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Enzyme Kinetics for Complex System Enables Accurate Determination of Specificity Constants of Numerous Substrates in a Mixture by Proteomics Platform*

  • Zhenzhen Deng
    Affiliations
    Key Laboratory of Separation Science for Analytical Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China;

    Graduate School of Chinese Academy of Sciences, Beijing 100049, China
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  • Jiawei Mao
    Affiliations
    Key Laboratory of Separation Science for Analytical Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China;

    Graduate School of Chinese Academy of Sciences, Beijing 100049, China
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  • Yan Wang
    Affiliations
    Key Laboratory of Separation Science for Analytical Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China;

    Graduate School of Chinese Academy of Sciences, Beijing 100049, China
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  • Hanfa Zou
    Footnotes
    Affiliations
    Key Laboratory of Separation Science for Analytical Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China;
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  • Mingliang Ye
    Correspondence
    To whom correspondence should be addressed:Dalian Institute of Chemical Physics, Chinese Academy of Sciences, CAS Key Lab of Separation Sciences for Analytical Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023 China Tel.:86-411-84379620; E-mail:.
    Affiliations
    Key Laboratory of Separation Science for Analytical Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China;
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  • Author Footnotes
    * This work was supported, in part, by funds from the China State Key Basic Research Program Grants (2016YFA0501402, 2013CB911202), the National Natural Science Foundation of China (21235006, 21321064, 21535008, 81430072, 81361128015). MY is a recipient of the National Science Fund of China for Distinguished Young Scholars (21525524).
    This article contains supplemental material.
    † Deceased April 25, 2016.
Open AccessPublished:November 16, 2016DOI:https://doi.org/10.1074/mcp.M116.062869

