Logistic vs. W-Lambert Information in Modeling Enzyme Kinetics at Quantum Level

The logistic temporal solution of the generalized Michaelis-Menten kinetics is employed to provide a quantum basis for the tunneling time and energy evaluations of Brownian enzymic reactions. The monosubstrate and mixed inhibition cases are treated and the associated quantum diagrams of the reaction mechanisms are depicted in terms of intermediate enzyme complexes. The methodology is suited for practically controlling of the enzymic activity throughout absorption spectroscopy.

[1]  B Chance,et al.  Studies of photosynthesis using a pulsed laser. I. Temperature dependence of cytochrome oxidation rate in chromatium. Evidence for tunneling. , 1966, Biophysical journal.

[2]  Ndubuisi Ekekwe,et al.  Nanotechnology and Microelectronics: Global Diffusion, Economics and Policy , 2010 .

[3]  R. Duggleby.  Progress-curve analysis in enzyme kinetics. Numerical solution of integrated rate equations. , 1986, The Biochemical journal.

[4]  Santiago Schnell,et al.  Mechanism Equivalence in Enzyme–Substrate Reactions: Distributed Differential Delay in Enzyme Kinetics , 2004 .

[5]  J. Klinman,et al.  Evidence that both protium and deuterium undergo significant tunneling in the reaction catalyzed by bovine serum amine oxidase. , 1989, Biochemistry.

[6]  M. Sutcliffe,et al.  Enzymatic H-transfer requires vibration-driven extreme tunneling. , 1999, Biochemistry.

[7]  Ronald G. Duggleby,et al.  A Windows program for the derivation of steady-state equations in enzyme systems , 2006, Appl. Math. Comput..

[8]  Kutay O. Alper,et al.  Correlated conformational fluctuations during enzymatic catalysis: Implications for catalytic rate enhancement , 2001, Protein science : a publication of the Protein Society.

[9]  L. Guddat,et al.  Probing the mechanism of the bifunctional enzyme ketol‐acid reductoisomerase by site‐directed mutagenesis of the active site , 2005, The FEBS journal.

[10]  J. Klinman,et al.  Effects of protein glycosylation on catalysis: changes in hydrogen tunneling and enthalpy of activation in the glucose oxidase reaction. , 1997, Biochemistry.

[11]  Introducing logistic enzyme kinetics , 2007 .

[12]  E. Boeker,et al.  Integrated rate equations for irreversible enzyme-catalysed first-order and second-order reactions. , 1985, The Biochemical journal.

[13]  J. Morrison,et al.  The use of steady-state rate equations to analyse progress curve data. , 1979, Biochimica et biophysica acta.

[14]  Goedele Roos,et al.  A Computational and Conceptual DFT Study of the Reactivity of Anionic Compounds: Implications for Enzymatic Catalysis , 2003 .

[15]  Variational perturbation theory for Markov processes. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Hideyuki Câteau,et al.  Kinetic analysis of multisite phosphorylation using analytic solutions to Michaelis-Menten equations. , 2002, Journal of theoretical biology.

[17]  Dennis Shasha,et al.  DNA Hash Pooling and its Applications , 2007, Int. J. Nanotechnol. Mol. Comput..

[18]  K. Laidler.  THEORY OF THE TRANSIENT PHASE IN KINETICS, WITH SPECIAL REFERENCE TO ENZYME SYSTEMS , 1955 .

[19]  S. Benkovic,et al.  Hybrid enzymes: manipulating enzyme design. , 1998, Trends in biotechnology.

[20]  Arieh Warshel,et al.  How Important Are Quantum Mechanical Nuclear Motions in Enzyme Catalysis , 1996 .

[21]  D. A. Barry,et al.  Analytical approximations for real values of the Lambert W -function , 2000 .

[22]  E. Boeker,et al.  Integrated rate equations for enzyme-catalysed first-order and second-order reactions. , 1984, The Biochemical journal.

[23]  J F Morrison,et al.  Progress curve analysis in enzyme kinetics: model discrimination and parameter estimation. , 1978, Biochimica et biophysica acta.

[24]  D. A. Barry,et al.  A class of exact solutions for Richards' equation , 1993 .

[25]  M. Gordon,et al.  From Force Fields to Dynamics: Classical and Quantal Paths , 1990, Science.

[26]  Koichi Ito,et al.  Toward Biomolecular Computers Using Reaction-Diffusion Dynamics , 2009, Int. J. Nanotechnol. Mol. Comput..

[27]  Quan-Fang Wang.  Boundary Pointwise Control for Diffusion Hopfield Neural Network , 2010, Int. J. Nanotechnol. Mol. Comput..

[28]  R. Duggleby,et al.  Parameter estimation using a direct solution of the integrated Michaelis-Menten equation. , 1999, Biochimica et biophysica acta.

[29]  Mario J. Pérez-Jiménez,et al.  Cellular Solutions to Some Numerical NP-Complete Problems: A Prolog Implementation , 2005 .

[30]  V. Ostafe,et al.  Full Analytic Progress Curves of Enzymic Reactions in Vitro , 2006 .

[31]  Robert M. Corless,et al.  The Wright omega Function , 2002, AISC.

[32]  Adrian J. Brown,et al.  XXXVI.—Enzyme action , 1902 .

