Kinetics of protein modification reactions: analysis of modification-induced protein unfolding

A mathematical treatment of a two-sited, modification-induced protein unfolding model is presented, and it is shown that the dependence of the concentration of modified protein groups on reaction time is described by a linear, second-order, differential equation with nonzero right hand side. The analytic solution of this equation consists of a summation of exponential functions of reaction time. By assigning arbitrary values to the modification and isomerization rate constants of these equations, simulated cases of protein modification are presented, and the apparent end-point of the reaction is determined graphically. It is found that the apparent end-point of the reaction is, in most cases studied, different from the true value of two groups modified per protein molecule, and is a function of both the modification, and isomerization rate constants of the model. The first derivative of the protein modification reaction, at the start of the reaction, [E]'mod (0), is determined, for the same simulated cases of protein modification, by two different analytical methods. It is found that the [E]'mod(0) value, obtained from graphical and numerical analysis data, is in most cases in good agreement with the value expected from first principles. Finally, the different irreversible enzyme inhibition forms, contingent upon the different kinds of the enzyme inactivation-protein modification relationships of the protein modification model under consideration, are presented and discussed.     

On true and apparent Michaelis constants in enzymology. I. Differences

Differences between both true and apparent rate constants and Michaelis constants have been examined. Rate constants of elementary stages of real mechanisms are true ones. True Michaelis constant Km is expressed by equation Km = (k(-1) + k2)/k. True constants may be determined for reliable mechanism only for which the equation of initial rate was obtained which displays physical sense of these constants and permits to find the method of their calculation. The true constant values are independent of concentration of reactants, activators, inhibitors, extraneous agents and pH. The apparent rate constants are such constants of the composite reaction which are observed when this reaction is described by the equation of simple reaction. Michaelis constant calculated by a half of the ultimate constant is an apparent constant. The apparent constants may be functions of several true rate constants and/or concentrations of reacting substances. The evident physical sense of apparent constants being absent, only formal relation between the reaction rate and reactant concentration independent of the investigated mechanism is provided.     

Evidence that use of Triton WR1339 underestimates the triacylglycerol entry rate into the plasma of lactating rats owing to continued accumulation of lipid in the mammary gland.

An analysis is presented of the catalytic factors responsible for the rate-enhancement that may be observed when a protein modification reaction is compared with a reaction of the same modifying agent with a model micromolecular compound exhibiting the same reactive group as the protein under study. It is seen that affinity-mediated rate-enhancement of protein modification is realized by the loss of activation entropy. On the assumption that attainment of maximal affinity-mediated rate-enhancement presents with an activation entropy of the protein modification reaction equal to zero, whereas the activation enthalpy of the reaction remains unchanged, it is shown that the value for maximal affinity-mediated rate-enhancement is equal to e-delta s++/R. Accordingly, protein modification reactions may be differentiated into (i) reactions the rate-enhancement of which (relative to the reaction of the same modifying agent with a model compound) is primarily entropy-controlled and (ii) reactions the rate-enhancement of which is primarily enthalpy-controlled. It is seen that modifying agents of low reactivity towards model compounds, but with a high, i.e. highly negative, activation entropy are better suited as prospective affinity-based protein-modifying agents, since the potential affinity-mediated rate-enhancement, and hence the selectivity, of these compounds is necessarily high. Kinetic and thermodynamic constants of the reaction of modifying agents with proteins, and with model compounds, and values of maximal affinity-mediated rate-enhancement, based on published data of the reaction of several modifying agents with model compounds, are presented and discussed.     

