Single-Molecule Stochastic Analysis of Channeling Enzyme

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Single-Molecule Stochastic Analysis of Channeling Enzyme Tryptophan Synthase Dimitri Loutchko, Didier Gonze, and Alexander Mikhailov J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b12229 • Publication Date (Web): 10 Feb 2016 Downloaded from http://pubs.acs.org on February 11, 2016

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The Journal of Physical Chemistry

Single-Molecule Stochastic Analysis of Channeling Enzyme Tryptophan Synthase Dimitri Loutchko,† Didier Gonze,‡ and Alexander S. Mikhailov∗,†,¶ Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Berlin, Germany, Unité de Chronobiologie théorique, Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium, and Department of Mathematical and Life Sciences, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526 Japan E-mail: [email protected]

∗

To whom correspondence should be addressed Fritz Haber Institute Berlin ‡ Université Libre de Bruxelles ¶ Hiroshima University †

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Abstract The channeling enzyme tryptophan synthase provides a paradigmatic example of a chemical nanomachine. It possesses two active centers and, as a single molecule, catalyzes 13 different reaction steps with a complex pattern of allosteric regulation and with an intermediate product channeled from one active center to another. Here, the first single-molecule stochastic model of the enzyme is proposed and analyzed. All its transition rate constants were deduced from the experimental data available and no fitting parameters were thus employed. Numerical simulations reveal strong correlations in the states of the active centers and the emergent synchronization of intramolecular processes in tryptophan synthase.

Keywords Enzyme complex, Markov modeling, intramolecular synchronization and correlation

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Introduction As a growing volume of evidence suggests, many biochemical reactions within a cell may be catalyzed not by independently operating enzymes, but by multi-enzyme complexes. 1–7 Such complexes can consist of tens of different proteins and implement entire metabolic pathways or significant parts of them. Within a complex, intermediate products can be directly channeled 2,3 to other enzymes for further processing, resembling the operation of an industrial conveyor belt. Moreover, different enzymes in a complex are usually coupled through allosteric regulatory loops. 7 Because of the product channeling and multiple allosteric interactions, a complex can operate in a synchronous manner, exhibiting strong correlations in the turnover cycles of involved enzymes. Experimental investigations of multi-enzyme complexes encounter difficulties because the complexes are often transient and only exist in vivo, inside a cell. 4 There is however a class of channeling enzymes 8,9 (see also review 10 ) which are similar in their properties to multi-enzyme complexes, but, in contrast to them, are smaller and stable. An outstanding example of a channeling enzyme is provided by tryptophan synthase. 11 It catalyzes the biosynthesis of the essential amino acid tryptophan from serine and indole glycerol phosphate (IGP). This enzyme is employed by all bacteria, plants, yeasts and molds, but not by higher organisms and thus can be a target for the development of antibiotics. 12 Its substrate IGP is scarce inside the cell and therefore high catalytic efficiency is required. Furthermore, an intermediate product (indole) of the synthesis reaction is hydrophobic and can easily escape through the cell membrane. Therefore, its release into the cytoplasm must be avoided. Nature has found an elegant solution for these constraints. The entire synthesis encompassing 13 elementary reaction steps is performed within a single enzyme with two different catalytic centers and the intermediate indole is channeled within the protein from one center to another. Tryptophan synthase has been extensively experimentally investigated, both in terms of its kinetics and conformational dynamics. 13–25 Already in 1958, it has been found that the 3



