The enzyme aspartate transcarbamoylase (ATCase, EC 2.1.3.2 of Escherichia coli), which catalyzes the committed step of pyrimidine biosynthesis, is allosterically regulated by all four ribonucleoside triphosphates (NTPs) in a nonlinear manner. Here, we dissect this regulation using the recently developed approach of random sampling-high-dimensional model representation (RS-HDMR). ATCase activity was measured in vitro at 300 random NTP concentration combinations, each involving (consistent with in vivo conditions) all four NTPs being present. These data were then used to derive a RS-HDMR model of ATCase activity over the full four-dimensional NTP space. The model accounted for 90% of the variance in the experimental data. Its main elements were positive ATCase regulation by ATP and negative by CTP, with the negative effects of CTP dominating the positive ones of ATP when both regulators were abundant (i.e., a negative cooperative effect of ATP × CTP). Strong sensitivity to both ATP and CTP concentrations occurred in their physiological concentration ranges. UTP had only a slight effect, and GTP had almost none. These findings support a predominant role of CTP and ATP in ATCase regulation. The general approach provides a new paradigm for dissecting multifactorial regulation of biological molecules and processes.Many biochemical processes are sensitive to multiple signals, which may interact in a nonlinear manner. While such sensitivity often arises from complex reaction networks, even single enzymes can respond to multiple regulators. One such enzyme is aspartate transcarbamoylase (ATCase) (1), a complex in which activity and regulation are on distinct polypeptide chains (2). ATCase is composed of 12 polypeptides (6 c chains and 6 r chains), organized as two catalytic trimers bound to three regulatory dimers (3,4). It catalyzes the first committed step in the metabolic pathway for de novo pyrimidine biosynthesis: the condensation of aspartate with carbamoyl phosphate to yield carbamoyl aspartate. Binding of substrate to the enzyme is ordered, with carbamoyl phosphate binding before aspartate (5,6) and inducing local conformational changes leading to the formation of a viable aspartate-binding site (7). † Funding was provided by the NSF DDDAS program (CNS-0549181), the EPA STAR grant program, the DOD STTR program, the NSF CAREER award (MCB-0643859), the Beckman Foundation, the American Heart Association (0635188N), the NIH Center for Systems Biology at Princeton University (5 P50 GM071508), and NIH Grant GM26237. Both genetic and biochemical evidence support CTP, a primary end product of the pathway, being the key negative regulator of ATCase (a classical example of feedback inhibition) (8).Biochemical evidence also demonstrates that ATP substantially enhances enzyme activity (9), with this regulation serving to balance pyrimidine and purine concentrations. Crystal structures of the ATCase complex have been solved with ATP or CTP bound and confirm that ATP and CTP bind to and induce conformational changes in...