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Citation: Piccinini, A.; Lourenço,
E.C.; Ascenso, O.S.; Ventura, M.R.;
Amenitsch, H.; Moretti, P.; Mariani, P.;
Ortore, M.G.; Spinozzi, F. SAXS
Reveals the Stabilization Effects of
Modified Sugars on Model Proteins.
Life 2022,12, 123. https://doi.org/
10.3390/life12010123
Academic Editor: Eric R. May
Received: 13 December 2021
Accepted: 13 January 2022
Published: 15 January 2022
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life
Article
SAXS Reveals the Stabilization Effects of Modified Sugars on
Model Proteins
Astra Piccinini 1, Eva C. Lourenço 2, Osvaldo S. Ascenso 2, Maria Rita Ventura 3, Heinz Amenitsch 4,
Paolo Moretti 1, Paolo Mariani 1, Maria Grazia Ortore 1and Francesco Spinozzi 1,*
1Department of Life and Environmental Sciences, Polytechnic University of Marche, 60131 Ancona, Italy;
a.piccinini@pm.univpm.it (A.P.); p.moretti@pm.univpm.it (P.M.); p.mariani@univpm.it (P.M.);
m.g.ortore@univpm.it (M.G.O.)
2Extremochem, Rua Ivone Silva, 1050-124 Lisboa, Portugal; eva.lourenco@extremochem.com (E.C.L.);
osvaldo.ascenso@extremochem.com (O.S.A.)
3Instituto de Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa,
2780-157 Oeiras, Portugal; rita.ventura@extremochem.com
4Institute for Inorganic Chemistry, Graz University of Technology, 8010 Graz, Austria; amenitsch@tugraz.at
*Correspondence: f.spinozzi@univpm.it
Abstract:
Many proteins are usually not stable under different stresses, such as temperature and pH
variations, mechanical stresses, high concentrations, and high saline contents, and their transport
is always difficult, because they need to be maintained in a cold regime, which is costly and very
challenging to achieve in remote areas of the world. For this reason, it is extremely important to find
stabilizing agents that are able to preserve and protect proteins against denaturation. In the present
work, we investigate, by extensively using synchrotron small-angle X-ray scattering experiments, the
stabilization effect of five different sugar-derived compounds developed at ExtremoChem on two
model proteins: myoglobin and insulin. The data analysis, based on a novel method that combines
structural and thermodynamic features, has provided details about the physical-chemical processes
that regulate the stability of these proteins in the presence of stabilizing compounds. The results
clearly show that some modified sugars exert a greater stabilizing effect than others, being able to
maintain the active forms of proteins at temperatures higher than those in which proteins, in the
absence of stabilizers, reach denatured states.
Keywords:
small-angle X-ray scattering; protein stabilization; solvation; thermodynamic model;
myoglobin; insulin
1. Introduction
Over recent decades, protein therapeutics have increased significantly, owing to their
positive effects in the treatments of several diseases. The first human protein therapeutic
that was introduced was human insulin, derived from recombinant DNA techniques.
Proteins, among other small-molecules drugs, can perform complex functions that reduce
the drug toxicity and the immune response, because they are naturally produced by the
human body. Additionally, they have the most dynamic role of all the body macromolecules
and the biggest influence in terms of clinical utility [
1
]. Proteins are extensively used in
the treatment of several diseases, including cancer, HIV and diabetes. In this context,
monoclonal antibodies, cytokines and interferons are just a few examples of the wide range
of proteins that can be used as therapeutics macromolecules [
2
]. However, there are a lot of
limitations concerning the protein therapeutic strategy. First of all, they are very expensive
due to their expensive production cost, and this may limit their use in the global market.
Secondly, they need to be stored and transported by maintaining a cold regime, in order
to preserve their native structures, since a conformational change may result in a loss of
their activity. The degradation mechanisms that usually occur can involve both physical or
Life 2022,12, 123. https://doi.org/10.3390/life12010123 https://www.mdpi.com/journal/life
Life 2022,12, 123 2 of 25
chemical processes. Denaturation, noncovalent and covalent aggregation, deamination and
oxidation caused by heat, chemical factors or other types of stresses can indeed provoke the
loss of the three-dimensional structure of a protein. The hydrophobic patches of a protein
are usually folded inward when the macromolecule is in its native state, whereas they can
be exposed to the solvent during unfolding processes. As a consequence, the increase in the
available surface area intensifies the risk of adsorption and aggregation [
3
]. For all these
reasons, it is of great importance to find good ways to preserve proteins at a temperature as
close as possible to room temperature, and one of the best solutions is to use low molecular
weight, chemically unreactive stabilizer compounds. These stabilizers can encompass
a wide variety of molecules including sugars, salts, amino acids, and polymers such as
polyols and polyethylene glycols [
4
]. Stabilizers are used in many technological fields,
from biology to engineering [
5
]. The food industry, for example, is an important field where
stabilizers have reached a high resonance. Additives are largely employed to maintain
the physical stability of products, discouraging deteriorating processing that can damage
food [
6
]. Additionally, in biology, stabilizers are one of the most important sources that
can be used to preserve proteins against denaturation, which often occurs because of
several denaturing factors such as chemicals, high temperature, high pressure, and non-
physiological pH. These extreme factors are able to modify the native protein conformation,
which is stabilized by a network of intramolecular hydrogen bonds, salt bridges and van
der Waals interactions, as well as by the interactions with water and other molecules in
solution [
7
]. One of the main groups of compounds that are used for stabilizing proteins are
sugars, which are able to increase the energy barriers between folded and unfolded states
of a protein [
8
]. It has been shown that sugars do not interact directly with the protein
surface, but they can trap the water molecules in solution around the protein to preserve its
hydration shell and maintain its stability [
9
,
10
]. The major driving forces that are involved
in protein stabilization are considered to be the hydrogen bonds, which take place between
the protein and the water molecules that surround the protein shell [8].
In this work, we focused on five synthesized sugars (hereafter referred to as modified
sugar) developed by ExtremoChem. ExtremoChem has developed several new stabiliz-
ers [
11
] based on known osmolytes [
12
] that are able to stabilize biomolecules, including
nucleic acids and proteins, against stresses such as temperature excursions, shaking and
other mechanical stresses, high and low pH values and high concentration. In our exper-
iment, we tested these stabilizers on myoglobin and insulin at increasing temperatures,
with the aim to examine their stabilization properties. Samples were investigated by a syn-
chrotron small-angle X-ray scattering (SAXS) technique and data were analyzed in terms of
the distribution of proteins in different states (monomers, dimers, tetramers, and hexamers,
just for insulin), considering long-range protein–protein interactions and by employing
multimeric equilibrium processes in combination with exchange equilibrium processes
between modified sugar and water molecules that occur over the surface of individual
protein states. As a result, we were able to quantify the stabilizing effect of the five modified
sugars regarding each state of the model proteins myoglobin and insulin.
2. Materials and Methods
2.1. Sample Preparation
Myoglobin (MB) from equine heart was purchased from Sigma-Aldrich and used at
concentrations of 2 and 10 g/L dissolved in 10 mM phosphate buffer at pH 5. Insulin (IN)
from a bovine pancreas was prepared at 2 g/L and dissolved in the same buffer at pH 3.
Five synthesized modified sugars, (EC101, EC202, EC212, EC311 and EC312), made by
the Portuguese chemical synthesis company ExtremoChem, were dissolved in the protein
solutions at three different final concentrations: 0.05, 0.1, and 0.25 M. These modified sugars
contain a mannose, glucose or galactose moiety with different substituents at the anomeric
position [
11
], which can be charged or neutral. Two modified sugars, EC101 and EC202,
form ionic species when dissolved in water. Moreover, they were found to slightly increase
the pH values of the solutions (see Table S1 in the Supplementary Materials).
Life 2022,12, 123 3 of 25
2.2. SAXS Experiments
SAXS experiments were performed at the Austrian SAXS beamline of Elettra syn-
chrotron (Trieste, Italy) [
13
]. Measurements were carried out at 25
◦
, 35
◦
and 60
◦
C for
myoglobin, whereas the same analysis was performed at 25
◦
, 30
◦
, 35
◦
, 40
◦
, 45
◦
, 55
◦
and
60
◦
C for insulin. Over the course of the experiment, the new
µ
-Drop sample changer
recently developed in the Austrian beamline was used [
14
]. The modulus
q
of the scattering
vector, related to the scattering angle 2
θ
and to the X-ray wavelength
λ=
1.54 Å by the
relationship
q= (
4
π/λ)sin θ
, was fixed between 0.01 and 0.35 Å
−1
. For each sample,
twelve bidimensional and isotropic SAXS patterns were collected by a Pilatus3 1M detector
and subsequently treated with FIT2D [
15
] to apply the beamstop and detector mask and
to perform the radial average. Finally, by using the SAXS data reduction system (SAXS
dog) for the subtraction of the buffers isotropic SAXS signal from the one of the samples,
the normalization to the intensity of the primary beam and the correction for the samples’
transmissions, the experimental macroscopic scattering cross section
dΣ
dΩ(q)
of each sample
was obtained.
2.3. SAXS Data Analysis
The analysis of SAXS data was performed by assuming that proteins in solution can
be present in
Ns
different states (e.g., folded oligomers or unfolded chains), without any
preferential orientation, and that long-range isotropic protein–protein interactions may
occur. In these circumstances, the macroscopic differential scattering cross section (the
precious information provided by SAXS experiments) can be written as
dΣ
dΩ(q) = n P(q)SM(q). (1)
This equation contains three relevant factors. Firstly,
n
is the nominal number density
of the protein monomers, simply related to the w/v protein concentration,
c
, through
Avogadro’s number,
NA
, and the monomer molecular weight,
M1
, by
n=cNA/M1
.
The second term, P(q), is the so-called effective form factor,
P(q) =
Ns
∑
j=1
xj
αj
Pj(q)(2)
where
Pj(q)
is the form factor (the orientational average of the squared excess X-ray scatter-
ing amplitude) of the
j
-protein state,
αj
is the corresponding aggregation number, whereas
xj
is the molar fraction of nominal protein monomers that are forming the
j
-state, with the
condition
Ns
∑
j=1
xj=1 (3)
The third term,
SM(q)
, is known as the measured structure factor and depends on the
average protein–protein structure factor,
S(q)
, according to
SM(q) =
1
+β(q)[S(q)−
1
]
,
where
β(q)
is the coupling function, with
β(q) = |P(1)(q)|2/P(q)
and
P(1)(q)
being the
weighted average of the orientational average of the excess X-ray scattering amplitude
P(1)
j(q)of the j-state
P(1)(q) =
Ns
∑
j=1
xj
αj
P(1)
j(q). (4)
The calculation of both
Pj(q)
and
P(1)
j(q)
was carried out on the basis of protein data
bank (PDB, [
16
]) atomic structure associated with the
j
-state by using the SASMOL ap-
proach [
17
]. This method is based on the description of the solvent molecules in contact
Life 2022,12, 123 4 of 25
with the protein as dummy Gaussian spheres and determines the number and the geo-
metrical coordinates of such spheres by burying the protein in a tetrahedral close-packed
(TCP) lattice of dummy spheres. Consequently, the number and the positions of the water
molecules can be obtained in the first
Nsh
hydration shells of the
j
-protein state and a
scattering length density (SLD) that can differ from the one of the bulk solvent is assigned
to each of them. Typically, the thickness of each water shell is considered to be equal to
2.8 Å. Notice that in this work we have considered
Nsh =
2. This feature is particularly
useful in the presence of a binary solvent, such as a solution of water and modified sugar,
where preferential solvation effects can lead to a modification of the composition of the
binary solvent in contact with the protein surface with respect to the composition of the
bulk binary solvent.
2.3.1. Multimeric Equilibrium Processes in Binary Solvents
In equilibrium conditions, the distribution of proteins in the
Ns
states and the com-
position of the first protein hydration shell as a function of protein concentration, solvent
composition and temperature can be determined by considering the interplay of different
elementary processes. First, we consider the process of transformation of a protein (here-
after indicated by the symbol P) dissolved in water at a certain pH and at a certain ionic
strength (
I
) from the state 1 (which is assumed to be a monomeric state, typically a native
state) to the state j,
P1(Ws1)m1α−1
jPj(Wsj)mj+ (m1−α−1
jmj)Wb(5)
where
mj
is the number of water sites in the first hydration shell of the
j
-state (a value that
can be determined by SASMOL),
Wsj
represents a water molecule attached to the surface
of the protein in the
j
-state and
Wb
represents a water molecule in the bulk (see Figure 1).
