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Michel Pierre - One of the best experts on this subject based on the ideXlab platform.
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quasi steady state approximation for a Reaction diffusion system with fast intermediate
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Dieter Bothe, Michel PierreAbstract:Abstract We consider a Prototype Reaction–diffusion system which models a network of two consecutive Reactions in which chemical components A and B form an intermediate C which decays into two products P and Q. Such a situation often occurs in applications and in the typical case when the intermediate is highly reactive, the species C is eliminated from the system by means of a quasi-steady-state approximation. In this paper, we prove the convergence of the solutions in L 2 , as the decay rate of the intermediate tends to infinity, for all bounded initial data, even in the case of initial boundary layers. The limiting system is indeed the one which results from formal application of the QSSA. The proof combines the recent L 2 -approach to Reaction–diffusion systems having at most quadratic Reaction terms, with local L ∞ -bounds which are independent of the decay rate of the intermediate. We also prove existence of global classical solutions to the initial system.
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Quasi-steady-state approximation for a Reaction–diffusion system with fast intermediate
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Dieter Bothe, Michel PierreAbstract:Abstract We consider a Prototype Reaction–diffusion system which models a network of two consecutive Reactions in which chemical components A and B form an intermediate C which decays into two products P and Q. Such a situation often occurs in applications and in the typical case when the intermediate is highly reactive, the species C is eliminated from the system by means of a quasi-steady-state approximation. In this paper, we prove the convergence of the solutions in L 2 , as the decay rate of the intermediate tends to infinity, for all bounded initial data, even in the case of initial boundary layers. The limiting system is indeed the one which results from formal application of the QSSA. The proof combines the recent L 2 -approach to Reaction–diffusion systems having at most quadratic Reaction terms, with local L ∞ -bounds which are independent of the decay rate of the intermediate. We also prove existence of global classical solutions to the initial system.
Stanley K. Burt - One of the best experts on this subject based on the ideXlab platform.
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modeling of serine protease Prototype Reactions with the flexible effective fragment potential quantum mechanical molecular mechanical method
Theoretical Chemistry Accounts, 2004Co-Authors: Alexander V. Nemukhin, Igor A. Topol, B L Grigorenko, A V Rogov, Stanley K. BurtAbstract:A complete cycle of chemical transformations for the serine protease Prototype Reaction is modeled following calculations with the flexible effective fragment quantum mechanical/molecular mechanical (QM/MM) method. The initial molecular model is based on the crystal structure of the trypsin–bovine pancreatic trypsin inhibitor complex including all atoms of the enzyme within approximately 15–18 A of the oxygen center O γ of the catalytic serine residue. Several selections of the QM/MM partitioning are considered. Fractions of the side chains of the residues from the catalytic triad (serine, histidine and aspartic acid) and a central part of a model substrate around the C–N bond to be cleaved are included into the QM subsystem. The remaining part, or the MM subsystem, is represented by flexible chains of small effective fragments, whose potentials explicitly contribute to the Hamiltonian of the QM part, but the corresponding fragment–fragment interactions are described by the MM force fields. The QM/MM boundaries are extended over the C α –C β bonds of the peptides assigned to the QM subsystem in the enzyme, C–C and C–N bonds in model substrates. Multiple geometry optimizations have been performed by using the RHF/6-31G method in the QM part and OPLSAA or AMBER sets of MM parameters, resulting in a series of stationary points on the complex potential-energy surfaces. All structures generally accepted for the serine protease catalytic cycle have been located. Energies at the stationary points found have been recomputed at the MP2/6-31+G* level for the QM part in the protein environment. Structural changes along the Reaction path are analyzed with special attention to hydrogen-bonding networks. In the case of a model substrate selected as a short peptide CH3(NHCO-CH2)2 – HN–CO–(CH2–NHCO)CH3 the computed energy profile for the acylation step shows too high activation energy barriers. The energetics of this rate-limiting step is considerably improved, if more realistic model for the substrate is considered, following the motifs of the ThrI11–GlyI12–ProI13-–CysI14–LysI15–AlaI16–ArgI17–IleI18–IleI19 sequence of the bovine pancreatic trypsin inhibitor.
