A Model for the Action of Vinblastine in Vivo

A model for the action of vinblastine (VLB) on cells multiplying exponentially in vivo with a generation time, T_G, has been derived. It is based on the assumption that cells attempting to pass through mitosis in the presence of VLB lose their proliferative capacity and that this lethal effect occurs only when the cells are exposed to a concentration of VLB which is above a critical value, C_k. The model leads to two predictions. First, that the percentage of cells surviving at any time after exposure to a dose, D, of VLB is 100% if D < D_k and decreases to 0% after a time, T_G, following a dose D ≥ D_k·2^{T G/T1/2}, where D_k represents the dose of VLB required to produce the concentration C_k, and T_1/2 is the half-life of the VLB in vivo. Second, that the time, T_G, at which the percentage of cells surviving an exposure to VLB, at doses greater than D_k·2^{U G/T1/2}, decreases to zero should be equal to the generation time of the cells. Both of these predictions were confirmed experimentally which indicates that the model adequately explains the action of VLB in vivo.     

Studies on the reactivity of malondialdehyde. I. Effects of acid concentration and solvent composition on deuterium exchange reactions

The rates of deuterium exchange reactions of malondialdehyde (MDA) and deuterated malondialdehyde (MDAd) have been studied as a function of acidity and the content of dimethyl sulfoxide (DMSO) in binary mixtures with D₂O . MDA incorporates deuterium from D₂O solutions in a first-order reaction with a rate constant (k_obs) that depends on the acid concentration. From this dependence, a catalytic constant, k_cat, can be derived (k_cat^MDA = 2.25 × 10⁵M^?s^?1). Similar kinetic behavior was found for MDAd in H₂O solutions, and in this case, k_cat^MDA = 1.56 × 10⁵M^?1s^?1. Results from reactions of MDA and MDAd in identical H₂OD₂O mixtures show that primary and secondary isotope effects are small (k_H/k_D = 1.13) and that solvent isotope effects cause most of the differences found between reactions in D₂O and H₂O. Reactions in binary DMSOd₆D₂O mixtures show a six-fold rate increase as the proportion of DMSOd₆ increases from 50% to 90%. These results also illustrate the relatively high reactivity of MDA at pH values well above its pK_a and the importance of medium composition on its reaction rate.     

Quasi-elastic light scattering study of salt induced conformational transitions of chromatin subunit

The translational diffusion coefficient D_T of monodisperse solutions of 146 base pairs (bp) core particles was studied by the quasi-elastic light scattering technique. When the salinity was raised a change of D_T from 1.9 × 10^?7 cm² s^?1 to 3.2 × 10^?7 cm² s^?1 was detected at about 2 mM NaCl, followed by a smooth decrease of D_T beyond 0.6 M NaCl. The measurements of particle concentration and scattering vector effects on the D_T showed that the influence of interactions between particles can be disregarded. The interaction between particles and counterions is also discussed and does not appear to be the origin of the actual changes in D_T. These transitions of D_T are hence related to changes of shape and size of the particles. It is shown that the single transition at low salinity corresponds to a conformational change while the variation of D_T at high salinity can be interpreted by a destabilization of the edifice. In different regions of salinities, the observed values of D_T can lead to reasonable hydrodynamic models.     

Mathematical Model of Thermal Destruction of Bacillus stearothermophilus Spores

The experimental survival curves of Bacillus stearothermophilus spores in aqueous suspension, for six constant temperatures ranging from 105 to 130°C, displayed an initial shoulder before a linear decline. To interpret these observations, we supposed that, before the heat treatment, the designated spore suspension contained a countable and mortal N₀ population of activated spores and an M₀ population of dormant spores which remained masked during spore counting and had to be activated before being destroyed by heat. We also hypothesized that the mechanisms of both activation and destruction are, at constant temperature, ruled by first-order kinetics, with velocity constants k_A and k_D, respectively. Mathematical analysis showed that this model could represent not only our experimental survival curves, but also all other shapes (linear and biphasic) of survival curves found in the literature; also, there is an inherent symmetry in the model formulation between the activation and destruction reactions, and we showed that the dormancy rate (τ = M₀/N₀) is the only parameter which permits a distinction between the two reactions. By applying the model to our experimental data and considering that the dormancy rate is not dependent on the treatment temperature, we showed that, for the studied suspension, the limiting reaction was the activation reaction.     