By assuming an ideal thermodynamic behavior of the system, the equilibrium constant
KW1j
as well as the standard Gibbs free energy change
∆GW1j
associated with this process is
KW1j=
Cα−1
j
Pj(Wsj)mj
Xm1−α−1
jmj
Wb
CP1(Ws1)m1
=e−∆GW1j/(RT)(6)
where the symbol
C
is the molar concentration (used for the solutes, with
C=
1 M being
their standard state) and the symbol
X
stands for the molar fraction (used of the solvent
(water), with
X=
1 being its standard state). The second process refers to proteins dissolved
in a binary solvent constituted by water and a cosolvent (such as a modified sugar) and
describes the exchange of a cosolvent molecule attached to the first hydration shell of
the protein in the
j
-state (indicated by the symbol
Gsj
) with a bulk water molecules (see
Figure 2for a clarifying example),
Gsj+WbGb+Wsj(7)
that leads to the formation of a cosolvent molecule in the bulk (
Gb
) and a water molecule
in the first shell (
Wsj
). According to the well-established Schellmann
model [18–21],
this
exchange equilibrium has been found to be simply described by the thermodynamic constant
Kexjand the related standard Gibbs free energy change ∆Gexj,
Kexj=φjXGb
(1−φj)XWb
=φjxGb
(1−φj)(1−xGb)=e−∆Gexj/(RT)(8)
Life 2022,12, 123 5 of 25
where
φj
is the fraction of first hydration shell sites in the protein
j
-state occupied by water
molecules. We have introduced the molar fraction of cosolvent in the bulk binary solvent,
xGb=XGb
XGb+XWb
(9)
KW1j
1−state j−state
1
2
+ 6
Figure 1.
Sketch of an equilibrium process of the protein in water from the monomeric (1-)state to the
dimeric (j= 2)-state (scheme (6), with αj=2 and m1−α−1
jmj=6).
Kex j
surface of the j−state
Figure 2.
Sketch of the water-cosolvent (blue spheres and red ellipsoids, respectively) exchange
equilibrium process over the surface of the j-protein state.
To note, if water is preferentially attached to the protein,
Kexj>
1 (
∆Gexj<
0),
otherwise, when there is a preferential binding of protein with cosolvent molecules,
Kexj<
1 (
∆Gexj>
0). We assume that the exchange equilibrium processes are inde-
pendent events, so that the probability that
n
water sites are occupied by water molecules
and the remaining
mj−n
sites by cosolvent molecules is given by the binomial distribu-
tion,
p(n
,
mj) = mj!
n!(mj−n)!φn
j(
1
−φj)mj−n
. Hence, by referring to Equation (6), the molar
concentration of the protein in the
j
-state dissolved in a binary solvent with all its
mj
first
hydration shell sites occupied by water molecules is given by
CPj(Wsj)mj=Cjφmj
j
, where
Cj=α−1
jCPxj=∑mj
n=0CPj(Wsj)n(Gsj)mj−n
is the total molar concentration of the protein in
the
j
-state, independently on the occupation of the sites by water or cosolvent. Notice
that
CP=c/M1=n/NA
is the nominal molar concentration of monomers in solution.
As a consequence, in a binary solvent, the effective equilibrium constant
K1j
, which de-
scribes the transformation of a protein molecule by the 1-state to the
j
-state, irrespective
of the composition of the first hydration shell, and the related effective Gibbs free energy
change are
K1j=(α−1
jCPxj)α−1
j
CPx1=KW1j
φm1
1Xα−1
jmj−m1
Wb
φα−1
jmj
j
=e−∆G1j/(RT)(10)
The composition of the system is expressed by the nominal molar fractions of water,
XW
, cosolvent,
XG
, and protein monomers,
XP
, with the straightforward condition
XW+
XG+XP=1. Consequently, the nominal composition of the solvent is
xG=XG
1−XP(11)
Life 2022,12, 123 6 of 25
Since
XP
and
xG
are fixed parameters characterizing the sample, in any conditions of
protein distribution among the states and preferential solvation effects, the following two
constraints should hold,
XWb= (1−XP)(1−xG)−XP
Ns
∑
j=1
mjxjα−1
jφj(12)
XGb= (1−XP)xG−XP
Ns
∑
j=1
mjxjα−1
j(1−φj)(13)
Notice that the effective parameters
K1j
and
∆G1j
can change with the composition
(i.e., by varying
XP
or
xG
), whereas the exact thermodynamic parameters
KW1j
and
∆GW1j
as well as
Kexj
and
∆Gexj
, which refer to the two elementary processes of Equations (5)
and (7), should be independent on
XP
and
xG
. However, the Gibbs free energy change
∆GW1j
can be affected by pH and ionic strength, which could be modified by the presence
of cosolvent molecules, if they possess acid-base or ionic properties (such as for some of the
modified sugars exploited in this work; see Table S1). In order to deal with these cases, we
separate an electrostatic term from all the other non-electrostatic terms [
22
,
23
],
∆GW1j=
∆GW,el,1j+∆GW,nel,1j
, and we write
∆GW,el,1j=α−1GW,el,j−GW,el,1
in the framework of
the Debye–Hückel theory,
GW,el,j=q2
eZ2
j
8πε0εRj 1−κDRj
1+κD(Rj+a)!(14)
In this equation,
qe=
1.6
·
10
−19
C is the charge of the proton, expressed in SI units,
ε0
is the vacuum permittivity,
ε
is the relative dielectric constant of the solvent,
Zj
is the num-
ber of the elementary charges provided by the
j
-protein, which is assumed to be a spherical
macroion with radius
Rj
, and
a
is the average radius of the all the microions (including
protein counterions) in solution. Of note,
Zj
can be simply calculated as a function of pH
considering the side chain p
Ka
values of the amino acids [
24
]. The reciprocal Debye–Hückel
screening length,
κD= (
2
NAq2
eI/(ε0εkBT))1/2
is an other parameter of
GW,el,j
(
kB
is Boltz-
mann’s constant). It depends on the ionic strength due to the molar concentration
Ci
and the
charge number
zi
of all
i
-microions,
I=1
2∑iz2
iCi
. On the basis of the electroneutrality con-
dition, the molar concentration of protein counterions (assumed for the sake of simplicity to
have a charge
|zci|=
1) should be
Cci =CP∑Ns
j=1xjα−1
j|Zj|
. We can hence write
I=IS+Ici
,
where
IS
is the added ionic strength and
Ici
is the one due to counterions. Of note,
IS
is
calculated considering microions due to charged buffer molecules, if any, and microions
provided by the cosolvent, in the case they are charged species. The non-electrostatic
term
∆GW,nel,1j
includes all the other contributions to the thermodynamic stability of the
j
-protein state. Its temperature dependency, as well as the one of
∆Gexj
, is written accord-
ing to classical thermodynamics,
∆G=∆G◦+ (∆Cp−∆S◦)(T−T◦)−∆CpTlog(T/T◦)
,
where
∆G◦
and
∆S◦
are the changes of Gibbs free energy and entropy at the reference
temperature
T◦=
298.15 K, respectively, and
∆Cp
is the change of the heat capacity at
constant pressure, here considered to be independent on temperature. On the other hand,
due to thermal expansion, molar volumes are also affected by temperature. Regarding
water, according with Ref. [
25
], the molecular volume can be described by the approxi-
mation
νWb=ν◦
WbeαW(T−T◦)+ 1
2βW(T−T◦)2
, where the optimum values of the molar water
volume at
T◦
, the thermal expansivity at
T◦
and its first derivative are
ν◦
Wb=
0.018 L,
αw=
2.5
·
10
−4
K
−1
and
βw=
9.8
·
10
−6
K
−2
, respectively [
26
]. For cosolvent and protein
molar volumes, we adopt a simpler approximation, just in terms of molar volumes and
Life 2022,12, 123 7 of 25
thermal expansivities at
T◦
:
νGb=ν◦
GbeαG(T−T◦)
and
νP=ν◦
PeαP(T−T◦)
. The nominal molar
concentration of monomeric proteins (seen in Equation (10)) is
CP=XP
<ν>(15)
<ν>=νPXP+ (νWb(1−xG) + νGbxG)(1−XP)
+XP
Ns
∑
j=1
mjxjα−1
j((νWsj−νWb)φj+ (νGsj−νGb)(1−φj)) (16)
where the average molar volume
<ν>
is calculated as a function of the molar volume
occupied by water and by cosolvent in the sites of the
j
-state of the protein,
νWsj
, and
νGsj
,
respectively. In practice, only the former is considered to differ from the bulk value, since it
has been widely demonstrated that hydration water has a more compact structure than bulk
water [
27
,
28
]. Accordingly, we write
νWsj=νWb/dj
, where
dj
is the relative mass density
of hydration water, with typical values comprised in the range 1
÷
1.15. By combining
Equations (9), (12) and (13), it is straightforward to derive the cosolvent molar fraction of
the bulk solvent as a function of both the fixed sample parameters,
XP
and
xG
, and the
parameters depending on the interplay of the equilibrium processes, the molar fraction
xj
of nominal protein monomers that are forming the
j
-state and the water occupation fraction
φjof the first hydration shell of each j-state,
xGb=xG(1−XP)−XP∑Ns
j=1mjxjα−1
j(1−φj)
1−XP(1+∑Ns
j=1mjxjα−1
j)(17)
The nonlinear system of 2
Ns
equations, which includes Equations (3) and (8) (with
j=
1,
Ns
) and Equation (10) (with
j=
2,
Ns
), in which the parameters
XWb
,
CP
,
<ν>
and
xGb
are obtained from Equations (12)–(17), respectively, contains the following 2
Ns
unknown variables: xjand φj(both with j=1, Ns).
The system is solved by a numerical iterative method as described in the Section S1 of
the Supplementary Materials. In such a way, we have a method able to derive, from the
thermodynamic parameters
∆G◦
k
,
∆S◦
k
and
∆Cpk
that describe the two categories of el-
ementary processes (non electrostatic contribution of protein state formation in water
(Equation
(5)
) and water replacement of a cosolvent molecule over the surface of any
protein state (
Equation (7)
) the fraction
xj
of nominal protein monomers distributed in
the
j
-state and the fraction
φj
of the
mj
first hydration shell sites over the protein surface
occupied by water. Additionally, we are able to calculate the cosolvent molar fraction of
the bulk solvent,
xGb
, the effective constants
K1j
and the related Gibbs free energy change
∆G1j
. All these parameters are obtained as a function of the nominal protein molar fraction
XP
, the nominal binary solvent composition
xG
, the pH, the added ionic strength
IS
and
the temperature T.
2.3.2. Determination of SLDs
The results from this thermodynamic scheme allow also to calculate the SLDs of bulk
solvent and protein hydration shells. As widely discussed by Refs. [
29
,
30
], since the volume
of the cosolvent molecule is much larger than the one of water, we have to consider that
the cosolvent attached to the protein surface can in part occupy the hydration sites of
the second hydration shell. As a consequence, preferential solvation effects will change
the composition of a region in the vicinity of the protein surface, called local domain,
which will encompass the hydration sites of both the first and the second shell. More in
detail, the number of sites occupied by water and cosolvent in the first hydration shell
(corresponding to the number of water and cosolvent molecules attached to the protein
surface) are
NW,j,1 =mjφj
and
NG,j,1 =mj(
1
−φj)
, respectively. Hence, the number of
hydration sites of the second layer occupied by cosolvent molecules attached to the protein
will be
kj=mj(
1
−φj)(νGsj−νWsj)/νWb
. Indicating by
mj,2
the total number of hydration
Life 2022,12, 123 8 of 25
sites of the second layer, the ones that remain available to be occupied with the bulk
solvent (with composition
xGb
) will be
mj,2 −kj
. We can then calculate the number of
water and cosolvent molecules that occupies the available sites of the second hydration
shell, according to
NW,j,2 = (mj,2 −kj)(
1
−xGb)/(
1
+xGb(νGb/νWb−
1
))
and
NG,j,2 =
(mj,2 −kj)xGb/(
1
+xGb(νGb/νWb−
1
))
, respectively. On this basis, the cosolvent molar
fraction of the local domain is
xGldj=NG,j,1 +NG,j,2
NG,j,1 +NG,j,2 +NW,j,1 +NW,j,2 (18)
and the local domain molar volumes of water and cosolvent are
νWldj=NW,j,1νWsj+NW,j,2νWb
NW,j,1 +NW,j,2 (19)
νGldj=NG,j,1νGsj+NG,j,2 νGb
NG,j,1 +NG,j,2 (20)
Hence, the SLDs of bulk solvent and local domain are
ρ0=xGbbG+ (1−xGb)bW
xGbνGb+ (1−xGb)νWb
(21)
ρld,j=xGld jbG+ (1−xGld j)bW
xGldjνGldj+ (1−xGld j)νWldj
(22)
where
bW=reNW,e
and
bG=reNG,e
are the scattering lengths of water and cosolvent, with
NW,e
and
NG,e
being the corresponding number of electrons and
re=
0.28
·
10
−12
cm the
classical radius of the electron. Considering the intrinsic low resolution of SAXS, also due
to mobility effects over the protein surface, the calculation of both the form factors
P(q)
(Equation
(2)
) and
P(1)(q)
(Equation
(4)
) with SASMOL is performed by assigning to all the
sites of the first and the second hydration shell (their numbers are
mj
and
mj,2
, respectively)
a unique SLD, corresponding to ρld,j(Equation (22)).