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intermediate indole produced by cleavage of IGP is not released into solution. 26 Spectroscopic properties of the pyridoxal phosphate (PLP) cofactor at one catalytic site have allowed to study the kinetics of tryptophan synthase on short timescales. The use of equilibrium, rapid mixing stopped-flow techniques and pressure and temperature jump relaxation methods have led to the formulation of a detailed chemical reaction mechanism. 13–16 In 1990, rapid-scanning stopped-flow and single-wavelength stopped-flow experiments have indicated that binding of a ligand at one catalytic site affects the catalytic activity and conformational environment at the second catalytic center. 17 This has led to the studies where the kinetic 19–22 and stuctural 23–25 aspects of allostery in this enzyme were explored. Today, due to a large volume of data, tryptophan synthase plays a key role in the understanding of allostery, channeling and intramolecular synchronization. Several detailed reviews 11,27–29 are available, with the authors describing tryptophan synthase as an allosteric molecular factory, 27 a channeling nanomachine 28 or even a “mine for enzymologists”. 29 Kinetic models for tryptophan synthase have been previously proposed and investigated. 13,15 However, these models were based on classical kinetic rate equations: Effectively, the two catalytic centers in the same enzyme were treated as two different and statistically independent chemical species, so that correlations between them could not be considered. The aim of the present study is to construct and investigate the single-molecule model of tryptophan synthase which takes into account correlations between the states of the two catalytic centers arising through substrate channeling and mutual allosteric regulation. The stochastic model is formulated in terms of a Markov network. Because of extensive experimental data available, all rate constants of the model could be directly deduced from the data, so that no fitting parameters have been employed. Numerical simulations yield direct evidence of the presence of strong correlations and intramolecular synchronization of chemical processes in tryptophan synthase. They also allow us to analyze the role of allosteric regulations in raising the catalytic efficiency of this enzyme. Generally, this study sets a framework for analogous kinetic modeling of other channeling enzymes and of multi-enzyme

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complexes.

Single-Molecule Stochastic Model Tryptophan synthase is a heterodimeric enzyme with a linear αββα alignment of its subunits. Fig. 1A shows the structure of one αβ element from Salmonella Typhimurium with its characteristic features. The α-subunit of tryptophan synthase catalyzes the cleavage of indole glycerol phosphate (IGP) to yield indole and glyceraldehyde-3-phosphate (G3P) in a concerted reaction (Fig. 1B). The β-subunit catalyzes the substitution of a serine hydroxy group by indole to produce the final product tryptophan. The catalytic cycle at the β-site consists of 9 elementary reactions (Fig. S1). A reduced mechanism, which does not include one fast reaction (see Methods), is shown in Fig. 1B. The reactions at both subunits are coupled by allosteric interactions and substrate channeling. The presence of IGP at the α-site increases the rate of formation of the aminoacrylate A-A at the β-site. 22 The presence of A-A at the β-site in turn activates the cleavage of IGP . 19 The intermediate indole is released at the α-site and is then channeled through the internal tunnel to the β-site where it reacts with dehydrated serine to yield the final product tryptophan. The mutual rate enhancements of the two subunits are mediated by the COMM domain (residues β102 to β189) and the loops αL2 and αL6 (Fig. 1A): 22,23,30 When the enzyme enters its catalytically active state, the COMM domain performs a tilting motion, which serves to close the gate to the catalytic center of the β-subunit. It also induces conformational changes of αL2 and αL6 which adopt a conformation that prevents the escape of substrates from the α-site into the cytoplasm. 31 Two conformational states are distinguished: the catalytically inactive state with open gates (“open conformation”) and the state with enhanced catalytic activity and closed gates (“closed conformation”). 25 The catalytic operation and respective conformational changes of tryptophan synthase are schematically represented in Fig. 1C.

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Calorimetric measurements show that tryptophan synthesis is exergonic, accompanied by heat release. 32 There is a large difference in Gibbs free energies ∆r Gm = −50.7 kJ·mol−1 between products (G3P, tryptophan and water) and substrates (IGP and serine) in this reaction, corresponding to an energy difference of about 20 kB T between the substrates and products. For the reverse reaction to occur, the enzyme would have to extract 20 kB T from thermal fluctuations of its environment. This is highly improbable and therefore the reverse reaction is not observed for tryptophan synthase. There is no reverse indole channeling in the reaction scheme (Fig. 1B). Such processes could not be observed in the available experiments including the studies. 13,15,33 Apparently, this is because of a large energy difference in the states of indole before and after channeling. Reverse binding of products (G3P and tryptophan) is also not included in the reaction scheme. Such reactions are possible and their rate constants are known (see Table S1). However, the experiments are not performed at equilibrium conditions. Typically (see e.g. 13–16,20 ), they are started in absence of products and measurements are finished before a significant amount of products is accumulated. Previous kinetic models for tryptophan synthase 13,15 used classical chemical rate equations to describe the change in concentrations of reaction intermediates. Taking this approach, the α- and β-subunits of one tryptophan synthase molecule were effectively treated as separate enzyme species. Thus, intramolecular correlations and synchronization in the cycles of the two subunits, arising through allosteric interactions and substrate channeling could not be taken into acoount in such early studies. In contrast, below we construct and investigate a stochastic model describing the operation of a single tryptophan synthase molecule. The catalytic α- and β-sites can be empty or can have ligands (substrates, products and intermediates) bound. At any time, the enzyme has a certain chemical state defined by the ligands. At the α-site, the single tryptophan synthase enzyme can thus adopt four different chemical states, i.e. empty, IGP, indole+G3P or G3P. Similarly, there are five chemical

