Dissecting the Conformational Dynamics-Modulated Enzyme

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B: Biophysics; Physical Chemistry of Biological Systems and Biomolecules

Dissecting Conformational Dynamics Modulated Enzyme Catalysis with Single-Molecule FRET Shaowen Wu, Jianwei Liu, and Wenning Wang J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 16 May 2018 Downloaded from http://pubs.acs.org on May 16, 2018

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The Journal of Physical Chemistry

Dissecting Conformational Dynamics Modulated Enzyme Catalysis Catalysis with Singleingle-molecule FRET Shaowen Wu, Jianwei Liu* and Wenning Wang* Department of Chemistry and Institutes of Biomedical Sciences, Fudan University, Shanghai, P.R. China

1

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Abstract Conformational changes of enzyme proteins are often coupled with the catalytic reaction and modulate the enzyme activity. Single molecule technology is a powerful tool to study the mechanism of enzyme catalysis in these complicated cases. However, the chemical reaction cycles and conformational changes could not be monitored simultaneously in a single molecule detection experiment, resulting in some key kinetic parameters unresolved. Here, we describe a method to extract all kinetic parameters from comprehensive single molecule FRET (smFRET) measurements and model analysis. Based on the smFRET, we calculated the undetectable parameters by solving rate equations of the kinetic model with the input of smFRET measured conformational state populations and state transition rate constants. A case study of MalK2 ATPase demonstrates that this method could reveal the quantitative mechanism of catalytic reaction of the enzyme as well as its coupled conformational dynamics. The strategy employed in this study could be widely applied to investigate the conformational fluctuation-couple catalysis of other enzymes.

2


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Introduction Enzymes are specific biological catalysts that speed up the chemical processes of life. Beyond three-dimensional atomic structure, the catalytic activity of an enzyme is often modulated by a protein conformational dynamics. fluctuating enzymes, conformational

states

complexity (E1,

E2,

arises from E3…)

with

1

For the conformational

the co-existing of their

respective

multiple substrate

binding/dissociating rates and catalytic turnover efficiencies. This has forbidden a comprehensive study of catalysis mechanism using traditional ensemble-based kinetic methods.

2

Single molecule methods, which are capable of measuring the chemical

turnovers and conformational fluctuations of one molecule at a time, have shown unique power in dissecting catalytic mechanism of complex enzyme systems.2 One widely used single molecule approach to study enzyme catalysis, the so-called single molecule stamping spectroscopy, monitors the fluorescent catalytic products and records the stochastic time for catalytic turnover cycles.2-3 Conformational state fluctuations affect the kinetics of catalysis and manifest themselves in the recorded catalytic turnover time sequence, e.g., “trajectories”. Ideally, the conformational dynamics of the enzyme could be extracted from model analysis of the time trajectories of catalytic turnover cycles.

2-4

However, the deduction of protein

conformational dynamics is difficult and vague in many cases. In recent years, single molecule FRET technology has been extensively used to study conformational dynamics of many biologically important proteins including enzymes. 5-11 By labeling donor and acceptor dye molecules on certain sites of protein, smFRET method 3



directly monitors the time-resolved conformation fluctuations.

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5, 8, 10-17

For enzyme

systems modulated by conformational dynamics, smFRET measurement could reveal the equilibrium distribution of multiple conformational states and the kinetics of state transformation. However, smFRET is not able to measure the substrate binding/dissociation and catalytic turnover cycles directly and thereby some key kinetic parameters for understanding the catalytic mechanism of the enzyme are missing. To maximize the capability of smFRET in the study of enzyme catalysis, we proposed a strategy to retrieve the undetectable kinetic information from comprehensive smFRET measurements. We first measure the conformational dynamics of enzyme under various conditions, e. g. in the absence or presence of substrates, and under catalytic active or inactive conditions. Then we extract the conformational state populations and transformation rate constants of the states from data analysis. Based on the conformational state analysis results, we set up a kinetic model describing the whole reaction network about the coupling of conformational dynamics and catalytic reactions. Then we solve the mater equations of the kinetic model by optimizing all the rate constants and state populations to fit the available smFRET experimental measurements using a genetic algorithm. Through this procedure, we could obtain the undetectable parameters in smFRET experiments, such as the rate constants of substrate binding/dissociation and catalysis turnover number of a specific state. We applied this strategy to study the conformational dynamics regulated 4


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catalysis of ATPase MalK2, which is the nucleotide-binding domain (NBD) of maltose transporter MalFGK2. Unlike conventional NBDs in many other ATP-binding cassette (ABC) transporters, MalK has a C-terminal extension called the regulatory domain (RD), which helps MalK to form a stable dimer even in the absence of ATP. The isolated MalK2 has very low ATPase activity, and the crystallographic studies suggested that MalK2 could adopt three conformations depending on the nucleotide-binding state, i.e. the open, semi-open and closed states.

