Escherichia coli phosphoenolpyruvate carboxylase: kinetics and mechanism of inactivation

In dilute solution phosphoenolpyruvate carboxylase of Escherichia coli undergoes a spontaneous inactivation that can be described mathematically by a two-component declining exponential equation. The rate constant for the decay of the first component is 3.05 ± 0.52 × 10^?2 min^?, whereas that for the second component is variable, smaller in magnitude, and dependent upon the dilution conditions. Analysis of the coefficients for the exponential equation suggests that the decline of enzymatic activity with time is a function of the initial concentrations of catalytically active dimer and tetramer. From the concentrations of these two species, as determined from their initial activities, an equilibrium constant of 3 × 10^?7m for the tetramer-dimer dissociation was determined.The diluted enzyme exhibits properties similar to those ascribed to hysteretic enzymes. The appearance of hysteresis is a function of the time after dilution and the presence of modifiers of catalytic activity, i.e., it is not present immediately after dilution and can be prevented from occurring if aspartate is present in the dilution buffer. The data are consistent with a scheme in which dimeric and tetrameric forms of the enzyme undergo inactivation by dissociation to monomers. The tetramer can dissociate directly to monomers and become inactivated or it can dissociate first to dimers than to monomers before undergoing inactivation. Monomer-to-dimer reassociation occurs to form a catalytically active species, but monomer-to-tetramer reassociation to an active species is not apparent. Hysteresis is presumed to result from reversible isomerization of the monomeric species to a form that can also result in an irreversibly inactivated enzyme.     

Changes in catalytic activity and association state of pyruvate carboxylase which are dependent on enzyme concentration

The specific activity of chicken liver pyruvate carboxylase has been shown to decrease with decreasing enzyme concentration, even at 100 microM, which is close to the estimated physiological concentration. The kinetics of the loss of enzyme specific activity following dilution were biphasic. Incubation of dilution-inactivated enzyme with ATP, acetyl CoA, Mg2+ + ATP or, to a lesser degree, with Mg2+ alone resulted in a high degree of reactivation, while no reactivation occurred in the presence of pyruvate. The association state of the enzyme before, during, and after dilution inactivation has been assessed by gel filtration chromatography. These studies indicate that on dilution, there is dissociation of the catalytically active tetrameric enzyme species into inactive dimers. Reactivation of the enzyme resulted in reassociation of enzymic dimers into tetramers. The enzyme was shown to form high molecular weight aggregates at high enzyme concentrations.     

THE KINETICS OF THE DECOMPOSITION OF PEROXIDE BY CATALASE

It has been shown that the experimental results obtained by Morgulis in a study of the decomposition of hydrogen peroxide by liver catalase at 20°C. and in the presence of an excess of a relatively high concentration of peroxide are quantitatively accounted for by the following mechanisms. 1. The rate of formation of oxygen is independent of the peroxide concentration provided this is greater than about 0.10 M. 2. The rate of decomposition of the peroxide is proportional at any time to the concentration of catalase present. 3. The catalase undergoes spontaneous monomolecular decomposition during the reaction. This inactivation is independent of the concentration of catalase and inversely proportional to the original concentration of peroxide up to 0.4 M. In very high concentrations of peroxide the inactivation rate increases. 4. The following equation can be derived from the above assumptions and has been found to fit the experiments accurately. See PDF for Equation in which x is the amount of oxygen liberated at the time t, A is the total amount of oxygen liberated (not the total amount available), and K is the inactivation constant of the enzyme.     

The self-association of jack bean urease and its modification by silver ions.

At low ionic strength urease has been found to dissociate at protein concentrations below 1 × 10⁸m. The inhibition of enzyme activity by Ag⁺ has been used to demonstrate this. The inhibition by Ag⁺ has been shown to be independent of dissociation but, at dilutions where dissociation occurs, silver ion modifies the process. Urease is aggregated by Ag⁺ at high Ag⁺:protein ratios. Such inactive aggregates can be solubilized and reactivated by dithiothreitol. Further evidence has been obtained indicating the similarity of the (8n) and (16n) forms of urease. The phenomena of inhibition and aggregation in the presence of the heavy metal ion have been shown to be separate processes.     