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Energy profiles for the rate‐limiting stage of the serine protease Prototype Reaction
International Journal of Quantum Chemistry, 2002Co-Authors: Alexander V. Nemukhin, Igor A. Topol, Stanley K. BurtAbstract:The energy profiles of Reaction, modeling the rate-limiting stage of serine protease catalyzed transformations, have been computed by quantum chemistry methods. The model includes fragments of the residues of the catalytic triad (serine, histidine, and aspartic acid), two water molecules as an oxyanion hole, represented by effective fragment potentials, and a formamide molecule as a substrate. Geometry optimizations have been performed along the Reaction coordinate, chosen as the distance between oxygen of serine and carbon of substrate, by using the Hartree–Fock method. The density functional theory B3LYP/6-31+G(d,p) calculations have been employed to recalculate energies along the Reaction path in the gas phase and in the dielectric environment. The computed barrier heights are fairly consistent with the data cited in the literature. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 34–40, 2002
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energy profiles for the rate limiting stage of the serine protease Prototype Reaction
International Journal of Quantum Chemistry, 2002Co-Authors: Alexander V. Nemukhin, Igor A. Topol, Stanley K. BurtAbstract:The energy profiles of Reaction, modeling the rate-limiting stage of serine protease catalyzed transformations, have been computed by quantum chemistry methods. The model includes fragments of the residues of the catalytic triad (serine, histidine, and aspartic acid), two water molecules as an oxyanion hole, represented by effective fragment potentials, and a formamide molecule as a substrate. Geometry optimizations have been performed along the Reaction coordinate, chosen as the distance between oxygen of serine and carbon of substrate, by using the Hartree–Fock method. The density functional theory B3LYP/6-31+G(d,p) calculations have been employed to recalculate energies along the Reaction path in the gas phase and in the dielectric environment. The computed barrier heights are fairly consistent with the data cited in the literature. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 34–40, 2002
Dieter Bothe - One of the best experts on this subject based on the ideXlab platform.
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quasi steady state approximation for a Reaction diffusion system with fast intermediate
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Dieter Bothe, Michel PierreAbstract:Abstract We consider a Prototype Reaction–diffusion system which models a network of two consecutive Reactions in which chemical components A and B form an intermediate C which decays into two products P and Q. Such a situation often occurs in applications and in the typical case when the intermediate is highly reactive, the species C is eliminated from the system by means of a quasi-steady-state approximation. In this paper, we prove the convergence of the solutions in L 2 , as the decay rate of the intermediate tends to infinity, for all bounded initial data, even in the case of initial boundary layers. The limiting system is indeed the one which results from formal application of the QSSA. The proof combines the recent L 2 -approach to Reaction–diffusion systems having at most quadratic Reaction terms, with local L ∞ -bounds which are independent of the decay rate of the intermediate. We also prove existence of global classical solutions to the initial system.
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Quasi-steady-state approximation for a Reaction–diffusion system with fast intermediate
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Dieter Bothe, Michel PierreAbstract:Abstract We consider a Prototype Reaction–diffusion system which models a network of two consecutive Reactions in which chemical components A and B form an intermediate C which decays into two products P and Q. Such a situation often occurs in applications and in the typical case when the intermediate is highly reactive, the species C is eliminated from the system by means of a quasi-steady-state approximation. In this paper, we prove the convergence of the solutions in L 2 , as the decay rate of the intermediate tends to infinity, for all bounded initial data, even in the case of initial boundary layers. The limiting system is indeed the one which results from formal application of the QSSA. The proof combines the recent L 2 -approach to Reaction–diffusion systems having at most quadratic Reaction terms, with local L ∞ -bounds which are independent of the decay rate of the intermediate. We also prove existence of global classical solutions to the initial system.
Alexander V. Nemukhin - One of the best experts on this subject based on the ideXlab platform.
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modeling of serine protease Prototype Reactions with the flexible effective fragment potential quantum mechanical molecular mechanical method
Theoretical Chemistry Accounts, 2004Co-Authors: Alexander V. Nemukhin, Igor A. Topol, B L Grigorenko, A V Rogov, Stanley K. BurtAbstract:A complete cycle of chemical transformations for the serine protease Prototype Reaction is modeled following calculations with the flexible effective fragment quantum mechanical/molecular mechanical (QM/MM) method. The initial molecular model is based on the crystal structure of the trypsin–bovine pancreatic trypsin inhibitor complex including all atoms of the enzyme within approximately 15–18 A of the oxygen center O γ of the catalytic serine residue. Several selections of the QM/MM partitioning are considered. Fractions of the side chains of the residues from the catalytic triad (serine, histidine and aspartic acid) and a central part of a model substrate around the C–N bond to be cleaved are included into the QM subsystem. The remaining part, or the MM subsystem, is represented by flexible chains of small effective fragments, whose potentials explicitly contribute to the Hamiltonian of the QM part, but the corresponding fragment–fragment interactions are described by the MM force fields. The QM/MM boundaries are extended over the C α –C β bonds of the peptides assigned to the QM subsystem in the enzyme, C–C and C–N bonds in model substrates. Multiple geometry optimizations have been performed by using the RHF/6-31G method in the QM part and OPLSAA or AMBER sets of MM parameters, resulting in a series of stationary points on the complex potential-energy surfaces. All structures generally accepted for the serine protease catalytic cycle have been located. Energies at the stationary points found have been recomputed at the MP2/6-31+G* level for the QM part in the protein environment. Structural changes along the Reaction path are analyzed with special attention to hydrogen-bonding networks. In the case of a model substrate selected as a short peptide CH3(NHCO-CH2)2 – HN–CO–(CH2–NHCO)CH3 the computed energy profile for the acylation step shows too high activation energy barriers. The energetics of this rate-limiting step is considerably improved, if more realistic model for the substrate is considered, following the motifs of the ThrI11–GlyI12–ProI13-–CysI14–LysI15–AlaI16–ArgI17–IleI18–IleI19 sequence of the bovine pancreatic trypsin inhibitor.
