Biology Reference
In-Depth Information
Approaches in traditional nanotechnology are often distinguished
between “top down” and “bottom up” approaches.
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However,
in virology, functional nanostructures have been studied by both
“bottom up” and “top down” approaches for decades,
55,86-89
despite
not using these specific terms to describe the process. “Top down”
approaches include structural studies on viral components or the dis-
section of the complete viral particles into subunits or single mole-
cules, using various methods of molecular biology.
8,86,90-93
“Bottom
up” approaches exploit the efficiency of viral assembly. Not only viral
components, but also complete infectious virions, can be assembled
in vitro
from single molecules or synthetic materials.
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In both “top down” and “bottom up” approaches, stoichiometric
determination of the components of the nanostructure is critical.
Hill Cooperativity Coefficient
The use of mathematical rationales in combination with experimental
analyses is a versatile and powerful tool for stoichiometric quantification.
Biological systems and molecular processes have been analyzed by a vari-
ety of mathematical methods, depending on the desired scientific objec-
tive.
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. One method widely used to analyze binding equilibrium in
ligand-receptor interaction is the application of the Hill equation. The
most common measure of cooperativity was produced by A. V. Hill,
when he devised a method based on plotting the partial pressure of oxy-
gen against the fractional saturation of myoglobin and hemoglobin.
99
He defined the steepness of the slope at 50% saturation in a double-log-
arithmic graph to be the Hill coefficient. If this coefficient is 1, repre-
senting only one binding site, this indicates complete non-cooperativity,
as was found for myoglobin. With only one binding site, it would not be
possible for there to be any interaction between two myoglobin mole-
cules. Hill coefficients larger than one indicate positive cooperativity, as
is the case with hemoglobin, where the value is close to 3. An adap-
tation of the basic equation from which the Hill coefficient is derived
is:
n
Y
)]/
d
log
X
, where
Y
is the overall fractional satu-
ration, and X is the ligand activity. This equation provides a method not
only to measure the affinity of a ligand for a receptor, but also to estimate
=
d
log[
Y
/(1
−
