A high-throughput pH-based colorimetric assay: application focus on alpha/beta hydrolases

Article abstract of DOI:10.1016/j.ab.2018.03.009

Research involving α/β hydrolases, including α-amino acid ester hydrolase and cocaine esterase, has been limited by the lack of an online high throughput screening assay. The development of a high throughput screening assay capable of detecting α/β hydrolase activity toward specific substrates and/or chemical reactions (e.g., hydrolysis in lieu of amidase activity and/or synthesis instead of thioesterase activity) is of interest in a broad set of scientific questions and applications. Here we present a general framework for pH-based colorimetric assays, as well as the mathematical considerations necessary to estimate de novo the experimental response required to assign a ‘hit’ or a ‘miss,’ in the absence of experimental standard curves. This combination is valuable for screening the hydrolysis and synthesis activity of α/β hydrolases on a variety of substrates, and produces data comparable to the current standard technique involving High Performance Liquid Chromatography (HPLC). In contrast to HPLC, this assay enables screening experiments to be performed with greater efficiency.

Full text of DOI:10.1016/j.ab.2018.03.009

Accepted Manuscript
A high-throughput pH-based colorimetric assay: Application focus on alpha/beta
hydrolases
Mariétou F. Paye, Harrison B. Rose, John M. Robbins, Diana A. Yunda, Seonggeon
Cho, Andreas S. Bommarius
PII:
S0003-2697(18)30265-3
10.1016/j.ab.2018.03.009
YABIO 12962
DOI:
Reference:
To appear in: Analytical Biochemistry
Received Date: 30 November 2017
Revised Date: 26 February 2018
Accepted Date: 12 March 2018
Please cite this article as: Marié.F. Paye, H.B. Rose, J.M. Robbins, D.A. Yunda, S. Cho, A.S.
Bommarius, A high-throughput pH-based colorimetric assay: Application focus on alpha/beta
hydrolases, Analytical Biochemistry (2018), doi: 10.1016/j.ab.2018.03.009.
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ACCEPTED MANUSCRIPT
Manuscript Submission to Analytical Biochemistry
Subject Category: Enzymatic Assays and Analysis
A high-throughput pH-based colorimetric assay: application focus on
alpha/beta hydrolases
Author Names and Affiliations
Mariétou F. Paye 1, ‡, Harrison B. Rose 2, ‡, John M. Robbins 2, Diana A. Yunda 1, 3, Seonggeon Cho 3, and Andreas S.
Bommarius 1, 2,*
1
2
3
School of Chemistry & Biochemistry, School of Chemical & Biomolecular Engineering, School of Biomedical
Engineering. Krone Engineered Biosystems Building, Georgia Institute of Technology, Atlanta, Georgia,30332, United
States.
‡
*
These authors contributed equally to this work. Corresponding Author: Prof. Andreas Bommarius, 5018 Krone
Engineered Biosystems Building, Georgia Institute of Technology, 30332-2000. Email:
andreas.bommarius@chbe.gatech.edu

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Abstract
Research involving α/β hydrolases, including α-amino acid ester hydrolase and cocaine esterase, has been
limited by the lack of an online high throughput screening assay. The development of a high throughput screening
assay capable of detecting α/β hydrolase activity toward specific substrates and/or chemical reactions (e.g., hydrolysis
in lieu of amidase activity and/or synthesis instead of thioesterase activity) is of interest in a broad set of scientific
questions and applications. Here we present a general framework for pH-based colorimetric assays, as well as the
mathematical considerations necessary to estimate de novo the experimental response required to assign a ‘hit’ or a
‘miss,’ in the absence of experimental standard curves. This combination is valuable for screening the hydrolysis and
synthesis activity of α/β hydrolases on a variety of substrates, and produces data comparable the current standard
technique involving High Performance Liquid Chromatography (HPLC). In contrast to HPLC, this assay enables
improved efficiency obtained from a single experiment.
1 Introduction
1.1 AEH and CocE Enzymes
Hydrolases are ubiquitous enzymes involved in a myriad of chemical processes and are essential to the
survival of all living organisms.1 The most widely studied enzymes in this class are in the α/β hydrolase family, which
have applications in analytical, industrial, and pharmaceutical fields. Some uses include synthesis of β-lactam
antibiotics (β-LA) with α amino acid ester hydrolase (AEH, Figure 1 A),2 treatment of cocaine addiction with cocaine
esterase (CocE, Figure 1 B),3 and hydrolysis of insecticides by organophosphorus hydrolase (reaction scheme not
shown).4
Figure 1: Popular applications of the α-amino acid ester hydrolase (AEH) and cocaine esterase (CocE) enzymes used in this
study. A) AEH catalyzes the synthesis of ampicillin from D-phenylgylycine methyl ester and 6-aminopenicillinate B) CocE
catalyzes the hydrolysis of cocaine into benzoic acid and ecgonine methyl ester.
There have been intensive efforts to identify amino acid substitutions and reaction conditions that improve
3, 5
thermostability and catalytic rates of AEH and CocE.
However, those efforts have been limited by dependence on
HPLC-based assays, which are low throughput and resource-intensive. Thus, an alternative, high-throughput assay is
desirable to accelerate the process of generating improved enzyme variants. For this purpose, a model reaction in which
AEH or CocE catalyzes the sequential peptide synthesis of multiple D-phenyl glycine methyl ester (D-PGME)
molecules, thus resulting in a mixture of various peptide methyl esters, has been proposed (Figure 2).6 A crucial side-
reaction also catalyzed by these enzymes is the primary hydrolysis of D-PGME, which releases D-phenyl glycine (D-
PG) and methanol (Figure 2). Because hydrolysis of the reacting methyl ester limits the amount of active substrate
available for the synthesis reaction, biocatalysts capable of promoting the synthesis reaction while suppressing, if not
blocking completely, the hydrolysis reaction is coveted by industry.7 Given the need for a less resource-intensive
analytical method, the current study serves to utilize this model reaction to identify a high throughput assay capable of
differentiating between the ester hydrolysis and amide synthesis reactions in general.

