Rigorous determination of the Hill coefficient of non-Michaelian substrate-inhibited enzymes

The Hill coefficient (n), the max. velocity (VM) and the dissociation constants of the competent enzyme-substrate complex (Ks) and of the inhibitory bindings of substrate to both pure enzyme (Kse) and to ES (Kses) can be determined using a particular property of the representative equation. Choosing successive pairs of substrate concns (Si, Sj) in such a way as Si.Sj = 1, and plotting Sj-1 versus Si-1 gives a family of straight lines whose slopes are: b = Ks.kses, i.e.b = Sm2n, independent of Si, Sj. Then: n = Lnb/2 LnSm, where Sm corresponds to vm, maximum value of v on the curve. All of the other parameters can be calculated from the value of n.     

Kinetics of the hydrolysis of N-benzoyl-l-serine methyl ester catalysed by bromelain and by papain. Analysis of modifier mechanisms by lattice nomography, computational methods of parameter evaluation for substrate-activated catalyses and consequences of postulated non-productive binding in bromelain- and papain-catalysed hydrolyses

1. N-Benzoyl-l-serine methyl ester was synthesized and evaluated as a substrate for bromelain (EC 3.4.22.4) and for papain (EC 3.4.22.2). 2. For the bromelain-catalysed hydrolysis at pH7.0, plots of [S(0)]/v(i) (initial substrate concn./initial velocity) versus [S(0)] are markedly curved, concave downwards. 3. Analysis by lattice nomography of a modifier kinetic mechanism in which the modifier is substrate reveals that concave-down [S(0)]/v(i) versus [S(0)] plots can arise when the ratio of the rate constants that characterize the breakdown of the binary (ES) and ternary (SES) complexes is either less than or greater than 1. In the latter case, there are severe restrictions on the values that may be taken by the ratio of the dissociation constants of the productive and non-productive binary complexes. 4. Concave-down [S(0)]/v(i) versus [S(0)] plots cannot arise from compulsory substrate activation. 5. Computational methods, based on function minimization, for determination of the apparent parameters that characterize a non-compulsory substrate-activated catalysis are described. 6. In an attempt to interpret the catalysis by bromelain of the hydrolysis of N-benzoyl-l-serine methyl ester in terms of substrate activation, the general substrate-activation model was simplified to one in which only one binary ES complex (that which gives rise directly to products) can form. 7. In terms of this model, the bromelain-catalysed hydrolysis of N-benzoyl-l-serine methyl ester at pH7.0, I=0.1 and 25 degrees C is characterized by K(m) (1) (the dissociation constant of ES)=1.22+/-0.73mm, k (the rate constant for the breakdown of ES to E+products, P)=1.57x10(-2)+/-0.32x10(-2)s(-1), K(a) (2) (the dissociation constant that characterizes the breakdown of SES to ES and S)=0.38+/-0.06m, and k' (the rate constant for the breakdown of SES to E+P+S)=0.45+/-0.04s(-1). 8. These parameters are compared with those in the literature that characterize the bromelain-catalysed hydrolysis of alpha-N-benzoyl-l-arginine ethyl ester and of alpha-N-benzoyl-l-arginine amide; K(m) (1) and k for the serine ester hydrolysis are somewhat similar to K(m) and k(cat.) for the arginine amide hydrolysis and K(as) and k' for the serine ester hydrolysis are somewhat similar to K(m) and k(cat.) for the arginine ester hydrolysis. 9. A previous interpretation of the inter-relationships of the values of k(cat.) and K(m) for the bromelain-catalysed hydrolysis of the arginine ester and amide substrates is discussed critically and an alternative interpretation involving substantial non-productive binding of the arginine amide substrate to bromelain is suggested. 10. The parameters for the bromelain-catalysed hydrolysis of the serine ester substrate are tentatively interpreted in terms of non-productive binding in the binary complex and a decrease of this type of binding by ternary complex-formation. 11. The Michaelis parameters for the papain-catalysed hydrolysis of the serine ester substrate (K(m)=52+/-4mm, k(cat.)=2.80+/-0.1s(-1) at pH7.0, I=0.1, 25.0 degrees C) are similar to those for the papain-catalysed hydrolysis of methyl hippurate. 12. Urea and guanidine hydrochloride at concentrations of 1m have only small effects on the kinetic parameters for the hydrolysis of the serine ester substrate catalysed by bromelain and by papain.     

