Abstract
The Beyer-Swinehart (BS) algorithm, which calculates vibrational state density and sum, was modified for simultaneous treatment of degenerate vibrations. The modified algorithm was used in the grouped-frequency mode of the Rice-Ramsperger-Kassel-Marcus (RRKM) unimolecular reaction rate constant calculation for proteins with relative molecular mass as large as 100,000. Compared to the original BS method, reduction in computation time by a factor of around 3000 was achieved. Even though large systematic errors arising from frequency grouping were observed for state densities and sums, they more or less canceled each other, thus enabling reliable rate constant calculation. The present method is thought to be adequate for efficient and reliable RRKM calculations for any macromolecule in the gas phase such as the molecular ions of proteins, nucleic acids, and carbohydrates generated inside a mass spectrometer. The algorithm can also be used to calculate the internal energy distribution of a macromolecule at thermal equilibrium.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Urbanc, B.; Borreguero, J. M.; Cruz, L.; Stanley, H. E. Ab Initio Discrete Molecular Dynamics Approach to Protein Folding and Aggregation. Methods Enzymol. 2006, 412, 314–338.
Hardin, C.; Pogorelov, T. V.; Luthey-Schulten, Z. Ab Initio Protein Structure Prediction. Curr. Opin. Struc. Biol. 2002, 12, 176–181.
Agostini, F. P.; Soares-Pinto, D. D. O.; Moret, M. A.; Osthoff, C.; Pascutti, P. G. Generalized Simulated Annealing Applied to Protein Folding Studies. J. Comput. Chem. 2006, 27, 1142–1155.
Holbrook, K. A.; Pilling, M. J.; Robertson, S. H. Unimolecular Reactions 2nd ed.; Wiley: Chichester, UK; 1996.
Marcus, R. A.; Rice, O. K. The Kinetics of the Recombination of Methyl Radicals and Iodine Atoms. J. Phys. Colloid. Chem. 1951, 55, 894–908.
Rosenstock, H. M.; Wallenstein, M. B.; Wahrhaftig, A. L.; Eyring, H. Absolute Rate Theory for Isolated Systems and the Mass Spectra of Polyatomic Molecules. Proc. Natl. Acad. Sci. U.S.A. 1952, 38, 667–678.
Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and Dynamics. Blackwell Scientific: Oxford, UK, 1990; 342–401.
Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions. Oxford Univ. Press: Oxford, UK, 1990; 136–211.
Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics: Theory and Experiments. Oxford Univ. Press: Oxford, UK, 1996; 171–211.
Lifshitz, C. Recent Developments in Applications of RRKM-QET. Adv. Mass Spectrom. 1989, 11A, 713–729.
Rosenstock, H. M.; Stockbauer, R.; Parr, A. C. Kinetic Shift in Chlorobenzene Ion Fragmentation and the Heat of Formation of the Phenyl Ion. J. Chem. Phys. 1979, 71, 3708–3714.
Rosenstock, H. M.; Stockbauer, R.; Parr, A. C. Photoelectron-Photoion Coincidence Study of the Bromobenzene Ion. J. Chem. Phys. 1980, 73, 773–777.
Lifshitz, C. Time-Resolved Appearance Energies, Breakdown Graphs, and Mass Spectra: The Elusive “Kinetic Shift.” Mass Spectrom. Rev. 1982, 1, 309–348.
Moon, J. H.; Oh, J. Y.; Kim, M. S. A Systematic and Efficient Method to Estimate the Vibrational Frequencies of Linear Peptide and Protein Ions with Any Amino Acid Sequence for the Calculation of Rice-Ramsperger-Kassel-Marcus Rate Constant. J. Am. Soc. Mass Spectrom. 2006, 17, 1749–1757.
Paizs, B.; Suhai, S. Combined Quantum Chemical and RRKM Modeling of the Main Fragmentation Pathways of Protonated GGG: II. Formation of b2, y1, and y2 Ions. Rapid Commun. Mass Spectrom. 2002, 16, 375–389.
