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Applied Biochemistry and Biotechnology

, Volume 9, Issue 5–6, pp 455–474 | Cite as

The effect of hydrogen ions on the steady state multiplicity of substrate-inhibited enzymatic reactions

III. Asymmetrical steady states in enzyme membranes
  • S. S. E. H. Elnashaie
  • G. Ibrahim
  • S. S. Elshishini
Original articles

Abstract

The present investigation concentrates on the study of the complex phenomenon of multiplicity in membranes carrying substrate-inhibited, hydrogen ion-sensitive enzyme. The investigation takes into consideration both symmetrical and asymmetrical steady states. The number of steady states (symmetrical and asymmetrical) found in this case is quite large, giving rise to multiple hysteresis loops and multiple “isolas.”

Index Entries

Hydrogen ions, effects on multiplicity of substrate-inhibited enzymatic reactions multiplicity of enzymatic reactions, effect of H+ ions on enzymatic reactions, effects of H+ ions on multiplicity of membranes, asymmetrical steady states in isolas hysteresis loops 

List of Symbols

BH

V m /Kg H Kh

Bs

V m /KgsKs

DH

Diffusion coefficient for hydrogen ions (cm2 s-1)

DOH

Diffusion coefficient for hydroxyl ions (cm2 s-1)

DS

Diffusion coefficient for substrate (cm2 s-1)

E

Enzyme

H

Hydrogen ions

h

Dimensionless concentration of hydrogen ions inside the membrane

Ks,Ki,Kh, Kh

Constants characteristic the enzyme

Kw

Equilibrium constant of water (mol2 cm-6)

Kgs

Mass-transfer coefficient for substrate (cm s-1)

KgH

Mass-transfer coefficient for hydrogen ions (cm s-1)

KgOH

Mass-transfer coefficient for hydroxyl ions (cm-1)

Depth across the membrane (cm)

L

Membrane thickness (cm)

OH

Hydroxyl ions

P-

Fully ionized product

P1

Product

R

Dimensionless reaction rate

r

Rate of reaction (moles per gram enzyme per second)

rw

Rate of water formation

S

Substrate

S

Dimensionless substrate concentration inside the membrane

{ie474-01}

Dimensionless substrate concentration in the compartment (o)

{ie474-02}

Dimensionless substrate concentration in compartment (1)

S0

Dimensionless substrate concentration at surface (o)

S1

Dimensionless substrate concentration at surface (1)

w

Dimensionless length = ℒ/L

ShH

L KgH/DH, Sherwood number

Shs

L Kgs/Ds, Sherwood number

Vm

Maximum reaction rate (moles per gram of enzyme per second)

γ

DOHKw/DHK h 2

α1

K s K i

δ

K h /K h

θ

KgOH K WKgH K h 2

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References

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Copyright information

© Humana Press Inc 1984

Authors and Affiliations

  • S. S. E. H. Elnashaie
    • 1
  • G. Ibrahim
    • 1
  • S. S. Elshishini
    • 1
  1. 1.Chemical Engineering DepartmentCairo UniversityCairoEgypt

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