Revealing Multiple Pathways in T4 Lysozyme Substep Conformational

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Revealing Multiple Pathways in T4 Lysozyme Sub-Step Conformational Motions by Single-Molecule Enzymology and Modeling Maolin Lu, and H. Peter Lu J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b03039 • Publication Date (Web): 20 Apr 2017 Downloaded from http://pubs.acs.org on April 25, 2017

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The Journal of Physical Chemistry

Revealing Multiple Pathways in T4 Lysozyme Sub-Step Conformational Motions by Single-Molecule Enzymology and Modeling Maolin Lu, H. Peter Lu* Department of Chemistry and Center for Photochemical Sciences, Bowling Green State University, Bowling Green, Ohio 43403, United States E-mail: [email protected] ABSTRACT: Enzyme conformational dynamics play crucial roles in catalytic functions. Obtaining molecular level insights into the conformational transition dynamics of enzyme-substrate complex from the inactive state to the active state is fundamental for understanding enzymatic function and dynamics. Here, we report our progress on the real-time conformational transition dynamics of T4 lysozyme under enzymatic reactions using single-molecule fluorescence resonance energy transfer. The time duration in forming the active enzyme-substrate complex state (ES*) show distinctive Poisson and Non-Poisson statistics, including exponential and non-exponential, convoluted Poisson distributions and Gaussian-like distributions. These complex dynamic behaviors of T4 lysozyme are in excellent agreement with a Markov dynamic simulation and a transition steps modeling. Specifically, we are able to obtain mechanistic understandings: 1) Transiting from enzyme (E) to ES*, T4 lysozyme hinge-bending conformational changes undergo multiple steps following multiple pathways. In the case of shortest pathway, this transition only requires one elementary transition or reaction step; 2) Sub-step conformational motions, associating with multiple nuclear coordinates and a common projected FRETsensitive nuclear coordinate, can give rise to multiple conformational intermediate states; 3) The consequence of the multiple pathways, intermediate states, and nuclear coordinates is the time bunching effect, i.e., time durations of conformational changes tend to bunch in a narrowly distributed time window. The physical picture of multiple intermediate states along with bunching effect suggests that the conformational dynamics of T4 lysozyme shows a complementary characteristic behavior of convoluted enzyme conformation selection and induced-fit dynamics driven by substrate-enzyme interactions.

1. INTRODUCTION According to the Michaelis–Menten mechanism, a typical enzymatic reaction process consists of substrate-enzyme non-specific binding (E + SES), substrate-enzyme complex formation (ESES*), chemical reaction (ES*EP), and product releasing (EPE + P), where E, S, and P represent enzyme, substrate, and product, respectively. In this process, the interplay between the conformational stability and flexibility is critical for enzymatic activity: stability is required for retaining native three-dimensional structures, and flexibility is necessary for allowing efficient substrate binding, complex formation, and product releasing. In terms of flexibility, it is generally recognized that conformational changes are essential for catalytic functions of many enzymes in defining enzymatic dynamics, energy landscape, reaction nuclear coordinates, and reaction pathways.1-14 To function, an enzyme adjusts its conformational flexibility from inactive state to a catalytically-active state ES*, the specific binding enzymesubstrate complex in which the reactive groups are

brought into close proximity in a position-favoring catalysis. Enzymes may adopt multiple intermediate states or transient states or reaction states in the microseconds to milliseconds timescale before reaching the catalytically-active state.5, 9-10, 15-17 In the ensembleaveraged studies, a set of experimental methods, such as X-ray crystallography,18 NMR relaxation dispersion,12, 19 and mass spectroscopy,14, 20 have been applied to identify intermediate states. In the single-molecule studies, singlemolecule fluorescence spectroscopy has served as an effective approach to obtain molecular level insights into protein/enzyme conformational transition dynamics.5, 9, 13, 21-24 The results of steady-state kinetic measurements, such as single-exponential decay of waiting time distribution or two-state Gaussian-like distribution of FRET efficiency, have suggested that many enzymes exhibit two major states (open/closed or on/off). In a dynamic equilibrium, the two states associate with two distinct grooving structures of enzyme, from which the enzyme can be envisioned as an open-close hinge with the active site locating between the two halves of the hinge. Furthermore, more sequential or parallel states in

