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Cosolutes Modify Alkaline Phosphatase Catalysis through Osmotic
Stress and Crowding Mechanisms
Oksana A. Yavorska, Lukas Syriste, Chantal M. du Plessis, Maryam Yaqoob, Kyle Loogman,
Michael Cordara, and John K. Chik*

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sı Supporting Information
*

ABSTRACT: Examining the eﬀects of diﬀerent cosolutes on in vitro enzyme
kinetics yielded glimpses into their potential behavior when functioning in their
natural, complex, in vivo milieu. Viewing cosolute in vitro inﬂuences on a model
enzyme, calf intestinal alkaline phosphatase, as a combination of competitive
and uncompetitive behaviors provided quantitative insights into their eﬀects on
catalysis. Observed decreases in the apparent speciﬁcity constant, Kasp, caused by
the presence of polyethylene glycols or betaine in the reaction solution,
indicated interference with enzyme−substrate complex formation. This
competitive inhibition appeared to be driven by osmotic stress. Dextran 6 K
and sucrose strongly impeded the subsequent conversion of the bound substrate
into a free product, which was marked by sharp reductions in Vmax, uncompetitive inhibition. For the same step, smaller
noncarbohydrate cosolutes, triethylene glycol, polyethylene glycol 400, and betaine, also behaved as uncompetitive inhibitors but to
a lesser extent. However, polyethylene glycol 8000 and 20,000 were uncompetitive activators, increasing Vmax. Polyethylene glycol of
molecular weight 1000 displayed intermediate eﬀects between these two groups of noncarbohydrate cosolutes. These results
suggested that crowding has a strong inﬂuence on free product formation. The combination of competitive and uncompetitive eﬀects
and mixed behaviors, caused by the cosolutes on calf intestinal alkaline phosphatase kinetics, was consistent with the trends seen in
similar enzyme−cosolute studies. It is proposed that the double-displacement mechanism of alkaline phosphatases, shared by many
other enzymes, could be the root of this general observation.

■

INTRODUCTION
In contrast to the highly dilute solutions traditionally used in in
vitro studies, enzymes evolved to function within densely ﬁlled,
in vivo environments.1,2 Inside Escherichia coli, cosolutes, such
as proteins and nucleic acids, constitute approximately 30−
40% by weight of the intracellular milieu.3 Additionally, smallmolecule metabolites are estimated to be present at a total
concentration of 0.3 M.4 Far from being inert, the presence of
these nonbinding cosolutes is felt in many biochemical
processes including enzyme kinetics.5−8 A better understanding of how these complex environments can modify
enzyme activity will enable better prediction of actual in vivo
behavior from in vitro data.
When treated as hard spheres or rectangular parallelepipeds
in a continuum solvent, cosolutes modify enzyme activity
through crowding and the reduction of volume available for
proteins to function.8,9 Crowding particularly aﬀects steps
involving signiﬁcant volume changes through alterations in
shape or assembly. For enzymes, this is especially the case
when ligands are similarly sized, resulting in substantial volume
or shape changes upon enzyme−substrate complex formation
and product release. The binding of much smaller ligands is
not expected to induce suﬃcient shape or volume change on
the enzyme to be markedly aﬀected by crowding.9 Crowding is
© 2021 The Authors. Published by
American Chemical Society

also predicted to be important when the enzyme exists as an
equilibrium of diﬀerent oligomeric states each with unique
kinetic properties, as observed for glyceraldehyde-3-phosphate
dehydrogenase (GAPDH), which exists in an equilibrium
between tetrameric, dimeric, and monomeric forms.10 Kinetic
rate constants associated with transition state incurring
signiﬁcant shape or volume change should also be susceptible
to crowding.8,9 Crowding eﬀects strongly depend on both the
fraction of volume occupied by the cosolute/crowder and their
relative shape and size. This property is valuable when trying to
distinguish whether crowding is at work when using polymeric
cosolutes.5 While crowding drives systems to adopt more
compact states, often with higher symmetries, in the related
concept of conﬁnement, systems favor conformations that
better match the “architecture” of the crowded milieu. The
complex environment results in systems taking on a smaller
Received: June 21, 2021
Accepted: September 16, 2021
Published: September 30, 2021

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cosolute eﬀects on enzyme kinetics.26,27 Like most previous
enzyme−cosolute studies, the Michaelis−Menten kinetic
scheme, described in Figure 1, was used for modeling catalysis.

conformational subset than those in dilute solutions that may
not be the most compact.8,11
Although hard-sphere modeling provided several important
insights, it omits many chemical details of the cosolutes
themselves. In osmotic stress12 and preferential hydration,13
the nonbinding chemical nature is expressed as the degree of
cosolute exclusion from the immediate enzyme vicinity. This
exclusion leads to enhanced or preferential hydration near their
surfaces. Hard-sphere models also lead to preferential surface
hydration through steric interference, leading to depletion
forces.14,15 The centrality of cosolute surface exclusion in these
diﬀerent mechanisms is a manifestation of the Gibbs−Duhem
equation.16 Solution osmotic pressure is the central parameter
in osmotic stress measurements and replaces the volume
occupied and relative cosolute size in hard-sphere models. The
competition for water, as more osmotic pressure is applied,
results in the system favoring the more dehydrated state. The
osmotic stress approach has yielded insights across a diverse
set of molecular biological systems such as channels,17 proteinDNA interactions,18 the allosteric transition of hemoglobin,19
and hexokinase kinetics.20,21
Cosolute-induced enzyme conformation changes would be
an obvious means for altering protein function. Crowding by
Ficoll 70 resulted in structural changes, monitored by FRET, of
ﬂuorescently modiﬁed phosphoglycerate kinase connected
with enhanced enzyme activity.22 Molecular simulations
associated these observations with the relative movement of
the enzyme domains. In other studies, the presence of
crowding agents decreased the distances between ﬂuorescent
donor proteins connected by a ﬂexible linker to ﬂuorescent
acceptor proteins, as measured by FRET.23,24 This was
attributed to crowding instead of conﬁnement since the
overlap concentration of Ficoll-70 was cited to be > 500 g/L.
For hemoglobin, the presence of cosolutes osmotically favors
the transition from its fully oxygenated, relaxed R-state to its
more dehydrated, fully deoxygenated, tense T-state.19 This
transition was accompanied by a loss of ∼60 water molecules.
Assuming that the cosolutes did not signiﬁcantly alter the
three-dimensional structures of these states, the calculated
reduction in the accessible surface area was approximately 700
Å2. This was also accompanied by a decrease of the apparent
speciﬁc volume of 0.002 cm3/g, a slight change given that the
volume of methemoglobin is taken to be 0.748 cm3/g.25 This
last example highlights the diﬀerence between crowding and
osmotic stress, which stems from how to attribute the cause of
the observed eﬀects. From the osmotic stress point of view, the
cosolute competing for available water results in systems
favoring states of greater dehydration, leading to reduced
accessible surface area and therefore a smaller volume. From
the crowding perspective, adopting a smaller volume naturally
leads to decreased accessible surface area and thus
dehydration. Although the cause may be diﬀerent, both
osmotic stress and crowding essentially lead to an equivalent
end point.16 This is not necessarily the case for conﬁnement
where the complex solution environment could favor
conformations with larger surface areas. Viewing cosolute
eﬀects through these diﬀerent lenses provides contrasting
insights into the mechanism of their action.
Employing a form of the Michaelis−Menten equation that
uses Vmax and Kasp, the apparent speciﬁcity constant, rather
than the conventional Vmax and Km, facilitated leveraging
concepts borrowed from reversible, small-molecule competitive and noncompetitive inhibitors to systematically quantitate

Figure 1. “Classic” ﬁrst-order (or pseudo-ﬁrst-order) Michaelis−
Menten scheme. In step ①, the rate constants k1 and k−1 represent the
reversible binding and unbinding of the substrate, S, to the enzyme, E,
forming the enzyme−substrate complex, ES. Step ② represents the
conversion of the ES into free product, P, and the return of E. In the
initial-rate assumption, where the product is absent, step ② is
essentially “irreversible”, and it is represented only by a forward rate
constant, kcat.

