Crystals, proteins, stability and isoperimetry

Gromov, Misha

doi:10.1090/S0273-0979-2010-01319-7

Crystals, proteins, stability and isoperimetry
HTML articles powered by AMS MathViewer

by Misha Gromov PDF

Bull. Amer. Math. Soc. 48 (2011), 229-257 Request permission

Abstract:

We attempt to formulate several mathematical problems suggested by structural patterns present in biomolecular assemblies. Our description of these patterns, by necessity brief and over-concentrated in some places, is self-contained, albeit on a superficial level. An attentive reader is likely to stumble upon a cryptic line here and there; however, things will become more transparent at a second reading and/or at a later point in the article.

References

S. Andersson, K. Larsson, M. Larsson, Virus Symmetry and Dynamics, http://www. sandforsk.se/sandforsk-articles/all.all.articles.htm.
A.J. Cann, Principles of molecular virology; 4th ed. Amsterdam: Elsevier Academic Press, 2005.
S. Casjens, Principles of virion structure, function and assembly, and J.S. Baker and J.E. Johnson, Principles of virus structure determination in Structural Biology of Viruses, W. Chu R.M. Burnett, R.L. Garcia, Wah Chiu, (eds.), 1997; Oxford University Press.
D. L. D. Caspar, A. Klug, (1962) “Physical Principles in the Construction of Regular Viruses” Cold Spring Harbor Symposia on Quantitative Biology XXVII, Cold Spring Harbor Laboratory, New York. pp. 1-24.
Y.S. Chiang, T.I. Gelfand, A.E. Kister, I.M. Gelfand, New classification of supersecondary structures of sandwich-like proteins uncovers strict patterns of strand assemblage. Proteins, 2007.
Collision between a Vulture and an Aircraft. THE WILSON BULLETIN December, 1974, Vol. 86, No. 4, http://elibrary.unm.edu/sora/Wilson/v086n04/p0461-p0462.pdf.
Conformational Proteomics of Macromolecular Architecture: Approaching the Structure of Large Molecular Assemblies and Their Mechanisms of Action (with CD-Rom) (Paperback) by R. Holland Cheng (Author), Lena Hammar (Editor), 2004, a historical survey by Morgan.
H. R. Crane, Principles and problems of biological growth. The Scientific Monthly, Volume 70, Issue 6, pp. 376-389 (1950). (This article is often referred to but I could not see it since it is not freely available on the web.)
Alan Fersht, Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding, W.H. Freeman $\&$ Co Ltd; 3rd Revised edition, 1998.
A. V. Finkelstein, O. B. Ptitsyn, Protein Physics: A Course of Lectures. Academic Press, 2002.
Howard Griffiths, Designs on Rubisco, Nature 441, 940-941 (22 June 2006).
M. Gromov, Isoperimetry of waists and concentration of maps, Geom. Funct. Anal. 13 (2003), no. 1, 178–215. MR 1978494, DOI 10.1007/s000390300004
M. Gromov, Mendelian Dynamics and Sturtevant’s Paradigm. In Geometric and Probabilistic Structures in Contemporary Mathematics Series: Dynamics, (Keith Burns, Dmitry Dolgopyat, and Yakov Pesin, editors), American Mathematical Society, Providence RI (2007).
Larry Guth, Minimax problems related to cup powers and Steenrod squares, Geom. Funct. Anal. 18 (2009), no. 6, 1917–1987. MR 2491695, DOI 10.1007/s00039-009-0710-2
W. Helfrich, Z. Naturforsch, Bending energy of vesicle membranes: General expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders, Phys. Rev. A 39, 5280 - 5288 (1989).
Mike Howard, Introduction to Crystallography and Mineral Crystal Systems. http://www.rockhounds.com/rockshop/xtal/index.html.
John E. Johnson, Virus assembly and maturation, in Folding and Self-assembly of Biological Macromolecules, E. Westhof, and N. Hardy, editors, World Scientific, 2004.
