DOI: 10.14704/nq.2015.13.4.875

Calabi-Yau Manifolds in Biology and Biological String-Brane Theory

Yi-Fang Chang

Abstract


Based on topological biology and structural biology, and combined the extensive quantum biology and general biological string, we propose that Calabi-Yau manifolds can provide a mathematical method to be applied to biology. Some Calabi-Yau spaces may possibly describe the biological spatial structures, in particular, in NeuroQuantology. In biology usual Calabi-Yau manifolds are also smaller and cannot be observed except microscope. It is used to superstring and brane, so may also describe some biological strings, and biological branes, etc. Further, this may combine the extensive graph theory, which includes five types of the basic elements: various solid lines, dotted lines, wavy lines, and vertices, fields. Variegated Calabi-Yau manifolds and superstring-branes correspond to multiformity of biological structures.

Keywords


biology; topology; structure; Calabi-Yau manifold; graph theory; string; quantum theory

Full Text:

Full Text PDF

References


Adams C and Franzosa R. Introduction to Topology: Pure and Applied. Prentice Hall, 2007.

Akey CW and Luger K. Histone chaperones and nucleo-some assembly. Curr Opin Struc Biol. 2003; 13:6-14.

Alam MT, Yamada T, Carlsson U and Ikai A. The importance of being knotted: effects of the C-terminal knot structure on enzymatic and mechanical properties of bovine carbonic anhydrase II. FEBS Lett. 2002; 519: 35-40.

Babtie AC, Kirk P and Stumpf MP. Topological sensitivity analysis for systems biology. Proc Natl Acad Sci USA. 2014; 111(52):18507-18512.

Ban N, Nissen P, Hansen J, et al. The complete atomic structure of the large ribosomal subunit at 2.4 ang-strom resolution. Science. 2000; 289(5481):905-920.

Belmont P, Constant J-F and Demeunynck M. Nucleic acid conformation diversity: From structure to func-tion and regulation. Chem Soc Rev. 2001; 30:70-81.

Bon M, Vernizzi G, Orland H and Zee A. Topological classification of RNA structures. Journal of Molecular Biology. 2008; 379(4): 900-911.

Branden C and Tooze J. Introduction to Protein Struc-ture (2nd Ed). New York: Garland Publishing, 1999.

Bremermann HJ and Thieme HR. A competitive-exclusion principle for pathogen virulence. J Math Biol. 1989; 27:179-190.

Candelas P, Horowitz GT, Strominger A and Witten E. Vacuum configurations for superstrings. Nucl.Phys.B. 1985; 258:46-74.

Chang Yi-Fang. Extensive quantum biology, applications of nonlinear biology and nonlinear mechanism of memory. NeuroQuantology. 2012a; 10(2):183-189.

Chang Yi-Fang. Nonlinear whole biology and loop quantum theory applied to biology. NeuroQuantology. 2012b; 10(2):190-197.

Chang Yi-Fang. Chaos, fractal in biology, biothermo-dynamics and matrix representation on hypercycle. NeuroQuantology. 2013; 11(4): 527-536.

Chang Yi-Fang. Extensive quantum theory of DNA and biological string. NeuroQuantology. 2014a; 12(3): 356-363.

Chang Yi-Fang. New tree-field representations in graph theory, extension of Dirac extraction, differential test for series of positive terms, complex dimension and their applications. International Journal of Modern Mathematical Sciences. 2014b; 9(1):1-12.

Chang Yi-Fang. New development on graph theory from Feynman diagram, and their applications in biology and other regions. International Journal of Modern Mathematical Sciences. 2014c; 12(1): 43-54.

Chang Yi-Fang. Topological physics, topological sciences and new research of string. International Journal of Modern Mathematical Sciences. 2015a; 13(1):86-100.

Chang Yi-Fang. Some solutions of extensive quantum equations in biology, formation of DNA and neurobiological entanglement. NeuroQuantology. 2015b; 13(3): .

Cupal J, Kopp S and Stadler PF. RNA shape topology. Alife. 2000; 6:3-23.

D'Auria R, Ferrara S and Trigiante M. On the super-gravity formulation of mirror symmetry in generalized Calabi-Yau manifolds. Nucl Phys. B. 2007; 780(1-2): 28-39.