Kinetic Mechanism of Na<Superscript>+</Superscript>-Glucose Cotransport through the Rabbit Intestinal SGLT1 Protein

No consensus has yet been reached regarding the order of substrate addition to the high-affinity Na+ -D-glucose cotransporter (SGLT1). This problem was addressed by computer-assisted derivation of the steady-state velocity equations characterizing the eight-state Na+:Na+:substrate (NNS) and Na+:substrate:Na+ (NSN) mechanisms of cotransport. A notable difference was found in their denominator expressions and used to device a new strategy aimed at model discrimination in which the initial rate data are recorded at fixed S and analyzed relative to the N dependence of transport using a Hill equation. According to this protocol, the values of the Hill coefficient (n(H)) should be finite at all S (1.0 < n(H) < or =2.0) or decrease down to a limit value of 1.0 at high S in the case of the NNS and NSN models, respectively. These key experiments were performed in rabbit intestinal brush border membrane vesicles and demonstrated that a Hill equation with n(H) = 2.0 best describes the steady-state kinetics of Na+ -glucose cotransport at all S. We therefore propose a kinetic mechanism whereby Na+ binding should occur with very strong cooperativity within a rapid equilibrium segment of the transport cycle and be followed by a slow isomerization step before glucose addition.     

Kinetic characteristics of the ATP-pyrophosphate isotope exchange catalyzed by RNA ligase from T4 bacteriophage

The dependence of initial rate v0 of ATP--PPi exchange reaction catalyzed by RNA-ligase of bacteriophage T4 on the concentration of ATP(s), pyrophosphate (z) and Mgcl2 has been determined. The dependence of v0 on s and z described by the equation v0 = k-1k2E0/(k-1 + K2) (1 + K1/s + k2/z) has been obtained for the reaction of E + S in equilibrium ES in equilibrium E1 + Z, where E--enzyme, E1--adenylylenzyme, S--ATP, Z--pyrophosphate, K1 and K2--constants of equilibrium, k-1, k2--velocity constants of transition of ES to E + S and E1 + Z, E0--complete concentration of enzyme. The low inhibition of the ATP--PPi exchange by the acceptor A(pA)2 and donors pAp, p(Ap)3, pCp has been shown. The dependence of v0 on the concentration of MgCl2 is consent with the incorporation of only dimagnesium salts of substrates in the isotope-exchange reaction.     

The general modifier ("allosteric") unireactant enzyme mechanism: redundant conditions for reduction of the steady state velocity equation to one that is first degree in substrate and effector

The general unireactant modifier mechanism in the absence of product can be described by the following linked reactions: E + S k1 in equilibrium k-1 ES k3----E + P; E + I k5 in equilibrium k-5 EI; EI + S k2 in equilibrium k-2 ESI k4----EI + P; and ES + I k6 in equilibrium k-6 ESI where S is a substrate and I is an effector. A full steady state treatment yields a velocity equation that is second degree in both [S] and [I]. Two different conditions (or assumptions) permit reduction of the velocity equation to one that is first degree in [S] and [I]. These are (a) that k-2k3 = k-1k4 (Frieden, C., J. Biol. Chem. 239, pp. 3522-3531, (1964)) and (b) that the I-binding reactions are at equilibrium (Reinhart, G. D., Arch. Biochem. Biophys. 224, pp. 389-401 (1983)). It is shown that each condition gives rise to the other (i.e., if the I-binding reactions are at equilibrium, then k-2k3 must equal k-1k4 and vice-versa). If one assumes equilibrium for the I-binding steps, the velocity equation derived by the method of Cha (J. Biol. Chem. 243, pp. 820-825 (1968)) is apparently second degree in [I] (Segel, I. H., Enzyme Kinetics, p. 838, Wiley-Interscience (1975)), but reduces to a first degree equation when the relationship derived by Frieden is inserted. If one starts by assuming a single equilibrium condition for I binding, e.g., k-5[EI] = k5[E][I] or k-6[ESI] = k6[ES][I], then a traditional algebraic manipulation of the remaining steady state equations provides first degree expressions for the concentrations of all enzyme species and also discloses the Frieden relationship.     