Combining the scheme in Figure 1 with the usual initial-rate
and steady-state assumptions gives the familiar Michaelis−
Menten equation in eq 1 describing the dependence of the
initial velocity, v0, on substrate concentration, [S].26
ν0([s]) =

νmax[S ]
KM + [S ]

(1)

KM, the Michaelis constant, and Vmax are given in eq 2.
KM =

k −1 + kcat
k1

and Vmax = E Tkcat

(2)

ET is the total concentration of the enzyme accounted for by
the sum of [E] and [ES].
While Vmax represents the asymptotic initial velocity at
saturating substrate concentration, the change in v0 at
vanishingly small substrate concentration is given Kasp, deﬁned
in eq 1 (see Figure 1 from Johnson27)
K asp =

Vmax
KM

(3)

Equation 1 can be easily transformed to use Vmax and Kasp, as
shown in eq 4.
ν0([S ]) =

K asp[S ]
1 + (K asp/Vmax )[S ]

(4)

27

However, unlike Johnson, eq 4 retained Vmax rather than
normalizing it by Et to give kcat (eq 2) and converting Kasp into
kcat/KM, the speciﬁcity constant.26 Although the traditional
Michaelis constant, KM, is unambiguously the substrate
concentration where v0 = Vmax/2, interpreting the signiﬁcance
behind changes in KM is more complicated.26 Furthermore, KM
is the least precise parameter compared with either Vmax or
Kasp.26 Calculating the error in Kasp by propagating the standard
deviation of Vmax and KM results in an exaggeration of the error
versus ﬁtting Kasp directly.27
An advantage of using eq 4 is that Vmax and Kasp are ideally
suited for interpreting cosolute eﬀects as a mixture of
competitive and uncompetitive behaviors. Pure competitive
inhibitors exclusively interfere with step ① (Figure 1),
preventing ES formation by competing with substrate binding.
This lowers Kasp and leaves Vmax unchanged since saturating
the substrate will outcompete any ﬁnite amount of the
inhibitor.26 Pure uncompetitive inhibitors, on the other hand,
bind speciﬁcally to already formed ES complexes, solely
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preventing step ②, product formation, and release. This
reduces Vmax, while Kasp remains constant.26 For mixed
inhibitors, both Vmax and Kasp decrease. In contrast, the eﬀect
of inhibitors on the Vmax and KM combinations of parameters is
slightly more complex. Although for pure competitive
inhibition, Vmax remains constant and KM increases, pure
uncompetitive inhibition lowers both Vmax and KM proportionally.
Competitive, uncompetitive, and mixed behaviors are
conveniently measured by calculating the ratio of Kasp and
Vmax in the absence and presence of inhibitors or cosolutes, α
and α′ respectively, as shown in eq 5.
α=

K asp
V /K
= max M
*
* /KM
*
K asp
V asp

and α =

Article

studies on AP, the assay reaction used was the hydrolysis of
para-nitrophenyl phosphate, PNPP, into free phosphate, Pi,
and para-nitrophenol, PNP, shown in Figure 2.

Figure 2. Hydrolysis of PNPP to PNP and free phosphate, Pi.

Vasp
*
V asp

PNP absorbance around 400 nm was used to follow the
reaction progress.

(5)

■

In eq 5, the asterisk (*) indicates the presence of inhibitors
or cosolutes. For competitive inhibition, α > 1 and α′ = 1,
while for uncompetitive inhibition α = 1 and α′ > 1. For mixed
inhibitors, both α and α′ would be greater than one.
The ratios, α, and α′, also accommodate situations where
cosolutes behave as activators,26 increasing Kasp* or Vasp*
relative to the dilute control. Activation results in α or α′ being
less than one. In this paper, competitive, uncompetitive, and
mixed behavior refers to eﬀects on steps ① or ②, independent
of the form of their action, inhibition, or activation. In this
regard, cosolute-induced mixed behaviors on enzyme kinetics
could be divided into four subtypes depending on the α and α′
ratios. These diﬀerent subtypes are summarized in Table 1.

RESULTS
Eﬀects of 30% PEG 400 Versus 30% PEG 8 K on CIAP
CatalysisA Speciﬁc Example. Figure 3 demonstrated the
success of modeling the eﬀects of 30% (w/w) polyethylene
glycol, PEG, molecular weight 400, and PEG, molecular weight
8 K, on CIAP kinetics using eq 4. It justiﬁed leveraging the
concepts of competitive and uncompetitive behaviors to
quantitatively contrast the inﬂuences of these cosolutes.
Table 2 shows the Vmax, Kasp, and Km values derived from
Figure 3 data and the consequent α and α′ values. At 30%
concentration, both PEG 8 K and PEG 400 were competitive
inhibitors, interfering with step ① and hence ES formation.
This was evidenced by their reduced Kasp relative to dilute
control. This resulted in α > 1, with values of 1.63 and 1.9 for
PEG 8 K and PEG 400, respectively (Table 2). However, their
eﬀect on step ② was opposite with PEG 8 K acting as an
uncompetitive activator, causing an increase in Vmax and
leading to α′ = 0.79 < 1. PEG 400; on the other hand, was an
uncompetitive inhibitor, decreasing Vmax and resulting in α′ =
1.44 > 1 (Table 2). The eﬀects of 30% PEG 8 K and PEG 400
on CIAP kinetics are examples of CIUA and CIUI mixed
behavior (Table 1). Although 30% PEG 8 K increased KM to a
greater extent than PEG 400, 0.59 mM versus 0.38 mM,
respectively, when changes in Vmax are accounted for, PEG 400
emerged as a more potent competitive inhibitor, as quantitated
by α, 1.9 versus 1.63 (Table 2). This underlined the advantages
of interpreting changes in Kasp versus KM and the general
importance of collecting complete kinetic data versus singlesubstrate concentration activity measurements.
Overview of α and α′ of Diﬀerent Cosolutes. Like the
above speciﬁc case of PEG 400 and PEG 8 K (Figure 3), the
eﬀects of all examined cosolutes on CIAP kinetics were well
modeled by eq 4, supporting the use of α and α′ to quantitate
their eﬀects. Figure 4 summarizes the α and α′ versus wt % for
the examined cosolutes.
From Figure 4A, TEG and all the PEGs exerted similar
competitive inhibitory eﬀects, α > 1, on CIAP kinetics,
independent of the wide range of molecular weights used, from
150 Da for TEG to PEG 20 kDa. However, their
uncompetitive behavior displayed a striking mass dependency
(Figure 4C). Smaller PEGs, TEG, and PEG 400, behaved as
uncompetitive inhibitors, reducing Vmax, α′ > 1, with similar
concentration dependence. In contrast, the larger PEGs, PEG 8
K and 20 K, increased V max, α′ < 1, making them
uncompetitive activators. From Table 1, the smaller PEGs
exhibited CIUI mixed behavior, while larger PEGs were CIUA.

Table 1. Summary of the Diﬀerent Cosolute-Induced Mixed
Behaviors
behavior

subtypes

abbr.

α

α′

CIUI

>1

>1

CAUI

<1

>1

mixed

competitive inhibitor,
uncompetitive inhibitor
competitive activator,
uncompetitive inhibitor
competitive inhibitor,
uncompetitive activator
competitive activator,
uncompetitive activator

CIUA

>1

<1

CAUA

<1

<1

Using α and α′ enables examination of cosolute eﬀects on
the diﬀerent steps in the Michaelis−Menten scheme (Figure
1). Finally, it is essential to emphasize that although the
concepts from reversible inhibition are being used to
quantitate cosolute eﬀects, it is not implied nor required that
the cosolutes directly bind to the enzyme or the enzyme−
substrate complex.
Alkaline phosphatases (APs) are ubiquitous dimeric metallophosphomonoesterases that retain a high degree of sequence
similarity despite their occurrence in diverse species from E.
coli to humans.28 One signiﬁcant diﬀerence between the highly
studied AP from E. coli versus mammalian AP is the latter’s
well-documented uncompetitive inhibition by amino acids
such as L-leucine and L-phenylalanine, L-phe.29 This property
is attributed to an approximately 30-amino-acid insert which
forms the “crown” domain observed in the mammalian AP
structures.30,31 Intestinal alkaline phosphatase (IAP) is one of
four related, tissue-speciﬁc mammalian isozymes, with the
others being placental, germline, and tissue-nonspeciﬁc.32 The
calf-intestinal form (CIAP), whose expression vanishes in
mature animals,33 is noted for its high activity.28 Like most
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Figure 3. Eﬀects of 30% PEG 8 K versus 30% PEG 400 on the initial velocity of PNPP hydrolysis catalyzed by CIAP. (A) Observed initial velocity
of AP-catalyzed PNPP hydrolysis versus substrate concentration under dilute/control conditions in 30% PEG 8 K and in 30% PEG 400 ﬁtted to the
Michaelis−Menten eq 4. [Insert shows the absorbance at 400 nm, Abs400, versus time data used to determine the initial velocity at [PNPP] = 4.4
mM, highlighted in the dashed box.]; (B) same data in the main ﬁgure of panel A shown using a log scale for [PNPP]. The PNPP concentration
range was 0.06−8.9 mM.