Saccharomyces cerevisiae phosphoenolpyruvate carboxykinase: physicochemical characteristics of the nucleotide binding site, as deduced from fluorescent spectroscopy measurements

Saccharomyces cerevisiae phosphoenolpyruvate carboxykinase [ATP:oxaloacetate carboxy-lyase (transphosphorylating), EC 4.1.1.49] is inactivated by the fluorescent sulfhydryl reagent N-(iodoacetyl-N'-(5-sulfo-1-naphthyl)ethylenediamine (1,5-IAEDANS). The inactivation reaction follows pseudo-first-order kinetics with respect to active enzyme to less than 10% remaining enzyme activity, with a second-order inactivation rate constant of 2.6 min-1 mM-1 at pH 7.5 and 30 degrees C. A stoichiometry of 1.05 mol of reagent incorporated per mole of enzyme subunit was found for the completely inactivated enzyme. Almost complete protection of the enzyme activity and of dansyl label incorporation are afforded by MnADP or MnATP, thus suggesting that 1,5-IAEDANS interacts with an enzyme sulfhydryl group at the nucleotide binding site. The fluorescence decay of the AEDANS attached to the protein shows a single-exponential behavior with a lifetime of 18 ns. A comparison of the fluorescence band position and the fluorescence decay with those of the adduct AEDANS-acetylcysteine indicates a reduced polarity for the microenvironment of the substrate binding site. The quenching of the AEDANS moiety in the protein can be described in terms of a collisional and a static component. The rate constant for the collisional component is much lower than that obtained for the adduct in a medium of reduced polarity. These last results indicate that the AEDANS moiety is considerably shielded from the solvent when it is covalently attached to PEPCK.     

Kinetic analysis of biphasic protein modification reactions cooperative effects

A mathematical treatment of protein modification reactions is presented, and it is shown thai in these cases protein modification is described by a summation of exponential functions of reaction time, the number of exponentials being equal to the number of modified protein species. It is shown that in cases of protein modification cooperativity, there is a strict dependence of the coefficients of the multiexponential modification equation on the constants of the same equation. The conditions necessary for a reduction of a multiexponential protein modification equation to one of a summation of two exponentials only are examined. The possible formulae for the coefficients of a two-exponential-summation equation, used to describe the modification of protein models with two, three or four modifiable residues (as well as some aspects of models with five and six modifiable residues) per protein molecule are derived. It is seen that the number of such coefficients is severely limited. The most frequently obtained formula for the lower stoichiomelric coefficient of a 'wo-exponential-summation equation is Ak_a/(k_a-k_b). where k_b and k_b are the constants of the two exponentials of the equation, and A is a constant. The value most frequently arrived at for A is (n?1)/n, where n is the number of modifiable residues per protein molecule, while values such as 1/n, or a/n (where a is an integer, and also where a < n) are also possible. In most of the cooperative protein modification models worked out, k_a is identical with k_n, viz., k_a is identical with the rate constant for the first stoichiometric protein modification.     

Modification and inactivation of rhodanese by 2,4,6-trinitrobenzenesulphonic acid

Bovine liver rhodanese (thiosulphate sulphurtransferase, EC 2.8.1.1) is modified by 2,4,6-trinitrobenzenesulphonic acid, by the use of modifying agent concentrations in large excess over enzyme protein concentration. The end-point of the reaction, viz., the number, n, per enzyme protein molecule, of modifiable amino groups was determined graphically by the Kézdy-Swinbourne procedure. It was found that the value for n depends on the pH of the reaction medium, and ranges from 2, at pH 7.00, to 10.66, at pH 9.00. Again, the value for n increases with an increase in the concentration of 2,4,6-trinitrobenzenesulphonic acid used, with values ranging from 3.52, at 0.10 mM modifying agent, to 8.96, at 2 mM modifying agent. Rhodanese primary amino groups modification by 2,4,6-trinitrobenzenesulphonic acid is described by a summation of exponential functions of reaction time at pH values of 8.00 or higher, while at lower pH values it is described by a single exponential function of reaction time. However, the log of the first derivative, at initial reaction conditions, of the equation describing protein modification, is found to be linearly dependent on the pH of the reaction. An identical linear dependence is also found when the log of the first derivative, at the start of the reaction, of the equation describing modification-induced enzyme inactivation is plotted against the pH values of the medium used. In consequence, the fractional concentration of rhodanese modifiable amino groups essential for enzyme catalytic function is equal to unity at all reaction pH values tested. It is accordingly concluded that, when concentrations of 2,4,6-trinitrobenzenesulphonic acid in excess of protein concentration are used, all rhodanese modifiable amino groups are essential for enzyme activity. A number of approaches were used in order to establish a mechanism for the modification-induced enzyme inactivation observed. These approaches, all of which proved to be negative, include the possible modification of enzyme sulfhydryl groups, disulphide bond formation, enzyme inactivation due to sulphite released during modification, modification-induced enzyme protein polymerization, syncatalytic enzyme modification and hydrogen peroxide-mediated enzyme inactivation.     

