HMxD(I / A)

Hyperbolic mixed, dual modification (inhibition → activation)

Fingerprints of HMxD(I/A): Dependence of the parameters on [X]
Fingerprints of HMxD(I/A): Specific velocity plot and replots

Featured examples

The relative critical substrate concentration σ 0 = (αβ)/(β −1) was calculated for this table from α and β, if provided by the authors.

EC no.ModifierSubstrate(1)Name given by authors(2)Reference (3)
1Arachidonate 15-lipoxygenase
Homo sapiensγ-Linolenic acidK-type inhibition & V-type activation
α = 7.3, β = 1.6, KX = 9.8 μM, σ 0 = 9.5
2Arachidonate 15-lipoxygenase
Homo sapiensγ)γ-Linolenic acidK-type inhibition & V-type activation
α = 3.5, β = 1.2, KX= 4.9 μM, σ 0 = 11.5
3Glutathione transferase
Mus musculus acid1-Chloro-2,4-dinitrobenzeneAnomalous inhibition (4)Phillips
4Cathepsin K
Homo sapiens (5)Abz–HPGGPQ–EDDnp (6)σ < σ 0 (inhibition), σ > σ 0 (activation)
α = 2.4, β = 1.3, KX = 28 μM, σ 0 = 3.7
5Cathepsin K
Homo sapiens malonic acidCbz-Phe-Arg-7-amino-4-methylcoumarylamideσ < σ 0 (inhibition), σ > σ 0 (activation)
α = 5.6, β = 1.5, KX = 100 μM, σ 0 = 8.2
6Cathepsin K
Homo sapiens,4,7,9B-TetraazaphenaleneCbz-Phe-Arg-7-amino-4-methylcoumarylamideσ < σ 0 (inhibition), σ > σ 0 (activation)
α = 4.8, β = 1.5, KX = 20 μM, σ 0 = 6.6
Not specifiedα-NapthylamineN-Acetylglycine ethylesterNo name (7)Martinek
Not specified ethylesterNo name (7)Martinek
Homo sapiens N,N,N-trimethylaniliniumInhibition at low [S], activation at high [S]
α = 5.7, β = 3.1, KX = 0.05 μM, σ 0 = 1.2
Torpedo californica name (8)
KX = 0.87 μM
Torpedo californica name (8)
KX = 30 μM
Torpedo californica name (8)
KX = 33 μM
Torpedo californica name (8)
KX = 200 μM
14Aldehyde dehydrogenase (NAD+)
Homo sapiens at low [S], activation at high [S] (9)
α = 8.6, β = 1.6
Homo sapiens 11D-glutamic acid γ-4-nitro-
anilide HCl (10)
V-type activation (11)
α > β, β = 5.4
(2012, 2013)
Homo sapiens 14Glutathione (10)V-type activation (12)
β = 4.0
(2012, 2013)
17Dipeptidyl-peptidase I (tetramer)
Homo sapiens'-Nitrophthalanilic acidH-Gly-Phe-7-amino-4-methylcoumarylamideHyperbolic mixed inhibition/activation
α = 3.7, β = 1.9, KX = 130 μM, σ 0 = 2.0
Humicola insolens
Mutant: D237V/P389H/E395G/K475R
Stimulation (13)
α = 3.3, β = 1.3, Ka = 19.7 mM
Humicola insolens
Mutant: N89Y/H307Y
Stimulation (13)
α = 5.2, β = 3.3, Ka = 31.1 mM

(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) ‘…simultaneously as a competitive inhibitor and as an uncompetitive activator’. Fig. 3 (Phillips, 1991) strongly suggest HMxD(I/A) as the mechanism. The authors proposed a mechanism with 12 complexes and 15 parameters.

(5) NSC13345 = 2-[(2-carbamoylsulphanylacetyl)-amino]benzoic acid.

(6) Abz–HPGGPQ–EDDnp = Fluorogenic, internally quenched substrate, where Abz represents o-aminobenzoic acid and EDDnp represents N -(2,4-dinitrophenyl)-ethylenediamine]. Cleavage by cathepsin K occurs at the Gly-Gly bond, Km = 3.8 ± 0.5 μM, kcat = 2.9 ± 0.1 s–1.

(7) The dual behavior of the modifier (called by the authors effector) was demonstrated unambiguously. Parameter determination was not attempted.

(8) In double-reciprocal plots ‘The intersection point occurred in the upper right quadrant’.

(9) ‘Unusual intersection of the lines of the double-reciprocal plot in the first quadrant of the Cartesian plane’.

(10) Hydrolysis reaction of gamma-glutamyltransferase.

(11) The identity of the mechanism, HMxD(I/A), has been unmistakably demonstrated in Figs. 5A and 5B by Wickham (2012). Using the data in Fig. 5A, all dependencies of the kinetic parameters and the specific velocity plot could be drawn. The profiles were identical with those in the ‘Fingerprints’ above. For α only an approximate value could be inferred from the specific velocity plot and this was larger than the value of β calculated by the authors as ‘fold activation’ i.e. as the ratio of the limiting rates at saturating modifier and in the absence of modifier. The reason why only activation, not inhibition, has been observed in the experiment of Figs. 5A and 5B can be sought in the substrate (D-GpNA) concentrations used in the measurements, which spanned from 0.25 to 3.0 mM (Km = 0.16 mM, as reported by the authors), i.e. there were no substrate concentrations below or in the range of Km. Since the critical substrate concentration calculated from the specific velocity plot was in the range 0.03-0.04, the inhibitory part of this system could obliviously not be seen.

(12) Also in this case, the identity of the mechanism, HMxD(I/A), is clear  as shown in Fig. 5, Wickham (2013). This is the only one among the 17 basic modifier mechanisms showing hyperbolically increasing Vapp and hyperbolically decreasing Vapp/Kmapp for increasing modifier concentration. A value of α could nor be guessed from Fig. 5 because no raw data have been shown. Note: Fig. 5 shows  that Vapp increases in a nearly linear fashion with increasing modifier concentration. As we know, there is no apparent limiting rate (or kcatapp) that can increase linearly with modifier concentration. This is possibly due to high substrate concentrations, close to saturation.

(13) The parameter α was calculated from the Kmapp-values in Table 2, while the values of  β are listed in Table 3 as stimulation factor (fold). Ka was reported by the authors as the modifier concentration needed for half-maximal activation.


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