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 x 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.