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D-phenylglycine
methyl ester
(D-PGME)
n-phenylglycyl methyl ester
diphenylglycyl methyl ester
[D-PGME]n
D-PGME
NH2
O
O
H
O
H
N
O
N
H2N
N
H
O
H2N
[CH3OH]n
O
O
O
O
CH3OH
peptide synthesis
sequential peptide synthesis
n
primary
hydrolysis
secondary
hydrolysis
terminal
hydrolysis
H2O
H2O
H2O
CH3OH
CH3OH
CH3OH
[D-PGME]n
O
D-PGME
NH2
OH
O
H
H
OH
N
N
N
H
O
H2N
H2N
OH
O
O
O
CH3OH
peptide synthesis
[CH3OH]n
sequential peptide synthesis
n
D-phenylglycine
diphenylglycyine
n-phenylglycine
Figure 2: Proposed scheme for the α-amino ester hydrolase (AEH) or cocaine esterase (CocE) catalyzed model reaction of D-
PGME to various products. Sequential peptide synthesis reactions (left to right) are proposed to occur in competition with ester
hydrolysis reactions (top to bottom).
1.2 Literature Survey of Existing Assays
Since the substrates and products (i.e. primary amines and carboxylic acids, respectively) of these enzymes
have labile protons, it was proposed that weakly buffered systems may experience a change in pH value over the course
of ester hydrolysis or amide synthesis reactions such as those shown in Figure 1 and Figure 2. The use of pH-based
colorimetry to detect enzyme activity has been reported with certain hydrolases (enantioselective hydrolases),8
transketolases (e.g., TK, EC 2.2.1.1),9 transferases (e.g., galactosyltransferase),10 acylases (e.g. cephalosporin C
acylase),11 and kinases (e.g., glucokinase).12 These published assays are dependent on low buffering capacity and salt
content, selection of pH-indicator based on initial pH (the ꢀꢁꢂ of the indicator should equal the starting pH), and high
concentrations of pH-indicators. Additionally, each set of conditions requires unique standard curves, which are time-
consuming to collect. Collectively, these restrictions limit the extent to which various substrates and reaction conditions
can be explored, and the rapidity with which such investigations can be conducted.
Two colorimetric assays for AEH activity have been described previously, one endpoint assay, and one for
real-time monitoring (see Figure S-2 in the Supporting Information). The endpoint assay is designed to measure the
absorbance of the chromophore diketopiperazine (DKP) derivative, which is formed by ring-opening of β-LA coupled
with nucleophilic attack by reduced ascorbic acid13 However, the reaction does not effectively distinguish between
substrates and products.14 On the other hand, the real-time assay tracks the production of the chromophore 5-amino-2-
nitrobenzoic acid, which is produced by hydrolysis of an AEH substrate analog, 5-(2’-amino-5-phenylacetamido)-2-
nitrobenzoic acid (APANiB).14 APANiB is not commercially available and is difficult to synthesize due to its
precursors’ tendency to self-polymerize.
Similarly, a real-time CocE assay using substrate analogs has been reported.15 In this assay scheme
(illustrated in Figure S-2 of the Supporting Information), enzymatic cleavage of the thioester bond in benzoyl-3-
mercapto ecgonine methyl ester produces benzoate and 3-mercapto ecgonine methyl ester, which is reacted with 5-
5’dithiobis(2-nitrobenzoic acid) (DTNB, Ellman’s reagent) to produce 3-5' dithio(ecgonine methyl ester)- (2-
nitrobenzoic acid), and the chromophore, 5-mercapto-2-nitrobenzoic acid.15 However, this assay is limited to detecting
thioesterase activity and requires the use of a thioester analog of each target substrate.

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1.3 Generalizing pH-based Colorimetric Assays
The development of an improved assay method was motivated by the challenges surrounding current AEH
and CocE assays, as well as pH-based assays in general. In reaction theory, conversion is a single value that
encapsulates the multitude of variables related to the progress of a reaction or, in an assay context, the success of a
catalyst. We present a general mathematical approach for creating a direct mapping between the absorbance of a
colorimetric indicator and the conversion of a pH-altering reaction. Our model quantitatively predicts how an assay will
respond to a reaction, eliminating the need for experimental standard curves in ‘hit’ or ‘miss’ activity assessment and
reducing the time and material resources needed to conduct high throughput screens, and even enabling real-time
monitoring and hypothesis testing. Assay response curves are typically unintuitive – changes in solution pH tend to be
accompanied by changes to ionic strength which in turn alter the effective ꢀꢁꢂ values of participating species and may
broaden, narrow, or shift the buffering capacity of the reaction mixture. By allowing operators to visualize the response
and sensitivity of an assay to each design parameter, these tools can also serve to support and inform decisions made in
assay development and troubleshooting. We present some examples of general experimental guidelines and
troubleshooting recommendations that have been borne out by the modeling in this manner.
For aqueous hydrolysis reactions of known stoichiometry, it is possible to estimate the degree of conversion
that is required to produce a particular pH value, so long as the starting concentrations and acidity constants of all
species are known. Generally, pH can also be related to the color of a halochromic indicator. Phenol red was selected as
the indicator for this work, as it exhibits a visible color change over the pH range (4.5-8.5) of interest for monitoring
hydrolysis and synthesis reactions. By combining these relationships, it is possible to predict the spectrophotometric
response of a hydrolysis reaction. Plots of absorbance vs. hydrolysis conversion produced with this method can be used
to identify assay conditions that provide reasonable sensitivity and to rule out specific reactions for which pH-based
assays are inappropriate. Once experimental absorption data (either endpoint or real-time) are collected, the predicted
responses may be used in lieu of experimental standard curves for data interpretation and rapid qualification of “hits”
and “misses.”
In the sections that follow, we validate and demonstrate this approach to pH-based colorimetric assays in
several steps. First, we compare enzymatic reaction data obtained by high performance liquid chromatography (HPLC)
using traditional standard curves (i.e., for quantification of individual species) with data obtained by colorimetry using
simulated standard curves (i.e. solutions that have been deliberately prepared to simulate the state of a reaction system
at a given level of conversion). Next, we compare predicted standard curves (i.e., calculated by the model without
fitting) to those simulated standard curves. Finally, we use the predicted standard curves from the model to interpret
experimental enzymatic reaction data and perform hypothesis testing to demonstrate “hit” or “miss” screening. The
proposed workflow for an assay experiment with hypothesis testing is illustrated in Figure 3 (and in more detail in
Figure S-1 of the Supporting Information).
Figure 3: The workflow required to use the generalizable pH-based colorimetric assay. The experimental conditions used in wet
lab experimentation are tabulated and combined with existing knowledge of substrate, product, and buffer pKa values, which are
used to predict the relationship between spectrophotometric measurements and reaction conversion. Experimental data and
predicted relationships are then combined to perform hypothesis testing and qualify each experiment as either a hit or a miss.
2 Materials & Methods
2.1 Materials
Sodium dodecyl sulfate, nicotinamide, D-phenylglycine methyl ester, phenol red, and methyl picolinate were
purchased from Sigma Aldrich while acetamide, nicotinic acid, imidazole, and picolinic acid were purchased from
Alpha Aesar. Other commercial sources include Fisher Scientific for ammonium acetate, sodium hydroxide, and
HPLC-grade acetonitrile; Fluka Chemika for 6-aminopenicillanic acid and D-phenylglycine; VWR analytical for
dibasic anhydrous sodium phosphate and sodium chloride. Other purchased materials were sodium ampicillin (Gold
Biotechnology), Overnight Express (Novagen), monobasic sodium phosphate monohydrate (J.T. Baker), molecular
biology grade LB broth lennox (US Biological Life Sciences) and hydrochloric acid (Acros Organics). The expression
vector for α-amino acid ester hydrolase (AEH) was produced by a past member of this research group6, 16 while that for
cocaine esterase was graciously donated by Dr. Neil Bruce’s laboratory at the University of York, UK.