      Abstract

      Many important experiments in proteomics including protein digestion, enzyme substrate screening, enzymatic labeling, etc., involve the enzymatic reactions in a complex system where numerous substrates coexists with an enzyme. However, the enzyme kinetics in such a system remains unexplored and poorly understood. Herein, we derived and validated the kinetics equations for the enzymatic reactions in complex system. We developed an iteration approach to depict the enzymatic reactions in complex system. It was validated by 630 time-course points from 24 enzymatic reaction experiments and was demonstrated to be a powerful tool to simulate the reactions in the complex system. By applying this approach, we found that the ratio of substrate depletion is independent of other coexisted substrates under specific condition. This observation was then validated by experiments. Based on this striking observation, a simplified model was developed to determine the catalytic efficiencies of numerous competing substrates presented in the complex enzyme reaction system. When coupled with high-throughput quantitative proteomics technique, this simplified model enabled the accurate determination of catalytic efficiencies for 2369 peptide substrates of a protease by using only one enzymatic reaction experiment. Thus, this study provided, in the first time, a validated model for the large scale determination of specificity constants which could enable the enzyme substrate screening approach turned from a qualitative method of identifying substrates to a quantitative method of identifying and prioritizing substrates. Data are available via ProteomeXchange with identifier PXD004665.
      Enzymes play a key role in nearly all signal transduction cascades and metabolic pathways. Overexpression and/or dysregulation of enzymes result in many diseases, thus providing numerous drug targets for multiple therapeutic areas (
      • Kho C.
      • Lee A.
      • Jeong D.
      • Oh J.G.
      • Gorski P.A.
      • Fish K.
      • Sanchez R.
      • DeVita R.J.
      • Christensen G.
      • Dahl R.
      • Hajjar R.J.
      Small-molecule activation of SERCA2a SUMOylation for the treatment of heart failure.
      ,
      • Mirtschink P.
      • Krishnan J.
      • Grimm F.
      • Sarre A.
      • Horl M.
      • Kayikci M.
      • Fankhauser N.
      • Christinat Y.
      • Cortijo C.
      • Feehan O.
      • Vukolic A.
      • Sossalla S.
      • Stehr S.N.
      • Ule J.
      • Zamboni N.
      • Pedrazzini T.
      • Krek W.
      HIF-driven SF3B1 induces KHK-C to enforce fructolysis and heart disease.
      ,
      • Webb B.A.
      • Forouhar F.
      • Szu F.E.
      • Seetharaman J.
      • Tong L.
      • Barber D.L.
      Structures of human phosphofructokinase-1 and atomic basis of cancer-associated mutations.
      ). Identification and further prioritizing new substrates are important for the study of the enzymology of the selected enzymes and the next generation of drug targets (
      • Noble M.E.
      • Endicott J.A.
      • Johnson L.N.
      Protein kinase inhibitors: insights into drug design from structure.
      ). Because of the well-developed enzyme kinetics theories and assay methods, the screening for optimal substrates is often performed by using the in vitro enzymatic reaction system involving an enzyme and a substrate (
      • Rossé G.
      • Kueng E.
      • Page M.G.
      • Schauer-Vukasinovic V.
      • Giller T.
      • Lahm H.W.
      • Hunziker P.
      • Schlatter D.
      Rapid identification of substrates for novel proteases using a combinational peptide library.
      ,
      • Saghatelian A.
      • Trauger S.A.
      • Want E.J.
      • Hawkins E.G.
      • Siuzdak G.
      • Cravatt B.F.
      Assignment of endogenous substrates to enzymes by global metabolite profiling.
      ,
      • Schlüter H.
      • Rykl J.
      • Thiemann J.
      • Kurzawski S.
      • Gobom J.
      • Tepel M.
      • Zidek W.
      • Linscheid M.
      Mass spectrometry-assisted protease substrate screening.
      ,
      • Patterson A.W.
      • Wood W.J.
      • Ellman J.A.
      Substrate activity screening (SAS): a general procedure for the preparation and screening of a fragment-based non-peptidic protease substrate library for inhibitor discovery.
      ). However, such approach requires purified substrate and large amounts of material. There is an increasing interest in using a pool of different substrates for substrate screening. Highly complex substrate libraries including the synthetic oligonucleotide or peptide mixture (
      • Gläsner W.
      • Merkl R.
      • Schellenberger V.
      • Fritz H.J.
      Substrate preferences of Vsr DNA mismatch endonuclease and their consequences for the evoluton of the Escherichia coli K-12 genome.
      ,
      • Turk B.E.
      • Huang L.L.
      • Piro E.T.
      • Cantley L.C.
      Determination of protease cleavage site motifs using mixture-based oriented peptide libraries.