Table 2. Vmax, Kasp, KM, α, and α′ Derived from Figure 1 Data
solution (w/w)

Vmax (μM/s)a

Kasp (×10−3/s)a

KM (mM)b

SSRc

αd

α′d

control
30% PEG 8 K
30% PEG 400

0.291 ± 0.002
0.367 ± 0.004
0.202 ± 0.002

1.01 ± 0.03
0.62 ± 0.02
0.54 ± 0.02

0.28 ± 0.01
0.59 ± 0.02
0.38 ± 0.02

0.00042
0.000069
0.00036

1.63 ± 0.07
1.9 ± 0.1

0.79 ± 0.01
1.44 ± 0.02

Values of parameters ±standard deviation ﬁtting data to eq 4. bValue of Km ± standard deviation ﬁtted to eq 1. Fitting to either eq 1 or eq 4 did
not signiﬁcantly alter Vmax. cSum of squares residues of the ﬁt to eq 4. Number of observations = 18 for each solution. dValues ± error estimate.
Error calculated by propagating standard deviation of ﬁtted Kasp and Vmax, respectively.
a

competitive inhibition as PEG 8 K and 20 K, as highlighted by
the black dashed box in Figure 5A. The data points for the
smaller cosolutes such as TEG and betaine appear in the righthand part of the box, and the larger cosolutes occupy the left
region. As previously mentioned, the strong uncompetitive
inhibition by dextran 6 K and sucrose led to inconclusive
scattering around α = 1 across the full range of log(Π)
examined.
In contrast, Figure 5B, showing α′ versus log(Π), highlighted the molecular mass-based segregation of noncarbohydrate cosolutes into uncompetitive activators and inhibitors, as
well as the starkly stronger uncompetitive inhibition by
carbohydrate cosolutes. PEG 20 K and PEG 8 K exhibited
similar uncompetitive activator behavior across their combined
osmotic pressure range. Increased Vmax in the presence of
larger PEGs (8 K and 20 K) was also observed by Sekiguchi et
al.34 for bovine intestinal AP. However, this was accompanied
by increased speciﬁcity constant (α < 1), competitive
activation, which could be a result of the diﬀerence in solution
pH (9.8 vs. 8.8 in this study).34 Over a similar log(Π) range,
the small PEG’s and betaine acted as uncompetitive inhibitors.
At log(Π) below 6.2, PEG 1 K initially appeared to behave as
an uncompetitive activator, like PEG 20 K and PEG 8 K,
before joining the other small noncarbohydrate cosolutes as an
uncompetitive inhibitor. The larger dextran 6 K was a more
potent uncompetitive inhibitor compared to sucrose. Although,
it should be noted that the osmotic pressure data of dextran
T10,35 used in place of dextran 6 K, should be slightly lower
than the actual osmotic pressure. A similar size-dependent
eﬀect of carbohydrate cosolutes has been previously reported
by Homchaudhuri et al.36 At concentrations between 0.25 and

PEG 1 K began to show uncompetitive inhibition (α′ > 1) at
high concentration, CIUI. Otherwise, PEG 1 K appeared to act
as a pure competitive inhibitor and served as a “boundary”
separating uncompetitive behaviors of the small and large
PEGs.
Compared to the PEGs, sucrose and dextran 6 K,
carbohydrate-based cosolutes, showed greater uncompetitive
inhibition (α′ > 1) at similar concentrations compared to the
glycols (Figure 4C,D), with dextran 6 K displaying the
strongest uncompetitive inhibition. These signiﬁcant decreases
in Vmax made it more challenging to measure Kasp reliably,
contributing to the scatter in α displayed in Figure 4B. Both
sucrose and dextran 6 K appeared to show similar competitive
behavior. Much of the α values tended to be scattered around
one and perhaps trending toward being less than one,
suggesting that sucrose and dextran 6 K could act as
competitive inhibitors at low concentrations before becoming
activators with increasing wt %. Overall, dextran 6 K and
sucrose appear to behave largely as uncompetitive inhibitors.
Lastly, betaine, a neutral zwitterion, acted as a CIUI mixed
inhibitor with more signiﬁcant competitive inhibition than the
PEGs at similar concentrations and similar uncompetitive
inhibition to the small PEGs (Figure 4B,D).
Figure 5 shows the same α and α′ data in Figure 4 from the
osmotic stress perspective. The similarity in the correlation
between α and log(Π) of PEG 20 K and PEG 8 K is
highlighted by the heavy dashed blue line in Figure 5A. PEG 1
K initially followed a similar trend with PEG 20 K and PEG 8
K for log(Π) between 6.0 and 6.8. Beyond this region, PEG 1
K and the other smaller, noncarbohydrate-based cosolutes
required greater osmotic pressure to reach the same degree of
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Figure 4. Eﬀects of diﬀerent concentrations of various cosolutes on CIAP kinetics, as quantitated by α and α′. The heavy, dashed, horizontal line in
all panels represents α or α′ equal to 1 (i.e., no change). Error bars represent the estimated error in α and α′ calculated by propagating the standard
deviations of Vmax and Kasp. (A) α versus weight % (wt %) of triethylene glycol (TEG), PEG 400, 1, 8, and 20 K molecular weight. (B) α versus wt
% of betaine, sucrose, and dextran 6 K molecular weight. (C) α′ versus wt % of TEG, PEG 400, 1, 8, and 20 K molecular weight [insert: an
enlargement of the dotted rectangle region in panel C. Axes are the same as in panel C]. (D) α′ versus wt % of betaine, sucrose, and dextran 6 K
molecular weight. Data ﬁles of the Vmax and Kasp values determined by ﬁtting data to eq 4, and Vmax and KM values by ﬁtting to eq 1 are found in
Supporting Information, All Data-Kasp-csv.txt and AllData-Km-csv.txt, respectively.

cosolute eﬀects through the lens of crowding and osmotic
stress provides contrasting perspectives on their mechanism.
The qualitative similarity between α versus log(Π) of the
noncarbohydrate cosolutes in Figure 5A combined with the
largely molecular weight-independent relationship between α
versus wt % of the same cosolutes (Figure 4A,B), and the
inconclusive competitive inhibition from sucrose and dextran 6
K suggested that step ① (Figure 1) was primarily sensitive to
osmotic stress from the noncarbohydrate cosolutes. The small
volume change expected from PNPP (MW 217 Da) binding to
the signiﬁcantly larger CIAP dimer (MW 140 KDa) predicted
that crowding should have little inﬂuence on this step. AP
monomers also dimerize spontaneously with few free
monomers remaining,38 making crowding-induced changes in
oligomerization, as observed for GAPDH,10 an unlikely
contributing factor. The molecular weight attenuation highlighted by the dashed box in Figure 5A could be attributed to
the decreased exclusion of smaller cosolutes from the
immediate enzyme environment compared to larger cosolutes.
The greater inclusion of smaller cosolutes near the enzyme
requires larger concentrations away from the enzyme to
generate the same net diﬀerence in cosolute concentration.16
This size-dependent exclusion has been observed in
alamethicin ion channel conductance,39 in glucose binding to
hexokinase,20,21 and in the radius of gyration and hydration of

1 M, sucrose has also been reported to be a noncompetitive
inhibitor on human placental alkaline phosphatase.37 Noncompetitive inhibition is a particular case of CIUI, where α =
α′ > 1.
Overview of Kinetic Data Collected in the Absence of
Cosolutes. Quantitating cosolute-induced changes in CIAP
kinetics as the relative change in Kasp, α, and Vmax, α′, provided
an insightful framework for interpreting these alterations.
Equally important, it facilitated combining data from several
researchers, six undergraduate students, and one faculty
member, over a 6 year period. Figure 6 shows Vmax versus
Kasp and Km from the 73 dilute control results by all
contributors.
As seen in Figure 6, the spread in Vmax, Kasp, and KM stems
largely from variation between individual authors rather than
within a single contributor. The larger error bars for KM
compared to both Vmax and Kasp in Figure 6B and C are
consistent with KM being the least well-deﬁned parameter
compared to Kasp and Vmax.26 This is further demonstrated in
Supporting Information Figure S1 showing the histograms of
the relative error of each of these variables.

