Hemoglobin/O2 systems: using short-lived intermediates for mechanistic discrimination.

The kinetics of the reaction of hemoglobin with molecular oxygen, in which rapid mixing is followed by a very fast temperature jump, is numerically simulated. Four different mechanisms are considered. In two of them, oxygen reacts with the alpha-chains first, in the other two with the beta-chains first. Furthermore, either the third or the fourth measured (Adair) dissociation constant is composed of the product of a local dissociation constant and an allosteric interconversion constant. We explore whether these alternative mechanisms may be distinguished experimentally. We show that reaction steps not resolvable by rapid mixing can be resolved by chemical relaxation at appropriate points in time. Discrimination under experimental conditions is possible at higher oxygen concentrations (above 100 microM), but high resolution in time and concentration amplitude are required.

Short-lived intermediates in hemoglobin/O2 systems.

The kinetics of the reaction of hemoglobin with molecular oxygen, in which rapid mixing is followed by a very fast temperature jump, is numerically simulated. Values for rate constants are used to the extent known, otherwise interpolated or extrapolated. It is shown that reaction steps not resolvable by rapid mixing can be resolved by subsequent chemical relaxation at appropriate points in time. Four different mechanisms are considered, all assuming no distinction between the two kinds of chains of hemoglobin. Bimolecular rate constants for oxygen binding are either the same for all four sites, or are governed by "frequency factors" (the kinetic equivalent of statistical factors for equilibrium constants in allosteric models). Furthermore, either the third or the fourth measured (Adair) dissociation constant is composed of the product of a "local" dissociation constant and an allosteric interconversion constant. These two pairs of choices give rise to four different mechanisms. Can these mechanisms be distinguished experimentally? As the final parameter values are so similar for the first two binding steps, discrimination is essentially impossible at low oxygen concentration levels (less than 100 microM with 50 microM hemoglobin). Discrimination becomes possible at higher oxygen concentrations, but high resolution in time and concentration amplitude are required. Much depends upon the differences in molar extinction coefficients of components over the accessible wave length range. Some of these values are as yet unknown or not known to a sufficient precision. Nevertheless, distinction between mechanistic alternatives is possible in principle.

Short-lived intermediates in aspartate aminotransferase systems.

The kinetics of the reaction of aspartate aminotransferase with erythro-beta-hydroxy-aspartate, in which rapid mixing is followed (upon reaching a suitable stationary state) by a very fast temperature jump, is numerically simulated. Values for rate constants are used to the extent known, otherwise estimated. It is shown that reaction steps not resolvable by rapid mixing can be resolved by subsequent chemical relaxation. Since several absorption spectra of enzyme complexes overlap, use of a pH-indicator is investigated. When the pH-indicator is coupled to the protonic dissociation of free enzyme, the fast steps are easily detected in the chemical relaxation portion of the simulation. When the pH-indicator is coupled to the protonic dissociation of the (short-lived) quinoid intermediate, protonic dissociation is easily detectable in the stopped flow phase and in the chemical relaxation phase. Such transient protonic dissociation has not been detected experimentally, but is predicted by the simulation. When natural substrates are used, the magnitude of the rate constants makes it unlikely that transient proton dissociation can be detected by stopped flow alone, but a combination of stopped flow with very fast temperature perturbation allows detection of the transient proton through use of a suitable nonbinding pH-indicator. This is demonstrated by simulation for a specific case. Finally, an alternate mechanism is introduced and distinction of its kinetics from that of the original mechanism is demonstrated.

Resolving the fast equilibrations of ternary complexes in liver alcohol dehydrogenase.

