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Algorithms for Mapping Nucleic Acid Free Energy Landscapes


Othmer, Jonathan Andrew (2009) Algorithms for Mapping Nucleic Acid Free Energy Landscapes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VJX1-6376.


To complement the utility of thermodynamic calculations in the design and analysis of nucleic acid secondary structures, we seek to develop efficient and scalable algorithms for the analysis of secondary structure kinetics. Secondary structure kinetics are modeled by a first-order master equation, but the number of secondary structures for a sequence grows exponentially with the length of the sequence, meaning that for systems of interest, we cannot write down the rate matrix, much less solve the master equation. To address these difficulties, we develop a method to construct macrostate maps of nucleic acid free energy landscapes based on simulating the continuous-time Markov chain associated with the microstate master equation. The method relies on the careful combination of several elements: a novel procedure to explicitly identify transitions between macrostates in the simulation, a goodness-of-clustering test specific to secondary structures, an algorithm to find the centroid secondary structure for each macrostate, a method to compute macrostate partition functions from short simulations, and a framework for computing transition rates with confidence intervals. We use this method to study several experimental systems from our laboratory with system sizes in the hundreds of nucleotides, and develop a model problem, the d-cube, for which we can control all of the relevant parameters and analyze our method's error behavior. Our results and analysis suggest that this method will be useful not only in the analysis and design of nucleic acid mechanical devices, but also in wider applications of molecular simulation and simulation-based model reduction.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:model reduction; multi-scale modeling; nucleic acids
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Pierce, Niles A.
Thesis Committee:
  • Pierce, Niles A. (chair)
  • Meiron, Daniel I.
  • Owhadi, Houman
  • Marsden, Jerrold E.
Defense Date:9 June 2008
Record Number:CaltechETD:etd-12312008-153810
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5172
Deposited By: Imported from ETD-db
Deposited On:13 May 2009
Last Modified:25 May 2021 00:17

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