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2.2 Protein Expression and Purification
Both AEH and CocE were expressed in Rosetta™(DE3)pLysS competent cells (Novagen) using pET28 and
p234 under selective pressure from kanamycin and ampicillin-carbenicillin, respectively. Because wildtype AEH is not
thermostable, only its quadruple variants
H
(N186D/A275P/V622I/E143H: AEH QV-H) and
G
(N186D/A275P/V622I/E143G: AEH QV-G) were used in this paper.16 Chloramphenicol was used to maintain the
plasmid supplying tRNAs for exogenous codons. 5 mL seed cultures (LB broth, 37 °C, 200 rpm) were grown
overnight, passaged to 200 mL of Overnight Express, and incubated for an additional 8 hours (37 °C, 250 rpm).
Cultures were incubated at room temperature for 16 hours after which they were centrifuged. The resulting pellets were
suspended in lysis buffer (18 mL per 1 g of pellet; 10 mM Imidazole, 50 mM NaPO4, 300 mM NaCl, pH 8.0) and lysed
by sonication on ice. Enzymes were purified by nickel affinity chromatography with Novagen Ni-NTA HisBind Resin.
Bound proteins were washed (1 mL of 50 mM Imidazole, 50 mM NaPO4, 300 mM NaCl, pH 8.0; repeated 20x),
followed by 1 mL washes with buffers containing imidazole increasing in concentration from 60 mM to 240 mM in
20 mM increments (remaining buffer composition: 50 mM NaPO4, 300 mM NaCl, pH 8.0). Washed proteins were
eluted with 8 mL of elution buffer (250 mM Imidazole, 50 mM NaPO4, 300 mM NaCl, pH 8.0). For each enzyme, the
combined fractions were dialyzed twice against 2 L of dialysis buffer (100 mM NaPO4, 100 mM NaCl, pH 7.0) to
remove the imidazole, which inhibits enzyme activity. Purified enzyme was quantified using Bradford reagent at the
absorbance maxima of 595 nm.
2.3 Enzymatic Hydrolysis and Synthesis Reactions
Five types of hydrolysis and synthesis reactions were carried in this study: the reactions of (1) 6-
aminopenicillinate and D-phenylglycine methyl ester to ampicillin and methanol; (2) methyl picolinate to picolinate
and methanol; (3) ampicillin to 6-aminopenicillinate and D-phenylglycine; (4) D-phenylglycine methyl ester to D-
phenylglycine and methanol, (5) and D-phenylglycine methyl ester to di- and tri-peptides and methanol.
All reactions were carried out in 96-well clear flat-bottom plates at room temperature in 200 µL of 100 mM
sodium phosphate buffer with 20 µM phenol red. Substrates were added to the required concentration, which varied
between experiments. Reaction start-time was taken upon addition of purified enzyme, either CocE or AEH. Enzymes
were suspended in dialysis buffer and added to the required final concentration. Non-enzymatic controls were prepared
using dialysis buffer without enzyme. Additional controls were performed to verify that phenol red is neither a
substrate nor an inhibitor of CocE or AEH, including trials with enzyme and substrate but without phenol red, as well
as with enzyme and phenol red in the absence of substrate. These controls are described in the Supporting Information,
in the section titled Validation of Phenol Red.
Reactions were monitored with direct measurements of product formation by high performance liquid
chromatography (HPLC) using a Shimadzu HPLC 20A (DGU-20A5, LC-20AT, SIL-20AC HT, CBM-20A, SPD-
M20A, CTO-20A) and a reverse-phase Phenomenex C-18 column (Luna 5 µ C18 (2) 100 Å 250×4.60 mm 5 micron).
The mobile phase consisted of 70% 5 mM phosphate buffer at pH 3.0 with 300 mg/L SDS and 30% acetonitrile
supplied at a rate of 1 mL/minute. Reaction time points were taken by 10-fold dilution of reaction aliquots into the
mobile phase. Diluted samples were then supplied to the column in a 2.0 µL injection. Column eluent was monitored at
215 nm to monitor all substrates and products.
The pH of each reaction mixture is an aggregate result of the relative buffering capacity contributions of the
background buffer, the reaction substrate(s) and the reaction product(s). For that reason, the pH value of each sample
was indirectly monitored by tracking changes in the absorbance of phenol red on a Biotek Synergy H4 Hybrid (plate)
reader. Absorbance measurements were taken over time at 557 nm and 479 nm, the alkaline absorbance maximum and
isosbestic point of phenol red, respectively. All downstream data processing was performed using the (557 nm/479 nm)
absorbance ratio. Full wavelength scans from 300 nm to 700 nm were also performed on each well after 4 hours to
check for baseline deviation.
2.4 Simulated Conversion Standard Solutions
Samples were prepared to standardize the spectrophotometer analyses for each hydrolysis and synthesis
reaction. Stock solutions of reactants were prepared in 100 mM sodium phosphate. For reasons discussed later in the
modeling section, precise accounting of total ions is critical to the success of this method. The sodium concentration
was adjusted to give the reactant stocks a pH value of 7.0. Individual product stocks were prepared in a 2x buffer of the
same relative salt composition as the reactant stocks, such that mixing the reactant and corresponding product stocks in
predefined ratios simulates a desired conversion without changing the buffer composition. For example, mixing a
1:3:3 ratio of the stocks for a reactant and both products generates a solution with the same composition and pH as a
reaction at 75% conversion. Each sample was evaluated by spectrophotometry and HPLC as described above.
2.5 Determination of Enzymatic Kinetic Parameters
Using the simulated conversion standards to interpret the spectrophotometric and HPLC data, initial rates
were determined in triplicate for each reaction in both the presence and absence of enzyme. The contribution of

