HMx(Sp > Ca)I

Hyperbolic  mixed, predominantly specific inhibition

Fingerprints of HMx(Sp>Ca)I: Dependence of the parameters on [X]
Fingerprints of HMx(Sp>Ca)I: Specific velocity plot and replots

Featured examples

  • Km↑         The apparent Michaelis constant increases with increasing [X]
  • V (∴kcat )      The apparent limiting rate, and therefore the catalytic constant, decrease with increasing [X]
  • (V/Km)↓ (∴kcat/Km )  The apparent V/Km ratio, and therefore the specificity constant, decrease with increasing [X]

These symbols are shown only when the featured dependencies of the parameters on modifier concentration have been demonstrated by the authors.

EC no.ModifierSubstrate(1)Name given by authors (2)Reference(3)
1Stratum corneum chymotryptic enzyme
Homo sapiens (4)MeO-Succinyl-Arg-Pro-Tyr-
Hyperbolic mixed-type inhibition
α = 5.6, β = 0.16, KX = 63 nM
2Non-specific serine/threonine protein kinase
Rattus norvegicus fragment
Peptide RRRADDSDDDDDHyperbolic partial non-competitive mixed type inhibition
Parameters inconsistent (5)
3Leukocyte elastase
Homo sapiens thiomalatet-Butyloxycarbonyl-alanyl-p-nitrophenyl esterHyperbolic mixed-type inhibition
α = 1.6, β = 0.6, KX = 33 μM
4Coagulation factor Xa
Homo sapiens (6)CH3SO2-Leu-Gly-Arg-
Mixed, primarily competitive inhibition
KX= 0.3-0.6 nM (6)
α ≈ 1.3, β ≈ 0.4, KX ≈ 0.3 nM
5Leukocyte elastase
Homo sapiens Partial inhibition
α = 4.0, β = 0.43, KX = 0.18 μM
6Cathepsin G
Homo sapiens
Partial inhibition
α = 2.3, β = 0.29, KX = 0.08 μM
Homo sapiens inhibition
α = 1.8, β = 0.63, KX = 0.5 μM
8Leukocyte elastase
Homo sapiens sulfate
Mr= 31,000; 62 DU/chain
MeO-Suc-Ala-Ala-Pro-Val-p-nitroanilideHyperbolic mixed, predominantly competitive inhibition (7)
α = 4.2, β = 0.23
K0.5= 0.25 μMDU, h = 1.1
9Leukocyte elastase
Homo sapiens 4-sulfate
Mr =18,000; 36 DU/chain
MeO-Suc-Ala-Ala-Pro-Val-p-nitroanilideHyperbolic mixed, predominantly competitive inhibition (7)
α = 3.1, β = 0.09
K0.5= 45 μMDU, h = 1.1
10Leukocyte elastase
Homo sapiens 6-sulfate
Mr = 29,000; 58 DU/chain
MeO-Suc-Ala-Ala-Pro-Val-p-nitroanilideHyperbolic mixed, predominantly competitive inhibition (7)
α = 2.1, β = 0.59
K0.5= 0.16 μMDU, h = 1.6
11Leukocyte elastase
Homo sapiens sulfate low-Mr
Mr = 10,200; 20 DU/chain
MeO-Suc-Ala-Ala-Pro-Val-p-nitroanilideHyperbolic mixed, predominantly competitive inhibition (7)
α = 2.2, β = 0.85
K0.5= 1.1 μMDU, h = 1.8
12Leukocyte elastase
Homo sapiens 4,6-disulfate
Mr = 27,600; 46 DU/chain
MeO-Suc-Ala-Ala-Pro-Val-p-nitroanilideHyperbolic mixed, predominantly competitive inhibition (7)
α = 2.4, β = 0.34
K0.5= 0.07 μMDU, h = 2.9
13Leukocyte elastase
Homo sapiens 4,6-disulfate
Mr = 25,000; 41 DU/chain
MeO-Suc-Ala-Ala-Pro-Val-p-nitroanilideHyperbolic mixed, predominantly competitive inhibition (7)
α = 2.0, β = 0.24
K0.5= 0.07 μMDU, h = 2.5
14Leukocyte elastase
Homo sapiens N,4-disulfate
Mr = 6,900; 12 DU/chain
MeO-Suc-Ala-Ala-Pro-Val-p-nitroanilideHyperbolic mixed, predominantly competitive inhibition (7)
