Enzyme kinetics in crowded solutions from isothermal titration calorimetry

Article abstract of DOI:10.1016/j.ab.2018.11.006

Isothermal titration calorimetry (ITC) is a universal technique that directly measures the heat absorbed or released in a process. ITC is typically used to determine thermodynamic parameters of association of molecules without the need to label them. However, ITC is still rarely applied to study chemical reactions catalyzed by enzymes. In addition, these few studies of enzyme kinetic measurements that have been performed were in diluted solutions. Yet, to estimate realistic kinetic parameters, we have to account for the fact that enzymatic reactions in cells occur in a crowded environment because cells contain 200–400 g/L of macromolecular crowders such as proteins, ribosomes and lipids. Thus we expanded the ITC application for solutions mimicking the cellular environment by adding various macromolecular crowders. We investigated how these crowders affect the kinetics of trypsin-catalyzed reactions and determined the Michaelis-Menten parameters for hydrolysis of two trypsin substrates: Nα-benzoyl-L-arginine ethyl ester (BAEE) and Nα-benzoyl-DL-arginine β-naphthylamide (BANA). Since ITC enables investigations of complex and turbid solutions with label-free reagents, it seems a perfect technique for kinetic analyses in crowded solutions. ITC also offers the opportunity to control enzyme-crowder and substrate-crowder interactions.

Full text of DOI:10.1016/j.ab.2018.11.006

Accepted Manuscript
Enzyme kinetics in crowded solutions from isothermal titration calorimetry
Ksenia Maximova, Jakub Wojtczak, Joanna Trylska
PII:
S0003-2697(18)30401-9
https://doi.org/10.1016/j.ab.2018.11.006
YABIO 13179
DOI:
Reference:
To appear in: Analytical Biochemistry
Received Date: 16 April 2018
Revised Date: 8 July 2018
Accepted Date: 5 November 2018
Please cite this article as: K. Maximova, J. Wojtczak, J. Trylska, Enzyme kinetics in crowded solutions
from isothermal titration calorimetry, Analytical Biochemistry (2018), doi: https://doi.org/10.1016/
j.ab.2018.11.006.
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Enzyme kinetics in crowded solutions from isothermal titration calorimetry
ACCEPTED MANUSCRIPT
Ksenia Maximova1,*, Jakub Wojtczak1,2 and Joanna Trylska1,*
1Centre of New Technologies University of Warsaw, Banacha 2C, 02-097 Warsaw, Poland
2Faculty of Biology, University of Warsaw, Miecznikowa 1, 02-096 Warszawa, Poland
*e-mail: k.maximova@cent.uw.edu.pl and joanna@cent.uw.edu.pl
Abstract
Isothermal titration calorimetry (ITC) is a universal technique that directly measures the heat
absorbed or released in a process. ITC is typically used to determine thermodynamic
parameters of association of molecules without the need to label them. However, ITC is still
rarely applied to study chemical reactions catalyzed by enzymes. In addition, these few
studies of enzyme kinetic measurements that have been performed were in diluted solutions.
Yet, to estimate realistic kinetic parameters, we have to account for the fact that enzymatic
reactions in cells occur in a crowded environment because cells contain 200-400 g/L of
macromolecular crowders such as proteins, ribosomes and lipids. Thus we expanded the ITC
application for solutions mimicking the cellular environment by adding various
macromolecular crowders. We investigated how these crowders affect the kinetics of trypsin-
catalyzed reactions and determined the Michaelis-Menten parameters for hydrolysis of two
trypsin substrates: Nα-benzoyl-L-arginine ethyl ester (BAEE) and Nα-benzoyl-DL-arginine β-
naphthylamide (BANA). Since ITC enables investigations of complex and turbid solutions
with label-free reagents, it seems a perfect technique for kinetic analyses in crowded
solutions. ITC also offers the opportunity to control enzyme-crowder and substrate-crowder
interactions.
Key words: enzyme kinetics, trypsin, isothermal titration calorimetry, macromolecular
crowding
1

Introduction
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Thousands of various enzymes play important roles in cells speeding up numerous vital
reactions. The accurate determination of the enzyme activity, especially in cell-mimicking
conditions, is crucial for the understanding of biochemical processes and further drug design.
Isothermal titration calorimetry (ITC) is a well-known physical technique that measures the
change of heat of the processes and is commonly applied to study thermodynamic parameters
of binding of unlabeled reagents [1]. Technically, the procedure consists of (i) titration of a
ligand into the cell with a receptor, (ii) observation of the occurring heat changes and (iii)
estimation of the reaction enthalpy and equilibrium association constants. Surprisingly, such
a straightforward technique has not gained widespread appreciation in the studies of enzyme
kinetics, where a catalyzed reaction may be monitored by titration of the substrate into the
cell with the enzyme.
Only few studies have shown the benefits of ITC for enzyme kinetic analysis
[2,3,12,13,4–11]. Moreover, ITC allows detecting if an enzyme is inhibited by the products
of the reaction (or by other inhibitors), proposing the inhibition mechanism, and estimating
the inhibition constants [2,3,13–15]. However, up to now almost all of the few known kinetic
ITC experiments have been performed in non-crowded (dilute) solutions, whereas cells
contain 200-400 g/L of macromolecular crowders such as proteins, ribosomes, and lipids
[16]. These crowders may affect enzyme structure, folding, shape, conformational stability,
aggregation and, thereby, kinetics [17,18].
Many spectrophotometric and radioactive assays have confirmed the impact of
crowding on the enzyme catalytic activities and showed that the kinetic constants estimated
in diluted solutions differ by many orders of magnitude from the living cell parameters [19–
22]. For example, it was shown that an inactive DNA ligase in a dilute assay condition
became active in the presence of high concentrations of various macromolecules, such as
polyethylene glycol (PEG), Ficoll and bovine serum albumin (BSA) [23]. The activity
enhancement was also observed for RNAse T1 in the presence of dextran [24]. Thus
macromolecules may dramatically affect the structure, function and folding landscape of the
2