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the dynamic non-equilibrium buried in a two-state model, have been reported on the basis of multipleexponential or non-exponential decay of the waiting time distributions.24-25 Those multiple-exponential or nonexponential behaviors have been attributed to fluctuating reaction rates with dynamic disorder in terms of catalytic or conformational dynamics.24-26 Correspondingly, different statistical modeling analyses have been applied to reveal the hidden events under those behaviors.16, 27-28 For example, the hidden Markov model has been reported to extract the sequence of hidden states from observables through the construction of probabilistic model parameters such as transition probability matrix, emission probability matrix and initiation probability matrix.29-32 By all possible approaches, although the complex hidden dynamics is still difficult to resolve, the complexity of multiple-state conformational dynamics can be better identified and characterized by single-molecule spectroscopic experiments and related model analysis. T4 lysozyme, a member of the lysozyme family produced by bacteriophage, has been extensively studied in both ensemble-average 33-35 and single-molecule measurements 7-8, 11, 16, 36-38 to reveal the catalytic reaction mechanism and characterize conformational dynamics. T4 lysozyme has two domains connected by an α-helix. The two domains undergo hinge-bending open-close conformational motions under an enzymatic reaction condition.34-35 T4 lysozyme catalyzes the hydrolysis of poly-saccharide chains in bacterial cell walls by attaching and binding to the cell walls and further degrading the cell.33 The enzyme specifically cleaves the glycosidic bonds connecting the repeating subunits of cell walls between N-acetylglucosamine (NAG) and N-acetylmuramic acid (NAM) that are substituted with peptide side chains.39 Previously, we have probed T4 lysozyme hinge-bending conformational motions by single-molecule FRET spectroscopy and imaging.16, 22, 40 Inhomogeneity of overall enzymatic reaction rate constants from molecule to molecule and a time bunching effect of conformational motion dynamics have been revealed by single-molecule spectroscopic results, molecular dynamics simulation, and a random walk model analysis.16, 22, 40 In addition, our above observations have been recently further confirmed by recently reported works using single-molecule electronic circuits to sense T4 lysozyme conformational motions through circuit conductance.11, 38, 41 Here, we report a new progress on our single-molecule spectroscopic experiments and model analysis. In this work, we are able to continuously observe single T4 lysozyme for extended periods of time, for example, a couple hundreds of seconds. More hidden information about conformational transition dynamic and bunching structure are directly observed from single-molecule experimental results. A Markov process model and a transition shortest pathway model are applied to reproduce our experimental results and to decipher intermediate states from bunched sub-step conformational motions during the multi-step open-close conformational process in the enzymatic reactions.

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2. EXPERIMENTAL Materials: Wild-type T4 lysozyme plasmid is provided by Prof. Brian Matthews from the University of Oregon through Addgene Company. The wild-type T4 lysozyme has two cysteines groups (residue 54 on N-domain and residue 97 on C-domain), which are accessible to thiolation reactions. Two dyes of a Cy3/Cy5 FRET pair (GE Healthcare Company) are non-selectively tethered on these two cysteines to sense the relative motion between two domains in T4 lysozyme. The individual donoracceptor labeled T4 lysozyme can be distinguished and selected by two-channel optical images because only donor-acceptor labeled molecule can simultaneously exhibit emission spots in two-channel optical images. The detailed description of site-specific donor-acceptor dye labeling protocol and the discernible optical images of single donor-acceptor labeled T4 lysozyme can be found in our previous publication.42 Figure 1 shows the crystal structure of wild-type T4 lysozyme labeled with a FRET pair (Cy3/Cy5) and the corresponding ensemblelevel emission spectrum. The emission peaks of Cy3 and Cy5 are well separated, which is a favorable condition for FRET measurements. Peptidoglycan from Micrococcus luteus, a major component of the bacterial cell wall, is purchased from Sigma-Aldrich and used as a substrate without further purification. The substrate is suspended to a final concentration of 25 µg/mL in PBS at PH 7.3.

