Membrane-Based Nanotechnology and Drug Delivery - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 129

where f denotes a function of L , H , m , and ρ np , ext . Here, H is the

average Hamiltonian of any nanoparticle inside the membrane and m is the relative
dielectric constant characteristic of the membrane. The most important component
contributing to H can be expressed as follows:

( L , H , ε m , ρ np , ext )

H = U np − lip + T np (6.4)

Here, U np − lip stands for the sum of all interaction potentials felt by a nanoparticle
and T np stands for the nanoparticle's kinetic energy while inside the membrane. For
experimental purposes, synthetic lipids (for example from Avanti Polar, 700 Indus-
trial Park Drive, Alabaster, Alabama 35007-9105) are used in model membrane sys-
tems. If we use no other membrane proteins but the lipids and membrane-stabilizing
hydrocarbons to form a membrane (e.g., see [ 1 , 2 ]), we can consider the expression
of U np-lip to follow the relation

U np-lip = U ES + U vdW + U mechanical + U hydration (6.5)

where U ES is the total electrostatic interaction (ES) energy and U v dW is the sum of
the van der Waals (vdW) interaction energies of the nanoparticle with lipids in the
pathways of the nanoparticle. U mechanical is the energy arising from the mechanical
properties, namely the membrane elasticity and membrane monolayer curvature.
U hydration is the contribution due to the hydration energy. For the sake of simplicity,
we have ignored the energy contributions due to the interactions with hydrocarbons
and any other possible sources.
Previous chapters have discussed how the various energy contributions can be
derived if the structural and charge properties of the participating components are
known. Since this chapter is dedicated to a better understanding needed to develop
new technology which will help to deliver nanoparticles into the cell's interior
regions, here we focus more on developing engineering insights and less on the
understanding of scientific analogies. To understand the general particle diffusion
across membranes, the interested reader can consult many excellent articles or books
(e.g. [ 24 ]). In this chapter, we aim to develop an understanding of how nanoparticles
interact with membranes, which is a key to the engineering of nanotechnology tools
needed to deal with controlled nanoparticle transport across the membrane.

6.3.1 Certain Nanoparticles Disrupt Membranes

Instantaneous disruption of membrane's barrier properties may raise the possibility
for various agents to reach inside the cellular interior regions. Nanoparticles that are
designed to deliver drugs beyond the membrane may interact with the membrane
itself and create holes or defects there. The meaning of the term 'hole' or 'pore'
with respect to a living cell membrane used here is consistent with that described in
Chap. 4 . The complete loss of a region of the plasma membrane where the lipids are