THE NATURE AND CONTROL OF REACTIONS IN BIOLUMINESCENCE : WITH SPECIAL REFERENCE TO THE MECHANISM OF REVERSIBLE AND IRREVERSIBLE INHIBITIONS BY HYDROGEN AND HYDROXYL IONS,TEMPERATURE, PRESSURE,ALCOHOL, URETHANE,AND SULFANILAMIDE IN BACTERIA

On the basis of available data with regard to the chemical and physical properties of the "substrate" luciferin (LH₂) and enzyme, luciferase (A), and of kinetic data derived both from the reaction in extracts of Cypridina, and from the luminescence of intact bacteria, the fundamental reactions involved in the phenomenon of bioluminescence have been schematized. These reactions provide a satisfactory basis for interpreting the known characteristics of the system, as well as the theoretical chemistry with regard to the control of its over-all velocity in relation to various factors. These factors, here studied experimentally wholly with bacteria, Photobacterium phosphoreum in particular, include pH, temperature, pressure, and the drugs sulfanilamide, urethane, and alcohol, separately and in relation to each other. Under steady state conditions of bacterial luminescence, with excess of oxidizable substrate and with oxygen not limiting, the data indicate that the chief effects of these agents center around the pace setting reactions, which may be designated by the equation: A + LH₂ → ALH₂ following which light emission is assumed proportional to the amount of the excited molecule, AL*. The relation between pH and luminescence intensity varies with (a), the buffer mixture and concentration, (b), the temperature, and (c), the hydrostatic pressure. At an optimum temperature for luminescence of about 22° C. in P. phosphoreum, the effects of increasing or decreasing the hydrogen ion concentration are largely reversible over the range between pH 3.6 and pH 8.8. The relation between luminescence intensity and pH, under the experimental conditions employed, is given by the following equation, in which I ₁ represents the maximum intensity, occurring about pH 6.5; I ₂ the intensity at any other given pH; K ₅ the equilibrium constant between hydrogen ions and the AL_-; and K ₆ the corresponding constant with respect to hydroxyl ions: See PDF for Equation The value of K ₅, as indicated by the data, amounts to 4.84 x 10⁴, while that of K ₆ amounts to 4.8 x 10⁵. Beyond the range between approximately pH 3.8 and 8.8, destructive effects of the hydrogen and hydroxyl ions, respectively, were increasingly apparent. By raising the temperature above the optimum, the destructive effects were apparent at all pH, and the intensity of the luminescence diminished logarithmically with time. With respect to pH, the rate of destruction of the light-emitting system at temperatures above the optimum was slowest between pH 6.5 and 7.0, and increased rapidly with more acid or more alkaline reactions of the medium. The reversible effects of slightly acid pH vary with the temperature in the manner of an inhibitor (Type I) that acts independently of the normal, reversible denaturation equilibrium (K ₁) of the enzyme. The per cent inhibition caused by a given acid pH in relation to the luminescence intensity at optimum pH, is much greater at low temperatures, and decreases as the temperature is raised towards the optimum temperature. The observed maximum intensity of luminescence is thus shifted to slightly higher temperatures by increase in (H⁺). The apparent activation energy of luminescence is increased by a decrease in pH. The value of ΔH‡ at pH 5.05 was calculated to be 40,900 calories, in comparison with 20,700 at a pH of 6.92. The difference of 20,200 is taken to represent an estimate of the heat of ionization of ALH in the activation process, and compares roughtly with the 14,000 calories estimated for the same process, by analyzing the data from the point of view of hydrogen ions as an inhibitor. The decreasing temperature coefficient for luminescence in proceeding from low temperatures towards the optimum is accounted for in part by the greater degree of ionization of ALH. At the optimum temperature and acid reactions, pressures up to about 500 atmospheres retard the velocity of the luminescent oxidation. At the same temperature, with decrease in hydrogen ion concentration, the pressure effect is much less, indicating a considerable volume increase in the process of ionization and activation. In the extremely alkaline range, beyond pH 9, luminescence is greatly reduced, as compared with the intensity at neutrality, and under these conditions pressure causes a pronounced increase in intensity, presumably by acting upon the reversible denaturation equilibrium of the protein enzyme, A. Sulfanilamide, in neutral solutions, acts on luminescence in a manner very much resembling that of hydrogen ions at acidities between pH 4.0 and pH 6.5. Like the hydrogen ion equilibrium, the sulfanilamide equilibrium involves a ratio of approximately one inhibitor molecule to one enzyme molecule. The heat of reaction amounts to about 11,600 calories or more in a reversible combination that evidently