      ), the peptide library derived from the digestion of proteins in total cell lysate (
      • Schilling O.
      • Overall C.M.
      Proteome-derived, database-searchable peptide libraries for identifying protease cleavage sites.
      ,
      • Wang C.
      • Ye M.
      • Bian Y.
      • Liu F.
      • Cheng K.
      • Dong M.
      • Dong J.
      • Zou H.
      Determination of CK2 specificity and substrates by proteome-derived Peptide libraries.
      ) and the proteins in total cell lysate (
      • Bian Y.
      • Ye M.
      • Wang C.
      • Cheng K.
      • Song C.
      • Dong M.
      • Pan Y.
      • Qin H.
      • Zou H.
      Global Screening of CK2 Kinase Substrates by an Integrated Phosphoproteomics Workflow.
      ,
      • Sivars U.
      • Aivazian D.
      • Pfeffer S.R.
      Targets of the cyclin-dependent kinase Cdk1.
      ) were used for substrate screening. In such experiments, an enzyme was incubated with numerous competing substrates for enzymatic reaction which would generate numerous different products. The state of art high throughput assay approaches like mass spectrometry-based proteomics are able to monitor the changing of substrates or products during the course of this type of complex enzymatic reactions. As a result, numerous new substrates could be identified by such substrate screening approach (
      • Gläsner W.
      • Merkl R.
      • Schellenberger V.
      • Fritz H.J.
      Substrate preferences of Vsr DNA mismatch endonuclease and their consequences for the evoluton of the Escherichia coli K-12 genome.
      ,
      • Turk B.E.
      • Huang L.L.
      • Piro E.T.
      • Cantley L.C.
      Determination of protease cleavage site motifs using mixture-based oriented peptide libraries.
      ,
      • Schilling O.
      • Overall C.M.
      Proteome-derived, database-searchable peptide libraries for identifying protease cleavage sites.
      ,
      • Wang C.
      • Ye M.
      • Bian Y.
      • Liu F.
      • Cheng K.
      • Dong M.
      • Dong J.
      • Zou H.
      Determination of CK2 specificity and substrates by proteome-derived Peptide libraries.
      ,
      • Bian Y.
      • Ye M.
      • Wang C.
      • Cheng K.
      • Song C.
      • Dong M.
      • Pan Y.
      • Qin H.
      • Zou H.
      Global Screening of CK2 Kinase Substrates by an Integrated Phosphoproteomics Workflow.
      ,
      • Sivars U.
      • Aivazian D.
      • Pfeffer S.R.
      Targets of the cyclin-dependent kinase Cdk1.
      ,
      • Xue L.
      • Wang W.
      • lliuk A.
      • Hu L.
      • Galan J.A.
      • Yu S.
      • Hans M.
      • Geahlen R.L.
      • Tao W.A.
      Sensitive kinase assay linked with phosphoproteomics for identifying direct kinase substrates.
      ). However, prioritizing new substrates is usually not achieved because the kinetic constants were typically not determined due to the lacking of well-studied kinetics theory for such a complex reaction system. Because the high specificity and efficiency of the enzymatic reactions, enzyme is also an important tool for biological studies. Especially the genomics and proteomics techniques are enabled by the application of some well characterized enzymes as the tool to selectively cleave the sites on the sequences (
      • Swaney D.L.
      • Wenger C.D.
      • Coon J.J.
      Value of using multiple proteases for large-scale mass spectrometry-based proteomics.
      ,
      • Anders C.
      • Niewoehner O.
      • Duerst A.
      • Jinek M.
      Structural basis of PAM-dependent target DNA recognition by the Cas9 endonuclease.
      ). The enzymatic reactions for such applications are also often performed in the complex system where numerous competing substrates present. For example, the digestion of proteome sample in shot-gun proteomics involves the incubation of a protease with all proteins presented in total cell lysate (
      • Bian Y.
      • Ye M.
      • Song C.
      • Cheng K.
      • Wang C.
      • Wei X.
      • Zhu J.
      • Chen R.
      • Wang F.
      • Zou H.
      Improve the coverage for the analysis of phosphoproteome of HeLa cells by a tandem digestion approach.
      ), the enzymatic labeling of peptides for quantitative proteomics involves the incubation of an enzyme with all peptides derived from a proteome (
      • Petritis B.O.
      • Qian W.J.
      • Camp 2nd, D.G.
      • Smith R.D.
      A simple procedure for effective quenching of trypsin activity and prevention of 18O-labeling back-exchange.
      ,
      • Pan Y.
      • Ye M.
      • Zhao L.
      • Cheng K.
      • Dong M.
      • Song C.
      • Qin H.
      • Wang F.
      • Zou H.
      N-terminal labeling of peptides by trypsin-catalyzed ligation for quantitative proteomics.
      ). Unfortunately, the kinetics model to describe the enzymatic reactions in such a complex system is still lacking.
      The classic Michaelis-Menten model derived one century ago (
      • Michaelis L.
