Does increasing substrate concentration affect noncompetitive inhibition?

8.2.4 Mixed inhibition

In section 8.2.3 we obtained an expression for simple linear non-competitive inhibition which depended on the equilibrium-assumption (section 7.1.1) being valid, and further assumed that substrate-binding and inhibitor-binding were completely independent. Let us now consider the situation where the second assumption is not made.

There are two processes by which inhibitor may bind to the enzyme:

E+I⇌EI(inhibitor constantKi);andES+I⇌ESI (inhibitor constantKI.Hence,Ki=[E][I]/[EI]andKI=[ES][I]/[ESI]

As in section 8.2.3, [E][S]/[ES] = Km; and,

[E0]=[E]+[ES]+[EI]+[ESI].

If we develop the argument as before, but this time without assuming that Ki and KI are identical:

[E0]=[E]+[ES]+[E][I]Ki+[ES][I]KI=[E](1+[I]Ki)+[ES](1+[I]KI)∴[E]=[E0]−[ES](1+[I]KI)(1+[I]Ki)

Substituting for [E] in the expression for Km:

([E0]−[ES](1+[I]KI))[S](1+[I]Ki)[ES]=Km

∴[E0][S]−[S][ES](1+[I]KI)=Km[ES](1+[I]Ki)∴[ES]([S](1+[I]KI)+Km(1+[I]Ki))=[E0][S]∴[ES]=[E0][S][S](1+[I]KI)+Km(1+[I]Ki)

Continuation as before gives:

(8.22)v0=Vmax[S0][S0](1+[I0]KI)+Km(1+[I0]Ki)

If numerator and denominator are both divided by (1 + ([I0]/KI))

(8.23)v0=Vmax(1+[I0]KI).[S0][S0]+Km(1+[I0]Ki)(1+[I0]KI)

This is of the same form as the Michaelis-Menten equation and can be written:

(8.24)v0=V′max[S0][S0]+K′m

where

(8.25)V′max=Vmax(1+[I0]KI)andK′m=Km(1+[I0]Ki)(1+[I0]KI)

Similarly, the Lineweaver-Burk equations is:

(8.26)1v0=K′mV′max.1[S0]+1V′max

and a Lineweaver-Burk plot will be linear. However, in general, Km, Vmax and slope, which equals

(8.27)K′mV′max=KmVmax(1+[I0]Ki)

are all affected by the inhibitor. Thus, plots at different inhibitor concentrations (at fixed [E0]) will not intersect on either axis, nor will the slope be the same, so the pattern will be different from those characteristic of competitive, non-competitive and uncompetitive inhibition, and is given the name mixed inhibition. It must be realized that this describes the overall pattern observed and does not imply that more than one type of inhibitor is present.

In the situation where Ki > KI, the plots cross to the left of the 1/v0 axis but above the 1/[S0] axis (Fig. 8.11a). This situation has been termed competitive-non-competitive inhibition, because the pattern observed lies between those for competitive (Fig. 8.2) and non-competitive (Fig. 8.8) inhibition.

In the situation where Ki > KI, the plots cross to the left of the 1/v0 axis and below the 1/[S0] axis (Fig. 8.11b). This form of mixed inhibition has been termed non-competitive-uncompetitive inhibition because the pattern is intermediate between those for non-competitive (Fig. 8.8) and uncompetitive (Fig. 8.6) inhibition.

In either case, Ki and KI can be determined using secondary plots. For mixed inhibition:

(8.28)1V′max=1Vmax(1+[I0]KI)

and slope for the inhibited reaction = slope for the uninhibited reaction × (1 +([I0]/Ki)). Hence a secondary plot of 1/V′maxagainst [I0] will be linear, the intercept on the [I0] axis giving −Ki (Fig. 8.12a). A graph of slope of primary plot against [I0] will also be linear, the intercept on the [I0] axis giving −Ki (Fig. 8.12b).

However,

(8.29)K′m=Km(1+[I0]Ki)(1+[I0]KI)

which means that a graph of K′m against [I0] will not be linear.