Kinetics of the activation of human prothrombin by human coagulation factor Xa. Initial rate studies in the presence of Ca2+ and phospholipid.

Steady state kinetic studies have been performed to investigate the formation of thrombin from prothrombin by human coagulation Factor Xa in the presence of Ca2+ and phospholipid. The concentration of ligand which gives 50% of the maximum velocity (K0.5) is 2.3 mM for Ca2+, 7.4 microM for phospholipid, and 0.006 microM for prothrombin. Hill plots of the Ca2+ enhancement of the reaction give a Hill coefficient of 3.1, indicating positive cooperativity. The initial velocity patterns are consistent with an ordered addition of reactants with phospholipid as the second reactant to bind to the enzyme. Although our results do not differentiate between Ca2+ or the prothrombin substrate as the first reactant to bind to Factor Xa, it is established that Ca2+ can bind to Factor Xa in the absence of the other reactants. Thus, the most probable order of addition of reactants is Ca2+, phospholipid, and the prothrombin substrate. Plots of (v)-1 versus (prothrombin)-1 or (v)-1 versus [(Ca2+)3]-1 at several constant concentrations of phospholipid indicate that the major effect of phospholipid is to increase the turnover number of Factor Xa.     

Evaluation of Hill slopes and Hill coefficients when the saturation binding or velocity is not known.

1. The Hill coefficient (nH), an often-used measure of deviations from hyperbolic behaviour (nonhyperbolicity) in kinetic and binding systems, is usually estimated from the maximum or minimum slope of the Hill plot. The method depends strongly on the assumed magnitude of the asymptotic velocity (V) or binding (P) whose evaluation may be difficult in nonlinear/co-operative systems. Therefore, alternative procedures were devised for the estimation nH which do not require the prior knowledge of V or P. 2. When pairs of velocity/binding readings (v and w) are obtained at concentrations of c and alpha c, respectively (where alpha is a fixed constant), then the relation between w and v is described by a hyperbola, provided that Hill's equation is valid. In this case, linearizing plots, v/w versus v, w versus, w/v, and 1/w versus 1/v, can be used for estimation of the degree of the equation. However, if the Hill expression is applicable, these methods are not efficient and traditional procedures, particularly nonlinear regression, should be used. 3. The 'linearizing' plots of the Hill equation can be applied advantageously for the evaluation of the Hill slope and of nH also in the general case, when the Hill expression is actually not valid, provided that deviations from hyperbolic behaviour are positive. Appropriately extrapolated intercepts of the first two plots estimate alphanH. Furthermore, the slope of the third plot yields, similarly to the method of Kurganov et al., a continuous measure of the Hill slope (including its maximum) at all concentrations. The agreement is, at positive nonhyperbolicities, excellent theoretical values of Hill slopes and coefficients and those estimated by the proposed methods. 4. A coefficient of nonhyperbolicity (theta) is defined for 2nd-degree rate equations which provides a quantitative measure of positive or negative deviation from first-degree, hyperbolic characteristics. It is closely related to the Hill coefficient.     

