A Biochemical Oscillator Controlled by Membrane Geometry

We present a computational model of a biochemical oscillator that exploits the distinct reaction kinetics of lipid-modifying enzymes between the 2D membrane and 3D cytosolic environments. The system demonstrates how membrane localization of these enzymes creates natural positive feedback loops through enhanced binding kinetics between membrane-localized partners, driving synchronized oscillations in the membrane-bound fraction of conserved protein species. The oscillator's dynamics and period are directly coupled to the volume-to-surface-area ratio, demonstrating how a purely geometric parameter can tune reaction network behavior without modifying the underlying biochemistry. The segregation of enzyme complexes between membrane and cytosol drives temporal self-organization in the behavior of the broader reaction network, generating regular periodic assembly and disassembly of downstream molecular complexes. This coupling between membrane shape and spatiotemporal dynamics in generating periodic behavior offers potential applications ranging from temporally-controlled drug delivery to biomolecular sensors that respond to changes in cellular architecture.