The equation for v0 derived above is a relatively general one, since no assumptions were made about the values of Ki and KI, and it can be simplified for special cases. If ESI cannot be formed, then KI = ∞ and the equation becomes that for competitive inhibition (section 8.2.1), regardless of whether the substrate and inhibitor bind to the same or different sites. If the complex ESI can occur but not EI, then KI = ∞ and the equation simplifies to that for uncompetitive inhibition (section 8.2.2). When Ki = KI, the equation reduces to that for simple linear non-competitive inhibition (section 8.2.3).

Non-competitive inhibitors

The inhibitory effects of heavy metals, and of cyanide on cytochrome oxidase and of arsenate on glyceraldehyde phosphate dehydrogenase, are examples of non-competitive inhibition. This type of inhibitor acts by combining with the enzyme in such a way that for some reason the active site is rendered inoperative. The inhibition may or may not be reversible but it is not affected by the addition of extra substrate.

If a substrate concentration curve is constructed for the enzyme in the presence of sufficient non-competitive inhibitor to cause partial but not complete inhibition, as shown in Figure 6.7, it is found that the Km of the reaction is unaffected although Vmax is greatly reduced. The effect may be explained in terms of a reduction in the concentration of enzyme, i.e. that whereas some of the enzyme molecules are rendered completely inactive by combination with the inhibitor, others remain uncombined and normally reactive.

Echinocandins

The three echinocandins caspofungin, micafungin and anidulafungin demonstrate in vitro and in vivo activity against Aspergillus spp. The common mode of action is the non-competitive inhibition of 1,3-β-glucan synthase, the enzyme involved in the synthesis of 1,3-β-glucan.134 The echinocandins do not exhibit fungicidal activity against Aspergillus spp. but rather induce profound morphologic changes: hyphae become short and excessively branched. Histologic studies suggest that drug-exposed organisms have a reduced propensity for angioinvasion, which results in reduced pulmonary injury in experimental invasive pulmonary aspergillosis.134

The echinocandins are large water-soluble molecules, which exhibit linear pharmacokinetics.134 They can be used safely in patients with organ dysfunction, exhibit few significant drug interactions and are associated with a relative paucity of serious adverse effects.134 Caspofungin and micafungin have an established role for the prophylaxis of invasive fungal infection in high-risk patients,136,137 and caspofungin may be used as salvage treatment of invasive aspergillosis.138 The echinocandins may have a unique role in combination regimens, especially with triazoles,139 although randomized trials to address this concept are pending. The role of the echinocandins as first-line agents for the treatment of invasive aspergillosis remains undefined.

Mechanisms

Drug interactions with the antifungal azoles are common for several reasons:

they are substrates of CYP3A4, but also interact with the heme moiety of CYP3A, resulting in non-competitive inhibition of oxidative metabolism of many CYP3A substrates; to a lesser extent they also inhibit other CYP450 isoforms;

although fluconazole undergoes minimal CYP-mediated metabolism, it nevertheless inhibits CYP3A4 in vitro, albeit much more weakly than other azoles [5,6]; however, fluconazole also inhibits several other CYP isoforms in vitro and interacts with enzymes involved in glucuronidation [7];

interaction of antifungal azoles and other CYP3A substrates can also result from inhibition of P-glycoprotein-mediated efflux; P-glycoprotein is extensively co-localized and exhibits overlapping substrate specificity with CYP3A [7]; in a cell line in which human P-glycoprotein was overexpressed, itraconazole and ketoconazole inhibited P-glycoprotein function, with 50% inhibitory concentrations of about 2 and 6 μmol/l respectively; however, fluconazole had no effect [8].

the systemic availability of the antifungal azoles depends in part on an acidic gastric environment and the activity of intestinal CYP3A4 and P-glycoprotein.

For details of interactions with individual antifungal azoles, see individual monographs (fluconazole, itraconazole, ketoconazole, miconazole, and voriconazole).

Inhibition of metabolism by CYP3A4, and inhibition of transport by multidrug transporters. Both were important in a boy with toxicity from a chemotherapeutic regimen containing drugs that are handled by these systems [9].

A 14-year-old boy with Hodgkin’s lymphoma was given vinblastine, doxorubicin, methotrexate, and prednisone chemotherapy and low-dose radiotherapy. When he was given itraconazole for a presumed fungal infection during an episode of neutropenia, unexpectedly severe bone marrow toxicity and neuropathy suggested toxicity from the chemotherapy due to enhancement by itraconazole. The itraconazole was withdrawn and the neutropenia and neuropathic pain improved.