Light dependence of the decay of the proton gradient in broken chloroplasts

The initial rates and steady-state values of proton uptake by broken chloroplasts have been measured as functions of light intensity at various concentrations of chlorophyll, pyocyanine, supporting electrolyte, buffer, as well as pH and temperature. Kinetic analysis of the data shows that the rate of decay of proton gradient due to backward leakage depends on light intensity. Under steady illumination, the decay constant k_L is equal to k_D + mR₀, where R₀ is the initial rate of proton uptake which is a function of light intensity, k_D is the decay constant in the dark and m is a parameter which is independent of light intensity. Treatment of chloroplasts with lysolecithin, neutral detergent, 2,4-dinitrophenol, or valinomycin in the presence of K⁺ increases k_D without affecting m. Treatment with N,N′-dicyclohexylcarbodiimide or adenylyl imidodiphosphate under appropriate conditions decreases m without affecting k_D. Treatment with glutaraldehyde makes k_L independent of light intensity and hence m = 0. These results suggest that the light-dependent part (mR₀) of k_L is due to leakage of protons through the coupling factor (CF₁-CF₀) complex which can open or close depending on light intensity and that the light-independent part (k_D) of the decay constant k_L is due to proton leakage elsewhere.     

Chemometric Methods to Quantify 1D and 2D NMR Spectral Differences Among Similar Protein Therapeutics

NMR spectroscopy is an emerging analytical tool for measuring complex drug product qualities, e.g., protein higher order structure (HOS) or heparin chemical composition. Most drug NMR spectra have been visually analyzed; however, NMR spectra are inherently quantitative and multivariate and thus suitable for chemometric analysis. Therefore, quantitative measurements derived from chemometric comparisons between spectra could be a key step in establishing acceptance criteria for a new generic drug or a new batch after manufacture change. To measure the capability of chemometric methods to differentiate comparator NMR spectra, we calculated inter-spectra difference metrics on 1D/2D spectra of two insulin drugs, Humulin R® and Novolin R®, from different manufacturers. Both insulin drugs have an identical drug substance but differ in formulation. Chemometric methods (i.e., principal component analysis (PCA), 3-way Tucker3 or graph invariant (GI)) were performed to calculate Mahalanobis distance (D _M) between the two brands (inter-brand) and distance ratio (D _R) among the different lots (intra-brand). The PCA on 1D inter-brand spectral comparison yielded a D _M value of 213. In comparing 2D spectra, the Tucker3 analysis yielded the highest differentiability value (D _M = 305) in the comparisons made followed by PCA (D _M = 255) then the GI method (D _M = 40). In conclusion, drug quality comparisons among different lots might benefit from PCA on 1D spectra for rapidly comparing many samples, while higher resolution but more time-consuming 2D-NMR-data-based comparisons using Tucker3 analysis or PCA provide a greater level of assurance for drug structural similarity evaluation between drug brands.     