enzymes, and it is evident that to estimate the realistic kinetic parameters the measurements
ACCEPTED MANUSCRIPT
have to be performed in cell mimicking conditions.
However, general methods to study macromolecular crowding effects have some
drawbacks such as the need to label the substrates with radioactive, chromophore or
fluorophore tags and requirement of multi-step purification procedures due to turbidity of
solutions. On the contrary, the ITC technique avoids the above limitations and will speed up
the assays for complex solutions. Up to now, the only study that applies kinetic ITC in a
crowded environment is for the hexokinase reaction in the solution with up to 250 g/L of
BSA [25]. The author of this study has shown that both Michaelis-Menten kinetic constants
(Km and kcat) decreased with increasing BSA concentration.
Our aim was to expand the ITC technique for kinetic studies in crowded solutions.
We chose to assay enzymatic hydrolysis, which is widespread in nature. In particular, ester
and amide hydrolysis is one of the most common reactions in cells and is essential in the
degradation pathways of many substances [26] (Scheme 1, top). So as an example, we
studied trypsin-catalyzed reactions: ester hydrolysis of Nα-benzoyl-L-arginine ethyl ester
(BAEE) and amide hydrolysis of Nα-benzoyl-DL-arginine β-naphthylamide (BANA)
(Scheme 1, bottom). The assays were performed in dilute solutions and with the crowding
agents: ethylene glycol (EG), polyethylene glycol (PEG) and bovine serum albumin (BSA),
which are commonly used to mimic cellular environment in non-ITC studies of the crowding
effect on enzyme kinetics [27]. For instance, Asaad and Engberts used PEG8000 to
spectrophotometrically explore the influence of crowding on the trypsin-catalyzed hydrolysis
of p-nitrophenyl acetate. They showed the kcat decrease over the PEG concentration up to 395
g/L [19]. BSA, in turn, as a crowder is significant due to its abundance (about 60% of serum
total protein content) and its transport function for organic compounds in the blood stream
[28]. That is why BSA is a good control crowder that mimics the protein cell environment
[29]. Moreover, our selected crowders also differed in the molecular weights (in the range of
0.06 - 66 kDa) and concentrations (100 - 300 g/L).
3

Materials and Methods
ACCEPTED MANUSCRIPT
All chemicals were purchased from Sigma Aldrich and used without further purification.
Enzyme: The stock solution (1 mM) of trypsin from bovine pancreas was prepared in 1 mM
HCl and stored at -20 °C.
Substrates: The stock solution (1.5 mM) of BAEE was freshly prepared in the running buffer.
The stock solution (70 mM) of BANA was prepared in DMSO and stored at -20 °C.
Buffers: All experiments were performed in 200 mM TRIS-HCl, 50 mM CaCl2 buffer, at pH
8.0, at 37 °C, with 0.05% Igepal. The composition of the buffer solution of the substrates and
the enzyme with 0, 100, 200 or 300 g/L macromolecular agents for the assay experiments
was identical. The concentration of DMSO in assays with BANA was kept at 10%.
Equipment: The ITC assays were carried out on the power-compensated instrument Nano
ITC (TA Instruments, New Castle, DE, USA). The Nano ITC has a gold cell of 190 µL
volume (the working volume is 165 µL) and a syringe of 50 µL volume. The stirring speed in
the calorimeter cell was 350 rpm, and thermal power was recorded every 2 s. In each
experiment the control injections of the substrate to the buffer and of the buffer to the enzyme
were carried out, and the heat of the dilution was corrected if necessary. The Nano ITC was
used with the control software provided by the manufacturer - NanoAnalyze. The
fluorometric assays were measured on F-7000 FL spectrophotometer using the emission scan
mode. The excitation wavelength was 335 nm, the scan speed - 1200 nm/min, the excitation
and emission slits – 2.5 nm and PMT voltage – 500 V. The fluorescence signals were
analyzed as the height of the emission peak at 410 nm. The fluorescence and ITC data were
fitted by GraphPad. All experiments were performed in independent triplicates. The averages
with their standard deviations are shown as results.
4

Determination of apparent molar enthalpy ∆Happ and kinetic parameters, verification of
ACCEPTED MANUSCRIPT
product inhibition by continuous assay
Trypsin catalyzed hydrolysis of BAEE
The trypsin solution (10 nM) or buffer was equilibrated at 37 °C for 200 s. Then ten aliquots
of 3 µL of the 1.5 mM BAEE, BA solution or the buffer were injected (see Figure 1, and
Figures 2A, S2 and S3A) or two aliquots of 15 µL of the 1.5 mM BAEE solution (Figures
2B,and S3B). The experiments were performed in buffer solutions without the crowders or
crowded by 300 g/L of EG, PEG600 or PEG6000. The change in the thermal power was
monitored until the signal returned to the original base line. Data analysis is presented in
Figures 2 and S3 and in Tables 1 and 2.
Trypsin catalyzed hydrolysis of BANA
The trypsin solution (25, 12.5 or 2.5 µM) or buffer was equilibrated at 37 °C for 200 s. Then
seven aliquots of 5 µL of the 4 mM BANA solution, buffer (Figure 5) or two aliquots of 25
µL of the 4 mM BANA solution (Figure 2C, only the first injection is shown) were injected.
The change in the thermal power was monitored until the signal returned to the original base
line. Data analysis is presented in Figure 2 and Table 1.
Determination of kinetic parameters by the multiple injection assay
Trypsin catalyzed hydrolysis of BAEE
The 10 nM trypsin solution or buffer was equilibrated at 37 °C for 200 s. Then 15 aliquots of
3 µL of the 1.5 mM BAEE solution were injected every 100 sec. The experiments were
performed in buffer solutions without the crowders or crowded by 100, 200 or 300 g/L of EG,
PEG600 or PEG6000. The data was analyzed by nanoAnalyze and fitted by GraphPad
(Figures 3, 4, S4-S6 and Table 3).
5