[33]  W. Stemmer.  Rapid evolution of a protein in vitro by DNA shuffling , 1994, Nature.

[34]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[35]  S. Schnell,et al.  Time-dependent closed form solutions for fully competitive enzyme reactions , 2000, Bulletin of mathematical biology.

[36]  Dagmar Ringe,et al.  Quantum enzymology: Tunnel vision , 1999, Nature.

[37]  P. Maini,et al.  A Century of Enzyme Kinetics: Reliability of the K M and v v max Estimates , 2003 .

[38]  J. Knowles,et al.  Evolution of enzyme function and the development of catalytic efficiency. , 1976, Biochemistry.

[39]  C. J. Murray,et al.  Hydrogen tunneling in enzyme reactions. , 1989, Science.

[40]  J. Klinman,et al.  Hydrogen tunneling in the flavoenzyme monoamine oxidase B. , 1994, Biochemistry.

[41]  M. Sutcliffe,et al.  Enzymology takes a quantum leap forward , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[42]  Y. Leong Yeow,et al.  An alternative way of analyzing the progress curves of enzyme-catalyzed reactions , 2004 .

[43]  Santiago Schnell,et al.  Enzyme kinetics of multiple alternative substrates , 2000 .

[44]  Rudolph A. Marcus,et al.  Electron Transfer Reactions in Chemistry: Theory and Experiment (Nobel Lecture) , 1993 .

[45]  M. Putz.  On the Reducible Character of Haldane-Radić Enzyme Kinetics to Conventional and Logistic Michaelis-Menten Models , 2011, Molecules.

[46]  C. Goudar,et al.  Progress curve analysis for enzyme and microbial kinetic reactions using explicit solutions based on the Lambert W function. , 2004, Journal of microbiological methods.

[47]  J. A. McCammon,et al.  Quantum-Classical Molecular Dynamics Simulations of Proton Transfer Processes in Molecular Complexes and in Enzymes , 1996 .

[48]  J. Leszczynski,et al.  Visualization of the Differential Transition State Stabilization within the Active Site Environment , 2004 .

[49]  S. Schnell,et al.  Closed Form Solution for Time-dependent Enzyme Kinetics , 1997 .

[50]  P. Rigby,et al.  Gene duplication in experimental enzyme evolution , 1974, Nature.

[51]  W. Bialek,et al.  Vibrationally enhanced tunneling as a mechanism for enzymatic hydrogen transfer. , 1992, Biophysical journal.

[52]  E. A. Boeker.  Analytical methods for fitting integrated rate equations. A discontinuous assay. , 1987, The Biochemical journal.

[53]  J. Klinman,et al.  [14] Hydrogen tunneling in enzyme catalysis , 1995 .

[54]  C. Niemann,et al.  The Evaluation of the Kinetic Constants of Enzyme-catalyzed Reactions by Procedures Based upon Integrated Rate Equations. II1 , 1955 .

[55]  Ramón Varón,et al.  Computer program for the equations describing the steady state of enzyme reactions , 1997, Comput. Appl. Biosci..

[56]  Enzymatic control of the bio-inspired nanomaterials at the spectroscopic level , 2007 .

[57]  Jesuleye O. Aquila,et al.  Emerging Technology Penetration: The Case of Solar Electricity in Nigeria , 2010 .

[58]  L. A. Segel,et al.  The Quasi-Steady-State Assumption: A Case Study in Perturbation , 1989, SIAM Rev..

[59]  C. Niemann,et al.  The Kinetics of the α-Chymotrypsin-Catalyzed Hydrolysis of Acetyl- and Nicotinyl-L-phenylalaninamide in Aqueous Solutions at 25° and pH 7.91 , 1951 .

[60]  International Journal of Nanotechnology and Molecular Computation , 2022 .

[61]  J. Klinman,et al.  Experimental Evidence for Extensive Tunneling of Hydrogen in the Lipoxygenase Reaction: Implications for Enzyme Catalysis , 1996 .

[62]  W. A. Clark,et al.  Simultaneous Studies of Firing Patterns in Several Neurons , 1964, Science.

[63]  Linus Pauling,et al.  Molecular Architecture and Biological Reactions , 1946 .

[64]  R. E. Shafer,et al.  Algorithm 443: Solution of the transcendental equation wew = x , 1973, Commun. ACM.

[65]  R. Duggleby,et al.  Quantitative analysis of the time courses of enzyme-catalyzed reactions. , 2001, Methods.

[66]  R G Duggleby,et al.  Analysis of progress curves for enzyme-catalysed reactions. Automatic construction of computer programs for fitting integrated rate equations. , 1989, The Biochemical journal.

[67]  Westerhoff,et al.  Effects of oscillations and energy-driven fluctuations on the dynamics of enzyme catalysis and free-energy transduction. , 1989, Physical review. A, General physics.

[68]  P. Hambäck.  Seasonality, Optimal Foraging, and Prey Coexistence , 1998, The American Naturalist.

[69]  J. Morrison,et al.  The analysis of progress curves for enzyme-catalysed reactions by non-linear regression. , 1977, Biochimica et biophysica acta.

[70]  D. A. Barry,et al.  Real values of the W-function , 1995, TOMS.

[71]  T. Chachibaia.  Strategy and Policy Issues Related to Nanotechnology Innovations in Medical Education , 2012 .