Helix-coil transition in nucleoprotein. Effect of ionic strength on thermal denaturation of polylysine-DNA complexes

Thermal denaturation of direct-mixed and reconstituted polylysine–DNA complexes in 2.5 × 10^?4 M EDTA, pH 8.0 and various concentrations of NaCl has been studied. For both complexes, increasing ionic strength of the solution raises T_m, the melting temperature of free base pairs. The linear dependence of T_m on log Na⁺ indicates that the concept of electrostatic shielding on phosphate lattice of an infinitely long pure DNA by Na⁺ can be applied to short free DNA segments in a nucleoprotein. For a direct-mixed polylysine–DNA complex, the melting temperature of bound base pairs T_m′ remains constant at various ionic strengths. On the other hand, the T_m′ in a reconstituted polylysine–DNA complex is shifted to lower temperature at higher ionic strength. This phenomenon occurs for reconstituted complex with long polylysine of one thousand residues or short polylysine of one hundred residues. It is shown that such a decrease of T_m′ is not due to a reduction of coupling melting between free and bound regions in a complex when the ionic strength is raised. It is also not due to intermolecular or intramolecular change from a reconstituted to a direct-mixed complex. It is suggested that this phenomenon is due to structural change on polylysine-bound regions by ionic strength. It is suggested further that Na⁺ may replace water molecules and bind polylysine-bound regions in a reconstituted complex. Such a dehydration effect destabilizes these regions and lowers T_m′. This explanation is supported by circular dichroism (CD) results.     

On the problem of comparing protein structures: Development and applications of a new method for the assessment of structural similarities of polypeptide conformations

The development of prediction schemes and the search for evolutionary relationships amongst proteins require reliable methods for the comparison of polypeptide structures. It is shown that methods which attempt to describe structural similarities by a single value generally do not yield reliable estimates of the relatedness of two conformations. A new method is reported, called the D_k procedure, which yields a spectrum of deviations between two structures. Each particular D_k value is a measure of the similarity of the diagonals of the distance matrices of the compared conformations, k being the distance of the diagonals relative to the main diagonal.The method has the following features. (1) D_k is independent of chain length; (2) the method yields the relatedness of two conformations in terms of different structural levels; (3) D_k is a high-speed algorithm; (4) the D_k deviations of random structures from any particular conformation are predictable.The following applications are reported. (1) The success of both secondary and tertiary structure predictions are measured in terms of a reliable quality index. (2) The route of a conformation during simulation studies is followed on different structural levels, which exhibit the characteristics of the simulation. (3) The significance of hypotheses on protein folding subject to prediction schemes can be established. (4) A priori information (fixing pieces of secondary structure derived from X-ray investigations during prediction) is extractable from the predicted structures. (5) The evolutionary relatedness of two nucleotide binding proteins is established.The simplicity and speed of the D_k procedure allow its implementation even on minicomputers.     

A Kinetic Analysis of 6-[18F]Fluoro-l-Dihydroxyphenylalanine Metabolism in the Rat

Abstract: A previous study of the metabolism of 6-[¹⁸F]-fluoro-l -3,4-dihydroxyphenylalanine (FDOPA) in rats pretreated with carbidopa contained information amenable to kinetic analysis. Using these data, tracer transfer coefficients and metabolic rate constants were estimated. After intravenous injection, FDOPA in circulation was O-methylated (k^D₀ = 0.055 min^?1), and the metabolite (O-methyl-FDOPA) escaped from plasma with a rate constant (k^M_?1) of 0.01 min^?1. The initial clearance of FDOPA to striatum (K^D₁) was 0.07 ml g^?1 min^?1, and the equilibrium distribution volume (V^D_e) was 0.67 ml g^?1. The initial clearance of O-methyl-FDOPA to striatum (K^M₁) was 0.08 ml g^?1 min^?1, and the equilibrium distribution volume (V^M_e) was 0.75 ml g^?1. The rate constant of FDOPA decarboxylation (k^D₃) was 0.17 min^?1 in striatum. The elimination of 6-[¹⁸F]fluorodopamine (FDA) from striatum suggested an apparent rate constant for monoamine oxidase activity (k′₇) of 0.055 min^?1. 6-[¹⁸F]Fluorohomovanillic acid (FHVA) was formed from 6-[¹⁸F]fluoro-l -3,4-dihydroxyphenylacetic acid with a rate constant (k₁₁) of 0.083 min^?1, and FHVA was eliminated from striatum (k₉) with a rate constant of 0.12 min^?1. The steady-state concentration ratios of FDA and its metabolites were shown to be functions of these rate constants.     