evolves heat. Like the action of H ions, sulfanilamide causes a slight shifting of maximum luminescence intensity in the direction of higher temperatures, and an increase in the energy of activation. The effect of sulfanilamide on the growth of broth cultures of eight species of luminous bacteria indicates that there is no regular relationship among the different organisms between the concentration of the drug that prevents growth, and that which prevents luminescence in the cells which develop in the presence of sulfanilamide. p-Aminobenzoic acid (PAB) antagonizes the sulfanilamide inhibition of growth in luminous bacteria, and the cultures that develop are luminous. When (PAB) is added to cells from fully developed cultures, it has no effect on luminescence, or causes a slight inhibition, depending on the concentration. With luminescence partly inhibited by sulfanilamide, the addition of PAB has no effect, or has an inhibitory effect which adds to that caused by sulfanilamide. Two different, though possibly related, enzyme systems thus appear to limit growth and luminescence, respectively. The possible mechanism through which both the inhibitions and the antagonism take place is discussed. The irreversible destruction of the luminescent system at temperatures above that of the maximum luminescence, in a medium of favorable pH to which no inhibitors have been added, proceeds logarithmically with time at both normal and increased hydrostatic pressures. Pressure retards the rate of the destruction, and the analysis of the data indicates that a volume increase of roughly 71 cc. per gm. molecule at 32° C. takes place in going from the normal to the activated state in this reaction. At normal pressure, the rate of destruction has a temperature coefficient of approximately 90,000 calories, or about 20,000 calories more than the heat of reaction in the reversible denaturation equilibrium. The data indicate that the equilibrium and the rate process are two distinct reactions. The equation for luminescence intensity, taking into account both the reversible and irreversible phases of the reaction is given below. In the equation b is a proportionality constant; k'' the rate constant of the luminescent reaction; A₀ the total luciferase; A_0i the total initial luciferase at time t equals 0; k_n the rate constant for the destruction of the native, active form of the enzyme; k_d the rate constant for the destruction of the reversibly denatured, inactive form; t the time; and the other symbols are as indicated above: See PDF for Equation For reasons cited in the text, k_n evidently equals k_d. Urethane and alcohol, respectively, act in a manner (Type II) that promotes the breaking of the type of bonds broken in both the reversible and irreversible reactions and so promotes the irreversible denaturation. This result is in contrast to the effects of sulfanilamide, which at appropriate concentrations may give rise to the same initial inhibition as that caused by urethane, but remains constant with time. The inhibition caused by urethane and alcohol, respectively, increases as the temperature is raised. As a result, the apparent optimum is shifted to lower temperatures, and the activation energy for the over-all process of luminescence diminishes. An analysis for the approximate heat of reaction in the equilibrium between these drugs and the enzyme, indicates 65,000 calories for urethane, and 37,000 for alcohol. A similar analysis with respect to the effect of hydroxyl ions as the inhibitor gives 60,300 calories. The effects of alcohol and urethane are sensitive to hydrostatic pressure. Moderate inhibitions at optimum temperature and pH, caused by relatively small concentrations of either drug, are completely abolished by pressures of 3,000 to 4,000 pounds per square inch. At optimum temperature and pH, increasing concentrations of alcohol caused the apparent optimum pressure for luminescence to shift markedly in the direction of higher pressures. Analysis of the data with respect to concentration of alcohol at different pressures indicated that the ratio of alcohol to enzyme molecules amounted to approximately 4, at 7,000 pounds, but only about 2.8 at normal pressures. This phenomenon was taken to indicate that more than one equilibrium is established between the alcohol and the protein. A similar interpretation was suggested in connection with the fact that analysis of the relation between concentration of urethane and amount of inhibition at different temperatures also indicated a ratio of urethane to enzyme molecules that increased with temperature in the equilibria involved. Analysis of the data with respect to pressure and the inhibition caused by a given concentration of alcohol at different temperatures indicated that the volume change involved in the combination of alcohol with the enzyme must be very small, while the actual effect of pressure is apparently mediated through the reversible denaturation of the protein enzyme, which is promoted by alcohol, urethane, and drugs of similar type.     