Trypsin catalyzed hydrolysis of BANA monitored by ITC and FL spectrophotometer
ACCEPTED MANUSCRIPT
The 7.5 µM trypsin solution or buffer was equilibrated at 37 °C for 200 s. Then 15 aliquots of
3 µL of the 4 mM BANA solution were injected every 100 sec. The experiments were
performed in buffer solutions without the crowders or crowded by 100, 200 or 300 g/L of EG,
PEG600, PEG6000 or BSA. The data was analyzed and fitted by GraphPad (Figures 6, S10
and Table 4).
Trypsin catalyzed hydrolysis of BSA
The 7.5 µM trypsin solution in buffer without the crowders or crowded by 200 g/L of BSA
was equilibrated at 37 °C for 200 s. Then 15 aliquots of 3 µL of the 0.3 mM BSA solution or
buffer were injected every 100 sec. The experiments were performed with or without adding
10% DMSO (Figure 7).
β-Naphthylamine calibration monitored by FL spectrophotometer
10 aliquots of 30 µL of the 1 mM β-NA solution were injected to the cuvette filled with the
10 nM trypsin solution, buffer without the crowders or buffer crowded by 100, 200 or 300
g/L of EG, PEG600, PEG6000 or BSA. The fluorescence signals were analyzed as the height
of the emission peaks at 410 nm (Figure S11).
Results and Discussion
We carried out the ITC experiments for the reactions catalyzed by trypsin using two
substrates: BAEE and BANA (Scheme 1). Both substrates possess the label-groups, BAEE –
the chromophore (Nα-benzoyl-L-arginine) and BANA – the fluorophore (β-naphthylamine).
That is why the kinetic results determined by ITC could be compared with those estimated by
classical spectrophoto- and fluorometrical assays.
Experiments were performed in solutions crowded by various agents: ethylene glycol
(EG), polyethylene glycol (PEG), and bovine serum albumin (BSA). We chose crowding
agents differing by molecular weights: EG – 0.06, PEG600 – 0.6, PEG6000 – 6 and BSA –
6

66 kDa. Also, we increased the concentration of the crowders gradually up to 300 g/L, which
ACCEPTED MANUSCRIPT
is the closest concentration to the cellular conditions [16]. Additionally, we performed the
fluorometric assays to compare with the ITC results. Since ITC gives opportunity to study
label-free systems, we performed all possible control reactions, i.e. injections of the enzyme
or substrate to the cell with the crowders in order to account for any enzyme-crowder or
substrate-crowder interactions. That is why one of the chosen crowders was BSA, which is
subjected to the trypsin proteolysis [30] and served as an example of how to consider and
control the background reactions in ITC.
Scheme 1. Top: The cartoon representation of trypsin (PDB code: 1S0Q, with β-sheets in
yellow and helices in magenta and blue) and hydrolysis of ester and amide bonds. Bottom:
The substrates: Nα-benzoyl-L-arginine ethyl ester (BAEE) and Nα-benzoyl-DL-arginine β-
naphthylamide (BANA) and the products of trypsin catalyzed hydrolysis: Nα-benzoyl-
arginine (BA) and β-naphthylamine (β-NA).
L-
7

1. The hydrolysis of BAEE by trypsin
ACCEPTED MANUSCRIPT
BAEE is a common substrate recommended for use to estimate trypsin activity in the ester
bond cleavage by spectrophotometry [31] (Scheme 1). However, such measurements are
complicated by close values of the extinction coefficients for the substrate and product (ε
equal to 2.3 x 103 for BAEE and ε is about 3.45 x 103 for BA at 253 nm) [32] and require
complementary techniques such as pH-stat or ITC.
1.1. ∆Happ of the BAEE hydrolysis and verification of the reaction inhibition by the
products
The rate of the reaction determined by calorimetry has to be calculated from Eq. 1, where Rt
is the calculated rate of the reaction equal to the concentration of the formed product over
time, d[P]t/dt; Vcell is the given calorimetric cell volume, which in our case was equal to 165
µL; ∆Happ is the measured apparent molar enthalpy of the reaction (see details below); dQ/dt
is the observed heat change over time; vmax and Km are the fitted maximum observed velocity
and the Michaelis constant, respectively, [S]t is the concentration of the substrate at time t.
To solve Eq. 1 first of all we have to estimate the apparent enthalpy of the reaction (∆Happ),
namely, the heat consumed per one mole of the hydrolyzed substrate. Thus, we have to carry
out the experiment during which the substrate is injected into the cell containing the enzyme
and the heat of the full substrate conversion by the enzyme is detected (Figure 1, red line -
first peak). The sign of the full conversion or, in other words, the completion of the reaction,
is the return of the baseline to the initial position. The integration of the area under the peak
gives the total heat of the reaction, which has to be divided by the moles of the substrate in
the reaction (nsub) to obtain the required
∆Happ (Eq. 2).
ꢅ
ꢂꢍ
ꢂꢁ
ꢎ
.[ꢑ]
ꢀꢁ = ꢂ[ꢃ]
=
=
ꢒ ꢓ[ꢑ]
ꢏ ꢄ
(1)
ꢄ
ꢏꢋꢐ ꢄ
ꢂꢁ
ꢆ
ꢇꢈꢉꢉ
∙∆ꢊ
ꢋꢌꢌ
ꢅ
ꢁꢜ∞ ꢂꢍ
ꢁꢜꢝ
∆ꢔꢕꢖꢖ
=
ꢞꢟ
ꢂꢁ
(2)
ꢛ
ꢗ
ꢘꢙꢚ
8