2.3.3. Effective Protein–Protein Structure Factor
The protein–protein structure factor
S(q)
in the presence of a mixture of
Ns
protein
states is due to a complex interplay of the partial structure factors
Sj1,j2(q)
between any
j1
,
j2
pair of states weighted by their relative populations, which in turn depend on pair
interaction potentials
uj1,j2(r)
. Here, according to Pedersen et al. [
31
], we adopt a simpler
point of view by taking into account a unique effective radial interaction potential
u(r)
between two protein particles, irrespective of their state. This potential is described by the
HSDY (Hard-Sphere Double-Yukawian) model,
u(r) = uHS(r) + uYC (r) + uYA(r)
, which
combines a hard-sphere (HS) term,
uHS(r) = ∞r<2R
0r>2R, (23)
and two Yukawian terms, described by the equation
uYk (r) = B1kexp[−B2k(r−
2
R)]/r
.
They are a screened Coulombian (C) repulsive term, with
B1C=
4
πZ2q2
e/(ε0ε(1+κDR)2)
and
B2C=κD
, and an attractive (A) term, with
B1A=−
2
JR
and
B2A=
1
/d
. In these
equations,
R
is the average protein radius. It is calculated as an average of the protein radii
Rj
of any state, according to
R= (
1
/<α−1>)∑Ns
j=1xjα−1
jRj
, where
<α−1>=∑Ns
j=1xjα−1
j
.
The average net number of elementary electric charges is calculated in a similar man-
ner,
Z= (
1
/<α−1>)∑Ns
j=1xjα−1
jZj
. The attractive term depends on two parameters,
J
,
the energy when two proteins are at contact, (
r=
2
R
), and the scale length
d
. All attrac-
tive contributions, such as van der Waals forces, dipole-dipole or similar interactions are
Life 2022,12, 123 9 of 25
represented by
uYA(r)
. In the presence of cosolvent, which can provide variations of the
surface properties of proteins, the values of
J
and
d
can change in a way that is not easily
rationalized. Therefore, we have decided to leave the two parameters free to change for
each experimental condition investigated by SAXS. The calculus of
S(q)
on the basis of
u(r)
was carried out by using the perturbation of the Percus–Yevick (PY) structure factor,
S0(q)
, due to the two Yukawian terms, on the basis of the Random-Phase Approximation
(RPA) [32–34]. The details are shown in Section S3 of the Supplementary Materials.
2.3.4. Global-Fit of SAXS Data
On the basis of the model described in the previous sections, we are able to set a
unique fit of a batch of
Nc
SAXS curves recorded for water solutions of the protein of
interest (which can show different states) by varying protein concentration and in the
presence of different amounts of a cosolvent. This so-called global-fit can include several
series of SAXS measurements performed with distinct types of cosolvents, provided single
samples never contain two or more types of cosolvents. More specifically, SAXS curves are
labeled with
Np=
4curve parameters: protein w/v concentration at
T◦
,
c◦
, temperature,
T
, type of cosolvent, G, and its concentration at
T◦
,
C◦
G
. The task is accomplished by
minimising the merit function H=χ2+γL, where χ2is the average reduced chi-square
χ2=1
Nc
Nc
∑
k=1
1
Nq,k
Nq,k
∑
i=1
dΣ
dΩk,expt(qi)−dΣ
dΩk,theo(qi)
σk(qi)
2
(24)
In this equation,
dΣ
dΩk,expt(qi)
is the
kth
measured SAXS curve recorded over a number
Nq,k
of
q
-points,
dΣ
dΩk,theo(qi)
is the theoretical curve calculated on the basis of Equation (1)
and
σk(qi)
is the experimental standard deviation. The other term of the merit function,
L
,
is the regularization factor,
L=
2
∑
i=1
Nc
∑
k=1
Np
∑
p=11−Xi,k0
Xi,k2, (25)
which increases with the difference between the
ith
single curve fitting parameter (
i=
1, 2
refers to
J
and
d
, respectively) of the
k
-curve,
Xi,k
, and the one of the
k0
-curve,
Xi,k0
, where
k0
is the label of the curve having the same curve parameters of the
k
-curve but the
pth
(
p=
1,
Np
refers to
c◦
,
T
, G and
C◦
G
). The constant
γ
is selected in order to guarantee
that when
χ2≈
1, indicating a good fit, the product
γL
is
≈
10% of the merit function
H
.
The present model has been included in the freely available GENFIT software [35].
2.3.5. Myoglobin
According to a number of experimental as well as computational evidences [
36
–
43
],
myoglobin (MB) in solution at pH
=
5.0 and as a function of temperature can be present in
three states, native (
N
), intermediate (
I
), and unfolded (
U
). The native state is monomeric
and its form factor has been calculated on the basis of the PDB entry
1wla
[
44
]. The
corresponding form factor has been then calculated with SASMOL. The average numbers of
hydration sites in the first and in the second shell are found to be
mN=
404 and
mN,2 =
465,
respectively. The intermediate state is considered to be a compact dimer [
42
], which has
proven to maintain its active form [
36
,
38
]. Its form factor has been calculated with SASMOL
from the PDB entry
3vm9
[
38
]. The number of hydration sites are
mI=
753 and
mI,2 =
827.
The unfolded state of MB has been described by a set of 50 conformations obtained by
FOX, a home made software that preserves the secondary structure of a native structure
and randomly modifies the Ramachandran angles of the residues that do not belong to
helices or strands [
45
]. Steric clashes are avoided by controlling the overlap between the
van der Waal spheres associated to each atom. The input PDB entry
1wla
has been adopted.
The average form factor has been then calculated with SASMOL. The number of hydration
Life 2022,12, 123 10 of 25
sites in the first and in the second shell are
mU=
844 and
mU,2 =
1141, respectively. The
form factors of the
Ns=
3 states of MB are shown in the Figure S1 of the Supplementary
Materials in the form of semi-logarithmic and Kratky plots, together with the coupling
function
β(q)
. The number of elementary charges for the
N
-state,
ZN
, calculated on the
basis of the primary sequence of MB and as a function of pH are reported in Table S1 of the
Supplementary Materials. For the
I
and
N
states, we simply fixed
ZI=
2
ZN
and
ZU=ZN
.
2.3.6. Insulin
Insulin (IN) in water solution has been found to mainly form
Ns=
4 folded states, cor-
responding to monomers (1), dimers (2), tetramers (4) and hexamers (6) [
46
–
53
]. Monomers
are formed by two polypeptide chains, named A and B, linked by two disulfide bridges.
It is known that insulin is present in its hexameric form, which is the best way to store
and stabilize the functional monomers. Once hexamers dissociate into monomers, dimers,
and tetramers, they can be transported in the bloodstream and they are ready to exert
their physiological activity [
54
]. The basic processes of oligomers’ formation have been
identified as follows [46],
2 I1I2
2 I2I4
I2+I4I6
(26)
Related thermodynamic constants have been determined at room temperature. They
are
¯
K12 =
2.22 10
5
M
−1
,
¯
K24 =
40 M
−1
and
¯
K46 =
220 M
−1
[
46
,
47
]. These constants are
connected to the effective constants defined in Equation (10) by the following relationships:
¯
K12 =K2
12
,
¯
K24 = (K14/K12)4
and
¯
K46 =K6
16/(K4
14K2
12)
. Form factors of the different states
have been calculated with SASMOL on the basis of the PDB entry
3aiy
[
55
]. For the
monomer, only chains A and B have been considered, for the dimer the chains A–D, for the
tetramer the chains A–H and for the hexamer the whole PDB file (A-L chains). Figure S2
of the Supplementary Materials reports semi-logarithmic and Kratky plots of the form
factors of the
Ns=
4 states and their coupling function
β(q)
. For the monomer, the average
numbers of hydration sites in the first and in the second shell are found to be
m1=
199 and
m1,2 =
268, respectively. For the dimer, the tetramer and the hexamer corresponding values
are:
m2=
320,
m2,2 =
385;
m4=
548,
m4,2 =
625;
m6=
741,
m6,2 =
739. In Table S1 of
the Supplementary Materials the number of elementary charges for the 1-state,
Z1
, which
has been obtained considering the primary sequence of IN and the pH of the solution are
reported. For the other states we have simply fixed Zj=αjZ1.
3. Results
3.1. Myoglobin
SAXS curves recorded at the Elettra synchrotron (Austrian SAXS beam-line) for sam-
ples of myoglobin in the presence of five different ExtremoChem modified sugars, by vary-
ing protein or modified sugar concentration as well as temperature, are shown in Figure 3
in the form of semi-logarithm plots. To note, several curves show an upward curvature at
low
q
, suggesting a predominant long-range attraction among the protein particles. Kratky
plots, shown in Figure S3 of the Supplementary Materials, reveal, on the one hand, the pres-
ence of a main peak at a
q
-position that changes as a function of sample composition and
temperature and, on the other hand, the absence of an asymptotic behavior at high
q
. These
features suggest that the aggregation number of myoglobin can change with sample com-
positions and that most of the protein states are compact, also at the highest temperatures.
Hence, since the information content of the SAXS dataset on the
U
-state is low, the ensemble
of unfolded conformations calculated with the FOX method [
45
] has been left fixed. On
the basis of these preliminary observations, the whole set of
Nc=
92 SAXS curves has
been globally analyzed by using the new method introduced in Section 2.3. Three possible
myoglobin states have been taken into account: two of them, the native monomer (
N
) and
the intermediate dimer (
I
), are biologically active states, whereas the monomeric unfolded
Life 2022,12, 123 11 of 25
(
U
) state represents a denatured (inactive) form of the protein. The full list of the model
parameters, together with their short descriptions and the validity range we have defined
is reported in Table S2 of the Supplementary Materials. Best fitting curves are reported as
solid lines in Figure 3: the high quality of the fit, in the entire
q
-range, can be appreciated.
By fixing the dimensionless regularization parameter
γ=
10
−7
, the overall merit function
H=
1.15 has been obtained, corresponding to
χ2=
1.03 (
γL=
0.12; see Equation (25)).
The thermodynamic fitting parameters obtained by the simultaneous analysis of the whole
set of SAXS data are reported in Table 1.
10−4
10−2
100
102
104
106
108
1010
1012
1014
0 0.1 0.2 0.3
T=25° Cc°=2 g/L
dΣ/dΩ(q) (cm−1)
q (Å−1)
0
1
0.05
2
0.1
3
0.25
4
0.05
5
0.1
6
0.25
7
0.05
8
0.25
9
0.05
10
0.1
11
0.25
12
0.05
13
0.1
14
0.25
0 0.1 0.2 0.3
T=35° Cc°=2 g/L
0
1
0.05
2
0.1
3
0.25
4
0.05
5
0.1
6
0.25
7
0.05
8
0.1
9
0.25
10
0.05
11
0.1
12
0.05
13
0.1
14
0.25
0 0.1 0.2 0.3
T=60° Cc°=2 g/L
0
1
0.05
2
0.1
3
0.05
4
0.1
5
0.25
6
0.05
7
0.1
8
0.25
9
0.05
10
0.1
11
0.25
12
0.05
13
0.1
14
0.25
0 0.1 0.2 0.3
T=25° Cc°=10 g/L
0
1
0.05
2
0.1
3
0.25
4
0.05
5
0.1
6
0.05
7
0.1
8
0.25
9
0.05
10
0.1
11
0.25
12
0.05
13
0.1
14
0.25
0 0.1 0.2 0.3
T=35° Cc°=10 g/L
0
1
0.05
2
0.1
3
0.25
4
0.05
5
0.1
6
0.25
7
0.05
8
0.1
9
0.25
10
0.05
11
0.1
12
0.25
13
0.05
14
0.1
15
0.25
0 0.1 0.2 0.3
T=60° Cc°=10 g/L
0
1
0.05
2
0.1
3
0.25
4
0.05
5
0.1
6
0.25
7
0.05
8
0.1
9
0.25
10
0.05
11
0.1
12
0.25
13
0.05
14
0.1
15
0.25
Figure 3.
