**4. Conclusions**

We investigated the ultrafast fluorescence decay dynamics in CPs and the aptamer-based 6-FAM/TAMRA complex. In this FRET system, the conformational change by K<sup>+</sup> ions promoted the sequential energy transfer from CPs, through 6-FAM, to TAMRA, as well as the fundamental one-step FRET due to the complexation. To understand the energy migration mechanisms within the system, we phenomenologically analyzed and modelled in terms of the exciton population. Also, we experimentally observed the evidence of two-step FRET and the role of three fluorophores thorough the time-resolved spectroscopic technique. As we expected, the presence of the two-step FRET process due to the presence of the K<sup>+</sup> ion was identified by the fluorescence enhancement (4 folded) and

the change in the decay curvature. In particular, we found the role of the transition of 6-FAM as an intermediator as well as the energy receiver during the energy transfer process. To distinguish the individual energy transfer step, we also calculated the energy transfer efficiency by the rate equation. Our transfer efficiency calculation, relevant only to total energy variation, minimizes the overestimation due to the theoretical FRET rate calculus. Consequently, a steady energy transfer efficiency (230%) was observed within the period of radiative decay time.

**Author Contributions:** Conceptualization, J.-E.J. and H.Y.W.; Data curation, I.K. and J.-E.J.; Formal analysis, I.K. and K.K.; Funding acquisition, K.K.; Investigation, I.K., J.-E.J., W.L. and S.P.; Methodology, J.-E.J. and H.Y.W.; Project administration, K.K.; Resources, J.-E.J. and H.Y.W.; Supervision, H.Y.W. and K.K.; Visualization, I.K. and K.K.; Writing—original draft, I.K.; Writing—review and editing, H.K., Y.-D.J. and K.K.

**Funding:** This research was supported by a two-year research gran<sup>t</sup> from Pusan National University.

**Conflicts of Interest:** The authors declare no conflict of interest.