Substrate inhibition in the hydrolysis of N-acylglycine esters by carboxypeptidase A

The rates of hydrolysis of a series of 21 N-acylglycine esters (YCONHCH2CO2CH(CH2CH3)CO2H (2)) by bovine pancreatic carboxypeptidase A (peptidyl-L-amino-acid hydrolase, EC 3.4.12.2) have been studied over the substrate concentration range 10(-4)-10(-1) M at pH 7.5, 25 degrees C, ionic strength 0.5. All substrates display substrate inhibition except Y = CH3, CH3CH2 and (CH3)3C for which normal Michaelis-Menten kinetics are observed. In all cases substrate inhibition is consistent with the formation of an ES2 complex and parameters for the second-degree rate equation v/E = (kapp2 S + kapp3 S2/KappSS)/(KappS + S + S2/KappSS) have been evaluated. For a series of eight aliphatic groups varying in size between Y = CH3 and Y = cyclo-C6H11 the following linear correlations were observed: -log KappS = 0.82 pi + 1.32 and log kapp2/KappS = 0.71 pi + 5.81 (pi is Hansch's hydrophobicity parameter). Aryl and aralkyl Y moieties deviate from these correlation lines. KappSS also depends on the hydrophobicity of Y but no quantitative correlation is obvious. Thus the Y unit of 2 is involved in a hydrophobic interaction with the enzyme when 2 binds at both the catalytically productive and inhibitor sites. Parameters for the enzymic hydrolysis of the esters YCONHCH2CO2CH(CH2CH(CH3)2)CO2H (3) (Y = C6H5(CH2)n (n = 0, 1, 2)) are also presented. Pronounced nonproductive 1: 1 enzyme.substrate complex formation is observed for each of 2: Y = C6H5(CH2)n (n = 2, 3) and 3: Y = C6H5(CH2)2. Hippurate anion is shown to be an uncompetitive inhibitor (Ki = 12 mM) for the hydrolysis of 2: Y = (CH3)3C. Data are now available which can only be interpreted in terms of at least three enzymic sites being available for hydrophobic interactions with ester substrate molecules.     

Kinetic properties of the 2-oxoglutarate dehydrogenase complex from Azotobacter vinelandii evidence for the formation of a precatalytic complex with 2-oxoglutarate.

The 2-oxoglutarate dehydrogenase complex was purified from Azotobacter vinelandii. The complex consists of three components, 2-oxoglutarate dehydrogenase/decarboxylase (E1o), lipoate succinyltransferase (E2o) and lipoamide dehydrogenase (E3). Upon purification, the E3 component dissociates partially from the complex. From reconstitution experiments, the Kd for E3 was found to be 26 nM, about 30 times higher than that for the pyruvate dehydrogenase complex. The Km values for the substrates 2-oxoglutarate, CoA and NAD+ were found to be 0.15, 0.014 and 0.17 mM, respectively. The system has a high specificity for 2-oxoglutarate, which is determined by the action of both E1o and E2o. Above 4 mM substrate inhibition is observed. From steady-state inhibition experiments with substrate analogs, two substrate-binding modes are revealed at different degrees of saturation of the enzyme with 2-oxoglutarate. At low substrate concentrations (10(-6) to 10(-5) M), the binding mainly depends on the interaction of the enzyme with the substrate carboxyl groups. At a higher degree of substrate saturation (10(-4) to 10(-3) M) the relative contribution of the 2-oxo group in the binding increases. A kinetic analysis points to a single binding site for a substrate analog under steady state conditions. Saturation of this site with an analog indicates that two kinetically different complexes are formed with 2-oxoglutarate in the course of catalysis. From competition studies with analogs it is concluded that one of these complexes is formed at the site that is sterically identical to the substrate inhibition site. The data obtained are represented by a minimal scheme that considers formation of a precatalytic complex SE between the substrate and E1o before the catalytic complex ES, in which the substrate is added to the thiamin diphosphate cofactor, is formed. The incorrect orientation of the substrate molecule in SE or the occupation of this site by analogs is supposed to cause substrate or analog inhibition, respectively.     

