To explore the functional dynamics underlying our data, we compared likelihoods of several kinetic models using hidden Markov modeling (HMM) (Bronson et al., 2009; Nicolai and Sachs, 2013) (Figure 3E; Table 1). Models were globally optimized for smFRET time series from all molecules and fcAMP concentrations and ranked according to their Akaike information criterion (AIC) (Akaike, 1974) (Figure 3F). Consistent with dwell time distributions discussed above, models with two unbound (U1, U2) and two bound (B1, B2) states performed better than models with fewer states, whereas adding additional unbound and bound states did not improve the likelihood. Remarkably, all of the models with two bound states converged to a similar set of rate constants governing an initial binding step followed by a subsequent first order transition (Table 1). The most direct interpretation of this finding is that the CNBD undergoes a reversible conformational change between distinct cAMP-bound conformations. Importantly, simulated data from such a model reproduced the experimentally observed dwell time distributions (Figure 3G).
Table 1. Kinetic model rate constants. Optimized rate constants (s-1 or M-1s-1) for models shown in Figure 3E. U* and B* denote unbound and bound states, respectively.
DOI: http://dx.doi.org/10.7554/eLife.20797.013
Model U1→ B1 B1→ U1 B1→B2 B2→B1 U1→U2 U2→U1 U1→B2 B2→U1
1 1.3 × 105 0.34 - - - - - -
2 1.4 × 105 0.91 0.52 0.31 - - - -
3 1.3 × 105 0.98 0.49 0.23 - - 0.10 × 105 0.04
4 2.3 × 105 0.95 0.51 0.31 0.04 0.15 - -
5 2.2 × 105 1.00 0.49 0.25 0.04 0.15 0.14 × 105 0.03
6 2.4 × 105 1.00 0.48 0.27 0.01 0.04 - -
7 2.8 × 105 1.11 0.85 0.56 0.17 0.55 - -
Model U2→B2 B2→U2 U2→U3 U3→U2 B2→B3 B3→B2
6 0.24 × 105 0.02 - - - -
7 - - 0.02 0.07 0.03 0.08