The absorption properties of gold nano conjugated with proteins

29 
HNUE JOURNAL OF SCIENCE DOI: 10.18173/2354-1059.2020-0045 
Natural Sciences 2020, Volume 65, Issue 10, pp. 29-35 
This paper is available online at  
THE ABSORPTION PROPERTIES OF GOLD NANO CONJUGATED 
WITH PROTEINS 
Luong Thi Theu1, Le Anh Thi2, Tran Quang Huy1, Nguyen Quang Hoc3 
and Nguyen Minh Hoa4 
 1Faculty of Physics, Hanoi Pedagogical University 2 
2Institute of Research and Development, Duy Tan University 
2Faculty of Natural Sciences, Duy Tan University 
3Faculty of Physics, Hanoi National University of Education 
4Faculty of Basic Sciences, Hue University of Medicine and Pharmacy 
Abstract. The absorption properties of protein-conjugated metallic nanoparticles are 
theoretically investigated based on the Mie theory and the core-shell model. Our 
numerical calculations show that this finding is in good agreement with previous 
experiments. We provide a better interpretation of the origin of optical peaks in the 
absorption spectrum of the nanoparticle complex system. Our results can be used in 
biomedical applications. 
Keywords: gold nanoparticle, BSA protein, Mie theory. 
1. Introduction 
Gold nanoparticles (GNPs), with a diameter between 1 nm and 100 nm, have been 
widely used in chemical and biological sensors because of their excellent physical and 
chemical properties. The unique optical property of GNPs is one of the reasons that GNPs 
attract immense benefits from various fields of science, especially in the development of 
sensors. The spherical GNP solutions show a range of vibrant colors including red, blue, 
and violet when the particle size increases, and they can be used to dye glass in ancient 
times. The strong color is caused by the strong absorption and scattering of 520 nm light [1], 
which is the result of the collective oscillation of conduction electrons on the surface of 
GNPs when they are excited by the incident light. This phenomenon is called surface 
plasmon resonance (SPR), and it depends greatly on particle size and shape. Therefore, 
the SPR peak can be adjusted by manipulating the size of GNPs, and this property cannot 
be observed on bulk gold and GNPs with a diameter smaller than 2 nm. 
The SPR peak is not only sensitive to the size and the shape, but also many factors 
such as a protective ligand, refractive index of solvent, and temperature. The distance 
Received June 17, 2020. Revised October 16, 2020. Accepted October 23, 2020. 
Contact Nguyen Minh Hoa, e-mail address: nguyenminhhoa@hueuni.edu.vn 
Luong Thi Theu, Le Anh Thi, Tran Quang Huy, Nguyen Quang Hoc and Nguyen Minh Hoa 
30 
between particles particularly shows the great influence on SPR. Thus, the red-shifting 
and the broadening of the peak are observed when GNPs are synthesized due to analyte 
binding. The color change of synthesized GNPs from red to blue is the principle of 
colorimetric sensors. Several recent pieces of research and reviews provide a detailed 
discussion of the factors that affect the SPR of GNPs [2-6]. 
Bovine serum albumin (BSA) protein has been widely used in the field of biophysics 
and medical science, due to its low cost, structural/ functional similarity to human serum 
albumin (HSA) [7]. A recent study found that the ribosylation of BSA resulted in reactive 
oxygen species (ROS) accumulation which killed breast cancer cells [8]. Particularly the 
anomalous thermal denaturing of proteins increased signal in the tests, biochemical 
reactions [9, 10]. This effect is strong in BSA proteins and is particularly useful for the 
design of bio-sensors and devices. 
In recent years, the plasmonic properties of metallic nanoparticles are of great interest 
because they have various potentially technological applications, especially the magnetic 
nanoparticles (NPs). Localized surface plasmon resonances with gold nanoparticles have 
many applications for a variety of application areas e.g. chemical analysis and catalytic, 
detect biomolecules, pharmaceutical, diagnosis, imaging, and therapy [1, 11, 12]. 
Complex systems of biological gold nanoparticles have also been investigated to 
construct functional devices for cell imaging, drug delivery, and biomolecule detection. 
Bovine Serum Albumin (BSA) proteins have been particularly useful in this issue [1]. 
The BSA substances not only prevent AuNPs from together combination but also are 
effective for treatment delivery and attaching AuNPs in living matter. Because of their 
large scattering crossing sections, BSA-AuNPs themselves can be imaged under white 
light illumination. Moreover, adjusting the optical plasmon resonance on the visible 
spectrum is implemented by changing the particle size and shape that have been especially 
helpful in optimizing the application of complex systems of biological gold nanoparticles. 
In this paper, we theoretically study the optical properties of AuBSA core-shell nano 
using the Mie theory and effective medium approximation, which has been synthesized 
experimentally in Ref. 13 in the visible range. 
2. Content 
2.1. Theoretical background 
 Calculating exactly the number of BSA molecules on a gold nanoparticle’s surface 
based on the absorption spectrum and the extended Mie theory [13] shows that the core-
shell model and the effective medium approximation provides a good agreement between 
theoretical calculations and experimental for spherical nanoparticles. Now, we apply 
these theories to the complex system to investigate and predict the properties of protein-
conjugated gold nanoparticles. An idea of modeling nanoparticles conjugated 
nanoparticles as a core-shell structure has been widely used [14, 15]. In this work, the 
absorption and scattering of AuNP conjugated BSA protein in aqueous solutions are 
theoretically considered. The system is formed when BSA and AuNP proteins are placed 
in water. Some of the water is mixed with protein and this aqueous solution of BSA is 
attracted to AuNP through Van der Waals interaction. As a result, a protein conjugated 
nanoparticle is formed in water as shown in Figure 1. 
The absorption properties of gold nano conjugated with proteins 
31 
Figure 1. The core-shell model for protein-conjugated gold nano 
 The general solution to the problem of scattering of a spherical metal sphere 
according to electrodynamics theory was first proposed by Mie in 1908 [16]. Mie's theory 
applied an overview theory of scattering on small particles to explain the color changing 
of the colloidal gold nanoparticles with arbitrary size and shows s good agreement with 
experimental results. When the radius of the nanoparticles is much smaller than the 
wavelength of the incident light ( d  , or an approximation max /10d  ), the Mie 
coefficients can be simplified by quasi-static approximations. Thus, using the exact 
solution of Mie theory is necessary to calculate accurately the extinction, scattering, and 
absorption coefficients cross-section of isotropically coated spherical nanoparticles are 
given by [17]. 
( )
( )
1
2 2
scat
a
1
sc t .
2
(2 1) Re ,
2
(2 1) ,
ext
ab
n
s ext
n
n
n n
n
C n a b
C n a
C C
b
C