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chemical (non-enzymatic) hydrolysis was subtracted, and the kinetic parameters were determined from the best fit of
data to the Michaelis-Menten equation using Kaleidagraph1.
2.6 Characterization of Phenol Red
In addition to spectrophotometric evaluation of the simulated conversion standards, a 20 µM solution of
phenol red in 100 mM phosphate buffer was titrated with sodium hydroxide (10 N) and hydrochloric acid (6 N) to
reveal the dependence of its absorption spectrum on pH in the absence of other compounds.
2.7 Modeling and Prediction of Assay Response Curves
A general mathematical model was developed to predict how the colorimetric assay would respond to
different hydrolysis reactions. The predictions are used for experimental planning, and to interpret experimental results
for hypothesis testing, as described below.
Hydrolysis reactions examined here are of the general form ꢃ + ꢄꢅꢆꢇꢈ ⇌ ꢉ + ꢊ where A, B, and C may be
weakly acidic or basic. Model formulation begins with the general consideration of a weak acid reversibly dissociating
in aqueous solution: ꢃꢋꢍꢎꢏ ⇌ ꢋꢎ + ꢃꢋꢍ where ꢑ is the charge of the conjugate base and ꢒ is the number of labile
ꢌ
ꢌꢐꢏ
protons in each protonation state.
The degree to which a weak acid dissociates is typically reported as a ꢀꢁꢂ value which may be presented as a
ꢀꢁꢂꢓ (‘concentration basis’), ꢀꢁꢂꢔꢕ (‘thermodynamic value’ or ‘activity-basis’), or ꢀꢁꢂ∗ (‘mixed-mode’ or ‘practical’),
depending on the data source and application.17 2 ꢀꢁꢂvalues determined using a potentiometric pH probe are typically
in the form of ꢀꢁꢂ∗, unless they have been extrapolated to infinite dilution (ꢀꢁꢂꢔꢕ), or the probe has been standardized
using particularly rigorous methods (ꢀꢁꢂꢓ).18 Acid-base equilibria inherently involve charged species and are sensitive
to (and result in) changes in ionic strength. As a result, deviations between ꢀꢁꢂꢓ, ꢀꢁꢂꢔꢕ, and ꢀꢁꢂ∗, as well as between
activity- and concentration-based measures of ꢀꢋ tend to increase with increasing ionic strength.
The concentration-based ꢀꢁꢂ value, ꢀꢁꢂꢓ, may be written as the sum of the thermodynamic value and a
‘lumped activity coefficient’ correction factor that is dependent on ionic strength. To keep this model as general as
possible, an extended Debye-Hückel relationship is used to estimate the correction factor. This correction can be
expressed as a special case of the correlation derived by Sun et al:19
ꢜ
√
ꢀꢁꢂꢖ = ꢀꢁꢂꢗꢘ + 1.02ꢑ ꢛꢏꢎꢝ ꢜ + ꢉꢞꢟ − ꢊꢞ
(1)
ꢙ
ꢚ
√
where ꢑ is the charge of the conjugate base, ꢞ is the ionic strength, and ꢃ, ꢉ, and ꢊ are empirically derived
parameters with mean values of 1.50, -0.09, and -0.09, respectively. The correction is valid up to ionic strengths of
ꢞ = 0.5 M, and enables the use of concentrations rather than activities elsewhere in this model. A detailed explanation
of this correction is provided in the Supporting Information.
Similarly, ꢀꢋ can be adjusted for ionic strength, to convert between the concentration-based value, ꢀꢋꢓ, and
the activity-based value, ꢀꢋꢂ, with the latter corresponding to readings from a typical potentiometric pH electrode.
ꢜ
√
ꢀꢋꢂ = ꢀꢋꢓ + 0.51 ꢛꢏꢎꢏ.ꢠꢡ ꢜ − 0.11ꢞꢟ
(2)
√
where
ꢙꢢ ꢎꢣꢚ
ꢀꢋꢓ = − logꢏꢡ
ꢋ
(3)
Finally, these general relationships may be used to determine the distribution of protonation states:
ꢨꢩꢪꢫ×ꢏꢡꢩꢬꢭ
ꢀꢁꢂꢖ,ꢤ,ꢌ = − logꢏꢡ ꢥꢦꢝꢧ
ꢮꢯ
(4)
ꢦꢝꢧꢨꢫ
for all ionizable species, ꢰ, and number of labile protons, ꢒ. Note that ꢀꢋꢓ is used here to avoid over-correcting for ionic
strength.
The protonation state of water can also be represented, using the definition of the ionic product of water:
ꢐꢲꢳꢴꢮ
ꢮ
= 10ꢐꢲꢧ
(5)
ꢢ
ꢐꢣ
ꢱꢋ × 10
Here also, ꢀꢋꢓ is used. The value of ꢀꢁꢵ may be corrected as in Equation 1, however, a value of ꢑ = 1 must be used.
It is necessary to link these expressions together using a charge balance:
∑ ∑
0 =
ꢌꢶꢷꢤ,ꢌ × ꢑꢤ,ꢌ
ꢸ
(6)
ꢤ
where ꢷꢤ,ꢌ and ꢑꢤ,ꢌ are the molar concentration and charge number of each ion in each protonation state, respectively. If
the solutions are titrated to a specific pH and/or prepared using salts, then the concentrations of the co-salt ions and
titrants must be included in the charge balance equation. Precision is required in the accounting of all salt species. An
error in accounting for a monovalent anion on paper, for example, is comparable to the erroneous addition of
hydrochloric acid in the laboratory.
Additionally, since specific protonation states cannot be measured or pipetted, total concentrations are used to
specify and track the analytical composition of the reaction system:
1 Synergy Software, KaleidaGraph V4.1.1, Reading, PA (1986-2000)
2 A complete discussion of these bases, with guidelines for standardizing literature values to a thermodynamic basis is provided
in the Supporting Information. Additionally, a tool for standardizing and curating ꢀꢁꢂ values is provided in the first ‘sheet’ of the spreadsheet
accompanying this publication.

