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Investigating the relationship between the substrates’ consumption and their abundances in a complex enzymatic system Zhenzhen Deng, Yan Wang, Jiawei Mao, and Mingliang Ye Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b03616 • Publication Date (Web): 03 Oct 2017 Downloaded from http://pubs.acs.org on October 4, 2017
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Analytical Chemistry
Investigating the relationship between the substrates’ consumption and their abundances in a complex enzymatic system Zhenzhen Deng,†,‡ Yan Wang,†,‡ Jiawei Mao,†,‡, Mingliang Ye *,† 5
†
CAS Key Laboratory of Separation Sciences for Analytical Chemistry, National Chromatographic Research and Analysis Center, Dalian Institute of Chemical Physics, Chinese Academy of Sciences (CAS), Dalian 116023, China; ‡ University of Chinese Academy of Sciences, Beijing 100049, China. Supporting Information
ABSTRACT: The enzymatic process involving the incubation of a library of substrates with an enzyme is the key step for a few important experiments for bioanalytical chemistry including proteomics analysis, enzymatic labeling, substrate screening, etc. The relationship between the substrates’ consumption and their abundances in a complex enzymatic system with huge number of coexisted substrates of different abundances was not well known. It was often thought that this step bias to high abundant substrates. In this study, we have demonstrated theoretically and experimentally that the priority of substrate consumption depended on their specificity constants but not abundances. We derived the expression between the fractions of the substrates consumed (pi) and their 15 specificity constants. Using the enzymatic system of five synthetic peptide substrates of trypsin, we validated through 24 experiments that the ln(1-pi) of competing substrates have linear correlation with their specificity constants and thus the priority of substrate depletion has no relation with their abundances. Using state of art quantitative proteomics approach, we found that the ln(1pi) of 144 competing substrates between any two of four experiments have linear relationship and the prioritization of substrates can be achieved by sorting their consumption rates in the experiment. This study will improve our understanding on the enzymatic ki20 netics in the complex system and will benefit the design of enzymatic analytical approaches. 10
Many bioanalytical chemistry experiments involve the addition of an enzyme to a complex substrate mixture for in vitro enzyme catalyzed reaction. In shot-gun proteomics, the proteins in cell lysate are subjected to protease catalyzed hydroly25 sis to yield peptides for LC-MS/MS analysis, which could identify thousands of proteins.1-3 In enzyme substrate screening, the proteins in cell lysate or the peptides derived from cell lysate are incubated with an enzyme, such as a kinase or protease, to be enzymatically modified and identified as in vitro 4-6 30 substrates. For example, a peptide library was incubated with protease for enzymatic reaction followed with the isolation of carboxy-peptide cleavage products for LC-MS identifications.6 Using this method, hundreds to over one thousand individual substrate peptides could be identified. Enzymatic 18 35 labeling like proteolytic O labeling for quantitative proteomics also involves the incubation of a peptide library with an enzyme.7,8 In these experiments, the substrate mixture is extremely complex. It could contain thousands of substrates with abundance varied over a few orders of magnitude.9 Although 40 the kinetics of a system in which two alternative substrates compete for a single enzyme has been investigated by many authors since Haldane introduced in 1930,10-14 and the internal competition method has been applied to determine the enzyme rate constant,15-17 the relationship between the substrates’ con45 sumption and their abundances in a complex enzymatic process has not been systematically investigated. Thus, the enzyme kinetics in such a system is not well understood. Take the protein digestion step in proteomics analysis as the example. It was thought that high abundant proteins were preferen18 50 tially digested during an enzymatic digestion. If this was true
then the shot-gun proteomics would be more bias to high abundant proteins as the digestion step bias to high abundant proteins. However, we have found that the digestion priority was almost independent of the proteins’ abundance by apply19,20 55 ing quantitative proteomics. In fact, digestion priority depends mainly on the kinetics properties of the cleavage sites on the proteins and the cleavage kinetics-based fractionation could be used to improve proteomics analysis coverage.21 Through a simplified derivation beginning with a classical 60 Michaelis-Menten competitive substrate model, Fonslow et al. indicated that the relative cleavage rates were governed by each site’s relative specificity constant.22 However, their theoretic model was not validated by experiments. In this study, we demonstrated theoretically and experimentally that the 65 consumption rate of each substrate (p i) in a complex enzymatic system under a condition depended on its own specificity constant and the competing substrates’ specificity constants. Specially, the ln(1-pi) of competing substrates only have linear correlation with their specificity constants and thus the priority 70 of substrate depletion has no relation with their abundances. Similar to Fonslow et al’ work22 and our previous work23, the derivation in this study was also based on MichaelisMenten kinetics. When numerous substrates are present simultaneously in an enzyme reaction and compete for the same 75 active site of an enzyme, the rate for the consumption of an individual substrate Si (vi,t) could be determined by the Equation (1).