■

DISCUSSION
Diﬀerent Steps in the Michaelis−Menten Scheme
Were Aﬀected by Diﬀerent Mechanisms. Viewing
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Figure 5. Data from Figure 4 replotted as a function of the logarithm
of cosolute osmotic pressure (in dyne/cm2), log(Π). For clarity, the
error bars have been omitted. (A) α versus log(Π). The heavy blue
dashed line is an exponential ﬁt to PEG 20 K and PEG 8 K data and
serves only as a visual guide (see text). The region around α = 1.75 is
indicated by the box outlined with a black dashed line (see text). (B)
α′ versus log(Π). The insert shows the entire data set. The insert axes
are the same as in the main panel ﬁgure.

Article

Figure 6. Vmax versus Kasp and Km for control data by the authors of
this paper. The horizontal and vertical dashed black lines represent
the mean of KM and Vmax, respectively, and the median of the
histograms is shown by the solid red line. The error bars represent
one standard deviation of the ﬁtted parameters. (A) Histogram of
Vmax determined from ﬁtting data to eq 4. Mean = 0.319 ± 0.138 μM/
s. Median = 0.293 μM/s. (B) Vmax versus Kasp based on ﬁtting to eq 4.
(C) Histogram of Kasp determined from ﬁtting to eq 4. Mean = 1.06 ±
0.54 × 10−3/s. Median = 1.04 × 10−3/s. (D) Vmax versus KM
determined from ﬁtting data to eq 1. There was very little diﬀerence
in Vmax and its standard deviation using eq 1 versus eq 4 (E)
Histogram of KM determined from ﬁtting to eq 1. Mean = 0.332 ±
0.119 mM. Median = 0.281 mM.

lysozyme and guanylate kinase.40 Increasing osmotic stress
favors the more dehydrated enzyme state resulting from the
competition for water by cosolutes. The increase in
competitive inhibition suggests that this drier state disfavors
ES formation, which could result from closure or obstruction
of the binding site, as proposed for hexokinase20,21 and
phosphoglycerate kinase.22
The eﬀects of the examined cosolutes in step ②,
uncompetitive behavior, presented a more complex situation
where crowding was likely an important factor. Both dextran 6
K and sucrose exerted greater uncompetitive inhibition than
the smaller PEGs and betaine when either as a function of wt
% or log(Π) (Figures 4B,D and 5). Most strikingly, although
PEG 400 and sucrose share very similar osmotic pressure
versus wt % proﬁles (Figure S2 in Supporting Information),
largely a result of their similar molecular weights, their eﬀect
on uncompetitive inhibition was very diﬀerent in Figure 5B.
This illustrates PEG’s less-than-ideal crowding behavior
compared to carbohydrates8,41 due to its observed attractive
and repulsive interactions beyond the basic hard-sphere
potential.42,43 The relatively weak competitive inhibition in
the presence of sucrose and dextran 6 K compared to their
uncompetitive behaviors further supports the idea that step ①
was less aﬀected by crowding (Figure 4). Also, the magnitude
of these additional forces would scale with PEG size and
possibly be the source behind their mass-dependent eﬀects on
competitive and uncompetitive behavior.44,45 Figures 4D and
5B also highlight the enhanced uncompetitive inhibition by
dextran 6 K. This could be due to conﬁnement eﬀects since
Rong reported that the overlap concentration of dextran T10
was 22%,46 which is in the range reported by Squire47 and

coincides with the highest dextran 6 K concentration
examined, 20%, as seen in Figure 4D.
Although the strong uncompetitive inhibition by dextran 6 K
and sucrose suggested that step ② was susceptible to crowding,
the mechanism is unclear. Once bound, PNPP and the
catalytic pocket should be shielded from the solvent and hence
unaﬀected by cosolutes, as already noted for α-chymotrypsin.48
Also, the catalytic step and release of small products should be
accompanied by little notable volume change. These two issues
make it diﬃcult to attribute changes in kcat to crowding. An
alternative explanation would be to instead consider cosolute
eﬀects on Et, the total enzyme concentration (eq 2). It has
been suggested that the excluded volume by the cosolute
would eﬀectively increase the enzyme concentration, Et.6
Although this would account for increases in CIAP Vmax from
the larger PEGs, it alone does not completely explain the
reduction in Vmax from the smaller PEGs over the same wt %
range nor the absence of progressive increases in Vmax with
greater wt % of large PEGs seen in Figure 4C,D. This
“plateauing” of Vmax with increased Ficoll concentration was
also observed in EcoRV.49 Pastor et al.50 reported monotonic
and dextran weight-independent decreases in Vmax as a function
of increased concentration for horseradish peroxidase and
chymotrypsin. Only lactate dehydrogenase showed a dextran
molecular weight-dependent decrease in Vmax with the larger
dextrans being the stronger uncompetitive inhibitor.
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Figure 7. α and α′ resulting from the presence of diﬀerent cosolutes on diﬀerent enzymes from Table S1 by Silverstein and Slade5 (reproduced in
Table S1 in Supporting Information) with selected results from this report. (A) α and α′ plotted on a log scale. The cosolute concentration used by
Silverstein and Slade5 was between 300 and 400 g/L. The dextran, PEG, Ficoll, and other results were taken from Silverstein and Slade.5 PEG 400,
PEG 1 K, and PEG 8 K at concentrations 30−40 wt % and sucrose data at 24 wt % from this paper are also shown. The shaded blue and red cross
mark α and α′ between 0.95 and 1.05, which were taken to indicate no substantive change in α or α′. The red arms of the cross are for inhibition; α
and α′ > 1 (horizontal and vertical, respectively). The blue components are for activation; α and α′ < 1 (horizontal and vertical, respectively). The
labels CAUI, CIUI, CAUA, and CIUA mark the diﬀerent mixed-behavior “quadrants” (Table 1). (B) Enlargement of the region marked by the
dashed box in panel (A) using the same markers. Both α and α′ were plotted on a linear scale.

common cosolute eﬀect on enzyme kinetics was CIUI mixed
behavior at 33% of the time (Figure S3 in Supporting
Information). Overall, 77% of the time, the presence of
cosolutes resulted in some sort of mixed behavior with pure
competitive and uncompetitive behaviors accounting for the
rest. The most “extreme” results reported by Silverstein and
Slade5 occurred from the presence of PEG, leading to CAUA
and CIUI mixed behavior (Figure 7). As previously discussed,
this could be simply attributed to large changes in Et through
stabilization or destabilization of weakly folded enzymes.
Figure 7 also includes PEG 400, PEG 1 K, and PEG 8 K from
this paper examined at similar concentrations, 30−40 wt %, to
those compiled by Silverstein and Slade (300−400 g/L).5 In
this representation, the vertical stratiﬁcation between the
diﬀerent PEGs examined emphasizes the various eﬀects on
step ② where PEG 400 acted as an inhibitor (α′ > 1) and PEG
8 K as an activator (α′ < 1).
The apparent common occurrence of cosolutes inducing
mixed behavior across a wide variety of enzymes suggested a
possible underlying general mechanism. To explain mixed
inhibition, CIUI, of α-chymotrypsin caused by dextran, Pastor
et al.48 suggested product inhibition, where catalysis products
exert an inhibitory eﬀect through enzyme rebinding.26
Although the initial-rate assumption used to derive the
Michaelis−Menten equation removes the possibility of product
rebinding, it is intuitive that product binding to the “original”
free enzyme should result in competitive inhibition.53 The
greater challenge is understanding the mechanism of
uncompetitive inhibition. Generally, small-molecule, uncompetitive inhibitors are less common compared to competitive
inhibitors likely because they need to recognize and bind to a
transient enzyme intermediate.26,53 The hydrolysis of PNPP by
CIAP occurs stepwise with the release of PNP and then
followed by Pi.54 In this double-displacement mechanism,
further described below, PNP binding to the covalently
modiﬁed CIAP would be the potential candidate for
product-induced uncompetitive inhibition.
Although a distinguishing feature of mammalian AP, such as
CIAP, is its uncompetitive inhibition by single amino acids