Liver alcohol dehydrogenase is an enzyme system which has been investigated extensively. In a recent paper by Sekhar & Plapp (1989), possibly as many as eight steps were revealed, most of them interconversions among ternary complexes. Many of the rate constants reported were near or above the reciprocal of the reported dead time of the mixing apparatus used. Thus, many of these rate constants may represent lower limits. However, even with a higher speed mixing apparatus, some of the rate constants still can only be estimated. In particular, there is a proton transfer step to/from the buffer system which is expected to be much faster than adjoining rearrangements. To the extent some steps involve purely electronic changes, they most likely are also faster than adjoining structural rearrangements. It can be shown that chemical relaxation can be used to analyze the kinetics of fast steps between slower ones, not accessible by rapid mixing (also not accessible at overall equilibrium where the required concentrations are too small). Using the best data from the literature, one may simulate two experimental protocols to demonstrate what can be accomplished by combining rapid flow with chemical relaxation. In one protocol, the ternary complexes are formed by mixing the pre-mixed binary complex of enzyme and NADH with acetaldehyde; the rate conditions are such that chemical relaxation has to be initiated 4 msec after mixing to observe the rapid proton transfer reactions.(ABSTRACT TRUNCATED AT 250 WORDS)

Boundaries in gravitational and magnetic activation of cells for sorting.

Standard deviations in the distribution of radii of cells and particles are considered to arrive at realistic limits in the use of gravitational and magnetic activation of cells for sorting. Using a specific fractionation design, it is shown that the radius of particles (or cells) may be fractionated down to a precision of +/- 0.76%. Although higher precisions could be obtained with other designs, the number of particles available per fraction is inversely proportional to the precision desired. Thus, one would prefer to keep the precision as moderate as permissible by the experiments.

Cooperative coupling in allosteric systems.

Allosterism of the Monod type applies only to systems with more than one binding site and two (noncooperative) states with intrinsic binding constants. Allosterism is then defined by an interconversion constant Lo (greater than 1) and a ratio of intrinsic binding constants, c (less than 1). The value of c determines whether weak or strong cooperativity among binding sites prevails. Cooperativity is weak, if 1 greater than c greater than 0.1, and strong, when c less than or equal to 0.1. Cooperativity is the stronger, the smaller c. Cooperativity may exist only between a restricted number of binding sites. The binding of Ca2+ to calmodulin shows this behavior under certain conditions. An (internal) indicator for binding may signal binding to both states or to only one. The results would be quite different with the extent of the difference determined by the extent of cooperativity (c in relation to the particular Li near 1). The size of Lo cannot be ignored in reference to the size of c. Effectors external to the ligand could alter Lo to shift cooperative behavior. Effectors could also make Lo too small or too large for any allosteric behavior to appear.

Differential analysis of allosteric behavior.

Differential analysis of allosteric systems focuses on the ratio of consecutive binding constants obtained for multiple binding as originally used by Adair. If this ratio of experimental constants is smaller than the ratio of statistical constants for multiple binding, cooperativity among subunits is indicated. The conditions are evaluated with the aid of the model of Monod et al and compared with available data on calmodulin. Calmodulin shows cooperativity among some subunits, not among others, depending strongly upon experimental details. Values of Ln (the interconversion constant of fully occupied sites) can be estimated for c much less than 1 (and Ln-1 much greater than 1).

Cell sedimentation with gravity activation.

Murine monoclonal antibody T101 has been coupled to thinly polymer-coated heavy alloy particles (LaMn2Ge2). These conjugates are coupled to cultured cells of the human T-cell leukemia line RPMI 8402 (T8402). The sedimentation velocities of cells, of particles, and of cells with particles attached are measured. After determining the mean radii of cells, of particles, and of cells with particles attached, one may compute a mean number of 33 particles attached to a cell. Independently one may compute a mean number of 144 particles/cell for surface saturation. The Appendix handles the underlying theory in three parts: number of particles/cell, saturation number of particles/cell, and resolution for gravity activation. Regarding the latter, cell radii from 4 to 10 microns and particle radii from 0.01 to 1 micron are considered.

Coupling of redox indicator dyes into an enzymatic reaction cycle.