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,
∑ ,
E ! S#,
indicates that the consumption rate of any substrate during the enzymatic process is not independent. We then used the data of enzymatic experiments with synthetic peptide substrates we obtained before,23 to validate the 60 Equation (5). Trypsin catalyzed reactions were known to obey Michaelis–Menten kinetics.25 In the experiments, five synthetic peptide substrates containing one tryptic cleavage site with known specificity constants (Table S1) were incubated with trypsin to simulate the reactions in the complex system.23 En65 zymatic reaction experiments were performed with equal initial concentration of 50 µM for four peptide substrates while the initial concentration of the other one substrate FLKSALSGHLEK (PEP5, the poorest substrate among the five substrates) was varied to be 50, 100, 200, 500, 1000 and 70 2500 µM respectively to mimic the reaction system with different substrate abundances. For each experiment, an aliquot of sample was removed from the reaction tube after reaction for 10 min and analyzed by HPLC with UV detection. The amounts of individual peptides consumed within 10 min for 75 above six experiments were show in Fig. 1.
(1) where [E]tot represents the total enzyme concentration, [Sx,t] is the concentration of any substrate at time point t, $%& and & 5 '() are the Michaelis-Menten constant and catalytic constant, respectively, for each substrate. ∑
*,
is the sum of instanta-
neous concentration of any substrate in the system divided by its own Michaelis-Menten constant. Clearly vi,t depends not only on its own substrate concentration and kinetics constants 10 but also on the concentrations and kinetics constants of other coexisted substrates. For any other substrate Sj in the system, its reaction rate can also be expressed as: +, 15
, , , ∑
E ! S-,
(2) The ratio of the reaction rates for the two substrates for any time (vi,t /vj,t) can be obtained by dividing Equation (1) by Equation (2): . ,
.,,
/, /
,
,
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/+,
(3) Clearly, the relative rate for the consumption of a pair of substrates in the complex system during any period of time depends only on their concentrations and specificity constants. The reason for this is that the coexisting substrates, which mutually act as competitive inhibitors and decrease the con25 centration of free enzyme for all substrates. Equation (3) is further used to study the relationship between substrate consumption and their initial concentration. Integration of Equation (3), we get the expression between the consumption rates (pi and pj) of substrates Si and Sj as a function of their specific30 ity constants: 20
ln 3
4 ,
4 ,5
6 /ln 3
4,,
4,,5
6 ln 1 8 9 /ln 1 8 9+
/
,
Figure 1. The enzymatic experiments of five peptide substrate system with various concentrations of a poor peptide substrate. (a) The linear relationship of substrates’ ln(1-pi) and their 80 specificity constants for different experiments. (b) The substrate consumption ratios (pi) and product amount (c) for all the five peptide substrates. The concentration of PEP5 was varied from 50-2500 µM while those for the other four peptides were kept at 50 µM. All values represented the average ± 85 standard derivation from three replicate experiments. The list of the five peptides and their specificity constants were given in Table S1.
