The bulk of this thesis considers how biological rhythms (oscillators) can be made to synchronize their rhythms by virtue of coupling to an external signal. Such externally controlled synchronization, known as entrainment, is explored using a synthetic biology approach in E.~coli, where I have used rationally designed gene circuits as an experimental model. Two novel modes of entrainment are explored: entrainment by competition between components for degradation, and entrainment by a noisy (aperiodic) stimulus. Both of these modes of entrainment can be shown to strongly synchronize ensembles of synthetic gene oscillators, and thus, these modes of entrainment may be important to understand the appearance of synchrony in natural systems. In addition to the study of entrainment, this thesis contains a general background of relevant material, contributions to the biophysics of multisite proteases, and updated protocols for experimental procedures in microfluidics and microscopy.