=
=
= −
= + +
= + +


(1) 
where 
' '
' '
' '
' '
2
( ) ( ) ( ) ( )
,
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
,
( ) ( ) ( )
,
) (
p p p p
n
p p p p
p p p p
n
p p p
i
i
p
m mka ka ka mka
a
m mka ka ka mka
mka ka m ka mka
b
mka ka m ka ka
C
Q
m
R
   
   
   
  

−
=
−
−
=
=
−
(2) 
in which, Qi are the extinction, scattering, and absorption efficient, with i = [ext, scat, abs] 
is running index and R gold nanoparticle radius.  is Riccati–Bessel function of the first 
and second kind, and s
N
m
N
= , Ns and N are the refractive index of the noble metal sphere 
 NP 
 r1 
r2 
Protein 
 NP 
 r1 
Luong Thi Theu, Le Anh Thi, Tran Quang Huy, Nguyen Quang Hoc and Nguyen Minh Hoa 
32 
and the surrounding medium (perovskite), respectively, and 2 /k = is the 
wavenumber with  the dielectric function of core-shell spherical and n represent the 
mode. Expansion of infinite series exhibits the different excitation symmetry like a dipole, 
quadrupole, and octupole corresponding to different values of n, respectively. Since it is 
very difficult to find the solution of the sum of infinite series, we can easily handle the 
situation if we truncated the series up to a certain value of n. If we are interested to study 
dipolar effects, choose n = 1, for quadrupolar n = 2, and so on. 
2.2. The absorption efficiency of BSA protein-conjugated gold nano 
An effective dielectric function of core-shell nanoparticle dispersed in a solution can 
be found from Maxwell-Garnett theory as 
2 2
1 1
1 2
2 2
2 2
1 1
1 2
2 2
2
1 2 2 1 ,
1 2 ,
,
a
b
a
b
r r
r r
r r
r r
  
