Spatio–temporal analysis of changes of shape for constituent bodies within biomolecular aggregates

Roberts, Carl (2012) Spatio–temporal analysis of changes of shape for constituent bodies within biomolecular aggregates. Doctoral thesis, University of East Anglia.

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Changes of shape are important in many situations of interest in biology at different typical
length scales. Approaches for modelling the behaviour of droplets in suspension and thermallydriven
motion of the molecular chains in enzymes are presented. Both models use orthogonal
basis functions to describe the spatial dependences in a spherical geometry. Both models also
describe the effect of time-dependent boundary data on the shape of the bodies involved, a
stochastic response for the enzyme model (dimensions of the order 10−9 m) and smooth response
for the colloidal model (dimensions of the order 10−6 m).
The first model presented considers the behaviour of a droplet of fluid surrounded by a thin
film of host fluid, both fluids being Newtonian and immiscible, with a well-defined continuous
and smooth interface between these regions. The flows for the droplet and host fluid are assumed
axisymmetric with small Reynold numbers. An extension of traditional lubrication theory is
used to model the flow for the host fluid and a multi-modal Stokes flow is used to derive the flow
within the droplet, subject to continuity conditions at the interface between the droplet and
host fluid. The interface is free to move in response to the flows, under the effects of interfacial
tension. Asymptotic expansions for the flow variables and interface are used to find the simplest
behaviour of the system beyond the leading order.
The second unique modelling approach used is the method of Zernike moments. Zernike
moments are an extension of spherical harmonics to include more general radial dependence and
the ability to model holes, folded layers etc. within and on the unit sphere. The method has
traditionally been used to describe the shape of enzymes in a static time-independent manner.
This approach is extended to give results based on the thermally-driven motion of atoms in
molecules about their equilibrium positions. The displacements are assumed to be fitted by
Normal probability distributions. The precision and accuracy of this model are considered and
compared to similar models.
Results are plotted and discussed for both regimes and further extensions, improvements
and basis for further work are discussed for both approaches.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Users 2259 not found.
Date Deposited: 20 Dec 2012 10:32
Last Modified: 21 Feb 2013 12:53

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