Charges on proteins and distances of electron transfer in metalloprotein redox reactions

A modified form of the Debye-Marcus equation relating electron transfer rate constants to charges on proteins and distances of electron transfer has been applied to the reaction of chemically modified cytochrome f, in which positively charged amino groups are replaced with negatively charged carboxyl groups. The rate of electron transfer from reduced cytochrome f to ferricyanide decreased with increasing ionic strength when the native and singly substituted cytochrome f were used, although a sharp decrease was observed in the former case. When doubly or more than triply substituted cytochrome f was used, the rate of electron transfer was almost constant or increased with increasing ionic strength, respectively. The kinetic-ionic strength effects on this reaction can be well explained by the Debye-Marcus equation in which the charge and radius of the protein are treated as variable parameters. The results show the importance of local positive charges of about 2.0 on native cytochrome f and effective radius of about 11 A of cytochrome f for the electron transfer to ferricyanide. Since the net charge on the native cytochrome f is negative and the calculated radius of the protein is 22.8 A, the above results indicate that positive charges on the electron transfer site control the electrostatic interactions in this reaction. Previously reported data which had been analyzed by using the total net charge and full radius of the protein, were also well explained by the local charge and effective radius of the protein.(ABSTRACT TRUNCATED AT 250 WORDS)     

Physico-chemical properties of terrylytin modified by a copolymer based on vinylpyrrolidone

The proteolytic activity of terrylytin produced by the culture of Asp. terricola and modified by a water-soluble copolymer of vinylpyrrolidone and acrolein remained unchanged after enzyme modification. Using micro-thin layer chromatography, it was shown that the bulk of the epsilon-amino groups of lysine residues of the protein enter the reaction with the aldehyde groups of the polymeric matrix. The sedimentation and diffusion patterns of the polymerenzyme adduct demonstrated that the molecular weight of the modified enzyme is the total of molecular weights of its constituent components. Evidence from viscosimetry and gel chromatography allowed to develop a hydrodynamic model of the macromolecular product. It was shown that the rate of the enzyme inactivation in the solution calculated from the first order reaction equation depends on the nature of the enzyme electrochemical microenvironment. Under conditions close to physiological ones the rate inactivation constant for terrylytin modified by a neutral polymeric matrix is 10 times less than that for the native enzyme. At the isoelectric point (pH 4,6) a positively charged polymeric form of terrylytin is found to be the most stable one. The pH and temperature optima for casein hydrolysis remained unchanged throughout polymeric modification. The polymeric membrane did not hamper the diffusion during approximation of the substrates (casein and insulin) to the enzyme molecule during the catalytic act, which manifested itself in a constancy of Michaelis curves. Terrylytin modification by a copolymer causes an increase of stability with respect to trypsin proteolysis and a decrease of human blood plasma affinity for the inhibitors. The apparent inhibition constants for modified enzyme forms do not depend on the nature of electrochemical microenvironment and exceed that for native terrylytin 10-fold.     

Horse liver alcohol dehydrogenase. A study of the essential lysine residue.