18-19

The closed

conformation is stabilized by ATP-binding and considered the catalytic active state. Therefore, the low ATPase activity of MalK2 could be attributed to the conformational movements. However, the conformational dynamics coupled catalytic mechanism of MalK2 has not been completely understood. The exact relationship between the conformational dynamics and catalysis turnovers remain elusive. This information would be crucial for understanding the working mechanism of the intact MalFGK2 transporter, in which the ATPase activity is tightly regulated. 20-21 Here, we performed comprehensive smFRET measurements of MalK2 under different nucleotide-binding conditions to obtain state populations and kinetic parameters of the conformational transitions. Using the above-mentioned strategy, we obtained all the kinetic information under hydrolyzing condition, revealing that the conformational transition and ADP dissociation are the major limiting factors of the ATPase activity of MalK2.

Methods 5



Protein Preparation Gene of E. coli wild type MalK with an N-terminal poly-histidine tag (His6) was cloned into the HindIII and XhoI sites of the PET-28a vector. MalK could form dimer both in the presence and absence of ATP 18. For fluorophore labeling, Ser3 or Ser153 in the NBD domain was mutated to cysteine respectively, and Cys40, Cys352 and Cys362 were mutated to serine residues using the standard PCR-based mutagenesis method and confirmed by DNA sequencing. These two labeling mutants are referred to MalK2-S3C and MalK2-S153C. When designing labeling sites, we carefully analyzed various conformations in crystal structures of MalK2 and found that the conformational changes are mainly manifested on the NBDs as shown in Fig. S1a&b. The suitable sites for dye-labeling have to fulfill several requirements, such as obvious inter-residue distance variations among different conformations, proper inter-residue distance close to R0, exposed side chains, polar/charged residues rather than hydrophobic. Moreover, residues at the inner side of NBD dimer could not be chosen since they might interfere nucleotide binding and hydrolysis. In Fig. S1c, we listed some candidate residues and their distance variations in different conformations. It can be seen that some amino acids have very little inter-residue distance variations, like K20, R178. Some of the mutants are expressed in inclusion bodies (Fig. S1d). To generate the hydrolysis inactive mutants, additional Q140L mutation was introduced into the above two mutants, resulting in the MalK2-S3C/Q140L and MalK2-S153C/Q140L variants. All genes were cloned into the HindIII and XhoI sites of a PET-M3C vector. Wild type MalK2 and all mutants were expressed in E. coli 6


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BL21 (DE3) host cells at 16 °C and purified using Ni2+-NTA agarose affinity chromatography followed by size-exclusion chromatography. Fluorescent labeling of protein For dye labeling, 25 µM MalK2 mutant proteins were incubated with 200 µM donor (Alexa fluor 555-maleimide, Thermo Fisher Scientific Inc., MA, U.S.), and 400 µM acceptor (Alexa fluor 647-maleimide, Thermo Fisher Scientific Inc., MA, U.S.) in the presence of 1 mM Tris (2-carboxyethyl) phosphine (TCEP) hydrochloride at 8 °C overnight. Afterward, the unreacted dyes were removed from the protein solution by size-exclusion chromatography using normal buffer (50 mM Tris pH 8.0, 20% glycerol, 100 mM NaCl, 1 mM β-ME). smFRET experiments The coverslip and slide were cleaned by following the protocol

12

and then

coated with NTA-functionalized Poly (L-lysine)-g-Poly (Ethylene Glycol)

22

to

prevent nonspecific adsorption of proteins to the surface and the protein having His-Tag was immobilized on the surface by Ni2+-NTA affinity. Single-molecule fluorescence images were taken by using a home-built wide field fluorescence imaging system. 11 A 532 nm laser was used to excite the donor and generate FRET. A dual viewer (Optosplit II, Andor Technology Plc., U.K.) was used to separate the fluorescence of different colors emitted by donor and acceptor respectively, and then the fluorescence image was taken by an EMCCD camera (iXon 897, Andor Technology Plc., U.K.) with an exposure time of 100 ms. Analysis of smFRET data 7



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Time trajectories of the fluorescent intensity of donor and acceptor from a single molecule were extracted from the recorded serial of images by using the ISMS software (MATLAB encoded).

