I. Conformational Fluctuation Mediated Protein Function

Many Proteins are structurally flexible spanning a range of motions from picoseconds to seconds. Conformational changes in proteins are related to a variety of biological functions, such as signal transduction, signal cascading, or enzymatic activity. Recently, researchers had discovered that protein matrix can adapt to preserve quantum coherence of its reaction center induced by optical excitation. It is interesting to note that some proteins even employ conformational fluctuations to improve chemical reactivity. Here we like to show that conformational fluctuations of signal transduction proteins, such as rhodopsin and fluorescent protein, can guide the energy landscape evolution and regulate function of the proteins.

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FIG.1: (Left) Schematic showing the open quantum system of single-molecule KFP1. (Right) Energy-landscape model of KFP1. The forward transition M1 onsets after absorption of a green photon to reach the transient excited state S1(trans) of the trans-chromophore. After overcoming an enrgy barrier at S1(trans)/S0(cis), it becomes a bright fluorophore in a cis configuration. The reverse transition M2 is from the cis to the trans configuration. The irreversible photobleaching of the chromophore to the dark state is described by M3.

We developed a stochastic dynamic theory and applied the formalism to a real biomolecular system KFP1. KFP1 is a photoactivated fluorescent protein, which is photoswitchable between a fluorescent on- and off-state along the reactive coordinate with the chromophores in a cis- and trans-configuration, respectively. A hydrogen bonding formed between Glu215 and the N-H proton of the chromophore [see Fig. 1(a)] plays an important role in regulating the photon-emitting process of the chromophore. We model KFP1 with three components: a reservoir, a fluorescent quantum system, and a triplet state, as illustrated in Fig. 1(b). The optically excited active center was modeled as a two-level quantum system. The fluctuating protein matrix perturbs the intersection of the excited state of the trans-chromophore and the electronic ground state of the cis-chromophore, causing a variation in the population of the cis chromophores.

The inset figure in Fig. 2 is an experimental observation on an ensemble of KFP1 molecules. We irradiated the sample continuously at 532 nm and superposed the excitation with a periodically pulsed light at 473 nm. The fluorescence light was periodically reduced to the level of the off-state by the pulsed 473 nm light; this clearly revealed the photoswitching functionality of the KFP1 ensemble.

FIG. 2: Experimental arrangement of the single-molecule apparatus. Inset shows the photoactivated switching behavior of a film of KFP1, which was irradiated continuously at 532 nm and superposed the excitation with a periodically pulsed light at 473 nm.

For a single-molecule measurement, we first irradiated the sample with 473 nm light with an appropriate exposure in order to convert the KFP1 molecules to their fluorescent off-state. Afterwards, we recorded the photon trajectories of each of the KFP1 molecules in parallel. Two typical traces shown in Fig. 3(a) revealed a difference in overcoming the barriers between two basins on the energy landscape. For stronger trapping at each site between two energy basins on an energy landscape, KFP1 in the off state is more difficult to reach the on-state, therefore yields longer optical emission duration than that with smaller trapping strength. By converting the measured fluorescent signal traces from the time domain to the trapping strength n, we obtained a bimodal profile as shown in Fig. 3(b), indicating that in KFP1 molecules the mean number of traps between two energy basins falls into two subsets.

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FIG. 3: (Left) Two measured fluorescent photon fluctuation traces from each single-molecule KFP1 molecule. (Right) A distribution of the mean trapping strength was deduced from the KFP1 data set.

To gain deeper insight into the energy-landscape dynamics, we proposed a stochastic hopping model [see Fig. 4(a)]. The simulation based on this model can reproduce the observed bimodal profile, implying that the model has captured the essential physics of dynamic regulation of conformational fluctuations on the energy landscape of KFP1.

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FIG. 4: (Left) Schematic showing a model of the stochastic hopping between two basins on the energy landscape of an active center along the reactive coordinate. (Right) The calculated distribution of the mean trapping strength.

From this investigation, we concluded that the optical brightness of KFP1 is controlled by the fluctuation of its protein matrix via dynamic adjusting the number of hoppings on the energy landscape. Recently, Kruger and co-workers also showed that the intrinsic multifunctionality of plant light harvesting complexes can be controlled by slow conformational fluctuations. Our theoretical and experimental study verified that the slow fluctuations of a fluorescent protein can modulate its optical emission property by regulating the energy landscape evolution of the protein-embedded pigment.

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II. Decipher Catalysis-associated Conformational Changes of Adenylate Kinase

Single-molecule optical characterization techniques are versatile tools to unravel structural and dynamical information of the molecule under study. However, the information is often hidden in the photon trajectories. We developed a data analysis procedure to retrieve the embedded information. To verify the effectiveness of the method, we conducted an experimental study on single-molecule adenylate kinase (AK) and then retrieved the information from the photon trajectories. Higher-order correlated motion and dynamic cooperativity of AK were revealed.