1. The inactivation of horse liver alcohol dehydrogenase by pyridoxal 5'-phosphate in phosphate buffer, pH8, at 10 degrees C was investigated. Activity declines to a minimum value determined by the pyridoxal 5'-phosphate concentration. The maximum inactivation in a single treatment is 75%. This limit appears to be set by the ratio of the first-order rate constants for interconversion of inactive covalently modified enzyme and a readily dissociable non-covalent enzyme-modifier complex. 2. Reactivation was virtually complete on 150-fold dilution: first-order analysis yielded an estimate of the rate constant (0.164min-1), which was then used in the kinetic analysis of the forward inactivation reaction. This provided estimates for the rate constant for conversion of non-covalent complex into inactive enzyme (0.465 min-1) and the dissociation constant of the non-covalent complex (2.8 mM). From the two first-order constants, the minimum attainable activity in a single cycle of treatment may be calculated as 24.5%, very close to the observed value. 3. Successive cycles of modification followed by reduction with NaBH4 each decreased activity by the same fraction, so that three cycles with 3.6 mM-pyridoxal 5'-phosphate decreased specific activity to about 1% of the original value. The absorption spectrum of the enzyme thus treated indicated incorporation of 2-3 mol of pyridoxal 5'-phosphate per mol of subunit, covalently bonded to lysine residues. 4. NAD+ and NADH protected the enzyme completely against inactivation by pyridoxal 5'-phosphate, but ethanol and acetaldehyde were without effect. 5. Pyridoxal 5'-phosphate used as an inhibitor in steady-state experiments, rather than as an inactivator, was non-competitive with respect to both NADH and acetaldehyde. 6. The partially modified enzyme (74% inactive) showed unaltered apparent Km values for NAD+ and ethanol, indicating that modified enzyme is completely inactive, and that the residual activity is due to enzyme that has not been covalently modified. 7. Activation by methylation with formaldehyde was confirmed, but this treatment does not prevent subsequent inactivation with pyridoxal 5'-phosphate. Presumably different lysine residues are involved. 8. It is likely that the essential lysine residue modified by pyridoxal 5'-phosphate is involved either in binding the coenzymes or in the catalytic step. 9. Less detailed studies of yeast alcohol dehydrogenase suggest that this enzyme also possesses an essential lysine residue.     

The MgATP-binding site on chicken gizzard myosin light chain kinase remains open and functionally competent during the calmodulin-dependent activation-inactivation cycle of the enzyme.

An ATP-like affinity labeling reagent, 5'-[p-(fluorosulfonyl)benzoyl]adenosine (FSBA), was used to probe the MgATP-binding site of smooth muscle myosin light chain kinase from chicken gizzard (smMLCK) and its calmodulin (CaM) complex. Native smMLCK has an absolute requirement for the binding of the calcium complex of CaM for expression of its catalytic activity. FSBA reacted with smMLCK-CaM and with the CaM-free, inactive enzyme as well. Both reactions were dependent on time and FSBA concentration. Reaction was accompanied by the incorporation of covalently bound [14C]FSBA into smMLCK protein at a molar ratio of approximately 1:1 in each case. p-(Fluorosulfonyl)benzoic acid, an analogue of FSBA lacking the adenosine targeting group, did not react at a significant rate with either form of smMLCK. Reaction of CaM-free and CaM-bound smMLCK with FSBA displayed saturation kinetics. The first-order rate constants for the conversion of the reversible, noncovalent enzyme-FSBA complex to form the irreversibly inhibited, covalently modified enzyme were similar for both smMLCK and smMLCK-CaM, 0.15 and 0.07 min-1, respectively. The concentrations of FSBA yielding the half-maximal rate of inactivation, KI, were essentially identical--0.65 and 0.64 mM, respectively--for smMLCK and smMLCK-CaM. MgATP, but not MgGTP or a substrate peptide, potently inhibited reaction with FSBA. Inhibition by MgATP was competitive. The measured inhibitory constant for MgATP was essentially the same--33 versus 34 microM--for both smMLCK and smMLCK-CaM. It therefore is concluded that the MgATP-binding site on smMLCK remains accessible and recognizable as such when the enzyme becomes inactivated upon dissociation of CaM.     

Soluble high molecular weight derivatives of pancreatic inhibitors. Kinetic-thermodynamic studies of inhibitors linked to differently charged matrices]

The effects of electrostatic charge of the matrix on the pH-dependence of interactions of commercial trypsin with preparations of pancreatic inhibitor modified by soluble polysaccharide coupling were studied. It was shown that the rate constants of trypsin association with native and modified pancreatic inhibitor preparations as well as the rate constants of dissociation of their complexes and, consequently, the inhibition constants are identical. The invariability of the rate constants for the association reaction after the increase in the molecular weight of pancreatic inhibitor may be probably accounted for by the fact that the limiting step of a stable trypsin-inhibitor complex formation is not controlled by diffusion. Thermal denaturation of pancreatic inhibitor preparations modified by binding to polysaccharides (pH 4.7--8.0, 97 degrees C) suggests an essential role of the negative charge of matrix in stabilization of the protein inhibitor globule.     