Quantitative structure-activity relationships for the pre-steady state of Pseudomonas species lipase inhibitions by p-nirophenyl-N-substituted carbamates

The pre-steady states of Pseudomonas species lipase inhibitions by p-nitrophenyl-N-substituted carbamates (1-6) are composed of two steps: (1) formation of the non-covalent enzyme-inhibitor complex (E:I) from the inhibitor and the enzyme and (2) formation of the tetrahedral enzyme-inhibitor adduct (E-I) from the E:I complex. From a stopped-flow apparatus, the dissociation constant for the E:I complex, KS, and the rate constant for formation of the tetrahedral E-I adduct from the E:I complex, k2 are obtained from the non-linear least-squares of curve fittings of first-order rate constant (k(obs)) versus inhibition concentration ([I]) plot against k(obs)=k2+k2[I]/(KS+[I]). Values of pKS, and log k2 are linearly correlated with the sigma* values with the rho* values of -2.0 and 0.36, respectively. Therefore, the E:I complexes are more positive charges than the inhibitors due to the rho* value of -2.0. The tetrahedral E-I adducts on the other hand are more negative charges than the E:I complexes due to the rho* value of 0.36. Formation of the E:I complex from the inhibitor and the enzyme are further divided into two steps: (1) the pre-equilibrium protonation of the inhibitor and (2) formation of the E:I complex from the protonated inhibitor and the enzyme.     

Further theoretical refinement on the internal thermodynamics of perfect enzymes.

By solving simultaneously the equation for ''uniform binding'' [Albery & Knowles (1976) Biochemistry 15, 5631-5640] and the equation for ''differential binding'' [Chin (1983) J. Am. Chem. Soc. 105, 6502-6503], I derived the following simple equation for perfect enzymes (with single substrate and single product) under irreversible conditions: K2 = beta(1 + Rs)/1-beta(1 + Rs) where K2 is the internal equilibrium constant and beta is the Brönsted coefficient of the elementary catalytic step, and Rs is defined as [S]0/Ks, with [S]0 being the physiological substrate concentration and Ks being the substrate dissociation constant. The equation suggests that the perfect enzyme can have different internal thermodynamic properties depending on physiological conditions.     

A mathematical analysis of the substrate effect observed in 3beta-hydroxysteroid dehydrogenase reactions of rat testicular microsomes.

The substrate effect in enzyme reactions has been explained mostly in terms of an additional substrate binding site on the enzyme other than the catalytic site. A rate equation for the reaction is introduced according to the steady state mechanism as follows: v = (Ps3+Qs2+Rs)/(s3+Ls2+Ms+N), were the six parameters, L,M,N,P,Q, and R, can be determined by the least-squares method from the experimental points. The v vs. s curve has an asymptote parallel to the s abscissa, and can be classified into one of four types. The type A curve has an intersection with the asymptote and an apparent maximum velocity; the curve descends toward the asymptote. Type B has no intersection and no stationary point; the curve ascends toward the asymptote. Type C has two intersections and two stationary points, an apparent maximum velocity and a minimum velocity; the curve ascends toward the asymptote. Type D has no intersection and two stationary points; the curve ascends toward the asymptote. The equation was applied to the 3beta-hydroxysteroid dehydrogenase [EC 1.1.1.145] reaction of rat testicular microsomes. The conversion of 3beta-hydroxyandrost-5-ene-17-one was represented by type C, with an apparent maximum velocity of 0.338 nmole/min/mg protein at 0.912 muM of the substrate concentration, minimum velocity of 0.108 nmole/min at 16.6 muM, and saturating velocity of 0.169 nmole/min at infinite concentration of the substrate. The converson of 3beta-hydroxypregn-5-ene-20-one was of type B, having two inflexion points, 0.320 nmole/min at 2.735 muM and 0.814 nmole/min at 12.39 muM, and a saturating velocity of 3.80 nmoles/min at infinite concentration of the substrate.     

