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Volumn 54, Issue 5, 2008, Pages 1344-1357

A new perturbation solution to the michaelis-menten problem

Author keywords

Bioengineering; Mathematical modeling; Reaction kinetics

Indexed keywords

BIOMEDICAL ENGINEERING; MATHEMATICAL MODELS; PARAMETER ESTIMATION; REACTION KINETICS;

EID: 43749083008     PISSN: 00011541     EISSN: 15475905     Source Type: Journal    
DOI: 10.1002/aic.11461     Document Type: Article
Times cited : (29)

References (31)
  • 1
    • 0004026407 scopus 로고    scopus 로고
    • Lehninger Principles of Biochemistry
    • 1 Nelson DL, Cox MM. Lehninger Principles of Biochemistry, 4th ed. New York, NY: Worth Publishing, 2000.
    • (2000)
    • Nelson, DL1    Cox, MM2
  • 2
    • 0004009662 scopus 로고    scopus 로고
    • Bioprocess Engineering: Basic Concepts
    • 2 Shuler ML, Kargi F. Bioprocess Engineering: Basic Concepts, 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2002.
    • (2002)
    • Shuler, ML1    Kargi, F2
  • 3
    • 0004122931 scopus 로고    scopus 로고
    • Biochemistry
    • 3 Garrett RH, Grisham CM. Biochemistry, 3rd ed. Belmont, CA: Thomson Brooks/Cole, 2005.
    • (2005)
    • Garrett, RH1    Grisham, CM2
  • 4
    • 0000870544 scopus 로고
    • Die kinetik der invertinwirkung
    • 4 Michaelis L, Menten ML. Die kinetik der invertinwirkung. Biochem Z. 1913 ; 49: 333–369.
    • (1913) Biochem Z. , vol.49 , pp. 333-369
    • Michaelis, L1    Menten, ML2
  • 5
    • 33644807093 scopus 로고    scopus 로고
    • Feedback dynamics and cell function: why systems biology is called systems biology
    • 5 Wolkenhauer O, Mesarovic M. Feedback dynamics and cell function: why systems biology is called systems biology. Mol BioSystems. 2005 ; 1: 14–16.
    • (2005) Mol BioSystems. , vol.1 , pp. 14-16
    • Wolkenhauer, O1    Mesarovic, M2
  • 7
    • 0007589020 scopus 로고
    • The mode of action of urease and enzymes in general
    • 7 Van Slyke D, Cullen GE. The mode of action of urease and enzymes in general. J Biol Chem. 1914 ; 19: 141–180.
    • (1914) J Biol Chem. , vol.19 , pp. 141-180
    • Van Slyke, D1    Cullen, GE2
  • 8
    • 85120587892 scopus 로고
    • Chapters 9 and 10, in: Mathematics Applied to Deterministic Problems in the Physical Sciences
    • 8 Lin CC, Segel LA. Mathematics Applied to Deterministic Problems in the Physical Sciences. New York: SIAM, 1988 ; Chapters 9 and 10.
    • (1988)
    • Lin, CC1    Segel, LA2
  • 9
    • 85120594497 scopus 로고
    • Chapters 7–9, in: Advanced Mathemetical Methods for Scientists and Engineers
    • 9 Bender CM, Orszag SA. Advanced Mathemetical Methods for Scientists and Engineers. New York: McGraw‐Hill, 1974 ; Chapters 7–9.
    • (1974)
    • Bender, CM1    Orszag, SA2
  • 10
    • 85120595830 scopus 로고
    • Chapters 1 and 2, in: Introduction to Perturbation Methods
    • 10 Holmes MH. Introduction to Perturbation Methods. New York: Springer‐Verlag, 1995 ; Chapters 1 and 2.
    • (1995)
    • Holmes, MH1
  • 11
    • 85120591898 scopus 로고    scopus 로고
    • O(x)=“order of x” in an asymptotic sense
    • 11 O(x)=“order of x ” in an asymptotic sense. Ibid 10, chapter 1.3.
  • 12
    • 85120595467 scopus 로고    scopus 로고
    • Ibid. 8
    • 12 Ibid. 8, chapter 9.1; ibid 9, chapter 3.4.
  • 14
    • 0000416179 scopus 로고
    • Singular perturbation refinement to quasi‐steady state approximation in chemical kinetics
    • 14 Bowen J, Acrivos A, Oppenheim A. Singular perturbation refinement to quasi‐steady state approximation in chemical kinetics. Chem Eng Sci. 1963 ; 18: 177–188.
    • (1963) Chem Eng Sci. , vol.18 , pp. 177-188
    • Bowen, J1    Acrivos, A2    Oppenheim, A3
  • 15
    • 0000292524 scopus 로고
    • A note on the kinetics of enzyme action
    • 15 Briggs GE, Haldane JBS. A note on the kinetics of enzyme action. Biochem J. 1925 ; 19: 338–339.
    • (1925) Biochem J. , vol.19 , pp. 338-339
    • Briggs, GE1    Haldane, JBS2
  • 16
    • 0344395658 scopus 로고    scopus 로고
    • Michaelis‐Menten kinetics at high enzyme concentrations
    • 16 Tzafriri AR. Michaelis‐Menten kinetics at high enzyme concentrations. Bull Math Biol. 2003 ; 65: 1111–1129.
