Biomedical Engineering Reference
In-Depth Information
up to 48 h) while spherical and elliptical disc-shaped particles did not have an
impact on these properties (Doshi and Mitragotri
2010
).
Recent studies focused on dynamic manipulation of particle geometry as a tool
to precisely control particle-cell interactions (Caldorera-Moore et al.
2010
). As an
example, Yoo and Mitragotri have designed polymeric particles able to switch
shape in a stimulus-responsive manner (Yoo and Mitragotri
2010
). The shape-
switching behavior was a result of a fine balance between polymer viscosity and
interfacial tension and could be tuned based on external stimuli (temperature, pH,
or chemicals in the medium). Shape changes altered phagocytosis of elliptical par-
ticles that were previously not internalized by the cells (Yoo and Mitragotri
2010
).
These results clearly emphasize the importance of size, shape and surface physico-
chemical properties in controlling the rate of uptake of nanovectors.
A number of mathematical models and design maps were proposed to explain the
effect of particles geometry on the intracellular uptake kinetics and to enable rational
design of the nanocarriers, respectively. Based on the above experimental results, the
rate of uptake can be described through a first order kinetic law where the intracel-
lular concentration
C
i
(
t
) increases with time following the relationship (1)
dC t
()
(1)
i
=
k Ct k
c
−
()
=
t
−
1
int
i
int
w
dt
where
t
w
is the characteristic time for the nanovector to be wrapped by the cell
membrane, which can be related to the nanovector geometry (size, shape) and sur-
face chemistry (zeta potential, specific ligands). Mathematical modeling for receptor-
mediated internalization based on an energetic analysis has shown that there is a
minimal threshold particle radius to enable intracellular uptake. Below this point the
internalization is energetically unfavorable. Similar analysis shows that the surface
physico-chemical properties of the nanovector related to that of the cell membrane
can dramatically increase or decrease the uptake rate (Decuzzi and Ferrari
2007,
2008b
). A mathematical model developed to predict the rate of uptake for ellipsoidal
particles as a function of their aspect ratio indicate that spherical or oval particles can
be more rapidly internalized by cells compared to elongated particles.
The effect of geometry on the intracellular delivery properties of nanovectors
can further be integrated together with other geometry-affected biological pro-
cesses (e.g. margination, vascular transport, adhesion to vessel walls, etc.) to gener-
ate generalized design maps which recapitulate the performances of nanovectors in
terms of transport, specific recognition and adhesion, and uptake as a function of
the design parameters and physiological/biophysical conditions. As an example,
design maps have been generated in the simpler case of spherical particles as a
function of the non-specific interaction factor, which accounts for the steric and
electrostatic surface interactions between the particle and a cell; and of the ratio
between the number of ligand molecules distributed over the particle surface and
the number of receptor molecules expressed over the cell membrane. As a function
of these parameters, design maps allow for estimating the propensity of a circulat-
ing nanovector to adhere and be internalized by cells (Decuzzi and Ferrari
2008a
).
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