Combination plots as graphical tools in the study of enzyme inhibition

A much better replacement of the Michaelis–Menten equation and its application

Michaelis–Menten equation is a basic equation of enzyme kinetics and gives acceptable approximations of real chemical reaction processes. Analyzing the derivation of this equation yields the fact that its good performance of approximating real reaction processes is due to Michaelis–Menten curve (8). This curve is derived from Quasi-Steady-State Assumption (QSSA), which has been proved always true and called Quasi-Steady-State Law by Banghe Li et al. [Quasi-steady state laws in enzyme kinetics, J. Phys. Chem. A 112(11) (2008) 2311–2321].

Here, we found a polynomial equation with total degree of four [Formula: see text] (14), which gives more accurate approximation of the reaction process in two aspects: during the quasi-steady-state of the reaction, Michaelis–Menten curve approximates the reaction well, while our equation [Formula: see text] gives better approximation; near the end of the reaction, our equation approaches the end of the reaction with a tangent line the same to that of the reaction process trajectory simulated by mass action, while Michaelis–Menten curve does not. In addition, our equation [Formula: see text] differs to Michaelis–Menten curve less than the order of [Formula: see text] as [Formula: see text] approaches [Formula: see text].

By considering the above merits of [Formula: see text], we suggest it as a replacement of Michaelis–Menten curve. Intuitively, this new equation is more complex and harder to understand. But, just because of its complexity, it provides more information about the rate constants than Michaelis–Menten curve does.

Finally, we get a better replacement of the Michaelis–Menten equation by combing [Formula: see text] and the equation [Formula: see text].

Mating Disruption for the 21st Century: Matching Technology With Mechanism

Progress toward proof of the principal cause of insect mating disruption under a particular set of conditions has been hindered by a lack of logical rigor and clean falsifications of possible explanations. Here we make the case that understanding of mating disruption and optimization of particular formulations can be significantly advanced by rigorous application of the principles of strong inference. To that end, we offer a dichotomous key for eight distinct categories of mating disruption and detail criteria and methodologies for differentiating among them. Mechanisms of mating disruption closely align with those established for enzyme inhibition, falling into two major categories-competitive and noncompetitive. Under competitive disruption, no impairments are experienced by males, females, or the signal of females. Therefore, males can respond to females and traps. Competitive disruption is entirely a numbers game where the ratio of dispensers to females and traps is highly consequential and renders the control pest-density-dependent. Under noncompetitive disruption, males, females, or the signal from females are already impaired when sexual activity commences. The control achieved noncompetitively offers the notable advantage of being pest-density-independent. Dosage-response curves are the best way to distinguish competitive from noncompetitive disruption. Purely competitive disruption produces: a smoothly concave curve when untransformed capture data are plotted on the y-axis against density of dispensers on the x-axis; a straight line with positive slope when the inverse of catch is plotted against density of pheromone dispensers; and, a straight line with negative slope when catch is plotted against density of pheromone dispensers × catch. Disruption operating only noncompetitively produces: a straight line with negative slope when untransformed capture data are plotted on the y-axis against density of dispensers on the x-axis; an upturning curve when the inverse of catch is plotted against density of pheromone dispensers; and, a recurving plot when catch is plotted against density of pheromone dispensers x catch. Hybrid profiles are possible when some males within the population begin the activity period already incapacitated, while those not preexposed have the capacity to respond either to traps or pheromone dispensers. Competitive mechanisms include competitive attraction, induced allopatry, and induced arrestment. Noncompetitive mechanisms include desensitization and inhibition, induced allochrony, suppressed calling and mating, camouflage, and sensory imbalance. Examples of the various disruption types within the two major categories and suggested tactics for differentiating among them are offered as seven case studies of the disruption of important pest species using various formulations are analyzed in depth. We point out how economic optimizations may be achieved once the principal and contributory causes of disruption are proven. Hopefully, these insights will pave the way to a broader and more reliable usage of this environmentally friendly pest management tactic.

Mutual regioselective inhibition of human UGT1A1-mediated glucuronidation of four flavonoids