Experimental SAXS curves of MB in 10 mM phosphate buffer (pH
=
5) with and without
ExtremoChem modified sugar superimposed with the best fits obtained with GENFIT (solid lines).
Colors refer to the following conditions: no-modified sugar (black), EC312 (red), EC101 (green),
EC311 (blue), EC202 (magenta), EC212 (cyan). Whenever present, the modified sugar concentration
is reported on the right side of each curve in molar unit. Each column refers to a fixed temperature
and MB concentration, as indicated on the top. Curves are multiplied by the factor 10
k
, with
k
being
reported on the top right of each curve. Experimental standard deviations are reported as error bars
every 10 points, for clarity.
First of all, the results indicate that, in water at pH
=
5, the
NI
transition of myoglobin
from native monomer to intermediate dimer has a low non-electrostatic reference Gibbs free
energy barrier (
∆G◦
W,nel,N I = (
2.95
±
0.03
)
kJ mol
−1
, Table 1) when compared to the value
related to the
NU
transition from native monomer to unfolded monomers (
∆G◦
W,nel,NU =
(
167
±
3
)
kJ mol
−1
). Another fitting parameter, which is relevant in determining the effect
of temperature, is the reference entropy variation,
∆S◦
Wj1j2
, related to the two
NI
and
NU
processes. The
NI
transition from native monomer to intermediate and still active
dimer causes an increase in reference entropy, an effect that can be explained considering
that this process determines the release of hydration water to the bulk solution. Indeed,
since there are 404 hydration water molecules in the monomeric
N
-state and 753 in the
dimeric
I
-state (see Section 2.3.5), 28 molecules of water for each monomer are released in
solution when the dimer is formed, resulting in an increase in the reference entropy up to
(
564
±
6
)
J mol
−1
K
−1
(Table 1). On the other hand, when monomeric myoglobin switches
from native to unfolded state (
NU
transition), a different scenario emerges. Although in
the
U
-state the protein shell is surrounded by 844 water molecules, a value much higher if
compared to 404 molecules that encircle the
N
-state, with a concomitant decrease in entropy,
the formation of an unfolded disordered state is surely accompanied by a huge increase in
Life 2022,12, 123 12 of 25
entropy, so that the balance between the two phenomena leads to the observed large and
positive value of the reference entropy change
∆S◦
WNU = (
1600
±
500
)
J mol
−1
K
−1
, Table 1.
The almost zero variation of the
∆CpWNI
and the large and positive value
∆CpWNU =
(
8400
±
400
)
J mol
−1
K
−1
are expected, considering the large accessible surface area of the
protein unfolded state [
56
]. The other fitting parameters reported in Table 1regard the
changes of reference Gibbs free energy, reference entropy and heat capacity at constant
pressure that occur when a modified sugar molecule bound to the myoglobin surface in
each of the three envisaged
j
-states (
N
,
I
and
U
) is replaced by a water molecule. In general,
we observe that whereas the experimental uncertainty of
∆G◦
exj
is low (on average in
the order of 1%), the ones of
∆S◦
exj
and
∆Cpexj
are much larger, a result that can be in
part explained considering that we have investigated our samples only at three different
temperatures. These high uncertainties reflect the correctness of the global-fit SAXS data
analysis method (see details in Section S2 of the Supplementary Materials), which does not
lead to an overestimation of the parameters when their information content in the dataset
is low.
Table 1.
Thermodynamic fitting parameters obtained by the global-fit of MB SAXS curves shown in
Figure 3.
∆G◦
W,nel,j1j2
,
∆S◦
Wj1j2
and
∆CpWj1j2
: changes of non-electrostatic reference Gibbs free energy,
reference entropy and heat capacity at constant pressure, respectively, occurring at the
j1j2
transition;
∆G◦
exj
,
∆S◦
exj
and
∆Cpexj
: changes of reference Gibbs free energy, reference entropy and heat capacity
at constant pressure, respectively, occurring at the modified sugar–water exchange over the j-state.
j1j2∆G◦
W,nel,j1j2
∆S◦
Wj1j2
∆CpWj1j2
kJ mol−1J mol−1K−1J mol−1K−1
NI 2.95 ±0.03 564 ±6 0 ±2
NU 167 ±3 1600 ±500 8400 ±400
j∆G◦
exj∆S◦
exj∆Cpexj
kJ mol−1J mol−1K−1J mol−1K−1
EC312
N1.5 ±0.2 −10 ±10 −7±3
I−8±1 10 ±10 −9±6
U−8.7 ±0.5 −10 ±9 2 ±3
EC101
N2.2 ±0.1 −9±4 3 ±3
I−8.5 ±0.7 9 ±6 4 ±7
U−4±1−10 ±7 0 ±8
EC311
N−0.4 ±0.6 2 ±4 1 ±5
I−2.4 ±0.8 9 ±9 3 ±7
U−3±4−9±2−1±4
EC202
N−3±3−10 ±10 0 ±4
I−8.5 ±0.5 1 ±4 7 ±6
U−8±1 6 ±9−7±7
EC212
N−1.3 ±0.4 9 ±7−7±8
I−7±2−8±8 3 ±3
U−9.3 ±0.5 3 ±3−2±4
Life 2022,12, 123 13 of 25
The meaning of all the fitting parameters shown in Table 1can be better appreciated by
considering the temperature dependency of the most relevant physical-chemical parameters
inherent to the adopted model that have been derived by them. Their trends are shown
in Figure 4. Notice that in this figure the colors and the thickness (together with the
symbols) of the curves have been assigned according to the type and the concentration
of the modified sugar, respectively, whereas dotted and solid lines refer to 2 or 10 g/L
myoglobin concentration, respectivley. Panels
A
,
B
and
C
report the molar fractions of the
nominal myoglobin monomers distributed into the three different
N
,
I
or
U
states (
xN
,
xI
and
xU
, respectivley). It is possible to appreciate that, even if at 25
◦
C the
N
monomers are
the only fraction present in solution, the temperature rise gradually affects the protein state,
resulting in the decay of the monomeric
N
-state and the concomitant formation of dimeric
I
-state. It is known that the oxygen binding rate constant of myoglobin dimer is similar to
that of the monomer, whereas the oxygen dissociation rate constant of the dimer is smaller
than that of the monomer [
38
]. Hence, our results could provide suggestions concerning
monomer–dimer function and role. However, the particular pH and buffer conditions
which do not resemble in vivo conditions, suggest not to infer them by this experimental
set-up. Of note, although in our experiment we did not reach temperatures higher than
60
◦
C, the adopted model with the fitting parameters derived by the set of SAXS data allows
to predict that at higher temperatures the population of the
U
-state grows at the expense
of the
I
-state. The fractions
φj
of first hydration shell sites of the
j
protein state occupied
by water are reported in panels
D
,
E
and
F
. Since in our samples the presence of water is
dominant, values of
φj
are very close to 1, with small but detectable differences, depending
on the modified sugar type. Such small differences, on the basis of Equation (10), are
sufficient to describe the modified sugar-induced modification of the effective equilibrium
constant
KNj
describing transition from the
N
-state to the
j
-state (
j=I
,
U
): results are
shown in Figure 4, panels
G
and
H
. Corresponding Gibbs free energy changes
∆GNj
, which
comprise both the electrostatic and the non-electrostatic contributions, are shown as a
function of
T
in panels
I
and
J
. Exchange modified sugar–water equilibrium constants
Kexj
for each of the three
j
-states are reported in panels
K
,
L
and
M
and corresponding
Gibbs free energy changes
∆Gexj
are in panels
N
,
O
and
P
. Notice that both parameters do
not depend on protein or modified sugar concentration, but only on modified sugar type.
Finally, in panels
Q
and
R
, we report the depth of the attraction protein–protein potential
J
and its scale length d, which have been treated as single-curve fitting parameters.
Protein–protein structure factors
S(q)
(Equation (S1) of the Supplementary Materials),
calculated with the fitting parameters and included in the fitted
dΣ
dΩk,expt(qi)
function
(Equation
(24)
), are plotted in Figure S4 of the Supplementary Materials. Corresponding
effective radial interaction potentials
u(r)
are reported in Figure S5 of the Supplementary
Materials.
Other fitting parameters of the model are the relative densities of hydration water,
dj
. We have found similar values for each of the
Ns=
3 MB states, with an average value
of 1.07
±
0.02. The average radius
Rj
of
N
,
I
and
U
states found by the global-fit are
(
17.0
±
0.2
)
Å,
(
26.7
±
0.3
)
Å and
(
43
±
2
)
Å, respectively. The ionic strength due to the
buffer results (10.0 ±0.1)mM.
We discuss in the next paragraphs results obtained in the absence of modified sugars
and in the presence of each of the five investigated modified sugars.
Life 2022,12, 123 14 of 25
0
0.2
0.4
0.6
0.8
1
1.2 A
xN
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1B
xI
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4 C
xU
0.986
0.988
0.99
0.992
0.994
0.996
0.998
1D
φN
0.997
0.9975
0.998
0.9985
0.999
0.9995
1E
φI
0.99
0.992
0.994
0.996
0.998
1
1.002
1.004
1.006
1.008
25 30 35 40 45 50 55 60 65 70 75 80
F
φU
10−3
10−2
10−1
100
101
102
103
104
105G
KNI (M−1/2)
10−25
10−20
10−15
10−10
10−5
100
105
1010 H
KNU
−40
−30
−20
−10
0
10
20 I
∆GNI (kJ/mol)
−100
−50
0
50
100
150
200 J
∆GNU (kJ/mol)
10−1
100
101K
Kex N
100
101
102
25 30 35 40 45 50 55 60 65 70 75 80
L
Kex I
100
101
102M
Kex U
−6
−5
−4
−3
−2
−1
0
1
2
3N
∆Gex N (kJ/mol)
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1 O
∆Gex I (kJ/mol)
−11
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
0P
∆Gex U (kJ/mol)
−100
0
100
200
300
400
500
600
700 Q
J (kJ/mol)
−20
−10
0
10
20
30
40
50
60
25 30 35 40 45 50 55 60 65 70 75 80
R
temperature (°C)
d (Å)
Figure 4.
Temperature behaviors of the most relevant physical-chemical parameters (panels
A
–
R
)
obtained by the global-fit of MB SAXS curves shown in Figure 3. Color refers to: no-modified sugar
(black), EC312 (red), EC101 (green), EC311 (blue), EC202 (magenta), and EC212 (cyan). Thickness
refers to: 0.05 M (thin), 0.10 M (intermediate), and 0.25 M (thick). Point-type refers to: no-modified
sugar (square), 0.05 M (circle), 0.10 M (up-sided triangle), and 0.25 M (down-sided triangle). Dotted
and solid lines refers to c◦=2 g/L and c◦=10 g/L, respectively.
3.1.1. Myoglobin without and with Modified Sugar
In the absence of modified sugars, MB at 2 g/L maintains its monomeric form (
N
-state)
up to about 60
◦
C (Figure 4, panel
A
, black dotted lines), whereas the molar fraction of
nominal MB monomers that are forming dimers (
I
-states) reaches the maximum peak of
xI≈
0.3 (Figure 4, panel
B
, black dotted lines). At higher temperatures, dimers sharply
disappear and the unfolded
U
state becomes the predominant species in solution (Figure 4,
panel
C
, black dotted lines). On the contrary, at 10 g/L MB starts its transition from
monomer to dimer at 45
◦
C (Figure 4, panel
A
, black solid lines) and up to 65
◦
C the molar
fraction of nominal MB monomers that are forming dimers is as large as
xI≈
0.9 (Figure 4,
panel B, black lines).
