Theoretical analysis of radioactivity profiles during fast axonal transport: Effects of deposition and turnover

Abstract

In a preceding study [Blum, J.J., and Reed, M.C. (1985): Cell Motil. 5:507-527], factors responsible for the shape and velocity of the leading edge of the radiolabeled organelle profile were analyzed, but processes that might influence the shape of the plateau-like region behind the advancing wave were ignored. It is now shown that deposition of material from the fast transport system into membrane-associated structures, degradation of such deposited material and its return to the soma by the retrograde transport system, or leakage of radiolabeled material from the axon can account for the shape of the plateau. Furthermore, these processes are compatible with the maintenance of such structural inhomogeneities as the nodes of Ranvier.

Probabilistic methods for a linear reaction-hyperbolic system with constant coefficients

“…In nerve cells, protein synthesis occurs only in the cell body (soma); thus, the proteins, membrane-bound neurotransmitters and other essential structural elements must be transported down the axon. Since the mid-1980's, Reed and Blum have been formulating mathematical models of fast axonal transport [Blum and Reed (1985), Reed and Blum (1986)]. Each of their models is of the form Lu = f u where u x t is a vector of chemical concentrations, x represents distance along the axon, t represents time, L is a linear hyperbolic operator and f is a linear or nonlinear mapping representing the interactions of the various chemical constituents.…”

Coarse-graining intermittent intracellular transport: Two- and three-dimensional models

“…Indeed, similar mathematical models of axonal transport have a long and rich history. Following experimental work in the 1970s and 1980s that showed radio-labeled amino acids progressing through axons as slowly spreading waves, Reed and Blum developed PDE models of axonal transport that remarkably exhibited this same behavior [22][23][24]. These PDE models have been generalized and have generated lots of rigorous mathematical analysis [25][26][27][28].…”