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∑
ꢷꢤ,ꢔꢹꢔ
=
ꢌꢶꢷꢤ,ꢌ
ꢸ
(7)
This treatment is not necessary for the concentrations of sodium and chloride, as both can be calculated based
on solution and stock preparation, and are assumed to be fully dissociated.
To predict the spectrophotometric response of the system due to the colorimetric indicator, the ratio of the
molar extinction coefficient at one select wavelength relative to that of the isosbestic point is calculated for each
protonation state of the indicator:
ꢃꢺꢻ = ꢝꢼꢽ
(8)
ꢨ,ꢾ
ꢿꣀꣁꢿꣂꣃꣂ꣄ꣀ
ꢌ
ꢝꢼꢽꢾꣂꢿꣅꢿ꣆ꣀꢿꣃꣂꢮ
When phenol red is used as the assay indicator, we use 557nm for ꣇ꢽ꣈꣉ꢽꢤꢔꢤ꣊꣈ and 479 nm for ꣇ꢤꢽꢹꢽꢼ꣈ꢽꢔꢤꢓ
Next, the sum of the absorbance ratios of all protonation states of the indicator is normalized by the total
indicator concentration:
.
ꢃꢺꢻ = ∑
(9)
ꢨꢶꢝꢼꢽꢨ×ꢓꣂꣁ꣋ꣂꢮ꣌ꣃꣅ꣍,ꢨ
ꢸ
꣎
ꣂꣁ꣋ꣂꢮ꣌ꣃꣅ꣍,ꣃꣅꣃ
It is also necessary to define the stoichiometric relationships between the reacting species in a manner that
considers the conversion of the enzymatic reaction, and accounts for the possibility of non-zero starting concentrations
of the products:
ꢢ
ꢢ
ꢢ
ꢣ
ꢢ
ꢢ
ꢢ
ꢣ
ꢣ
ꢣ
ꢙ
ꢢ
ꢢ
ꢚ
ꢃꢔꢹꢔ = ꢃꢤ꣉ꢤꢔ × 1 − ꣏
ꢣ
ꢣ
ꢣ
ꢉꢔꢹꢔ = ꢉꢤ꣉ꢤꢔ + ꢃꢤ꣉ꢤꢔ × ꣏
(10)
ꢣ
ꢊꢔꢹꢔ = ꢊꢤ꣉ꢤꢔ + ꢃꢤ꣉ꢤꢔ × ꣏
The inclusion of the reaction in this manner relies on the assumption that the acid-base equilibrium reactions
are significantly faster than the enzymatic reaction for any level of reaction conversion.
The ionic strength of the solution is dependent on the distribution of charged species present, and is
calculated as follows:
ꢏ ∑ ∑
ꢞ = ꣐
ꢌꢶꢷꢤ,ꢌ × ꢑꢤ꣐,ꢌꢸ
(11)
ꢤ
Relating the total absorbance of the reacting mixture to its conversion requires solving the system of
Equations (1-11). These equations are written in their expanded forms with additional explanation in Table S-4 of the
Supporting Information.
In general, models of this form can be difficult to solve numerically, as the species concentrations spanning
several orders of magnitude makes them poorly scaled. It is also difficult to solve such systems analytically for pH as a
function of the species distribution. As such, approximations and simplifying techniques are frequently deemed
necessary to make even seemingly straightforward buffer calculations (such as those without ionic strength corrections
or concurrent hydrolysis reactions) more mathematically tractable.20
However, by treating ꢀꢋꢓ as the independent variable, it is possible to solve the system of Equations (3-11)
ꢢ ꢣ
ꢢ ꢣ
algebraically. Solution sets are defined by fixed parameters, including the initial assay composition ( ꢃ ꢤ꣉ꢤꢔ, ꢉ
,
ꢤ꣉ꢤꢔ
ꢔꢕ
ꢢ ꢣ
ꢊ
ꢢ
ꢣ
ꢢ
ꢣ ꢢ
ꢞ꣓꣔ꢰꢷꢅꢆ꣒ꢈ ,
ꢔꢹꢔ
ꢎꢣ
ꢢ
ꢐꢣ
,
꣑ℎ꣒ꢻ
,
꣕ꢅ , and ꢊ꣖ ), thermodynamic ionization constants ꢀꢁꢂ,ꢤ,ꢌ, and indicator
ꢤ꣉ꢤꢔ
ꢔꢹꢔ
absorptivities ꢃꢺꢻ . Wolfram Mathematica3 was used to solve Equations (3-11) symbolically, producing algebraic
ꢌ
expressions for ionic strength, absorption, and conversion as functions of ꢀꢋꢓ.4 These expressions are embedded within
a MATLAB5 framework, which allows them to be easily evaluated for a variety of reactions and reaction conditions
which are specified within an accompanying spreadsheet.
In each execution of the MATLAB code, the complete expression for ionic strength is evaluated over a range
of ꢀꢋꢓ values, using the thermodynamic values for each acid dissociation constant. The calculated ionic strengths are
then used in Equation (1) to estimate the concentration-based ꢀꢁꢂꢓ value of each species over the ꢀꢋꢓ range, and the
ionic strength is calculated again, using the new ꢀꢁꢂꢓ values. Three such iterations are typically sufficient for
reasonable convergence. The resulting ꢀꢁꢂꢓ values are then used in the evaluation of the complete expressions for
absorbance and conversion at each ꢀꢋꢓ value. Finally, ꢀꢋꢂ is calculated as described in Equation (2), so that the pH
axis of the displayed data plots will correspond to traditional potentiometric measurements. A guide to using the
accompanying MATLAB script is provided in the section ‘Modeling Quick-Start Guide’ of the Supporting
Information, and a more detailed explanation can be found in the section titled ‘MATLAB Script Explanation.’
As it is unlikely that perfect information will be available when parameterizing the model, the model
framework has been structured to draw parameters from distributions mimicking the uncertainty of the experimental
information. When using this Monte Carlo approach, reasonable estimates of uncertainty in model parameters (standard
deviations of ±0.1 on ꢀꢁꢂꢔꢕ values and ±2.5% on nonzero concentrations) are sufficient to encompass most of the
experimental simulated conversion data. Implementation of Monte Carlo uncertainty propagation and sensitivity
analysis in the model are discussed in more detail in the ‘Model Resolution, Sensitivity, and Error Analysis’ section of
the Supporting Information.
3 Wolfram Research, Inc., Mathematica, Version 10.4, Champaign, IL (2016)
4
The Mathematica inputs and outputs are provided in the Supporting Information, in sections ‘Mathematica Input: Solving the Model Equations’ and
‘Mathematica Output: Expressions for Absorbance, Conversion, and Ionic Strength’ respectively, as well as in the accompanying Mathematica
Notebook file.
5 MATLAB Release 2016a, The MathWorks, Inc., Natick, MA.

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This model was used to predict assay response curves that might be observed under various conditions for
each of the hydrolysis reactions considered, as well as to estimate the uncertainties associated with each prediction.
Each prediction was initialized using a spreadsheet containing the model parameters, including the initial experimental
conditions of the assay reaction, as well as the charges and ꢀꢁꢂꢔꢕ values of each of the ionizable species. An example
spreadsheet for initializing the model is also included in the Supporting Information section titled ‘Excel Spreadsheet.’
The charges and ionization constants used in this study are listed in Table S-3 of the Supporting Information.
2.8 Hypothesis Testing
The predicted relationship between reaction conversion and absorbance ratio can be used to interpret
experimentally measured absorbance ratios as reaction conversions, with appropriate levels of uncertainty. This
calculation can be performed for both enzymatic and non-enzymatic experiments, and their interpreted conversion
levels can then be compared to determine if the presence of an enzyme has any effect on reaction conversion. This
comparison requires the formation of two hypotheses: ꢋꢡ (the null hypothesis), which states that the enzyme has no
impact on reaction conversion (an assay ‘miss’), and ꢋꢏ (the alternative hypothesis), which states that the enzyme does
impact the reaction (an assay ‘hit’). The ‘Welch’s t-test,’ using the Welch-Satterthwaite equation to estimate the
underlying degrees of freedom, is applied to determine the probability that the enzymatic and non-enzymatic
conversion values are equal.21 Finally, using any desired p-value threshold ꣗, the null hypothesis ꢋꢡ is either accepted
or rejected. This analysis can be performed with a single set of experimental measurements or with time-series kinetic
data, and is performed automatically with the spreadsheet supplied in the Supporting Information.
3 Results
3.1 Characterization and Validation of Phenol Red
The color change of phenol red over a range of pH values from 6.2 to 8.1 is presented in Figure 4. Full
absorption spectra of phenol red under varied conditions and over a broader range of pH values are provided in Figure
S-4 of the Supporting Information. After baseline removal, spectrophotometric analyses of reactions were performed by
normalizing (Figure S-5 in the Supporting Information) the absorbance at 557 nm by that at the isosbestic point,
479 nm, and nonlinear regression was performed in MATLAB (Figure S-6) to parameterize the model. No change in
the absorbance of phenol red was detected in the presence or absence of CocE (Figure S-7 in the Supporting
Information), and HPLC analysis of reaction controls revealed no change in the activities of either CocE or AEH in the
presence or absence of phenol red (Figure S-8 in the Supporting Information). These results suggest that phenol red is
neither a substrate nor an inhibitor of the enzymes used in this study.
Figure 4: The color change of 20 µM phenol red in 100 mM sodium phosphate over a range of ꢀꢋꢂ values from 6.20 to 8.10.
This broad range of pH sensitivity makes phenol red a suitable indicator for assaying a wide variety of hydrolysis and synthesis
reactions.
3.2 Evaluation of Hydrolysis Activity by Colorimetry and HPLC
To validate the colorimetric assay, both HPLC and spectrophotometry were used to evaluate enzymatic
hydrolysis activity and the results were compared. Two reactions were tested: the hydrolysis of methyl picolinate by
CocE (Figure 5), and the hydrolysis of ampicillin by AEH variant QV-G.