ACCEPTED MANUSCRIPT
Figure 1. The continuous assay for the hydrolysis of BAEE. Red line: The thermogram of the
full conversion of the BAEE substrate in each repeated injection of 3 µL of 1.5 mM BAEE
into the cell containing 10 nM trypsin. Blue line: The control thermogram for the dilution of
BAEE showing injections of BAEE into the cell containing the buffer. Green line: The
control thermogram for the binding of BA to trypsin showing injections of 3 µL of 1.5 mM of
BA into the cell containing 10 nM trypsin.
The thermogram for the BAEE trypsin-catalyzed reaction shown in Figure 1 presents
the full substrate conversion in repeated injections. Approximately 300 s was required for the
total decomposition of 4.5 nmoles of BAEE by trypsin (Figure 1, red line). The total heat of
the hydrolysis was about -47 µcal. The heat of the substrate dilution was equal to -0.7 µcal
(Figure 1, blue line). The heat of the trypsin dilution (the injection of only the buffer to the
cell with trypsin) was neglegible due to the low concentration of the enzyme.
Additionally, we wanted to quantify if there is any change of heat coming solely from the
binding event of the BAEE substrate and not its cleavage, so we used Nα-benzoyl-L-arginine
(BA) as the BAEE substrate mimic because BA is not cleaved by trypsin (Scheme 1). The
observed heat of the BA injections into the cell containing the enzyme was equal to -0.4 µcal
(Figure 1, green line). We assumed it as negligible and did not take the binding heat into
account. Thereby the apparent molar enthalpy ∆Happ of the BAEE hydrolysis was about 10
kcal/mol (Table 1). The ∆Happ was in accord with the previously published ITC-determined
9

values obtained under similar conditions: -9.2 kcal/mol [33] and -11.5 kcal/mol [3] (at 25
ACCEPTED MANUSCRIPT
°C).
Additionally, this experiment with the full conversion of the substrate to products in
each injection provided further information about possible inhibition of the enzymatic
activity by the released products [2,3]. The heat from several injections of equal amounts of
the BAEE substrate to trypsin, as well as the shape of the curves and peak heights, were
compared (Figure 1, red line). Ten equal injections gave the same amount of heat for each
injection (around -47 µcal) and similar curve shapes. This result signifies either none or
negligible inhibition by the products of the BAEE hydrolysis. Note that to detect product
inhibition, the intervals between the injections have to be of the same duration as the first
injection (in our case 300 sec was required to complete the hydrolysis of 27 µM BAEE and
return the signal to the baseline). Also, previously no product inhibition for the hydrolysis of
BAEE by trypsin was observed [3].
We checked further if crowding influences the ITC determination of ∆Happ. Note, that
to minimize the background heat, the compositions of the buffer solutions in the titrating
syringe, sample cell and reference cell were identical (Figure S1). Thus, we prepared the
solutions crowded by EG, PEG600 or PEG6000 at the maximal concentrations of 300 g/L
and repeated the trypsin-catalyzed BAEE hydrolysis (Figure 2A). Table 1 shows the
components of ∆Happ for the non-crowded system and for the highest concentration of
crowders. At 300 g/L crowder concentrations, the substrate dilution heat contributes more to
the measurements, also bearing a larger error; the same applies to the total heat of the
reaction. Thus, determination of ∆Happ under crowded conditions beared larger errors so in all
further calculations we used ∆Happ equal to -10 kcal/mol, which is the enthalpy of the BAEE
hydrolysis in non-crowded solution (Eq. 1, Table 1). Further, trypsin was not inhibited by the
reaction products in all crowded solutions (Figure S2). However, it is obvious from Figure
2A that crowding influenced the reaction itself: it takes more time to convert the substrate
into the products in the crowded solutions. Thus we can already estimate the effect of
crowding on the enzyme kinetics.
10

ACCEPTED MANUSCRIPT
Table 1. The results of the ITC assays performed to determine the apparent molar enthalpy
∆Happ (Eq. 1). To determine the total heat of the reaction, the substrate was injected into the
cell with trypsin; the heat of the substrate dilution - the substrate was injected into the cell
with the buffer; the heat of the substrate binding - BA was injected into the cell with trypsin.
Averages and standard deviations are shown from three experiments.
Trypsin, Substrate,
Crowding
300 g/L
Injected
volume,
µL
Total heat
of reaction,
µcal
Heat of
substrate
Dilution heat,
µcal
∆Happ
,
µM
mM
kcal/mol
binding, µcal
None
EG
3
3
3
3
-46.9 ± 0.9
-54.2 ± 2.1
-56.4 ± 2.9
-59.6 ± 9.4
-0.7 ± 0.2
-2.7 ± 0.6
-6.0 ± 0.8
-7.0 ± 1.0
-0.4 ± 0.1
-10.3±0.2
-11.4±0.5
-11.2±0.7
-11.7±2.1
-
-
-
0.01
BAEE,
1.5
PEG600
PEG6000
BANA,
4
25
None
5
-
-51.1 ± 6.1 -10.2 ± 1.5
-2.0±1.4
11

ACCEPTED MANUSCRIPT
Figure 2. Continuous assays of the trypsin-catalyzed hydrolysis of BAEE monitored either in
a non-crowded or crowded buffer (Left: Raw calorimetric data. Right: The transformed raw
data with Eqs. 1 and 2). A: Injection of 3 µL of 1.5 mM BAEE into the cell containing 10 nM
trypsin. B: Injection of 15 µL of 1.5 mM BAEE into the cell containing 10 nM trypsin. C:
Injection of 25 µL of 4 mM BANA into the cell containing 25, 12.5 or 2.5 µM trypsin in a
non-crowded buffer.
12

1.2. The Michaelis-Menten kinetics from the continuous BAEE hydrolysis assay
ACCEPTED MANUSCRIPT
The data from the experiment performed to determine ∆Happ can be transformed to the kinetic
Michaelis–Menten curve (the detailed information is in the references [2,3,34,35]). The
reaction rate is estimated from the decay of the heat curve of the substrate (Eq. 1, Figure 2
right), and instantaneous substrate concentrations at time t are calculated from Eq. (3):
ꢄꢢꢣ
ꢛ
ꢤ
ꢢꢄ
[ꢠ]ꢁ = [ꢠ]ꢁꢜꢡ
−
(3)
ꢆ
ꢇꢈꢉꢉ
∙∆ꢊ
ꢋꢌꢌ
The hydrolysis of BAEE by trypsin in either non-crowded or crowded solutions (Figure 2A,
left) were thus turned into continuous kinetic curves (Figure 2A, right), which were fitted to
the Michaelis-Menten equation (Table 2, Figure S3). However, note that the kinetic
parameters of Table 2 are only shown for the discussion purposes and cannot be considered
accurate because they depend on the concentration of the BAEE substrate used and on the
injected volume. The reasons could be the following.
Table 2. Kinetic constants of the trypsin-catalyzed BAEE hydrolysis estimated with
continuous isothermal titration calorimetry assay (averages from three experiments with st.
dev. are shown).
No crowding
EG
PEG600
PEG6000
27 µM BAEE, 3 µL injected
vmax*, µM/s
Km*, µM
0.25 ± 0.01
5.1 ± 0.1
0.22 ± 0.01
8.7 ± 0.1
0.15 ± 0.01
6.9 ± 0.2
0.15 ± 0.01
5.4 ± 0.1
136 µM BAEE, 15 µL injected
vmax*, µM/s
Km*, µM
0.41 ± 0.01
8.8 ± 0.1
0.40 ± 0.01
18.9 ± 0.2
0.38 ± 0.01
16.8 ± 0.2
0.35 ± 0.01
20.1 ± 0.1
* The data are approximate and only the ranges are meaningful.
13