The spectral properties of ten redox indicator dyes were evaluated with the aim of finding the optimal choice for coupling to enzymatic reactions with high sensitivity for the production of the reduced form. Eight of the dyes were selected for coupling into a reaction cycle formed by yeast alcohol dehydrogenase with substrates ethanol and nicotinamide adenine dinucleotide (NAD+) and diaphorase with substrates reduced nicotinamide adenine dinucleotide (NADH, produced by the prior reaction) and the oxidized form of the respective dye. Two of the dyes exhibited decreased absorption on reduction, whereas all (eight) tetrazolium dyes increased in their absorption substantially upon reduction. Bis-tetrazolium dyes had a significantly higher molar extinction coefficient (up to 23,000 M-1.cm-1) than mono-tetrazolium dyes (down to 8000 M-1.cm-1). Kinetically, most dyes could be reduced with NADH (and diaphorase), but the rate of reduction varied considerably among the dyes with nitroblue tetrazolium (NBT) and tetranitroblue tetrazolium (TNBT) being the fastest. Therefore, NBT and TNBT seem to be the most suitable for fast response.

Gravitational and magnetic activation methods applied to cultured cells (LK 35.2).

Monoclonal antibody 10.2-16 is directed toward the mouse class II major histocompatibility complex gene product 1-Ak expressed on the cell line LK35.2. Instead of activating cells by fluorophor we used (acrylamide-coated) heavy and magnetic microspheres of 0.6 micron in radius. These microspheres are chemically coupled (carbodiimide method) with the antibody toward the surface antigen. The cells are observed through a microscope with horizontal alignment, as they sediment in a (temperature controlled) tube with square cross-section. Stokes Law allows the determination of the density of cells (first alone) using viscosity and density of Dulbecco's modified Eagle's Medium together with the observed mean sedimentation velocity (66 microns/min) and a mean diameter of 10 microns. We found a density of 1.0558 +/- 0.0028 g/cm3 at 10 degrees C. Independently, thinly coated, heavy (and magnetizable) microspheres with the cited antibody are attached to cells and observed likewise. The increased sedimentation velocity permits us to show that the cells were fully covered with microspheres (290 per cell). A magnetic field gradient opposing gravity moved these cells against gravity with two different mean velocities, 340 microns/min and 850 microns/min. The higher velocity resulted in 290 particles per cell, the lower one in 130 particles per cell. The limits for the expansion of this method to smaller particle sizes (down to 10 nm) are evaluated.

Density of TEPC-15 plasmacytoma cells as function of size.

TEPC-15 plasmacytoma cells were observed under the microscope, as they sedimented at 1 G in Dulbecco's modified Eagle's medium. A mean density of 1.0422 g/cm3 (30 degrees C) was found. The density difference of smaller cells (15 micron diameter) was significantly higher than the density difference of larger cells (25 micron diameter). The ratio in density difference was close to 3.

Steady state enzyme kinetics for systems with three enzyme-binding species.

The steady state enzyme kinetics of those systems are discussed, which involve three species binding to enzymes. Two specific systems are considered. In one system, all three species bind only once to the enzyme. In the other system, two species bind once and one binds twice to the enzyme. The species are labeled S, A and B. The general case is considered, in which all possible complexes involving enzyme E and species S generate product P. Species A and B may become co-substrates, activators or inhibitors. The steady state enzyme kinetic equations for the general case for both systems are presented. These equations are further discussed for a number of special cases, which may be of interest to enzymologists and others using enzymes.

A stopped-flow investigation of calcium ion binding by ethylene glycol bis(beta-aminoethyl ether)-N,N'-tetraacetic acid.

The kinetics of calcium ion complexation by ethylene glycol bis(beta-aminoethyl ether)-N,N'-tetraacetic acid (EGTA) were investigated using the stopped-flow technique. This study was performed within the pH range 5.8 to 8.4. The reaction was found to be first order in EGTA and complex order in calcium, with an observed second-order rate constant (pH 7, T = 25 degrees C, ionic strength = 0.1 M) of about 1.5 X 10(6) M-1 s-1. The rate constant was independent of hydrogen ion concentration between pH 5.8 and 7.3; above pH 7.3 it increased in magnitude with increasing pH, and was 2.0 X 10(8) M-1 s-1 at pH 8.4. The rate constant at 16 and 38 degrees C (pH 6.8) was found to be 0.9 and 7 X 10(6) M-1 s-1, respectively. These data imply that calcium ion buffering by EGTA will require times on the order of milliseconds when EGTA is present in millimolar concentrations.

Chemical relaxation studies on the horse liver alcohol dehydrogenase system.