Kenneth E. NeetDagger, Enzyme Catalytic Power Minireview Series, J. Biol. Chem., Vol. 273, Issue 40, 25527-25528, October 2, 1998.
A. Klug, The tobacco mosaic virus particle: structure and assembly. Philos. Trans. R. Soc. Lond. B Biol. Sci. March 29, 1999, 354(1383): 531–535.
Rachel Kolodny, Patrice Koehl, Leonidas Guibas and Michael Levitt, Small Libraries of Protein Fragments Model Native Protein Structures Accurately, J. Mol. Biol. (2002) 323, 297–307.
D.J. Kushner, Self-Assembly of Biological Structures, Bacteriol Rev. 33:302-345. 1969.
Arthur M. Lesk, Introduction to Protein Architecture Oxford University Press, 2000.
Wen-Hsiung Li, Molecular Evolution, Sinauer Associates, Sunderland, MA, USA. 1997.
D.B. Lukatsky, E.I. Shakhnovich, Statistically enhanced promiscuity of structurally correlated patterns. Physical Review E 77 (2) 020901, 2008; and $arxiv.org/pdf/q-bio/0603017$.
Klaus Mainzer, Symmetrien der Natur, Walter de Gruyter & Co., Berlin, 1988 (German). Ein Handbuch zur Natur- und Wissenschaftsphilosophie. [A handbook on the philosophy of nature and science]. MR 953086, DOI 10.1515/9783110853650
B.G. Miller, R. Wolfenden, “Catalytic proficiency: the unusual case of OMP decarboxylase.”. Annual Rev. Biochem. 71 (2002), 847–885.
Masayoshi Nakasako, Water-protein interactions from high-resolution protein crystallography. Philos. Trans. R. Soc. Lond. B Biol. Sci. August 29, 2004; 359(1448): 1191–1206.
Christo N. Nanev, How do crystal lattice contacts reveal protein crystallization mechanism? Cryst. Res. Technol. 43, No. 9, 914–920 (2008).
Laszlo Patthy, Protein Evolution, Blackwell Science, 1999.
R. C. Penner, Michael Knudsen, Carsten Wiuf, Joergen Ellegaard Andersen, Fatgraph Models of Proteins, eprint arXiv:0902.1025.
A. Radzicka, R. Wolfenden, Rates of uncatalyzed peptide bond hydrolysis in neutral solution and the transition state affinities of proteases, J. Amer. Chem. Soc., 1996, Vol. 118 (No.26)
K. K. Reddi, Tobacco mosaic virus with emphasis on the events within the host cell following infection, Advances in Virus Research, Volume 17, Kenneth Manley Smith ed., 1972, Science.
Alejandro P. Rooney and Masatoshi Nei, Purifying Selection and Birth-and-death Evolution in the Histone H4 Gene Family. Molecular Biology and Evolution 19:689-697 (2002).
F. Robert Tabita, Thomas E. Hanson, Huiying Li, Sriram Satagopan Jaya Singh and Sum Chan, Function, Structure, and Evolution of the RubisCO-Like Proteins and Their RubisCO Homologs, Microbiol. Mol. Biol. Rev. December 2007; 71(4): 576–599.
Bernard Testa, Joachim M. Mayer, Hydrolysis in Drug and Prodrug Metabolism: Chemistry, Biochemistry, and Enzymology, Science, 2003.
G. A. Vliegenthart, G. Gompper, Mechanical deformation of spherical viruses with icosahedral symmetry, Biophys. J., August 1, 2006; 91(3): 834–841.
Virology, $http://pathmicro.med.sc.edu/mhunt/intro-vir.htm$. Virus Structure, $http://www.microbiologybytes.com/introduction/structure.html$. Principles of Virus Architecture, $http://web.uct.ac.za/depts/mmi/stannard/virarch.html$.
History of Structural Virology, $http://virologyhistory.wustl.edu/timeline.htm$.
David Baker lab, $http://depts.washington.edu/bakerpg/$.
Andrzej Kolinski group, $http://biocomp.chem.uw.edu.pl/$.
Eugene Koonin group, $http://www.ncbi.nlm.nih.gov/CBBresearch/Koonin/$.
Olivier Lichtarge lab, $http://mammoth.bcm.tmc.edu/$.
Rama Ranganathan lab, $http://www.hhmi.swmed.edu/Labs/rr/$.
Eugene Shakhnovich group, $http://www-shakh.harvard.edu/research/index.html$.
Jeffrey Skolnick group, $http://cssb.biology.gatech.edu/skolnick/$.