Cosolutes’ potential to stabilize or destabilize proteins
provides another explanation for the changes in Vmax and
Kasp. While experimentally, the same volume of fresh enzyme
was added to the solutions, cosolutes could stabilize or
destabilize weakly folded CIAP present in the sample.8,51 This
would lead to an increase or decrease in Et, causing Vmax to rise
or fall, respectively. Given the already mentioned extra
interactions from PEG, this mode of operation could account
for the mass dependence changes Vmax. Many standard enzyme
assay protocols often include albumin, typically at 0.1%
concentration, as a stabilizing agent.52 Also, in the case
where there is little to no change in the underlying rate
constants, k1, k−1, and kcat, changes in Et should also be directly
reﬂected in Kasp (eqs 2 and 3). This could provide a simple
explanation for CAUA and CIUI behavior where there are
signiﬁcant changes in both α and α′.
Recognizing that α and α′ are kinetic parameters deﬁned
under initial rate and steady-state assumptions, it is not
surprising that they exhibit nonlinearity as a function of wt %
and log(Π). Data linearity is commonly seen in the crowding
and the osmotic pressure literature, where experiments are
largely conducted under equilibrium conditions. The outcomes
of these types of experiments can be expressed as an
equilibrium constant between two states, such as unfolded
versus folded proteins and open versus closed channels. In
these situations, linearity can be meaningfully interpreted
through thermodynamics.16
Mechanistic Reason for the Prevalence of CosoluteInduced Mixed-Behavior on Enzyme Kinetics. The
observed cosolutes induced mixed behaviors on CIAP kinetics
is consistent with other enzyme studies summarized by
Silverstein and Slade.5 Figure 7 shows α and α′ calculated
from 79 instances drawn from 30 studies on approximately 40
diﬀerent enzymes using 12 diﬀerent cosolutes where changes
in KM and Vmax were reported in Table S1 from Silverstein and
Slades.5
If α and α′ between 0.95 and 1.05, indicated by the blue and
red cross in Figure 7, respectively, are taken to represent “no
changes” in step ① and ② kinetics, then, by far, the most
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Figure 8. Mechanism of PNPP hydrolysis catalyzed by CIAP and how cosolutes could aﬀect kinetics. Top row shows the double-displacement
mechanism of hydrolysis of CIAP. PNPP binding to CIAP is followed by PNP release and covalent modiﬁcation of Ser92 by phosphate. A water
molecule then binds to the covalently modiﬁed CIAP, leading to Pi release and returning CIAP to its initial state. Bottom row shows one possible
combination of cosolute eﬀects on CIAP kinetics, leading into CIUI mixed behavior. The presence of cosolutes could prevent PNPP binding by
collapsing the binding site. They could also induce additional conformational change preventing the water binding needed to release the covalently
bound phosphate.

mechanisms,26 substrates bind, PNPP and H2O in the case
of CIAP, sequentially and are interweaved between stepwise
product release. At no point are all substrates bound to the
enzyme, as implied in Figure 2.54 For CIAP, this is
diagrammed in the top row of Figure 8.
PNPP binding to CIAP results in cleavage of its ester bond,
releasing the colored PNP into solution and leaving the
phosphate covalently attached to Ser92, forming an intermediate enzyme state. In the next step, a water molecule binds
to this covalently modiﬁed CIAP, which ultimately dephosphorylates Ser92, resetting CIAP to its original condition and
ready to catalyze the hydrolysis of another PNPP molecule.
Modifying PNPP or water molecule binding could lead to
competitive or uncompetitive behaviors, ultimately resulting in
mixed behaviors when both occur. The prevalence of the
double-displacement mechanism in numerous other enzymes,
such as trypsin, chymotrypsin, and lysozyme, provides an
explanation for the widespread cosolute-induced mixed
behavior.
Cosolute-induced changes in the vicinity of the enzyme
active site, regardless of whether caused by crowding,
conﬁnement, or dehydration, would be an obvious means for
altering substrate binding or product release in CIAP.
Conformational changes resulting in steric obstruction of the
catalytic site, from cleft closure, for example, would impede the
enzyme−substrate complex and decrease k1 (eq 2), leading to
an increase in KM, a decrease in Kasp (eq 3), competitive
inhibition, all other rate constants, and Et being the same.20,21
Further cosolute-induced conformational changes to the
covalently modiﬁed enzyme intermediate could slow entry of
the mechanistically critical water molecule, lowering Vmax by
decreasing k2 (eq 2) and leading to uncompetitive inhibition.
Alternatively, observed uncompetitive inhibition could result
from the steric hindrance of Pi release. A simultaneous

such as L-phe, PNP is unlikely an uncompetitive inhibitor in
the presence of cosolutes. Both PNP and Pi are observed to be
purely competitive inhibitors in traditional dilute solutions.55
When cocrystallized with human placental AP, L-phe directly
interacted with the negatively charged phosphorylated Ser92
through its positively charged amino terminus.31,56 Binding of
L-phe was further stabilized by interactions between its
negatively charged carboxylic acid group and the surrounding
basic amino acids such as Arg150 and Arg166. Bound this way,
L-phe would block subsequent water-molecule binding, which
provided a mechanistic explanation for its uncompetitive
inhibition. Although further reﬁnement of the original X-ray
structure in the absence of L-phe56 revealed a PNP bound near
the catalytic site, its lack of charged groups similar to L-phe
meant that it was located further away from the phosphorylated Ser92 and likely would not interfere with water binding.31
A distal L-phe site, approximately 28 Å away from the catalytic
site, was also observed.31,56 Although PNP was observed to
bind here, whether this site plays any role in inhibition is
unclear. A further complication is that the eﬀects of PNP
product binding would need to be sensitive to cosolute identity
and size. In the presence of PEG 8 K and 20 K, PNP acts as a
competitive inhibitor and an uncompetitive activator, CIUA,
while the other examined cosolutes generally behaved as CIUI
inhibitors. In the presence of sucrose and dextran 6 K, its
uncompetitive inhibition is even stronger. Assuming that
cosolutes would neither alter the products of PNPP hydrolysis,
PNP, and Pi, nor the double-displacement enzyme mechanism,
a possible and challenging explanation would be to imagine the
diﬀerent cosolute inducing diﬀerent CIAP conformations,
enabling individual responses to PNP binding.
A proper explanation of the observed cosolute-induced
mixed behavior on CIAP needs to take into account its speciﬁc
double-displacement mechanism.54 In double-displacement
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combination of these eﬀects, one of which is diagrammed in
the bottom row of Figure 8, provides a simple explanation for
CIUI mixed inhibition in CIAP and suggests a framework for
this most commonly observed mixed behavior. Pure
competitive inhibition, on the other hand, could result from
cosolutes only being able to induce suﬃcient conformational
change to aﬀect substrate binding but not enough to aﬀect
subsequent substrate binding such as H2O in CIAP. Pure
uncompetitive inhibition could be a result of a cosolute’s
ability to cause suﬃcient structural changes to block the
second substrate binding step only after covalent modiﬁcation.
However, the same proposed conformational changes could
also account for competitive and uncompetitive activation.
Cleft closure around the active site could lower k−1 ES
dissociation to a much greater extent than k1, leading
ultimately to an increase in Kasp and competitive activation
through extra stabilization of the ES complex (eqs 2 and 3).
Similarly, conformational modiﬁcation of the covalently
modiﬁed enzyme could increase the “residence” time when
the water molecule stays “trapped” at the active site or enable
quicker escape of Pi, leading to an increase in kcat and
uncompetitive activation. The additional steps involving water
binding to the covalently modiﬁed state are not explicitly
recognized in the simple Michaelis−Menten scheme (Figure
1). This suggests that a more comprehensive appreciation of
how cosolutes inﬂuence enzyme kinetics needs to take into
account their actual mechanistic steps.

■

Article

1). In the case of CIAP, these two steps appeared to be
inﬂuenced by diﬀerent mechanisms.
(a). Step ①, enzyme−substrate complex formation,
appeared to be more sensitive to osmotic stress than
crowding. The noncarbohydrate cosolutes exhibited
similar correlation in their α as a function of log(Π)
with diﬀerences potentially resulting from size-dependent exclusion, a common observation in osmotic stress
experiments. They also showed molecular weight
independence in their concentration eﬀects on α.
Carbohydrates, considered to be more ideal crowders,
showed weak competitive behavior consistent with the
expected small volume change upon substrate binding.
(b). For step ②, product formation and release, the
carbohydrate cosolutes exerted noticeably more potent
uncompetitive inhibition versus noncarbohydrates. The
latter showed distinct molecular weight-dependent
behavior. PEG 20 K and PEG 8 K acted as
uncompetitive activators. The smaller noncarbohydrates
were uncompetitive inhibitors over the same osmotic
pressure range. The great uncompetitive inhibition by
dextran 6 K versus sucrose could be due to conﬁnement.
Although all this suggested that step ② in CIAPcatalyzed PNPP hydrolysis was sensitive to crowding,
the question remains about the source of the volume
change necessary for this mode of inﬂuence to be
eﬀective.