23

and following the ISMS user guide. We determined

the minimum number of conformational states by performing the analysis of Bayesian inference of smFRET trace with vbFRET

24

and comparing the calculated mean log

evidence. Afterward, the HMMs analysis was performed by using the vbFRET software to recognize the change point of transitions in smFRET trajectories and meanwhile generate the ideal trajectories. To distinguish MalK2 conformational states, we performed a threshold analysis on the ideal trajectories,

25-26

where the thresholds

for each state were set by using the full width at half height of the Gaussian distributions. These thresholds were 0.06-0.33 FRET for E1, 0.39-0.63 FRET for E2 and 0.66-0.97 FRET for E3. Histograms of FRET were obtained by combining all time points of each raw FRET trajectories and fitted to the three Gaussian functions. To estimate the error of state populations derived in the measurements, we repeated the four smFRET experiments in the absence of ATP/ADP. The state populations obtained from the two measurements are very similar (Table S3), indicating that the population differences are robust. For kinetic analysis, transitions between E1 and E2, E2 and E3 were counted based on the idealized smFRET trajectories. Dwell times in each state before a transition were also analyzed and the distribution of dwell time was fitted by a single exponential decay function to obtain the mean first passage time and the corresponding rate constants for state transitions (Table S2). 24 Derivation of the rate equations 8


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Based on the nine-state kinetic model in Fig. 4, the master equations27-28 under steady state of ATP hydrolysis could be written as: − + + + + + = 0

(11)

= 0

(12)

− + + + + + +

− = 0

(13)

− + + = 0

+ − + + + = 0 − + − = 0

− + + = 0

+ − + + + = 0 + − = 0

(14) (15) (16) (17) (18) (19)

Based on the approximations that were mentioned in the Results part, Eq. (11-12) can be simplified as: − + + = 0

− + + = 0

(11b) (12b)

Using Eq. (11b) and (12b), the other rate equations will be simplified as: − + + = 0

− + + + = 0 − − = 0

(14b) (15b) (16b)

− + + = 0

(17b)

− + + + = 0 9


(18b)


+ − = 0

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(19b)

Therefore, the kinetic model is simplified to the six-state master equation Eq. (1). GA optimization We used the GA optimization algorithm provided by MATLAB.29-31 It finds a local unconstrained minimum to the objective function. Objective function used in this study is defined as,29

= ∑$

, !", !",

#

where %&'(,$ represents the GA optimized values of parameters $) , $) , $ and *$) ,

and %+,,$ represented the corresponding values obtained from the smFRET experiments. By setting initial values of the rate constants in (1a), Eq. (1) was solved

to get all the terms in -. . Then, the apparent state probability $ and apparent

transition rate constant *$) were calculated using -. and Eq. (2)-(9). Next, the

objective function was estimated and the average relative change of the calculated objective function value over generations was compared with a threshold value (a value of 10-12 was used in this study). If the average change of the calculated objective function value is larger than the threshold, new values of the parameters in (1a) were generated and Eq. (1) was solved to get new -. , followed by another round of

calculation of objective function. This procedure was repeated until the average change of the calculated objective function value is less than or equal to 10-12.

Assay of ATP hydrolysis activity The amounts of inorganic phosphate (Pi) released by ATP hydrolysis were measured to assay the ATPase activity with the use of Malachite green reagent as described previously.

20, 32

10 µL 34% sodium citrate was used to halt the non-enzymatic

hydrolysis of ATP. The curve of hydrolysis rate was analyzed by classical Michaelis-Menten equation. 10


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Results To monitor the domain movement of MalK2, two mutants were generated by introducing cysteine to the site of Ser3 and Ser153, respectively. In the resulted MalK2 mutants (refer to MalK2-S3C and MalK2-S153C, respectively), a pair of cysteine residues were placed at equivalent positions in the MalK2 dimer (Fig. 1a). According to the crystal structures of MalK2, 18-19 the inter-cysteine distances in the two mutants could sufficiently characterize the differences between various conformations in crystal structures (Fig. 1a, Table S1). The purified MalK2-S3C and MalK2-S153C showed similar elution profiles on size exclusion chromatography (SEC) (Fig. S2), indicating that the WT and two mutants of MalK form dimers in the absence of ATP. The ATP hydrolysis rate of MalK2-S153C (143.2 nm Pi⋅min-1⋅mg-1) was close to that of WT MalK2 (155.4 nm Pi⋅min-1⋅mg-1), while the hydrolysis rate of MalK2-S3C (82.7 nm Pi⋅min-1⋅mg-1) was slightly reduced (Fig. S3a-c). The fluorophore-labelling did not disturb the ATPase activities of the two mutants (Fig. S3d&e). smFRET experiments were performed using a laboratory-built setup. The typical lifetime of the dye attached to MalK2 is about 20 s and the longest bleaching time is about 60 s.

