Biomedical Engineering Reference
In-Depth Information
(
Centi et al., 2008
), (d) binding of different concentrations of cholesterol (in mg/dl) to a cho-
lesterol biosensor (
Shin and Liu, 2007
), (e) binding and dissociation of PSA to different gold
nanocrystals for different immunoprobe concentrations (10
7
M) in solution (
Cao et al.,
2009
), (f) binding of the transcription factors rhSP1 and rhNF-
k
B to their corresponding oli-
gonucleotides on a microcantilever array (
Huber et al., 2006
), and (g) binding and dissocia-
tion of different concentrations (in nM) of thrombin in solution to the best aptamer in
generation 4(G4.0422) immobilized on a SA chip (
Platt et al., 2009a,b
). The fractal dimen-
sion values provide a quantitative indicator of the degree of heterogeneity present on the sen-
sor chip surface. Binding and dissociation values, and affinity values are provided whereever
possible. The fractal dimension for the binding and the dissociation phase is not a typical
independent variable that may be directly manipulated. It
is estimated from Equations
(15.1-15.3), and one may consider it as a derived variable.
In a general sense, fractal models are fascinating. Newer avenues are required to analyze and
help detect protein biomarkers for disease and medically-oriented analytes at very dilute
levels. The sooner one is able to help detect these protein biomarkers for certain diseases
accurately, the better is the prognosis for that disease. Of course, the detection of these pro-
tein biomarkers (and subsequently the onset of the disease) is more and more difficult during
the early stages. If one may take the liberty of mentioning cancer, it generally goes through
roughly three stages: the initial, intermediate, and “blast” stage. The initial stage is rather
lengthy (perhaps a time period of years) and is very difficult to detect. During the blast stage
(time period of months or even weeks) the cancer is easier to detect, but by then perhaps it is
too late. This example lays emphasis on the ability to be able to detect the different protein
biomarkers for the different diseases at continuously lower and lower levels.
An increase in the fractal dimension value or the degree of heterogeneity on the biosensor
surface leads, in general, to an increase in the binding and in the dissociation rate coefficient.
It is suggested that the fractal surface (roughness) leads to turbulence, which enhances
mixing, decreases diffusional limitations, and leads to an increase in the binding rate coeffi-
cient (
Martin et al., 1991
). For this to occur, the characteristic length of the turbulent bound-
ary layer may have to extend a few monolayers above the senor chip surface to affect bulk
diffusion to and from the surface. However, given the extremely laminar regimes in most
biosensors, this may not actually take place. The sensor chip surface is characterized by
grooves and ridges, and this surface morphology may lead to eddy diffusion. This eddy dif-
fusion can then help to enhance the mixing and extend the characteristic length of the bound-
ary layer to affect the bulk diffusion to and from the surface.
The predictive relationships are developed for the binding rate coefficient as (a) a function of
the fractal dimension for the screen-printed cholesterol biosensor (
Shin and Liu, 2007
), and
(b) for the binding rate coefficient k as a function of the thrombin concentration in the
16-130 nM range and (c) for the binding to the best aptamer in generation 4 (G4.04422)
