scholarly journals A study case for the analysis of asymptotic expansions beyond the tQSSA for inhibitory mechanisms in enzyme kinetics.

2019 ◽  
Vol 10 (1) ◽  
pp. 162-181
Author(s):  
A. M. Bersani ◽  
A. Borri ◽  
A. Milanesi ◽  
G. Tomassetti ◽  
P. Vellucci
Keyword(s):  
Singular Perturbation ◽  
Enzyme Kinetics ◽  
Chemical Reaction ◽  
Asymptotic Expansions ◽  
Competitive Inhibition ◽  
Perturbation Techniques ◽  
Inhibitory Mechanisms ◽  
Perturbation Order ◽  
Study Case ◽  
Uniform Expansions

Abstract In this paper we study the model of the chemical reaction of fully competitive inhibition and determine the appropriate parameter ∊ (related to the chemical constants of the model), for the application of singular perturbation techniques. We determine the inner and the outer solutions up to the first perturbation order and the uniform expansions. Some numerical results are discussed.

On the shape of small sessile and pendant drops by singular perturbation techniques

1991 ◽  
Vol 233 ◽  
pp. 519-537 ◽  
Author(s):  
S. B. G. O'Brien
Keyword(s):  
Boundary Layer ◽  
Singular Perturbation ◽  
Asymptotic Expansions ◽  
Numerical Results ◽  
Matched Asymptotic Expansions ◽  
Perturbation Techniques ◽  
Pendant Drop ◽  
Asymptotic Expressions ◽  
Good Agreement ◽  
Pendant Drops

The problem of obtaining asymptotic expressions describing the shape of small sessile and pendant drops is revisited. Both cases display boundary-layer behaviour and the method of matched asymptotic expansions is used to obtain solutions. These give good agreement when compared with numerical results. The sessile solutions are relatively straightforward, while the pendant drop displays a behaviour which is both rich and interesting.

Singular Perturbation Techniques and Asymptotic Expansions for Some Complex Enzyme Reactions

2020 ◽  
pp. 43-53 ◽  
Author(s):  
Alberto Maria Bersani ◽  
Alessandro Borri ◽  
Alessandro Milanesi ◽  
Giovanna Tomassetti ◽  
Pierluigi Vellucci
Keyword(s):  
Singular Perturbation ◽  
Asymptotic Expansions ◽  
Perturbation Techniques ◽  
Enzyme Reactions

scholarly journals Tihonov theory and center manifolds for inhibitory mechanisms in enzyme kinetics

2017 ◽  
Vol 8 (1) ◽  
pp. 81-102
Author(s):  
A. M. Bersani ◽  
A. Borri ◽  
A. Milanesi ◽  
P. Vellucci
Keyword(s):  
Phase Space ◽  
Enzyme Kinetics ◽  
Chemical Reaction ◽  
Center Manifold ◽  
Sufficient Conditions ◽  
Numerical Results ◽  
Center Manifolds ◽  
Inhibitory Mechanisms

Abstract In this paper we study the chemical reaction of inhibition, determine the appropriate parameter ε for the application of Tihonov's Theorem, compute explicitly the equations of the center manifold of the system and find sufficient conditions to guarantee that in the phase space the curves which relate the behavior of the complexes to the substrates by means of the tQSSA are asymptotically equivalent to the center manifold of the system. Some numerical results are discussed.

Kinetic Aspects of the Interaction of Blood Clotting Enzymes

1968 ◽  
Vol 19 (03/04) ◽  
pp. 364-367 ◽  
Author(s):  
H. C Hemker ◽  
P. W Hemker
Keyword(s):  
Enzyme Kinetics ◽  
Blood Clotting ◽  
Competitive Inhibition ◽  
Competitive Inhibitor ◽  
Kinetics Of

SummaryThe enzyme kinetics of competitive inhibition under conditions prevailing in clotting tests are developed and a method is given to measure relative amounts of a competitive inhibitor by means of the t — D plot.

scholarly journals A New Asymptotic Treatment of g-modes of a Star

1995 ◽  
Vol 155 ◽  
pp. 285-286
Author(s):  
P. Smeyers ◽  
T. Van Hoolst ◽  
I. De Boeck ◽  
L. Decock
Keyword(s):  
Singular Perturbation ◽  
Fourth Order ◽  
Asymptotic Expansions ◽  
Equilibrium Model ◽  
Asymptotic Representation ◽  
Radial Displacement ◽  
Low Frequency ◽  
Order System ◽  
Oscillation Modes ◽  
Perturbation Problems

An asymptotic representation of low-frequency, linear, isentropic g-modes of a star is developed without the usual neglect of the Eulerian perturbation of the gravitational potential. Our asymptotic representation is based on the use of asymptotic expansions adequate for solutions of singular perturbation problems (see, e.g., Kevorkian & Cole 1981).Linear, isentropic oscillation modes with frequency different from zero are governed by a fourth-order system of linear, homogeneous differential equations in the radial parts of the radial displacement ξ(r) and the divergence α(r). These equations take the formThe symbols have their usual meaning. N2 is the square of the frequency of Brunt-Väisälä. The functions K1 (r), K2 (r), K3 (r), K4 (r), depend on the equilibrium model, e.g.,We introduce the small expansion parameterand assume, for the sake of simplification, N2 to be positive everywhere in the star so that the star is everywhere convectively stable.

scholarly journals Singular perturbation for nonlinear boundary-value problems

1979 ◽  
Vol 2 (1) ◽  
pp. 61-68 ◽  
Author(s):  
Rina Ling
Keyword(s):  
Differential Equations ◽  
Singular Perturbation ◽  
Energy Distribution ◽  
Boundary Value Problems ◽  
Asymptotic Expansions ◽  
Nuclear Energy ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

Asymptotic solutions of a class of nonlinear boundary-value problems are studied. The problem is a model arising in nuclear energy distribution. For large values of the parameter, the differential equations are of the singular-perturbation type and approximations are constructed by the method of matched asymptotic expansions.

On the appropriate use of asymptotic expansions in enzyme kinetics

2014 ◽  
Vol 52 (10) ◽  
pp. 2475-2481 ◽  
Author(s):  
Guido Dell’Acqua ◽  
Alberto Maria Bersani
Keyword(s):  
Enzyme Kinetics ◽  
Asymptotic Expansions ◽  
Appropriate Use
Sign in / Sign up

Export Citation Format

Share Document