A mathematical model of p62-ubiquitin aggregates in autophagy

Aggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. Three different parameter regimes are identified, where either aggregates are unstable, or their size saturates at a finite value, or their size grows indefinitely as long as free particles are abundant. The boundaries of these regimes as well as the finite size in the second case can be computed explicitly. The growth in the third case (quadratic in time) can also be made explicit by formal asymptotic methods. In the absence of rigorous results the dynamic stability of these structures has been investigated by numerical simulations. A comparison with recent experimental results permits a partial parametrization of the model. This work has been supported by the PhD program Signalling Mechanisms in Cellular Autophagy, funded by the Austrian Science Fund (FWF), project no. W1261. CS also acknowledges support by FWF, Grant Nos. W1245 and SFB65. MD and JD have been partially supported by the ERC Starting Grant SKIPPERAD (Number 306321). MD thanks the Wolfgang Pauli Institute for the sabbatical stay in Vienna during which this work has been initiated.