In the experiments presented in Figure 2A, only 3 µL of the substrate solution was
ACCEPTED MANUSCRIPT
injected into the cell with trypsin, which gave 27 µM of BAEE for one injection; this amount
was not enough to reach the saturating substrate concentration for the trypsin-catalyzed
reaction. Thus, the concentration of the substrate had to be increased up to 136 µM in each
injection (Figure 2B, left). Technically, we enlarged the injected volume of BAEE up to 15
µL. As before, the observed calorimetric data was then converted to the Michaelis-Menten
curves (Figure 2B, right) and fitted by GraphPad (Eqs. 1 and 3, Figure S3, Table 2).
The results for both 27 and 136 µM BAEE concentrations showed that crowding
influenced the reaction and kinetic parameters; in crowded solutions vmax decreased and Km
increased (Table 2). However, note that the vmax and Km values estimated based on the two
experiments (differing by concentrations and injected volumes of BAEE) were different. In
spite of the advantages of the low injected volume for the ∆Happ determination and
verification of the inhibition by products (Figure 1), this low-volume approach cannot be
applied to determine the kinetics due to the substrate concentration below the saturation level.
On the other hand, for the larger injected volume, with the substrate concentration enough to
reach the saturation plateau, other drawbacks appear (Figure 2B). The substrate dilution heat
becomes significant (Table 1) and the substrate hydrolysis during the prolonged injection
cannot be controlled what complicates the accurate calculation of the substrate concentration
over time.
We [2] and others [3] have previously shown that some reactions cannot be
transformed to kinetic curves from the continuous assay. In general, this could be for a
number of reasons. For instance, in the cases where a reaction is inhibited by its products: the
substrate conversion results in the accumulation of products, which could significantly
influence the kinetic parameters. For substrates with large Km, high concentrations of the
injected substrate solution are required, which could affect the dilution heat or impose
technical problems such as substrate insolubility and precipitation. For enzymes with low
turnover, the duration of the reaction could slow down the whole assay leading to errors. In
14

these particular instances determination of reliable kinetics requires the multiple injection
ACCEPTED MANUSCRIPT
assay instead of the continuous assay described above.
1.3. The multiple injection assay for the BAEE hydrolysis
The measurement and determination of kinetic constants for the BAEE hydrolysis needs to be
performed in a fast experiment with high enough concentration of the substrate to avoid all
the above pitfalls. The multiple injection assay meets such conditions [2,3]. In this assay,
multiple portions of the substrate solution are injected into the cell containing the enzyme but
the spacing time between each injection is kept short, not to allow for full substrate
conversion. This way, the substrate concentration is much higher than the product
concentrations. Thus, in this assay the concentration of the substrate in the reaction mixture is
increased stepwise, until the saturation of the enzyme and maximum velocity are reached
(Figures 3 and S4).
Figure 3. Multiple injections of 1.5 mM BAEE solution into the cell with 10 nM trypsin.
Left: Raw calorimetric data of the BAEE hydrolysis by trypsin. Right: Data analyzed by
nanoAnalyze (dots) and fitted by GraphPad (line).
To transform the data of the multiple injection assay into the reaction rates (Rt) and
estimate the kinetic constants (Km, and kcat), the apparent molar enthalpy of the reaction
(∆Happ) has to be known (Figure 3, Eq. 1). As it was discussed above, ∆Happ is estimated in
the continuous assay with the full substrate conversion (Figure 1, Eq. 2). For the BAEE
15

hydrolysis ∆Happ, was equal to -10 kcal/mol. Thus, the kinetic parameters Km and vmax were
ACCEPTED MANUSCRIPT
equal to 26 µM and 0.35 µM/s, respectively (Table 3). The Km determined by this approach is
higher than in the full substrate conversion experiment. However, the better accuracy of the
ITC multiple injection assay was confirmed by other non-calorimetrical assays [2,3]. For
instance, our result is in agreement with the Michaelis constant (18 µM) determined for the
BAEE hydrolysis by pH-stat method by Inagami and Sturtevant [36].
The multiple injection assay was further performed in the crowded solutions. First, we
studied the BAEE hydrolysis in ethylene glycol (Figures 4, S5 and Table 3). We did not
observe any significant influence of EG crowders on the hydrolysis, and EG as a crowder did
not affect the heat of dilution. Thus, neutral small molecular weight crowders can be freely
used for the ITC studies of enzymatic reactions.
Figure 4. The analyzed calorimetric data for the multiple injections of 1.5 mM BAEE into
the cell with 10 nM trypsin in solutions crowded by EG (A), PEG600 (B), and PEG6000 (C).
16

