However, a close look into Figure 3 shows that
the shift has a maximum at 0.8uM heparin, after
which it decreases.
Our interpretation of these results follows
Bradley’s and Wolf‘s (1959). The idea is illustrated
in Figure 4. Denoting BO21 as D and heparin
binding site as P, we propose that at low heparin
concentrations, namely P/D<1,
the heparin binding
sites are completely occupied with BO21 and the
surplus BO21 remains unbound in the solution
(Figure 4a). In the case where P/D~1 (Figure 4b), all
BO21 molecules are expected to occupy all heparin
binding sites and consequently, to yield maximum
metachromasia. With further increase of the heparin
concentration, P/D>1 (Figure 4c), the competition
between heparin molecules on BO21 molecules will
finally lead to an equilibrium state where the BO21
molecules only partially occupy heparin binding
sites, hence lessening the proximity between BO21
molecules attached to each of the heparin molecules
and consequently lowering the chance for BO21
aggregation to occur on a single heparin.
Figure 4: Aggregation schematic of the dye (D) on the
anionic binding site of the polymer (P). a) Low polymer
concentration leaves free dye molecules in the hosting
solution. b) At an equal number of polymer binding sites
and dyes, the dye molecules occupy all polymer binding
sites. c) The number of polymer anionic binding sites is
larger than that of dye molecules, hence yielding partial
occupancy of the binding sites by the dye.
The experimental results and proposed
mechanism was further strengthened by the use of
computational chemistry. BO21 molecules is a
multi-bodied electronic structure containing 47
nuclei and 169 electrons (despite the chlorine that
dissolves in water), and therefore, the Schrödinger
equation is impractical as a modelling method,
hence, the Density Functional Theory (DFT)
approach was applied (Hohenberg and Kohn 1964).
DFT is a quantum mechanical modelling method
which investigates the electronic structure
(principally the ground state) of many-body systems.
With this theory, instead of using N wave function
that depend on 3N coordination for x,y,z, the
properties of a many-electron system can be
determined by using the charge density ρ. This
method is based on two Hohenberg-Kohn theorems
(H-K). The first H-K theorem demonstrates that the
ground state properties of a many-electron system
are uniquely determined by an electron density that
depends on only 3 spatial coordinates, while the
second H-K theorem defines energy functional for
the system, and proves that the correct ground state
electron density minimizes this energy functional.
We calculated the electric dipole of the BO21
molecule. This molecule is cation due to a positive
charge surrounding the nitrogen atom connected to
the methyl group. Based on density function, a 3-d
MEP (Molecular Electrostatic Potential) was
produced in Figure 5a.
The molecule electric dipole moment µ was
estimated by the formula:
1
nucl
N
dZ
rr r
(2)
Where ࣋
ሺ
࢘
ሻ
is the density function, Z is atomic
number and α is the nuclei index. The integral is
above the electron coordinates and the summation
yields the nucleus contribution to the dipole
moment. The dipole moment vector of BO21 was
found to be
29
21
1.43 10
BO
Cm
, which is twice
the water molecule (
2
30
6.2 10
HO
Cm
).
21BO
is indicated in Figure 5a by a light blue
arrow in respect to the molecule axis. In order to
support the aggregation theorem that causes the blue
shift, we test the feasibility of dimer or trimer
formation of BO21 molecules. In the tested model,
the molecular electrical dipoles of dimers and
trimers of BO21 are oriented in a parallel fashion as
shown in Figure 5b. Surprisingly, the related binding
energies were found to be even lower than those
calculated for anti-parallel arrangements, a fact
which explains the blue shift in the absorption
spectrum.
2 OUTLINE OF OBJECTIVES
To study the spectroscopic characteristics of
BO21 in bulk solution in the presence and in the
absence of biomolecules in general, as well as
those which exist in leukocytes, in particular.
To explore unique spectroscopic features of
BO21 stained leukocytes, if they exist
BIOSTEC2014-DoctoralConsortium
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