Hu, Y.; Hadas, B.; Davidovitz, M.; Balta, B.; Lifshitz, C. Does IVR Take Place Prior to Peptide Ion Dissociation? J. Phys. Chem. A. 2003, 107, 6507–6514.
Current, J. H.; Rabinovitch, B. S. Decomposition of Chemically Activated Ethyl-d3 Radicals: Primary Intramolecular Kinetic Isotope Effect in a Nonequilibrium System. J. Chem. Phys. 1963, 38, 783–795.
Schlag, E. W.; Sandsmark, R. A. Computation of Statistical Complexions as Applied to Unimolecular Reactions. J. Chem. Phys. 1962, 37, 168–171.
Wilde, K. A. Anharmonicity in Vibrational State Sums. J. Chem. Phys. 1964, 41, 448–451.
Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley-Interscience: New York, 1972; 125–126.
Whitten, G. Z.; Rabinovitch, B. S. Accurate and Facile Approximation for Vibrational Energy-Level Sums. J. Chem. Phys. 1963, 38, 2466–2473.
Morse, P. M.; Feshbach, H. Methods of Theoretical Physics, Part I.; McGraw-Hill: New York, 1953; 434–443.
Derrick, P. J.; Lloyd, P. M.; Christie, J. R. Physical Chemistry of Ion Reactions in Advanced Mass Spectrometry, vol. 13; Wiley: Chichester, UK, 1995; pp 25–52.
Beyer, T.; Swinehart, D. F. Algorithm 448 Number of Multiply Restricted Partitions [A1]. Commun. ACM. 1973, 16, 379–379.
Griffin, L. L.; McAdoo, D. J. The Effect of Ion Size on Rate of Dissociation RRKM Calculations on Model Large Polypeptide Ions. J. Am. Soc. Mass Spectrom. 1993, 4, 11–15.
Laskin, J.; Bailey, T. H.; Futrell, J. H. Fragmentation Energetics for Angiotensin II and Its Analogs from Time- and Energy-Resolved Surface-Induced Dissociation Studies. Int. J. Mass Spectrom. 2004, 234, 89–99.
Sun, M.; Moon, J. H.; Kim, M. S. Improved Whitten-Rabinovitch Approximation for the Rice-Ramsperger-Kassel-Marcus Calculation of Unimolecular Reaction Rate Constants for Proteins. J. Phys. Chem. B. 2007, 111, 2747–2751.
Oh, J. Y.; Moon, J. H.; Kim, M. S. Tandem Time-of-Flight Mass Spectrometer for Photodissociation of Biopolymer Ions Generated by Matrix-Assisted Laser Desorption Ionization (MALDI-TOF-PD-TOF) Using a Linear-Plus-Quadratic Potential Reflectron. J. Am. Soc. Mass Spectrom. 2004, 15, 1248–1259.
Hillenkamp, F.; Karas, M.; Beavis, R. C.; Chait, B. T. Matrix-Assisted Laser Desorption/Ionization Mass Spectrometry of Biopolymers. Anal. Chem. 1991, 63, 1193A-1202A.
Zenobi, R.; Knochenmuss, R. Ion Formation in MALDI Mass Spectrometry. Mass Spectrom. Rev. 1998, 17, 337.
Karas, M.; Bachmann, D.; Bahr, U.; Hillenkamp, F. Matrix-Assisted Ultraviolet Laser Desorption of Non-Volatile Compounds. Int. J. Mass Spectrom. Ion Process. 1987, 78, 53–68.
Cole, R. B. Electrospray Ionization Mass Spectrometry Wiley-Interscience: New York, 1997; pp 3–65.
Author information
Authors and Affiliations
Corresponding author
Additional information
Published online April 19, 2007
Rights and permissions
About this article
Cite this article
Moon, J.H., Sun, M. & Kim, M.S. Efficient and reliable calculation of rice-ramsperger—kassel-marcus unimolecular reaction rate constants for biopolymers: Modification of beyer-swinehart algorithm for degenerate vibrations. J Am Soc Mass Spectrom 18, 1063–1069 (2007). https://doi.org/10.1016/j.jasms.2007.03.012
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1016/j.jasms.2007.03.012