Oscillation and Synchronization of Molecular Machines by the Diffusion of Inhibitory Molecules

The systems of distributed molecular machines (i.e., devices with a size in the nano- to micro-scale range) are anticipated to perform nanoscale to microscale precision functions for future medical applications with cells and for manufacturing applications to pattern molecules. In these applications, molecular machines are mobile and distributed about an environment. The molecular machines coordinate to perform system-level functionality. One common form of coordination is synchronization of molecular machines. Since a single molecular machine has limited ability, multiple molecular machines may synchronize to perform some functionality at the same time to produce a larger scale effect. Synchronization may also be required for multiple molecular machines to coordinate a sequential process. This paper focuses on a simple model for oscillation by molecular machines which release pulses of inhibitory molecules. The inhibitory molecules diffuse and cause synchronization of pulses. Analysis was performed to determine how the number of oscillators, distance between oscillators, and noise of measured concentration impacted the period of oscillation and phase difference among molecular machines.