Delay Differential Equation Approach to Oligomerization Reveals the Delay Dynamics Underlying Oscillations in Mitochondrial Fission.

Disruptions in the balance of mitochondrial fission and fusion are implicated in a host of diseases including cardiovascular, metabolic, and neurodegenerative, as well as cancer. Leinheiser et al. proposed a mechanistic model for mitochondrial fission which relies on the oligomerization of Dynamin-related protein 1 (Drp1). In this work, we propose an alternative state-dependent delay-differential equation (sdDDE) framework for mitochondrial fission, which reveals that the intrinsic delay dynamics in Drp1 oligomerization can drive oscillations in the rate of mitochondrial fission. To develop this sdDDE model, we generate a simplified model which disallows oligomer disassembly on the mitochondrial membrane. Following homogenization, the simplified model approaches a steady state dominated by oligomers too small to reach the threshold for fission. Therefore, the fission rate approaches zero when initial conditions reside within the basin of attraction of this fission-free equilibrium. We therefore reincorporate oligomer disassembly on the mitochondrial membrane. However, the attracting, fission-free equilibrium persists. To eliminate this fission-free equilibrium, we incorporate an atomization term into the oligomerization mechanism, highlighting the importance of oligomer disassembly in sustaining mitochondrial fission. Using homogenization techniques, we derive an advection PDE with nonlocal interactions and obtain a reduced sdDDE system governing oligomer partial moments. Analysis of this reduced system reveals an analogous Hopf bifurcation to the Leinheiser et al. fission model, demonstrating that intrinsic delays in Drp1 oligomerization are sufficient to generate oscillatory mitochondrial fission dynamics.