Turing's conditions and the analysis of morphogenetic models.

The conditions under which changes in parameters lead to changes in the pattern-generating behaviour of Turing's two-morphogen linear model can be expressed in terms of two reduced rate constants, k′₁ and k′₄ which represent autocatalytic and self-inhibitory rates in relation to cross-catalysis and cross-inhibition, and the ratio of the diffusivities for the two morphogens. This allows a new type of diagram to be drawn in which a two-dimensional k′₁k′₄ space is divided by Turing's conditions into regions where the various morphogenetic behaviours occur.An analysis using this type of diagram is applied to the linear limit of two non-linear models, those of Gierer and Meinhardt and of Tyson's modification of the Brusselator, and is used to clarify what is happening in their non-linear development. Several possible applications are mentioned; to the stability of a simple binary pattern in slime moulds, to the development and decay of a succession of patterns in the imaginal wing discs of Drosophila as treated by Kauffman et al., and to the apparent ease of disturbing the sea urchin blastula to produce a three-part, rather than a two-part pattern.     

Reversible linkage isomerization of pentaamminecobalt(III) complexes of urea and its N-methyl derivatives

The (NH₃)₅CoOC(NH₂)₂³⁺ ion is consumed in water according to the rate law k(obs.) = k₁ + k₂[OH⁻], where k₁ = 4.0 × 10⁻⁵ s⁻¹ and k₂ = 14.2 M⁻¹ s⁻¹ (0–0.1 M [OH⁻];μ = 1.1 M, NaClO₄, 25 °C). A hitherto unrecognized intramolecular O- to N- linkage isomerization reaction has been detected. In strongly acid solution only aquation to (NH₃)₅CoOH₂³⁺ is observed, but in 0.1–1.0 M [OH⁻], 7% of the directly formed products is the urea-N complex (NH₃)₅CoNHCONH₂²⁺ which has been isolated. In the neutral pH region a much greater proportion (25%) of the products is the urea-N species. These results are interpreted in terms of an urea-O to urea-N linkage isomerization reaction competing with hydrolysis for both spontaneous (k₁) and base-catalyzed (k₂) pathways; the rearrangement is not observed in strongly acidic solution (pH ⩽ 1) because the protonated N-bonded isomer (pK′_a ≈ 3) is unstable with respect to the O-bonded form. The appearance of the isomerization pathway as the pH is raised in the 0–6 region is commensurate with a rate increase which cannot be attributed to a contribution from the base catalysis term k₂[OH⁻]. It is argued that this observation establishes, for the spontaneous pathway, that hydrolysis and linkage isomerization are separate reaction pathways — there is no common intermediate. The product distribution and rate data lead to the complete rate law, k(obs.) = k₁ + k₂[OH⁻] = (k_s + k_ON) + (k_OH + k′_ON) [OH⁻] for the reactions of the O-bonded isomers, where k_s, k_OH are the specific