Growth laws emerging from studies of cell populations provide essential constraints on the global mechanisms that coordinate cell growth^1-3. The foundation of bacterial cell cycle studies relies on two interconnected dogmas that were proposed more than 50 years ago-the Schaechter-Maaloe-Kjeldgaard growth law that relates cell mass to growth rate¹ and Donachie's hypothesis of a growth-rate-independent initiation mass⁴. These dogmas spurred many efforts to understand their molecular bases and physiological consequences^5-14. Although they are generally accepted in the fast-growth regime, that is, for doubling times below 1 h, extension of these dogmas to the slow-growth regime has not been consistently achieved. Here, through a quantitative physiological study of Escherichia coli cell cycles over an extensive range of growth rates, we report that neither dogma holds in either the slow- or fast-growth regime. In their stead, linear relations between the cell mass and the rate of chromosome replication-segregation were found across the range of growth rates. These relations led us to propose an integral-threshold model in which the cell cycle is controlled by a licensing process, the rate of which is related in a simple way to chromosomal dynamics. These results provide a quantitative basis for predictive understanding of cell growth-cell cycle relationships.