concepts in biochemistry
WILLIAM M. SCOVELL edited by Bowling Green State University Bowling Green, OH 43403
4 Theoretical Approach to the Discrimination and Characterization of the Different Classes of Reversible Inhibitors Josep Lluis Gelpi, Joan Josep Avilbs, Montserrat Busquets, Santiago Imperial, Adela Maro and Antoni ~ o r t b s ' Departament de Bioquimica i Fisiologia, Facultat de Quimica, Universitat de Barcelona, Marti i Franques, 1 08028-Barcelona, Spain David J. Halsall and J. John Holbrwk Molecular Recognition Centre and Department of Biochemistry, University of Bristol, School of Medical Sciences University Walk, Bristol BS8 lTD, United Kingdom The Study of lnhibition Metabolic Pathways and Control Mechanisms Inhibitors are compounds that slow down the activity of enzymes by preventing either the formation or productive breakdown of euzyme-substrate and enzyme-product complexes. Inhibitors have been used to help elucidate metabolic pathways by causing accumulation of intermediates. This is well exemplified by the classic case of malonate which, as an inhibitor of succinate dehydrogenase, played a crucial role in the discovery of the tricarboxylic acid cycle (I). In the cell, inhibition of key reactions involves substances that may be products of the reaction itself or of the same (or even of a different) metabolic pathway. This provides a ready and delicately poised control mechanism for the maintenance of a relatively constant intracellular environment, and for its response to alteration in the external milieu. The inhibitions of hexokinase by glucose-6phosphate (2)and of y-glutamylcysteine synthetase by glutathione (3)are examples of physiologically significant control mechanisms. Pharmaceutical Products Inhibitors of enzymatic reactions have acquired a very vast dimension in medical and pharmaceutical research and in the treatment of a large number of diseases. For example, sulfonamides have been used as chemotherapeutic agents to destroy or prevent growth of unwanted organisms. These compounds inhibit bacterial dihydropteroate synthetase, due to the similarity in the steric and electronic properties of the p-aminobenzoic acid and sulfonamides (4).Allopurinol is an effective inhibitor of xanthine oxidase and a successful agent for regulating production of uric acid and gout (5). Mevinolin reduces the circulating levels of cholesterol and cholesterol esters in blood. In addition to inhibiting cholesterol biosynthesis within the liver by serving as an inhibitor of hydroxymethylglutaryl-CoA reductase (61, it has been demonstrated that the administration of this 'Author to whom correspondence should be addressed.
drug increases the low-density lipoprotein (LDL)receptors in the liver (7).These receptors are responsible for the uptake of cholesterol and cholesterol esters by the tissues, so mevinolin may have a positive effect in treating some typeI11 hyperlipoproteinemia patients (8). Product lnhibition In the area of kinetics, product inhibition studies have been carried out using inhibitors that are neither substrates nor products of the reaction. These studies also included runs that used no inhibitor and thus proved of great value in choosing between mechanisms that could not be distinguished on the basis of studies of the uninhibited reaction alone. For example, the inhibition of aspartate aminotransferase by L-glutamate revealed the existence of several productive enzyme ternary complexes containing this product. They had not been previously detected in the simple ping-pong kinetic mechanism postulated for this enzyme (9). In turn, the inhibition patterns of guanosine monophosphate (GMP) reductase by xanthosine monophosphate (XMP), 2'-dXMP, and 8-azaXMP were consistent with an ordered sequential mechanism for this enzyme with GMP binding first (10). QSAR Studies Quantitative structure-activity relationships (QSAR) based on the use of inhibitors can provide clues to the inhibition mechanism and can give very valuable information about the chemical architecture of the active site. QSAR studies try to explain the observed variations in biological activity of a group of congeners in terms of the variance of electronic characteristics, steric factors, hydrophobic effects, and structural properties caused by a change of the substituents (11). For example, QSAR studies of a variety of derivatives of benzamidine in combination with molecular graphics analyses have shown that these inhibitors of trypsin are bound in a hydrophobic pocket in the active site of the enzyme. The positively charged amidine interacts electrostatically with the carboxylate group of Asp-189 a t the back of this hydrophobic pocket (12). However, the interaction of the small 4-substituents of benzamidiues does not occur Volume 70 Number 10 October 1993
805
within the hydrophobic space hut with the polar hydroxyl group of Ser-195. This interaction is hindered by a sufficient bulky group (12). Full and Partial Inhibitors
Reversible inhibitors (i.e., compounds whose action can be eliminated by simple treatments such as dialysis or dilution) that read with one or more enzyme forms to give complexes that cannot participate in the reaction sequence are referred to as dead-end or full inhibitors. When the enzymeinhibitor complex can undergo the same reaction the enzyme would have undergone in the absence of inhibitor but a t a slower rate. there are alternate reaction sequences in the mechanism, and the inhibitor is classified as partial (13).Several partial inhibitors have clearly been identified. Some e x m i l e s are the inhibition of NADH oxidase by NAD' (14) glycogen phosphorylase by glucose-Bphosphate (15) adenylate cyclase by adenosine (16) leukocyte elastase by glycosaminoglycan polysulfate (17) (Na+-K+)ATPase by canrenone (18) cytoehrome oxidase by diaminomalwnitrile (19) However, in order to diagnose this type of inhibition, i t is necessary to measure the inhibition behavior at several values of inhibitor concentration spread over a wide range. Failure to do this is probably the main reason partial inhibitors have often been overlooked and encountered so rarely in comparison with full inhibitors (20). Extent of the Inhibition I n this paper only reversible combinations between inhibitor and various enzyme forms will be considered because these cover most of the cases met in ~ractice.I m ~-~~ versible inhibition is also important for t i e mechanism studv of enzvmes. e ordi" . but it is somewhat s e ~ a r a t from nary kinetic investigations, and we shall not discuss i t here. I n studying reversible inhibitors several parameters have been renorted to desnibe the extent of inhibition. The more common are the dissociation constant of the enzyme species to which the inhibitor binds 'the fractional inhibition (i.e., the relative inhibition potency) .the inhibitor concentration that is necessary to reduce the enzymatic activity by one half ~~
~~~~~~
This last parameter has frequently been used in pharmacological A d QSAR studies because it provides a practical and readily comprehensible potency index that permits the comparison of a series of enzyme inhibitors, drugs, and other pharmacologically important compounds (21,211. Full reversible have been classified bv the No~ ~inhibitors ~ menclature Committee of the International LJnidn of Biochemistry (22) into a number of types according to their effects on the Michaelis-Menten equation (23) parameters. competitive noncompetitive mixed uncompetitive ~
.