Protein-ligand binding with a missing species

Considerable experimental evidence has been produced recently that shows that in the binding of oxygen or carbon monoxide to certain tetrameric hemoglobins, the triply-ligated species is virtually non-existent. The binding polynomial representing this phenomenon for the general case is P(x) = 1 + beta 1x + ... + beta n-1xn-1 + beta nxn, where beta n-1 is nearly zero. The zeros, factorization and associated Hill plots of such binding polynomials with beta n-1 = 0 are investigated for the general case, and are analyzed in detail for n = 3 and n = 4. These results are then compared with the results obtained from experimental data on a number of tetrameric hemoglobins for which beta 3 is small. One concludes that, apart from the slope of the high-saturation asymptote of the Hill plot, a small perturbation of beta 3 from zero produces small changes in other properties associated with the binding process, such as fractional saturation, maximum Hill slope, and zeros and factorization of the binding polynomial.     

PH-dependence of the steady-state rate of a two-step enzymic reaction.

1. The pH-dependence is considered of a reaction between E and S that proceeds through an intermediate ES under "Briggs-Haldane' conditions, i.e. there is a steady state in ES and [S]o greater than [E]T, where [S]o is the initial concentration of S and [E]T is the total concentration of all forms of E. Reactants and intermediates are assumed to interconvert in three protonic states (E equilibrium ES; EH equilibrium EHS; EH2 equilibrium EH2S), but only EHS provides products by an irreversible reaction whose rate constant is kcat. Protonations are assumed to be so fast that they are all at equilibrium. 2. The rate equation for this model is shown to be v = d[P]/dt = (kcat.[E]T[S]o/A)/[(KmBC/DA) + [S]o], where Km is the usual assembly of rate constants around EHS and A-D are functions of the form (1 + [H]/K1 + K2/[H]), in which K1 and K2 are: in A, the molecular ionization constants of ES; in B, the analogous constants of E; in C and D, apparent ionization constants composed of molecular ionization constants (of E or ES) and assemblies of rate constants. 3. As in earlier treatments of this type of reaction which involve either the assumption that the reactants and intermediate are in equilibrium or the assumption of Peller & Alberty [(1959) J. Am. Chem. Soc. 81, 5907-5914] that only EH and EHS interconvert directly, the pH-dependence of kcat. is determined only by A. 4. The pH-dependence of Km is determined in general by B-C/A-D, but when reactants and intermediate are in equilibrium, C identical to D and this expression simplifies to B/A. 5. The pH-dependence of kcat./Km, i.e. of the rate when [S]o less than Km, is not necessarily a simple bell-shaped curve characterized only by the ionization constants of B, but is a complex curve characterized by D/B-C. 6. Various situations are discussed in which the pH-dependence of kcat./Km is determined by assemblies simpler than D/B-C. The special situation in which a kcat./Km-pH profile provides the molecular pKa values of the intermediate ES complex is delineated.     

On porcine pancreatic alpha-amylase action: kinetic evidence for the binding of two maltooligosaccharide molecules (maltose, maltotriose and o-nitrophenylmaltoside) by inhibition studies. Correlation with the five-subsite energy profile