Figure 1. (A) Crystal structure of wild-type T4 lysozyme (PDB-code, 3LZM). A Cy3/Cy5 FRET pair is covalently labeled to two cysteines on a single T4 lysozyme: cysteine 54 on N-domain and cysteine 97 on C-domain, where two cysteines are highlighted with dots. The fluorescence intensity or FRET efficiency fluctuations of this FRET pair reflects relative distance changes between the two domains involved in open-close hinge-bending conformational motions. (B) Normalized fluorescence spectrum of Cy3/Cy5 labeled T4 lysozyme. The emission peaks of Cy3 and Cy5 are spectrally well-separated. In single-molecule FRET measurements, donor and acceptor fluorescence signals are further split by a dichroic beam splitter with appropriate optical filters. Single-Molecule Measurements: In our single-molecule FRET experiments, T4 lysozyme is tethered through a bifunctional cross-linker molecule to a hydrocarbon modified glass cover-slip surface. The glass cover-slip is first sonicated with acetone for half an hour, followed by rinsing with alcohol solution and distilled water three times. The clean cover-slip is treated overnight with a


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10% (v/v) mixture of 3-mercaptopropyl-trimethoxysilane and isobutyltrimethoxy-silane (1/1000 ratio) in 15.0 mL DMSO. After rinsing with ethanol and water, the coverslip is put in the PBS buffer solution (pH 7.3) for one hour to remove un-reacted solvent. The cover-slip is then incubated with 40.0 μL 250 mM bi-functional cross-linker stock solution (NHS-PEG6-Malemiade, Thermo Scientific) in 12.0 mL PBS buffer solution for two hours at 4°C. The amine-to-sulfhydryl cross-linkers with hydrophilic polyethylene glycol (PEG) spacer arms are attached to the glass cover-slip surface. After additional washing, the cover-slip is incubated with 0.66 nM T4 lysozyme in the PBS buffer for two hours at 4°C followed by rinsing with water and PBS buffer. After the linkage between aminereactive group of NHS-PEG6-Malemiade and T4 lysozyme’s lysine group, the tethered enzyme sample is assembled on the glass cover-slip surface. During our single-molecule measurements, the assembled T4 lysozyme on the cover-slip is further incubated with 25.0 μg/mL substrate for half an hour at room temperature in PBS buffer solution (pH 7.3). The Trolox-oxygen scavenger solution, which contains 0.8% D-glucose, 1.0 mg/mL glucose oxidase, 0.04 mg/mL catalase, and 1.0 mM Trolox (6-hydroxy-2,5,7,8-tetramethylchroman-2carboxylic acid), 15, 43-45 is added to the above sample chamber to prevent the possible photo-bleaching of the Cy3/Cy5-labeled T4 lysozyme molecules for lengthening the measurements time. A detailed description of our experimental setup is presented in our previous reports.15, 42, 46 Briefly, an inverted confocal microscope with 532 nm CW (continuous wave) excitation generated from diodepumped solid-state laser is used to image single T4 lysozyme molecule and record the single-molecule donor/acceptor intensity trajectories. Emission signals from donor Cy3 and acceptor Cy5 were detected separately by a pair of Si avalanche photodiode detectors (APD, SPCM-AQR-14, Perkin Elmer Optoelectronics) after passing through a 640 nm dichroic beam splitter (640dcxr, Chroma). An approximate 15% leakage from donor fluorescence to acceptor channel was taken into account and was corrected by Matlab programming in our data analysis process.