The authors suggested that itraconazole had interfered with the metabolism of vinblastine, resulting in neurotoxicity, and with the metabolism of doxorubicin and methotrexate and the transport of doxorubicin, resulting in bone marrow suppression.

Posaconazole is an exception, since it is eliminated unchanged in the feces [10].

A novel mechanism whereby azoles may take part in drug interactions has been described [11]. Drug metabolism is controlled by a class of orphan nuclear receptors that regulate the expression of genes such as CYP3A4 and MDR-1 (multi-drug resistance-1). Xenobiotic-mediated induction of CYP3A4 and MDR-1 gene transcription was inhibited by ketoconazole, which acted by inhibiting the activation of human pregnenolone X receptor and constitutive androstene receptor, which are involved in the regulation of CYP3A4 and MDR-1. The effect was specific to this group of nuclear receptors.

2.1 Mechanism of action

Many fungal human pathogens contain the polysaccharide β-(1,3)-d-glucan as a major cell wall structural component. In common with the echinocandin antifungals, ibrexafungerp exerts its antifungal effects through selective, non-competitive inhibition of β-(1,3)-d-glucan polymer assembly via direct inhibition of the β-(1,3)-d-glucan synthase protein complex. This compromises the integrity of the fungal cell wall, causing a leakage of cytoplasmic contents from yeast and abnormal growth morphology in molds (Onishi et al., 2000; Walker et al., 2011). However, triterpenoids are structurally distinct from the echinocandins. The interaction of ibrexafungerp with the catalytic FKS subunit of β-(1,3)-d-glucan synthase is different from that of the echinocandins, with overlapping but non-identical binding sites (Onishi et al., 2000; Jiménez-Ortigosa et al., 2014, 2017). Its antifungal potency is generally comparable to that of the echinocandins (Davis et al., 2020).

Trisodium Phosphonoformate (PFA, Foscarnet)

Trisodium phosphonoformate, known also as phosphonoformic acid (PFA) or foscarnet (Fig. 12.1), is a non-nucleoside inhibitor of the DNA polymerases of herpesviruses and hepatitis B, as well as the reverse transcriptase of HIV. It acts through a non-competitive inhibition of the pyrophosphate-binding site on the enzyme. Resistance maps to the DNA polymerase gene. PFA may be given intravenously to treat CMV retinitis and severe herpesvirus infections, particularly those resistant to other antiviral drugs. The drug also displays some activity against hepatitis B in vitro but has been ineffective in vivo.

Although foscarnet displays some selectivity in that it inhibits cellular DNA polymerase α only at higher concentrations than the level required to inhibit viral DNA polymerase, it accumulates in bone and can lead to renal toxicity, electrolyte disturbances, and genital ulceration. Accordingly, it tends to be reserved for life-threatening conditions.

Polyenes and Echinocandins

Alternative drug agents, such as amphotericin B lipid formulations and echinocandins are also used in refractory diseases following primary antifungal therapy with voriconazole (or other triazole agents) and when there is a need for transition to salvage therapy. Amphotericin B binds to ergosterol and induces pores within membranes which is rapidly fungicidal. Liposomal amphotericin B has demonstrated efficacy for the treatment of established IA in children and adults (Walsh et al., 2001).

The three echinocandins caspofungin, micafungin and anidulafungin demonstrate in vitro and in vivo activity against Aspergillus species. The common mode of action is the non-competitive inhibition of (1,3)-β-glucan synthase, the enzyme involved in the synthesis of (1,3)-β-glucan (Denning, 2003). Although echinocandins are not fungicidal, they induce profound morphological changes in Aspergillus hyphae that reduce its angioinvasive propensity. Recently, rezafungin (CD101) a novel echinocandin in development for the treatment and prevention of invasive fungal infections has been shown to be effective in a mouse model of disseminated aspergillosis (Ong et al., 2016). Rezafungin demonstrated potent in vitro activity against Aspergillus spp., including azole-resistant A. fumigatus isolates and cryptic species with elevated posaconazole and voriconazole MICs (Wiederhold et al., 2018). An increased plasma half-life (Lakota et al., 2018) of rezafungin allows once-weekly intravenous dosing. Caspofungin and micafungin have an established role for the prophylaxis of invasive fungal infection in high-risk patients (Walsh et al., 2004; van Burik et al., 2004).