    • (2003) Bull Math Biol. , vol.65 , pp. 1111-1129
    • Tzafriri, AR1
  • 17
    • 33947359087 scopus 로고    scopus 로고
    • Quasi‐steady‐state kinetics at enzyme and substrate concentrations in excess of the Michaelis‐Menten constant
    • 17 Tzafriri AR, Edelman ER. Quasi‐steady‐state kinetics at enzyme and substrate concentrations in excess of the Michaelis‐Menten constant. J Theor Biol. 2007 ; 245: 737–748.
    • (2007) J Theor Biol. , vol.245 , pp. 737-748
    • Tzafriri, AR1    Edelman, ER2
  • 18
    • 85120595241 scopus 로고
    • Chapter 8, in: Kinetics and Mechanism
    • 18 Moore JW, Pearson RG. Kinetics and Mechanism, 3rd ed. New York: Wiley, 1981 ; Chapter 8.
    • (1981)
    • Moore, JW1    Pearson, RG2
  • 19
    • 85120589246 scopus 로고
    • Chapter 8, in: Chemical Kinetics
    • 19 Laidler KJ. Chemical Kinetics, 3rd ed. New York: Prentice‐Hall, 1987 ; Chapter 8.
    • (1987)
    • Laidler, KJ1
  • 20
    • 0023734558 scopus 로고
    • On the validity of the steady state assumption of enzyme kinetics
    • 20 Segel LA. On the validity of the steady state assumption of enzyme kinetics. Bull Math Biol. 1988 ; 50: 579–593.
    • (1988) Bull Math Biol. , vol.50 , pp. 579-593
    • Segel, LA1
  • 21
    • 0001283963 scopus 로고
    • Theory of the transient phase in kinetics, with special reference to enzyme systems
    • 21 Laidler KJ. Theory of the transient phase in kinetics, with special reference to enzyme systems. Can J Chem. 1955 ; 33: 1614–1624.
    • (1955) Can J Chem. , vol.33 , pp. 1614-1624
    • Laidler, KJ1
  • 22
    • 0018905932 scopus 로고
    • Analytical solutions of a simple enzyme kinetic problem by a perturbative procedure
    • 22 Seshadri MS, Fritzsch G. Analytical solutions of a simple enzyme kinetic problem by a perturbative procedure. Biophys Struct Mech. 1980 ; 6: 111–123.
    • (1980) Biophys Struct Mech. , vol.6 , pp. 111-123
    • Seshadri, MS1    Fritzsch, G2
  • 23
    • 0024731820 scopus 로고
    • The quasi‐steady‐state assumption: a case study in perturbation
    • 23 Segel LA, Slemrod M. The quasi‐steady‐state assumption: a case study in perturbation. SIAM Rev. 1989 ; 31: 446–477.
    • (1989) SIAM Rev. , vol.31 , pp. 446-477
    • Segel, LA1    Slemrod, M2
  • 24
    • 0002595354 scopus 로고
    • On the mathematical status of the pseudo‐steady state hypothesis of biochemical kinetics
    • 24 Heineken FG, Tsuchiya HM, Aris R. On the mathematical status of the pseudo‐steady state hypothesis of biochemical kinetics. Math Biosci. 1967 ; 1: 95–113.
    • (1967) Math Biosci. , vol.1 , pp. 95-113
    • Heineken, FG1    Tsuchiya, HM2    Aris, R3
  • 25
    • 0004271975 scopus 로고
    • Introduction to Mathematical Biology
    • 25 Rubinow SI. Introduction to Mathematical Biology. New York: Wiley, 1975.
    • (1975)
    • Rubinow, SI1
  • 26
    • 0003475470 scopus 로고    scopus 로고
    • Mathematical Biology: An Introduction
    • 26 Murray JD. Mathematical Biology: An Introduction, 3rd ed. New York: Springer, 2002.
    • (2002)
    • Murray, JD1
  • 27
    • 0029681614 scopus 로고    scopus 로고
    • Extending the quasi‐steady state approximation by changing variables
    • 27 Borghans JAM, de Boer RJ, Segel LA. Extending the quasi‐steady state approximation by changing variables. Bull Math Biol. 1996 ; 58: 43–63.
    • (1996) Bull Math Biol. , vol.58 , pp. 43-63
    • Borghans, JAM1    de Boer, RJ2    Segel, LA3
  • 28
    • 0033778534 scopus 로고    scopus 로고
    • Enzyme kinetics at high enzyme concentrations
    • 28 Schnell S, Maini PK. Enzyme kinetics at high enzyme concentrations. Bull Math Biol. 2000 ; 62: 483–499.
    • (2000) Bull Math Biol. , vol.62 , pp. 483-499
    • Schnell, S1    Maini, PK2
  • 29
  • 31
    • 1242338790 scopus 로고    scopus 로고
    • The condition for pseudo‐first‐order kinetics in enzymatic reactions is independent of the initial enzyme concentration
    • 31 Schnell S, Mendoza C. The condition for pseudo‐first‐order kinetics in enzymatic reactions is independent of the initial enzyme concentration. Biophys J. 2004 ; 107: 165–174.
    • (2004) Biophys J. , vol.107 , pp. 165-174
    • Schnell, S1    Mendoza, C2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.