rates for hydrolysis, and k_ON, k′_ON are the specific rates for O- to N-linkage isomerization, by spontaneous and base-catalyzed pathways respectively; k_ON = 1.3 × 10⁻⁵ s⁻¹ and k′_ON = 1.1 M⁻¹ s⁻¹ (μ = 1.0 M, NaClO₄, 25 °C). The O- to N- linkage isomerization has been observed also for complexes of N-methylurea, N,N-dimethylurea and N-phenylurea, but not for the N,N′-dimethylurea species. There is an approximately statistical relationship among the data for −NH₂ capture (versus H₂O), while −NHR and −NR₂ do not compete with water as nucleophiles for Co(III) in either the spontaneous or base-catalyzed hydrolysis processes. For each urea-O complex, O- to N-isomerization is a more significant parallel reaction in the spontaneous as opposed to the base-catalyzed pathway. This is interpreted as being indicative of more associative character in the spontaneous route to products, a conclusion supported by other evidence. Some activation parameter data have been recorded and the effect of the N-substitution on the rates of solvolysis (H₂O, Me₂SO) is discussed. The urea-N complexes have been isolated as their deprotonated forms, [(NH₃)₅CoNHCONRR′](ClO₄)₂·xH₂O (R,R′ = H, CH₃). They are kinetically inert in neutral to basic solution but in acid they protonate (H₂O, pK′_a 2–3; μ = 1.0 M, 25 °C) and then isomerize rapidly back to their O-bonded forms. Some solvolysis accompanies this N- to O-rearrangement in H₂O and Me₂SO. Specific rates and activation parameters are reported. The kinetic data follow a rate law of the form k_NO(obs.) = (k + k_NO)[H⁺]/(K′_a + [H⁺]) and the active species in the reaction is the protonated form; k, k_NO are the specific rates for hydrolysis and isomerization, respectively. Proton NMR data establish that the site of protonation (in Me₂SO) is the cobalt-bound nitrogen atom. For the unsubstituted urea species (NH₃)₅CoNH₂CONH₂³⁺, diastereotopic exo-NH₂ protons arising from restricted rotation about the CN bond are observed. The relevance to the mechanism of the linkage isomerization process is considered. ¹³C and ¹H NMR and electronic absorption spectral data are presented, and distinctions between linkage isomers and the solution structures (electronic and conformational) are discussed. The urea-N/urea-O complex equilibrium is governed by the relation K′_NO(obs.) = K′_NO[H⁺]/[H⁺](K′_a), where K′_NO is the equilibrium constant = [(NH₃₅Co(urea-O)³⁺]/[(NH₃)₅Co(urea-N)³⁺]. Values for K′_NO(=k_NO/k_ON = 260 and pK′_a ≈ 3 for the NH₂CONH₂ system are consistent with the stability of the N-isomer in feebly acidic to basic solution (e.g. pH 6, K′_NO(obs.) = 2.6 × 10⁻²) and instability in acid solution (e.g. pH 1, K′_NO(obs.) = 240). The equilibrium data for this and other urea complexes of (NH₃)₅Co(III) are contrasted with the result for the analogous Rh(III)NH₂CONH₂ system K′_NO ≈ 1).     