Figure 2. (A) Scheme of responsive donor-acceptor distance and FRET efficiency changes associated with enzyme open-close hinge-bending motion in ES* formation. Multiple intermediate states of non-specific enzyme-substrate complex (ES) are involved. (B) A Markov process model of multiple intermediate states. The conformational intermediate states sequence of T4 lysozyme being modeled is a Markov process. From E+S to ES*, the enzyme can adopt multiple intermediate states in a series of identical state-to-state transitions (n=1, 2, 3, 4, 5, 6). The formation time of ES*, also considered as open time, is the time duration from E+S to ES*. Markov Model Analysis: T4 lysozyme exhibits hingebending open-close conformational motions under enzymatic reactions. In our study, the open time or the formation time of active enzyme-substrate complex (ES*), tES*, is determined by the time duration between when an enzyme opens up to intake substrate and closes down to form ES* as shown in Figure 2A. To simulate the probability density of tES* and to determining the number of conformational intermediate states present in this open process, a Markov process model (Figure 2B) is proposed here on the basis of experimental observations. We first assume that multiple conformational intermediate states are involved during the open process and the adjacent state-to-state transition is a Poisson process; therefore, the conformational state-to-state transitions are homogenously governed by single exponential decay kinetics, which is defined by

/

(1)

where f (t) is the probability density function of time duration t of an intermediate state in a single state-tostate transition step, and τis the mean value of time duration. We assume τ = 3.25 ms in our simulation, based on our experimentally determined sub-step time



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using a Random Walk Model analysis reported in our previous publications.16, 22 For a standard Markov process, n (=1, 2, 3, 4, 5, 6) identical Poisson processes in succession are involved in the overall dynamics (Figure 2B). Therefore, the formation time of intermediate states ESn or ES* is given by

!

/

(2)

where f (t) is the probability density function of the overall time duration, which is the formation time in forming ESn or ES*, and n is the length of transition steps. A specific number of n (n=1, 2, 3, 4, 5, 6) is assigned to generate simulated data. Two-Dimension (2D) Joint Probability: The twodimension (2D) joint probability distribution16, described as f(ti, ti+j), on the basis of experimental and simulated data at different transition steps is used to identify bunching structures by analyzing pairs of formation times ti and ti+j separated by index number j. For any pair of formation times (ti, ti+j), ti vs ti+j is plotted in x-y plane. The occurrence of these pairs is counted as probability in the z dimension and shown by a color bar in the 2D joint probability distribution. The detailed description of our two-dimension joint probability distribution analysis is presented in our previous publication.16

3. RESULTS AND DISCUSSION Single-Molecule Observation of Distinctive Open Time Distributions: To obtain insights into the conformational motions of T4 lysozyme, we have used single-molecule FRET spectroscopy and imaging to probe the relative domain motions by monitoring the fluorescence resonance energy transfer between a Cy3/Cy5 FRET pair covalently tethered to T4 lysozyme domains. Figure 1A shows the crystal structure of wildtype T4 lysozyme labeled with a FRET pair (Cy3/Cy5) capable of probing the open-close hinge-bending motions. The labeling sites, cysteine 54-N domain / cysteine 97-C domain, are highlighted using dots shown in Figure 1A, where dye substitutions do not perturb T4 lysozyme activity on the basis of enzymatic reaction control assay.47 Figure 1B is the ensemble-level emission spectrum of Cy3/Cy5-labeled T4 lysozyme with wellseparated emission peaks. Peaks at approximately 565/610 nm come from Cy3 emission, and the peak at approximately 665 nm comes from Cy5 emission. In single molecule measurements, T4 lysozyme is tethered through a bi-functional cross-linker molecule to a hydrocarbon modified glass cover-slip surface. In this way, the tethered enzyme is fully mobile and no other considerable perturbations on its activity are available except for spatial confinement from tethering.48 Donor and acceptor intensity trajectories are simultaneously recorded under enzymatic reactions with 25.0 μg/mL peptidoglycan, shown separately in Figure 3A. Green dots connected by lines indicate Cy3 (donor, D) emission and red ones indicate Cy5 (acceptor, A) emission. The