  
 


 = + + − 
 = − + + 
=
(3) 
in which,  , 1 and 2 are the wavelength of the incident in a vacuum, the dielectric 
function for the core (Au), shell (BSA + surrounding medium), respectively. Parameters 
and analytical expressions for these dielectric functions can be taken from a previous 
study [18]. We introduce the filling factor of protein BSA on metallic surface f, 
2 protein (1 ) mf f  = + − , where m is the dielectric constant of the medium. na and nb are 
given by 
( )
2
2 2
2
1
( ) ( ) ,
2 8
1 ( ) log ( ) ( )
2 4
1
2 ( ) ( ) .
2 4
m
n m
m m m
m
n m
m
R
a kR
i
kR kR kR
R
b kR
  
 
 
   
  
 
 
 −
 = − +
 + − − 
 −
= + − 
+ 
(4) 
Figure 2 shows the absorption efficiency of BSA conjugated gold nanoparticles in 
water. We found that Qabs behaves as a function of the wavelength. Here, we take that 
1 10r = nm for the AuNP and 2 11.5r = nm for the shell. The recent experiments indicate 
that such a configuration corresponds to a BSA monolayer around the Au core [18]. There 
is a very good agreement with the reported data in Ref. 18 for the AuNP/water system. 
The absorption properties of gold nano conjugated with proteins 
33 
Figure 2. The absorption of AuNPs in water with BSA in the visible spectrum 
and the diameter of AuNPs in the calculations is 20 nm 
We assume that the equation is independent of frequency and a complex function 
that depends on the energy. The resonant condition is satisfied when ( )1 2 m  = − and 
2 is small or weakly dependent  . The Eq.1 has been used to explain the absorption 
spectrum of small metal nanoparticles both qualitatively and quantitatively. Using Mie 
theory, we obtained the absorption coefficient at the maximum wavelength. 
 
3/2
2
abs 2 2
1 2
16 ( )
,
3 ( ) ( )
m
m
V
Q
   
     
=
+ +
 (5) 
where ( ) ( )1 2i    = + is the effective dielectric function of the object calculated by 
Eq.4, ( ) 2 is the imaginary part of ( )  , m is the dielectric constant of the medium, 
V R = 3
4
3
 is the volume of one BSA protein molecule and R is the radius of the 
nanoparticle complex. We also show two theories that have a good agreement that 
maxima of the absorption spectrum of nanoparticle exhibit at ( ) 0m  + = . While the 
localized surface plasmon resonance of a spherical nanoparticle complex is at 
( ) 0m  + = . 
3. Conclusions 
In conclusion, we have presented a comprehensive explanation for optical peaks of 
BSA-conjugated gold nanoparticles. The peak at the wavelength of 510 nm is due to 
Luong Thi Theu, Le Anh Thi, Tran Quang Huy, Nguyen Quang Hoc and Nguyen Minh Hoa 
34 
biological molecules binding on nanoparticles and strongly depends on the dielectric 
function of the protein and the adsorption of protein on gold nanoparticles. The results 
show that there is a good agreement between theory and experiment. Our work shows 
that the finite size of the nanoparticles may play an important role in the plasmon spectral 
shift and it is directly related to the number of protein molecules attached to the AuNP surface. 
Acknowledgment. This work was financially supported by the Hue University of Science 
and Technology under grant number DHH2018-04-83. 
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