Hydrolysis of small substrates (maltose, maltotriose and o-nitrophenylmaltoside) catalysed by porcine pancreatic alpha-amylase was studied from a kinetic viewpoint over a wide range of substrate concentrations. Non-linear double-reciprocal plots are obtained at high maltose, maltotriose and o-nitrophenylmaltoside concentrations indicating typical substrate inhibition. These results are consistent with the successive binding of two molecules of substrate per enzyme molecule with dissociation constants Ks1 and Ks2. The Hill plot, log [v/(V-v)] versus log [S], is clearly biphasic and allows the dissociation constants of the ES1 and ES2 complexes to be calculated. Maltose and maltotriose are inhibitors of the amylase-catalysed amylose and o-nitrophenylmaltoside hydrolysis. The inhibition is of the competitive type. The (apparent) inhibition constant Kiapp varies with the inhibitor concentration. These results are also consistent with the successive binding of at least two molecules of maltose or maltotriose per amylase molecule with the dissociation constants Ki1 and Ki2. These inhibition studies show that small substrates and large polymeric ones are hydrolysed at the same catalytic site(s). The values of the dissociation constants Ks1 and Ki1 of the maltose-amylase complexes are identical. According to the five-subsite energy profile previously determined, at low concentration, maltose (as substrate and as inhibitor) binds to the same two sites (4,5) or (3,4), maltotriose (as substrate and as inhibitor) and o-nitrophenyl-maltoside (as substrate) bind to the same three subsites (3,4,5). The dissociation constants Ks2 and Ki2 determined at high substrate and inhibitor concentration are consistent with the binding of the second ligand molecule at a single subsite. The binding mode of the second molecule of maltose (substrate) and o-nitrophenylmaltoside remains uncertain, very likely because of the inaccuracy due to simplifications in the calculations of the subsite binding energies. No binding site(s) outside the catalytic one has been taken into account in this model.     

The interaction of FBPase with aldolase: a kinetic and fluorescence investigation on chicken muscle enzymes

Fructose-1,6-bisphosphatase (FBPase; EC 3.1.3.11) is strongly inhibited by AMP in vitro and, therefore, at physiological concentrations of substrate and AMP, FBPase should be completely inhibited. Desensitization of rabbit muscle FBPase against AMP inhibition was previously observed in the presence of rabbit muscle aldolase. In this study, we analysed the kinetics of an FBPase catalyzed reaction and interaction between chicken muscle FBPase and chicken muscle aldolase. The initial rate of FBPase reaction vs. substrate concentration shows a maximum activity at a concentration of 20 microM Fru-1,6P2 and then decreases. Assuming rapid equilibrium kinetics, the enzyme-catalyzed reaction was described by the substrate inhibition model, with Ks approximately 5 microM and Ksi approximately 39 microM and factor beta approximately 0.2, describing change in the rate constant (k) of product formation from the ES and ESSi complexes. Based on ultracentrifugation studies, aldolase and FBPase form a hetero-complex with approximately 1:1 stoichiometry with a dissociation constant (Kd) of 3.8 microM. The FBPase-aldolase interaction was confirmed via fluorescence investigation. The aldolase-FBPase interaction results in aldolase fluorescence quenching and its maximum emission spectrum shifting from 344 to 356 nm. The Kd of the FBPase-aldolase complex, determined on the basis of fluorescence changes, is 0.4 microM at 25 degrees C with almost 1:1 stoichiometry. This interaction increases the I(0.5) for the AMP inhibition of FBPase threefold, and slightly affects FBPase affinity to magnesium ions, increasing the Ka and Hill coefficient (n). No effect of aldolase on the FBPase pH optimum was observed. Thus, the decrease in FBPase sensitivity to AMP inhibition enables FBPase to function in vivo thanks to aldolase.     

Hill coefficient for estimating the magnitude of cooperativity in gating transitions of voltage-dependent ion channels

A frequently used measure for the extent of cooperativity in ligand binding by an allosteric protein is the Hill coefficient, obtained by fitting data of initial reaction velocity (or fractional binding saturation) as a function of substrate concentration to the Hill equation. Here, it is demonstrated that the simple two-state Boltzmann equation that is widely used to fit voltage-activation data of voltage-dependent ion channels is analogous to the Hill equation. A general empiric definition for a Hill coefficient (n(H)) for channel gating transitions that is analogous to the logarithmic potential sensitivity function of Almers is derived. This definition provides a novel framework for interpreting the meaning of the Hill coefficient. In considering three particular and simple gating schemes for a voltage-activated cation channel, the relation of the Hill coefficient to the magnitude and nature of cooperative interactions along the reaction coordinate of channel gating is demonstrated. A possible functional explanation for the low value of the Hill coefficient for gating transitions of the Shaker voltage-activated K(+) channel is suggested. The analogy between the Hill coefficients for ligand binding and for channel gating transitions further points to a unified conceptual framework in analyzing enzymes and channels behavior.     