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corresponding FRET efficiency trajectory is deduced from EFRET = IA / [IA+ID], where ID, IA are fluorescence intensities of donor and acceptor, respectively (Figure 3B). The anticorrelated features of donor intensity decreasing along with the increasing of acceptor intensity are evident in DA intensity trajectories (Figure 3A and inset). Furthermore, the anti-correlated D-A intensity fluctuation behavior is not observed in the absence of substrates, as we have reported in our previous work.22 From the vertical inset of Figure 3B, the FRET efficiency wiggling between an averaged higher FRET state and a lower FRET state is observed beyond the measurement shot noise. Since both the anti-correlated D-A intensity fluctuation and FRET wiggling are the reflection of D-A distance changes associated with the enzyme conformational motions, we attribute each wiggling to individual switching event between open and closed conformational states during T4 lysozyme open-close hinge-bending conformational motions under the enzymatic reaction conditions. The bimodal Gaussian-like distribution of FRET efficiency (lateral inset in Figure 3B) further proves this attribution. During the whole process of T4 lysozyme open-close hinge-bending conformational motions, the enzyme first opens up to intake the substrate initiated by electrostatic attraction between enzyme and substrates, and then forms the nonspecific enzyme-substrate complex (ES), corresponding to the process E+SES. After several steps of conformation adaptability, specific enzyme-substrate complex (ESES*, from inactive state/states to active state ready to react) is formed, followed by the chemical reaction and product releasing (ES* EPE+P). Our previous MD simulation and single-molecule experimental results have implied no significant conformational motions in the process of the chemical reaction or product releasing in T4 lysozyme enzymatic reaction. 7, 16, 22, 40 Therefore, reflected in the FRET efficiency or donor-acceptor FRET-dimension nuclear coordinate, FRET remains low or donor-acceptor distance remains unchanged during the chemical reaction and product releasing process. We have modeled that the open process consists of E+SESES*, in which the time span is the open time or the formation time of ES*. The close time is the time duration of the chemically hydrolysis reaction, product releasing, and the enzyme searching for the next substrate. The left panel in Figure 2A shows the response process of donor-acceptor distance and FRET efficiency changes associated with T4 lysozyme conformational motions, in which the formation of ES or ES* involve remarkable domain motions reflected in the FRET-dimension or donor-acceptor distance nuclear coordinate. To quantitatively analyze the hinge-bending conformational dynamics, we have used a threshold algorithm approach 22, 49 in which the cutoff between open and closed states was set as 50% of the bimodal FRET efficiency distribution (Figure 3B) to read out the formation time of ES* or open time. We have treated the time duration of each FRET wiggling below the cutoff value as the formation time of ES*.


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On the foundation of the above threshold algorithm, a series of formation time distributions characterized with distinct mean values were obtained from T4 lysozyme FRET trajectories in Figure 4 (A1-A6). Figure 4A1 shows a single exponential distribution of formation times. We suggest this single exponential distribution as a result of single state-to-state transition regulated by a Poisson process. While, Figures A2-A6 presents neither singleexponential nor multi-exponential distribution, the results are most likely generated by consecutive sub-step motions associated with multiple convoluted intermediate states. Furthermore, after scrutinizing into mean values of each formation time distribution, we identify a repeatable pattern: mean formation time derived from each distribution under enzymatic reactions takes on only a discrete set of values. This pattern is not found in control experiments without substrates. The formation times present approximately single or multiple times of a certain value (3.25 ± 0.3 ms), and the formation time increases geometrically if listed with step-by-step rising trend shown in Figure 4 (A1-A6). From Figure 4A1 to 4A6, the distributions gradually exhibit more and more close to Gaussian-like distributions which confirm our previous results that the formation times populate a Gaussian-shaped distribution with mean 19.5±2.0 ms. 16, 22

conformational states and exhibits bimodal Gaussian-like distributions.

Figure 4. (A panel) Distributions of experimental formation times or open times during T4 lysozyme openclose hinge-bending conformational motions under enzymatic reactions. Formation time is the duration time of each wiggling of the FRET trajectory below the threshold cutoff. The threshold cutoff is determined by 50% of the bimodal Gaussian-like FRET distribution. (B panel) Distributions of simulated formation times on the basis of Markov process model at different transition steps (n=1, 2, 3, 4, 5, 6).