Evaluation of kinetic data: What the numbers tell us about PRMTs

Protein arginine N-methyltransferase (PRMT) kinetic parameters have been catalogued over the past fifteen years for eight of the nine mammalian enzyme family members. Like the majority of methyltransferases, these enzymes employ the highly ubiquitous cofactor S-adenosyl-l-methionine as a co-substrate to methylate arginine residues in peptidic substrates with an approximately 4-μM median K_M. The median values for PRMT turnover number (k_cat) and catalytic efficiency (k_cat/K_M) are 0.0051 s⁻¹ and 708 M⁻¹ s⁻¹, respectively. When comparing PRMT metrics to entries found in the BRENDA database, we find that while PRMTs exhibit high substrate affinity relative to other enzyme-substrate pairs, PRMTs display largely lower k_cat and k_cat/K_M values. We observe that kinetic parameters for PRMTs and arginine demethylase activity from dual-functioning lysine demethylases are statistically similar, paralleling what the broader enzyme families in which they belong reveal, and adding to the evidence in support of arginine methylation reversibility.     

Analysis of conformationally-linked dissociation of proteins

Conformationally-linked dissociation equilibria of dimeric proteins have been examined to determine how experimentally obtainable parameters, such as the apparent dissociation constant, k_D, and the apparent conformational transition constant, K_conf, are related to intrinsic subunit interaction constants, K_A or K_B, and intrinsic isomerization constants, K₁ or k₂. Limiting models are considered in which either the conformational change occurs before dissociation or in which the dissociation occurs before the conformational change, as well as a general model including both possibilities. Models are also considered in which three conformations are allowed or in which four subunits (tetramers) are involved. Simulated data for the dimer equilibria are presented to show how variation of protein concentration and variation of certain constants affect the proportion of various molecular species, the weight-average molecular weight, and the overall extent of conformational change. Methods are suggested to distinguish between the different limiting cases based upon the dependence of K_D and/or K_conf on protein concentration, perturbant concentration, and temperature. It is concluded that methods used to calculate self-dissociation constants oligomeric proteins include linked isomerization reactions such that the equilibrium constant obtained should not be considered as a true subunit interaction term. Indeed, dissociation can occur under the influence of a perturbant with no change in the intrinsic affinity of the subunits but with the sole effect of the perturbant being on a linked conformational change. Additional experiments on the thermodynamics of the conformational change are required to determine the actual relationship. Depending on the complexity of the equilibria involved and the relative value of the equilibrium constants, the extent of the conformational change can vary directly with, vary inversely with, or he independent of the total protein concentration. Even when intrinsic subunit affinities are not affected by the perturbant, the extent of conformational change can vary with protein concentration. Interpretation of data from proteins which may be involved in conformationally-linked dissociation reactions, therefore, must be made with caution.     

Continuous optical scanning in polyacrylamide gel electrophoresis:estimation of the apparent diffusion coefficient of beta-lactoglobulin B.

The continuous scanning apparatus developed by Catsimpoolas was applied to an analysis of the concentration profiles of a protein, β-lactoglobulin B, while it was subjected to polyacrylamide gel electrophoresis (PAGE) in a multiphasic buffer system. Continuous optical scanning in PAGE permitted reliable estimation of the standard deviation of the concentration profile (σ), the relationship between σ² and time, and the apparent diffusion coefficient, D′, derived from σ², as the current density varied from 2 to 9 mA/cm², protein load varied from 250 to 900 μg/cm², and the ionic strength varied from 0.015 to 0.065 m. Under these conditions, D′ was linearly related to current density and protein load. Further, log (D′) was linearly related to gel concentration (%T) ranging from 6 to 14%. However, D′ was nonlinearly related to ionic strength. Due primarily to the ionic strength factor, the apparent diffusion coefficient of protein in gels appeared to be approximately 10-fold larger than under the conditions of high ionic strength conventionally used in sedimentation and diffusion studies. Extrapolation of D′ to 0% T, zero protein load, zero current density, and “infinite” ionic strength (assuming noninteraction of these factors), as well as correction for viscosity and temperature, yielded an estimated free-diffusion coefficient, D_20,w, of 3.1 × 10^?7 cm²/s, which is compatible with previously reported values. These studies indicate that the optimal resolution obtained by PAGE will be considerably lower than that predicted theoretically on the basis of free-diffusion coefficients, and suggest that electrostatic interaction between the proteins and/or deformation of voltage gradient and pH within the protein zones may contribute significantly to band spreading.     

Influence of external chloride concentration on the kinetics of mobile charges in the cell membrane of Valonia utricularis: Evidence for the existence of a chloride carrier

Charge pulse relaxation studies were performed on cells of the giant marine alga Valonia utricularis. Two exponential voltage relaxations were recorded as found previously (Benz, R., and U. Zimmermann. 1983. Biophys. J. 43:13-26.). The parameters of the two exponential voltage decays were studied as a function of the chloride concentration in the artificial sea water. Replacement of external chloride by 2(N-morpholino)ethanesulfonate (Mes^-) had a dramatic influence on the four relaxation parameters. This chloride dependence could not be satisfactorily explained by the simplified model used earlier. Accordingly, additional reaction steps had to be included in the model. Only two relaxation processes could be resolved under all experimental conditions. This means that the heterogeneous complexation reactions, k_R (association), and k_D (dissociation) were too fast to be resolved. Therefore a carrier model with equilibrium heterogeneous surface reactions was used to fit the experimental results. From the charge pulse data at different chloride concentrations the translocation rate constants of the free and complexed carriers, k_S and k_AS, through the membrane, as well as the total surface concentration of carrier systems, N₀, could be evaluated. The results described here indicate that the cell membrane of Valonia utricularis contains an electrogenic transport system for chloride.     

