Quantum mechanical model for information transfer from DNA to protein.

Area of Science:

• Quantum Information Science
• Molecular Biology
• Computational Biology

Background:

• The central dogma of molecular biology describes information flow from DNA to protein.
• Understanding this process at a fundamental level requires advanced theoretical frameworks.

Purpose of the Study:

• To present a novel model for DNA to protein information transfer.
• To utilize quantum information and computation techniques to describe this biological process.

Main Methods:

• Modeling DNA as the sender and proteins as the receiver of information.
• Employing a 64-dimensional Hilbert space for DNA triplets (codons) and constructing a Hamiltonian matrix.
• Describing protein information using a 64-dimensional Hilbert space with degenerate eigenvalues, reflecting amino acid composition.

Main Results:

• The DNA information space uses non-degenerate eigenvalues for its Hamiltonian matrix.
• The protein information space exhibits degenerate eigenvalues, with Hilbert subspaces representing individual amino acids.
• The shift in Hilbert space structure models the degeneracy of the genetic code and protein synthesis.

Conclusions:

• Quantum information theory provides a robust framework for understanding biological information transfer.
• The mathematical structure of Hilbert spaces and Hamiltonians can elucidate the degeneracy and conservation principles in the genetic code.