Functional multiplicity of motor molecules revealed by a simple kinetic analysis.

We present a simple analytical solution for a kinetic model of motor molecule function with multiple arms. This model has a rate of motion proportional to the probability that all arms in a complex are detached from the cytoskeleton and, therefore, we refer to it as obligate cooperativity. The model has the form: v = Vmax/(1 + q/S)n, where Vmax is the maximum velocity, the product nq is the effective Michaelis constant at high [ATP], and n is the number of arms. Values of n = 2 and n = 1 give good fits to the heavy meromyosin and myosin S1 sliding velocity data, respectively, consistent with the number of active sites. Despite the complexity of the eukaryotic axoneme, beat frequency data from Chlamydomonas wild-type and oda mutants are also fit by this model.     

Identification of substrate binding site of cyclin-dependent kinase 5

Cyclin-dependent kinase 5 (CDK5), unlike other CDKs, is active only in neuronal cells where its neuron-specific activator p35 is present. However, it phosphorylates serines/threonines in S/TPXK/R-type motifs like other CDKs. The tail portion of neurofilament-H contains more than 50 KSP repeats, and CDK5 has been shown to phosphorylate S/T specifically only in KS/TPXK motifs, indicating highly specific interactions in substrate recognition. CDKs have been shown to have a high preference for a basic residue (lysine or arginine) as the n+3 residue, n being the location in the primary sequence of a phosphoacceptor serine or threonine. Because of the lack of a crystal structure of a CDK-substrate complex, the structural basis for this specific interaction is unknown. We have used site-directed mutagenesis ("charged to alanine") and molecular modeling techniques to probe the recognition interactions for substrate peptide (PKTPKKAKKL) derived from histone H1 docked in the active site of CDK5. The experimental data and computer simulations suggest that Asp86 and Asp91 are key residues that interact with the lysines at positions n+2 and/or n+3 of the substrates.     

Synthesis,characterization, and biological evaluation of technetium(III) complexes with tridentate/bidentate S,E,S/P,S coordination (E = O,N(CH(3)), S): a novel approach to robust technetium chelates suitable for linking the metal to biomolecules

A novel type of mixed-ligand Tc(III) complexes, [Tc(SCH(2)CH(2)-E-CH(2)CH(2)S)(PR(2)S)] (E = S, N(CH(3)); PR(2)S = phosphinothiolate with R = aryl, alkyl) is described. These "3+2"-coordinated complexes can be prepared in a two-step reduction/substitution procedure via the appropriate chloro-containing oxotechnetium(V) complex [TcO(SES)Cl] [E=S, N(CH(3)]. Tc(III) compounds have been fully characterized both in solid and solution states and found to adopt the trigonal-bipyramidal coordination geometry. The equatorial trigonal plane is formed by three thiolate sulfur atoms, whereas the phosphorus of the bidentate P,S ligand and the neutral donor of the tridentate chelator occupy the apical positions. The (99)Tc(III) complexes have been proven to be identical with the (99m)Tc agents prepared at the no-carrier-added level by comparison of the corresponding UV/vis and radiometric HPLC profiles. Challenge experiments with glutathione clearly indicate that this tripeptide has no effect on the stability of the (99m)Tc complexes in solutions. Biodistribution studies have been carried out in rats at 5 and 120 min postinjection. The substituents at the bidentate P,S ligand significantly influence the biodistribution pattern. Remarkable differences are observed especially in brain, blood, lungs, and liver. All the complexes are able to penetrate the blood-brain barrier of rats and showed a relatively fast washout from the brain.