Competitive Binding Facilitates Oscillations in a Non-Cooperative Repressilator

The repressilator is the simplest transcriptional regulatory network known to exhibit sustained oscillations. Deterministic models predict that oscillations are generally conditional to repressor cooperative binding. Here we present a repressilator made from deactivated CRISPR cas proteins, which, despite binding non-cooperatively to their target sites, nevertheless exhibit sustained oscillations over many cellular generations as observed in single cell microfluidics experiments. We explain how the cooperativity requirement can be circumvented by sequestration of repressors via competitive binding sites housed on a tunable copy number plasmid. These findings are explained through deterministic and stochastic models which are used to guide further inquiry into how the period, amplitude, and statistical properties of these oscillations can be controlled by competitive binding.