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Figure 1: Tryptophan synthase as a chemical nanomachine. (A) Structure of the enzyme from Salmonella Typhimurium (PDB code: 2J9X 22 ). (B) Reduced reaction scheme. The internal aldimine E(Ain) corresponds to the PLP cofactor without any bound ligand. It is therefore referred to as empty throughout the text. (C) Operation of the machine: Once substrates are bound (a) at both catalytic sites, IGP activates (b) the formation of A-A and the enzyme adopts the closed conformation. A-A activates (c) the cleavage of IGP and indole is channeled (d) to the β-site where it reacts (e) with A-A to give Q3 . Q3 undergoes (f) further transformations that return of the enzyme to the open conformation where tryptophan and G3P are released (g).

states empty, Q1 , A-A, Q3 and Aex2 which can be adopted by the β-site (see SI for details). Below, we denote the states of the α- and β-sites by sα and sβ . Then, each chemical state of a single tryptophan synthase molecule can be written as a combination (sα |sβ ). Within its catalytic cycle, the tryptophan synthase molecule undergoes a sequence of reaction events each associated with a change of its chemical state. This sequence can be considered as a random walk over the set of states (sα |sβ ). The set of states together with the possible transitions between them defines a Markov network. The complete Markov network for tryptophan synthase corresponding to the reaction scheme (Fig. 1B) is shown in Fig. 2A. Note the presence of the “futile” states (indole+G3P|Q3 )

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or (G3P|A-A) (orange boxes in Fig. 2A). In these states, the enzyme cannot catalyze any fertile reactions, because it either contains two indole equivalents (state (indole+G3P|Q3 )) or no indole equivalents (state (G3P|A-A)). Thus, to proceed further with fertile catalytic reactions, the enzyme has to return to an open conformation to release the product bound at one catalytic site and bind new substrate. “Futile” states do not contribute to the catalytic reaction, but lead to an increase of the turnover time. Alternatively, the same stochastic model can be formulated in terms of the two interacting Markov chains for the α- and β-sites (Fig. 2B). The reactions modify the states of one subunit, but they can be enhanced or inhibited (blocked) depending on the state of the other subunit. Additionally, there is one reaction (i.e., indole channeling) which simultaneously changes the states of both subunits.

Results In our stochastic numerical simulations, we reproduce the chemical reaction course inside a single tryptophan synthase enzyme (see Methods). Starting from the state (empty|empty), the enzyme performs a random walk on the Markov network shown in Fig. 2A. This walk represents a series of transitions whose probability rates are all known. The cycle ends when both products are released and the enzyme returns to its initial state. An example of a 2.13 s time series is shown in Fig. 3A. In the simulations, numerical data for one million turnover cycles has been collected and analyzed. Fig. 3B shows the distribution of overall turnover times for tryptophan synthase. The mean turnover time is µ = 0.15 s. However, it has a thin long tail of cycle durations on the order of several seconds. This tail is a result of stochastic fluctuations that drive the two catalytic sites out of phase and lead to prolonged retention in the “futile” states (indole+G3P|Q3 ) and (G3P|A-A). We have checked that, if the transitions to all “futile” states (orange boxes in Fig. 2A) are blocked, the tail disappears.