Proton uptake mechanism of bacteriorhodopsin as determined by time-resolved stroboscopic-FTIR-spectroscopy

Bacteriorhodopsin's proton uptake reaction mechanism in the M to BR reaction pathway was investigated by time-resolved FTIR spectroscopy under physiological conditions (293 K, pH 6.5, 1 M KCl). The time resolution of a conventional fast-scan FTIR spectrometer was improved from 10 ms to 100 μs, using the stroboscopic FTIR technique. Simultaneously, absorbance changes at 11 wavelengths in the visible between 410 and 680 nm were recorded. Global fit analysis with sums of exponentials of both the infrared and visible absorbance changes yields four apparent rate constants, k₇ = 0.3 ms, k₄ = 2.3 ms, k₃ = 6.9 ms, k₆ = 30 ms, for the M to BR reaction pathway. Although the rise of the N and O intermediates is dominated by the same apparent rate constant (k₄), protein reactions can be attributed to either the N or the O intermediate by comparison of data sets taken at 273 and 293 K. Conceptionally, the Schiff base has to be oriented in its deprotonated state from the proton donor (asp 85) to the proton acceptor (asp 96) in the M₁ to M₂ transition. However, experimentally two different M intermediates are not resolved, and M₂ and N are merged. From the results the following conclusions are drawn: (a) the main structural change of the protein backbone, indicated by amide I, amide II difference bands, takes place in the M to N (conceptionally M₂) transition. This reaction is proposed to be involved in the “reset switch” of the pump, (b) In the M to N (conceptionally M₂) transition, most likely, asp-85's carbonyl frequency shifts from 1,762 to 1,753 cm^-1 and persists in O. Protonation of asp-85 explains the red-shift of the absorbance maximum in O. (c) The catalytic proton uptake binding site asp-96 is deprotonated in the M to N transition and is reprotonated in O.     

OptZyme: Computational Enzyme Redesign Using Transition State Analogues

OptZyme is a new computational procedure for designing improved enzymatic activity (i.e., k_cat or k_cat/K_M) with a novel substrate. The key concept is to use transition state analogue compounds, which are known for many reactions, as proxies for the typically unknown transition state structures. Mutations that minimize the interaction energy of the enzyme with its transition state analogue, rather than with its substrate, are identified that lower the transition state formation energy barrier. Using Escherichia coli β-glucuronidase as a benchmark system, we confirm that K_M correlates (R² = 0.960) with the computed interaction energy between the enzyme and the para-nitrophenyl- β, D-glucuronide substrate, k_cat/K_M correlates (R² = 0.864) with the interaction energy of the transition state analogue, 1,5-glucarolactone, and k_cat correlates (R² = 0.854) with a weighted combination of interaction energies with the substrate and transition state analogue. OptZyme is subsequently used to identify mutants with improved K_M, k_cat, and k_cat/K_M for a new substrate, para-nitrophenyl- β, D-galactoside. Differences between the three libraries reveal structural differences that underpin improving K_M, k_cat, or k_cat/K_M. Mutants predicted to enhance the activity for para-nitrophenyl- β, D-galactoside directly or indirectly create hydrogen bonds with the altered sugar ring conformation or its substituents, namely H162S, L361G, W549R, and N550S.     