The addition of the modified sugars produces different effects depending on the type
of the compound used, but it is in general evident that when the cosolvents are used
together with the highest concentration of protein, MB tends to have a marked transition
from monomer to dimer and it becomes unfolded at temperature higher than 70
◦
C. On the
other hand, MB at 2 g/L shows a different behavior, leaving out the dimeric form, except for
the two cosolvents that form ionic species in solution (EC101 and EC202).
Life 2022,12, 123 15 of 25
3.1.2. Myoglobin with EC312
Myoglobin at 2 g/L in the presence of EC312 maintains its native monomeric state
with a slow transition to dimers at
≈
60
◦
C, which slightly depends on EC312 concentration
(Figure 4, panel
A
, red lines). Dimers (
I
-state) do not overcome the fraction
xI≈
0.2 of
the myoglobin molecules in solution and gradually decrease and disappear at 65
◦
C with
the development of the unfolded state (Figure 4, panel
B
, red lines). On the contrary,
myoglobin at 10 g/L in the presence of EC312 is prone to form dimers at 50
◦
C when the
EC312 concentration is 0.05 M, leading to a solution rich in dimers (
xI≈
0.9) that unfold at
75
◦
C. At increasing concentration of EC312, the
NI
transition shifts from 55
◦
C to 70
◦
C,
twenty degrees more than what occurs to the protein without modified sugar. These results
are also described by the behavior of the effective equilibrium constant
KNI
(Figure 4,
panel
G
, red curves). For both 2 and 10 g/L MB concentrationa (dotted and solid red
curves),
KNI
, with an increasing concentration of EC312, is lower than the value without
EC312 (black lines). This aspect underlines the tendency of MB with EC312 to maintain its
monomeric
N
-state for temperatures higher than the protein without EC312. Moreover,
the temperature increase leads to higher values of
KNI
, corresponding to a a preference
for the dimeric state. For MB in the monomeric
N
-state, the exchange constant
KexN
owns
values lower than 1 (Figure 4, panel
K
, red line), indicating a preference to be surrounded
by EC312. On the other hand, the dimeric and the unfolded states show an increase in
Kexj
(panels
L
(
j=I
) and M (
j=U
)), suggesting the preference of these MB states to be solvated
by water. The effect of EC312 in modifying protein–protein long-range interactions is not
marked, as can be observed by comparing the structure factors
S(q)
shown in Figure S4 of
the Supplementary Materials (red and black curves) and the corresponding
u(r)
reported
in Figure S5 of the Supplementary Materials. Of note, at 60
◦
C and 2 g/L myoglobin,
a condition close to the
NU
transition, stronger attractive interactions among proteins have
been seen, both with and without EC312, whereas at 60
◦
C and 10 g/L, when most of the
proteins are I-dimers, a less marked attraction is seen.
3.1.3. Myoglobin with EC101
Depending on its concentration, EC101 strongly affects the transition of MB from
native monomer to intermediate dimer (Figure 4, panels
A
and
B
, green lines). While,
at lower modified sugar concentration, the decay of
N
-monomers in favor of
I
-dimers
begins
≈
15
◦
C earlier than for the samples without EC101 at both 2 or 10 g/L myoglobin,
by increasing the EC101 concentration this transition occurs at higher temperatures. In par-
ticular, dimers begin to be present in solution at
≈
40
◦
C and subsequently totally substitute
the
N
-monomers. The unfolded state is not present, except at temperatures above 80
◦
C
and with lower concentration of modified sugar. The trends of the effective constant
KNI
(Figure 4, panel
G
) also confirms that by increasing EC101 concentration, especially at
10 g/L, the protein tends to remain in the monomeric
N
-state at higher temperatures than in
the absence of EC101. Concerning the unfolded state, the very low values of
KNU
(Figure 4,
panel
H
) show that there is no propensity for the protein to unfold except for temperatures
higher than
≈
80
◦
C and in presence of the lowest EC101 concentration. The exchange
constant
Kexj
varies according to the type of protein state. When MB is the
N
state,
KexN
is less than one (Figure 4, panel
K
, green line), showing its preference to be surrounded
by modified sugar, while for the intermediate and the unfolded states (panels
L
and
M
,
green lines),
Kexj
is greater than one, underlining the preference of the protein in such states
to be surrounded by water. Likewise the EC312 case, also EC101 shows weak effects in
modifying protein–protein long-range interactions (Figures S4 and S5 of the Supplementary
Materials, green and black curves), confirming the presence of more marked attractions at
60 ◦C and 2 g/L myoglobin, which are weaker at 60 ◦C and 10 g/L.
3.1.4. Myoglobin with EC311
Myoglobin, at 2 and 10 g/L, in the presence of EC311, retains its monomeric
N
-state
up to 55
◦
C and 45
◦
C, respectively (Figure 4, panels
A
and
B
, blue lines), similarly to
Life 2022,12, 123 16 of 25
the protein in the absence of EC311, showing only a slight dependence on the EC311
concentration. At 2 g/L and in the presence of EC311, myoglobin appears to be present
mainly in the form of
N
-monomer, except for a small gap between 55
◦
C and 70
◦
C, in which
a small amount of dimer starts to grow, but it does not exceed the fraction
≈
0.3 of the
particles in solution. At 70
◦
C all dimers formed with myoglobin 2 g/L are unfolded, while,
at MB 10 g/L,
I
-dimers’ fraction reach
≈
0.9 and then disappear, with an increment of the
unfolded state at 75
◦
C. The equilibrium constant
KNI
(Figure 4, panel
G
, blue curves)
slightly depends on EC311 concentration, which in turn resembles the one of protein in
absence of EC311 (black lines). The results indicate that, with increasing quantities of
EC311, the value of
KNI
decreases, highlighting a tendency of the protein to be present in
its monomeric
N
-state at higher temperatures in respect to the protein in the absence of
EC311. A similar behavior is found also during the transition
NU
: the low
KNU
values
(Figure 4, panel
H
, blue curves) confirm the propensity of the protein, at low temperatures,
to be present in the
N
-state until 60
◦
C. The exchange constant
Kexj
is close to 1 when the
protein is present in the
N
-state (Figure 4, panel
K
, blue curve), suggesting that there is no
preference to be surrounded by water or by EC311. On the other hand, when we consider
the intermediate and the unfolded state, the
Kexj
values rise slightly (Figure 4, panels
L
and
M
, blue curves), suggesting a preference of MB in these states to be surrounded by water.
Additionally, for EC311, more pronounced effects on protein–protein long-range attractions
(Figures S4 and S5 of the Supplementary Materials, blue curves) are seen at 60
◦
C and 2 g/L
myoglobin and moderate effects are seen both at 60
◦
C and 10 g/L and at 35
◦
C and 2 g/L.
3.1.5. Myoglobin with EC202
In the presence of EC202, the behavior of MB at 2 and 10 g/L is quite similar (Figure 4,
panels
A
and
B
, magenta lines), showing a bigger shift if compared to the protein with-
out EC202, which increases additionally as a function of the EC202 concentration. This
means that MB switches from
N
-monomer to dimer at lower temperatures with respect
to the protein without EC202 (black lines). The transition occurs at around 40
◦
C for MB
10 g/L, ten degrees before the normal transition temperatures of the protein without EC202.
A bigger effect is evident for MB 2 g/L, when the protein, in presence of EC202, has the
NI
transition that occurs at 45
◦
C, twenty degrees before the protein without modified sugar in
solution. The unfolded fraction is almost absent, with a slight onset at the lowest modified
sugar concentrations at around 80
◦
C. The trends of
KNI
are almost independent on MB
concentration (Figure 4, panel
G
, magenta lines) and only slightly dependent on EC202
concentration. The results confirm the tendency of the protein to be in the intermediate state
at lower temperatures compared to what happens in absence of EC202. The transition from
the native to unfolded state, on the other hand, is disadvantaged as the
KNU
value is almost
constantly lower than 1, except for temperatures higher than 80
◦
C (Figure 4, panel
H
,
magenta lines). As in the EC312 case, also with EC202 there is a slight dependence on the
modified sugar concentration, without any effect due to protein concentration. Indeed,
curves of MB 2 and 10 g/L are almost superimposed.
Kexj
, which indicates the protein
preference to be surrounded by water or modified sugar, is much greater than 1 in each
of the three envisaged states. In particular, a slight decreasing trend of the
Kexj
parameter
can be noted as a function of temperature, which, however, is not considered very relevant.
The modified sugar EC202 shows, in general, week protein–protein long-range attractions
(Figures S4 and S5 of the Supplementary Materials, magenta curves), the most relevant
occurring at 60 ◦C both at 2 and 10 g/L myoglobin.
3.1.6. Myoglobin with EC212
Myoglobin at 2 or 10 g/L, in the presence of EC212, retains the
N
state up to 55
◦
C and
45
◦
C, respectively, showing only a slight dependence on the EC212 concentration (Figure 4,
panel
A
and
B
, cyan curves). While MB at 2 g/L does not show a fraction of dimers greater
than
xI≈
0.3, at 10 g/L MB, the dimers’ fraction reaches
≈
0.9. In the first case (2 g/L MB),
at around 70
◦
C the dimer has completely disappeared, replaced by the unfolded state,
Life 2022,12, 123 17 of 25
while at 10 g/L, a similar behavior happens at temperatures above 75
◦
C. Both
xN
and
xI
curves follow a trend that is very similar to that of protein in absence of modified sugars
(black lines). The effective equilibrium constants
KNI
(Figure 4, panel
G
, cyan curves) are
almost overlapping to the values in absence of EC212 (black lines). The exchange constant
Kexj
is always greater than 1 for each of the considered states (
N
,
I
and
U
), highlighting a
constant preference of the protein to be surrounded by water molecules.
3.2. Insulin
SAXS curves recorded as a function of temperature for 2 g/L insulin in the presence
of two modified sugars, EC312 and EC101, are shown in form of semi-logarithm plots in
Figure 5. We first observe that several curves show an upward curvature at low
q
, indicating
the prevalence of attraction forces at long range among the particles. In Figure S6 of the
Supplementary Materials, Kratky plots of the experimental SAXS curves are shown: in all
cases the presence of a main peak and the absence of asymptotic trends at high
q
revels the
presence of compact IN shapes, with possible different aggregation states. On this basis,
the simultaneous analysis of the
Nc=
40 SAXS curves shown in Figure 5with the model
introduced in Section 2.3 has been carried out by considering four possible states: monomer
(1), dimer (2), tetramer (4), and hexamer (6). Table S3 of the Supplementary Materials
reports the complete list of the model parameters, their description and the validity range.
10−4
10−2
100
102
104
106
0 0.1 0.2 0.3
T=25° C
dΣ/dΩ(q) (cm−1)
q (Å−1)
0
0.05
1
0.1
2
0.25
3
0.05
4
0.1
5
0.25
0 0.1 0.2 0.3
T=35° C
0
1
0.05
2
0.1
3
0.25
4
0.05
5
0.1
0 0.1 0.2 0.3
T=40° C
0
1
0.05
2
0.1
3
0.25
4
0.05
5
0.1
6
0.25
0 0.1 0.2 0.3
T=45° C
0
1
0.05
2
0.1
3
0.25
4
0.05
5
0.1
6
0.25
0 0.1 0.2 0.3
T=55° C
0
1
0.05
2
0.1
3
0.25
4
0.05
5
0.1
6
0.25
0 0.1 0.2 0.3
T=60° C
0
1
0.05
2
0.1
3
0.25
4
0.05
5
0.1
6
0.25
Figure 5.
Experimental SAXS curves of 2 g/L IN in 10 mM phosphate buffer (pH
=
3) with and
without ExtremoChem modified sugar superimposed with the best fits obtained with GENFIT (solid
lines). Colors refer to the following conditions: no-modified sugar (black), EC312 (red), EC101 (green).
Whenever present, the modified sugar concentration is reported on the right side of each curve in
molar unit. Each column refers to a fixed temperature, as indicated on the top. Curves are multiplied
by the factor 10
k
, with
k
being reported on the top right of each curve. Experimental standard
deviations are reported as error bars every 10 points, for clarity.
Fitting curves, shown as solid lines in Figure 5, are well superimposed to the exper-
imental curves in the entire
q
-range. The regularization parameter
γ
has been fixed to
10
−7
, leading to a merit function
H=
0.825 and a corresponding
χ2=
0.764 (
γL=
0.061,
Equation (25)).