11



Fig. 1 The crystal structures of MalK2 and sample smFRET trajectories. (a) The labeling sites Ser3 (cyan sphere) and Ser153 (magenta sphere) are highlighted in four crystal structures including: isolated MalK2 in the nucleotide-free form (PDB-ID 3FH6); nucleotide-free MalK2 in the pre-translocation state of MalFGK2 transporter (PDB-ID 3PV0); ATP-bound MalK2 in the outward-facing state of MalFGK2 12


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transporter (PDB-ID 2R6G); isolated MalK2 in Mg2+-ADP bound form (PDB-ID 2AWN). (b) Sample smFRET trajectories of MalK2-S3C system. (c) Sample smFRET trajectories of MalK2-S153C system.

Conformational dynamics of MalK2 Fig. 1b and 1c shows typical FRET trajectories of MalK2 in the absence of

nucleotide and Mg2+. Before the fluorophore was photo-bleached, multiple distinct levels can be observed in the FRET trajectory (Fig. 1b&c), implicating the conformational changes of MalK2.

33-34

Three peaks were identified in the FRET

efficiency distributions that were fitted with the sum of three Gaussian functions (Fig. 2a&d). The FRET efficiency values at the centers of the three peaks are 0.20, 0.45,

0.73 for MalK2-S3C and 0.19, 0.46, 0.75 for MalK2-S153C, respectively. The similar values of FRET efficiency at the peak centers of MalK2-S3C and MalK2-S153C are in line with the similar inter-dye distances in the two mutants (Fig. 1a, Table S1). The conformational states corresponding to the low-, middle- and high-FRET efficiency peaks were named as E1, E2 and E3 respectively. The E1, E2 and E3 states were approximately assigned to the open, semi-open and closed conformations observed in crystal structures. The population probabilities of E1, E2 and E3 are 43.9%, 37.2%, 18.9% for MalK2-S3C and 43.8%, 30.9%, 25.3% for MalK2-S153C, respectively (Fig. 2a&d). In agreement with the crystal structural study,

18

the semi-open conformation

has large population probability in nucleotide-free MalK2. It is interesting to note that in the absence of ATP, the closed conformation still possesses considerable population probabilities (18.9% and 25.3%), although the closed state is not observed in the 13



nucleotide-free crystal structures of MalK2.

18

The conformational distributions of

nucleotide-free proteins suggest that MalK2 has remarkable intrinsic flexibility in solution and samples large conformational space.

Fig. 2 Conformational state distributions of MalK2 measured by smFRET under nucleotide-free, ADP-bound and ATP-bound condition. FRET efficiency histogram for MalK2-S3C without nucleotide (a), in the presence of 5 mM ADP (b), and in the presence of 5 mM ATP (c). FRET efficiency histogram for MalK2-S153C without nucleotide (d), in the presence of 5 mM ADP (e), and in the presence of 5 mM ATP (f). Cartoons denoted E1, E2 and E3 represent the open, semi-open and closed state of MalK2.

The effect of nucleotide binding on the conformational equilibrium of MalK2 Parallel smFRET measurements were performed under five different conditions. Under the hydrolyzing condition, Mg2+-ATP was added in the buffer. It is worth noting that due to the hydrolysis of ATP, Mg2+-ADP bound MalK2, Mg2+-ATP bound 14


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MalK2 and nucleotide-free MalK2 co-exist in the system. Under the other four conditions, ADP, ATP, Mg2+-ADP or Mg2+ was added in the buffer, respectively. These conditions are obviously non-hydrolyzing, and we named them as ADP-only, ATP-only, Mg2+-ADP and Mg2+-only conditions, respectively. Under the ADP-only condition, ADP binding shifted the populations toward more closed states. It is interesting that the effect of ADP binding on MalK2-S153C is slightly different from that on MalK2-S3C. For the MalK2-S3C, the population of the E2 state increased obviously (Fig. 2b), while in the MalK2-153C system the E3 state exhibited obvious increase (Fig. 2e). Under the ATP-only condition, ATP binding further reduced the E1 population and increased the E3 population (Fig. 2c&f). Under the Mg2+-ADP condition, Mg2+-ADP hardly affected the state populations of MalK2-S3C with respect to the Mg2+-only condition (Fig. 3a&b). Unlike the MalK2-S3C system, Mg2+-ADP increased the E2 population of MalK2-S153C by ~7%, but the population of E3 is slightly decreased (Fig. 3d&e). Therefore, the semi-open state is stabilized upon Mg2+-ADP binding. Under the hydrolyzing condition, the addition of Mg2+-ATP led to obvious increase of E2 state in MalK2-S3C (Fig. 3c). Different from the case of ATP-only condition, there is no obvious increase of E3 state (Fig. 3c), probably due to the hydrolysis of ATP. For the MalK2-S153C system, Mg2+-ATP increased the population of E3 state remarkably, although to a less extent with respect to the ATP-only condition (Fig. 3f). Overall, nucleotide binding under various conditions shifts the conformational equilibrium of MalK2 toward more closed states. Relative to ADP, ATP binding 15



