Fig 1.
Overview of in vitro firefly Luciferase complementation assay (FLCA) system.
(A) With interaction of a protein pair (shown here, protein A and B), the N and C domains of luciferase (NFLuc and CFLuc, respectively) reconstitute the active site of the enzyme. The amount of the reconstituted enzyme (NC complex) is thought to correlate with the affinities of the protein pair. (B) Upon the addition of the substrates, LH2 and ATP, catalysis occurs in a two step process. The enzyme first adenylate LH2 with ATP, forming the intermediate LH2-AMP. The intermediate is then oxidized to form L-oxyluciferin (L-oxy) during the light emission reaction. Alternatively, the intermediate is oxidized to form dehydroluciferyl-AMP (L-AMP) without emitting light (dark reaction). Both products inhibit luciferase activity competitively. NFLuc has low luciferase-activity on its own [12, 13].
Fig 2.
Luminescence kinetics of full length luciferase (black) and of the FLCA (red) are different.
Changes in the relative luminescence of full length luciferase and of the FLCA in vitro were monitored every 0.2 s and 0.1 s, respectively, for 120 s in a 96-well plates. Detected luminescence was normalized so that the maximum luminescence in each assay is 1. Notice that the kinetics of 150 nM full length firefly luciferase has a sharp peak within 1 s followed by quick decay. On the other hand, the kinetics of 50 nM NFLuc and 50 nM CFLuc has a more delayed peak and slower decay.
Fig 3.
Curve fit of the in vitro luminesence kinetics of the N domain of firefly luciferase.
Data originally published in [12] was digitized using Plot Digitizer [61]. Digitized data was curve fit to estimate parameters unavailable from previously published papers. (A) The addition of 3.7 nM LH2-AMP to 1 μM of the N domain shows a sharp peak. This curve fit provided an estimation of the adenylation forward and reverse rates. (B) When a substrate solution (300 μM LH2, 10 mM ATP) is added to 1 μM of the N domain, the luminescence kinetics have a slow rise and no peak. This curve fit provided more optimized values for the available NFLuc alone binding and catalysis rates in the FLCA.
Fig 4.
Diagram describing the complete set of reactions used to develop a mathematical model for the in vitro FLCA.
The interaction of the protein pair (orange arrows) fused to NFLuc (grey panels) and CFLuc (not shown) forms the NC complex (white panels), which reconstitutes enzymatic activity. The reconstituted activity produces luminescence by the adenylation and oxidation of LH2. NFLuc contains all known substrate binding residues and can catalyze the reactions on its own [12, 13], and some luminescence can be produced without the interaction of the protein pair. The mathematical model takes into account enzymatic reaction of NFLuc alone and NC complex. The equations describing the reactions of NFLuc mirror that of the NC complex. “x” refers to variable number in the model for each species, and “c” refers to the reaction rate parameters. N: NFLuc. NC: NC complex. A: ATP. L: LH2. NC-A: NC bound to ATP. NC-L: NC bound to LH2. NC-LA: NC bound to LH2 and ATP. NC-I: NC bound to LH2-AMP. I: Free LH2-AMP. NC-LOXY: NC bound to L-oxy. NC-LAMP: NC bound to L-AMP. LOXY: Free L-oxy. LAMP: Free L-AMP. LIGHT: Observed luminescence. N-A: NFLuc bound to ATP. N-L: NFLuc bound to LH2. N-LA: NFLuc to LH2 and ATP. N-I: NFLuc bound to LH2-AMP. N-LOXY: NFLuc bound to L-oxy. N-LAMP: NFLuc bound to L-AMP.
Table 1.
Parameters Derived from the Literature.
Fig 5.
Model simulation (red) of the luminescence kinetics of p53-NFLuc and mdm2-CFLuc using in vitro FLCA compared to the data (black) after optimization.
The values for the parameters in the mathematical model were estimated in three steps. First, parameter values were taken from the previously published literature when able, or calculated from previous data (Table 1). Second, additional parameter values were estimated by curve fitting the model to the luminescence kinetics of NFLuc alone [12] (Fig 3). Finally, the binding and catalysis rates of the NC complex were optimized by curve fitting (red) to the luminescence kinetics of 50 nM each of p53-NFLuc and mdm2-CFLuc obtained in this study (black).
Table 2.
Comparison of Experimental and Estimated Values.
Fig 6.
Nutlin-3 IC-50 curve (red), simulated using the in vitro FLCA model, agrees with the experimental data (black).
Experimental RLU values of the FLCA with 100 nM each of p53-NFLuc and mdm2-CFLuc at 0.2 s (black) are compared with simulated RLU values (red) across a range of nutlin-3 concentrations [4]. The calculated IC-50 of the experimental data is 390 nM, while the simulation IC-50 is 440 nM.
Fig 7.
The model predicts a linear relationship between maximum RLU and concentration of the protein pair.
Maximum RLU values obtained experimentally (black) are compared with simulated RLU values for (A) NFLuc-FRB, CFLuc-FKBP, and equimolar rapamycin (red) and (B) NFLuc-p53 and CFLuc-mdm2 (blue). The linear trendlines were calculated using nonlinear regression. The experimental data was obtained from [4].
Fig 8.
The model suggests that the delayed peak of the FLCA is due to dissociation of the protein pair, while the slow decay is due to the lower adenylation rate and higher affinity toward LH2-AMP.
(A) Luminesence kinetics of FLCAs and full length luciferase was predicted by the model. The protein pair with Kd = 10 pM (blue) shows a faster peak and decay, compared with the protein pair with Kd = 212 nM (red). (B) Luminesence kinetics of FLCA, hypothetical split luciferase, and full length was predicted by the model. FLCA with the protein pair Kd of 212 nM (red) compared with a hypothetical split luciferase (blue) with the same Kd. The hypothetical split luciferase has the same adenylation rate and affinity to LH2-AMP as full length luciferase. Enzyme concentration used for these simulations was 50 nM.
Fig 9.
Directly comparing the RLU obtained by the FLCA may cause misunderstandings about their affinities.
(A) Predicted relationship between changes of Kd (from 2.5 nM to 3 μM) for a protein pair and the RLUs detected in the FLCA. The model predicts an exponential relationship between changes of Kd and maximum RLU. (B) Predicted relationship between changes of Kd (from 10 nM to 50 nM) for a protein pair and the RLUs detected in the FLCA. Notice the RLU detected at 10 nM (orange grid) is only 1.45 times higher that that at 50 nM (grey grid). Enzyme concentration used for these simulations was 50 nM.