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Figure 2: Single-molecule stochastic model of tryptophan synthase. (A) Markov network with numerical values of transition rates [s−1 ]. Green and blue colors correspond to open and closed conformations. (B) Equivalent representation as two interacting Markov chains. Magenta: transitions blocked in the states A-A and Q3 of the β-site. Green (light and dark): blocked in the state empty of the α-site. Light green: enhanced by a factor of 9.7 in the state IGP of the α-site. Blue (light and dark): blocked in the states empty, Q1 , Aex2 of the β-site. Light blue: enhanced by a factor of 27.7 in the state A-A of the β-site. Red: Channeling instantaneously changes the states of both sites. Using the simulation data, joint probabilities P (sα , sβ ) to find the enzyme in different compatible combinations of internal states (sα |sβ ) were determined. These probabilities are displayed in Fig. 4; their numerical values are given in Table S2. Once both substrates have arrived, the enzyme quickly proceeds to indole formation and channeling. After that, it stays however for a long time in the state (G3P|Q3 ). The probabilities P (sα ) and P (sβ ) to find the enzyme in the states sα and sβ irrespectively of the states at the other subsite can be obtained by summing P (sα , sβ ) over all states of the other subsite (see Supplementary Information for their numerical values). If the α- and β-subunits of the enzyme were independent chemical species, the joint prob9



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clearly demonstrates the buildup of synchronization in tryptophan synthase. Our stochastic model can be used not only to reproduce the actual operation of tryptophan synthase, but also to perform in silico studies of its operation mechanism and of the role of allosteric regulation in its function. As shown in Fig. 2, there are two reactions steps which are allosterically activated, i.e. the transitions of Q1 to A-A and of IGP to indole+G3P. How does the action of the enzyme at the single-molecule level change if both allosteric regulations are switched off or both permanently activated? To answer this question, we have performed simulations in the absence or permanent presence of both activations. They show that the mean turnover time of the native enzyme (µ = 0.15 s) is about two times shorter than that of the hypothetical enzyme with absent (µ = 0.26 s) and more than three times shorter than that of the hypothetical enzyme with permanently present (µ = 0.52 s) activations. While the increase of the turnover times in absence of activations is well expected, since some transitions in the main catalytic pathway become slower, their increase under permanent activations needs further analysis. Figure 6 shows occupation probabilities of different enzyme states in such two cases. Comparing Fig. 6A with Fig. 4A, we can notice that, in absence of activations, the enzyme spends more time in the states (IGP|Q1 ) and (IGP|AA), the transitions from which are slowed down. When both activations are permanently present (Fig. 6B), the occupations probabilities of these states become close to those for the native enzyme (Fig. 4A). However, the enzyme now spends much time in the futile state (indole+G3P|Q3 ). This explains a decrease in the catalytic efficiency when both allosteric activations are permanently present. The turnover time distribution of the enzyme with permanent activations closely resembles the distribution of the native enzyme for small turnover times. In these cases, the enzymes do not enter “futile” states. However, the histogram of the enzyme with permanent activations has a long tail of cycle durations ranging up to 14 s (Fig. 7). Once a “futile” state is reached, this enzyme can dwell there for a long time thus decreasing the catalytic

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that allows a detailed exploration of intramolecular synchronization phenomena. Because tryptophan synthase has been broadly invesigated in the past, providing indeed a "mine for enzymologists", 29 all model parameters could be extracted from the available experimental data. Through numerical simulations of the developed stochastic model, the statistics of turnover cycles in this enzyme could be determined. The predicted mean turnover time under the saturation concentrations was found to be equal to 0.15 s which is comparable with the values of 0.20 18 and 0.30 s 19 reported under different experimental conditions. As we have found, the distribution of turnover times possesses a long tail and, with significant probability, turnover cycles with the duration of a few seconds should also be observed. They are explained by dwelling of the enzyme in the futile states where the catalytic conversion becomes blocked. The dependence of the turnover rate on substrate concentrations is discussed in the Supplementary Information, Section 4. The model yields direct theoretical evidence for intramolecular synchronization phenomena. We find that correlations between instantaneous chemical states of the two catalytic subunits can be as high as 0.61, while the absence of correlations corresponds to the zero value and the maximal possible correlation level is one. We could also see how temporal correlations become enhanced along the main catalytic pathway in the enzyme molecule, with the mean-square-root time dispersion falling from about 22 ms for the arrival of substrates to only about 2 ms for the arrival of intermediate products for the final catalytic conversion event. By using the model, the aspects of catalytic efficiency and allosteric regulation in tryptophan synthase could furthermore be explored. While intramolecular channeling of indole is already strongly contributing towards the efficiency by preventing its loss in a biological cell and minimizing the time needed for the transfer of this intermediate from one catalytic center to another, complex allosteric regulation contributes to further efficiency gains. Particularly, this allows to avoid, to a large extent, dwelling in the futile states which correspond to the non-productive side branches of the intramolecular catalytic pathway and thus accelerates