Trans effects in cell membrane transport

The efflux of a substrate from preloaded cells may be decelerated by an inhibitor in the external medium or accelerated by a compatible substrate in the external medium. The derivations of rate equations for the initial velocity of the zero-trans reaction, trans efflux inhibition, and accelerated exchange diffusion are described for steady state conditions. The rate constants making up the Michaelis constant for the trans inhibition reaction are the same as the corresponding parameters in the zero-trans reaction. The rate constants making up the Michaelis constant for the accelerated exchange reaction, however, are different from the corresponding parameters in the zero-trans reaction. The rate equation for trans inhibition shows that the velocity constant for recovery of the unloaded carrier may be determined with steady state experimental data. It is suggested that the observed recovery constant is independent of the substrates and trans inhibitors chosen for an assay of a particular carrier system. An experiment is briefly described to show a determination of a tentative value for the recovery constant of the unloaded nucleoside carrier in yeast cells and the apparent inhibition constant for a trans inhibitor.     

Automated kinetic exclusion assays to quantify protein binding interactions in homogeneous solution.

A method was developed for the quantification of protein-ligand interactions in which the free protein present in homogeneous reaction mixtures was separated and quantified using a KinExA immunoassay instrument. Separation was achieved by rapid percolation of the reaction mixture over a column of microbeads whose surfaces were coated with an immobilized form of the ligand. The protein thus captured was quantified using a fluorescently labeled anti-protein antibody. The features of this new method were illustrated using a model system in which each of the principal reagents was covalently labeled with a different fluorescent molecule: mouse monoclonal anti-biotin primary antibody (fluorescein), biotin (B-phycoerythrin), and goat anti-mouse polyclonal secondary antibody (indodicarbocyanin). Values for the equilibrium and kinetic rate constants for the binding between the anti-biotin antibody and biotin conjugated with B-phycoerythrin were determined and shown to be independent of whether the fluorescent label was located on the primary or secondary antibody. Equilibrium binding experiments conducted with (F(AB))(2) and corresponding F(AB) fragments showed that the valency of the binding protein had no influence on the value of the dissociation constant. The values of the equilibrium and rate constants obtained by this new method are those for the binding reaction in homogeneous solution; the immobilized ligand is only a tool exploited for the separation and quantification of the free protein.     

Model for the irreversible dissociation kinetics of cooperatively bound protein–nucleic acid complexes

We present a quantitative model for the irreversible dissociation kinetics of cooperatively bound nonspecific protein–nucleic acid complexes. The model assumes that the major pathway of dissociation is via singly contiguously bound protein that “peels” off the ends of clusters of bound protein. It should therefore be most applicable for proteins that bind nucleic acids with high cooperativity (w > 10³). Furthermore, the model assumes that no redistribution of bound protein occurs during the time course of the dissociation. Solutions to the rate equations are presented for the entire time course of the dissociation. Under initial conditions such that the nucleic acid is less than fully saturated with protein, a single-exponential decay is predicted (if w is large). However, when the nucleic acid lattice is initially fully saturated, zero-order kinetics, corresponding to a constant rate of protein dissociation, is predicted. The experimental observation of zero-order dissociation kinetics in a cooperative protein–nucleic acid system is a good qualitative indicator for the dissociation mechanism discussed here. A discussion of the analysis of experimental data that enables one to extract molecular rate constants is presented. Furthermore, comparisons are made between the nonredistributing model presented here and Epstein's model [Epstein, I. R. (1979) Biopolymers 18 , 2037–2050] in which protein can translocate infinitely quickly while bound to the nucleic acid, and hence protein clusters redistribute during dissociation and maintain an equilibrium distribution on the nucleic acid at all times.     