Dickerson RE and Geis I. The Structure and Action of Proteins. New York: Harper and Rowe, 1969.

Diestel R. Graph Theory (2nd Ed.). Springer. 2000.

Distler J and Greene B. Some exact results on the superpotential from Calabi-Yau string compactifications. Nucl Phys B. 1988; 309:295-316.

Doyle DA, Cabral JM, Pfuetzner RA, et al. The structure of the sotassium channel: Molecular basis of K conduction and selectivity. Science. 1998; 280: 69-77.

Edelman GM. Neural Darwinism. New York: Basic Books, 1987.

Eccles JC. Evolution of the Brain: Creation of the Self. Routledge, 1990.

Eigen M. The origin of biological information. The Physicist’s Conception of Nature. D.Reidel Publishing Company, 1973. 594-632.

Eigen M and Schuster P. The Hypercycle: A Principle of Natural Self-organization. Berlin: Springer-Verlag, 1979.

Ellenberger T and Silvian LF. The anatomy of infidelity. Nat Struc Biol. 2001; 8:827-828.

Ellis RJ. Macromolecular crowding: an important but neglected aspect of the intracellur environment. Curr Opin Struc Biol. 2001; 11:114-119.

Erol M. Schrödinger wave equation and function: Basics and concise relations with consciousness/mind. NeuroQuantology. 2010; 8(1):101-109.

Fontana W and Schuster P. Continuity in evolution: on the nature of transitions. Science. 1998; 280:1451-1455.

Fried AA. Topological factors in radiation biology. Life Sciences and Radiation. 2004; 69-77.

Gepner D. Yukawa couplings for Calabi-Yau string compactifications. Nucl Phys B. 1988; 311:191-204.

Grandpierre A, Chopra D and Kafatos MC. The universal principle of biology: determinism, quantum physics and spontaneity. NeuroQuantology. 2014; 12(3):

Greene B, Vafa C and Warner N. Calabi-Yau manifolds and renormalization group flows. Nucl Phys B. 1989; 324:371-390.

Greene B and Plesser MR. Duality in Calabi-Yau moduli space. Nucl Phys B. 1990; 338:15-37.

Gross JL and Tucker TW. Topological Graph Theory. New York: Wiley, 1989.

Gross M, Huybrechts D and Joyce D. Calabi-Yau Mani-folds and Related Geometries. Berlin: Springer, 2003.

Groves MR and Barford D. Topological characteristics of helical repeat proteins. Current Opinion in Structural Biology. 1999; 9(3): 383-389.

Hartl FU and Hayer-Hartl M. Molecular chaperones in the cytosol: from nascent chain to folded protein. Science. 2002; 295:1852-1858.

Izhikevich EM. Neural excitability, spiking and bursting. Int J Bifurcat Chaos. 2000; 10(6): 1171-1266.

Khrennikov A and Basieva I. Quantum model for psychological measurements: from the projection postulate to interference of mental observables represented as positive operator valued measures. NeuroQuantology. 2014; 12(3):

Konishi M. Listening with two ears. Sci Am. 1993; 268(4): 34-41.

Lefschetz S. Applications of Algebraic Topology. Springer-Verlag, 1975.

Lee JM. Introduction to Topological Manifolds. Springer, 2000.

Lerche W, Vafa C and Warner N. Chiral rings in N=2 superconformal theories. Nucl Phys B. 1989; 324:427-474.

Leuther KK, Hammarsten O, Kornberg RD, et al. Structure of DNA-dependent protein kinase: implications for its regulation by DNA. EMBO J. 1999; 18:1114-1123.

Macgregor RJ. Quantum mechanics and brain uncertainty. Journal of Integrative Neuroscience. 2006; 5(3):373-380.

Marino M and Moore G. Counting higher genus curves in a Calabi-Yau manifold. Nucl Phys B. 1999; 543(3): 592-614.

Micklos DA, Freyer GA and Greg DA. DNA Science: A First Course (2nd Ed.). Cold Spring Harbor Laboratory Press, 2003.

Monastyrsky MI. ed. Topology in Molecular Biology. Springer, 2006.