,
(4) where /,: and /, denote the substrate concentrations of Si at times zero and t, respectively. This equation could be 35 applied to determine the specificity constant of a substrate if the constant for the coexisted substrate is known.24 Considering there are n substrates in the system, we can get the following expression according to Equation (4): ;< 1 8 9 : ;< 1 8 9> : … : ;< 1 8 9 : … : ;< 1 8 9@ 40
A
:
A
:…:
:…:
B B
(5) Above equation indicates that in a complex system with multiple substrates, the ln(1-pi) of competing substrates have linear correlation with their specificity constants. Thus, the priori45 ty of substrate consumption depends on their relative values of their specificity constants and has no relation with their abundances. When Equation (4) is transformed into the following equation, ln 1 8 9 50
CDEFG, H , I ,
With the increase of the initial concentration of PEP5, the amount of products yielded from substrate peptides other than 90 PEP5 decreased (Fig. 1c). This is not surprising since more substrates compete the enzyme for reaction. For PEP5, the yielded products increased with the increase of its initial concentration. Especially, when its initial concentration was 50fold higher than other substrates (2500 µM vs. 50µM), the 95 amount of its product was more than the product of any other substrates. When the PEP5 represents a high abundant but poor substrate (with kcat/Km value 25.6-fold smaller than the best substrate) in the reaction mixture, the amount of yielded product obviously cannot reflect the kinetics property. We 100 then compared the percentages of the substrates consumed (pi) under different initial concentrations of PEP5 (Fig. 1b). It can be seen that the pi decreased for all the substrates in a general trend. This explains the slopes for the correlation increased with the increasing of PEP5 concentration according to Equa105 tion (6). Interestingly, the order of the pi for the five substrate
(6)
we can see that the slope for the linear correlation depends on the fractions of substrates consumed. Equation (4) can also be transformed to the following equation, , I I / ,
9 1 8 1 8 9+ (7) Above function is monotonically increasing. The increase of 55 pi always accompanies with the increasing of pj. Equation (7)
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Analytical Chemistry even when ∑
peptides (pPEP1 > pPEP2 > pPEP3 > pPEP4 > pPEP5) never change. The best substrate (PEP1) always has the highest pi even though the presence of huge amount of PEP5. This can be explained by Equation (7) as it is monotonically increasing. 5 Any increasing in pi of one substrate will accompany with the increase of pj for other substrates in the system. Equation (5) predicted that ln(1-pi) for substrates have linear relationship with their specificity constants. Indeed, great linear correlations (R2>0.992) were observed for all the 6 experiments (Fig. 10 1a) no matter what the initial concentration was for PEP5. Another series of experiments varying the initial concentrations of substrate PEP1 (the best substrate among the five substrates) from 50 to 2500 µM were also investigated. The consistence of pi order and good linear correlation between ln(115 pi) and their specificity constants were also observed (Fig. S1). We then investigated the correctness of Equation (5) under other conditions. We first investigated the enzymatic reaction experiments with different reaction times. These experiments were performed with equal initial concentration of 50 µM for 20 all the five peptide substrates, and aliquots of samples were removed from the reaction tube after reacted for 2, 5, 10, 15, 20 and 25 min, and analyzed respectively. It was found that more products were yielded (Fig. 2c) and more fraction of substrates were consumed (Fig. 2b) with the increase of reac25 tion times. The good linear correlation between ln(1-pi) and their specificity constants (R2>0.986) were also obtained for the six reaction time points (Fig. 2a). The slopes for the correlation decreased with the increasing of reaction time in general trend (the deviation of the last time point probably because 30 experimental error). Another series of experiments by diluting the substrate mixtures were performed and the good linear correlation (R2>0.96) were also observed (Fig. S2).
50
*,
is significant. As shown in Table S2, among
the 24 experiments we performed, only 2 experiments with their ∑
*,
O 0.2. All of these experiments, including those
with this term over 10, indicated the order of the pi for the five substrate peptides (pPEP1 > pPEP2 > pPEP3 > pPEP4 > pPEP5) kept consistent and ln(1-pi) and their specificity constants had great 55 linear correlation. Clearly Equation (5) is not limited to the diluted enzymatic system. The correctness of Equation (5) should be further validated in a complex enzymatic system with numerous substrates of different abundances. However, the specificity constants for 60 these substrates typically are not known. According to Equation (5), the following equation could be derived for any two experiments A and B: S;< 1 8 9 : ;< 1 8 9> : … : ;< 1 8 9 : … : ;< 1 8 9@ TU A
:
A
:…:
:…:
B B
S;< 1 8 9 : ;< 1 8
(9) 9> : … : ;< 1 8 9 : … : ;< 1 8 9@ TV This equation indicated that the ln(1-pi) of different substrates between any experiments should be linearly correlated. Indeed, the ln(1-pi) of the five peptide substrates for any two experiments among the 24 experiments had linear relationship 70 as illustrated in Table S3. 65
Figure 2. The enzymatic experiments with various reaction times. (a) The linear relationship of substrates’ ln(1-pi) and their specificity constants under different experiment. (b) The substrate consumption ratios (pi) and product amount (c) for all the five peptide substrates. The concentration of the five peptides were fixed to be 50 µM. All values represented the 40 average ± standard derivation from three replicate experiments. 35
Figure 3. The complex enzymatic experiments by incubating the peptide library derived from the trypsin digestion of Jurkat cell lysate with a protease of Glu-C. (a) Workflow for quanti75 tative LC-MS/MS analysis using triplex dimethyl isotope labeling (b) Correlation of ln(1-pi) between any two enzymatic experiments under different conditions of A, B, C and D.