stabilizes the E3 state more effectively. Notably, the MalK2-S3C and MalK2-S153C exhibit different conformational equilibrium features. In the MalK2-S153C system, the E3 state is more stable and has higher population. This correlates to the observation that MalK2-S153C has higher ATPase activity than MalK2-S3C (Fig. S3).

Fig. 3 Conformational state distributions of MalK2 measured by smFRET under Mg2+-only, Mg2+-ADP and hydrolyzing condition. FRET efficiency histogram for MalK2-S3C in the presence of 5mM Mg2+ (a), 5mM Mg2+-ADP (b), and 5 mM Mg2+-ATP (c). FRET efficiency histogram for MalK2-S153C in the presence of 5 mM Mg2+ (d), 5 mM Mg2+-ADP (e), and 5 mM Mg2+-ATP (f).

Non-catalytic mutant Q140L To further explore the correlation between conformational equilibrium and ATPase activity, we studied the Q140L mutant that could not hydrolyze ATP 35-36. In previous studies, Erwin Schneider et al. found that Q140L mutation induced conformational changes at the periplasmic loop of MalF/MalG in the transporter complex MalFGK2, and similar conformational changes was observed in the 16


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ATP-bound wild type complex.37 In agreement with the previous study, no ATPase activity of Q140L mutants could be detected in our experiment (data not shown). SmFRET measurements demonstrated that in both Q140L (MalK2-S3C/Q140L and MalK2-S153C/Q140L) mutants, the E1 state dominates the conformational ensemble with ~ 70% population, and the E3 population is very low (Fig. S4). Therefore, the loss of ATPase activity in Q140L mutants can be explained by the remarkably conformational shift towards the open states. This observation further validates the correlation between the closed state population and ATPase activity. Transition rates between three conformational states To analyze the FRET data more rigorously, we performed hidden Markov model (HMM) analysis of the trajectories using the vbFRET method

24

. The minimum

number of conformational states was determined to be three (Fig. S5), in agreement with the above Gaussian-function fitting. The rate constants of conformational transitions were calculated under various conditions based on the above HMM analyses (see Methods for more details). The transition rate constants shown in Table S2 demonstrate that in the absence of nucleotide, the conformational transitions of MalK2-S153C are generally faster than those of MalK2-S3C, suggesting that MalK2-S153C has relatively higher intrinsic conformational flexibility. Nucleotide binding

modulates

the

transition

rate

constants

(Table

S2).

For

the

MalK2-Q140L/S3C and MalK2-Q140L/S153C mutants, the E1 → E2 and E2 → E3 transitions corresponding to closing motions could hardly be detected. Kinetic model of conformational fluctuation coupled ATP hydrolysis of MalK2 17



Based on the above analysis, a nine-state kinetic model for the conformational transition and ATP catalysis of MalK2 was set up (Fig. 4). E1 and E2 with open or semi-open conformation are assumed to be able to bind Mg2+-ADP or Mg2+-ATP, while the closed state E3 cannot. The Mg2+-ATP bound E3 state could only be achieved through the conformational transition from the Mg2+-ATP bound E2 state. For simplicity, the conformational states corresponding to the Mg2+-ATP bound, Mg2+-ADP bound and nucleotide-free are named as ETi, EDi and Ei respectively. ATP hydrolysis only occurs in the ET3 (Mg2+-ATP bound E3) state. To simplify the model, the following approximations are made: (1) Since it is hard to imagine that the partial closing of MalK2 could significantly affect the binding or dissociation of nucleotides with MalK2, the rate constants of nucleotide binding and dissociation for E1 and E2 states are approximated to be equal, i.e. = , = , = , = (2) Because the smFRET experiments were performed with saturate ATP concentration, the ADP generated from the hydrolysis of ATP has extremely low concentration relative to the concentration of ATP and thus the binding of ADP to E1 or E2 and the dissociation of ATP could be ignored ( = = 0, =

= 0 ).