CONCLUSIONS
1 Fitting initial velocity data to the Kasp and Vmax form of
the Michaelis−Menten equation (eq 4) oﬀered numerous advantages compared to using the traditional KM
and Vmax parameters (eq 1). Particularly, it led to
insights into how cosolutes altered the individual steps
of the classic Michaelis−Menten scheme (Figure 1)
using ideas taken from small-molecule competitive and
uncompetitive inhibition.
2 For PNPP hydrolysis catalyzed by CIAP, the carbohydrate cosolutes, dextran 6 K and sucrose, altered the
kinetics of steps ① and ② (Figure 1) diﬀerently from the
noncarbohydrate cosolutes, PEG’s, TEG, and betaine. In
step ①, all the noncarbohydrate cosolutes acted as
competitive inhibitors. Comparatively, dextran 6 K and
sucrose demonstrated little conclusive competitive
inhibition and perhaps even slight activation. Cosolute
eﬀects on step ② displayed greater complexity. The
observed uncompetitive behavior of the noncarbohydrates divided them into two groups. The large PEG’s,
PEG 20 K and PEG 8 K, acted as uncompetitive
activators, increasing Vmax of CIAP kinetics. The
remaining smaller noncarbohydrate cosolutes behaved
as uncompetitive inhibitors. Compared to these small
noncarbohydrates, dextran 6 K and sucrose were much
stronger uncompetitive inhibitors. Overall, PEG 20 K
and PEG 8 K showed CIUA mixed behavior, while PEG
1 K, PEG 400, TEG, and betaine were CIUI mixed
inhibitors. Dextran 6 K and sucrose demonstrated
uncompetitive inhibition, but the signiﬁcant decrease
in Vmax made it diﬃcult to identify the form of
competitive behavior, activating or inhibiting.
3 Using α and α′ enabled quantifying cosolute eﬀects on
the two steps of the Michaelis−Menten scheme (Figure

■

4 The generally observed mixed behavior induced by
cosolutes on CIAP kinetics is consistent with the
broader literature reviewed by Silverstein and Slade.5
Cosolute-induced mixed behavior, CAUA, CAUI, CIUA,
and CIUI, on enzyme kinetics was observed 77% of the
time, with CIUI being the most common behavior at
33%. For CIAP, interference with or enhancement of
water-binding after release of PNP could be a source of
uncompetitive behavior. This double-displacement
mechanism of CIAP is common in other enzymes.
Alternatively, changes in Et, through excluded volume,
stabilizing or destabilizing weakly folded enzymes, would
lead to parallel changes in Vmax and Kasp, leading to
CAUA or CIUI behavior. These possibilities could
account for the widespread occurrence of cosoluteinduced mixed behavior.

MATERIALS AND METHODS
CIAP Kinetic Assays. The hydrolysis of para-nitrophenyl
phosphate (disodium salt from Sigma) by calf-IAP, CIAP
(Worthington), was carried out in a reaction solution of 80
mM NaCl, 20 mM sodium borate buﬀer (pH 8.8), 2 mM
MgCl2, and 0.01 mM ZnCl2. The cosolute solutions were
made by weight percent, wt %, using the reaction solution as
the solvent. The cosolutes, betaine, sucrose, dextran 6 K, TEG,
and polyethylene glycol of molecular weight 400, 1, 8, and 20
K (PEG 400, PEG 1 K, PEG 8 K, and PEG 20 K) were all at
least reagent grade. These cosolutes represent both carbohydrate and noncarbohydrate across a wide mass range. Sucrose
was selected because it is a nonreducing sugar which removes
the possibility of it covalently modifying CIAP. Betaine is a
neutral zwitterionic osmolyte. Approximately 0.2 U of CIAP,
prepared in a 50% glycerol/reaction solution (v/v), was added
by a minimum volume (∼1% of ﬁnal volume) to both the
uncrowded (i.e., dilute control) and crowded reaction solution.
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The reaction was initiated by introducing a small volume
(∼1% of ﬁnal volume) of freshly made PNPP dissolved in the
reaction solutions to the reaction mixture to give a ﬁnal
substrate concentration. After quickly and gently mixing using
a pipettor and/or a vortexer for more viscous solutions (i.e.,
PEG 8 K and PEG 20 K), the enzymatic formation of PNP was
followed spectrophotometrically using a Cary 50 UV−vis set at
λ = 400 nm. There was approximately a 30 s delay between
initiating the reaction and the start of data collection. Data
were typically collected in 1 s time-averaged intervals for 45 s
and saved in a CSV-formatted ﬁle for analysis.
The normal daily experimental protocol consisted of
preparing a fresh stock concentrated PNPP solution and
CIAP. A “control” series (i.e., without cosolutes) was ﬁrst done
consisting of four PNPP substrate concentrations, between 0.1
and 1 mM, normally done in triplicate. This data was used to
establish a control Vmax and Kasp for that day. Using the same
amount of enzyme and PNPP concentrations as in the control,
kinetic experiments in the presence of cosolutes condition
were conducted in the same manner to determine the apparent
* and Kasp
* ). Calculating α and α′ using
Vmax and Kasp (Vmax
measurements taken on the same day by the same investigator
using the same solutions helped correct for changes in stock
enzyme solutions and variabilities introduced by individual
experimentalists. Experiments for each cosolute were conducted by at least two authors.
Data Analysis. CSV data from the Cary 50 was analyzed
using Python within Jupyter Notebooks57 online through
Google Colaboratory58 or locally installed. A linear ﬁtting
algorithm from the Python statsmodels module was used to
determine the slope of the Abs400 versus time data (in
seconds). These slopes were converted into initial velocities
using our experimentally determined molar extinction
coeﬃcient of 1.79 × 105 M−1 cm−1. The velocities versus
initial PNPP concentrations were nonlinearly ﬁtted to the
Michaelis−Menten equation, eq 4 or 1, to determine Vmax and
Kasp or Vmax and KM, respectively, using the curve_ﬁt routine
from the scipy.optimize module. The curve_ﬁt routine uses the
Leveberg−Marquardt algorithm, which returns both the bestﬁt value and its standard deviation. Using control and apparent
Vmax and Kasp, the values of α and α′ were determined for the
crowded conditions (eq 5). The results of ﬁtting data to both
eqs 1 and 4 can be found in Supporting Information, AllDataKM-csv.txt and AllData-Kasp-csv.txt, respectively.
Osmotic Pressure Data. The osmotic pressure for all
cosolutes except dextran 6 K was previously available at http://
lpsb.nichd.nih.gov/osmotic_stress.htm, which is no longer
accessible. A copy of that data and ﬁts relevant for this paper
can now be found at https://sites.google.com/mtroyal.ca/
johnchik/osmotic-resource.
The logarithm of osmotic pressure data for each cosolute
was ﬁtted to the following function.
log10(π) = a + b × (wt %)c

Table 3. Resulting Fitted Parameters for Eq 6
cosolute

a

b

c

approximate
Range of use
(wt %)

betaine
sucrose
TEG
PEG 400
PEG 1 K
PEG 8 K
PEG 20 K

3.90 ± 0.61
4.29 ± 0.41
5.08 ± 0.16
5.25 ± 0.18
4.89 ± 0.39
3.90 ± 1.34
1.57 ± 0.44

2.45 ± 0.59
1.60 ± 0.37
1.26 ± 0.14
0.77 ± 0.15
0.79 ± 0.30
0.99 ± 0.96
2.75 ± 0.40

0.16 ± 0.03
0.21 ± 0.03
0.24 ± 0.02
0.33 ± 0.04
0.34 ± 0.07
0.36 ± 0.17
0.21 ± 0.02

1−23
2−58
2−50
3−30
3−60
10−36
2−48

Dextran T10 being larger in molecular weight than dextran 6
K (10 kDa vs 6 kDa) should yield an osmotic pressure smaller
than actual. Figure S2 in Supporting Information shows the ﬁt
between the data and ﬁt to eq 6 using the parameters Table 3
as well as eq 7.