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Figure 5: Cocaine Esterase (CocE) catalyzes the hydrolysis of methyl picolinate, producing picolinate and methanol. The
carboxylic acid group on picolinic acid will release a proton under basic or neutral conditions, allowing the progress of this
reaction to be tracked by indirect (spectrophotometric) monitoring of the solution pH using phenol red.
Experimental data and kinetic parameters for the hydrolysis of methyl picolinate by CocE are presented in
Table 1, while experimental data and kinetic parameters for the hydrolysis of ampicillin by AEH variant QV-G are
presented in Figure S-10 of the Supporting Information. Plots of CocE (0.148 µM) hydrolysis activity monitored by
both colorimetric and HPLC methods as a function of methyl picolinate concentration are shown in Figure 6, and fitted
kinetic parameters are reported in Table 1 (±SEꢚ. Parameter values determined by colorimetry (ꢁ꣘ = 17.3 ± 5.6 mM,
ꢐꢏ ꢢ
ꢣ
CocE = 0.148 μM) were consistent with those determined
꣙
= 234 ± 18 pmole/s, ꣜ꢓꢂꢔ = 7.89 ± 0.60 ꣝ꢐꢏ
ꢻ
꣚ꢂ꣛
by HPLC (ꢁ꣘ = 14.02 ± 6.7 mM, ꣙
= 196 ± 20 pmole/s, ꣜ꢓꢂꢔ = 6.62 ± 0.70 ꣝ꢐꢏꢻꢐꢏ, ꢢCocEꢣ = 0.148 μM).
꣚ꢂ꣛
Additionally, values of ꣙
were shown to increase proportionally with enzyme concentration, further confirming the
꣚ꢂ꣛
validity and sensitivity of the colorimetric assay. Additional kinetic data are provided in Figure S-9 of the Supporting
Information.
Table 1: Apparent net kinetic parameters for hydrolysis of methyl picolinate by CocE
꣜ꢓꢂꢔ ꢙsꢐꢏ
ꢚ
꣜ꢓꢂꢔ ꢁ꣘ ꢙMꢐꢏsꢐꢏ
ꢚ
⁄
ꢢ
ꢣ ꢙ
ꢚ
ꢙ
ꢚ
ꢙ
⁄ ꢚ
pmole s
꣚ꢂ꣛
Analytical Method
HPLC
No.
1
CocE μM
ꢁ꣘ mM
꣙
0.148
0.123
0.148
0.177
14.02±6.7
16.9±6.0
17.3±5.6
17.2±5.6
196±20
204±20
234±18
266±20
6.62±0.70
8.30±0.70
7.89±0.60
7.49±0.57
472±50
492±41
456±35
437±33
2
Spectrophotometry
(Plate reader)
3
4
Figure 6: Steady-state kinetics of the hydrolysis of methyl picolinate to picolinate and methanol by wild-type cocaine esterase
(CocE) (0.148 µM), as determined by spectrophotometry (blue squares) and by HPLC (red circles). The blue dotted curve and red
dashed curve represent the best fit of the spectrophotometry and HPLC data, respectively, to the Michaelis-Menten equation.
The ability of the colorimetric assay to capture kinetic parameters for both the hydrolysis of methyl picolinate
by AEH and the hydrolysis of ampicillin by AEH was consistent with the liberation of a carboxylic acid causing
solution pH to decrease as either reaction progresses. Both analytical methods evaluated here, HPLC and colorimetry,
revealed kinetic data consistent with each other and supported the use of pH-based colorimetry as a viable alternative to
HPLC.

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3.3 Differentiation Between Synthesis and Hydrolysis Activity
To demonstrate that the colorimetric assay was able to differentiate between synthesis and hydrolysis
activity, a model reaction with D-PGME serving as the sole substrate was implemented (Figure 2). Because the
colorimetric assay was shown to be sensitive to pH, hydrolysis reactions that decreased the pH value of initially neutral
solutions could be distinguished from amide bond forming synthesis reactions that increased the pH value of initially
neutral solutions. The hydrolysis and synthesis reactions of 25 mM D-PGME by either CocE or a thermally stabilized
variant of wild type AEH (AEH QV-H) were evaluated, and the solution pH was indirectly monitored by tracking the
absorbance of phenol red at 557 nm in the reaction mixtures (Figure 7).
Figure 7: Absorbance at 557 nm over time for reaction mixtures containing 25 mM D-PGME and either AEH QV-H (red) or
CocE (green). A control with no enzyme is also shown (black). All reactions occur in 100 mM PO4, 20 °C, and are initially at
pH 7.0.
While all three reaction mixtures began at the same neutral pH value, they each exhibited different behaviors
in the colorimetric assay. The non-enzymatic control showed no appreciable change in pH, which was consistent with
the lack of any appreciable conversion. Both the AEH- and CocE-catalyzed reactions initially dropped in absorbance.
This decrease in the measured absorbance of phenol red was attributed to a decrease in the pH value of the solution,
and was consistent with the carboxylic acid production associated with the hydrolysis reactions (Figure 2). In the AEH-
catalyzed reaction, this decrease continued unabated until all activity stopped, which was consistent with reports that
the QV-H variant used did not exhibit measurable n-phenylgycyl polymer synthesis activity (Figure 2).6 For the CocE-
catalyzed reaction, the decrease in absorbance was more gradual, and was eventually overtaken by a greater magnitude
increase in absorbance after 45 minutes (Figure 7). These results were consistent with the CocE reaction exhibiting
competing pH effects, likely due to the presence of both hydrolysis and synthesis reactions (Figure 2). Although the
mechanism behind the initial decrease in pH prior to the increase in pH warrants future investigations, it is likely that
the rate of primary hydrolysis initially outpaced synthesis due to uncoupling; as excess D-PGME was eliminated, fewer
primary hydrolysis side-reactions occurred leading to more efficient catalysis of n-phenylgycyl polymer synthesis from
the available D-PGME remaining in solution. Synthesis of dipeptide methyl ester by CocE was confirmed by liquid
chromatography mass spectrometry (LCMS) analysis (Figure S-11).
3.4 Prediction of Assay Response Curves
The mathematical model described above and provided in the Supporting Information was used to predict the
assay response to hydrolysis of methyl picolinate (Figure 5) under different conditions. Reaction mixtures with
concentrations of 20, 50, or 85 mM methyl picolinate in 100 mM sodium phosphate were predicted by modeling and
confirmed by experimental measurements of physical samples simulating various conversion levels, prepared by
mixing methyl picolinate, picolinic acid, and methanol in predefined ratios as described in the Methods section. The
model predictions and experimental measurements of simulated samples are shown in Figure 8.

