I completed my PhD in May 2015 under the guidance of Shamgar Gurevich.
My thesis consists of two projects:
Chapter 2, "Semi-algebraic geometry of common lines", descrbes the geometry of "common lines" datasets. Common lines datasets are computed from images produced in cryo-electron microscopy (cryo-EM), and can be used to build 3D models of biological molecules from 2D projections.
Chapter 3, "A remark on detecting 3D molecular symmetries from 2D cryo-EM images", describes an algorithm for computing the 3D symmetries of a biological molecule from 2D cryo-EM images.
In 2015-2018, I will be a Morrey Assistant Professor (
=postdoc) at UC - Berkeley.
I'll be mentored by Eva Nogales (Molecular & Cell Biology) and Bernd Sturmfels (Mathematics).
- Applications of algebra to structural biology
- Real algebraic geometry
- Implementing algorithms based on these ideas
I am interested in applications of algebra to problems outside mathematics. My thesis uses tools from real algebraic geometry, optimization and group theory to study the geometry and symmetry of datasets produced in cryo-electron microscopy (cryo-EM). Cryo-EM is a technique used in structural biology to produce 3D models of proteins from very noisy 2D projections.
In October 2014 I was awarded my department's John Nohel prize for outstanding thesis work in Applied Mathematics.
In my postdoc I am interested in using the mathematical viewpoint I have developed to create algorithms that improve 2D to 3D reconstruction in cryo-EM. Please contact me for my research statement which outlines several specific projects along these lines.
An important goal of my research plan is to collaborate directly with cryo-EM experimentalists. I hope that working closely with scientists will help produce algorithms suitable for laboratory use and which address actual problems of the cryo-EM community.
- David Dynerman, Shamgar Gurevich, and Yoel Shkolnisky. A remark on detecting molecular symmetry from cryo-EM images. In preparation. 2014.
- David Dynerman. Semi-algebraic Geometry of Common Lines. Research in the Mathematical Sciences, December 2014.
- David Dynerman, Erick Butzlaff, and Julie C. Mitchell. CUSA and CUDE: GPU-Accelerated Methods for Estimating Solvent Accessible Surface Area and Desolvation. Journal of Computational Biology. 2009.
- FlowSym: A flowchart algorithm for detecting molecular symmetry from cryo-EM images. In preparation.
- CUDESA: GPU accelerated code for calculating solvent accessible surface area and desolvation for protein-protein interfaces. Download. 2008.