Photon Factory Activity Report 2014 #32 (2015) B

BL-10C/2014G165

Model-potential-free analysis of an inter-particle interference of protein solution
scattering: insights into solvent effects on the intermolecular interaction
Hiroshi Imamura1, Tomonari Sumi2, Hiroyo Ohgi1, Yasuhiro Isogai3,*
1
Graduate School of Advanced integration Science, Chiba University, 1-33 Yayoi, Inage-ku, Chiba
263-8522, Japan2
Department of Chemistry, Faculty of Science, Okayama University, 3-1-1 Tsushima-Naka, Kita-ku,Okayama 700-8530, Japan3
Department of Biotechnology, Toyama Prefectural University, 5180 Kurokawa, Imizu, Toyama,939-0398, Japan

3 Results and Discussion
The model-potential-free (MPF) method has been
described in our papers [3-5] in detail. Briefly, a closure

1.5

2.0(a)(b)

1.5Experiment
MPF
DLVO
DLVO + SIP

0.5
0.0
0.00

0.10

0.20
-1q /Å

1ΔV

1.0

V(r) / kBT

2 Experiments
The SAXS experiments were performed at the beamline BL-10C. The X-ray wavelength was 0.1488 nm; thecamera length was 957 or 1048 mm, which was calibrated
by use of a scattering pattern of silver behenate. X-rayintensities were recorded using PILATUS (DECTRISLtd., Switzerland). Lysozyme from hen egg white (SigmaAldrich, St. Louis, MO) was dissolved in 25 mM bis-Trisbuffer at pH 7. To obtain the scattering of the form factor,a lysozyme solution of 2.6 mg/mL was measured. During
the measurement, the sample was flowed to avoid thedamage by X-ray radiation. The exposure time was 80
minutes for decreasing noises at large q values.

relation to solve Ornstein-Zernike (OZ) equation in theintegral equation theory is given byh(r) = exp[-V(r)/kBT+h(r)-c(r)+B(r)]-1,(1)where h(r), V(r), kB, T, c(r) and B(r) are the total
correlation function, the pair interaction poteintial, theBoltzmann constant, the thermodynamic temperature, thedirect correlation function and the bridge function,
respectively. We divide both c(r) and V(r) into two terms,
V(r) = VHS(r) + Vex(r), (2)c(r) = cHS(r) + cex(r). (3)The subscripts ‘‘HS’’ and ‘‘ex’’ denote hard sphere andexcess, respectively. Next, we introduce the following
assumption for Vex(r):–Vex(r)/kBT = cex(r). (4)Accordingly, we obtainh(r) = exp[-VHS(r)/kBT+h(r)-cHS(r)+B(r)]-1, (5)where the excess potentail, Vex(r), does not explicitly
appear. The experimental S(q) is converted to h(r) in theright side of the eq. (5), with the relation, S(q) = nh(q) + 1(n is number density). After iterative numericalcalculation, Vex(r) is determined through OZ eq. and eq.
(3-5).
The SAXS intensity of a protein, I(q), is described byI(q) = ckP(q)S(q),(6)
where c is the protein concentration, k is a constant. TheSAXS profile of the dilute protein solution (2.6 mg/mL),S (q)1 Introduction
The intermolecular interaction between proteins, selfinteraction, governing its aggregation or precipitation
increasingly attracts attention as a fundamental issue inbiophysics and biopharmaceutical field. A mechanism
avoiding aggregation is likely to exist in naturally
occurring soluble proteins, while that is yet to beelucidated. In fact, the present artificially designed
proteins are prone to aggregate [1]. An inter-particle
interference, called S(q), in a small angle X-ray scattering
captures a radial distribution of protein molecules insolution, which is related to the self-interaction potential,V(r), through liquid theory [2]. To determine V(r) fromS(q), a classical method optimizes variable parameter in amodel potential such as Derjaguin–Laudau–Verwey–
Overbeek (DLVO) to reproduce the experimental S(q).
However, it is often ambiguous whether the model
potential selected is appropriate for the system. To
overcome this drawback, we developed a method that
determines V(r) without assuming model potentials bymodifying an integral equation theory [3-5]. Then, weelucidate V(r) of a soluble protein, lysozyme, by applying
this model-potential-free (MPF) method to theexperimental SAXS data. This demonstrates solvent
effect on the intermolecular interaction between proteins.

1.00-10.5

200.060

MPF
DLVO
DLVO+SIP-0.5-1.0
20404060

80

100r/ÅFig. 1: (a) The experimental (red circle), MPF-derived(black line), DLVO-derived (blue line), DLVO+SIPderived (blue dashed line) structure factors, S(q), oflysozyme at the concentration of 100 mg/mL. (b) theintermolecular interaction potentials, V(r), of lysozyme
calculated by MPF, DLVO and DLVO+SIP using theexperimental S(q). In the inset of (b), the difference
between V(r)/kBT of DLVO+SIP and that of DLVO isshown.

Photon Factory Activity Report 2014 #32 (2015) B

at the concentration of which the inter-particle
interferences are negligibly small, yields kP(q). We
determined the experimental S(q) of lysozyme at theconcentration of 100 mg/mL shown in Fig. 1(a). The
corresponding S(q) calculated in MPF agrees well withthe experimental S(q) (Fig. 1(a)). We also analyzed theexperimental S(q) using the classical procedure assuming
DLVO-type model potential, where the effective chargeof lysozyme is 8. This does not give the sufficient S(q)comparable to the experimental S(q) (Fig. 1(a)). Thus, we
introduced an additional potential called “solvent-inducedpotential (SIP)” [4]. The DLVO + SIP potential shown inFig. 1(b) reproduces the experimental S(q) well (Fig.
1(a)). The difference between V(r)/kBT of DLVO+SIP andthat of DLVO shown in the inset of Fig 1(b), ΔV,indicates what DLVO lacks to reproduce the experimental
S(q): ΔV shows the repulsion, which decays rapidly withincreasing the distance between the proteins, and theattraction exists in ΔV at short range. According totheoretical studies [6,7], we attribute both thecharacteritic ΔV potential to solvent effects: when theprotein molecules approach each other to form the contact
configurations, it needs energy to remove watermolecules in the hydration shell surrounding the protein,
and the contact configurations are stablized not only bydirect interactions, but by translational motion of watermolecules.
Acknowledgement
This work was supported in part by Izumi Science andTechnology Foundation (to H.I.).
References[1] H. Imamura, Y. Isogai, M. Kato, Biochemistry 51,3539 (2012).
[2] H. Imamura, T. Morita, T. Sumi, Y. Isogai, M. Kato,K. Nishikawa, J. Synchrotron Rad. 20, 919 (2013).
[3] H. Imamura, T. Sumi, H. Ohgi, Y. Isogai, Photon
Factory Activity Report 2013 PART B, No. 62, 2014.
[4] T. Sumi, H. Imamura, T. Morita, Y. Isogai, K.
Nishikawa, Phys. Chem. Chem. Phys. 16, 25492(2014)[5] T. Sumi, H. Imamura, T. Morita, K. Nishikawa, J.
Mol. Liq. 200, 42 (2014)[6] T. Sumi, T. H. Sekino, J. Chem. Phys. 126, 2007,144508.
[7] R. Akiyama, T. Yamashita, S. Fujihara, J. Mol. Liq.
200, 2014, 72.
Research Achievements
H. Imamura, The 9th Mini-Symposium on Liquids (MSL),
Invited talk, Fukuoka, Japan, July 2015.
* yisogai@pu-toyama.ac.jp