(3) Similarly, due to the saturated concentration of Mg2+-ATP it was assumed that MalK2 is saturated by Mg2+-ATP and the state probabilities of nucleotide-free form E1, E2 and E3 are approximated to be zero ( 1 = 0, 2 =

0, 3 = 0). However, the transition from nucleotide-free states to Mg2+-ATP 18


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bound states are not neglected, i.e. ∙ 1 ≠ 0, ∙ 2 ≠ 0. Under these approximations and the steady state assumption, the kinetic model is simplified to a master equation of six states27-28

(See methods for the detailed

derivation.):

4 × = where:

− : 9 0 67 = 9 0 9 0 0 8 1

(1)

0

0 − + 0

− + 0 0 0 0 − + 0 0 − + + 0 0 1 1 1 1

0 0 = 0 < 0 < < − 1 ;

(1a) : = < 9 -. = 9 < 9 < 8 ;

and

0 0 : 0= < -7 = 9 9 0< 9 0< 0 8 1;

(1b)

(1c)

In this equation, the state transition rate constant $) (Mg2+-ADP bound EDi to EDj transition) could be obtained from the smFRET measurements under Mg2+-ADP condition. The rate constant $) (Mg2+-ATP-bound ETi to ETj state) could be approximately obtained from the smFRET measurements under the ATP-only condition (Table S2). The Mg2+-ADP dissociation rate constants , and the

ATP hydrolysis rate constant were unknown parameters that were not directly 19



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measured from the smFRET experiments. Neither were the components of state probability -. in Eq. (1b) measured, because the ETi, EDi and Ei (i=1,2) states were indistinguishable in the smFRET measurements that had the similar distribution profiles of FRET efficiency. Instead of the components of state probability -. in Eq. (1b), the smFRET experiments under the hydrolyzing condition measured the combined state probabilities (also can be referred as apparent state probabilities) $ as described in Eq. (2a-4a):

= + +

(2a)

= + +

(3a)

= + +

(4a)

Because the smFRET experiments were performed under saturated Mg2+-ATP concentration, we have the approximation of 1 = 0, 2 = 0, 3 = 0. Accordingly, Eq. (2a, 3a and 4a) can be simplified as:

= +

(2)

= +

(3)

= +

(4)

Similarly, the measured (apparent) state transition rate constants *$) (from the apparent i-th to j-th state) under the hydrolyzing condition would be the state-probability-weighted sum of $) and $) , which are the transition rate constants between Mg2+-ATP bound states and Mg2+-ADP bound states , respectively:

* =

* =

?@ AB ?B@

?@AC ?C@

+

+

?@ A B ?B@

?@ A C ?C@

(5)

(6) 20


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* =

* =

?@ AC ?C@

?@ AD ?D@

+ +

?@ A C ?C@

?@ A D ?D@

(7)

(8)

In addition, the ATP hydrolysis turnover rate could be calculated by: *EFGH =

(9)

where and are the ATP hydrolysis rate constant and the probability of ATP-bound ET3 state, respectively and both of them were not able to be measured experimentally and need to be calculated from the model. In summary, our goal is to obtain the undetectable rate constants and

from equation (1). The known quantities include the rate constants $) and $) , and

the apparent state probability $ and the apparent state-transition rate constants *$) ,

that are sums shown in Eq. (2)-(8). To achieve this goal, we used a genetic algorithm (GA) optimization procedure29-31 to solve Eq. (1) by fitting the parameters $) , $) , $ and *$) to their experimental values (see Methods for more details). We noticed that the master equations could also be solved using other methods.38-40

Fig. 4 Kinetic scheme of MalK2 ATPase. IJ , $) , $) are rate constants of conformational state transition. $ and $ are rate constants of Mg2+-ADP and Mg2+-ATP binding, and $ and $ 21



are rate constants of Mg2+-ADP and Mg2+-ATP dissociation.

Here, we performed a global optimization to fit the experimental data of the two mutants S3C and S153C by assuming that they have the same ADP dissociation rate constants, and (it is also approximated that = in the above),

and the same hydrolysis rate constant . All the state probabilities calculated from the GA optimization are quite consistent with the HMM analysis values (Fig. S6). The calculated is 5.49 s-1 (Table 1), and the corresponding *EFGH for S3C and

S153C are 0.09 and 0.121 s-1 respectively (Table S2). It is worth noting that is the hydrolyzing rate constant of E3 state, the closed conformation of MalK2, and represents the maximum hydrolysis capacity of MalK2. In fact, a big fraction of E3 state does not have hydrolysis activity as indicated by the results that the apparent state probability of E3 is ~ 0.4 and the majority of it is ADP-bound (Fig. S6). Therefore, *EFGH is much lower than . Therefore, there are two factors that limit the hydrolysis rate of MalK2 in solution. One is the conformational fluctuation and the

other is the slow dissociation rate of ADP ( = 0.382 s-1). The values of *EFGH

are in good agreement with the values measured in the ATPase activity experiments (Table 2), indicating that the kinetic model is consistent with both smFRET and ensemble measurements and well describes the conformational transition coupled catalysis of MalK2.