Chemical relaxation studies on the system horse liver alcohol dehydrogenase, nicotinamide adenine dinucleotide, and ethanol were conducted observing fluorescence changes between 400 and 500 nm. Temperature-jump experiments were performed at pH 6.5, 7.0, 8.0, and 9.0; concentration-jump experiments at pH 9.0. The reciprocal of the slowest relaxation time was found to be linearly dependent upon the enzyme concentration for relatively low enzyme concentrations, as predicted earlier. Use of the wide pH-range necessitated expression of the four apparent dissociation constants of the catalytic reaction cycle in terms of pH-independent constants. The system was described in terms of only one (or two) catalysis-linked protons not associated with the electron transfer. Protonic steps in a buffered system are in rapid equilibrium, too fast to be measured with the equipment available. Assuming only two of the four bimolecular reaction steps in the four-step cycle are fast compared to the remaining two, six cases may be considered with six expressions for the reciprocal of the slowest relaxation time. Comparison with the experimental data revealed that the bimolecular reaction steps governing the slowest relaxation time change with pH. Above the effective time resolution of the temperature-lump instrument with fluorescence detection (0.1 msec) only one other relaxation time was detectable and only at pH 9. This relaxation time, found to be independent of the concentration of all reactants within experimental error (r = 10 +/- 5 msec), is most likely due to an interconversion among ternary complexes.

Computer-based modeling in the teaching of steady-state enzyme kinetics.

Equations are derived for the steady-state treatment of enzyme reactions with one type of inhibitor, consisting of one reaction cycle or two connected cycles. Computerized stimulation programs are described which are designed to acquaint the student thoroughly with the behavior of enzyme systems. The user has freedom in the choice of parameters for the system, including up to three product-producing rate constants for the two-cycle system.

Chemical relaxation studies on the system liver alcohol dehydrogenase, NADH and imidazole.

Several years ago, Theorell and Czerlinski conducted experiments on the system of horse liver alcohol dehydrogenase, reduced nicotinamide adenine dinucleotide and imidazole, using the first version of the temperature jump apparatus with detection of changes in fluorescence. These early experiments were repeated with improved instrumentation and confirmed the early experiments in general terms. However, the improved detection system allowed to measure a slight concentration dependence of the relaxation time of around 3 ms. Furthermore, the chemical relaxation time was smaller than the one determined earlier (by factor 2). The data were evaluated much more rigorously than before, allowing an appropriate interpretation of the results. The observed relaxation time is largely due to rate constants in an interconversion of ternary complexes, which are faster than three (of the four) dissociation rate constants, determined previously by Theorell and McKinley-McKee.1,2 This fact contributed to earlier difficulties of finding any concentration dependence. However, the binding of imidazole to the binary enzyme-coenzyme complex can be made to couple kinetically into the interconversion rate of the two ternary complexes. The observed signal derives largely from the ternary complex(es). A substantial fluorescence signal change is associated with the observed relaxation process, suggesting a relocation of the imidazole in reference to the nicotinamide moiety of the bound coenzyme. Nine models are considered with two types of coupling of pre-equilibria (none-all). Quantitative evaluations favor the model with two ternary complexes connected by an interconversion outside the four-step (bimolecular) cycle. The ternary complex outside the cycle has much higher fluorescence yield than the one inside. The interconversion equilibrium is near unity for imidazole. If it would be shifted very much to the side of the "dead-end" complex (as in isobutyramide?!), stimulating action could not take place.

Coaxial alignment of laser beams for perturbation experiments.

An instrument is described for the coaxial alignment of two laser beams, one of which is a continuous wave helium-neon laser, the other one a pulsed neodynium glass laser. The helium-neon laser beam is aligned such that it propagates in the axis of the pulsed laser beam and thus permits observation of changes before, during, and after the occurrence of the pulsed laser event. Although the design emphasized the 1.35-mu sidebands of the neodymium laser, most tests were conducted at 1.06 mu, where neodymium in glass ordinarily operates. A residual nonlinearly polarized component of the pulsed laser light caused considerable disturbance in the detection circuit and prevented low level detection of perturbation effects.