Abstract
Joel Cohen proposed that “mathematics is biology’s next microscope, only better; biology is mathematics’ next physics, only better.” Here, we aim for something even better. We try to combine mathematical physics and biology into a picoscope of life. For this, we merge techniques that were introduced and developed in modern mathematical physics, largely by Ludvig Faddeev, to describe objects such as solitons and Higgs and to explain phenomena such as anomalies in gauge fields. We propose a synthesis that can help to resolve the protein folding problem, one of the most important conundrums in all of science. We apply the concept of gauge invariance to scrutinize the extrinsic geometry of strings in three-dimensional space. We evoke general principles of symmetry in combination with Wilsonian universality and derive an essentially unique Landau-Ginzburg energy that describes the dynamics of a generic stringlike configuration in the far infrared. We observe that the energy supports topological solitons that relate to an anomaly similarly to how a string is framed around its inflection points. We explain how the solitons operate as modular building blocks from which folded proteins are composed. We describe crystallographic protein structures by multisolitons with experimental precision and investigate the nonequilibrium dynamics of proteins under temperature variations. We simulate the folding process of a protein at in vivo speed and with close to picoscale accuracy using a standard laptop computer. With picobiology as next pursuit of mathematical physics, things can only get better.
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References
J. E. Cohen, PLoS Biology, 2, e439 (2004).
P. A. M. Dirac, Proc. Roy. Soc. London Ser. A, 133, 60–72 (1931).
L. D. Faddeev and A. A. Slavnov, Introduction to the Quantum Theory of Gauge Fields [in Russian], Nauka, Moscow (1988); English transl.: Gauge Fields: An Introduction to Quantum Theory, Benjamin/Cummings, Reading, Mass. (1991).
L. P. Kadanoff, Physics, 2, 263–272 (1966).
K. G. Wilson, Phys. Rev. B, 4, 3174–3183 (1971).
M. N. Chernodub, L. D. Faddeev, and A. J. Niemi, JHEP, 0812, 014 (2008); arXiv:0804.1544v2 [hep-th] (2008).
F. Frenet, J. de Math., 17, 437–447 (1852).
A. J. Niemi, Phys. Rev. D, 67, 106004 (2003).
S. Hu, Y. Jiang, and A. J. Niemi, Phys. Rev. D, 87, 105011 (2013).
T. Ioannidou, Y. Jiang, and A. J. Niemi, Phys. Rev. D, 90, 025012 (2014); arXiv:1403.4401v1 [hep-th] (2017).
R. L. Bishop, Amer. Math. Monthly, 82, 246–251 (1975).
A. J. Hanson, Visualizing Quaternions, Elsevier, London (2006).
L. Faddeev and A. J. Niemi, Phys. Rev. Lett., 82, 1624–1627 (1998).
L. Faddeev and A. J. Niemi, Phys. Lett. B, 449, 214–218 (1999).
L. Faddeev and A. J. Niemi, Phys. Lett. B, 464, 90–93 (1999).
L. Faddeev and A. J. Niemi, Nucl. Phys. B, 776, 38–65 (2007).
H. Hasimoto, J. Fluid. Mech., 51, 477–485 (1972).
L. D. Faddeev and L. A. Takhtajan, Hamiltonian Methods in the Theory of Solitons [in Russian], Nauka, Moscow (1986); English transl., Springer, Berlin (1987).
M. J. Ablowitz, B. Prinari, and A. D. Trubatch, Discrete and Continuous Nonlinear Schrödinger Systems (London Math. Soc. Lect. Note Ser., Vol. 302), Cambridge Univ. Press, Cambridge (2003).
A. M. Polyakov, Nucl. Phys. B, 268, 406–412 (1986).
O. Kratky and G. Porod, Rec. Trav. Chim., 68, 1106–1122 (1949).
N. Manton and P. Sutcliffe, Topological Solitons, Cambridge Univ. Press, Cambridge (2004).
P. G. Kevrekidis, The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations, and Physical Perspectives, Springer, Berlin (2009).
S. Hu, M. Lundgren, and A. J. Niemi, Phys. Rev. E, 83, 061908 (2011).
V. I. Arnold, Singularities of Caustics and Wave Fronts, Kluwer, Dordrecht (1990).
V. I. Arnold, Russ. Math. Surv., 50, 1–68 (1995).
V. I. Arnold, Amer. Math. Soc. Transl. Ser. 2, 171, 11–22 (1996).
F. Aicardi, Funct. Anal. Appl., 34, 79–85 (2000).
R. Uribe-Vargas, Enseign. Math., 50, 69–101 (2004).
N. Molkenthin, S. Hu, and A. J. Niemi, Phys. Rev. Lett., 106, 078102 (2011).
M. Herrmann, Appl. Anal., 89, 1591–1602 (2010).
M. Chernodub, S. Hu, and A. J. Niemi, Phys. Rev. E, 82, 011916 (2010).
S. Hu, A. Krokhotin, A. J. Niemi, and X. Peng, Phys. Rev. E, 83, 041907 (2011).
A. Krokhotin, A. J. Niemi, and X. Peng, Phys. Rev. E, 85, 031906 (2012).
A. Sieradzhan and A. J. Niemi, Preprint, Uppsala Univ., Uppsala (to appear).
U. H. Danielsson, M. Lundgren, and A. J. Niemi, Phys. Rev. E, 82, 021910 (2010); arXiv:0902.2920v2 [cond-mat.stat-mech] (2009).