Table 1. Calculated parameters in the kinetic model through global optimization 22


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Parameters

MalK2-S3C

MalK2-S153C

β12 (s-1)

0.551±0.0003

0.607±0.0005

β21 (s-1)

0.834±0.0004

0.723±0.0003

β23 (s-1)

0.261±0.0002

0.289±0.0009

β32 (s-1)

0.431±0.0001

0.579±0.0005

γ12(s-1)

0.443±0.0003

0.882±0.0004

γ21(s-1)

0.171±0.0002

0.628±0.0004

γ23(s-1)

0.277±0.0006

0.914±0.0005

γ32(s-1)

0.521±0.0001

0.773±0.0004

k-1D (s-1)

0.382±0.0002

0.382±0.0002

k3h (s-1)

5.49 ± 0.0014

5.49 ± 0.0014

Table 2. ATP hydrolysis turnover rates measured in ensemble experiment and calculated from the 9-state kinetic model. MalK mutants

KM

k2

fhydro

µM

s-1

s-1

WT

190.5±30.3

0.106

S3C

184.3±31.9

0.056

S153C

205.4±35.5

0.098

S3C/Dye

195.3±28.9

0.062

0.09±0.0017

S153C/Dye

196.0±28.4

0.092

0.121±0.0031

23



Page 24 of 35

Discussion The catalytic reactions of many enzymes are coupled with conformational changes that regulate the catalytic activity. Co-existing of multiple conformational states could result in very complicated reaction networks. In the case of MalK2, crystal structural studies revealed three conformational states (Fig. 1a) 18-19, 41-43 and it was established that the closed conformation is essential for ATPase activity.

44-45

Here, smFRET measurements allow us to obtain the populations of the three states and the transition kinetics among them under various nucleotide-binding conditions. It turns out that MalK2 has considerable intrinsic conformational flexibility, sampling all three states under both nucleotide-free and bound conditions. Many studies of protein dynamics show that this phenomenon is not rare, i.e. the protein has a remarkable population of a ligand-bound conformation in the absence of the ligand.11, 46-47 In this case, the ligand binding process is considered to follow a conformational selection mechanism. In the specific case of MalK2, we have shown that the population of the closed conformation (E3) (no matter in the absence or presence of nucleotides) is directly correlated with the ATPase activity. So the remarkable population of E3 in the absence of nucleotide is most likely beneficial for ATPase activity. We also noticed that though the E3 population under the hydrolyzing condition is as high as ~0.4, most of the proteins are Mg2+-ADP bound (Figure S5b&d). Therefore, it is likely that due to the inhibitory effect of Mg2+-ADP, a high population of E3 is crucial for ATPase activity of MalK2. Co-existing of three conformational states implicate a minimum nine-state 24


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reaction network of MalK2 during ATP hydrolysis (Fig. 4). Given the information of the state populations and transition kinetics, we derived the state-specific rate constants of hydrolysis reaction. For MalK2, the hydrolysis turnover number of E3 state is 50-fold larger than the overall turnover rate *EFGH . This turnover

number represents the upper limit of the ATPase activity of MalK2. In the intact MalFGK2 transporter, the ATPase activity of MalK2 could be stimulated by ~10-fold. 48

It is most likely that the transmembrane domains MalF and MalG help to stabilize

the closed conformation of MalK2. Under the hydrolyzing condition, the Mg2+-ATP bound E3 state occupies a very small portion in the measured E3 state (Fig. S6b&d), resulting in a small *EFGH corresponding to the low ATPase activity measured in the ensemble experiment. It is worth noting that the ATPase activity data of MalK2 from biochemical assay were based on Michaelis-Menten equation and agree well with the calculation result based on the kinetic model and the smFRET measurements. Previous studies of the validity of Michaelis-Menten equation in complex enzyme systems demonstrated that as the conformational transition rates are much slower than the catalytic reaction rates the MM equation remains valid.3 In the case of MalK2, the

rate constants of conformational transitions ($) , $) , $) and *$) ) are one order of

magnitude smaller than the ATP hydrolysis rate constant (Table 1). Besides the

population of E3 state, the other factor limiting the ATPase activity of MalK2 is the slow dissociation rate of Mg2+-ADP from the protein ( ). Therefore, our kinetic model analysis provides mechanism basis for the previous finding that Mg2+-ADP is a competitive inhibitor of ATP hydrolysis. 32 25



