Quantum algorithms and the genetic code

Pramana - Journal of Physics

Volumn 56, Issue 2-3, 2001, Pages 367-381

  Patel, Apoorva ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Amino acid; Computation; Database search; DNA; Enzyme; Genetic information; Nucleotide base; Protein; Quantum coherence; Quantum mechanics

Indexed keywords

AMINO ACIDS; DATABASE SYSTEMS; DNA; ENZYMES; GENETIC ENGINEERING; PROTEINS;

GENETIC CODE; QUANTUM ALGORITHMS;

QUANTUM THEORY;

EID: 0035247078     PISSN: 03044289     EISSN: None     Source Type: Journal    
DOI: 10.1007/s12043-001-0131-8     Document Type: Article

References (20)

1. I mention here the explanation of physical shapes of living organisms [2]. At microscopic level, the physical forces (e.g. diffusion, surface tension) are essentially isotropic. Consequently single free cells are found to be more or less spherical in shape (e.g. many bacteria, amoeba). At larger scales, the isotropy is explicitly broken by gravity. This leads to large stationary living organisms being axially symmetric about the vertical direction (e.g. plants, hydra). The symmetry is also broken spontaneously by the need of the organisms to move/grow in order to find food. For small enough organisms where the effects of gravity is not important, there arises an axial symmetry about the direction of movement (e.g. worms, some bacteria). For most animals, both gravity and movement are important, with gravity restricting the direction of movement to be horizontal. The surviving symmetry is then bilateral, i.e. mirror reflection in the plane formed by directions of gravity and movement. What is striking in this example is the simplicity of the logic, i.e. how far one can go with how little input once the ingredients are right. It is also obvious that there is a limit to how far simple logic can be pushed - to explain the structure in more depth, one would require more detailed physical data.
2. M Gardner, The new ambidextrous universe: Symmetry and asymmetry, from mirror reflections to superstrings, Third Edition (W H Freeman, 1991).
3. For the above explanation of shapes of living organisms, one can estimate the scale at which effects of gravity and motion would become important. The orders of magnitude estimates do come out right. On the other hand, many attempts have been made to link observed chirality of important molecules of life (sugars and amino acids) to the chirality of the weak interactions. But weak interactions are just too weak to produce any influence at the molecular scale, and no attempt has come anywhere close to convincing
4. The same physical laws used by living organisms for self-perpetuation, also imply that the atoms making up the organisms will last forever. In that case, why the atoms should first organise themselves in complicated structures, and then try to perpetuate them, is something that I cannot answer
5. Protein synthesis involves several steps. First the DNA synthesises messenger RNA molecules, much in the same manner that it replicates itself. These m-RNA molecules then travel from the nucleus of the cell to the ribosomes in its cytoplasm. There, with the help of transfer RNA molecules, they construct proteins from amino acids. The matching between m-RNA and t-RNA molecules follow the same rules as in DNA replication
6. E Schrödinger, What is life? (Cambridge University Press, first published, 1944)
7. L Grover, A fast quantum mechanical algoritlim for database search, Proceedings of the 28th Annual ACM Symposium on Theory of Computing (Philadelphia, 1996) p. 212, quant-ph/9605043
8. I am using the standard quantum mechanical notation introduced by Dirac. The suffix b is used, since that will correspond to the state which forms hydrogen bonds in nucleotide base-pairing.
9. 2 = 1
10. C Zalka, Grover's quantum searching algorithm is optimal, Phys. Rev. A60, 2746 (1999), quant-ph/9711070
11. L Grover, Pramana - J. Phys. 56, 333 (2001)
12. J D Watson, N H Hopkins, J W Roberts, J A Steitz and A M Weiner, Molecular biology of the gene. Fourth Edition (Benjamin/Cummings, 1987)
13. The START signal for synthesis of an amino acid chain is somewhat complicated; it is represented by the code for the amino acid methionine preceded by an arrangement of several bases. But the STOP signal for terminating the chain is encoded in the DNA base sequence in the same manner as the signals for specific amino acids
14. DNA replication should be error-free to faithfully pass on the hereditary information to the next generation. Protein synthesis can tolerate more errors, since proteins are disposable items, made in large numbers and broken up into parts once their use is over. With Q = 3 and N = 21, the quantum search algorithm has an error rate of about 1 part in 1000
15. L Stryer, Biochemistry, Fourth Edition (W H Freeman, 1995)
16. An informative book at popular level is: J Gribbin, In search of the double helix: Quantum physics and life (Penguin Books, 1995)
17. 2 or =O group). Then pairing occurs amongst bases differing in both the bits
18. In the cellular environment, it is far more likely that this binding energy is released as an inelastic collision or a phonon, than the radiation of a photon
19. A different nucleotide base, I, appears sometimes in the wobble position of t-RNA. In the base-pairing between t-RNA and m-RNA at this position, the additional combinations, I-A, I-C, I-U and U-G, are held together by two hydrogen bonds
20. We can also look at a different example. Living organisms also carry out information processing using their nervous systems. This processing takes place at the cellular level, where classical physics dominates. Expectedly, neural communications use binary code - neurons communicate with each-other by firing electrical pulses, and a neuron fires or does not fire depending on whether its input potential is above or below certain threshold