A membrane-driven biochemical oscillator tunable by the volume to surface area ratio.

Oscillations are ubiquitous features of biological organisms, playing crucial roles in processes from circadian rhythms to developmental patterning. Protein-based biochemical oscillators have particular applications in synthetic biology because they can access fast and slow timescales that are independent from the transcription-translation machinery required of genetic oscillators. Here, we introduce and model such a mass-conserving biochemical oscillator using mass-action reaction kinetics that exploits dynamic changes to membrane phospholipid concentrations to drive proteins on and off the membrane in robust, tunable rhythms. Importantly, the oscillations rely on amplification of reactions on the membrane via dimensional reduction, and they are therefore tunable by variations in the volume-to-surface area ratio (V/A) of the system. With components inspired by the endocytic machinery, we show that a wide range of physiologically relevant biochemical rates can produce oscillations in part due to this independent geometric control. A broad computational screen of the high-dimensional parameter space reveals that oscillations require relatively strict enzyme kinetic design rules for low V/A but much more permissive kinetics for larger V/A. We validate that oscillations persist with more realistic reaction-diffusion simulations that captures explicit diffusion and stochastic, integer valued copy numbers, in overall good agreement with the period and amplitude of the deterministic oscillators. Because the oscillations rely on time-dependent changes to the surface properties and not post-translational modifications to the protein subunits, we demonstrate that it can be coupled to a self-assembling trimer, driving not only changes in localization but trimer yield. Our analysis establishes this membrane-localization oscillator as a new, geometry tunable and programmable timing module and suggests a potential for geometry sensing in engineered or cell-free systems.