Morphological choicesAs now reported in the main text of the manuscript, given the axon cross-section and the proposed MTs densities (Bray and Bunge 1981, Fadic et al. 1985, Malbouisson et al. 1985) 19 rows of MTs were included in the axon RV, each containing two randomly placed discontinuities. The same approach was used in Peter and Mofrad (2012), Lazarus et al. (2015), Soheilypour et al. (2015). Mechanical properties of the MTs have been very well identifies by previous studies. Material properties These filaments represent the stiffest part of the cytoskeleton and the Youngs' modulus (E=830 MPa) was derived by Zhang et al. (2014) with a numerical approach and was in extremely good agreement with experiments by de Pablo et al (2003)where MTs are locally probed. In the latter study, older bending experiments (which estimate a modulus E=1 to 1.2 GPa) were considered to overestimate the material properties of MTs because they usually probe length scales much longer than the one necessary to assess material properties. Being these filaments far stiffer then the remainder of our model, it can be said that a slightly stiffer modulus would not affect the localization of strains on the membrane.
Tau proteins:Morphological choices Cross-connection between microtubules (MTs) and between neurofilaments (NFs) and MTs were quantified in a seminal study by Hirokawa (1982). There, MTs crosslinks were found to be less abundant than those between neurofilaments, which were reported having a 30-50 nm spacing. Inspecting the microscopy images in the same publication, a spacing of 120 nm was chosen for our model. Previous studies have also shown, through a sensitivity study, that tau protein density does not influence the energy associated with MTs stretching.
Material propertiesCompared to the MTs, the material properties of these filaments are far less studied. The properties that we chose are based on previous studies by Ahmadzadeh et al (2014,2015). In these studies the viscoelastic characteristic of these cross-links was derived from previous experimental studies. While the spring stiffness is in the range of previously tested motor proteins (kinesin stiffness = uN/m ), we agree that its viscous component is the biggest assumption behind our model, which would however would affect mostly the microtubule Bray, D. and Bunge, M.B., 1981. Serial analysis of microtubules in cultured rat sensory axons. ., 2003. Deformation and collapse of microtubules on the nanometer scale. Physical review letters, 91(9), p.098101. Hirokawa, N., 1982. Cross-linker system between neurofilaments, microtubules and membranous organelles in frog axons revealed by the quick-freeze, deep-etching method. The Journal of cell biology, 94(1), pp.129-142. Ahmadzadeh, H., Smith, D.H. and Shenoy, V.B., 2014. Viscoelasticity of tau proteins leads to strain rate-dependent breaking of microtubules during axonal stretch injury: predictions from a mathematical model. Biophysical journal, 106(5), pp.1123-1133. Ahmadzadeh, H., Smith, D.H. and Shenoy, V.B., 2015. Mech...