Suzanne Sindi

Address

Brown University
Division of Applied Mathematics
Box F / 182 George Street
Providence, RI 02912

Research interests

My research area focuses on varied problems in applied non-linear dynamics. I am particularly interested in computational biology and genomics as well as ideas concerning the measure theoretic properties of dynamical systems.  I am currently involved in the following areas of research:

Genome Assembly:  The first is a interdisciplinary group working on improving the process for determining the genome of an organism. This project has involved working with students and professors at the University of Maryland from the mathematics, computer science, physics and biology programs. We have also collaborated with experts at the Institute for Genomic Research and the Baylor College of Medicine.

Fractal Basin Boundaries:  My interest in the dynamical systems was what interested me in pursuing an advanced degree in applied mathematics. In this project I worked to understand some of the more recent ideas in the structure of basins of attraction of low dimensional maps.

Repetitive Regions in DNA:  The genome or DNA sequence of an organism is a sequence of nucleic acids represented by letters from the alphabet {A,C,G,T}. The length of this sequence varies from several million letters in types of bacteria to several billions in a mammalian genome.While genomes have been obtained for a variety of organisms, including fruit fly, worm and rat, there is still much to be learned about the properties of the genome itself. Repeat regions, sequences that occur repeatedly throughout the genome, are an area of significant interest.

Since DNA sequences come from a small alphabet we expect to see subsequences that occur more that once; for example if a DNA sequence is longer than (4k+k+1) letters for some positive integer k, by the Pigeon Hole Principle there will be at least one repeated k length subsequence. However there are substantially longer sequences that appear far more often than chance would allow in DNA. These repeated regions of DNA have been the focus of my research. The concept of a repetitive region in a genome is difficult to precisely define. Repeat regions can occur many times in a genome and distinct copies have differences between them. Papers on repetitive DNA tend to be vague when discussing what constitutes a repeat region.

I began my research by addressing this problem through providing a quantification of repeat regions that is well defined for an arbitrary DNA sequence. Let us define a repeat string S to be a subsequence of DNA where, for some fixed n, every n-letter word in S occurs at least twice in a genome. I have investigated the structure of repeat strings in the genomes of C. elegans (a worm) and Arabidopsis (a plant). I have found a surprising power law structure in the distribution of lengths of repeat strings.  I have used several simple models of evolution of repeat strings in the genome and found the that underlying power law structure will emerge as the stationary distribution of this evolutionary process.

Symbolic Dynamical System for Reconstructing Repetitive DNA:  The process of determining the DNA sequence of an organism, called genome assembly, remains extremely expensive and the process is far from perfected. The initial draft of the Human Genome took a decade to develop and cost many billions of dollars. In order for sequencing the genome of individual organisms to be viable, the process of genome assembly must be substantially improved.

The main algorithmic complication in genome assembly is the presence of highly repetitive DNA. Unfortunately repetitive DNA can make up a significant portion of the genome of an organism. For example, nearly 50% of the human genome is expected to be repetitive. The goal of my work in genome assembly was to use information present to construct what we call consensus copies of repetitive regions. I create a symbolic dynamical systems algorithm on a graph whose nodes are k-letter words from the DNA alphabet. A trajectory of our dynamical system is a string that hopefully corresponds to a repeat string in our genome.  I've tested my method for constructing consensus copies of repeat strings using data from several species including fruit fly, rat, chicken and mosquito. I am currently looking at developing software to assemble these regions that could be provided to the genome assembly community.

Wada Basins in One-Dimensional Maps:  In dynamical systems with more than one co-existing attractor the basins of attraction can become entangled in such a way that the boundary of all basins coincides. A special type of entangled basin boundaries is that of a Wada Basin, where every point on the boundary of the basin is also a boundary point of three attractors. Such phenomena have been show to occur in many physical systems such as a forced damped pendulum and forced Duffing Oscillator.  Additionally, under certain conditions Wada Basins also exist in One-Dimensional Maps. Wada Basins have been shown to emerge from tangent bifurcation when there are three co-existing attracting fixed points and particular conditions are met. My hope is to work toward extending these results on the emergence of Wada Basins to periodic points of arbitrary period and to higher dimensional systems.

Publications

Honors

Ruth Davis Award, University of Maryland; Award from the Dean of Computer, Mathematical and Physical Sciences (Spring 2005)

Spotlight on Graduate Research, University of Maryland; Winner of an annual graduate student conference in the math department. (Fall 2004) 

Nominee for Annual Department of Mathematics Excellence in Teaching Award  (Fall 2004) 

Graduate Research Interaction Day, University of Maryland; Winner of an annual university wide graduate student conference (Spring 2002) 

National Science Foundation Graduate Research Fellowship (Fall 2001) 

Outstanding Graduating Mathematics Student - California State University, Fullerton (Spring 2001) 

Award of Excellence - Phi Kappa Phi Honor Society (Spring 2001) 

American Association of University Women Scholarship: Award presented to an outstanding female student graduating with a bachelor’s degree. (Fall 2000) 

Runner-Up in Mathematical Sciences Category at the California State University Statewide Research Competition: Runner-Up in annual state-wide undergraduate research conference (Spring 2000)