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Axons are thought to be ultrathin membrane cables of a relatively uniform diameter, designed to conduct electrical signals, or action potentials. Here, we demonstrate that unmyelinated axons are not simple cylindrical tubes. Rather, axons have nanoscopic boutons repeatedly along their length interspersed with a thin cable with a diameter of ~60 nm like pearls-on-a-string. These boutons are only ~200 nm in diameter and do not have synaptic contacts or a cluster of synaptic vesicles, hence non-synaptic. Our in silico modeling suggests that axon pearling can be explained by the mechanical properties of the membrane including the bending modulus and tension. Consistent with modeling predictions, treatments that disrupt these parameters like hyper- or hypo-tonic solutions, cholesterol removal, and non-muscle myosin II inhibition all alter the degree of axon pearling, suggesting that axon morphology is indeed determined by the membrane mechanics. Intriguingly, neuronal activity modulates the cholesterol level of plasma membrane, leading to shrinkage of axon pearls. Consequently, the conduction velocity of action potentials becomes slower. These data reveal that biophysical forces dictate axon morphology and function and that modulation of membrane mechanics likely underlies plasticity of unmyelinated axons.

Biomembranes adopt varying morphological configurations that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared to traditional approximation-based methods (e.g., finite element method), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining expressive coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh based model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on Discrete Differential Geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. Mem3DG is designed to facilitate models in tandem with and mimicking experimental studies. It also supports the use of realistic membrane ultrastructure from 3D imaging as an input. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. While the first two examples serve as validation, the later examples provide a blueprint for extending Mem3DG to model a system of interest. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions. We hope that Mem3DG will be a useful tool to help advance the mission of computational membrane mechanobiology.

Biomembranes adopt varying morphological configurations that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared to traditional approximation-based methods (e.g., finite element method), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining expressive coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh based model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on Discrete Differential Geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. Mem3DG is designed to facilitate models in tandem with and mimicking experimental studies. It also supports the use of realistic membrane ultrastructure from 3D imaging as an input. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. While the first two examples serve as validation, the later examples provide a blueprint for extending Mem3DG to model a system of interest. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions. We hope that Mem3DG will be a useful tool to help advance the mission of computational membrane mechanobiology.