Recently we reported that the portion of substrate consumed (pi) for a substrate in a complex system for a given reaction time depended only on its own specificity constants when the 45
term ∑
*,
We then investigated if this was the case for complex system. A peptide substrate library was generated by trypsin di80 gestion of proteins in Jurkat cell lysate. Therefore, this library contained thousands of peptides with different abundance. This library was incubated with Glu-C, a protease that specifically cleaved at the C-terminus of either glutamic or aspartic acid residues, for enzymatic reactions. Quantitative proteomics 85 with triplex dimethyl isotope labeling was applied to quantify
≪ 1:23
I F
∙ M N ∙
9 1 8 e (8) Based on Equation (8), Equation (5) can also be derived. However, it should be mentioned that Equation (5) is valid
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the peptide substrates in the mixture after reaction as illustrated in Fig. 3a. Two enzymatic reaction experiments were performed by using the same amount of tryptic peptides as the substrates but with different concentrations: 25 µg in 1 mL and 5 0.2 mL buffer, respectively. They were treated with the same concentration of Glu-C (2.5 µg/mL) for 30 min, then labeled with light (L) (Experiment A) and intermediate (M) (Experiment B) dimethyl, respectively. After labeling, these two samples were mixed with the same amount of tryptic peptides 10 labeled with heavy (H) dimethyl as the internal standard. Therefore, the ratios of L/H and M/H quantified by MS represented the ratios of substrates remained in the mixture after reaction, and in fact were the (1-pi) values for Experiment A and B, respectively. Another two samples were subjected to 15 the enzymatic reactions with the same condition but with lower enzyme concentration of 0.5 µg/mL and longer time of 60 min. These two experiments were defined as Experiment C and D. After quantitative proteomics analysis, the peptide sub20 strates with quantified ratios were filtered by the following criteria: 1) Substrates with only one D/E cleavage site were remained. This is because the tryptic peptides containing multiple D/E cleavage sites would subjected to cleavage on multiple sites by Glu-C, which would make the dynamical changes 25 of these peptides very complex. 2) Quantified substrates with the relative standard deviation lower than 10% were remained. 3) Peptide substrates quantified in all the four experiments were kept. Finally, 144 peptides substrates were remained. We performed the correlation analysis of the (1-pi) values of these 30 144 substrates between any two experiments of above four experiments and found good correlations (Spearman correlation coefficient (SC) >0.83, Pearson correlation coefficient (PC) >0.85), indicating the correctness of Equation (5). The correlations of A&B, C&D were better than others. This is 35 because the relative ratios were more accurately determined as both experiments in each case (A and B, or C and D) used the same internal standards and quantified in the same quantitative proteomics experiments. The 144 peptides were derived from proteins with their abundances spanned at least 4 orders of 40 magnitude (Fig. S3). Clearly Equation (9) is also valid for such a complex system.
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strates in complex system could be achieved by comparing the pi. The 144 peptides substrates were sorted with their pi values. The weblogs for the top 20 and bottom 20 substrate peptides were given in Fig. 4. Cleavage sites surrounded by neutral residues tended to be quickly cut and those surrounded by negatively charged residues tended to be slowly cut, which 23,26 60 was consistent to previous reports. This result confirmed our claim that prioritization of enzyme substrates in a complex system could be achieved by comparing their consumption fractions. We also investigated if the consumption rates of peptide substrates depended on their abundance. It was found 65 that there was virtually no correlation (Spearman correlation coefficient (SC)