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Figure 8: Model predictions and simulated (non-enzymatic) reaction data for the hydrolysis of either 20 mM (blue, diamonds),
50 mM (red, squares), or 85 mM (black, circles) methyl picolinate in 100 mM sodium phosphate buffer. Panel A: ꢀꢋꢂ vs.
Conversion. This is the expected change in measured pH over the course of each reaction. Panel B: Conversion vs. Absorbance
Ratio. This is the expected relationship between the reaction conversion and the measured absorbance ratio (557 nm / 479 nm) of
phenol red in the assay. In both panels: simulated experimental data (manually prepared samples designed to different conversion
points in the hydrolysis reactions) are plotted as open symbols, and model predictions are plotted as curves. Solid lines show the
mean prediction value, while uncertainty estimates at ±1 standard deviation for 10,000 Monte Carlo samples are indicated by the
dashed lines.
In all three predictions (i.e., for initial substrate concentrations of 20, 50, and 85 mM), samples initially at
neutral pH value begin to acidify as hydrolysis proceeds, and the model predictions match the experimentally measured
samples within the estimated prediction error. In general, the magnitude of the pH change is an effect of the
background buffer capacity as well as the ꢀꢁꢂ values and concentrations of the hydrolysis reactants and products. For a
given (nonzero) conversion level, samples prepared with more substrate will have a greater amount of carboxylic acid
product, and thus a greater propensity to overcome the pH-stabilizing effect of the phosphate buffer. Both the
predictions and experimental data support this reasoning, and it is apparent in Panel A of Figure 8 that the 85 mM curve
has the greatest magnitude slope, and 20 mM the least. The range of the assay within the pH-range of the colorimetric
indicator (here, phenol red) dictates the shape of the plot of absorbance ratio vs. reaction conversion. As the pH
response in Panel A is relatively linear, and the absorbance response of the indicator is sigmoidal (Supporting
Information, Figures S-5 and S-6), the absorbance vs. conversion relationship for these samples is distorted and
transformed sigmoidal sections. The nonlinear and widely variable nature of the relationship between the observable
color change and the reaction progress is the reason that either experimental or simulated standard curves, or the pH
equilibrium model described in this work are required to reliably interpret experimental assay results.
The slope of the relationship between pH and conversion is inherently linked to the sensitivity of the assay,
with greater magnitude changes in pH corresponding to a more sensitive assay. This result is captured by the width of
the uncertainty bands in Panel B of Figure 8, which are widest for the sample with 20 mM substrate, and narrowest for
the sample with 85 mM substrate.
3.5 Hypothesis Testing and Interpretation of Assay Results
Two example assay samples were prepared to evaluate whether CocE would be classified as a ‘hit’ or a
‘miss’ in a first-pass high throughput screen (evaluating either enzyme variants or substrate alternatives). Reaction
mixes containing phenol red, 50 mM methyl picolinate, and either CocE or a non-enzymatic control in 100 mM sodium
phosphate were tracked in a plate reader over several hours. The ratio of optical absorbance (557 nm)/(479 nm) is
shown over time in the top panel of Figure 9. The non-enzymatic sample maintains a relatively steady absorbance ratio
while the absorbance ratio of the sample containing CocE drops over several hours. Using the model predictions of
conversion against absorbance ratio (Figure 8, Panel B) and the supplied spreadsheet for data interpretation and
hypothesis testing as described in the Methods section, these absorbance ratios were converted to predictions of
conversion with associated levels of prediction uncertainty (Figure 9, middle panel). The results of automatic
hypothesis testing, comparing the enzymatic and non-enzymatic samples, are shown in the bottom panel of Figure 9,

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and the null hypothesis is rejected after 20 minutes indicating that CocE has a statistically significant influence on
reaction conversion, and is therefore a ‘hit’ in this assay. This result is consistent with the established function of CocE
as a catalyst for the hydrolysis of methyl picolinate, and supports the use of pH-based colorimetry with model
predictions and hypothesis testing for enzyme or substrate screening.
Figure 9: Use of model predictions to perform hypothesis testing. The top panel shows the absorbance ratio (557 nm/479 nm)
over time for the hydrolysis of 50 mM methyl picolinate in 100 mM sodium phosphate by CocE (solid red), and non-enzymatic
control (dotted black). In the center panel, these data are transformed into hydrolysis conversion, with error bars at ±1 standard
deviation, after Monte Carlo simulation. The bottom panel illustrates how Welch’s t-test rejects the null hypothesis within twenty
minutes using a p-value threshold of ꣗ = 0.05.
4 Discussion
4.1 Summary of Results
The experimental results presented provide general support and validation for the application of pH-based
colorimetry and modeling to high throughput reaction screening. Several intermediate steps were taken to build up to
the use of pH and phenol red to track enzymatic reactions, as well as to model and verify predictions of assay behavior
for use in high throughput hypothesis testing. Multiple enzymatic hydrolysis and synthesis reactions, listed in Table 2,
were used to validate each of the different parts of this work. Phenol red was demonstrated to predictably reveal – but
not interfere with – enzymatic synthesis and hydrolysis reactions (reactions 1 and 2 in Table 2). Colorimetry and HPLC
were shown to produce comparable results for kinetic analysis of both CocE and AEH (reactions 2 and 3). Colorimetry
was also shown to differentiate between reaction regimes dominated by hydrolysis or synthesis activity
(reactions 4 and 5).

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Table 2: Hydrolysis and synthesis reactions evaluated in this study.
No.
1
Substrate
Enzymes
AEH
Expected Products
ampicillin
Reaction Type
synthesis
6-aminopenicillinate and D-
phenylglycine methyl ester
methanol
methanol
2
methyl picolinate
ampicillin
CocE
picolinate
hydrolysis
hydrolysis
hydrolysis
synthesis
3
CocE, AEH
AEH
6-aminopenicillinate
D-phenylglycine
3
D
-phenylglycine methyl ester
-phenylglycine methyl ester
D-phenylglycine
methanol
methanol
5
D
CocE
di- and tri-peptides
A generalizable mathematical model was shown to accurately predict the response of the colorimetric assay
to experimental samples simulating reaction 2 at various levels of conversion and performed under varied conditions.
Finally, an automated hypothesis test correctly classified CocE as having activity on methyl picolinate in an assay trial
(reaction 2). These data are the result of a limited range of experiments, but the principles behind them are sufficiently
general to warrant further investigation into the combination of pH-based colorimetry and modeling of pH equilibria
for high throughput assays and screening tests.
4.2 Limitations of the pH-Based Assay
The framework we present for colorimetric pH-based assays have the potential to accelerate the development
of hydrolase enzymes, such as those utilized for the biocatalytic synthesis of β-LA, by enabling efficient high-
throughput analysis of enzyme variants, substrates, or reaction conditions. These benefits notwithstanding, there are
some general cases in which the assay or mathematical model presented here may not be appropriate. It is inadvisable
to use this assay for reactions with unknown side product formation, because the exact hydrolysis stoichiometry, as
well as the acidity constants of all ionizable species, is necessary for the prediction of assay response curves.
Additionally, the model presented here should not be used for reactions that will exceed ionic strengths of 0.5 M – the
recommended limit of Sun’s extended Debye-Hückel parameterization.19 Beyond this range, specific ion interactions
may convolute simplified attempts at activity correction, and more detailed models are recommended. Finally, even
when all of the above criteria are met, a particular set of assay conditions might not provide satisfactory sensitivity for a
particular reaction. In such cases, slight adjustments to experimental conditions – such as reducing the buffer
concentration or starting at a different pH value – may resolve these issues.
In general, the experimental results in Figure 7 indicate that this assay approach would be effective for
researchers looking to increase either amide synthesis or ester hydrolysis activity by compressing results into simple
increases or decreases in absorbance. Nevertheless, there are limitations that must be considered: the assay would not
be able to capture equal and simultaneous increases in both activities due to their opposing effects on solution pH, and
certain hydrolysis reactions, such as those of amides, produce equimolar amounts of acid and base, significantly adding
to the buffering capacity of the reaction system around a certain pH value. If that particular pH value happens to be the
same as the initial pH of the assay, then the pH will not change as a function of conversion. Mathematically speaking,
the algebraic solutions to the pH equilibrium model become undefined, as the physical system they are modeling adopts
a one-to-many mapping from pH to conversion. This effect is illustrated in Figure 10, which shows the predicted pH
response to the hydrolysis of 300 mM acetamide. Acetamide hydrolysis produces equimolar acetic acid and ammonia
(Figure 11), which are commonly used together to buffer solutions to pH 7.0. Therefore, no matter the starting pH, the
solution will tend towards neutrality. Since CocE is most active at neutral pH, the assay must start at pH 7, meaning
that the predicted assay response is undefined.