Figure 3. (A) A typical portion of single-molecule intensity trajectories recorded from single Cy3/Cy5labeled T4 lysozyme under enzymatic reactions with 25.0 μg/mL peptidoglycan. Green dots connected by lines indicate Cy3 (donor) emission and red ones indicate Cy5 (acceptor) emission. The inset with a magnified time axis shows anti-correlation between donor and acceptor intensity fluctuations. (B) The corresponding FRET efficiency trajectory calculated from donor/acceptor intensity trajectory in (A). The detection of FRET is based on the intensity ratio-metric method. The energy transfer efficiency wiggles between open and closed

Multiple Pathways and Multiple Sub-Step Conformational Motions: Here, we propose a Markov process model for T4 lysozyme conformational dynamics under enzymatic reactions. The Markov model of intermediate states is based on the following assumptions: 1) the state-to-state transitions are governed by single exponential kinetics; 2) The likelihood of next intermediate state exclusively depends on the current state not on the sequence of states that preceded it; 3) The conformational intermediate states sequence being modeled is a Markov chain. The model details are shown in Figure 2, and the model analysis is given above in Markov Model Analysis. In this model, we assume 3.25 ms as the mean time duration of single state-to-state transition and n (=1, 2, 3, 4, 5, 6) as consecutive state-tostate transition steps. T4 lysozyme exhibits statistically distinguished slow productive motions and rapid nonproductive motions in the time-scale of 20-50 s−1 and



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200-400 s−1, corresponding to T4 lysozyme’s hydrolysis of peptidoglycan and unprocessed catalysis, respectively. 39 The single state-to-state transition time here interestingly agrees with the rapid nonproductive motion time. It is likely that T4 lysozyme successful hydrolysis process where enzyme opens up to intake peptidoglycan and close for catalysis comes from several rapid nonproductive conformational motions in the case of upfront non-optimal enzyme-substrate conformational configuration. T4 lysozyme enzyme needs to adjust its conformation with correct alignment of active site functional group to complete productive conformational changes ES*, evidenced in dynamic and static inhomogeneity of multiple dimensional conformational motions of T4 lysozyme. 40 In Figure 4 (B1-B6), We have further generated the simulated data of time duration in forming ES* or ES in terms of multiple state-to-state transitions (n=1, 2, 3, 4, 5, 6). Unambiguously, the simulated formation time distribution profile of ES* corresponding to different substep conformational motions are in good agreement with the real experimental formation time distribution in Figure 4 (A1-A6). The Gaussian-like formation time profiles are observed in both experimental and simulated results, implying that the open-close conformational motions of T4 lysozyme in the formation of active state ES* follow multiple pathway and involve multiple substep motions along with multiple intermediate states. The dominant driving force for ES formation is the electrostatic attraction of surface positively charged amino acid residues (Arginine and Lysine) in T4 lysozyme interacting with the negatively charged polysaccharide substrate when lysozyme opens up to interact with polysaccharide substrate. The driving force for ESES* process includes the formation of six hydrogen bonds in the active site of ES* when T4 lysozyme’s two domains close upon polysaccharide substrate.22 Our results are also in great agreement with that the conformational motions of forming ES or ES* involve multiple nuclear coordinates that can be projected to a common FRETdimension nuclear coordinate.40 Each sub-step motion cannot necessarily induce a significant increase or decrease in FRET efficiency or in donor-acceptor distance. Due to molecular orientation/domains orientations, reflected in the experimental results, it is hardly to observe distinguished FRET values for sub-step conformational motion. The Markov chain of state transitions based on the reproducible results between experimental and simulated data represents underlying conformational transition dynamics of T4 lysozyme in views of open time duration of T4 lysozyme hingebending conformational motions.

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to predict the number of elementary rate steps between two states along the shortest pathway.50 In their model, the number of elementary steps is determined by the initial rise of the waiting time distribution. lim → ∅ ∝

(3)

φ (t )

where is the probability distribution of waiting time t between perturbed state and probed state, the exponent L is the minimal number of elementary reaction steps, and kL is the product of the rate coefficients along the shortest pathway. We apply this initial-rise method to infer the shortest pathway between a pair of states and the minimal elementary steps between E and ES*. In our case, we use occurrence (the product of probability and total number of events N) instead of probability, and formation time instead of waiting time to infer the number of elementary steps. We make the natural logarithm transformation of the whole Equation (3), generating a new Equation (4). ln [lim ∅] ln[ lim ∅]

