#### Date of Award

9-2012

#### Document Type

Open Access Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Degree Program

Polymer Science and Engineering

#### First Advisor

Murugappan Muthukumar

#### Second Advisor

V. Adrian Parsegian

#### Third Advisor

Gregory Grason

#### Subject Categories

Engineering | Polymer and Organic Materials

#### Abstract

In this work we study three systems of biological interest: the translocation of a heterogeneously charged polymer through an infinitely thin pore, the wrapped of a rigid particle by a soft vesicle and the modification of the dynamical properties of a gel due to the presence of rigid inclusions.

We study the kinetics of translocation for a heterogeneously charged polyelectrolyte through an infinitely narrow pore using the Fokker-Planck formalism to compute mean first passage times, the probability of successful translocation, and the mean successful translocation time for a diblock copolymer. We find, in contrast to the homopolymer result, that details of the boundary conditions lead to qualitatively different behavior. Under experimentally relevant conditions for a diblock copolymer we find that there is a threshold length of the charged block, beyond which the probability of successful translocation is independent of charge fraction. Additionally, we find that mean successful translocation time exhibits non-monotonic behavior with increasing length of the charged fraction; there is an optimum length of the charged block where the mean successful translocation time is slowest and there can be a substantial range of charge fraction where it is slower than a minimally charged chain. For a fixed total charge on the chain, we find that finer distributions of the charge along the chain leads to a significant reduction in mean translocation time compared to the diblock distribution.

Endocytosis is modeled using a simple geometrical model from the literature. We map the process of wrapping a rigid spherical bead onto a one-dimensional stochastic process described by the Fokker-Planck equation to compute uptake rates as a function of membrane properties and system geometry. We find that simple geometrical considerations pick an optimal particle size for uptake and a corresponding maximal uptake rate, which can be controlled by altering the material properties of the membrane.

Finally, we use a mean field approximation, neglecting correlations among the embedded particles, to examine the effect of inclusions in a viscoelastic medium on the effective macroscopic properties of the gel. We find an essentially linear dependence of both components of the complex shear modulus up to arbitrary volume fractions of the inclusions, in contradiction to experimental observations. We conclude that the incorporation of correlations among the particles is needed in order to explain experiments, in analogy with the elastic case.

#### Recommended Citation

Mirigian, Stephen William, "Dynamics and Kinetics of Model Biological Systems" (2012). *Open Access Dissertations*. 653.

https://scholarworks.umass.edu/open_access_dissertations/653