α = 2.4, β = 0.52
K0.5= 0.4 μMDU, h = 1.7
15Leukocyte elastase
Homo sapiens N,4-disulfate
Mr = 6,600; 12 DU/chain
MeO-Suc-Ala-Ala-Pro-Val-p-nitroanilideHyperbolic mixed, predominantly competitive inhibition (7)
α = 3.2, β = 0.53
K0.5= 0.7 μMDU, h = 1.9
Homo sapiens (8)Acetyl-Val-Asp-Val-Ala-Asp-7-amino-4-methylcoumarylamideHyperbolic mixed, predominantly competitive inhibition
α = 2.9, β = 0.04, KX = 0.29 nM
17ADAMTS 13 endopeptidase (9)
Homo sapiens cVWF63 (10)Synthetic peptide (11)Hyperbolic mixed type inhibition
α = 5.4, β = 0.12, KX = 0.44 μM
Electrophorus electricus blueAcetylthiocholineHyperbolic mixed inhibition
α = 1.9, β = 0.28, KX = 0.035 μM
Electrophorus electricus blueAcetylthiocholineHyperbolic mixed inhibition
α = 1.8, β = 0.15, KX = 0.026 μM
Electrophorus electricus blueAcetylthiocholineHyperbolic mixed inhibition
α = 2.4, β = 0.18, KX = 0.017 μM
Electrophorus electricus triethiodide
(without acetonitrile)
AcetylthiocholineMixed-type inhibition with pronounced competitive component
α = 15, β = 0.25, KX = 270 μM
Electrophorus electricus 11AcetylthiocholineHyperbolic mixed-type inhibition
α = 2.0, β = 0.14, KX = 1.3 μM
Electrophorus electricus 12AcetylthiocholineHyperbolic mixed-type inhibition
α = 1.5, β = 0.17, KX = 1.9 μM
Electrophorus electricus 13AcetylthiocholineHyperbolic mixed-type inhibition
α = 1.6, β = 0.16, KX = 2.4 μM
Electrophorus electricus 14AcetylthiocholineHyperbolic mixed-type inhibition
α = 1.6, β = 0.12, KX = 1.5 μM
26Aminopeptidase N
Homo sapiens acidLeu-GlyHyperbolic mixed-type inhibition
α = 2.5, β = 0.33, KX = 0.91 mM
27Aminopeptidase N
Homo sapiens acidLeu-GlyHyperbolic mixed-type inhibition
α = 2.7, β = 0.13, KX = 0.24 mM
28Spermidine synthase
Bos taurus mixed-type inhibition (12)
Kic = 10-110 μM, Kiu > 500 μM
29Spermidine synthase
Bos taurus adenosylmethionineHyperbolic mixed-type inhibition (12)
Kic = 80-160 μM, Kiu > 500 μM
Homo sapiens mixed noncompetitive inhibition
α = 2.0, β = 0.77, KX = 0.09 mM
31Alpha,alpha trehalase
Chironomus riparius mixed-type inhibition
α = 4.8, β = 0.4, KX = 48 nM
32Alpha,alpha trehalase
Chironomus riparius mixed-type inhibition
α = 2.5, β = 0.5, KX = 810 nM
33Ethanolamine-phosphate phospho-lyase
Homo sapiens (pH = 8.8)O-phosphoethanolamineHyperbolic mixed-type inhibition
α = 8.5, β = 0.48, KX = 8 mM
34Cathepsin K
Homo sapiens 1Cbz-Phe-Arg-7-amino-4-methylcoumarylamideHyperbolic mixed, predominantly competitive inhibition
α = 6.7, β = 0.55, KX = 190 μM
35Cathepsin K
Homo sapiens 2Cbz-Phe-Arg-7-amino-4-methylcoumarylamideHyperbolic mixed, predominantly competitive inhibition
α = 7.2, β = 0.74, KX = 150 μM
36Cathepsin K
Homo sapiens 3Cbz-Phe-Arg-7-amino-4-methylcoumarylamideHyperbolic mixed, predominantly competitive inhibition
α = 1.7, β = 0.44, KX = 110 μM
37Sterol esterase
Sus scrofa domestica 4ap-Nitrophenyl butyrateHyperbolic mixed-type inhibition
α = 5.5, β = 0.13, KX = 1.22 μM