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Figure 10: The predicted pH response to conversion for hydrolysis of 300 mM acetamide, over a wide (exaggerated, for
emphasis) range of starting pH values. The tendency of the pH value towards neutral illustrates a fundamental limitation of the
pH-equilibrium model and colorimetric assay.
Figure 11: Wild-type CocE can catalyze the hydrolysis of acetamide into acetate and ammonium.
Finally, this approach should only be used for first-pass screening, as the extended Debye-Hückel method
used here is an empirical regression of experimental data, and may not provide satisfactory results for all compounds.
As with most colorimetric assays, insoluble and precipitating components will hinder correct measurements; assays
should be performed within the solubility limits of all reagents.
4.3 Advantages of the pH-Based Assay over Existing Methods
In traditional HPLC-based assays, the elution time and absorbance level of each compound are affected by
the pH of the mobile phase, as well as the column condition and temperature. Additionally, chromatography columns
rely on dynamic cross-linked functional groups that may exhibit varied behavior under different conditions of mobile
phase, storage solvents, upkeep level, and age. These variables are difficult to control, and failure to do so can result in
peak-splitting, degradation of assay quality, and inconsistent results. Furthermore, designing separation methods for
and producing standard curves for a wide variety of possible reactants and products is time consuming, and may require
switching between multiple HPLC columns or mobile phases. Finally, the challenges of using HPLC for high-
throughput analysis are exacerbated by the prolonged sample run-time – typically requiring at least 30 minutes to
collect a single data point.
As optical measurements in general are simpler and faster than HPLC, switching a first-pass screening
operation from HPLC to colorimetry could result in a significant reduction in time and material costs, as well as the
volume of data, in comparison to HPLC. Using the phenol red assay, multiple enzymatic reactions can be loaded into a
standard well-plate and can be reliably qualified as ‘hit’ or ‘miss’ in 100 minutes or less. Additionally, if hypothesis
testing is performed in real-time during absorbance measurement, then a consistently low p-value may permit early
termination of a sample. This is illustrated for the hydrolysis of 50 mM methyl picolinate by CocE over several hours
in the bottom panel of Figure 9. In this example, it is clear after less than an hour that the hydrolysis of 50 mM methyl
picolinate should be considered a positive ‘hit,’ and that the assay (or monitoring of that particular set of samples) may
be terminated early. There are also other benefits to continuously monitoring assay samples: a reduced number of
samples can be used, as repeated observation of an individual sample provides an effective denoising, and time-series
data provide opportunities for other uncertainty-management approaches such as low-pass filters, or more sophisticated
statistical methods involving sequential analysis.

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Alternative high throughput colorimetric assays exist for these and other reactions, but the current paradigm
in which every reaction must have its own specialized assay may not be the most efficient use of resources. The method
presented here relies only on acid-base equilibria, and is therefore generalizable to the analysis of many reactions and
enzymes. The mathematical model can predict direct mappings between optical absorbance and conversion for a
variety of reactions without necessarily requiring experimental standards, and cases in which the colorimetric assay will
not work can frequently be determined in advance of any experimentation in the laboratory.
5 Conclusions
The use of phenol red as an indicator for high-throughput pH-based colorimetric substrate scanning and
activity screening of enzyme variants was demonstrated to be successful. This assay can be employed to detect
reactions catalyzed by AEH and CocE as well as other enzymes within the α/β hydrolase family, and can be used to
distinguish hydrolysis from synthesis activity. A thermodynamic pH equilibrium and reaction-conversion model
compresses the multitude of variables embodied in a reaction system into simple and direct relationships between
optical absorbance and reaction conversion. This model provides insights into assay behavior that facilitate planning of
experiments. Model predictions can be used in lieu of experimental standard curves – the collection of which might
detract from the otherwise high-throughput nature of the assay – and facilitate real-time hypothesis testing to classify
samples as hits or misses. The approach used here is sufficiently general to enable use of colorimetric pH-based assays
for rapid screening of other aqueous reactions, which result in pH changes.
6 Supporting Information
Supporting Information is available on the publication website, and contains the following materials:
1. Supporting Information: Additional figures and enzymatic hydrolysis and synthesis data, as well as
detailed explanation of the mathematical model and Mathematica and MATLAB codes. (File type: PDF)
2. Mathematical Model: A compressed zip folder containing the files necessary to run and modify the
model described in this paper. (File type: ZIP) The contents of the compressed folder are:
a. License: A copy of the code license. (File type: .txt)
b. Model_File_1: Mathematica Input File for algebraically solving equations (3-11). (File type:
Mathematica .nb file)
c. Model_File_2: MATLAB code for the full pH equilibrium model. Requires MATLAB version
R2016a or later to run. (File type: MATLAB .m file)
d. Model_File_3: Microsoft Excel spreadsheet parameterizing the model for the hydrolysis of
methyl picolinate. (File type: .xlsx)
7 Acknowledgements
The authors would like to thank Dr. Nils Persson for his thoughtful suggestion of incorporating Monte Carlo
simulation for uncertainty propagation and sensitivity analysis, as well as Dr. M. Thomas Morgan, for his insights and
discussions relating to thermodynamic activity and ionic strength-associated phenomena.
The authors acknowledge financial support from the National Science Foundation (NSF) under contracts IIP-
1540017 and IIP-0969003 to the I/UCRC Center for Pharmaceutical Development (CPD).
8 Keywords
pH • Colorimetric • alpha/beta hydrolase • AEH • CocE
9 Abbreviations
6-APA, 6-Aminopenicillanic acid; APANiB, 5-(2-Amino-2-phenylacetamido)-2-nitrobenzoic; β-LA, β-
Lactam antibiotics; °C, Degrees Celsius; CocE, Cocaine esterase; D-PG, D-Phenylglycine; D-PGME, D-Phenylglycine

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methyl ester; DTNB, 5,5’-Dithiobis-(2-nitrobenzoic acid); HCl, Hydrochloric acid; HPLC, High performance liquid
chromatography; kcat, Catalytic turnover number (s-1); KM, Michaelis-Menten constant (mM); pH, Log of the
concentration of protons; pHa, pH reported on an activity basis; QV-G, Quadruple variant of AEH
(N186D/A275P/V622I/E143G); QV-H, Quadruple variant of AEH (N186D/A275P/V622I/E143H); NaCl, Sodium
chloride; SDS, Sodium dodecylsulfate; NaPO4, Sodium phosphate; UV-Vis, Ultraviolet-visible.
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