Intra-site differential inhibition of multi-specific enzymes

Figures & data

Figure 1. Competitive model of an intra-site differential inhibitor.

Figure 2. Predicted effect of a competitive DI on the transformation of two substrates catalysed by a multi-specific enzyme. The kinetic behaviour is described by the model reported in Figure 1 with the two substrates displaying the same K_M (i.e. K_A = K_B = 5 concentration units) and the same k_cat (100 time⁻¹ units) and is represented by the Hanes–Wolff plot. Panel A: the transformation of substrate B, which is susceptible to inhibition, is analysed. The red open and closed circles refer to substrate B present alone and in the presence of A at a concentration equal to 2K_M, respectively. Symbols ▪, ▲, ♦ and ▼refer to red closed circles in the presence of [I] equal to 1, 2, 3, and 5 times the K_i value, respectively. The K_i value is considered as K_M/10. Panel B: the transformation of the substrate A, which is insensitive to direct inhibition, is analysed. Blue open and closed circles refer to substrate A alone and in the presence of B at a concentration equal to 2K_M, respectively. Symbols ▪, ▲, ♦ and ▼ refer to blue closed circles in the presence of [I] equal to 0.5, 1, 2, and 5 times the K_i value, respectively. The K_i value is considered as K_M/10. In Panels A and B, the increase in [I] is emphasised by the red arrows. In Panel C, the B rate transformation (red curve) and A rate transformation (blue curve) are reported as a function of the inhibitor concentration expressed as K_i fold. The substrate concentrations were considered fixed at the 2K_M value and the K_i value is considered as K_M/10. The dotted line refers to the differential inhibition.

Figure 3. Effect of a competitive DI acting as a partial inhibitor of A transformation. The transformation rate of substrate B (red curve) and substrate A (blue curves) (see Figure 1) as a function of the inhibitor concentration (expressed as K_i fold) is reported. The substrate concentration is considered fixed at the K_M value (K_A = K_B). Curves 1, 2, 3 and 4 refer to k₊₆ values equal to 0.8, 0.6, 0.4 and 0.2 times the k₊₂ value, respectively. The K_i value is considered as K_M/10.

Figure 4. Non-competitive model of an intra-site differential inhibitor.

Figure 5. Effect of a non-competitive DI. The rate transformation of substrate B (open circles, see Equation (5)(5) $${\mathit{v}}_{\mathit{q}}=\frac{{\mathit{k}}_{+4}\mathrm{*}{\mathit{E}}_{\mathit{T}}}{\frac{{\mathit{K}}_{\mathit{B}}}{\left[\mathit{B}\right]}+\frac{{\mathit{K}}_{\mathit{B}}\mathrm{*}\left[\mathit{I}\right]}{{\mathit{K}}_{\mathit{i}}\mathrm{*}\left[\mathit{B}\right]}+\frac{\left[\mathit{I}\right]}{{\mathit{K}}_{\mathit{i}}^{\mathrm{\text{'}}}}+\frac{{\mathit{K}}_{\mathit{B}}\mathrm{*}\left[\mathit{A}\right]}{{\mathit{K}}_{\mathit{A}}\mathrm{*}\left[\mathit{B}\right]}+\frac{{\mathit{K}}_{\mathit{B}}\mathrm{*}\left[\mathit{A}\right]\mathrm{*}\left[\mathit{I}\right]}{{\mathit{K}}_{\mathit{A}}\mathrm{*}{\mathit{K}}_{\mathit{i}}\mathrm{*}\left[\mathit{B}\right]}+1}$$(5) and substrate A (closed circles, see Equation (4)(4) $${\mathit{v}}_{\mathit{p}}=\frac{({\mathit{k}}_{+2}+\frac{\left[\mathit{I}\right]}{{\mathit{K}}_{\mathit{i}}}\mathrm{*}{\mathit{k}}_{+6}){\mathrm{*}\mathit{E}}_{\mathit{T}}}{\frac{{\mathit{K}}_{\mathit{A}}}{\left[\mathit{A}\right]}+\frac{{\mathit{K}}_{\mathit{A}}\mathrm{*}\left[\mathit{I}\right]}{{\mathit{K}}_{\mathit{i}}\mathrm{*}\left[\mathit{A}\right]}+\frac{\left[\mathit{I}\right]}{{\mathit{K}}_{\mathit{i}}}+\frac{{\mathit{K}}_{\mathit{A}}\mathrm{*}\left[\mathit{B}\right]}{{\mathit{K}}_{\mathit{B}}\mathrm{*}\left[\mathit{A}\right]}+\frac{{\mathit{K}}_{\mathit{A}}\mathrm{*}\left[\mathit{B}\right]\mathrm{*}\left[\mathit{I}\right]}{{\mathit{K}}_{\mathit{B}}\mathrm{*}{\mathit{K}}_{\mathit{i}}^{\mathrm{\text{'}}}\mathrm{*}\left[\mathit{A}\right]}+1}$$(4) according to the model of Figure 4 are reported as a function of the inhibitor concentration (expressed as lowest K_i fold). The substrates concentration is considered fixed at the K_M value (K_A = K_B). The following combinations of inhibition constants are considered: red curves: K_i= K_M/10 and K′_i= K_M; blue curves K_i= K_M/10 and K′_i = K_M/5; green curves K_i= K_M/5 and K′_i= K_M/10; violet curves K_i= K_M and K′_i= K_M/10.

Figure 6. Differential inhibition of AKR1B1 by synthetic and natural compounds. The bars refer to the differential inhibition between aldoses reduction and HNE reduction. The letters along the bars refer to: a: D-glyceramide¹⁵; b: D-gluconamide¹⁵; c: pyrazol[1,5-a]pyrimidine derivative (compound 5e⁵²); d: soyasaponin⁵⁵; e: NHDC²⁰; f: sorbinil⁵²; g: epalrestat⁵²; h: [1,2,4]oxadiazol-5-yl-acetic acid derivative (compound 9¹⁵); i: Saccharin derivative (compound 16¹⁵).

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