A. Background of AK1

AK is a phosphotransferase enzyme that catalyzes the interconversion of adenine nucleotides (2ADP<-->AMP+ATP), and plays an important role in cellular energy homeostasis. Within the AK family there are several conserved regions, including the ATP-binding domains. In Escherichia coli, AK was complexed with diadenosine pentaphosphate, Mg2+, and 4 coordinated water molecules. ATP adenine and ribose moieties are loosely bound to AK. The phosphates in ATP are strongly bound to surrounding residues. Mg2+, coordination waters, and surrounding charged residues of AK maintain the geometry and distances of the AMP α-phosphate and ATP β- and γ-phosphates to effectively catalyze a phosphoryl group from ATP to AMP. The schematic is summarized in the following drawing:

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FIG. 1: Schematic diagram showing the dynamical processes of AK1 in the (left) substrate-free and (right) substrate-bound states. The red-colored dots indicate the labeling sites in ATPlid and core of AK1 with Alexa532 chromophore.

AK1 helps decoding the cellular information by catalyzing nucleotide exchange in the metabolic sensors. Knock out of AK1 disrupts the synchrony between inorganic phosphate and turnover at ATP-consuming sites and ATP-synthesis sites. This can reduce the energetic signal communication in the post-ischemic heart and precipitates inadequate coronary reflow following ischemia-reperfusion. Thus, understanding the dynamics of AK1 in the substrate-bound and substrate-free states at the single-molecule level is an important issue.

B. Research strategy

To reveal the underlying principle of AK1 at the single-molecule level, we implemented a research strategy depicted by the following flow chart:

FIG. 2: (Top) Research strategy used to investigate single-molecule dynamics of AK1. (Bottom) 3D models of AK1. (Left) Substrate-free AK1 in the open state is shown with different colors highlighting the CORE (orange), AMPbd (light green), and ATPlid (light blue) domains of AK1. C26 and C188 (the yellow-color helical segments) indicate the positions of the two cysteine residues to be tagged with Alexa-532 fluorophores. The 3D structure of substrate-bound AK1 in the close state is shown on the right side.

In short, we label the ATPlid and core of AK1 with Alexa532 (see Fig. 2b). By using the self-quench effect, we can convert the distance fluctuation between the two labeled amino residues in AK1 to fluorescent intensity fluctuation. Figure 3 shows the experimental arrangement, which allows us to acquire fluorescent photon fluctuation traces from single-molecule AK1 without the limitation of photobleaching. A short segment of fluorescent signal emitted from AK1 is presented in Figure 3b. The optical background is indicated by the dash line with a standard deviation highlighted by the light blue color. The red solid line denotes the fluorescent signal from AK1 and the observation time windows for each AK1 molecules are marked with pink color.

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FIG. 3: The experimental arrangement for single-molecule optical measurement. (Left) A microfluidic cell controls the flow of AK1 molecules and substrates from two separate channels into a confocal region of a tightly focused laser beam. The fluorescent photon fluctuation signal containing the information of single-molecule conformational dynamics is detected with single-photon avalanche diode. (Right) A recorded short segment fluorescent signal trace. The optical background is
marked by the dash line with the standard deviation highlighted in light blue color. The red solid line denotes the fluorescent signal from AK1 and the observation time windows for each AK1 molecules are emphasized with pink color.

C. Photon fluctuations via homoFRET reflect conformational changes of a protein

We first verify homoFRET to be sensitive enough to reveal conformational changes of a protein. Three AK1 species were prepared for this purpose. Figure 4a presents the fluorescent signals emitted from doubly tagged native AK1 (red trace in the top panel), singly tagged AK1 (blue curve, middle panel) and denatured doubly-tagged species (green trace, bottom pannel). The corresponding distributions of photon emission rate are shown in Figure 4b. Even though the doubly-tagged AK1 possesses two fluorophores, the brightness per AK1 is weaker than that of singly-tagged species, indicating a strong self-quenching effect in the doubly-tagged AK1. For comparison, we used guanidine hydrochloride (Gdn-HCl) to denature the doubly-tagged AK1. The resulting unfolded structure generates even higher fluorescent intensity owing to a much weaker self-quenching effect in the unfolded structure. The comparison strongly supports that the measured photon fluctuations with homoFRET originate from the changes of interprobe distance in AK1. From photon counting histogram (PCH) analysis, we can determine the number of doubly-tagged AK1 in the excitation volume to be 0.86, 0.98, and 1.97 for the doubly tagged AK1 species in substrate-free, ADP-bound, and the denatured form, respectively.