Table 3. Kinetic constants of the trypsin-catalyzed BAEE hydrolysis determined with the
ACCEPTED MANUSCRIPT
multiple injection ITC assay. vmax and Km for the reaction in non-crowded solution were 0.35
± 0.01 µM/s and 26 ± 3 µM, respectively. Averages from three experiments with st. dev. are
shown.
100 g/L
200 g/L
300 g/L
Crowder
EG
v
max, µM/s
0.34 ± 0.01
24 ± 2
0.35 ± 0.01
23 ± 2
0.34 ± 0.01
34 ± 6
Km, µM
vmax, µM/s
Km, µM
0.34 ± 0.01
21 ± 2
0.37 ± 0.01
31 ± 2
0.36 ± 0.01
43 ± 6
PEG600
vmax, µM/s
Km, µM
0.27 ± 0.01
22 ± 2
0.24 ± 0.01
66 ± 5
0.10 ± 0.01*
45 ± 4*
PEG6000
*denotes that the values are approximate and obtained for, the concentration of 250 g/L of PEG6000
because for 300 g/L we could not fit the kinetic parameters (see Figure 4c).
Next, we carried out the same experiment with PEG600 (Figures 4 and S5, Table 3).
Similar as for EG, PEG600 at 100 g/L concentration did not influence the hydrolysis
whereas at 200 g/L and 300 g/L of PEG600 the Michaelis constant increased noticeably
(Table 3). The effect of crowding on the ITC results and determined kinetic parameters was
even more obvious in thicker PEG6000 solutions where vmax decreased significantly at all
concentrations and Km first increased up to 66 µM at 200 g/L and then decreased to 45 µM at
250 g/L (Table 3, Figures 4, S5-S6). These Km fluctuations could be explained by the
substrate dilution heat, which at 250 and 300 g/L of PEG6000 noticeably increased, and,
most importantly, became at the same level as the reaction heat (Figure S6). Thus, all the
calculations were performed after subtracting the dilution heat and have to be treated with
caution. The observed decline in vmax indicates lower conversion of BAEE. This could be
because large crowders at high concentrations might affect the conformational dynamics of
trypsin, rehydration of the active site and dissociation of the product from the enzyme–
product complex. A similar effect for PEG8000 and PEG1500 was previously observed by
17

Asaad et al. [19]; crowding decreased the enzyme turnover over the PEG concentration up to
ACCEPTED MANUSCRIPT
395 g/L for the spectrophotometrically studied trypsin-catalyzed hydrolysis of p-nitrophenyl.
In summary, the ITC kinetic assay confirmed the influence of the thick PEG6000
crowder on the kinetic parameters and lack of such influence upon using low viscosity
PEG600 and EG solutions. From the technical point of view, ITC seems to be a good method
to measure kinetics in crowded solutions although the background heat, such as the substrate
dilution heat, has to be controlled and taken into consideration. For instance, the ITC method
in thick solutions (such as PEG6000 at 250 g/L and higher) is not suitable to accurately
determine kinetic parameters.
2. BANA trypsin-catalyzed hydrolysis
Nα-benzoyl-DL-arginine β-naphthylamide (BANA) is a synthetic trypsin substrate with amide
hydrolyzed bond (Scheme 1) [37]. The products of BANA hydrolysis are the chromophore -
Nα-benzoyl-
L-arginine (BA) and fluorophore - β-naphthylamine (β-NA). β-NA emits at 410
nm and was used to control the reaction fluorometrically to compare with the ITC results.
2.1. ∆Happ of the BANA hydrolysis and verification of the reaction inhibition by the
products
As with the BAEE hydrolysis for the kinetics study, the apparent enthalpy of the reaction had
to be determined by the full conversion of the substrate to the products (Eq. 1). In the case of
BANA, approximately 1000 seconds were required for the total decomposition of 121 µM
BANA by 25 µM trypsin. The total heat of the BANA injection was equal to -51 µcal (Figure
5, red line). The heat of the substrate dilution was about -10 µcal (Figure 5, blue line) and the
heat of trypsin dilution was -4.5 µcal (Figure 5, green line). Thus, the apparent molar
enthalpy ∆Happ of the BANA-trypsin hydrolysis was equal to -2 kcal/mol (Table 1).
18

ACCEPTED MANUSCRIPT
Figure 5. The continuous assay of the trypsin-catalysed hydrolysis of BANA. Red line: The
thermogram of the full BANA conversion in each repeated injection of 5 µL of 4 mM BANA
into the cell containing 25 µM of trypsin. Blue line: The control thermogram of the BANA
dilution: injections of 5 µL of 4 mM BANA into the cell containing the buffer. Green line:
The control thermogram of the trypsin dilution: injections of 5 µL of buffer into the cell
containing 25 µM trypsin.
The enthalpy of the BANA reaction was five times lower than the enthalpy of the
BAEE-trypsin hydrolysis. Therefore, the ITC signal was low, which complicated the kinetic
studies. For instance, the heat of the dilution contributed significantly (Figure 5, blue and
green lines), and the data had to be corrected by taking this background heat into account,
especially, for the crowded solutions. Moreover, BANA is less soluble, as compared to
BAEE, and required adding 10% DMSO. Further, BANA has lower affinity to trypsin
(indicated by a higher Km). That is why the concentration of the injected BANA solution had
to be increased up to 4 mM (as compared to 1.5 mM in the case of BAEE). Also, the trypsin
concentration had to be kept at 25 µM in the full substrate conversion experiment and 7.5 µM
in the multiple injection assay (as compared to 10 nM for the BAEE hydrolysis).
Consequently, due to the lower substrate affinity and enzyme activity, the duration of the full
conversion experiment had to be increased up to 1000 seconds, which in turn induced BANA
precipitation in the injecting syringe during last titrations because of poor substrate solubility.
19

