Chemistry Reference
In-Depth Information
The reduction of the water diffusion coefficient in tissue is not thought to be
caused by the presence of cell membranes. The plasma membrane is so perme-
able that diffusion is not restricted. The obstruction caused by large molecules
and subcellular organelles is thought to increase the diffusive path length. Wa-
ter molecules that are bound to macromolcules or other structures must also be
considered, as these contribute to image signal, but are not free to diffuse. The
characteristics of many subcellular structures are presumed to affect the motility
of a significant fraction of the water. Three factors are thought to influence intracel-
lular diffusion; fluid viscosity, binding to macromolecules and collisions between
solutes and macromolecules. Garcia-Perez et al. [64] investigated the influence of
molecular crowding and viscosity on the translational motion of metabolites in
subcellular organelles using a pulsed gradient spin echo (PGSE) NMR technique.
Their results indicated that the concentration of molecules of a similar size to the
metabolites under study, had the greatest influence on their observed diffusion co-
efficients. These results could be explained by an intracellular environment more
crowded, but not more viscous, than the extracellular environment. Large static
cellular structures did not significantly hinder the translational diffusion of water,
but are found to obstruct the movement of larger biomolecules.
J.
Anomalous Diffusion in Tissue
As discussed in Section II.A, in systems where particles or molecules diffuse
freely via Brownian dynamics, the mean-square displacement of the particles is
proportional to time. With more complex architecture, such as within living cells,
diffusion may be hindered by various factors, such as interactions with obstacles,
transient binding events, or molecular crowding [65]. In such environments, the
motion of the molecules is often anomalous, with a distribution of diffusion times,
and the mean-square displacement does not therefore increase linearly with time.
Searching for a specific target is a universal process in living systems, and
this ranges from the macroscopic field of zoology (e.g., prey-predator) to the
microscopic requirement for macromolecular binding in living cells [66]. It is
assumed that the random encounter rate of two interacting bodies is determined
by Brownian motion. The searching inside a living cell, however, is governed by
both normal diffusion and subdiffusion. Indeed we have seen that subdiffusion is
characterized a by mean-square displacement that grows like
t
α
,0
<α<
1, (i.e., a slower spreading than for normal diffusion is observed due to the exponent
α<
1). Guigas and Weiss [67, 68] have shown, using fluorescence correlation
spectroscopy, that diffusion in the cytoplasm and the nucleus of eukaryotic cells
is subdiffusive, with values of
α
in the range 0.5-0.85. Golding found similar
behavior for bacteria [69]. The origin of the subdiffusive behavior appears to arise
from molecular crowding. Crowding in cells is thought to influence not only protein
and nucleic acid diffusion, but also molecular recognition, protein assembly, and
x
2
(
t
)
∼