The main thermodynamic fitting parameters are reported in Table 2. We first ob-
serve that the non-electrostatic contribution of the reference Gibbs free energy changes,
∆¯
G◦
W,nel,j1j2
, related to the three processes shown in scheme
(26)
, occurring in water at
pH
=
3, are always negative, suggesting the presence of mechanisms other than charge-
charge interactions that favor the formation of IN oligomers. We also notice that the
reference entropy changes related to the three processes are positive, a results that can be
understood considering the release of water molecules in the bulk when these oligomers
are formed. Indeed, according to the number of waters sites found by SASMOL in the first
hydration shell of the four species (Section 2.3.6), the numbers of water that are released
due to the formation of dimers, tetramers or hexamers are are 78, 92, and 127, respectively.
The heat capacities at constant pressure are found to be negative (Table 2) and affected by a
quite large uncertainty (
≈
750 J mol
−1
K
−1
). According to Ref. [
57
], negative values of heat
Life 2022,12, 123 18 of 25
capacity change are due to the fragility of hydrogen bonds between water molecules at
the hydrophobic interfaces. However, of all the major thermodynamic variables measured
for proteins, heat capacity is the one with the most different set of definitions and the
richest set of implications for protein folding and binding. Its sign can distinguish apolar
from polar solvation, and it imparts a temperature dependence to entropy and enthalpy
that may change their signs and determine which of them will dominate [
58
]. The other
thermodynamic parameters shown in Table 2regards the modified sugar–water exchange
in the surface of the four states of insulin that can be found in solution. The reference
Gibbs free energy changes are obtained with low standard deviations (in the order of few
percent), whereas larger uncertainties have been found for the reference entropy and heat
capacity at constant pressure changes, confirming, such as for the MB case, that only a
rough estimation of them can be derived from the SAXS dataset.
Table 2.
Thermodynamic fitting parameters obtained by the global fit of IN SAXS curves shown in
Figure 5.
∆¯
G◦
W,nel,j1j2
,
∆¯
S◦
Wj1j2
and
∆¯
CpWj1j2
: changes of non-electrostatic reference Gibbs free energy,
reference entropy and heat capacity at constant pressure, respectively, occurring at the
j1j2
transition
(Equation
(26)
);
∆G◦
exj
,
∆S◦
exj
and
∆Cpexj
: changes of reference Gibbs free energy, reference entropy
and heat capacity at constant pressure, respectively, occurring at the modified sugar–water exchange
over the j-state.
j1j2∆¯
G◦
W,nel,j1j2
∆¯
S◦
Wj1j2
∆¯
CpWj1j2
kJ mol−1J mol−1K−1J mol−1K−1
12 −25.4 ±0.3 302 ±3−5200 ±700
24 −16 ±1 60 ±10 −100 ±800
46 −28.5 ±0.3 396 ±4−6400 ±700
j∆G◦
exj∆S◦
exj∆Cpexj
kJ mol−1J mol−1K−1J mol−1K−1
EC312
1−9.3 ±0.8 2 ±5 0 ±4
2 1.5 ±0.3 10.0 ±0.1 3 ±5
4−8±2 8 ±5−5±6
6−9.3 ±0.1 −1±5−2±4
EC101
1−9.7 ±0.1 6 ±7 8 ±9
2−9.5 ±0.4 4 ±9−9.5 ±0.2
4 4.3 ±0.2 −5±2−10 ±2
6 3.3 ±0.4 −8±2−9±6
To fully understand the meaning of the fitting results, we report in Figure 6the
temperature behavior of all the physical-chemical parameters of the model derived by the
fitting parameters. Of note, black curves refer to samples without modified sugar, whereas
red and green curves are devoted to EC312 and EC101 compounds, respectively. In detail,
panel
A
–
D
show the trends of the four fractions
x1
,
x2
,
x4
and
x6
, respectivley. Panels
E
–
H
reports the fraction
φj
of first hydration shell occupied by water in the
j
-state (
j=
1, 2, 4, 6).
Effective equilibrium constants of the three processes reported in scheme
(26)
are shown in
panels
I
–
K
and corresponding Gibbs free energy changes (including both non-electrostatic
and electrostatic terms) in panels
L
–
N
. Regarding the modified sugar–water exchange
processes, equilibrium constants and Gibbs free energy changes are reported in panels
Q
–
T
and
U
–
X
, respectively. Finally, panels
O
and
P
show the trend of the depth
J
and the
scale length
d
of the long-range protein–protein attractive potential, which are free fitting
parameters of each of the SAXS investigated curves.
Life 2022,12, 123 19 of 25
0
0.2
0.4
0.6
0.8
1
1.2 A
x1
0
0.2
0.4
0.6
0.8 B
x2
0
0.2
0.4
0.6
0.8
1
1.2 C
x4
0
0.2
0.4
0.6
0.8 D
x6
0.99965
0.9997
0.99975
0.9998
0.99985
0.9999
0.99995
1
1.00005 E
φ1
0.99
0.991
0.992
0.993
0.994
0.995
0.996
0.997
0.998
0.999
1F
φ2
0.97
0.975
0.98
0.985
0.99
0.995
1G
φ4
0.98
0.982
0.984
0.986
0.988
0.99
0.992
0.994
0.996
0.998
1
25 30 35 40 45 50 55 60
H
φ6
101
102
103
104
105I
K
−
12 (M−1)
100
102
104
106
108
1010 J
K
−
24 (M−1)
10−2
10−1
100
101
102
103
104
105
106K
K
−
46 (M−1)
−30
−28
−26
−24
−22
−20
−18
−16
−14
−12
−10 L
∆G
−
12 (kJ/mol)
−70
−60
−50
−40
−30
−20
−10
0M
∆G
−
24 (kJ/mol)
−35
−30
−25
−20
−15
−10
−5
0
5
10
15 N
∆G
−
46 (kJ/mol)
180
200
220
240
260
280
300
320
340 O
J (kJ/mol)
6
6.5
7
7.5
8
8.5
9
9.5
25 30 35 40 45 50 55 60
P
d (Å)
101
102Q
Kex 1
10−1
100
101
102R
Kex 2
10−1
100
101
102S
Kex 4
10−1
100
101
102T
Kex 6
−11
−10.5
−10
−9.5
−9
−8.5
−8
−7.5 U
∆Gex 1 (kJ/mol)
−12
−10
−8
−6
−4
−2
0
2V
∆Gex 2 (kJ/mol)
−10
−8
−6
−4
−2
0
2
4
6W
∆Gex 4 (kJ/mol)
−10
−8
−6
−4
−2
0
2
4
25 30 35 40 45 50 55 60
X
temperature (°C)
∆Gex 6 (kJ/mol)
Figure 6.
Temperature behaviors of the most relevant physical-chemical parameters (panels
A
–
X
)
obtained by the global-fit of 2 g/L IN SAXS curves shown in Figure 5. Color refers to: no-modified
sugar (black), EC312 (red), EC101 (green). Thickness refers to: 0.05 M (thin), 0.10 M (intermediate),
0.25 M (thick). Point-type refers to: no-modified sugar (square), 0.05 M (circle), 0.10 M (up-sided
triangle), 0.25 M (down-sided triangle).
These temperature trends firstly show that 2 g/L insulin molecules at pH
=
3, in the
absence of modified sugars (black curves), are mainly present in monomeric or dimeric state,
with a minimum x1≈0.8 at ≈40 ◦C and a maximum x1≈1 at the highest temperatures.
The relative densities of hydration water have been found very similar for each of
the
Ns=
4 IN states, with an average value of 1.06
±
0.01. Unique fitted values of the
Life 2022,12, 123 20 of 25
average radius
Rj
of 1, 2, 4 and 6 state are
(
9.6
±
0.1
)
Å,
(
13.2
±
0.5
)
Å,
(
23.3
±
0.2
)
Å and
(
27.0
±
0.3
)
Å, respectively. The buffer contribution to the ionic strength is
(
4.1
±
0.2
)
mM.
The results of insulin without modified sugar and the effects provided by each of the
two modified sugars are discussed in the next paragraphs.
3.2.1. Insulin without and with Modified Sugar
Insulin in solution is mainly found in the form of a monomer. The molar fraction of
nominal IN monomers that remain in the monomeric state in solution is indeed
x1≈
0.8
(Figure 6, panel
A
, black line) while the rest are forming dimers (
x2≈
0.2, Figure 6, panel
B
,
black line) and neither tetramers nor hexamers are found (Figure 6, panels
C
and
D
, black
lines). Both fractions
x1
and
x2
do not show a marked dependence on temperature, even if
at around 60 ◦C dimers disappears (x2tend to zero).
The addition of modified sugars, particularly one of them (EC101), induces a com-
pletely different behavior, with the prevalence of tetramers and hexamers that are negligible
in the absence of the other modified sugars. Because hexamers represent the best oligomers
to store and stabilize the functional monomers, this findings suggest that EC101 can be a
successful compound for storing insulin.
3.2.2. Insulin with EC312
The results show that the increase in the concentration of EC312 (red curves) deter-
mines a decrease in IN monomers in favor of dimers (Figure 6, panels
A
and
B
, red lines).
The major difference is visible at 0.1 M and 0.25 M, when the fraction of dimers,
x2
, increases
from
≈
0.3 to
≈
0.6 with a slight dependence on the temperature until 45
◦
C, after which
monomers slowly increase up to
x1≈
0.8. Tetramers and hexamers are not present in solu-
tion during the EC312 addition. This effect can be also observed in panels
I
–
K
: insulin in
absence of modified sugars shows the lowest value of
¯
K12
, indicating that the protein tends
to stay in the monomeric state, whereas the addition of EC312 yields to higher
¯
K12
values
and lower
¯
K24
and
¯
K46
values, confirming that EC312 favors the propensity of insulin to be
found as a dimer in solution. The stabilization of the dimer in the presence of EC312 is clear
considering the values of the exchange constants
Kexj
reported in panels
Q
–
T
: the monomer,
the tetramer and the hexamer shows
Kexj>
1, whereas for dimers
Kexj<
1, suggesting
a preferential solvation of the dimer with EC312 in respect to water. We underline that,
despite this preference only slightly modifies the water fraction in the first hydration shell
of the dimers (
φ2
has a minimum value of
≈
0.992, panel
F
), this small effect is sufficient
to provoke an important increase in the monomer–dimer effective equilibrium constant
¯
K12
(panel
I
). The trends of the IN–IN structure factors
S(q)
, as well as the ones of the
corresponding pair potentials
u(r)
, reported in Figures S7 and S8 of the Supplementary
Materials (red lines), clearly show a prevalence of long-range attractive forces in respect
to repulsive forces. We also note that, up to 0.1 M EC312, the trends are quite similar to
the ones observed for IN in the absence of modified sugar (black lines), without significant
variations with
T
. Conversely, at 0.25 M EC312, the attractive interactions increase and
become much more marked as the temperature increases.
3.2.3. Insulin with EC101
EC101 behaves in a totally different way from EC312. Although the lowest concentra-
tion of EC101 retains a small fraction of monomers in solution (
x1≈
0.2, Figure 6panel
A
,
green curves), which does not change considerably as a function of
T
, when insulin is
mixed with EC101, insulin is mainly present as a tetramer or a hexamer. At 0.25 M EC101
only tetramers are in solution (
x4≈
1), whereas at lower concentration, the EC101 causes
the formation of hexamers (
x6≈
0.5–0.6 at 40
◦
C, panel
D
), with the remaining percentage
occupied mainly by tetramers and in small part by monomers. The increase in temperature
determines a negative slope of the
x6
vs.
T
curve, leading to a decrease in hexamers in
favor of tetramers. The equilibrium constants
¯
K12
,
¯
K24
, and
¯
K46
(panels
I
–
K
, green curves)
are bigger than the ones of IN in the absence of EC101 (black curves), and they grow
Life 2022,12, 123 21 of 25
additionally at increasing concentrations of EC101. Of note, the higher value of
¯
K24
(panel
J
,
green curves), which describes how the equilibrium from dimers to tetramers changes in
presence of EC101, confirms the prevalence of tetramer at 0.25 M EC101, as indicated in
panel
C
(green curves). The exchange constants
Kexj
, reported in panels
Q
–
T
are found
to be greater than 1 both for monomers and dimers and smaller than 1 for tetramers and
hexamers. These results clearly show a preferential solvation of tetramers and hexamers
with EC101 with respect to water and an opposite preference of monomers and dimers for
water. This is the mechanism that shows the capability of EC101 in stabilizing tetramers and
hexamers. Concerning the protein–protein structure factors and the related pair potentials
of IN in the presence of EC101 (Figures S7 and S8 of the Supplementary Materials, green
lines), the results show that the prevalence of long-range attractive forces at any EC101
concentration, which grow with temperature.