      • Menten M.L.
      Die Kinetik der INvertinwirkung.
      ) is still routinely used to characterize the catalytic power and selectivity of enzymes. It should be mentioned that the equations derived from the classic model are usually derived and validated for the uni-uni enzymatic reaction system involving only one enzyme and one substrate. Application of these equations to the complex system without serious consideration of the competitive binding of the coexisted numerous alternative substrates is tend to draw wrong conclusion or obtain inaccurate results. For example, a conclusion that high-abundance proteins in a protein mixture could be digested earlier than low abundance proteins based on the kinetic equation derivation (
      • Fonslow B.R.
      • Stein B.D.
      • Webb K.J.
      • Xu T.
      • Choi J.
      • Park S.K.
      • Yates 3rd., J.R.
      Digestion and depletion of abundant proteins improves proteomic coverage.
      ) was later proved to be incorrect by experiments (
      • Ye M.
      • Pan Y.
      • Cheng K.
      • Zou H.
      Protein digestion priority is independent of protein abundances.
      ). Recently, pseudo-first-order kinetic equations have been applied to determine hundreds of catalytic efficiencies (i.e., specificity constants (kcat/Km)) of substrates by monitoring the appearance of the cleaved peptides in lysate as a function of time after a protease was added using LC-MS/MS (
      • Agard N.J.
      • Mahrus S.
      • Trinidad J.C.
      • Lynn A.
      • Burlingame A.L.
      • Wells J.A.
      Global kinetic analysis of proteolysis via quantitative targeted proteomics.
      ,
      • Julien O.
      • Zhuang M.
      • Wiita A.P.
      • O'Donoghue A.J.
      • Knudsen G.M.
      • Craik C.S.
      • Wells J.A.
      Quantitative MS-based enzymology of caspases reveals distinct protein substrate specificities, hierarchies, and cellular roles.
      ). This is truly a high throughput approach to prioritize enzyme substrates. It should be noted that the enzymatic reaction in a simple system could be considered as pseudo-first-order reaction only when the reaction is taken place at low substrate concentrations meeting [S] << Km. However, the protein concentration was not given in their studies. More importantly, pseudo-first-order kinetic equation has never been derived and validated for the complex system as above. Clearly direct application of this equation without knowledge of its applicable conditions is not scientifically rigorous and the catalytic efficiencies determined in their studies could be inaccurate. To prevent falsely or improperly using of kinetic equations, it is urgent to systematically investigate the enzymatic kinetics in the complex system.
      The derivation of theoretic models to depict the enzymatic reactions in the complex system is challenging. The obtaining of rate equation for the enzymatic reaction of each coexisted substrate is quite easy. However, solution solving of the resulting differential equation set is extremely difficult. In this study, we proposed an iteration approach to solve this problem. The detailed process for implementing this approach is outlined in Fig. 1A. By this way, the free enzyme concentration, the reaction rate for each substrate, the free concentration for each substrate and the portion of substrate consumed for any time point during the reaction could be predicted, which enabled the plotting of corresponding progress curves. It was validated by 630 time-course points from 24 enzymatic reaction experiments with various substrate concentrations. In addition, we found that the ratio of substrate depletion was independent of other coexisted substrates when the term x=1n[Sx]Kmx is insignificant, which resulted in the derivation of a simplified model to depict such system. When a high-throughput proteomics approach was applied to monitoring the Glu-C catalyzed hydrolysis of a peptide library, the catalytic efficiencies for 2369 peptide substrates were successfully determined by using this model. A feature of this model is that it enables the accurate determination of the catalytic efficiencies for numerous competing substrates in one reaction system.
      Figure thumbnail gr1
      Fig. 1Prediction of progress curves in a complex enzymatic system where multiple competing substrates coexist with a single enzyme by the iteration approach. (A), Computation workflow for the iteration approach; The computed progress curves of (B) free enzyme concentration, (C) substrate reaction rates and (D) percentage of substrates consumed during the course of enzymatic reactions in a system with five synthetic peptides coexisted with trypsin. The initial concentrations of the five peptides were 50 μm. Solid lines represent predicted results based on the iteration approach, and dots represent observed values under the same condition. All values represent the average ± one standard derivation from three replicates.