■

ASSOCIATED CONTENT

sı Supporting Information
*

The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acsomega.1c03243.
Histogram of the relative error in Kasp, KM, and Vmax, ﬁt
between log(Π) and wt % via eq 6 and the log(Π) of
dextran T10 by Jonsson in eq 7,35 the eﬀects of the
cosolute on enzyme kinetics measured by α and α′ using
data from Silverstein and Slade,5 and a summary of their
behaviors (PDF)
Determined Vmax and Kasp values by ﬁtting data to eq 4
(TXT)
Determined Vmax and KM values by ﬁtting data to eq 1
(TXT)

■

AUTHOR INFORMATION

Corresponding Author

John K. Chik − Department of Chemistry and Physics, Mount
Royal University, Calgary, Alberta T2N4N1, Canada;
orcid.org/0000-0002-7314-3251; Email: jchik@
mtroyal.ca

Authors

Oksana A. Yavorska − Department of Chemistry and Physics,
Mount Royal University, Calgary, Alberta T2N4N1, Canada
Lukas Syriste − Microbiology, Immunology & Infectious
Diseases, Cumming School of Medicine, University of Calgary,
Calgary, Alberta T3E 6K6, Canada
Chantal M. du Plessis − Department of Chemistry and
Physics, Mount Royal University, Calgary, Alberta T2N4N1,
Canada
Maryam Yaqoob − Department of Chemistry and Physics,
Mount Royal University, Calgary, Alberta T2N4N1, Canada
Kyle Loogman − Department of Chemistry and Physics,
Mount Royal University, Calgary, Alberta T2N4N1, Canada
Michael Cordara − Department of Chemistry and Physics,
Mount Royal University, Calgary, Alberta T2N4N1, Canada

(6)

where wt % is the weight % concentration of cosolute. The
ﬁtted a, b, and c results are shown in Table 3 below.
The dextran 6 K data was taken from dextran T10 ﬁts
published by Jonsson, as shown below.35

Complete contact information is available at:
https://pubs.acs.org/10.1021/acsomega.1c03243

π(in atm) = 0.116 × wt % − 0.00491 × (wt %)2
+ 0.000257 × (wt %)3

Article

Notes

The authors declare no competing ﬁnancial interest.

(7)
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All data, JupyterLab ﬁles, and Python scripts used in this report
can be found at https://doi.org/10.5683/SP2/N7ZKXV
(Mount Royal University Dataverse).

(17) Parsegian, V. A.; Bezrukov, S. M.; Vodyanoy, I. Watching Small
Molecules Move: Interrogating Ionic Channels Using Neutral Solutes.
Biosci. Rep. 1995, 15, 503−514.
(18) Sidorova, N. Y.; Rau, D. C. Linkage of EcoRI Dissociation from
Its Specific DNA Recognition Site to Water Activity, Salt
Concentration, and pH: Separating Their Roles in Specific and
Non-Specific Binding. J. Mol. Biol. 2001, 310, 801−816.
(19) Colombo, M.; Rau, D.; Parsegian, V. Protein Solvation in
Allosteric Regulation: A Water Effect on Hemoglobin. Science 1992,
256, 655−659.
(20) Rand, R. P.; Fuller, N. L.; Butko, P.; Francis, G.; Nicholls, P.
Measured Change in Protein Solvation with Substrate Binding and
Turnover. Biochemistry 1993, 32, 5925−5929.
(21) Reid, C.; Rand, R. P. Probing Protein Hydration and
Conformational States in Solution. Biophys. J. 1997, 72, 1022−1030.
(22) Dhar, A.; Samiotakis, A.; Ebbinghaus, S.; Nienhaus, L.;
Homouz, D.; Gruebele, M.; Cheung, M. S. Structure, Function, and
Folding of Phosphoglycerate Kinase Are Strongly Perturbed by
Macromolecular Crowding. Proc. Natl. Acad. Sci. U.S.A. 2010, 107,
17586−17591.
(23) Currie, M.; Leopold, H.; Schwarz, J.; Boersma, A. J.; Sheets, E.
D.; Heikal, A. A. Fluorescence Dynamics of a FRET Probe Designed
for Crowding Studies. J. Phys. Chem. B 2017, 121, 5688−5698.
(24) Leopold, H. J.; Leighton, R.; Schwarz, J.; Boersma, A. J.; Sheets,
E. D.; Heikal, A. A. Crowding Effects on Energy-Transfer Efficiencies
of Hetero-FRET Probes As Measured Using Time-Resolved
Fluorescence Anisotropy. J. Phys. Chem. B 2019, 123, 379−393.
(25) DeMoll, E.; Cox, D. J.; Daniel, E.; Riggs, A. F. Apparent
Specific Volume of Human Hemoglobin: Effect of Ligand State and
Contribution of Heme. Anal. Biochem. 2007, 363, 196−203.
(26) Cornish-Bowden, A. Fundamentals of Enzyme Kinetics; Wiley,
2013.
(27) Johnson, K. A. New Standards for Collecting and Fitting Steady
State Kinetic Data. Beilstein J. Org. Chem. 2019, 15, 16−29.
(28) Manes, T.; Hoylaerts, M. F.; Müller, R.; Lottspeich, F.; Hölke,
W.; Millán, J. L. Genetic Complexity, Structure, and Characterization
of Highly Active Bovine Intestinal Alkaline Phosphatases. J. Biol.
Chem. 1998, 273, 23353−23360.
(29) Hoylaerts, M. F.; Manes, T.; Millán, J. L. Molecular Mechanism
of Uncompetitive Inhibition of Human Placental and Germ-Cell
Alkaline Phosphatase. Biochem. J. 1992, 286, 23−30.
(30) Hoylaerts, M. F.; Manes, T.; Millán, J. L. Mammalian Alkaline
Phosphatases Are Allosteric Enzymes. J. Biol. Chem. 1997, 272,
22781−22787.
(31) Stec, B.; Cheltsov, A.; Millán, J. L. Refined Structures of
Placental Alkaline Phosphatase Show a Consistent Pattern of
Interactions at the Peripheral Site. Acta Crystallogr., Sect. F: Struct.
Biol. Cryst. Commun. 2010, 66, 866−70.
(32) Millán, J. L. Alkaline Phosphatases. Purinergic Signal. 2006, 2,
335.
(33) Besman, M.; Coleman, J. E. Isozymes of Bovine Intestinal
Alkaline Phosphatase. J. Biol. Chem. 1985, 260, 11190−11193.
(34) Sekiguchi, S.; Hashida, Y.; Yasukawa, K.; Inouye, K. Effects of
Amines and Aminoalcohols on Bovine Intestine Alkaline Phosphatase
Activity. Enzyme Microb. Technol. 2011, 49, 171−176.
(35) Jonsson, G. Boundary Layer Phenomena during Ultrafiltration
of Dextran and Whey Protein Solutions. Desalination 1984, 51, 61−
77.
(36) Homchaudhuri, L.; Sarma, N.; Swaminathan, R. Effect of
Crowding by Dextrans and Ficolls on the Rate of Alkaline
Phosphatase-Catalyzed Hydrolysis: A Size-Dependent Investigation.
Biopolymers 2006, 83, 477−486.
(37) Iino, S.; Fishman, L. The Effect of Sucrose and Other
Carbohydrates on Human Alkaline Phosphatase Isoenzyme Activity.
Clin. Chim. Acta 1979, 92, 197−207.
(38) Boulanger, R. R., Jr; Kantrowitz, E. R. Characterization of a
Monomeric Escherichia Coli Alkaline Phosphatase Formed upon a
Single Amino Acid Substitution. J. Biol. Chem. 2003, 278, 23497−
23501.

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ACKNOWLEDGMENTS
The authors acknowledge the ﬁnancial support from Mount
Royal University’s Internal Research Grant Fund and from the
Faculty of Science and Technology’s Innovation Grant, ESS
Grant, Student Research Assistant Funding, and Petro-Canada
Young Innovator Award. We also acknowlege Mount Royal
University Library Open Access Fund for underwriting
publication costs. Finally, we thank the faculty, staﬀ, and
students at Mount Royal University for their assistance and
support.