Homo sapiens competitive inhibition
α = 1.9, β = 0.6, KX = 1.7 mM
Electrophorus electricus greenAcetylthiocholineHyperbolic mixed inhibition
α = 2.7, β = 0.20, KX = 0.27 μM
40Linoleate 13S-lipoxygenase
Glycine max sulfateLinoleic acidHyperbolic mixed-type inhibition
α = 4.6, β = 0.85, KX = 0.7 μM
Km↑, kcat↓, kcat/Km
41Cytochrome P450 (13)
Rattus norvegicus
(14)PrimaquineAminopyrineSlope-hyperbolic, intercept-hyperbolic noncompetitive inhibition
α = 2.05, β = 0.54, KX = 21 μM
42Coagulation factor XIa
Homo sapiens factor IXL-Pyroglutamyl-L-prolyl-L-arginine-p-nitroanilideHyperbolic mixed inhibition
α = 2.7, β = 0.50, KX = 0.22 μM
43Coagulation factor XIa
Homo sapiens site-inhibited factor IXa (factor IXai)L-Pyroglutamyl-L-prolyl-L-arginine-p-nitroanilideHyperbolic mixed inhibition
α = 2.5, β = 0.9, KX = 0.11 μM
Homo sapiens
(native enzyme)
chloromethyl ketone
ButyrylthiocholineHyperbolic mixed inhibition
α = 41.6, β = 0.065, KX = 39 μM
Homo sapiens
(native enzyme) chloromethyl ketoneButyrylthiocholineHyperbolic mixed inhibition
α = 10.8, β = 0.26, KX = 16 μM
Homo sapiens
(heat desensitized enzyme, 24 h, 45°C)
chloromethyl ketone
ButyrylthiocholineHyperbolic mixed inhibition
α = 3.9, β = 0.52, KX = 17 μM
47Coagulation factor VIIa
Homo sapiens A-183
Coagulation factor XPartial mixed-type inhibition
α = 2.6, β = 0.27, KX ≈ 200 pM
48Cellulose 1,4-beta-cellobiosidase
Trichoderma reesei
(disaccharide, reaction product)
CelluloseMixed hyperbolic inhibition (14)
α = 37.9, β = 0.055, KX = 29 μM
(cellobiose present initially)
49Cellulose 1,4-beta-cellobiosidase
Trichoderma reesei
(disaccharide, reaction product)
CelluloseMixed hyperbolic inhibition (14)
α = 51.7, β = 0.063, KX = 29 μM
(no cellobiose present initially)
Carica papaya mixed inhibition
α = 1.8, β = 0.12, KX = 13.5 μM
51Acetolactate synthase
Escherichia coli V/K type inhibition
α = 3.2, β = 0.62, KX = 4.6 μM
52ABC-type quaternary amine transporter(15)
Homo sapiensγ-Aminobutyric acidMixed competitive/non-competitive inhibition
α ≈ 8, β ≈ 0.2, KX ≈ 2 μM (16)
53Serine racemase
Homo sapiens,4-dihydronicotinamide mononucleotideL-SerineHyperbolic mixed-type inhibition
α = 5, β = 0.8, KX = 18 μM
54Cathepsin B
Homo sapiens 8h6Cbz-Arg-Arg-7-amino-4-methylcoumarylamideMixed-mode inhibition with a very strong competitive component
α = 6.6, β = 0.15, KX = 34 pM
55Cathepsin B
Mus musculus 8h6Cbz-Arg-Arg-7-amino-4-methylcoumarylamideMixed-mode inhibition with a very strong competitive component
α = 6.1, β = 0.06, KX = 35 pM
56Leukocyte elastase
Homo sapiens acid (EDTA)MeO-Suc-Ala-Ala-Pro-Val-p-nitroanilideHyperbolic mixed inhibition with partial competitive and partial noncompetitive components (17)
α = 2.1, β = 0.26, KX = 6.6 mM
57Receptor protein-tyrosine kinase
Homo sapiens AATPHyperbolic mixed-type inhibition (18)
α > 1, β < 1, KX ≤ 1 nM
58Phosphoserine phosphatase
Mycobacterium tuberculosis mixed, predominantly specific inhibition (19)
α = 3.5, β = 0.0006, KX = 22 μM