UDP-glucuronosyltransferase (UGT) 1A1-catalyzed glucuronidation is an important elimination pathway of flavonoids, and mutually inhibitory interactions may occur when two or more flavonoids are coadministered. Our recent research suggested that glucuronidation of flavonoids displayed distinct positional preferences, but whether this will lead to the mutually regioselective inhibition of UGT1A1-mediated glucuronidation of flavonoids is unknown. Therefore, we chose three monohydroxyflavone isomers, 3-hydroxyflavone (3HF), 7-hydroxyflavone (7HF), and 4'-hydroxyflavone (4'HF), and one trihydroxyflavone, 3,7,4'-trihydroxyflavone (3,7,4'THF), as the model compounds to characterize the possible mutually regioselective inhibition of glucuronidation using expressed human UGT1A1. Apparent kinetic parameters [e.g., reaction velocity (V), Michaelis-Menten constant (Km), maximum rate of metabolism (Vmax), concentration at which inhibitor achieves 50% inhibition (IC50), and the Lineweaver-Burk plots were used to evaluate the apparent kinetic mechanisms of inhibition of glucuronidation. The results showed that UGT1A1-mediated glucuronidation of three monohydroxyflavones (i.e., 3HF, 7HF, and 4'HF) and 3,7,4'THF was mutually inhibitory, and the mechanisms of inhibition appeared to be the mixed-typed inhibition. Specifically, the inhibitory effects displayed certain positional preference. Glucuronidation of 3HF was more easily inhibited by 3,7,4'THF than that of 7HF or 4'HF. Compared to 7-O-glucuronidation of 3,7,4'THF, 3-O-glucuronidation of 3,7,4'THF was more inhibited by 3HF and 4'HF, whereas glucuronidation at both 3-OH and 7-OH positions of 3,7,4'THF was more easily inhibited by 7HF than by 3HF and 4'HF. In conclusion, 3HF, 7HF, 4'HF, and 3,7,4'THF were both substrates and inhibitors of UGT1A1, and they exhibited mutually regioselective inhibition of UGT1A1-mediated glucuronidation via a mixed-type inhibitory mechanism.

Inhibitor screening of pharmacological chaperones for lysosomal β-glucocerebrosidase by capillary electrophoresis

Pharmacological chaperones (PCs) represent a promising therapeutic strategy for treatment of lysosomal storage disorders based on enhanced stabilization and trafficking of mutant protein upon orthosteric and/or allosteric binding. Herein, we introduce a simple yet reliable enzyme assay using capillary electrophoresis (CE) for inhibitor screening of PCs that target the lysosomal enzyme, β-glucocerebrosidase (GCase). The rate of GCase-catalyzed hydrolysis of the synthetic substrate, 4-methylumbelliferyl-β-D: -glucopyranoside was performed using different classes of PCs by CE with UV detection under standardized conditions. The pH and surfactant dependence of inhibitor binding on recombinant GCase activity was also examined. Enzyme inhibition studies were investigated for five putative PCs including isofagomine (IFG), ambroxol, bromhexine, diltiazem, and fluphenazine. IFG was confirmed as a potent competitive inhibitor of recombinant GCase with half-maximal inhibitory concentration (IC(50)) of 47.5 ± 0.1 and 4.6 ± 1.4 nM at pH 5.2 and pH 7.2, respectively. In contrast, the four other non-carbohydrate amines were demonstrated to function as mixed-type inhibitors with high micromolar activity at neutral pH relative to acidic pH conditions reflective of the lysosome. CE offers a convenient platform for characterization of PCs as a way to accelerate the clinical translation of previously approved drugs for oral treatment of rare genetic disorders, such as Gaucher disease.

A graphical method for determining inhibition constants

A new simple graphical method is described for the determination of inhibition type and inhibition constants of an enzyme reaction without any replot. The method consists of plotting experimental data as (V-v)/v versus the inhibitor concentration at two or more concentrations of substrate, where V and v represent the maximal velocity and the velocity in the absence and presence of inhibitor with given concentrations of the substrate, respectively. Competitive inhibition gives straight lines that converge on the abscissa at a point where [I] = -K(i). Uncompetitive inhibition gives parallel lines with the slope of 1/K'(i). For mixed type inhibition, the intersection in the plot is given by [I] = -K(i) and (V-v)/v = -K(i)/K'(i) in the third quadrant, and in the special case where K(i) = K'(i) (noncompetitive inhibition) the intersections occur at the point where [I] = -K(i) and (V-v)/v = -1. The present method, the "quotient velocity plot," provides a simple way of determining the inhibition constants of all types of inhibitors.

Application of a normalised plot to the study of ter ter enzyme systems

The kinetic characterisation of multisubstrate systems is not a trivial task. Common approaches simplify the experimental procedures by sequentially fixing saturating concentrations of different substrates/products, thereby attempting to isolate the influence of the varying molecule. Even after such tedious work, only apparent Km values can be determined, preventing serious comparison among differential substrate behaviours. Moreover, the choice among rival kinetic models is not statistically guaranteed; instead, classical tools such as re-plots continue to be used. Here, we report the application of a normalisation of kinetic data, formerly applied to simpler systems, to the description of ter ter systems. This data treatment is able to provide true Km values and a reliable description of the system, at the same time reducing the experimental work and statistically supporting the choice of kinetic schemes.

