力学过程,刻画了神经轴突、生长锥及细胞外基质之间的力学相互作用过程.理论结果揭示了不同种类神经元力敏感行为差异性产生的分子机制,阐明了基质刚度对神经轴突生长的影响规律.综上,本文通过建立神经轴突力学模型,对神经元感知细胞外基质刚度的生理行为进行了定量化描述,从力学角度描述了“轴突-生长锥-细胞外基质”相互作用过程,为神经再生和修复提供了潜在理论依据.

Mechanical signals drive neural cell growth and migration during development and regeneration.Although most cells migrate towards stiffer substrates,neurons can migrate in the opposite direction.We hypothesized that neural growth cones,known to affect stiffness sensing,are stiffness sensors as well,and tested this hypothesis via a mathematical model.The model integrates interactions between axons,growth cones and substrate through a two-dimensional molecular clutch model of filopodial dynamics and a viscoelastic model of active axon contraction.The modeling results predict that different types of neurons should have distinct mechanosensing behaviors,with dorsal root ganglion cells behaving differently than hippocampal neurons.Also,substrate stiffness can guide growth cone motion through altering the traction force generated in the growth cone.The model provides the first explanation of how stiffness can be sensed and provides mechanistic insight into how axon-growth cone-substrate interactions drive neural regeneration and repair.Since existing models failed to address the interactions between axons,growth cones and ECM stiffness in neural mechanosensing,we constructed a mathematical model of growth cone based on the molecular clutch framework of Odde et al.,which treats focal adhesion proteins and the substratum as linear springs loaded by a cytoskeletal tension,to investigate how substrate stiffness affects growth cone dynamics and axonal retraction.Briefly,a group of i filopodia,each modeled as a single molecular clutch module,are attached to an axon that is modeled as a contractile element in parallel with a standard linear viscoelastic solid.Each molecular clutch module contains niadhesion clutches(linear springs of stiffness ki) and nicorresponding substrate clutches(linear springs with stiffness Ei).Substrate clutches are distributed randomly,and have values E1≤ Ei≤ E2that vary linearly with position as a first order approximation to the spatially graded,nonlinear mechanical properties of ECM.Adhesion clutches bind to substrate clutches with a rate of kon,forming a force transmission pathway from intracellular cytoskeleton,where contraction arises from inward actin flow,to the extracellular substrate.The unbinding rate of koff,ivaries with the force Fiin the connected clutch according to the Bell model.We first studied the different behaviors between neurons from dorsal root ganglion and hippocampus respectively and found that the expression of adhesion proteins on growth cone is vital for the generation of traction force.Since traction force is determinant to the axon dynamic processes including elongation and retraction,the expression of adhesion proteins thus plays a vital role in neuron mechanical behaviors.Then we tried to predict how the axon responds to substrate with different stiffness by combining the growth cone model with a viscoelastic contractile axon body model.The combined model illustrated how the contraction of myosin molecular motors decreases as the axon deformation rate goes down.The results further showed that low motor contraction can cause the axon retraction on high-stiffness substrate while much higher contraction force is needed for the axon retraction on low-stiffness substrate.The predictions conform to previous experimental observations in the literature and indicate that the increase of motor contraction leads to the axon retraction on the substrate with the same stiffness,providing the possible reasons that neurons usually migrate towards the low-stiffness area instead of durotaxis seen in other cell types.Altogether,our model results suggest that growth cone filopodial dynamics,including dynamics of turning,enlargement and contraction,can explain how substrate stiffness affects neuronal mechanosensing,and shed light on how the nervous system might develop to distinguish and reach target tissues and cells by mechanosensing.