On enzymic clotting processes V: Rate equations for the case of arbitrary rate of production of the clotting species

The rate theory for enzyme-triggered coagulation reactions, such as the clotting of fibrin or casein, is extended to the case of an arbitrary rate of production of the clotting species. It is shown that the general expression for the growth of the weight-average molecular weight of the clotting product, -M_w, is given by -M_w = M₁{1 + k_s {∫₀^tP(t)² dt}/P(t)}, where M₁ is the “monomer” molecular weight, k_s the smoluchowskian flocculation rate constant and P(t) the total number of monomers produced by the enzyme in t. In the purely smoluchowskian case P(t) stands for the total number of monomers at the beginning of the clotting process. Numerical examples in which the rate of enzymic production is governed by complete Michaelis-Menten kinetics, are compared to cases in which this rate equals V_max- It is shown that after exhaustion of the substrate the system continues to coagulate in a purely smoluchowskian way. Turbidimetric experiments on the clotting of micelles of whole and κ-casein are presented which suggest inactivation of the enzyme by non-productive binding in the flocs formed.     

Reductive methylation andpKa determination of the lysine side chains in calbindin D9k

The Lys residues in the 75-residue Ca²⁺-binding protein calbindin D_9k were reductively methylated with¹³C-enriched formaldehyde. The possible structural effects resulting from the chemical modification were critically investigated by comparing two-dimensional NMR spectra and the exchange rates of some of the amide protons of the native and the modified protein. Our results show that the protein retains its structure even though 10 Lys out of a total of 75 amino acid residues were modified. In the Ca²⁺- and apo-forms of the protein, the¹³C-methylated Lys residues can be detected with high sensitivity and resolution using two-dimensional (¹H,¹³C)-heteronuclear multiple quantum coherence (HMQC) NMR spectroscopy. ThepKa values of the individual Lys residues in Ca²⁺-calbindin D_9k and apo-calbindin D_9k were obtained by combiningpH titration experiments and (¹H,¹³C)-HMQC NMR spectroscopy. Each Lys residue in the Ca²⁺- and apo-forms of calbindin D_9k has a uniquepKa value. The LyspKa values in the calcium protein range from 9.3 to 10.9, while those in the apo-protein vary between 9.7 and 10.7. Although apo-calbindin D_9k has a very similar structure compared to Ca²⁺-calbindin D_9k, the removal of two Ca²⁺ ions from the protein leads to an increase of thepKa values of the Lys residues.     

The base exchange reaction of NAD+ glycohydrolase: identification of novel heterocyclic alternative substrates

ADP-ribosyl cyclase and NAD⁺ glycohydrolase (CD38, E.C.3.2.2.5) efficiently catalyze the exchange of the nicotinamidyl moiety of NAD⁺, nicotinamide adenine dinucleotide phosphate (NADP⁺) or nicotinamide mononucleotide (NMN⁺) with an alternative base. 4′-Pyridinyl drugs (amrinone, milrinone, dismerinone and pinacidil) were efficient alternative substrates (k_cat/K_M = 0.9-10 μM⁻¹ s⁻¹) in the exchange reaction with ADP-ribosyl cyclase. When CD38 was used as a catalyst the k_cat/K_M values for the exchange reaction were reduced two or more orders of magnitude (0.015-0.15 μM⁻¹ s⁻¹). The products of this reaction were novel dinucleotides. The values of the equilibrium constants for dinucleotide formation were determined for several drugs. These enzymes also efficiently catalyze the formation of novel mononucleotides in an exchange reaction with NMN⁺, k_cat/K_M = 0.05-0.4 μM⁻¹ s⁻¹. The k_cat/K_M values for the exchange reaction with NMN⁺ were generally similar (0.04-0.12 μM⁻¹ s⁻¹) with CD38 and ADP-ribosyl cyclase as catalysts. Several novel heterocyclic alternative substrates were identified as 2-isoquinolines, 1,6-naphthyridines and tricyclic bases. The k_cat/K_M values for the exchange reaction with these substrates varied over five orders of magnitude and approached the limit of diffusion with 1,6-naphthyridines. The exchange reaction could be used to synthesize novel mononucleotides or to identify novel reversible inhibitors of CD38.