4. Discussion and Conclusions
We have shown that, by using an approach that includes both structural and thermo-
dynamic features of a protein in solution, it is possible to extract from a batch of SAXS
curves recorded at several conditions of temperature and protein as well as cosolvent con-
centrations crucial information regarding the stabilizing effects of cosolvents. The model
we have developed focuses on the preferential water solvation properties over the surface
of each of the distinct states that proteins can form in solution and shows how the modifi-
cations of these properties, due to the presence of a cosolvent, can provide changes in the
distribution of protein molecules among the different states. Although SAXS experiments
can only concern a limited number of conditions in terms of temperature and proteins
or cosolvent concentration, most of the fitting parameters of our model do not refer to a
specific experiment but to the whole set of thermodynamic laws that regulate the behavior
of the protein system at any physical-chemical condition. An important consequence of this
approach is the possibility to calculate the phase-diagram of the protein as a continuous
function of temperature and cosolute concentration.
Phase-diagrams derived by the two sets of SAXS data that we have analyzed in this
work are shown in Figure 7, for MB in the presence of five ExtremoChem modified sugars,
and in Figure 8for IN in contact with two of these modified sugars. These diagrams contain
the same information provided by the plots of
xj
shown in Figure 4(panels
A
–
C
) and
Figure 6(panels
A
–
D
) but allow a more immediate visualization of the achieved results.
Of note, the solid lines represent the thermodynamic condition in which at least one
xj
is 0.5. Regarding the MB case, Figure 7(panels
A
and
F
) shows that EC312 is the best
stabilizing modified sugar, since, at 0.25 M, it preserves the monomeric
N
-state (blue area)
up to
≈
65
◦
C. On the other hand, we see that 0.25 M EC101 (panels
B
and
G
) stabilize the
N
-state as well as the folded and active dimeric
I
-state (gold area) against the unfolded
U
-state (magenta area). EC311 (panels
C
and
H
) looks similar to EC312, but at 10 g/L MB it
better stabilizes the
I
-state. We also see that EC202 (panels
D
and
I
) determines the largest
stabilization area of the
I
-state against the
U
-state. Finally, the EC212 (panels
E
and
J
)
results are similar to the EC312 ones, but with a more marked stabilization of the
I
-state at
10 g/L MB. In general, it is worth noting that the phase-diagrams of uncharged compounds
(EC312, EC311 and EC212) are qualitatively similar and differ from the phase-diagrams of
the two charged compounds (EC101 and EC202), which have an evident stabilization effect
of the active I-state.
Life 2022,12, 123 22 of 25
A
0
0.05
0.1
0.15
0.2
0.25 EC312
2 g/L
B
0
0.05
0.1
0.15
0.2
0.25 EC101
2 g/L
C
0
0.05
0.1
0.15
0.2
0.25 EC311
2 g/L
D
0
0.05
0.1
0.15
0.2
0.25 EC202
2 g/L
E
30 40 50 60 70 80
0
0.05
0.1
0.15
0.2
0.25 EC212
2 g/L
F
EC312
10 g/L
G
EC101
10 g/L
H
EC311
10 g/L
I
EC202
10 g/L
J
temperature (°C)
modified−sugar concentration (M)
30 40 50 60 70 80
EC212
10 g/L
Figure 7.
Temperature-modified sugar concentration phase-diagrams for MB in solution as obtained
by the global-fit analysis of the SAXS curves. Panels in the same row refer to the same modified sugar,
as indicated, whereas left and right column refer to 2 and 10 g/L MB concentration. The color code
of each condition has been calculated by mixing, according to the protein
j
-state distribution (
xj
),
the following pure colors assigned to each
j
-state:
N
(blue),
I
(gold) and
U
(magenta). Solid lines
are the contour levels corresponding to
xj=
0.5 and their color has been assigned on the basis of
the
j
-state. (Panels
A
–
J
) refer to the type of modified sugar and MB concentration as shown on the
top left.
Regarding insulin, the phase-diagrams shown in Figure 8confirm a totally different
behavior in the presence of EC312 (panel
A
) with respect to EC101 (panel
B
): the former
mainly stabilizes the monomer state, at least up to
≈
0.2 M, the latter, at 0.25 M, promotes the
tetramers, whereas at concentrations between 0.05 and 0.15 M and temperatures comprised
between 25◦and 50 ◦C favors the presence of hexamers.
Comparing the results obtained with MB and IN proteins, we could infer that the
stabilizing effect of the tested compounds works as a specific binomial modified sugar
protein. Although some sugars, such as trehalose, are commonly known to be stabilizers
for biological macromolecules, their effect is always related to the specific protein. In partic-
ular, when dealing with proteins that present oligomeric equilibria, compounds efficiency
in stabilizing each particular species is to be tested, since it depends on many features
characterizing the macromolecule (charge, cavities, exposed groups, flexibility, etc.).
SAXS data also contain information regarding the long-range interactions of proteins,
which our model is able to dissect. In the case of both MB at pH
=
5 and IN at pH
=
3
our result indicate the attractive forces dominate with respect to Coulumbian repulsion, in
particular at the highest concentrations of modified sugar and temperature. Although our
SAXS
q
-range does not allow to clearly identify the presence and the structure of high molec-
ular weight species, our data suggest that they would be present, probably as unspecific
aggregates. Further experimental evidences will be necessary to confirm this aspect.
The overall results achieved with the present study suggest that synchrotron-based
SAXS technique, combined with advanced data analysis methods, is an invaluable tool
Life 2022,12, 123 23 of 25
for obtaining a detailed picture of thermal stability, oligomer distribution and long-range
interactions of proteins in the presence of cosolvents.
A
0
0.05
0.1
0.15
0.2
0.25 EC312
B
temperature (°C)
modified−sugar concentration (M)
25 30 35 40 45 50 55 60
0
0.05
0.1
0.15
0.2
0.25 EC101
Figure 8.
Temperature-modified sugar concentration phase-diagrams for 2 g/L IN in solution
as obtained by the global-fit analysis of the SAXS. (Panels
A
and
B
) refer to EC312 and EC101,
as indicated. The color code of each condition has been calculated by mixing, according to the protein
j
-state distribution (
xj
), the following pure colors assigned to each
j
-state: monomers (
j=
1, blue),
dimers (
j=
2, gold), tetramers (
j=
4, magenta) and hexamers (
j=
6, green). Solid lines are the
contour levels corresponding to
xj=
0.5 and their color has been assigned on the basis of the
j
-state.
Supplementary Materials:
The following supporting information can be downloaded at: https:
//www.mdpi.com/article/10.3390/life12010123/s1, Figure S1: Form factors of the
Ns=
3 states of
MB; Figure S2: Form factors of the
Ns=
4 states of IN; Table S1: Experimental pH values determined
as a function of the concentration of EC101 or EC202 modified sugar; Table S2: Overview of the
model parameters and their validity range used in the global-fit analysis of
Nc=
92 SAXS curves
of MB samples; Table S3: Overview of the model parameters and their validity range used in the
global-fit analysis of
Nc=
40 SAXS curves of IN samples; Section S1: Numerical determination of
xj
and
φj
; Section S2: Minimization of the merit function; Section S3: Calculation of
S(q)
; Figure S3:
Kratky plots of the experimental SAXS curves of MB; Figure S4: Protein-protein structure factors
obtained by the analysis of SAXS data of MB; Figure S5: Protein-protein pair potentials obtained by
the analysis of SAXS data of MB; Figure S6: Kratky plots of the experimental SAXS curves of 2 g/L
IN; Figure S7: Protein-protein structure factors obtained by the analysis of SAXS data of IN; Figure S8:
Protein-protein pair potentials obtained by the analysis of SAXS data of IN.
Author Contributions:
Conceptualization, F.S. and M.G.O.; Methodology, F.S.; Software, F.S.; Formal
Analysis, A.P. and F.S.; Investigation, A.P., E.C.L., O.S.A., M.R.V., P.M. (Paolo Moretti), P.M. (Paolo
Mariani), M.G.O. and F.S.; Data Curation, A.P. and H.A.; Writing—Original Draft Preparation, A.P.
and F.S.; Writing—Review and Editing, A.P., M.R.V., P.M. (Paolo Moretti), P.M. (Paolo Mariani),
M.G.O. and F.S.; Supervision, F.S.; Funding Acquisition, M.R.V. and P.M. (Paolo Mariani). All authors
have read and agreed to the published version of the manuscript.
Funding:
This work has been partially funded from the European Union’s Horizon 2020 research
and innovation program under the Marie Skłodowska-Curie grant agreement No 823780. M.R.V.
acknowledges Most Micro Research Unit (financially supported by LISBON-01-0145-FEDER-007660
funded by FEDER funds through COMPETE2020 (POCI) and by national funds through FCT).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
The data presented in this study are available on request from the
corresponding author.
Acknowledgments:
We thank CERIC for access to beam-line SAXS (Proposal Number 20197129) at
Elettra and for the assistance of Barbara Sartori during the experiments. A.P. thanks Graz University
of Technology for the financial support of her PhD program.
Life 2022,12, 123 24 of 25
Conflicts of Interest: The authors declare no conflict of interest.
References
1. Murray, J.; Laurieri, N.; Delgoda, R. Proteins. In Pharmacognosy; Academic Press: Cambridge, MA, USA, 2017; pp. 477–494.
2.
Sane, R.; Sinz, M. Introduction of Drug Metabolism and Overview of Disease Effect on Drug Metabolism. In Drug Metabolism in
Diseases; Elsevier: Amsterdam, The Netherlands, 2017; pp. 1–19.
3.
Mensink, M.A.; Frijlink, H.W.; van der Voort Maarschalk, K.; Hinrichs, W.L. How sugars protect proteins in the solid state and
during drying (review): Mechanisms of stabilization in relation to stress conditions. Eur. J. Pharm. Biopharm.
2017
,114, 288–295.
[CrossRef] [PubMed]
4.
Kamerzell, T.J.; Esfandiary, R.; Joshi, S.B.; Middaugh, C.R.; Volkin, D.B. Protein–excipient interactions: Mechanisms and
biophysical characterization applied to protein formulation development. Adv. Drug Deliv. Rev.
2011
,63, 1118–1159. [CrossRef]
[PubMed]
5.
Ambrogi, V.; Carfagna, C.; Cerruti, P.; Marturano, V. 4-Additives in Polymers. In Modification of Polymer Properties; William
Andrew Publishing: Norwich, NY, USA, 2017; pp. 87–108.
6.
Kontogiorgos, V. Additives in Dairy Foods: Stabilizers. In Reference Module in Food Science; Elsevier: Amsterdam, The Netherlands,
2021.
7. Ragoonanan, V.; Aksan, A. Protein stabilization. Transfus. Med. Hemother. 2007,34, 246–252. [CrossRef]
8.
Ajito, S.; Hirai, M.; Iwase, H.; Shimizu, N.; Igarashi, N.; Ohta, N. Protective action of trehalose and glucose on protein hydration
shell clarified by using X-ray and neutron scattering. Phys. B Condens. Matter 2018,551, 249–255. [CrossRef]
9.
Olsson, C.; Swenson, J. The role of disaccharides for protein–protein interactions—A SANS study. Mol. Phys.
2019
,117, 3408–3416.
[CrossRef]
10.
Corezzi, S.; Bracco, B.; Sassi, P.; Paolantoni, M.; Comez, L. Protein Hydration in a Bioprotecting Mixture. Life
2021
,11, 995.
[CrossRef] [PubMed]
11.
Maycock, C.D.; Centeno, M.R.M.B.V.; Lourenço, E.C.; Dos Santos, M.H.D.; Miguel, A.S.D.C. Hexose Derivatives, Preparation and
Uses Thereof. U.S. Patent US20180170955A1, 21 June 2018.
12.
Kumar, V.; Chari, R.; Sharma, V.K.; Kalonia, D.S. Modulation of the thermodynamic stability of proteins by polyols: Significance
of polyol hydrophobicity and impact on the chemical potential of water. Int. J. Pharm. 2011,413, 19–28. [CrossRef] [PubMed]
13.