(1) Always the varied substrate. In two- or more-substrate reactions the concentration(s) of the non varied substrate(s) is/are kept constant.

(2) Name of the mechanism given by the authors in the quoted reference. α, β and the inhibition/activation constants for the modifier (X), uniformly denoted KX, are the values specified by the authors. In some cases,  missing parameters have been calculated from graphical or tabular data provided in the papers. In two- or more-substrate reactions, KX represents an apparent constant at given concentrations of the fixed substrates and no calculations of the intrinsic values have been attempted.

(3) Full references at the end of the page provide also the digital object identifier (doi), if available. Clicking the authors (highlighted) opens the reference in PubMed.

(4) Antileukoproteinase, or secretory leukocyte proteinase inhibitor, is a human endogenous inhibitor of serine peptidases.

(5) The results in Fig. 4 clearly demonstrate the HMx(Sp>Ca)I mechanism, whereas α = 0.88 and β = 0.013 (Table 2) are characteristic of HMx(Sp<Ca)I; Ki = 19 μM. The discrepancy is possibly due to the fitting procedure with intertwined parameters.

(6) Antistasin, a protein from the salivary glands of the Mexican leech Haementeria officinalis. It selectively inhibits Factor Xa acting as anticoagulant. This is an uncommon case of slow-onset inhibition described in ‘Kinetics of enzyme-modifier interactions‘ by A. Baici, pp. 408-414. The approximate values of α, β and KX were calculated from Fig. 3 (left) in the paper.

(7) One or more enzyme molecules can bind to a single chain of the glycosaminoglycans in a cooperative manner. The equation used to calculate the inhibition parameters was: vi = v0 -{(v0v)[X]h}/{K0.5h + [X]h}, where vi, v0 and v are the initial velocities in the absence of modifier, in its presence and at saturating modifier concentration, respectively. X is the modifier, K0.5 is the inhibitor concentration for which the velocity equals (v0v)/2 and h is the Hill coefficient that is usually not an integer. All glycosaminoglycans (the inhibitors) were oligodisperse with known molecular mass, composition and number of disaccharide units (DU) on the chain. Their concentration and K0.5 are expressed as micromoles of DU × L-1 (μMDU).  The electrostatically-driven interaction between elastase and glycosaminoglycans depends on ionic composition and ionic strength. The data in this table refer to a Tris/HCl buffer, pH = 7.40, ionic strength = 100 mM and 25°C.

(8) AR_F8 = designed ankyrin repeat protein specifically targeted to human caspase-2. Tight-binding with human caspase-2.

(9) Recombinant ADAMTS 13 truncated after the spacer domain.

(10) cVWF63 = C-terminal cleavage product of Von Willebrand factor.

(11) Synthetic peptide in which leucine at position 3 is isotopically doubly-labeled with (13)C and (15)N (GP([(13)C(15)N]L)GSDREQAPNLVY.

(12) Product inhibition. Hyperbolic inhibition clearly demonstrated (α > 1, β < 1 ) but the value of β was not shown.

(13) An ‘aminopyrine N-demethylase activity’ in a rat hepatic microsomal fraction, possibly due to ‘CYP2C19, EC (unspecific monooxygenase) or another cytochrome P450 activity.

(14) Assays conducted with complete progress curves to which the integrated Michaelis -Menten equation was fitted. Models comprising substrate inhibition and parabolic inhibition by the concomitant binding of two inhibitor molecules to the enzyme were considered. However, by applying the Akaike  information criterion, a simpler model equivalent to the general modifier mechanism was selected as the most probable.

(15) Transporters belong to the EC-enzyme class 7, translocases, added in 2018 to the other 6 enzyme classes. This paper by Kragholm et al. contains a kinetic study of a human ABC-type quaternary amine transporter commonly known as betaine/GABA transporter 1, a target for the treatment of epilepsy. Besides the inhibitor featured here, also N-(1-benzyl-4-piperidinyl)-2,4-dichlorobenzamide was investigated as inhibitor, see under LMx(Sp<Ca)I.

(16) Approximate calculations from the data in the paper.

(17) The same mechanism is shared with the chelators QUIN-2 and FURA-2.

(18) Notwithstanding a difficult method for measuring the kinetic courses of the reactions, the authors did a great job in providing sound experimental evidence to assert that the mechanism is of the tight-binding, slow-onset inhibition type. Moreover, the data in Fig. 6 are consistent with hyperbolic mixed, predominantly specific inhibition as the basic mechanism. The kinetic parameters are approximate, but epitomize very well the goal of this elegant study.

(19) The authors conducted an impeccable kinetic analysis in identifying the basic modifier mechanism in a complex system. HMx(Sp>Ca)I, an allosteric modifier, can be confused with the corresponding linear counterpart LMx(Sp>Ca)I because, as can be seen in some examples in the table above (see the studies 9, 44, 49, and 55) the parameter β is often very small. Only an accurate examination of the saturation curves in the presence of sufficiently high concentrations of the inhibitor can reveal the hyperbolic nature of this inhibition mechanism.


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