Simulating growth of TDP-43 cytosolic inclusion bodies in neuron soma

Abstract

This paper introduces a mathematical model for the growth of TDP-43 inclusion bodies. The model’s equations make it possible to determine numerically the concentrations of TDP-43 dimers, monomers, and aggregates. Assuming that all aggregates integrate into the inclusion bodies, the model predicts the size of TDP-43 inclusion bodies. In the scenario where protein degradation machinery is dysfunctional, resulting in infinite half-lives for TDP-43 dimers, monomers, and aggregates, an approximate solution of the model equations is derived. This solution, valid for large times, predicts that the inclusion body’s radius increases proportionally to the cube root of time. To the author’s knowledge, this study presents the first attempt to model the relationship between the size of TDP-43 inclusion bodies and time. The sensitivity analysis of the approximate solution indicates that the concentrations of TDP-43 monomers and aggregates, as well as inclusion body radii, are independent of the kinetic constants. However, the approximate solution becomes invalid for the scenario with physiologically relevant (finite) half-lives of TDP-43 dimers, monomers, and aggregates. In contrast to the situation with infinite half-lives, for various values of kinetic constants, the curves representing concentrations of monomers and aggregates, as well as the curves depicting inclusion body radii, converge to distinct constant values.