      DISCUSSION

      Many important experiments in biochemistry including enzyme substrate screening, enzymatic labeling, and protein digestion involve the enzymatic reactions in complex system. Due to the difficulty to resolve the differential rate equation set, the simulation of the enzymatic reactions in such a complex system is not achieved before. The iteration approach presented in this study is a powerful tool for this purpose. As long as the kinetic constants for the substrates of an enzyme are known, it can be used to generate a series of progress curves including the change of free enzyme concentration, the substrate/product concentration and the rates of substrate consumption. This will certainly facilitate our understanding on the enzymatic reaction in a complex system, which is more similar to those occurring in vivo. Compared with time-consuming and costly experiments, the prediction by iteration approach is high-throughput and cost-effective. We found the trends predicted by the iteration approach including the progress curves for the fraction of consumed substrates, the effect of the concentration of a competing substrate on the enzymatic reactions and the dependence of the enzymatic reactions on the Σ[Sx]Kmx were all highly consistent with those experimentally determined. Enzyme is an important catalyst for industrial synthetic chemistry due to its exquisite selectivity enabling the transformations without the need for the tedious blocking and deblocking steps (
      • Schmid A.
      • Dordick J.S.
      • Hauer B.
      • Kiener A.
      • Wubbolts M.
      • Witholt B.
      Industrial biocatalysis today and tomorrow.
      ). If there are competing interference substrates coexist with the substrate to be transformed, the byproducts from these interference substrates will be generated during the enzymatic reactions. This iteration approach could be used to simulate these reactions and optimize the reaction conditions to minimize the yield of byproducts. It can be expected that this iteration approach will have broad applications in both fundamental and applied enzymology.
      Catalytic efficiency (kcat/Km), also referred to as the “specificity constant,” is a useful index for comparing the relative rates of an enzyme acting on alternative, competing substrates (
      • Eisenthal R.
      • Danson M.J.
      • Hough D.W.
      Catalytic efficiency and kcat/KM: a useful comparator?.
      ,
      • Brot F.E.
      • Bender M.L.
      Use the specificity constant of alpha-Chymotrypsin.
      ). The higher the catalytic efficiency, the better the substrate for the enzyme. It is an important index to prioritize the substrates of an enzyme. Unfortunately, the conventional proteomics-based substrate screening approaches typically do not provide the values of catalytic efficiency even though several hundred substrates could be identified (
      • Schlüter H.
      • Rykl J.
      • Thiemann J.
      • Kurzawski S.
      • Gobom J.
      • Tepel M.
      • Zidek W.
      • Linscheid M.
      Mass spectrometry-assisted protease substrate screening.
      ,
      • Schilling O.
      • Overall C.M.
      Proteome-derived, database-searchable peptide libraries for identifying protease cleavage sites.
      ,
      • Bian Y.
      • Ye M.
      • Wang C.
      • Cheng K.
      • Song C.
      • Dong M.
      • Pan Y.
      • Qin H.
      • Zou H.
      Global Screening of CK2 Kinase Substrates by an Integrated Phosphoproteomics Workflow.
      ,
      • Xue L.
      • Wang W.
      • lliuk A.
      • Hu L.
      • Galan J.A.
      • Yu S.
      • Hans M.
      • Geahlen R.L.
      • Tao W.A.
      Sensitive kinase assay linked with phosphoproteomics for identifying direct kinase substrates.
      ). Although the simplified model presented in this study allowed for the accurate determination of the catalytic efficiencies of numerous substrates in the complex enzymatic reaction system. Compared with the approach reported by Schellenberger et al. (
      • Schellenberger V.
      • Siegel R.A.
      • Rutter W.J.
      Analysis of enzyme specificity by multiple substrate kinetics.
      ), the significant feature of this approach is that the addition of substrate of known catalytic efficiency into the reaction mixture is not necessary. As long as the enzymatic reaction is performed with the condition of x=1n[Sx]Kmx < 0.2, the catalytic efficiencies for substrates presented in the reaction mixture could be determined according to Equation (5). This condition could be easily achieved by diluting the reaction solution. This approach is a truly high throughput one as we have demonstrated that the catalytic efficiencies of over 2000 peptide substrates were determined for the enzyme of Glu-C. As a result, the prioritizing of these substrates could be achieved in high throughput, which is very important for enzyme substrate screening. Clearly this approach enabled the substrate screening changed from qualitative to quantitative. Classically, to determine the kinetic constants of the enzyme for a specific substrate, the substrate must be purified which is often tedious and labor intensive. The application of the simplified model also allows the characterization of specific substrates in a substrate mixture. For example, the catalytic efficiency of an enzyme for a specific protein in total cell lysate could be determined by performing the enzymatic reactions using total cell lysate as the substrate mixture followed with the determination of the portion of the specific protein consumed by immune assay methods like enzyme-linked immunosorbent assay (ELISA). It is expected that the simplified model will find broad applications in both high throughput substrate screening and the focused characterization of a few specific substrates.
      In conclusion, an iteration approach was established for the description of enzymatic reactions in a complex system. Its validation was achieved with 630 time-course points of 24 enzymatic reaction experiments with various substrate concentrations. A simplified model was further developed to depict the reactions in the complex system with x=1n[Sx]Kmx <0.2. It was found that the rate for the consumption of a substrate in such a complex system depends only on its own kinetic constants and concentration, while independent of other coexisting substrates. The simplified model, combined with high throughput proteomics platform, enabled the determination of the catalytic efficiencies of Glu-C for 2369 substrate peptides. Our study indicated that the iteration approach allowed the accurate simulation of the progress curves for the complex enzymatic reactions and the simplified model enabled the prioritizing of substrates in high throughput. They are expected to be important tools to understand and characterize the enzymatic reactions in complex system.

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