Nada SI and Zohny H. An application of relative topology in biology. Chaos, Solitons & Fractals. 2009; 42(1):202-204.

Oparin AI. Genesis and Evolutionary Development of Life. New York: Academic Press, 1968.

Paci E and Kamplus M. Unfolding proteins by external forces and temperature: The importance of topology and energetics. Proc Natl Acad Sci. 2000; 97:6521-6526.

Rashevsky N. Topology and life: In search of general mathematical principles in biology and sociology. Bull Math Biophysics. 1954; 16: 317-348.

Rashevsky N. Some theorems in topology and a possible biological implication. Math. Sci. Net. 1955; 17: 111-126.

Rashevsky N. Contributions to topological biology: Some considerations on the primordial graph and on some possible transformation. Math Sci Net. 1956; 18:113-128.

Rashevsky N. A comparison of set-theoretical and graph-theoretical approaches in topological biology. Bull Math Biophysics. 1958; 20(3): 267-273.

Rescher N. Complexity: A Philosophical Overview. Transaction Publishers, 1998.

Saibil HR and Ranson NA. The chaperonin folding machine. Trends Biochem Sci. 2002; 27: 627-632.

Stadler BMR, Stadler PF, Wagner G and Fontana W. The topology of the possible: Formal spaces underlying patterns of evolutionary change. J Theoretical Biology. 2001; 213:241-274.

Stadler BMR and Stadler PF. The Topology of Evolutionary Biology. Modelling in Molecular Biology. Springer, 2004. 267-286.

Strominger A, Yau ST and Zaslow E. Mirror symmetry is T duality. Nucl Phys B. 1996; 479:243-259.

Tarlaci S. Quantum field theory and consciousness. NeuroQuantology. 2005;3:228-245.

Tarlacı S. Why we need quantum physics for cognitive neuroscience. NeuroQuantology. 2010a; 8(1):66-76.

Tarlaci S. On probabilistic quantum thinking. NeuroQuantology. 2010b; 8(4):S1-2.

Tarlaci S. The brain in love: Has neuroscience stolen the secret of love? NeuroQuantology. 2012; 10(4): 744-753.

Thornton JM, Todd AE, Milburn D, et al. From structure to function: Approaches and limitations. Nat Struct Mol Biol. 2000; 7: 991-994.

von Heijne G. Membrane-protein topology. Nat. Rev. Mol. Cell Biol. 2006; 7(12):909-918.

Weeks JR. The Shape of Space. New York: Marcel Dekker, Inc, 2002.

Wickner S, Maurizi MR and Gottesman S. Posttranslational quality control: folding, refolding, and degrading proteins. Science. 1999; 286(5446): 1888-1893.

Wuthrich K, Billeter M and Braun W. Pseudo-structures for the 20 common amino acids for use in studies of protein conformations by measurements of intramolecular proton-proton distance constraints with nuclear magnetic resonance. J Mol Biol. 1983; 169:949-961.

Yau S-T. Calabi’s conjecture and some new results in algebraic geometry. Proc Natl Acad Sci USA. 1977; 74:1798-1799.

Yau S-T. A general Schwarz lemma for Kähler manifolds. Amer J Math. 1978; 100: 197-203.

Yau S-T. On Ricci curvature of a compact Kähler manifold and complex Monge-Ampére equation I. Comm Pure and App Math. 1979; 31: 339-411.

Yau S-T. Compact three dimensional Kähler manifolds with zero Ricci curvature. In: Symposium on Ano-malies, Geometry, and Topology, (Chicago, IL., 1985). Singapore: World Sci Publishing, 1985. 395-406.

Yau S-T. Nonlinear analysis in geometry. Enseignement Math. 1986; 33:109-158.

Yau S-T and Zaslow E. BPS states, string duality, and nodal curves on K3. Nucl Phys B. 1996; 471: 503-512.

Zahn R, Liu A, Luhrs T, et al. NRM solution structure of the human prion protein. Proc Natl Acad Sci USA. 2000; 97(1):145-150.


Supporting Agencies

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.



| NeuroScience + QuantumPhysics> NeuroQuantology :: Copyright 2001-2019