The Role of Magnesium in CaSR Function

A definitive role of Mg in CaSR function has not been identified. What follows is suggested by other studies and constitutes a plausible way in which Mg could function.

While the role of the putative Mg binding sites on the CaSR is not clear, there are other potential roles for Mg in CaSR function. Although it has been shown that certain Mg-dependent G-proteins may aid in the activation of PLC,2,3 deficiency of Mg, were it to affect those proteins, would reduce PLC activation and would stunt the release of cytosolic calcium. This is the opposite effect of what we see with Mg deficiency. A better possibility would be the noted interference of Mg with IP3-induced calcium release by non-competitive inhibition.4 In this case, Mg deficiency would enhance cytosolic calcium release as was demonstrated in vitro.4 While evidence suggests that the CaSR may be up-regulated in conditions that produce Mg deficiency, it is not entirely clear that Mg deficiency per se is associated with CaSR up-regulation, as we will demonstrate in some detail below. It is entirely possible that other abnormalities that are associated with Mg deficiency may influence the CaSR but not the actual deficit of Mg.

Also of importance is the mediation of CaSR transcription by 1,25-dihydroxyvitamin D that is resident in the parathyroid chief cells. When 1,25-dihydroxyvitamin D is low in serum the amount of CaSR decreases, as does its response to blood levels of ionized calcium. This reduction in CaSR transcription is thought to contribute to parathyroid hyperplasia in chronic kidney disease.5 It is not certain, however, that the reverse is the case, i.e., that high levels of 1,25-dihydroxyvitamin D in the parathyroid up-regulate the amount of CaSR above normal.

Now that we have identified a possible effect of Mg deficiency on the parathyroid CaSR, we will examine the clinical manifestations of Mg deficiency and the conditions in which it is encountered.

Evidence for the Physical Continuity of Soluble and Nerve Ending Tryptophan Hydroxylase

Additional evidence was sought for the cell body location of the soluble enzyme, for the nerve ending location of the particulate enzyme, and the relationship between them. This was done using the strategy of the acute administration of the tryptophan hydroxylase inhibitor parachlorophenylalanine (PCPA) and following the “flow” of reduced activity from the midbrain region to the septal areas. Due to the multiplicity of actions of PCPA, both in vitro and in vivo experiments were carried out. Figure 3 demonstrates that PCPA is a competitive inhibitor of uptake of labeled tryptophan into synaptosomes with a Ki of 9.7 × 10−6 M. Other work has demonstrated a dialyzable competitive and non-dialyzable non-competitive inhibition of soluble enzyme by PCPA several hours after administration (Jequier, Lovenberg & Sjoerdsma, 1967). In a series of in vivo experiments, PCPA (300 mg/kg) was administered and groups of animals (12 rats per group) were sacrificed after varying periods of time. Tryptophan hydroxylase activity was determined in the midbrain (soluble) and septal (particulate) areas. Figure 4 summarizes the results. The midbrain manifests a decreased activity during the first few hours (which was partially reversible by dialysis) and a delayed decrease (non-dialyzable) in two days which returned to control levels between eight and thirteen days after drug treatment. The septal area manifested a more immediate decrease, reversible in four hours, and a delayed decrease reaching the septal area in eight to thirteen days after drug administration.

The initial, quickly reversible, decrease in activity in the septal area can be seen as consistent with competition for the substrate uptake mechanism in synaptosomes by PCPA. One can interpret the more delayed decrease in septal enzyme activity as resulting from the axoplasmic flow of defective enzyme from midbrain cell bodies to septal nerve endings. These findings are also consistent with the view that the two enzyme forms are different only in physical state and do not represent two different enzymes. The apparent rate of flow is consistent with that reported for “slow” axoplasmic flow of soluble brain proteins at 1 mm/day in that the distance from the cell body area (median raphe area of the midbrain) and the nerve endings area (septum) in the rat is 1.2 to 1.5 cm.

Does substrate concentration affect noncompetitive inhibition?

What will happen if you increase the substrate concentration in competitive inhibition?

Can noncompetitive inhibitors be overcome by adding more substrate?

How does substrate concentration affect inhibition?