| dc.description.abstract | This thesis studies the dissociation of an adhesion cluster under shared linear loading
theoretically. A cluster of ligand-receptor pairs in cell adhesion can be modeled as Nt
parallel weak bonds between two surfaces. The cluster dissociates under an applied force
F which increases linearly with time t, that is, F = Gamma t, where Gamma is the loading rate. Monte
Carlo simulations of master equation are performed with two choices of kon and koff ,
the rebinding and unbinding rates of a bond, respectively. Our simulations show that
there exist a critical force per bond fc = Fc/Nt and a critical loading rate Gamma c, and some
universal properties of the clusters are associated with these quantities. At Gamma < Gamma c, the
rupture force per bond fr is close to but lower than fc. In this regime, cluster dissociation
can be regard as a one-dimensional barrier crossing process. We approximate the free
energy of the adhesion cluster G(Nb, F) at given F by a cubic function of Nb, number
of closed bonds in the cluster. From analytical solutions we obtained a scaling relation
< Fc - Fr >Nt^(-1/3) ~ [ln Gamma^(-1)]^(2/3) + constant. This scaling relation is consistent with the
numerical simulations of the master equation. At Gamma = Gamma c, the cluster dissociation occurs
at fr = fc for any cluster size. At Gamma > Gamma c, fr > fc and fr increases rapidly with Gamma,
especially for small clusters. There is no free energy barrier when the clusters rupture
at fr > fc, the numerical solutions of rate equation agree with numerical simulations of
the master equation.
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