  The effect of signal integration through cis-regulatory modules (CRMs) on
synchronization and clustering of populations of two-component genetic
oscillators coupled by quorum sensing is in detail investigated. We find that
the CRMs play an important role in achieving synchronization and clustering.
For this, we investigate 6 possible cis-regulatory input functions (CRIFs) with
AND, OR, ANDN, ORN, XOR, and EQU types of responses in two possible kinds of
cell-to-cell communications: activator-regulated communication (i.e., the
autoinducer regulates the activator) and repressor-regulated communication
(i.e., the autoinducer regulates the repressor). Both theoretical analysis and
numerical simulation show that different CRMs drive fundamentally different
cellular patterns, such as complete synchronization, various cluster-balanced
states and several cluster-nonbalanced states.
