Specific Adhesion of Soft Elastic Materials - Structural Interfaces and Attachments in Biology - page 157

adhesion can be significantly influenced by glycocalyx [ 64 - 66 ], we hypothesize
that cell surface repellers such as glycocalyx may also play a role in the phenome-
non of critical bond spacing. To address this issue, we considered an alternative
model of cell adhesion via opposing forces induced by polymer repellers and
ligand-receptor bonds, where we treat repellers and binders as worm-like chains
confined in a nanoslit in which ligand-receptor bonds transition stochastically
between open and closed states.
When a free polymer chain of contour length L , persistence length p , and mean-
squared radius of gyration R g [ 67 ] to be confined inside a nanoslit of separation h ,a
force f will be imposed on the opposing parallel walls. This force can be derived
based on the free energy expression given by Chen and Sullivan [ 68 ], which
appears as a repulsive force when h<<L .
In the case that the two ends of the polymer chain are tethered to the opposing
walls of the slit, the effect of end tethering is expected to be small for h ! 0. In the
opposite limit of h ! L , the chain becomes strongly stretched, and its force-
separation relationship can be given by the classical Marko and Siggia formula
[ 69 ]. For the intermediate range 0

< h < L , we propose an interpolating formula
on the force-separation relation [ 39 ]:

" #

k B T
p

1
4 ð 1 h=LÞ

1
4

h
2 L

2

R g k B T f ðh; p; LÞ¼

2

p

2

2 þ c 1 ðp=hÞþc 2 ðp=hÞ

(8.12)

5 = 3

2

6 h 3 ½ 1 þ c 3 ðp=hÞþc 4 ðp=hÞ

It can be easily verified that ( 8.12 ) matches the above-mentioned two limiting
cases of h ! 0 and h ! L .
Similar to the model as shown in Fig. 8.1 , we consider the molecular adhesion
mediated by polymer repellers of density r g and binders of density r 0 , among which
r b of them are actually closed. We adopt a rebinding rate per unit area of g ¼ k 0 g
ðr 0 r b Þ . Thus, ( 8.4 ) at steady state can be changed into

gðr 0 r b Þ¼ e f ðh eq ;L;pÞ=F b r b (8.13)

On the other hand, the stability of adhesion is considered as a competition
between attractive interactions of ligand-receptor binding and repulsive forces
due to the size mismatch between repellers and binders. According to ( 8.12 ), the
repulsive stress of polymer repellers and the attractive stress of the molecular bonds
can be expressed as s g ¼ r g f ðh eq ; p g ; L g Þ

and s b ¼ r b f ðh eq ; p b ; L b Þ , which must

balance, i.e.,

s b ¼ s g (8.14)