Application of a normalised plot to the study of uni-uni enzyme-inhibitor systems

Normalisation of kinetic data is a useful tool in the study of complex enzyme systems. In the present paper, we have applied the premises of the normalised plot to the description of uni-uni enzyme inhibition. Guidelines to the design of the experiments and to data managing using the freeware program SIMFIT (http:\\www.simfit.man.ac.uk) are offered. The treatment has a lessened demand in experimental data while ensuring biological consistence of the results. Moreover, the results are obtained without resorting to secondary plots, and the election between rival mechanisms is statistically granted. Hyperbolic mixed-type inhibition is studied as a general model for enzyme-inhibitor/activator interaction, and equations describing classical cases of linear inhibition are also considered.

A normalized plot as a novel and time-saving tool in complex enzyme kinetic analysis

A new data treatment is described for designing kinetic experiments and analysing kinetic results for multi-substrate enzymes. Normalized velocities are plotted against normalized substrate concentrations. Data are grouped into n + 1 families across the range of substrate or product tested, n being the number of substrates plus products assayed. It has the following advantages over traditional methods: (1) it reduces to less than a half the amount of data necessary for a proper description of the system; (2) it introduces a self-consistency checking parameter that ensures the 'scientific reliability' of the mathematical output; (3) it eliminates the need for a prior knowledge of Vmax; (4) the normalization of data allows the use of robust and fuzzy methods suitable for managing really 'noisy' data; (5) it is appropriate for analysing complex systems, as the complete general equation is used, and the actual influence of effectors can be typified; (6) it is amenable to being implemented as a software that incorporates testing and electing among rival kinetic models.

Cloning, purification and characterisation of cystathionine gamma-synthase from Nicotiana tabacum

Cystathionine gamma-synthase, the enzyme catalysing the first reaction specific for methionine biosynthesis, has been cloned from Nicotiana tabacum, overexpressed in Escherichia coli and purified to homogeneity. The recombinant cystathionine gamma-synthase catalyses the pyridoxal 5'-phosphate dependent formation of L-cystathionine from L-homoserine phosphate and L-cysteine with apparent Km-values of 7.1+/-3.1 mM and of 0.23+/-0.07 mM, respectively. The enzyme was irreversibly inhibited by DL-propargylglycine (Ki = 18 microM, k(inact) = 0.56 min(-1)), while the homoserine phosphate analogues 3-(phosphonomethyl)pyridine-2-carboxylic acid, 4-(phosphonomethyl)pyridine-2-carboxylic acid, Z-3-(2-phosphonoethen-1-yl)pyridine-2-carboxylic acid, and DL-E-2-amino-5-phosphono-3-pentenoic acid acted as reversible competitive inhibitors with Ki values of 0.20, 0.30, 0.45, and 0.027 mM, respectively. In combination these results suggest a ping-pong mechanism for the cystathionine gamma-synthase reaction, with homoserine phosphate binding to the enzyme first. Large single crystals of cystathionine gamma-synthase diffracting to beyond 2.7 A resolution were obtained by the sitting drop vapour diffusion method. The crystals belong to the orthorhombic space group P2(1)2(1)2(1) with unit cell constants a = 120.0 A, b = 129.5 A, c = 309.8 A, corresponding to two tetramers per asymmetric unit.

Polyanionic inhibitors of phosphoglycerate mutase: combined structural and biochemical analysis

The effects that the inhibitors inositol hexakisphosphate and benzene tri-, tetra- and hexacarboxylates have on the phosphoglycerate mutases from Saccharomyces cerevisiae and Schizosaccharomyces pombe have been determined. Their Kivalues have been calculated, and the ability of the inhibitors to protect the enzymes against limited proteolysis investigated. These biochemical data have been placed in a structural context by the solution of the crystal structures of S. cerevisiae phosphoglycerate mutase soaked with inositol hexakisphosphate or benzene hexacarboxylate. These large polyanionic compounds bind to the enzyme so as to block the entrance to the active-site cleft. They form multiple interactions with the enzyme, consistent with their low Kivalues, and afford good protection against limited proteolysis of the C-terminal region by thermolysin. The inositol compound is more efficacious because of its greater number of negative charges. The S. pombe phosphoglycerate mutase that is inherently lacking a comparable C-terminal region has higher Kivalues for the compounds tested. Moreover, the S. pombe enzyme is less sensititive to proteolysis, and the presence or absence of the inhibitor molecules has little effect on susceptibility to proteolysis.