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Article

REFERENCES

(1) Gierasch, L. M.; Gershenson, A. Post-Reductionist Protein
Science, or Putting Humpty Dumpty Back Together Again. Nat.
Chem. Biol. 2009, 5, 774−777.
(2) Ellis, R. J. Macromolecular Crowding: Obvious but Underappreciated. Trends Biochem. Sci. 2001, 26, 597−604.
(3) Zimmerman, S. B.; Trach, S. O. Estimation of Macromolecule
Concentrations and Excluded Volume Effects for the Cytoplasm of
Escherichia Coli. J. Mol. Biol. 1991, 222, 599−620.
(4) Bennett, B. D.; Kimball, E. H.; Gao, M.; Osterhout, R.; Van
Dien, S. J.; Rabinowitz, J. D. Absolute Metabolite Concentrations and
Implied Enzyme Active Site Occupancy in Escherichia Coli. Nat.
Chem. Biol. 2009, 5, 593−599.
(5) Silverstein, T. P.; Slade, K. Effects of Macromolecular Crowding
on Biochemical Systems. J. Chem. Educ. 2019, 96, 2476−2487.
(6) Balcells, C.; Pastor, I.; Pitulice, L.; Hernández, C.; Via, M.;
Garcés, J. L.; Madurga, S.; Vilaseca, E.; Isvoran, A.; Cascante, M.;
Mas, F. Macromolecular crowding upon in-vivo- like enzyme-kinetics:
Eﬀect of enzyme- obstacle size ratio http://newfrontchem.iqstorm.ro/
upload/02-NFC-24-1_Balcells%20et%20al.pdf (accessed Aug 3,
2021).
(7) Vöpel, T.; Makhatadze, G. I. Enzyme Activity in the Crowded
Milieu. PLoS One 2012, 7, No. e39418.
(8) Zhou, H.-X.; Rivas, G.; Minton, A. P. Macromolecular Crowding
and Confinement: Biochemical, Biophysical, and Potential Physiological Consequences. Annu. Rev. Biophys. 2008, 37, 375−397.
(9) Minton, A. P. Excluded Volume as a Determinant of
Macromolecular Structure and Reactivity. Biopolymers: Original
Research on Biomolecules 1981. 20. 2093. DOI: 10.1002/
bip.1981.360201006
(10) Minton, A. P.; Wilf, J. Effect of Macromolecular Crowding
upon the Structure and Function of an Enzyme: Glyceraldehyde-3Phosphate Dehydrogenase. Biochemistry 1981, 20, 4821−4826.
(11) Guin, D.; Gruebele, M. Weak Chemical Interactions That Drive
Protein Evolution: Crowding, Sticking, and Quinary Structure in
Folding and Function. Chem. Rev. 2019, 119, 10691−10717.
(12) Parsegian, V. A.; Rand, R. P.; Rau, D. C. [3] Macromolecules
and water: Probing with osmotic stress. Methods Enzymol. 1995, 259,
43−94.
(13) Timasheff, S. N. The Control of Protein Stability and
Association by Weak Interactions with Water: How Do Solvents
Affect These Processes? Annu. Rev. Biophys. Biomol. Struct. 1993, 22,
67−97.
(14) Asakura, S.; Oosawa, F. On Interaction between Two Bodies
Immersed in a Solution of Macromolecules. J. Chem. Phys. 1954, 22,
1255−1256.
(15) Sapir, L.; Harries, D. Is the Depletion Force Entropic?
Molecular Crowding beyond Steric Interactions. Curr. Opin. Colloid
Interface Sci. 2015, 20, 3−10.
(16) Parsegian, V. A.; Rand, R. P.; Rau, D. C. Osmotic Stress,
Crowding, Preferential Hydration, and Binding: A Comparison of
Perspectives. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 3987−3992.
26249

https://doi.org/10.1021/acsomega.1c03243
ACS Omega 2021, 6, 26239−26250

ACS Omega

http://pubs.acs.org/journal/acsodf

Article

(39) Vodyanoy, I.; Bezrukov, S. M.; Parsegian, V. A. Probing
Alamethicin Channels with Water-Soluble Polymers. Size-Modulated
Osmotic Action. Biophys. J. 1993, 65, 2097−2105.
(40) Stanley, C.; Krueger, S.; Parsegian, V. A.; Rau, D. C. Protein
Structure and Hydration Probed by SANS and Osmotic Stress.
Biophys. J. 2008, 94, 2777−2789.
(41) Parsegian, V. A.; Rand, R. P.; Rau, D. C. Macromolecules and
Water: Probing with Osmotic Stress. Methods in Enzymology;
Academic Press, 1995; Vol. 259, pp 43−94.
(42) Winzor, D. J.; Wills, P. R. Molecular Crowding Effects of Linear
Polymers in Protein Solutions. Biophys. Chem. 2006, 119, 186−195.
(43) Tubio, G.; Nerli, B.; Picó, G. Relationship between the Protein
Surface Hydrophobicity and Its Partitioning Behaviour in Aqueous
Two-Phase Systems of Polyethyleneglycol−dextran. J. Chromatogr. B
2004, 799, 293−301.
(44) Bekale, L.; Agudelo, D.; Tajmir-Riahi, H. A. The Role of
Polymer Size and Hydrophobic End-Group in PEG−protein
Interaction. Colloids Surf. B Biointerfaces 2015, 130, 141−148.
(45) Wu, J.; Zhao, C.; Lin, W.; Hu, R.; Wang, Q.; Chen, H.; Li, L.;
Chen, S.; Zheng, J. Binding Characteristics between Polyethylene
Glycol (PEG) and Proteins in Aqueous Solution. J. Mater. Chem. B
2014, 2, 2983−2992.
(46) Rong, Y. Probing the Structure of Dextran Systems and Their
Organization; Rutgers University-Graduate School-New Brunswick,
2008.
(47) Squire, P. G. Calculation of Hydrodynamic Parameters of
Random Coil Polymers from Size Exclusion Chromatography and
Comparison with Parameters by Conventional Methods. J.
Chromatogr. A 1981, 210, 433−442.
(48) Pastor, I.; Vilaseca, E.; Madurga, S.; Garcés, J. L.; Cascante, M.;
Mas, F. Effect of Crowding by Dextrans on the Hydrolysis of NSuccinyl-L-Phenyl-Ala-P-Nitroanilide Catalyzed by Alpha-Chymotrypsin. J. Phys. Chem. B 2011, 115, 1115−1121.
(49) Wenner, J. R.; Bloomfield, V. A. Crowding Effects on Eco RV
Kinetics and Binding. Biophys. J. 1999, 77, 3234−3241.
(50) Pastor, I.; Pitulice, L.; Balcells, C.; Vilaseca, E.; Madurga, S.;
Isvoran, A.; Cascante, M.; Mas, F. Effect of Crowding by Dextrans in
Enzymatic Reactions. Biophys. Chem. 2014, 185, 8−13.
(51) Timasheff, S. N. Control of Protein Stability and Reactions by
Weakly Interacting Cosolvents: The Simplicity of the Complicated.
Adv. Protein Chem. 1998, 51, 355−432.
(52) Albumin, in Worthington Enzyme Manual 280; Worthington, K.;
Worthington, V., Eds., 1993; p 13.
(53) Purich, D. L. Enzyme Kinetics : Catalysis & Control : A Reference
of Theory and Best-Practice Methods; Elsevier Academic ; Elsevier
Science [distributor]: San Diego, Calif.; Oxford, 2010.
(54) Stec, B.; Holtz, K. M.; Kantrowitz, E. R. A Revised Mechanism
for the Alkaline Phosphatase Reaction Involving Three Metal Ions. J.
Mol. Biol. 2000, 299, 1303−1311.
(55) Dean, R. L. Kinetic Studies with Alkaline Phosphatase in the
Presence and Absence of Inhibitors and Divalent Cations. Biochem.
Mol. Biol. Educ. 2002, 30, 401−407.
(56) Llinas, P.; Stura, E. A.; Ménez, A.; Kiss, Z.; Stigbrand, T.;
Millán, J. L.; Le Du, M. H. Structural Studies of Human Placental
Alkaline Phosphatase in Complex with Functional Ligands. J. Mol.
Biol. 2005, 350, 441−451.
(57) Kluyver, T.; Ragan-Kelley, B.; Pérez, F.; Granger, B.;
Bussonnier, M.; Frederic, J.; Kelley, K.; Hamrick, J.; Grout, J.;
Corlay, S.; Ivanov, P.; Avila, D.; Abdalla, S.; Willing, C. Jupyter
development team. Jupyter Notebooks − a Publishing Format for
Reproducible Computational Workﬂows. In Positioning and Power in
Academic Publishing: Players, Agents and Agendas; Loizides, F., Scmidt,
B., Eds.; IOS Press, 2016; pp 87−90.
(58) Google Colaboratory https://colab.research.google.com/
notebooks/intro.ipynb?utm_source=scs-index (accessed Sept 26,
2021).

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ACS Omega 2021, 6, 26239−26250