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D. ADP Binding reduces the conformational heterogeneity and improves the thermal stability of AK1

The doubly tagged substrate-free AK1 has a broader PCH than that from ADP-bound species. The Mandel's Q-parameter (i.e., the variance of photon fluctuations) for the substrate-free AK1 is 2.87, whereas the ADP-bound species exhibits a smaller Q-parameter of 1.48, suggesting that ADP binding reduces the structural heterogeneity of AK1. The weaker photon fluctuation as indicated by lower g(1)(0) in ADP-bound AK1 (see Fig. 3(c)) indicates that the thermal stability of the substrate-binding domain is improved by ADP binding. For comparison, the denatured species generates higher fluorescence due to weaker self-quenching and a larger Q-parameter of 3.24, indicative of a higher degree of structural heterogeneity than that in the native species.

E. Single-molecule AK1 is in a nonequilibrium steady state (NESS)

Note that a perfectly coherent source can exhibit coherence to all orders. However, correlations higher than second order are often difficult to measure because the vast amounts of data require extensive data analysis resources. In the literature, correlations up to third order have been measured for exciton-polaritons (T. Horikiri et al., Phys. Rev. B 81, 033307 (2010)) and to fourth order for photons (M. Assmann, F. Veit, M. Bayer, M. van der Poel, J. M. Hvam, Science 325, 297 (2009)).

In the case of AK1. we labeled the ATPlid (Ra) and core (Rc) with Alexa532 fluorophores. It is expected that if ordered motions among different parts of AK1 do exist, we anticipate a high-order correlation in photon uctuation traces. On the other hand, if the ATPlid and AMPbd domains move independently of each other, both the ATPlid-first-closing and the AMPbd-first-closing pathways are equally probable and a vanishing high-order correlation difference shall be obtained.. In Fig. 5a, we found del g(2)(t1,t2)=g(2)(t1,t2)-g(2)(t2,t1) for singly tagged AK1 to be essentially zero, indicating that photon fluctuations from single fluorophore possess high degree of time-reversal symmetry. However, when the conformational changes of AK1 are monitored correctly with doubly tagged homoFRET, the resulting del g(2)(t1, t2) shown in 5b is nonvanishing with the main peak occurring at 8 ms. The result suggests single-molecule AK1 to be in a NESS.

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FIG. 5: The difference of two-time correlation functions calculated using the fluorescent photon fluctuation traces from (Left) singly tagged AK1, (Right) doubly tagged AK1.

E. Conformational transition dynamics of AK1

As mentioned above, the structural and dynamical information of the molecule is hidden in the resulting photon fluctuation traces. The problem is how to retrieve the information. We can extract the catalysis-associated conformational switching of AK1 with hidden Markov model (HMM) from the photon fluctuation traces. Fig. 6a shows one of the HMM retrieval results from ligand-free AK1. The photon fluctuation traces can be viewed to originate from transitions among the open (o), intermediate (mid), and closed (c) states.

To further decipher the dynamics embedded in the photon trajectories, we implement the three-state model into a hidden Markov chain. Figs. 6b and 6c summarizes the results of the occurrence of transition for ligand-free AK1 (Fig. 6b), and for ADP-bound AK1 (Fig. 6c), which reveal that ADP binding suppresses the direct open-to-close transitions and promotes the mid-mediated pathway.

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FIG. 6: Results from HMM. (a) A photon fluctuation trace (red solid curve) and the HMM-labeling output (blue dashed line), The occurrences of transitions in (b) substrate-free AK1, and (c) in ADP-bound AK1 deduced from the measured photon fluctuation traces.

In this study, we investigated the catalysis-associated conformational motions of AK1 by labeling the molecule with two identical fluorophores, one near the substrate binding site and the other at the surface of the core domain. By invoking the self-quenching effect of two like fluorophores, we can probe into the large-scale conformational dynamics of AK1 with high spatial sensitivity. We investigated the influences of Mg2+ and ADP on AK1 and found that Mg2+ binding increases the structural heterogeneity of AK1, whereas ADP binding reduces the structural heterogeneity and suppresses the conformational fluctuations of the substrate-binding domain. Our HMM analysis further shows that the photon fluctuation traces are generated by transitions among three conformational states. ADP binding suppresses the direct open-to-close transitions and promotes the intermediate state-mediated catalytic pathway. The two-time correlation functions of photon fluctuation traces from AK1 reveal asymmetry in time permutation, indicating single-molecule AK1 to be in a NESS. This finding can serve as an important foundation to deepen our insight into the molecular mechanisms of cellular biochemistry.

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