Quanti � cation of protein abundance 1 and interaction de � nes a mechanism 2 for operation of the circadian clock

The mammalian circadian clock exerts control of daily gene expression through cycles 13 of DNA binding. Here we develop a quantitative model of how a nite pool of BMAL1 protein can 14 regulate thousands of target sites over daily time scales. We used quantitative imaging to track 15 dynamic changes in endogenous labelled proteins across peripheral tissues and the SCN. We 16 determine the contribution of multiple rhythmic processes coordinating BMAL1 DNA binding, 17 including cycling molecular abundance, binding a nities and repression. We nd nuclear BMAL1 18 concentration determines corresponding CLOCK through heterodimerization and de ne a DNA 19 residence time of this complex. Repression of CLOCK:BMAL1 is achieved through rhythmic 20 changes to BMAL1:CRY1 association and high a nity interactions between PER2:CRY1 which 21 mediates CLOCK:BMAL1 displacement from DNA. Finally, stochastic modelling reveals a dual role 22 for PER:CRY complexes in which increasing concentrations of PER2:CRY1 promotes removal of 23 BMAL1:CLOCK from genes consequently enhancing ability to move to new target sites. 24