Here we developed a strategy to dissecting the mechanism of conformational dynamics regulated enzyme catalysis using smFRET. Though we elucidate the method by applying to MalK2, it is generally applicable to other enzymes. The advantage of the method is obvious that smFRET based method provides explicit information of conformational dynamics of the enzyme and the model analysis could give all the kinetic parameters in a complex catalysis network. However, the method has its own limitations. Now the strategy is designed based on the discrete conformational states of the enzyme. For system with a continuum of conformational changes, kinetic analysis based on HMM methods would not be valid. The accuracy of HMM analysis also depends on the clear separation of the conformational states, i.e., the conformational states are separated by prominent energy barriers on the free energy landscape. Nevertheless, we anticipate that this strategy could be widely applied to dissecting the mechanism of many conformation fluctuating enzymes.

ASSOCIATED CONTENT The supporting information are available free of charge via the Internet at http://pubs.acs.org. A table of Cα-Cα distances between the two S3 or S153 residues in various MalK2 crystal structures; a table of rate constants of conformational transitions among the three states of MalK2; a figure showing that MalK forms dimer in the absence of ATP; a figure of ATPase activity measurements of WT MalK2; a figure of Conformational distributions of Q140L mutant of MalK2; a figure showing the determination of the number of states of MalK2 by using variational Bayesian method; a figure 26


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showing the Global optimization values of state populations of the kinetic model.

AUTHOR INFORMATION

*Corresponding authors: Jianwei Liu Email: [email protected] Wenning Wang Email: [email protected] Notes The authors declare no competing financial interest.

AUTHOR CONTRIBUTIONS W.W. and J.L. designed the research. S.W. performed the biochemical and smFRET experiments. S.W. analyzed the smFRET data. J.L. and W.W. performed the kinetic model analysis. W.W. and J.L. wrote the paper. All authors contributed to data interpretation.

ACKNOELEDGEMENTS This work was supported by National Key Research and Development Program of China (2016YFA0501702), National Science Foundation of China (21773038, 21473034, 21375028). W.W. thanks Prof. Hong Qian for helpful discussions and critical reading of the manuscript.

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TOC Graphic

31



Fig. 1 The crystal structures of MalK2 and sample smFRET trajectories. (a) The labeling sites Ser3 (cyan sphere) and Ser153 (magenta sphere) are highlighted in four crystal structures including: isolated MalK2 in the nucleotide-free form (PDB-ID 3FH6); nucleotide-free MalK2 in the pre-translocation state of MalFGK2 transporter (PDB-ID 3PV0); ATP-bound MalK2 in the outward-facing state of MalFGK2 transporter (PDB-ID 2R6G); isolated MalK2 in Mg2+-ADP bound form (PDB-ID 2AWN). (b) Sample smFRET trajectories of MalK2S3C system. (c) Sample smFRET trajectories of MalK2-S153C system. 133x192mm (300 x 300 DPI)


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Fig. 2 Conformational state distributions of MalK2 measured by smFRET under nucleotide-free, ADP-bound and ATP-bound condition. FRET efficiency histogram for MalK2-S3C without nucleotide (a), in the presence of 5 mM ADP (b), and in the presence of 5 mM ATP (c). FRET efficiency histogram for MalK2-S153C without nucleotide (d), in the presence of 5 mM ADP (e), and in the presence of 5 mM ATP (f). Cartoons denoted E1, E2 and E3 represent the open, semi-open and closed state of MalK2. 148x83mm (300 x 300 DPI)



Fig. 3 Conformational state distributions of MalK2 measured by smFRET under Mg2+-only, Mg2+-ADP and hydrolyzing condition. FRET efficiency histogram for MalK2-S3C in the presence of 5mM Mg2+ (a), 5mM Mg2+-ADP (b), and 5 mM Mg2+-ATP (c). FRET efficiency histogram for MalK2-S153C in the presence of 5 mM Mg2+ (d), 5 mM Mg2+-ADP (e), and 5 mM Mg2+-ATP (f). 149x82mm (300 x 300 DPI)


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Fig. 4 Kinetic scheme of MalK2 ATPase. α_ij, β_ij, γ_ij are rate constants of conformational state transition. k_iD and k_iT are rate constants of Mg2+-ADP and Mg2+-ATP binding, and k_(-iD) and k_(-iT) are rate constants of Mg2+-ADP and Mg2+-ATP dissociation. 116x65mm (300 x 300 DPI)


Dissecting the Conformational Dynamics-Modulated Enzyme

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