K. A. Dill, S. B. Ozkan, M. S. Shell, and T. R. Weikl, Ann. Rev. Biophys., 37, 289–316 (2008).
K. A. Dill and J. L. MacCallum, Science, 338, 1042–1046 (2012).
B. M. Pettitt, J. Biomol. Struct. Dyn., 31, 1024–1027 (2013).
H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov, and P. E. Bourne, Nucl. Acids Res., 28, 235–242 (2000).
B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan, and M. Karplus, J. Comp. Chem., 4, 187–217 (1983).
J. W. Ponder and D. W. Case, Adv. Prot. Chem., 66, 27–85 (2003).
K. Lindorf-Larsen, S. Piana, R. Dror, and D. Shaw, Science, 334, 517–520 (2011).
D. P. Scarpazza, D. J. Ierardi, A. K. Lerer, K. M. Mackenzie, A. C. Pan, J. A. Bank, E. Chow, R. O. Dror, J. P. Grossman, D. Killebrew, M. A. Moraes, C. Predescu, J. K. Salmon, and D. E. Shaw, “Extending the generality of molecular dynamics simulations on a special-purpose machine,” in: Proc. 27th IEEE Intl. Parallel and Distributed Processing Symposium (IPDPS’ 13) (Boston, Mass., USA, 20–24 May 2013), IEEE Computer Society, Boston, Mass. (2013), pp. 933–945.
V. S. Pande, I. Baker, J. Chapman, S. P. Elmer, S. Khaliq, S. M. Larson, Y. M. Rhee, M. R. Shirts, C. D. Snow, E. J. Sorin, and B. Zagrovic, Biopolymers, 68, 91–109 (2003).
P. A. Jennings and P. E. Wright, Science, 262, 892–896 (1993).
P. Westermark, C. Wernstedt, E. Wilander, D. W. Hayden, T. D. O’Brien, and K. H. Johnson, Proc. Natl. Acad. Sci. USA, 84, 3881–3885 (1987).
A. Liwo, Y. He, and H. A. Scheraga, Phys. Chem. Chem. Phys., 13, 16890–16901 (2011).
N. Gō, Ann. Rev. Biophys. Bioeng., 12, 183 (1983).
T. E. Lewis, S. Addou, A. Cuff, T. Dallman, M. Dibley, O. Redfern, F. Pearl, R. Nambudiry, A. Reid, I. Sillitoe, C. Yeats, J. M. Thornton, and C. A. Orengo, Nucl. Acids Res., 35, No. 1 (suppl.), D291–D297 (2007).
A. G. Murzin, S. E. Brenner, T. Hubbard, and C. Chothia, J. Mol. Biol., 247, 536–540 (1995).
G. A. Khoury, J. Smadbeck, C. A. Kieslich, and C. A. Floudas, Trends in Biotech., 32, 99–109 (2014).
Protein Structure Prediction Center, http://www.predictioncenter.org/index.cgi (2007–2014).
P. H. Hünenberger, “Thermostat algorithms for molecular dynamics simulations,” in: Advanced Computer Simulation Approaches for Soft Matter Sciences I (Adv. Polymer Sci., Vol. 173, C. Holm and K. Kremer, eds.), Springer, Berlin (2005), pp. 105–149.
S. Nosé, J. Chem. Phys., 81, 511–519 (1984).
W. G. Hoover, Phys. Rev. A, 31, 1695–1697 (1985).
S. Rackovsky, Proteins Struct. Funct. Genet., 7, 378–402 (1990).
J. Skolnick, A. K. Arakaki, S. Y. Lee, and M. Brylinski, Proc. Natl. Acad. Sci. USA, 106, 15690–15695 (2009).
A. Krokhotin, A. Liwo, G. Maisuradze, A. J. Niemi, and H. A. Scheraga, J. Chem. Phys., 140, 025101 (2014).
R. J. Glauber, J. Math. Phys., 4, 294–307 (1963).
A. B. Bortz, M. H. Kalos, and J. L. Lebowitz, J. Comput. Phys., 17, 10–18 (1975).
F. Martinelli and E. Olivieri, Commun. Math. Phys., 161, 447–486 (1994).
F. Martinelli and E. Olivieri, Commun. Math. Phys., 161, 487–514 (1994).
A. Krokhotin, M. Lundgren, A. J. Niemi, and X. Peng, J. Phys., 25, 325103 (2013).
P. G. De Gennes, Scaling Concepts in Polymer Physics, Cornell Univ. Press, Ithaca (1979).
L. Schäfer, Excluded Volume Effects in Polymer Solutions: As Explained by the Renormalization Group, Springer, Berlin (1999).
A. Krokhotin, A. J. Niemi, and X. Peng, J. Chem. Phys., 138, 175101 (2013).
C. Levinthal, “How to fold graciously,” in: Mössbauer Spectroscopy in Biological Systems (Allerton House, Monticello, 17–18 March 1969, J. T. P. Debrunner, J. C. M. Tsibris, and E. Munck, eds.), Univ. of Illinois Press, Champaign, Ill. (1969), pp. 22–24.
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Dedicated to Ludvig Faddeev on the occasion of his 80th birthday
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Niemi, A.J. Gauge fields, strings, solitons, anomalies, and the speed of life. Theor Math Phys 181, 1235–1262 (2014). https://doi.org/10.1007/s11232-014-0210-x
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DOI: https://doi.org/10.1007/s11232-014-0210-x