The present paper applies the experimentally driven, statistical modeling approach, RS–HDMR, to investigate regulation of the well-studied enzyme ATCase in response to varying concentrations of its nucleotide regulators ATP, CTP, GTP, and UTP (at fixed substrate concentrations).
A defining characteristic of RS–HDMR is breaking down a complex function of multiple variables (in this case, ATCase activity as a function of four different NTP regulators) into a sum of generally nonlinear functions of fewer variables. A second-order RS–HDMR model, comprising the sums of functions of single NTPs and pairs of NTPs, described the full four-dimension NTP input space well, as indicated by its capturing of 90% of the variance in the ATCase activity data.
The most significant component functions of the RS–HDMR model reflect the first-order effects of ATP and CTP (parts A and B of ). Notably, these modeled first-order effects deviate markedly from the effects of ATP and CTP when they are added as single nucleotides in isolation. This reflects the fact that the biochemical effects of ATP and CTP in isolation are quite different from those obtained in the physiological situation of all four nucleotides being present.
Focusing on the circles in , it is evident that addition of ATP alone always results in ATCase activity above the mean activity level found in the presence of all four nucleotides (f0
). In contrast, when other nucleotides are present (–), substantial quantities of ATP are required to reach the mean ATCase activity. This result is consistent with previous literature: ATP activates ATCase, while the other NTPs collectively inhibit it. More interesting is the change in the shape of the ATP response curve in the two cases. When ATP is added in isolation, its effects saturate at ~1 mM. The typical cellular concentration of ATP is ~6 mM. Thus, study of ATP in isolation would suggest that ATP is always saturating and, accordingly, not necessarily a physiologically relevant regulator of ATCase. In contrast, the first-order RS–HDMR function of ATP has a different shape, where the effects of ATP are strongest in its physiological range of 1–10 mM (33
). This difference can be biochemically explained by higher levels of ATP being needed to out-compete the other nucleotides (especially CTP) to drive ATCase into its active R state.
The result with CTP is similar to that with ATP (except with the direction of the effects reversed). Most importantly, whereas the effects of CTP alone nearly saturate at 0.1 mM (well below its reported cellular concentration of 0.5 mM) (35
), in the presence of the four other nucleotides, there is significant sensitivity to CTP in its physiological range.
For UTP, the single NTP data and the HDMR model closely agree, both showing a weak inhibitory effect, consistent with the presence of a low-affinity UTP-binding site that, when filled, favors the T conformation of the enzyme. For GTP, while the single nucleotide data show an inhibitory effect somewhat stronger than that seen for UTP, the HDMR model shows no effect.
Beyond the first-order component functions of ATP and CTP (f1 and f2), the next most significant function was f12([ATP],[CTP]). This indicates the dominant role of ATP and CTP in controlling ATCase activity. While the shape of f12 is complex, the most striking trend is for the ATCase-activity-enhancing effects of ATP to be strongest when CTP is low and least when CTP is high (i.e., an ability of CTP to overcome ATP to turn off ATCase). The other significant second-order effects involved interactions of ATP with UTP and GTP. While weak, the shape of the ATP–UTP interaction is consistent with an ability of ATP to trump UTP to turn on the enzyme. In contrast, the weak ATP–GTP interaction is consistent with an ability of GTP to substitute for ATP to activate the enzyme when ATP is low; when a substantial amount of ATP is present, the effect of GTP is negligible.
Interestingly, the previously reported synergistic interaction of CTP with UTP (20
) was not found in the present study. This may reflect the current experimental design: some CTP was present in all of the NTP combinations. If only a low concentration of CTP is needed to sensitize ATCase to the inhibitory effects of UTP, then adequate CTP may have been present in all cases, precluding identifying a cooperative effect of the two nucleotides. Whatever the cause of the failure to identify a cooperative effect of UTP and CTP in the present work, the absence of such an effect leads to an important conclusion: such a cooperative interaction, while a characteristic of the interaction of the enzyme with isolated nucleotides, is unlikely to be physiologically significant, because it (unlike the powerful first-order effects of ATP and CTP and negative cooperative effect of ATP × CTP) does not occur at physiologically relevant NTP concentrations.
With respect to such physiological interpretation of the present results, an important limitation of the present work is the use of fixed substrate concentrations. High aspartate levels (>10 mM) can drive ATCase into the R state even in the presence of high CTP and no ATP (9
). Accordingly, although the tested aspartate concentration was physiological, elevations in intracellular aspartate could presumably override the NTP-mediated regulation studied here.
Typical carbamoyl phosphate levels inside E. coli
are substantially below the concentration tested here. Despite the relatively low Km
of ATCase for carbamoyl phosphate of ~200 μ
), they may be subsaturating. Thus, cellular flux through ATCase may be sensitive to the intracellular concentration of carbamoyl phosphate. This concentration reflects not only the activity of carbamoyl phosphate synthetase relative to ATCase but also the rate of consumption of carbamoyl phosphate by the arginine biosynthetic pathway (via ornithine transcarbamoylase). Thus, the present results are inadequate to fully capture physiological regulation of ATCase flux. Nevertheless, partitioning of carbamoyl phosphate consumption between the pyrimidine and arginine pathways will substantially depend upon the rate of the ATCase steps occurring after carbamoyl phosphate binding. Accordingly, the present results regarding regulation of these steps by mixtures of all four NTPs provide a useful addition to studies investigating the effects of single or pairs of NTPs in isolation, as well as to efforts to model the overall activity of the pyrimidine pathway in E. coli
Beyond providing a more refined understanding of ATCase regulation, the present research also sheds light on the strengths and weaknesses of HDMR as a tool for investigating biochemical systems. A defining attribute of RS–HDMR is its statistical nature: comprehensive estimates of biochemical activity are obtained without regard to the underlying chemical mechanism. RS–HDMR thus provides an unbiased framework for confirming major principles (e.g., the dominant role of ATP and CTP in controlling ATCase activity) and dissociating them from ancillary observations (e.g., the synergistic effects of CTP and UTP in studies of the two nucleotides in isolation). It also has the potential to lead to unexpected discoveries (e.g., the substantially stronger sensitivity of ATCase activity to physiologically relevant concentrations of ATP and CTP than would have been anticipated from studies of the single nucleotides in isolation). The model-independent nature of RS–HDMR, on the other hand, means that the extracted input–output correlations are not an unambiguous representation of the underlying biophysical mechanism, although the latter can often be deduced by integration of RS–HDMR with biochemical insights and additional targeted experiments.
Accordingly, although no substitute for mechanistic modeling, RS–HDMR has value for studying other enzymes subject to regulation by numerous effectors. In addition, it may prove useful in dissecting other biochemical input–output relationships, both in vitro and in vivo. Particularly interesting cases involve multiple inputs whose effects are nonlinear and hard to capture via classical mechanistic models. Selected examples include sensitivity of protein folding to different environmental parameters (pH, salt concentration, denaturant concentration, and temperature), cellular transcriptional outputs to combinations of receptor ligands activating different signal transduction cascades, bioreactor yield to feedstock composition, and safety and efficacy of pharmaceutical mixtures to the concentrations of their component-active agents. In certain cases, such as bioreactor yields and pharmaceutical safety and efficacy, the resulting model may be valuable for enabling subsequent optimization of inputs to maximize the desired output.