EIcS
ESI k.4
-
EIcP
kb
Figure 1. General inhibition mechanism in single-substrate reactions. with this last type of inhibitor and are unaware of the mechanism of action. This is a serious problem because in most cases the double-reciprocal plot obtained for a given full inhibitor (e.g., fully competitive) is identical to that obtained for the corresponding partial inhibitor (e.g., partially competitive) in spite of their different reaction mechanisms (28). For all these reasons, the purpose of this paper is to provide the students with a more suitable approach to deduce the kinetic mechanism of the different types of reversible inhibitors that obev Michaelis-Menten kinetics 'their nmespondiil: rate equatmns and kinetic parameters 'the methods that allow them to be distinyl~hed Theory A eeneral inhibition mechanism that describes the interact& of the substrate (S) and a reversible inhibitor (I) with the enzyme (E) when no substrate inhibition exists is shown in Figure 1. The rate equation in this general case can be derived under rapid eauilibrium conditions or using the steady-state assnm&oi according to the ~ i c h a e l i c Menten (23) and Briggs-Haldane (29) hypotheses, respectively, These were originally applied to single-substrate enzyme-catalyzed reactions in the absence of external effectors. Rapid Equilibrium Approach
I n this treatment it is assumed that all the steps are in rapid equilibrium relative to the breakdown of ES and ESI to form product.
where Ks and KI are the dissociation constants of the ES and El complexes, respectively.
The differences among them are usually reflected in the Lineweaver-Burk plots (24). Distinguishing Full and Partial Inhibitors The ~ D ~ discussed C S above are well-known by students because 'they are widely discussed in almost all current biochemistrv textbooks. but this is not true for partial inhibitors, w k c h are n e h y always ignored (25%). As a consequence, students often lack adequate familiarity
806
Journal of Chemical Education
I& andK1are the dissociation constants of the ESI complex for the breakdown to EI + S and I S + I, respectively i k , and k'. are the rate constants of product formation from the ES and ESI complexes, respectively.)
For the four enzyme species shown in Figure 1 to be at equilibrium, the two routes for calculating [ESII from [El must be equivalent:
Table 1. Types of lnhibltlon for Mechanisms Predicting a Hyperbolic Saturation Cuwe of vversus [S]
E+ES+ESI
In other words, the ffinity of the inhibitor for the ES complex with respect to the ffinity for the free enzyme must change to the same extent as the a f f i t y of the substrate for the enzymatic species EI and E, respectively. This implies that KVKI = K'dKs. Deriving the Basic Equation
FNC
Because both ES and ESI release product, the velocity ofthe reaction (ul) will be described by u1 = kp[ES1+!dp [ESII
1
I 1+-
KI
PNC -
and
I+-
I 1+-
I
KI
FMa,b
1
7 I+%
Then we make the following substitutions.
KI
I I+K~ I I+%
1 -I 1+-
(a)> 1
(b)< 1
KI
[SI[Il [ESII = -[El
KsKf
The maximum velocity (V,) attained in the absence of inhibitor when the enzyme active sites are saturated by substrate is V, = k,[Elt. Taking P for the ratio k'& we easily obtain
FUC
PUCC
1
1
I
1 + I%
1 + -I
1 + -I KI -
A I 1+-
Ki
Obviously, in the absence of I, the velocity of the reaction is u = kJESI, and eq 1reduces to the simple Michaelis-Menten equation. u -
vm
[SI
KM+ [SI
'Inhibition typs are symbolized by F (Fully) (IC, = 0). P (Panially) (K, > O).C (ComWiNe). NC (Noncompeti~e),M (Mixed) and UC (Unwmpstitve). %rfull inhibitors V d I ) = 0 when1 +- except for FC (VAO = V,). Forpanial inlibtors when vm ?ha decrease of IC, wiih respec4 lo ko is higher (PMb), lower (PMc) or equal (PUC) than the decrese of M with r e s p d to I6
vrn
,+-,
(2)
whereV,= k,[El, and KM = Ks = k.llkl. This may be operationauy defined as that substrate concentration that gives half the maximum velodty ([SI for u = VJ2). Equation 1 shows that the apparent values of the Michaelis-Menten parameters (Vm(oand KM(I,)in the presence of I are
vm