→

→

∝ ln ln + ln In Equation (4), ln [lim ∅] vs

→

(4)

ln, the slope

indicates L- minimal number of elementary reaction steps. We used this model to recheck the relationship between occurrence and formation time in Figure 4A6 and the results are given in Figure 5. In this specific case, from E to ES*, the shortest pathway only needs one elementary step. The same result of one elementary step between E and ES* from Figures 4A4 and 4A5 was also obtained. Furthermore, Cao et al reported another model about transitions in genetic toggle switches demonstrated anti-correlation behavior between stochastic effect of the system with fluctuating conformational states and stateto-state switching rate.51 In particular, in the case of transitioning from one state to another, the decrease of action reflects a larger switching rate that makes the system easier to transit from one stable state to another stable state.51 The one elementary state from T4 lysozyme enzyme to active enzyme-substrate complex in the shortest pathway obtained here agrees with both the minimum action taken with shorter waiting time in genetic toggle switches model and single state-to-state transition in Markov model.

The Shortest Pathway with Minimum Step: A complex chemical reaction is composed of multiple elementary reaction steps, giving rise to non-exponential behavior of probability density function of waiting time. Based on the probability distribution function of the first passage time theory, Cao and Silbey had developed a statistical model


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Figure 5. Linear regression between ln (occurrence) and ln (formation time), the original experimental data was from Figure 4A6. One elementary step from E to ES* through the shortest pathway was obtained. Our single-molecule experimental results indicate multiple pathways involving multiple transition steps in the formation of T4 active enzyme-substrate complex. Theoretically, independent of multiple pathways, the transition from E to ES* can be done through the shortest pathway, which only requires one elementary reaction step. From our experimental data, most-likely, this transition of T4 lysozyme E to ES* needs multiple elementary steps, due to static and dynamic disorder in T4 lysozyme rate coefficients,40 intrinsic noise, and heterogeneous polysaccharide substrates. Regardless of the shortest pathway, average pathway, optimal pathway, or other pathways, both our single-molecule experiments result and models suggest the existence of multiple pathways from T4 lysozyme E to ES*. In fact, probably one, two, three, four, five, six, seven or more steps are involved in different pathways, which is beyond the scope of this paper. For example, Akhterov et al. have proposed that lysozyme open-close conformational transition follows a concerted pathway characterized with fast microseconds transient symmetric opening and closing motions,41 in agreement with the existence of multistep non-concerted pathways featured as observed state-tostate long pause. This inhomogeneity and variance can be only observed through single-molecule measurements, not in bulk due to its averaging effect. It is likely that multiple pathways (including the shortest pathway) of conformational motions are the intrinsic feature of enzymatic system, in consistent with conformational flexibility and adaptability, static and dynamic disorder of conformational fluctuation rates, and heterogeneity nature.

Figure 6. 2D joint probability distribution of adjacent open times for multiple transition steps n (=1, 3, 6) with xy plane of 50 ms × 50 ms. A1- A2-A3 are experimental results derived from the data in Figure 4(A1, A3, A6). B1-B2B3 are simulated results calculated from data in Figure 4(B1, B3, B6). Both A1 and B1 show similar wing structures deducted from exponential open time distributions (Figure 4A1 and 4B1), implying that there is no bunching effect in single state-to-state transition. Nevertheless, for successive multiple state-to-state transitions, such as 3 or 6 transitions, non-exponential distributions (Figure 4A3 or 4B3, 4A6 or 4B6) give rise to the bunching effect (in A3 or B3, A6 or B6) which implies the bunching nature in multiple sub-step conformational motions. Bunching Nature in Multiple Sub-Step Conformational Motions: The bunching effect characterized by the clustering of conformational motion times during catalysis, implying that the enzymatic conformational motion times in forming the ES* state tend to be distributed in a finite and narrow time window, has been previously reported.16 Nevertheless, the bunching nature of conformational motions has been only probed by the bunching structure of simulated open time distribution because of deficient experimental data points. Here, we fill this gap to show bunching structure not only in simulated results but also in experimental results. Figure 6 shows 2D joint probability distributions (described as f (ti, ti+j), details in Markov Model Analysis) of adjacent open times for multiple state-to-state transition steps n (=1, 3, 6). Figure 6(A1, A2, A3) demonstrates 2D joint probability distributions derived from the data in Figure 4(A1, A3, A6). Figure 6(B1, B2, B3) illustrates the distributions calculated from simulated data in Figure 4(B1, B3, B6). Clearly, the theoretical results from Markov model are in good agreement with the experimental data from single-molecule spectroscopic results. To be specific, both Figure 6A1 and 6B1 show similar wing structures deducted from exponential open time distribution (Figure 4A1 and 4B1, typical Poisson