That is why, after each subsequent injection, we observed heat decrease (both for the reaction
ACCEPTED MANUSCRIPT
and BANA dilution). This decrease was due to lower amounts of the injected sample and not
due to product inhibition (Figure 5). We further confirmed that the released products of the
BANA cleavage do not inhibit trypsin activity. Namely, we performed control titrations of β-
NA to the trypsin solution or buffer (Figure S7, left). Since β-NA is a fluorophore, we
supported the ITC results by the fluorescence data (Figure S7, right). The heat of the β-NA
titration to the cell with the trypsin solution was about -2 µcal and equal to the heat of the β-
NA titration to the cell with buffer (Figure S7, left). Likewise, the fluorescence signal for the
β-NA titration to trypsin was equal to the signal of the β-NA titration to the buffer meaning
that trypsin does not influence the product emission (Figure S7, right). Moreover, we
incubated trypsin with β-NA and then carried out the multiple injection assay, injecting the
BANA solution. The result showed that the rate of the BANA hydrolysis by trypsin (Figure
S8, red line) did not differ from the rate of the BANA hydrolysis by trypsin pre-incubated
with β-NA (Figure S8, green line). This was one more confirmation that the released product
does not influence the reaction.
Thus, we firmly confirmed the lack of reaction inhibition by the products and
assumed that the decline of heat after each subsequent injection in the full BANA conversion
experiment results from substrate precipitation (Figure 5). In this case, we took only the heat
of the second injection for estimation of the apparent molar enthalpy ∆Happ. Note, that the
heat of the first injection could not be taken into account in the ∆Happ determination because
of the effect of the diffusion of the solutions during the insertion of the syringe and
equilibration stage. Thus, we determined the apparent enthalpy of the BANA hydrolysis as -2
kcal/mol (Figure 5 and Table 1) and used this value for all the following analysis.
2.2. The Michaelis-Menten kinetics from the continuous BANA hydrolysis assay
The same as in the experiment with BAEE (Section 1.2), using Eqs. 1 and 3 we converted the
raw data from the full BANA hydrolysis to the Michaelis-Menten curves (Figure 2C).
However, due to low BANA affinity toward trypsin and thus lower trypsin activity, this
20

approach was not accurate. No reliable results were obtained from any attempt to adjust the
ACCEPTED MANUSCRIPT
experiment: (i) increasing the substrate concentration caused BANA precipitation in the
syringe; (ii) increasing the injection volume gave enormous dilution heat; (iii) decreasing the
trypsin concentration first prolonged the duration of the reaction (1000, 1500 or 3000 seconds
for 25, 12.5 or 2.5 µM trypsin, respectively), and second, gave a signal below the detectable
level. So, in the BANA case, only the multiple injection assay was applicable for kinetic
studies.
2.3. The multiple injection assay for the BANA hydrolysis
The multiple injection assay is the only possible approach to study the kinetics of complex
reactions by ITC [2]. As mentioned above, to obtain accurate kinetic data, especially for the
reaction with low enthalpy, the background heat has to be considered, e.g., the substrate
dilution at the conditions of the assay. Moreover, the change of the composition of the
running buffer may also affect the background heat (Figure S9). For example, during BANA
dilution, the baseline position returned close to zero in the non-crowded buffer or the buffer
crowded by 300 g/L PEG600, whereas the baseline drifted from the initial position in thicker
solutions of 300 g/L PEG6000 and BSA. The latter will significantly contribute to the
analysis of low-enthalpy reactions, and the raw data need to be corrected. Thus, in all
following experiments the dilution heat was taken into account and subtracted from the total
heat of the BANA-trypsin assays. The results of the multiple injection assay are shown in
Figure 6A-C, Figure S10 (red lines), and Table 4. Thus, Km and vmax for the trypsin-catalyzed
BANA hydrolysis were calorimetrically determined as 326 µM and 0.80 µM/s, respectively.
Since one of the reaction products, β-NA, is fluorescent (Scheme 1), we could also confirm
the ITC results by a fluorescent assay (Figure 6D-F, red lines, and Table 4). The Michaelis
constant obtained from the fluorescence assay (347 µM) was in the same range as Km
measured by ITC.
21

ACCEPTED MANUSCRIPT
Figure 6. Multiple injections of 4 mM BANA into the cell with 7.5 µM trypsin in the non-
crowded solution or in the solution crowded by 100 g/L, 200 g/L or 300 g/L of PEG600 (A,
D), PEG6000 (B, E) or BSA (C, F). A, B, C: The calorimetric data analyzed by nanoAnalyze
(symbols) and fitted by GraphPad (solid lines). D, E, F: The height of the emmision peak at
410 nm as a function of the BANA concentration from the fluorescence assay recalculated for
the product formation (symbols) and fitted by GraphPad (solid lines).
22

Table 4. Kinetic constants of the trypsin-catalyzed BANA hydrolysis determined with the
ACCEPTED MANUSCRIPT
multiple injection ITC assays. vmax and Km for the reaction in non-crowded solution were
equal to 0.80 ± 0.03 µM/s and 326 ± 29 µM (from the ITC assay) and 0.17 ± 0.02 µM/s and
347 ± 85 µM (fluorescence assay, FL), respectively. N/A stands for not applicable and means
that fitting of the Michaelis-Menten curve to data was not possible due to the effect of the
background reactions such as dilution heat in the case of PEG6000 and crowder hydrolysis in
the case of BSA. Furthermore, the Km and vmax values with errors over 20% can be only
treated as estimates.
100 g/L
200 g/L
300 g/L
Crowder
0.83 ± 0.07
520 ± 85
0.76 ± 0.03
510 ± 44
0.08 ± 0.01
1300 ± 200
N/A
1.15 ± 0.10
1000 ± 150
0.09 ± 0.03
2300 ± 1000
N/A
vmax, µM/s
Km, µM
ITC
FL
PEG600
0.12 ± 0.01
690 ± 120
vmax, µM/s
Km, µM
1.93 ± 0.35
2100 ± 500
0.08 ± 0.01
530 ± 110
vmax, µM/s
Km, µM
ITC
FL
N/A
N/A
PEG6000
0.07 ± 0.01
520 ± 140
N/A
vmax, µM/s
Km, µM
N/A
N/A
8.26 ± 1.95
8200 ± 2100
0.15 ± 0.03
1500 ± 470
vmax, µM/s
Km, µM
N/A
ITC
FL
BSA
N/A
N/A
vmax, µM/s
Km, µM
N/A
N/A
N/A
N/A
Next, we carried out the trypsin-catalyzed BANA hydrolysis in the solutions crowded
by PEG600 (Figure 6A, 6D, Figure S10), and PEG6000 (Figure 6B, 6E, Figure S10). The
ITC results show that PEG6000 affects the kinetic parameters to a larger extent than PEG600.
Surprisingly, the results of the fluorescence assay showed the slowdown of the reaction for
23

