Symmetry-breaking motility and RNA secondary structures

This thesis contains work on three separate topics: the spontaneous motility of functionalized particles, the designability of RNA secondary structures, and the statistical mechanics of homopolymer RNAs. For the work on spontaneous motility, we were motivated by in vitro experiments investigating the symmetry-breaking motility of functionalized spherical beads to develop a general theory for the dynamics of a rigid object propelled by an active process at its surface. Starting from a phenomenological expansion for the microscopic dynamics, we derive equations governing the macroscopic velocities of the object near an instability towards spontaneous motion. These equations respect symmetries in the object's shape, with implications for the phase behavior and singularities encountered at a continuous transition between stationary and moving states. Analysis of the velocity fluctuations of such an object reveals that these fluctuations differ qualitatively from those of a passive object. For the work on designability, we investigated RNA folding within a toy model in which RNA bases come in two types and complementary base pairing is favored. Following a geometric formulation of biopolymer folding proposed in the literature, we represent RNA sequences and structures by points in a high-dimensional "contact space." Designability is probed by investigating the distribution of sequence and structure points within this space. We find that one-dimensional projections of the sequence point distribution approach normality with increasing RNA length N.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2005

Author dc:creator

• Lee, Allen, S.M. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Mehran Kardar.

• Physics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34396

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34396