Chemistry Reference
In-Depth Information
protein folding [70]. A slow sampling process is implied by the slower spreading
associated with subdiffusion. Molecules remain at their original position for a
longer time. Using simulations to determine the probability of finding a molecular
binding partner by diffusion, Guigas et al. [66] concluded that for an infinite search
time anomalous subdiffusion is the optimum search strategy. While anomalous
subdiffusion (
α<
1) is slower than normal diffusion (
α
1), it is not slow enough
to prevent the occurrence of biochemical reactions. In addition, due to its fractal
nature, the subdiffusive random walk causes a particle to traverse (search) the
available space most thoroughly. The anomalous diffusion exponent
α
is found to
decrease continuously with increasing concentrations of obstacles and increasing
molecular weight [70, 71].
Fluorescence correlation spectroscopy (FCS) is an optical method that mea-
sures concentration fluctuations of molecules on a very short time scale. The FCS
detects fluorescence intensity fluctuations from a microscopic illuminated volume
containing only a small number of fluorochrome molecules (a femtoliter or less)
[72]. The molecules travel across the observed volume due to Brownian motion,
and this leads to changes in detected fluorescence. The other source of variation in
measured fluorescence is the switching of the fluorophore from its fluorescent to
nonfluorescent state. Through the application of time correlation analysis both the
hydrodynamic and photophysical properties of the molecules can be assessed. As
we will find later for diffusion MRI data, there is considerable debate concerning
the analysis of FCS data, including the choice of a mathematical model. The most
commonly used model assumes a power law scaling as quoted in the previous
paragraph and Eq. (86). Hypothetical mechanisms for this anomalous behavior
include corralling, immobile obstacles and binding with a distribution of binding
durations. An alternative is the two component model, where one fraction of the
sample molecules undergoes free Brownian motion with a diffusion coefficient
approximately five times smaller than in bulk solution, and the second fraction
diffuses one or two orders of magnitude slower.
Anomalous diffusion has been detected in biological tissue using a fringe field
NMR technique [73]. Field gradients in the usual pulsed-gradient stimulated echo
method are relatively small and consequently, the corresponding observable length
scale exceeds cellular dimensions. Thus the influence of cellular structure may be
approximated by solutions of the diffusion equation with boundary conditions.
The field gradient in the superconducting fringe field method exceeds the field
gradient of the pulsed-gradient stimulated-echo method by orders of magnitude,
which leads to length scales within cellular regions. The diffusion resolution of
this method is
=
m. The term resolution implies the mean-squared distance
a molecule must move to sense the gradient spatial encoding. The fringe-field
method was first developed by Kimmich et al. [74], to avoid some of the drawbacks
encountered when large field gradients are applied in standard NMR experiments,
such as heating, eddy currents, and vibrations.
∼
1-15