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Energy profiles for the rate‐limiting stage of the serine protease Prototype Reaction
International Journal of Quantum Chemistry, 2002Co-Authors: Alexander V. Nemukhin, Igor A. Topol, Stanley K. BurtAbstract:The energy profiles of Reaction, modeling the rate-limiting stage of serine protease catalyzed transformations, have been computed by quantum chemistry methods. The model includes fragments of the residues of the catalytic triad (serine, histidine, and aspartic acid), two water molecules as an oxyanion hole, represented by effective fragment potentials, and a formamide molecule as a substrate. Geometry optimizations have been performed along the Reaction coordinate, chosen as the distance between oxygen of serine and carbon of substrate, by using the Hartree–Fock method. The density functional theory B3LYP/6-31+G(d,p) calculations have been employed to recalculate energies along the Reaction path in the gas phase and in the dielectric environment. The computed barrier heights are fairly consistent with the data cited in the literature. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 34–40, 2002
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energy profiles for the rate limiting stage of the serine protease Prototype Reaction
International Journal of Quantum Chemistry, 2002Co-Authors: Alexander V. Nemukhin, Igor A. Topol, Stanley K. BurtAbstract:The energy profiles of Reaction, modeling the rate-limiting stage of serine protease catalyzed transformations, have been computed by quantum chemistry methods. The model includes fragments of the residues of the catalytic triad (serine, histidine, and aspartic acid), two water molecules as an oxyanion hole, represented by effective fragment potentials, and a formamide molecule as a substrate. Geometry optimizations have been performed along the Reaction coordinate, chosen as the distance between oxygen of serine and carbon of substrate, by using the Hartree–Fock method. The density functional theory B3LYP/6-31+G(d,p) calculations have been employed to recalculate energies along the Reaction path in the gas phase and in the dielectric environment. The computed barrier heights are fairly consistent with the data cited in the literature. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 34–40, 2002
Bin Zhao - One of the best experts on this subject based on the ideXlab platform.
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state to state mode specificity in h doh νoh 1 hd oh ν2 0 Reaction vibrational non adiabaticity or local mode excitation
Physical Chemistry Chemical Physics, 2018Co-Authors: Bin ZhaoAbstract:It is well established that chemical Reactions often involve only a small number of atoms near the Reaction site, and the remainder of the reactant molecules are mostly spectators. It is thus of great importance to understand the role played by the active as well as spectator modes in chemical dynamics. In this work, we examine in great detail the influence of reactant modes on the reactivity and product state distribution, using a four-atom prototypical Reaction as the example. State-of-the-art full-dimensional state-to-state quantum dynamics reveal a startling observation in which the DOH(νOH = 1) molecule reacts with a H atom to produce a vibrationless OH product. This is surprising because OH is considered as a spectator in this Reaction and its internal energy should be sequestered throughout the Reaction. By careful analysis within the local-mode regime, we demonstrate that the surprising reactivity is not due to vibrational non-adiabaticity during the Reaction. Rather, it can be attributed to a small OD excited local-mode component in the reactant wavefunction. The quantum state-resolved dissection of this Prototype Reaction helps to advance our understanding of larger reactive systems.
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State-to-state mode specificity in H + DOH(νOH = 1) → HD + OH(ν2 = 0) Reaction: vibrational non-adiabaticity or local-mode excitation?
Physical chemistry chemical physics : PCCP, 2017Co-Authors: Bin Zhao, Zhigang Sun, Hua GuoAbstract:It is well established that chemical Reactions often involve only a small number of atoms near the Reaction site, and the remainder of the reactant molecules are mostly spectators. It is thus of great importance to understand the role played by the active as well as spectator modes in chemical dynamics. In this work, we examine in great detail the influence of reactant modes on the reactivity and product state distribution, using a four-atom prototypical Reaction as the example. State-of-the-art full-dimensional state-to-state quantum dynamics reveal a startling observation in which the DOH(νOH = 1) molecule reacts with a H atom to produce a vibrationless OH product. This is surprising because OH is considered as a spectator in this Reaction and its internal energy should be sequestered throughout the Reaction. By careful analysis within the local-mode regime, we demonstrate that the surprising reactivity is not due to vibrational non-adiabaticity during the Reaction. Rather, it can be attributed to a small OD excited local-mode component in the reactant wavefunction. The quantum state-resolved dissection of this Prototype Reaction helps to advance our understanding of larger reactive systems.
