ABSTRACT
We study the dynamics of genetic code evolution. The model of Vetsigian et al. [Proc. Natl. Acad. Sci. USA 103, 10696 (2006)PNASA60027-842410.1073/pnas.0603780103] and Vetsigian [Collective evolution of biological and physical systems, Ph.D. thesis, 2005] uses the mechanism of horizontal gene transfer to demonstrate convergence of the genetic code to a near universal solution. We reproduce and analyze the algorithm as a dynamical system. All the parameters used in the model are varied to assess their impact on convergence and optimality score. We show that by allowing specific parameters to vary with time, the solution exhibits attractor dynamics. Finally, we study automorphisms of the genetic code arising due to this model. We use this to examine the scaling of the solutions to re-examine universality and find that there is a direct link to mutation rate.
ABSTRACT
Restriction enzymes recognize and bind to specific sequences on invading bacteriophage DNA. Like a key in a lock, these proteins require many contacts to specify the correct DNA sequence. Using information theory we develop an equation that defines the number of independent contacts, which is the dimensionality of the binding. We show that EcoRI, which binds to the sequence GAATTC, functions in 24 dimensions. Information theory represents messages as spheres in high dimensional spaces. Better sphere packing leads to better communications systems. The densest known packing of hyperspheres occurs on the Leech lattice in 24 dimensions. We suggest that the single protein EcoRI molecule employs a Leech lattice in its operation. Optimizing density of sphere packing explains why 6 base restriction enzymes are so common.
Subject(s)
DNA Restriction Enzymes/genetics , DNA-Binding Proteins/genetics , DNA/genetics , Deoxyribonuclease EcoRI/genetics , Bacteriophages/genetics , Base Sequence , DNA/chemistry , DNA Restriction Enzymes/chemistry , DNA-Binding Proteins/chemistry , Deoxyribonuclease EcoRI/chemistry , Models, MolecularABSTRACT
We present a consistent string theory model which produces a simple extension of the standard model, consisting of a D3-brane at a simple orbifold singularity. We envision this as a local singularity within a warped compactification. The phenomenology of the model has some novel features. We note that, for the model to be viable, the scale of stringy physics must be in the multi-TeV range. There are natural hierarchies in the fermion spectrum and there are several possible experimental signatures of the model.