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distributions), implying that there is no bunching effect but stochastic nature of Poisson rate process in single state-to-state transition. However, for successive multiple state-to-state transitions governed by multiple consecutive Poisson rate processes, such as 3 or 6 transitions, non-exponential or Gaussian-like distributions (Figure 4A3 or 4B3, 4A6 or 4B6) give rise to bunching effect (in Figure 6A2 or 6B2, 6A3 or 6B3), implying the bunching nature in multiple sub-step conformational motions stemming from enzymesubstrate interactions. The observed bunching effect in both experimental and theoretical results suggests that the hinge bending conformational motion time of T4 lysozyme tends to populate in a narrowly distributed time window with the defined first moment and finite second moment as a Gaussian-like distribution. The bunching effect, resulting from consecutive Poisson rate processes, is probably a perspective view of T4 lysozyme conformational flexibility to adjust from inactive state toward a catalytically-active state in which the reactive groups are brought into close proximity in a similar conformation favoring hydrolyzing catalysis. Our results of T4 lysozyme conformational dynamics show a complementary characteristic behavior of both convoluted enzyme conformation selection and induced-fit dynamics driven by substrate-enzyme interactions. Conformational selection mechanism predominately regulates protein conformational fluctuation/flexibility in the process of nonspecific binding between enzyme and substrate, shown in the modeled multiple pathways and multiple intermediate states of ES. The induced-fit mechanism most likely dominates the specific binding process between enzyme and substrate (from ES to ES*), in which the active state (ES*) drives the system across the intersection between conformational coordinate and catalytic coordinate, leading to the chemically catalytic reaction.

4. CONCLUSION In conclusion, herein we have investigated underlying conformational transition dynamics of T4 lysozyme from inactive state to active state by single-molecule fluorescence resonance energy transfer. Distinguished neither single nor multi-exponential, but Gaussian-like distributions of ES* formation time have been observed and the Markov process model has been employed to unravel the hidden intermediate states from sub-step conformational motions behind those distributions. The simulated results agree with the real experimental distributions. In addition, the bunching effect, interpreted as a result of a Markov chain conformational state transitions process during catalysis, has been directly observed from both experimental results and simulated results through visualizing the bunching feature in a narrowly distributed time window of conformational changes. Our results suggest multiple pathways involved and multiple conformational intermediate states formed in the process of T4 lysozyme

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open-close hinge-bending conformational motions under enzymatic reactions. For the shortest pathway from E to ES*, one elementary step is required to overcome transition barrier. Multiple intermediate states are suggested to be configured in convoluted sub-step conformational motions involving non-identical nuclear coordinates (like different domains orientations) besides a common FRET-dimension nuclear coordinate. The derived results of multiple intermediate states, sub-step conformational motions, and the bunching effect support a complementary mechanism between convoluted enzyme conformation selection and induced-fit dynamics.

AUTHOR INFORMATION Corresponding Author

* [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work is supported by NIH NIGMS, and it is also supported in part by Ohio Eminent Scholar Endowment.

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Figure 5

3.5 3

ln (Occurrence)

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2.5 2 1.5 1 y = 1.0849x - 0.7679 R² = 0.88616

0.5 0 1.5

2

2.5 3 ln (Formation Time)


3.5


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Figure 6


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Revealing Multiple Pathways in T4 Lysozyme Substep Conformational

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