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the overall catalytic conversion. Despite the fact that extensive kinetic measurements and X-ray diffraction observations have been performed, tryptophan synthase has not been so far investigated in experiments with single molecules, by employing, e.g., fluorescence correlation spectroscopy 34 or FRET 35,36 methods. We strongly hope that the results of our study would bring the attention to very interesting possible experiments with this enzyme, where intramolecular synchronization and the effects of strong correlations could be directly demonstrated at the single molecule level. As mentioned in the Introduction, tryptophan synthase represents a characteristic example of a channeling enzyme and, generally, can be viewed as an analog of multi-enzyme complexes that play an important role in biological cells. Beyond the case of this specific enzyme, our study provides a theoretical framework for single-molecule kinetic modeling of such chemical nano-factories where entire complex catalytic pathways are efficiently implemented within one molecular nanoscale aggregate or a single oligomeric enzyme.

Methods Analysis of experimental kinetic data and network construction The available experimental data for tryptophan synthase has been gathered and analyzed in order to extract the transition rate constants in the Markov model. This is explained in the Supplementary Information where a complete set of rate constants can be found in Fig. S2. The substrate concentrations were fixed to values of 2.08 mM for serine and 24.7 µM for IGP from the experiments. 15,19 Using these concentration values, first order rate constants for substrate binding reactions were obtained. The concentrations of both products, tryptophan and G3P, were set to zero. The adiabatic elimination procedure is explained in the Supplementary Information. The set of kinetic constants used in the final reduced model is given in Fig. 2.

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Stochastic simulations and data analysis The random walk on the Markov network of chemical states was simulated using the Gillespie algorithm. 37 Joint occupation probabilities P (sα , sβ ) for different states sα and sβ were always obtained from stochastic simulations of 106 turnover cycles. The following procedure has been used to characterize intramolecular correlations. For any two chosen states sα and sβ of α- and β-subunits, we define random binary variables X(sα ) and X(sβ ) which take values 1 if the respective subunit is in the chosen state and zero otherwise. The elements of the correlation matrix c(sα , sβ ) are defined as Pearson correlation coefficients of the random variables X(sα ) and X(sβ ), i.e. as hX(sα )X(sβ )i − hX(sα )ihX(sβ )i p c(sα , sβ ) = p hX(sα )2 i − hX(sα )i2 hX(sβ )2 i − hX(sβ )i2

(1)

where h...i denotes the ensemble averaging. Thus defined, the correlation coefficients take the maximum value of 1 if X(sα ) = X(sβ ) and the minimal value of -1 if X(sα ) = −X(sβ ). They are expressed in terms of the occupation probabilities as

c(sα , sβ ) = p

P (sα , sβ ) − P (sα )P (sβ ) p P (sα ) − P (sα )2 P (sβ ) − P (sβ )2

(2)

where P (sα , sβ ) is the joint probability to find the two enzyme subunits in the respective P P states and P (sα ) = sβ P (sα , sβ ), P (sβ ) = sα P (sα , sβ ). Figure 1A was created with VMD. 38

Acknowledgement The authors are grateful to Gerhard Ertl for his valuable support and stimulating discussions. Financial support from Deutsche Forschungsgemeinschaft through the Research Training Group GRK 1558 and from the Volkswagen Foundation (Germany) is acknowledged.

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Supporting Information Available Details for the construction of the Markov network model, numerical values for data shown in Figs. 3, 4, 5 and 6, and a discussion of the dependence of turnover rates on substrate concentrations are given in the Supplementary Information. This material is available free of charge via the Internet at http://pubs.acs.org/.