Methods of determining rate constants in single-substrate–single-product enzyme reactions. Use of induced transport: limitations of product inhibition

1. The calculation of the rate constants from steady-state kinetics of a single-substrate-single-product enzyme reaction in which there is an isomerization of the enzyme is described. 2. It is shown that even with the use of isotopically labelled substrates a set of solutions for the constants is obtained rather than a unique solution. However, limits are derived within which they must lie. 3. The most appropriate observations to determine the rate constants are measurements of V(max.) and K(m) for both substrate and product, and measurement of the degree of countertransport in an induced-transport test. 4. Experimental procedures for induced-transport tests and the quantitative interpretation of the results obtained are discussed. 5. Product inhibition is shown to be an ambiguous and imprecise means of determining the rate constants. Further, the absence of a [substrate]x[product] term in the denominator of the steady-state rate equation does not necessarily mean that the isomerization of the enzyme is rapid, since the term also disappears when the isomerization is very slow. 6. Similar considerations apply to carrier mechanisms.     

Inactivation mechanism of the beta-ketoacyl-[acyl carrier protein] reductase of bacterial type-II fatty acid synthase by epigallocatechin gallate.

Epigallocatechin gallate (EGCG), a major compound from green tea, reversibly inhibits beta-ketoacyl-[acyl carrier protein] reductase (FabG) from Escherichia coli. In this study, we found that EGCG exhibited an atypical time-dependent inhibition of FabG, which possibly resulted from the EGCG-induced aggregation of FabG. It was observed that FabG inactivation and aggregation occurred nearly simultaneously, with a lag time that decreased with increasing EGCG concentration. These results suggest that some chemical reactions, required for aggregation and inactivation, occurred during the lag time. Since EGC was detected by HPLC after the incubation of EGCG with FabG, EGCG probably covalently modified FabG. These further results showed that 1 tetramer of FabG must be modified by several, possibly 4, EGCG molecules before the formation of FabG aggregates. FabG aggregation was a first-order reaction independent of protein concentration. Due to an initial lag time, the first-order rate of aggregation gradually increased, reaching a maximal and constant value. The effect of increasing concentration of EGCG on the first-order rate constant for aggregation indicated that EGCG bound to FabG by affinity labeling. Based on the results, we propose a mechanism for the interaction of EGCG with FabG:EGCG first binds reversibly to each subunit of FabG, followed by covalent modification and then aggregation of the 4 EGCG-modified subunits.     

Denitrification and a numerical modelling approach for shallow waters

A numerical model (`DiffDeni') has been developed to describe the disappearance of nitrate from the water column of 10–200 cm deep waters. The disappearance is caused by bacterial denitrification in the sediments. The model employs the molecular diffusion constant, an acceleration factor describing eddy diffusion, and three bacterial growth constants, viz. the inoculum size, the maximum growth rate and the half saturation constant for the hyperbolic process. The values of these system-constants were varied over a wide range. The curves obtained were compared with the curves for well-defined situations, viz. in which diffusion takes place without any or with a complete, immediate reaction. These cases have analytical solutions, and were simulated closely by the model `DiffDeni', though this model is based on different assumptions. It is shown that, when the bacterial growth rate is above a critical value, a negative exponential curve describes the nitrate disappearance well. On the other hand, a more complicated negative exponential equation can be used to describe the first phase of this denitrification in which bacterial activity is low and nitrate behaves as a conservative compound. The change-over period from phase 1 (no reaction) to phase 2 (complete, immediate reaction) which may vary between <1 and 50 days cannot be described analytically (mathematically correctly). The influence of temperature on denitrification is assessed and it is shown that both bacterial activity and diffusion may influence the denitrification rate.     

