On Dielectric Properties of DNA Molecules

With the abundance of genomic sequence data available nowadays, DNA plays a vital role in any scientific process in the field of biology, from gene therapy to drug discovery. A multitude of DNA binding proteins have been identified and their structures have been solved in complex with the DNA sequence they have preference for to bind. Yet, it remains still very hard to design a protein with engineered DNA binding preferences even when detailed knowledge of DNA–DNA and DNA–ligand structures can nowadays be obtained by high-resolution techniques. A good explanation of this situation, comes from the fact that energetic analysis of protein-DNA complexes, still remains experimentally and theoretically challenging, because it requires quantification of the different contributions to such interactions, in particular the electrostatic energy term.

Electrostatic forces have long been recognized to inherently influence the DNA structure and interactions including DNA bending and folding and DNA–ligand recognition, owing to the high charge density of the DNA molecule backbone, as well as the polar associative interactions between the nucleotide bases. Standard dielectric characterization tools, such as impedance spectroscopy and dielectrophoresis, only yield average values of DNA polarizability in bulk solution that include major secondary structural contributions and DNA-solvent interfacial effects (shielding). Latest experiments, calculate a value of 8.5D for the dielectric constant, which differs substantially both from values measured by the aforementioned techniques as well as from standard theoretical models ( typically assuming DNA to be a low-polarizable medium with 2-4D).

This work, which is laid in the form of a self-imposed Problem Set, aims to understand frequency dependance of the dielectric constant of DNA in solutions, in order to inform modern computational and experimental DNA assays. It starts by diving into the fields of electrostatic polarization and dielectric relaxation with the hope (hold your breath) to formulate a theoretical model for the dielectric spectrum of polar materials, like DNA polymers. It continues with the use of state-of-the-art Molecular Dynamic simulations, in order to test the full-atom available DNA structures against the theoretical model. Lastly, an experimental validation of the theoretical model is proposed and hopefully will be soon realized.

Bio-inspired Constraint Optimization

This was my initial idea for a class project, but I had to abandon it, as it comprised mostly of mathematical modeling and programming than physics. in a few words, the project would involve the study of Evolutionary Algorithms, i.e. search and optimization algorithms inspired by evolution in nature, focusing on Genetic Algorithms and Gene-Expression Programming. I am planning to explore this project next year, in context of the class Nature of Mathematical Modeling.

The motivation behind the study is recent findings in molecular and cell biology, which revealed the complexity and elegance of the cellular evolutionary mechanisms, departing drastically from the naive Mendelian view of evolution, i.e. random mutations and natural selection, that the computational Evolutionary Algorithms were initially based on. Epigenetics, miRNAs, transcription factors and DNA methylation are but a few of the techniques that a cell uses to regulate the expression of specific genes and chromosomal regions based on an environmentally defined fitness function. In this project, I would explore the implications of those mechanisms to the convergence of evolutionary algorithms in the context of constraint optimization problems.

Readings:

• Convergence Analysis of Canonical Genetic Algorithms
• An algebra for theoretical genetics
• The Thermodynamics of Computation
• Epi-genetics
• Gene Expression Programming