Regulation of cathepsin B activity by cysteine and related thiols

We studied the mode of regulation of the activity of mature cathepsin B (CB) by L-cysteine and some related thiols. The activity of CB with Z-Arg-Arg-NHMec as substrate was gradually inhibited over a range of increasing concentration of Cys, Cys methyl ester (CysOMe), Cys ethyl ester (CysOEt), N-acetyl-Cys (N-AcCys) and 3-mercaptopropionic acid. However, the inhibition of CB peaked at a definite value of [Cys], [CysOMe], [CysOEt] and [N-AcCys] and was gradually reversed over a range of higher concentrations of Cys and its esters. The maximum inhibitory concentrations of Cys, CysOME, CysOEt and N-AcCys showed a positive relationship to the pKa(RSH) values of the thiols and those of CysOEt and Cys decreased with increasing pH. The capability of the thiols to overcome their own inhibitory effect on CB was dependent on the concentration of their thiolate anion (RS-). However, the preincubation-dilution experiments showed that Cys and N-AcCys did not interact with active CB via a covalent mode. The inhibition of CB by N-AcCys was competitive and could be reversed by CysOMe. This activity-recovering effect of CysOMe was concentration-dependent and obeyed the Michaelis-Menten saturation kinetics over a profound increase of [RS-]. CB reacting in an environment of concurrently decreasing [RS-] and increasing [RSH], which was achieved by means of carboxylesterase-catalyzed deesterification of CysOEt to Cys, was progressively inhibited. Cys and N-AcCys also inhibited the fragmentation of histone H4 by CB and their concentration-dependent inhibitory profiles were qualitatively similar to those observed with Z-Arg-Arg-NHMec. Taken together, the results indicate that the RSH form of Cys and related thiols inhibits the activity of CB while the RS- form of these thiols counteracts or reverses the inhibitory action of the RSH form. This previously unrecognized thiol-thiolate anion regulation mechanism might be involved in a dynamic regulation of CB activity in endosomes and lysosomes and at the sites of lysosome-driven pericellular proteolysis.

Analysis of the interactions between an enzyme and multiple inhibitors using combination plots

The concurrent effects of two enzyme inhibitors have been analysed previously with the Yonetani-Theorell plot to obtain insight into the interactions between bound inhibitors. This procedure, like many other traditional graphical methods in enzymology, is based on the estimation of intersecting tendencies in a family of lines. In a recent paper from this laboratory [Chan (1995) Biochem. J. 311, 981-985] it was shown that a plot of this nature may sometimes be replaced, with advantage, by a 'combination plot' in which all data points are accommodated in a single line. We have now extended this approach to analyse the effects of multiple inhibitors and have developed combination plots which illustrate the interaction behaviour in an optimal manner. Thus, in these plots, the synergistic or antagonistic nature of the interactions is clearly evident from the slope, which also provides a direct estimate of the interaction coefficient. The analysis is more efficient and consequently requires fewer enzyme assays. This approach is applicable to various special cases, including that in which three inhibitors bind simultaneously to the enzyme.

Demonstration that 1-trans-epoxysuccinyl-L-leucylamido-(4-guanidino) butane (E-64) is one of the most effective low Mr inhibitors of trypsin-catalysed hydrolysis. Characterization by kinetic analysis and by energy minimization and molecular dynamics simulation of the E-64-beta-trypsin complex

1-trans-Epoxysuccinyl-L-leucylamido(4-guanidino)butane (E-64) was shown to inhibit beta-trypsin by a reversible competitive mechanism; this contrasts with the widely held view that E-64 is a class-specific inhibitor of the cysteine proteinases and reports in the literature that it does not inhibit a number of other enzymes including, notably, trypsin. The K1, value (3 x 10(-5) M) determined by kinetic analysis of the hydrolysis of N alpha-benzoyl-L-arginine 4-nitroanilide in Tris/HCl buffer, pH 7.4, at 25 degrees C, I = 0.1, catalysed by beta-trypsin is comparable with those for the inhibition of trypsin by benzamidine and 4-aminobenzamidine, which are widely regarded as the most effective low Mr inhibitors of this enzyme. Computer modelling of the beta-trypsin-E64 adsorptive complex, by energy minimization, molecular dynamics simulation and Poisson-Boltzmann electrostatic-potential calculations, was used to define the probable binding mode of E-64; the ligand lies parallel to the active-centre cleft, anchored principally by the dominant electrostatic interaction of the guanidinium cation at one end of the E-64 molecule with the carboxylate anion of Asp-171 (beta-trypsin numbering from Ile-1) in the S1-subsite, and by the interaction of the carboxylate substituent on C-2 of the epoxide ring at the other end of the molecule with Lys-43; the epoxide ring of E-64 is remote from the catalytic site serine hydroxy group. The possibility that E-64 might bind to the cysteine proteinases clostripain (from Clostridium histolyticum) and alpha-gingivain (one of the extracellular enzymes from phyromonas gingivalis) in a manner analogous to that deduced for the beta-trypsin-E-64 complex is discussed.