both crowders: PEG600 and PEG6000 (Figure 6D, 6E and Table 4). Moreover, vmax
ACCEPTED MANUSCRIPT
determined by fluorescence was smaller than determined by ITC, both in non-crowded and
crowded solution. We suspect that it could be due to the poor product dissociation, especially,
in PEG-crowded solutions. In this case the reaction can still take place so ITC detects the heat
of the reaction directly, however if the formed product stays close to the quencher the
fluorescence emission signal is low. The results of the above experiments showed that in
some studies solely the fluorometric assay may not be enough, and other non-labeled
techniques, such as ITC, are necessary. Our further experiments with BSA as a crowder
further confirmed the above statement.
We carried out the BANA assay in the presence of BSA (Figure 6C, 6F, Figure S10,
and Table 4) and found that both in ITC and fluorescence experiments BSA influenced the
reaction. First, we tried to explain the calorimetric results, which showed deviation of the
plots from the Michaelis-Menten curves (Figure 6C). This could happen because of the
background processes such as dilution effects. However, we confirmed that the deviation was
not caused by the BANA dilution heat (Figure S10) or heat of the BA and β-NA interactions
with trypsin (Figure 1 and Figures S7-S8). Therefore, we suggest that it might be due to the
interactions of the crowders with the enzyme or substrate. It is known that trypsin hydrolyzes
BSA [30], so we expected that trypsin must interact with BSA. Thus, we further estimated the
trypsin interaction with the BSA crowder. We titrated the BSA solution into the cell with
trypsin immersed in a non-crowded buffer (Figure 7, purple line) and detected the new
baseline position associated with the expected proteolytic activity of trypsin toward BSA.
However, the result showed another trend for this reaction and did not explain the linear
increase of the signal for the BANA hydrolysis in BSA (Figure 6C).
24

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Figure 7. Trypsin hydrolysis of BSA and BANA. The BSA hydrolysis by trypsin: 0.3 mM
BSA was titrated to the non-crowded 7.5 µM trypsin solution in the cell (pink line). The
dilution of the BSA-trypsin system in 10% DMSO: non-crowded buffer was titrated to the
trypsin solution crowded by denatured 200 g/L BSA (blue line). The BSA-trypsin reaction in
10 % DMSO: denatured 0.3 mM BSA was titrated to the cell containing 7.5 µM trypsin
solution crowded by 0.3 mM BSA denatured with 10% DMSO (green line). The BANA
hydrolysis by trypsin: 1.5 mM BANA in the syringe was titrated to the non-crowded 7.5 µM
trypsin solution in the cell (red line).
The explanation is that in our above experiments with BANA we had to use 10%
DMSO to dissolve the BANA substrate, so we also kept 10% DMSO in the running crowded
buffer to have the same solutions in the syringe and in the cell. It is known that DMSO
denatures BSA [38] and causes complete unfolding of the protein at 40% (v/v) concentration.
That is why in the BANA experiments with BSA (Figure 6C), BSA was denatured by 10 %
DMSO, so we also had to check the trypsin activity for the denatured form of BSA. The
green line in Figure 7 is related to the background interaction of trypsin with the denatured
BSA, which we have to consider for explaining our ITC results.
25

ACCEPTED MANUSCRIPT
Figure 8. Multiple injections of 4 mM BANA into the cell with 7.5 µM trypsin in the
solution without crowders, or in the solution crowded by 100 g/L, 200 g/L or 300 g/L of
BSA. The GraphPad analyzed data taking into consideration the hydrolysis of BSA by
trypsin.
Therefore, based on the aforementioned controls, we could interpret the ITC results
for the trypsin-catalyzed hydrolysis of BANA in the BSA-crowded solution with 10%
DMSO. The data for the reactions in the crowded solution did not follow the Michaelis-
Menten kinetics due to the substrate competition for the cleavage by trypsin with denatured
BSA (see Figure 6C green, blue and black lines) opposite to the reaction in the non-crowded
buffer (see Figure 6C red line). To approximate this effect, we subtracted the calorimetric
data for the BSA hydrolysis from the ITC BANA hydrolysis data and obtained the Michaelis
–Menten curves (Figure 8). However, to accurately determine the kinetic parameters a more
detailed study of the BSA-trypsin reaction, e.g. the ∆Happ measurement, is necessary. Note
that we could not detect such an effect by fluorometry by simply measuring the fluorescent
BANA product (β-NA) (Figure 6F). Moreover, BSA quenches the emission of β-NA, so in
the fluorescence experiments the BSA concentration had to be limited to 200 g/L (Figure 6F
and S11). This shows an advantage of the ITC technique for the kinetics study, especially in
crowded solutions, in which many background reactions may take place. We would like to
emphasize that the above ITC experiments could be performed without any purifications or
26

labeling of the samples. Therefore, many additional crucial experiments could be carried out
ACCEPTED MANUSCRIPT
to interpret enzyme kinetics in the complex crowded solutions.
Conclusion
We have presented the ITC experiments for determination of the kinetic parameters of the
enzyme-catalyzed reactions. As shown above, various questions could be answered with ITC
by designing many control experiments, which do not require labeling of molecules. That is
why ITC can be used to study enzyme kinetics in cytosol mimicking solutions.
Note that in fluoro- and spectrophotometrical assays additional labels are typically
necessary and these labels could influence the reactions. Also, in these assays, typically only
the product of the reaction may be followed but, for instance, the fluorescence of the product
might be quenched or increased by its interactions with the crowders. Note that the product-
crowder interactions have to be taken into account for reliable kinetic data. Moreover, the
enzyme itself could interact with the crowder and thus lower enzymatic activity. So the
possible enzyme-crowder interactions must be checked and such controls require additional
labeling of the components. However, in some cases spectrophotometrical complementary
assays are necessary and useful, e.g., if one would like to perform FRET experiments to
monitor the distances between the attached probes or even use the intrinsic fluorescence of
protein tryptophans, substrates or products. Moreover, fluorescence assays are fast and
sensitive and 96 well plates might be used, so it is a good technique for screening.
Overall, we believe that the ITC approach, supported by spectrophotometric and
fluorometric assays, will significantly improve the outcome of the enzyme kinetics
experiments in environments mimicking the cellular ones.
Acknowledgements
Funding was provided by the National Science Centre, Poland DEC-2016/23/B/NZ1/03198.
27

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