A new photolabile precursor of glycine with improved properties: A tool for chemical kinetic investigations of the glycine receptor

The synthesis and characterization of a new photolabile precursor of glycine (caged glycine) is described. The alpha-carboxyl group of glycine is covalently coupled to the alpha-carboxy-2-nitrobenzyl (alphaCNB) protecting group. Photolysis of the caged glycine with UV light produces free glycine. At 308 nm, the compound photolyzes with a quantum yield of 0.38. The absorption spectrum and the pH dependence of a transient absorption produced after laser-flash illumination are typical for aci-nitro intermediates of alphaCNB-protected compounds. The time constant for the major component of the aci-nitro intermediate decay ( approximately 84% of the total aci-nitro absorbance) was determined to be 7 micros at physiological pH. A minor component ( approximately 16%) decays with a rate constant of 170 micros. The compound does not activate or inhibit the alpha(1)-homomeric glycine receptor transiently expressed in HEK293 cells. After photolysis with a 10 ns pulse of 325 nm laser light, the glycine released from the caged compound activates glycine-mediated whole-cell currents in the same cells. The rise of these currents can be measured in a time-resolved fashion and occurs on a millisecond to sub-millisecond time scale. It can be described with a single-exponential function over >85% of the total current. The rate constant of the current rise is about 2 orders of magnitude slower than the rate constant of caged glycine photolysis. Thermal hydrolysis of the alphaCNB-caged glycine takes place with a half-life of 15.6 h at physiological pH. The new caged glycine is the first in a series of photoprotected glycine derivatives that has the required properties for use with chemical kinetic methods for investigation of glycine-activated cell surface receptors. Photolysis is rapid and efficient with respect to the receptor reactions to be studied; hydrolysis in aqueous solution is sufficiently slow, and the compound is biologically inert. It will, therefore, be a useful tool for investigation of the processes leading to channel opening of glycine receptor channels and the effects of mutations of the glycine receptor and of inhibitors on these processes.     

Equations of substrate-limited growth: the case for blackman kinetics

A simplified model of cell metabolism, consisting of a series of linked reversible enzymatic reactions dependent on the concentration of a single external substrate has been developed. The general mathematical solution for this system of reactions is presented. This general solution confirms the concept of a rate-limiting step, or “master reaction”, in biological systems as first proposed by Blackman. The maximum rate of such a process is determined by, and equal to, the maximum rate of the slowest forward reaction in the series. Of practical interest in modeling the growth rate of cells are three cases developed from the general model. The simplest special case results in the Monod equation when the maximum forward rate of one enzymatic reaction in the cell is much less than the maximum forward rate of any other enzymatic reactions. More realistic is the case where the maximum forward rates of more than one enzymatic reaction are slow. When two slow enzymatic reactions are separated from each other by any number of fast reactions that overall can be described by a large equilibrium constant, the Blackman form results: and A third case is that in which two slow enzymatic steps are separated by an equilibrium constant that is not large. Unlike the Monod and Blackman forms, which contain only two arbitrary constants, this model contains three arbitrary constants: The Monod and Blackman forms are special cases of this three constant form. In comparing equations with two arbitrary constants the Monod equation gave poorer fit of the data in most cases than the Blackman form. It is concluded that workers modeling the growth of microorganisms should give a t least as much consideration to the Blackman form as is given to the Monod equation.     

Fluorescence anisotropy-based measurement of Pseudomonas aeruginosa penicillin-binding protein 2 transpeptidase inhibitor acylation rate constants

High-molecular-weight penicillin-binding proteins (PBPs) are essential integral membrane proteins of the bacterial cytoplasmic membrane responsible for biosynthesis of peptidoglycan. They are the targets of antibacterial β-lactam drugs, including penicillins, cephalosporins, and carbapenems. β-Lactams covalently acylate the active sites of the PBP transpeptidase domains. Because β-lactams are time-dependent inhibitors, quantitative assessment of the inhibitory activity of these compounds ideally involves measurement of their second-order acylation rate constants. We previously described a fluorescence anisotropy-based assay to measure these rate constants for soluble constructs of PBP3 (Anal. Biochem. 439 (2013) 37–43). Here we report the expression and purification of a soluble construct of Pseudomonas aeruginosa PBP2 as a fusion protein with NusA. This soluble PBP2 was used to measure second-order acylation rate constants with the fluorescence anisotropy assay. Measurements were obtained for mecillinam, which reacts specifically with PBP2, and for several carbapenems. The assay also revealed that PBP2 slowly hydrolyzed mecillinam and was used to measure the rate constant for this deacylation reaction.