Amenitsch, H.; Rappolt, M.; Kriechbaum, M.; Mio, H.; Laggner, P.; Bernstorff, S. First performance assessment of the small-angle
X-ray scattering beamline at ELETTRA. J. Sync. Rad. 1998,5, 506–508. [CrossRef]
14.
Haider, R.; Sartori, B.; Radeticchio, A.; Wolf, M.; Dal Zilio, S.; Marmiroli, B.; Amenitsch, H.
µ
Drop: A system for high-throughput
small-angle X-ray scattering measurements of microlitre samples. J. Appl. Crystallogr. 2021,54, 132–141. [CrossRef]
15. Hammersley, A.P. FIT2D: A Multi-Purp. Data Reduction, Anal. Vis. Program. J. Appl. Cryst. 2016,49, 646–652. [CrossRef]
16.
Berman, H.; Henrick, K.; Nakamura, H. Announcing the worldwide Protein Data Bank. Nat. Struct. Biol.
2003
,10, 980. [CrossRef]
17.
Ortore, M.G.; Spinozzi, F.; Mariani, P.; Paciaroni, A.; Barbosa, L.R.S.; Amenitsch, H.; Steinhart, M.; Ollivier, J.; Russo, D. Combining
structure and dynamics: Non-denaturing high-pressure effect on lysozyme in solution. J. R. Soc. Interface
2009
,6, S619–S634.
[CrossRef] [PubMed]
18.
Schellman, J.A. A simple model for solvation in mixed solvents. Applications to the stabilization and destabilization of
macromolecular structures. Biohpys. Chem. 1990,37, 121–140.
19. Schellman, J.A. The thermodynamics of the solvent exchange. Biopolymers 1994,34, 1015–1026. [CrossRef] [PubMed]
20.
Schellman, J.A. Protein Stability in Mixed Solvents: A Balance of Contact Interaction and Excluded Volume. Biophys. J.
2003
,
85, 108–125. [CrossRef]
21. Schellman, J.A. Destabilization and stabilization of proteins. Q. Rev. Biophys. 2005,38, 351–361. [CrossRef]
22.
Spinozzi, F.; Gazzillo, D.; Giacometti, A.; Mariani, P.; Carsughi, F. Interaction of proteins in solution from small angle scattering:
A perturbative approach. Biophys. J. 2002,82, 2165–2175. [CrossRef]
23.
Baldini, G.; Beretta, S.; Chirico, G.; Franz, H.; Maccioni, E.; Mariani, P.; Spinozzi, F. Salt induced association of
β
-lactoglobulin
studied by salt light, X-ray scattering. Macromolecules 1999,32, 6128–6138. [CrossRef]
24.
Moretti, P.; Mariani, P.; Ortore, M.G.; Plotegher, N.; Bubacco, L.; Beltramini, M.; Spinozzi, F. Comprehensive Structural and
Thermodynamic Analysis of Prefibrillar WT
α
-Synuclein and Its G51D, E46K, and A53T Mutants by a Combination of Small-Angle
X-ray Scattering and Variational Bayesian Weighting. J. Chem. Inf. Model. 2020,60, 5265–5281. [CrossRef] [PubMed]
25.
Kell, G.S. Density, thermal expansivity, and compressibility of liquid water from 0.deg. to 150.deg. Correlations and tables for
atmospheric pressure and saturation reviewed and expressed on 1968 temperature scale. J. Chem. Eng. Data
1975
,20, 97–105.
[CrossRef]
26.
Spinozzi, F.; Ortore, M.G.; Nava, G.; Bomboi, F.; Carducci, F.; Amenitsch, H.; Bellini, T.; Sciortino, F.; Mariani, P. Gelling without
Structuring: A SAXS Study of the Interactions among DNA Nanostars. Langmuir 2020,36, 10387–10396. [CrossRef] [PubMed]
27.
Svergun, D.; Richard, S.; Koch, M.H.J.; Sayers, Z.; Kuprin, S.; Zaccai, G. Protein hydration in solution: Experimental observation
by X-ray, neutron scattering. Proc. Natl. Acad. Sci. USA 1998,95, 2267–2272. [CrossRef]
28.
Sinibaldi, R.; Ortore, M.G.; Spinozzi, F.; Carsughi, F.; Frielinghaus, H.; Cinelli, S.; Onori, G.; Mariani, P. Preferential hydration of
lysozyme in water/glycerol mixtures: A small-angle neutron scattering study. J. Chem. Phys.
2007
,126, 235101–235109. [CrossRef]
29. Spinozzi, F.; Mariani, P.; Ortore, M.G. Proteins in binary solvents. Biophys. Rev. 2016,8, 87–106. [CrossRef] [PubMed]
Life 2022,12, 123 25 of 25
30.
Ortore, M.; Sinibaldi, R.; Spinozzi, F.; Carbini, A.; Carsughi, F.; Mariani, P. Looking for the best experimental conditions to detail
the protein solvation shell in a binary aqueous solvent via Small Angle Scattering. J. Phys. Conf. Ser.
2009
,177, 012007. [CrossRef]
31.
Oliveira, C.L.P.; Behrens, M.A.; Pedersen, J.S.; Erlacher, K.; Otzen, D.; Pedersen, J.S. A SAXS Study of Glucagon Fibrillation. J.
Mol. Biol. 2009,387, 147–161. [CrossRef] [PubMed]
32. Hansen, J.P.; McDonald, I.R. Theory of Simple Liquids; Academic Press: London, UK, 1976.
33.
Wertheim, M.S. Exact Solution of the Percus-Yevick Integral Equation for Hard Spheres. Phys. Rev. Lett.
1963
,10, 321–323.
[CrossRef]
34.
Ortore, M.G.; Mariani, P.; Carsughi, F.; Cinelli, S.; Onori, G.; Teixeira, J.; Spinozzi, F. Preferential solvation of lysozyme in
water/ethanol mixtures. J. Chem. Phys. 2011,135, 245103–245111. [CrossRef]
35.
Spinozzi, F.; Ferrero, C.; Ortore, M.G.; Antolinos, A.D.M.; Mariani, P. GENFIT: Software for the analysis of small-angle X-ray and
neutron scattering data of macromolecules in-solution. J. App. Cryst. 2014,47, 1132–1139. [CrossRef]
36.
Lin, Y.W.; Wang, J. Structure and function of heme proteins in non-native states: A mini-review. J. Inorg. Biochem.
2013
,
129, 162–171. [CrossRef]
37.
van den Oord, A.H.A.; Wesdorp, J.J.; van Dam, A.F.; Verheij, J.A. Occurrence and Nature of Equine and Bovine Myoglobin
Dimers. Eur. J. Biochem. 1969,10, 140–145. [CrossRef]
38.
Nagao, S.; Osuka, H.; Yamada, T.; Uni, T.; Shomura, Y.; Imai, K.; Higuchi, Y.; Hirota, S. Structural and oxygen binding properties
of dimeric horse myoglobin. Dalton Trans. 2012,41, 11378–11385. [CrossRef]
39.
Ono, K.; Ito, M.; Hirota, S.; Takada, S. Dimer domain swapping versus monomer folding in apo-myoglobin studied by molecular
simulations. Phys. Chem. Chem. Phys. 2015,17, 5006–5013. [CrossRef]
40.
Eliezer, D.; Chiba, K.; Tsuruta, H.; Doniach, S.; Hodgson, K.O.; Kihara, H. Evidence of an associative intermediate on the
myoglobin refolding pathway. Biophys. J. 1993,65, 912–917. [CrossRef]
41.
Baden, N.; Terazima, M. Intermolecular Interaction of Myoglobin with Water Molecules along the pH Denaturation Curve. J.
Phys. Chem. B 2006,110, 15548–15555. [CrossRef]
42.
Spinozzi, F.; Carsughi, F.; Mariani, P.; Saturni, L.; Bernstorff, S.; Cinelli, S.; Onori, G. Met-myoglobin association in dilute solution
during pressure-induced denaturation: An analysis at pH 4.5 by high-pressure small-angle X-ray scattering. J. Phys. Chem. B
2007,111, 3822–3830. [CrossRef] [PubMed]
43. Defaye, A.B.; Ledward, D.A. Pressure-Induced Dimerization of Metmyoglobin. J. Food Sci. 1995,60, 262–264. [CrossRef]
44.
Maurus, R.; Overall, C.M.; Bogumil, R.; Luo, Y.; Mauk, A.; Smith, M.; Brayer, G.D. A myoglobin variant with a polar substitution
in a conserved hydrophobic cluster in the heme binding pocket. BBA-Protein Struct. Mol. Enzymol. 1997,1341, 1–13. [CrossRef]
45.
Moretti, P. Innovative Methods to Investigate Intrinsically Disordered Proteins by X-ray and Neutron Scattering Techniques.
Ph.D. Thesis, Life and Environmental Sciences, Ancona, Italy, 2019.
46.
Jeffrey, P.D.; Coates, J.H. An Equilibrium Ultracentrifuge Study of the Self-Association of Bovine Insulin. Biochemistry
1966
,
5, 489–498. [CrossRef] [PubMed]
47.
Goldman, J.; Carpenter, F.H. Zinc binding, circular dichroism, and equilibrium sedimentation studies on insulin (bovine) and
several of its derivatives. Biochemistry 1974,13, 4566–4574. [CrossRef]
48.
Ganim, Z.; Jones, K.C.; Tokmakoff, A. Insulin dimer dissociation and unfolding revealed by amide I two-dimensional infrared
spectroscopy. Phys. Chem. Chem. Phys. 2010,12, 3579–3588. [CrossRef]
49.
Uversky, V.N.; Garriques, L.N.; Millett, I.S.; Frokjaer, S.; Brange, J.; Doniach, S.; Fink, A.L. Prediction of the association state of
insulin using spectral parameters. J. Pharm. Sci. 2003,92, 847–858. [CrossRef] [PubMed]
50.
Falk, B.T.; Liang, Y.; McCoy, M.A. Profiling Insulin Oligomeric States by 1H NMR Spectroscopy for Formulation Development of
Ultra-Rapid-Acting Insulin. J. Pharm. Sci. 2020,109, 922–926. [CrossRef]
51.
Zhou, C.; Qi, W.; Lewis, E.N.; Carpenter, J.F. Characterization of Sizes of Aggregates of Insulin Analogs and the Conformations of
the Constituent Protein Molecules: A Concomitant Dynamic Light Scattering and Raman Spectroscopy Study. J. Pharm. Sci.
2016
,
105, 551–558. [CrossRef] [PubMed]
52.
Sorci, M.; Belfort, G. Insulin Oligomers: Detection, Characterization and Quantification Using Different Analytical Methods. In
Bio-Nanoimaging; Uversky, V.N., Lyubchenko, Y.L., Eds.; Academic Press: Boston, MA, USA, 2014; pp. 233–245.
53.
Nettleton, E.J.; Tito, P.; Sunde, M.; Bouchard, M.; Dobson, C.M.; Robinson, C.V. Characterization of the Oligomeric States of
Insulin in Self-Assembly and Amyloid Fibril Formation by Mass Spectrometry. Biophys. J. 2000,79, 1053–1065. [CrossRef]
54.
Dreyer, L.S.; Nygaard, J.; Malik, L.; Hoeg-Jensen, T.; Høiberg-Nielsen, R.; Arleth, L. Structural Insight into the Self-Assembly of
a Pharmaceutically Optimized Insulin Analogue Obtained by Small-Angle X-ray Scattering. Mol. Pharm.
2020
,17, 2809–2820.
[CrossRef]
55.
O’Donoghue, S.I.; Chang, X.; Abseher, R.; Nilges, M.; Led, J.J. Unraveling the symmetry ambiguity in a hexamer: Calculation of
the R6 human insulin structure. J. Biomol. NMR 2000,16, 93–108. [CrossRef]
56.
Robertson, A.D.; Murphy, K.P. Protein Structure and the Energetics of Protein Stability. Chem. Rev.
1997
,97, 1251–1268. [CrossRef]
[PubMed]
57.
Zangi, R.; Berne, B.J. Temperature Dependence of Dimerization and Dewetting of Large-Scale Hydrophobes: A Molecular
Dynamics Study. J. Phys. Chem. B 2008,112, 8634–8644. [CrossRef]
58. Prabhu, N.V.; Sharp, K.A. Heat Capacity in Proteins. Annu. Rev. Phys. Chem. 2005,56, 521–548. [CrossRef]