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(7) Nussinov, R.; Ma, B.; Tsai, C. J. A Broad View of Scaffolding Suggests that Scaffolding Proteins Can Actively Control Regulation and Signaling of Multienzyme Complexes through Allostery. Biochim. Biophys. Acta 2012, 1834, 820-829. (8) Miles, E. W. The Molecular Basis of Substrate Channeling. J. Biol. Chem. 1999, 274, 12193-12196. (9) Chuenchor, W.; Doukov, T. I.; Resto, M.; Chang, A.; Gerratana, B. Regulation of the Intersubunit Ammonia Tunnel in Mycobacterium Tuberculosis Glutamine-Dependent NAD+ Synthetase. Biochem. J. 2012, 443, 417-426. (10) Huang, X.; Holden, H. M.; Raushel, F. M. Channeling of Substrates and Intermediates in Enzyme-Catalyzed Reactions. Annu. Rev. Biochem. 2001, 70, 149-180. (11) Dunn, M. F. Allosteric Regulation of Substrate Channeling and Catalysis in the Tryptophan Synthase Bienzyme Complex. Arch. Biochem. Biophys. 2012, 519, 154-166. (12) Amadasi, A.; Bertoldi, M.; Contestabile, R.; Bettati, S.; Cellini, B.; di Salvo, M. L.; Borri-Voltattorni, C.; Bossa, F. Mozzarelli, A. et al. Pyridoxal 5’-Phosphate Enzymes as Targets for Therapeutic Agents. Curr. Med. Chem. 2007, 14, 1291-1324. (13) Lane, A. N.; Kirschner, K. The Catalytic Mechanism of Tryptophan Synthase from Escherichia Coli. Eur. J. Biochem. 1983, 129, 571-582. (14) Drewe, W. F.; Dunn, M. F. Characterization of the Reaction of L-serine and Indole with Escherichia Coli Tryptophan Synthase via Rapid-Scanning Ultraviolet-Visible Spectroscopy. Biochemistry 1986, 25, 2494-2501. (15) Anderson, K. S.; Miles, E. W.; Johnson, K. A. Serine Modulates Substrate Channeling in Tryptophan Synthase. Eur. J. Biol. Chem. 1991, 266, 8020-8033. (16) Woehl, E.; Dunn, M. F. Mechanisms of Monovalent Cation Action in Enzyme Catalysis: the Tryptophan Synthase α-, β-, and α-β-Reactions. Biochemistry 1999, 38, 7131-7141. 18


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(17) Dunn, M.F.; Aguilar, V.; Brzović, P.; Drewe, W. F.; Houben, K. F.; Leja, C. A.; Roy, M. et al. The Tryptophan Synthase Bienzyme Complex Transfers Indole between the α- and β-Sites via a 25-30 Å Long Tunnel. Biochemistry 1990, 29, 8598-8607. (18) Lane, A. N.; Kirschner, K. The Mechanism of Tryptophan Binding to Tryptophan Synthase from Escherichia Coli. Eur. J. Biochem. 1981, 120, 379-387. (19) Brzović, P. S.; Ngo, K.; Dunn, M. F. Allosteric Interactions Coordinate Catalytic Activity Between Successive Metabolic Enzymes in the Tryptophan Synthase Bienzyme Complex. Biochemistry 1992, 31, 3831-3839. (20) Brzović, P. S.; Sawa, Y.; Hyde, C. C.; Miles, E. W.; Dunn, M. F. Evidence that Mutations in a Loop Region of the α-Subunit Inhibit the Transition from an Open to a Closed Conformation in the Tryptophan Synthase Bienzyme Complex. J. Biol. Chem. 1992, 267, 13028-13038. (21) Leja, C. A.; Woehl, E. U.; Dunn, M. F. Allosteric Linkages between β-Site Covalent Transformations and α-Site Activation and Deactivation in the Tryptophan Synthase Bienzyme Complex. Biochemistry 1995, 34, 6552-6561. (22) Ngo, H.; Kimmich, N.; Harris, R.; Niks, D.; Blumenstein, L.; Kulik, V.; Barends, T. R.; Schlichting, I.; Dunn, M. F. Allosteric Regulation of Substrate Channeling in Tryptophan Synthase: Modulation of the L-Serine Reaction in Stage I of the β-Reaction by α-Site Ligands. Biochemistry 2007, 46, 7740-7753. (23) Schneider, T. R.; Gerhardt, E.; Lee, M.; Liang, P. H.; Anderson, K. S.; Schlichting, I. Loop Closure and Intersubunit Communication in Tryptophan Synthase. Biochemistry 1998, 37, 5394-5406. (24) Weyand, M., Schlichting, I., Marabotti, A. & Mozzarelli, A. Crystal structures of a new class of allosteric effectors complexed to tryptophan synthase. J. Biol. Chem. 2002, 277, 10647-10652. 19



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Single-Molecule Stochastic Analysis of Channeling Enzyme

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