Growth, collapse, and stalling in a mechanical model for neurite motility

Abstract

Neurites, the long cellular protrusions that form the routes of the neuronal network, are capable of actively extending during early morphogenesis or regenerating after trauma. To perform this task, they rely on their cytoskeleton for mechanical support. In this paper, we present a three-component active gel model that describes neurites in the three robust mechanical states observed experimentally: collapsed, static, and motile. These states arise from an interplay between the physical forces driven by the growth of the microtubule-rich inner core of the neurite and the acto-myosin contractility of its surrounding cortical membrane. In particular, static states appear as a mechanical balance between traction and compression of these two parallel structures. The model predicts how the response of a neurite to a towing force depends on the force magnitude and recovers the response of neurites to several drug treatments that modulate the cytoskeleton active and passive properties.

Modeling molecular mechanisms in the axon

“…Two more recent approaches suggest to interpret neurons as active fluids or solids [7,55,62] that are capable of generating active forces, conceptually similar to skeletal muscle [32, 37]. In both cases, internal forces generated at the expenditure of adenosine triphosphate, ATP, explain internal tensions at the steady state as proposed by active matter hydrodynamics [51].…”

“…The active solid model [7,10] and the morphoelastic rod model [52] excellently capture the elastic properties of axons. The morphoelastic rod model characterizes the behavior of axons over long periods of time using the theory of finite growth [62]. It suggests that forces trigger the immediate addition of mass, whereas experiments indicate that forces first cause axons to stretch and then new mass is added gradually to restore the initial axonal diameter [39,47].…”

Modeling the Axon as an Active Partner with the Growth Cone in Axonal Elongation

“…Most research on the role of mechanics has focused on the pulling force generated at the growth cone through retrograde actin flow (4). Recent experiments and theory, however, reveal that forces are generated along the axon (5)(6)(7)(8)(9). Here, we build on that work to better understand how forces control axonal outgrowth.…”

“…Axons are complex materials, and interest in analytic and computational modeling has grown dramatically in the past few years to understand their elongation during development (5,6,9,37,38) and failure after injury (12,14,39,40). Analytic approaches have the strength of abstractly modeling the complex process of growth over long timescales of hours to days (6,9,38) but may not be well suited for understanding the internal geometry of axons and the roles of specific proteins. Finite element approaches, which conventionally treat neurons as elastic solids, are excellent for the study of traumatic injury over short timescales of <10 s (12,14).…”

“…They offer the advantage that elements in the model directly represent the configuration of individual proteins such as tau and microtubules. Nonetheless, the treatment of axons as solids does not capture the fluid-like permanent deformation that occurs during growth and retraction (7,9,41,42). Our group has recently extended the standard finite element method to allow elastic finite elements to make and break connections (5).…”