Article pubs.acs.org/JPCB
Two-Dimensional Fluorescence Lifetime Correlation Spectroscopy. 1. Principle Kunihiko Ishii and Tahei Tahara* Molecular Spectroscopy Laboratory, RIKEN, 2-1 Hirosawa, Wako , Saitama 351-0198, Japan S Supporting Information *
ABSTRACT: Fluorescence correlation spectroscopy (FCS) is a unique tool for investigating microsecond molecular dynamics of complex molecules in equilibrium. However, application of FCS in the study of molecular dynamics has been limited, owing to the complexity in the extraction of physically meaningful information. In this work, we develop a new method that combines FCS and time-correlated single photon counting (TCPSC) to extract unambiguous information about equilibrium dynamics of complex molecular systems. In this method, which we name two-dimensional fluorescence lifetime correlation spectroscopy (2D FLCS), we analyze the correlation of the fluorescence photon pairs, referring to the fluorescence lifetime. We first obtain the correlations of the photon pairs with respect to the excitation−emission delay times in the form of a two-dimensional (2D) map. Then, the 2D map is converted to the correlations between different species that have distinct fluorescence lifetimes using inverse Laplace transformation. This 2D FLCS is capable of visualizing the equilibration dynamics of complex molecules with microsecond time resolution at the single-molecule level. We performed a kinetic Monte Carlo simulation of a TCPSC-FCS experiment as a proof-of-principle example. The result clearly shows the validity of the proposed method and its high potential in analyzing the photon data of dynamic systems.
1. INTRODUCTION Many chemical changes take place spontaneously in the electronic ground state under equilibrium conditions. For example, we can readily think of many unimolecular isomerizations, associations/dissociations of molecular complexes, and conformational fluctuations of biopolymers that occur under equilibrium conditions. From the viewpoint of the potential energy surface, these chemical changes are characterized by the existence of multiple substates having thermodynamically similar energies. To study the dynamics of the conversion among these metastable states, we need to use a different method from ordinary time-resolved experiments because such processes are not synchronously initiated by an external trigger such as photoexcitation. Chemical exchange spectroscopy (CES), realized in twodimensional (2D) NMR1 as well as 2D IR,2,3 is a powerful tool for investigating the equilibrium dynamics. In 2D CES (Figure 1), the first interaction “labels” a group of molecules having the same spectroscopic property, that is, the chemical shift in 2D NMR and the vibrational frequency in 2D IR, by exciting their quantum state (selection). Subsequently, the second interaction after ΔT detects the change of the spectroscopic property of the labeled molecules (detection). By scanning the selection and detection frequencies, one can visualize equilibrium dynamics taking place during ΔT as cross peaks in 2D maps (Figure 1b). By selecting a specific substate with irradiation of the pulse, this method enables us to examine the equilibrium dynamics of an ensemble of molecules by a pump−probe type experimental scheme. © 2013 American Chemical Society
An alternative way, and probably a more general way, to study the equilibrium dynamics is single-molecule spectroscopy, which picks a single molecule and tracks the change of its spectroscopic property. In fact, the experiments analogous to 2D CES are possible with single-molecule spectroscopy, by measuring the spectroscopic property of a single molecule twice with the time interval of ΔT many times. Hoffmann et al. recently realized this idea by observing FRET (Förster resonance energy transfer) signals from freely diffusing single molecules in solution.4 In their method, each single molecule is recognized as a burst of photons in the measurements (Figure 2a), and the FRET efficiency E is evaluated for each molecule using the following equation:
E=
IA ID + IA
(1)
Here, ID and IA are the fluorescence intensity from the FRET donor and acceptor, respectively. Then, the information about the change of E after ΔT is summed up in the form of a 2D FRET efficiency map, where the vertical and horizontal axes correspond to the FRET efficiency at two time points separated with ΔT (see Figure 1). Their method, which they call recurrence analysis of single particles (RASP), offers a versatile approach to study equilibrium conformational changes of biological macromolecules through single-molecule spectroscopy. Nevertheless, the time resolution is limited to as low as ∼50 Received: July 11, 2013 Published: August 26, 2013 11414
dx.doi.org/10.1021/jp406861u | J. Phys. Chem. B 2013, 117, 11414−11422
The Journal of Physical Chemistry B
Article
μs because of the low efficiency of the photon detection, which is a general problem of single-molecule FRET experiments. In this work, we propose a new scheme of 2D spectroscopy for investigating equilibrium dynamics at the single-molecule level. We introduce two new features. First, instead of the strict burstwise single-molecule measurement, we employ the fluorescence correlation spectroscopy (FCS).5 FCS is a quasisingle-molecule measurement based on the fluctuation measurement of the fluorescence intensity (Figure 2b). FCS is known to provide high time resolution of