THE COUPLED REDOX POTENTIAL OF THE LACTATE-ENZYME-PYRUVATE SYSTEM

1. The term "coupled redox potential" is defined. 2. The system lactic ion See PDF for Equation pyruvic ion + 2H⁺ + 2e is shown to be reversible (when the enzyme is lactic acid dehydrogenase) and its coupled redox potential between pH 5.2 and 7.2 at 32°C. is: See PDF for Equation 3. The free energy of the reaction: lactic ion (1m) → pyruvic ion (1m) = -ΔF = –14,572. 4. The standard free energy of formation (ΔF ₂₉₈) of pyruvic acid (l) is estimated at –108,127. This is merely an approximation as some necessary data are lacking. 5. The importance of coupled redox potentials as a factor in the regulation of the equilibrium of metabolites is indicated.     

CONTRIBUTION TO THE THEORY OF PERMEABILITY OF MEMBRANES FOR ELECTROLYTES

On page 39, Vol. viii, No. 2, September 18, 1925, multiply the right-hand side of formula (2) by the factor See PDF for Equation. On page 44, immediately after formula (1) the text should be continued as follows: Let us suppose a membrane to be separated by two solutions of KCl of different concentrations K₁ and K₂ and these concentrations and the corresponding concentrations of K⁺ within the membrane, which are in equilibrium with the outside solutions, to be so high that the H⁺ ions may be neglected. When a small electric current flows across the system, practically the K⁺ ions alone are transferred and that in a reversible manner. Therefore the total P.D. is practically See PDF for Equation This P.D. is composed of two P.D.''s at the boundaries and the diffusion potential within the membrane. Suppose the immobility of the anions is not absolute but only relative as compared with the mobility of the cations, KCl would gradually penetrate into the membrane to equal concentration with the outside solution on either side and no boundary potential would be established. In this case the diffusion P.D. within the membrane is the only P.D., amounting to See PDF for Equation but, V being practically = 0, it would result that See PDF for Equation So the definitive result is the same as in the former case. Now cancel the printed text as far as page 48, line 13 from the top of the page, but retain Fig. 1. On page 50, line 19 from the top of the page, cancel the sentence beginning with the word But and ending with the words of the chain.     

New Perspectives in the Renin-Angiotensin-Aldosterone System (RAAS) I: Endogenous Angiotensin Converting Enzyme (ACE) Inhibition

Angiotensin-converting enzyme (ACE) inhibitors represent the fifth most often prescribed drugs. ACE inhibitors decrease 5-year mortality by approximately one-fifth in cardiovascular patients. Surprisingly, there are reports dating back to 1979 suggesting the existence of endogenous ACE inhibitors, which endogenous inhibitory effects are much less characterized than that for the clinically administered ACE inhibitors. Here we aimed to investigate this endogenous ACE inhibition in human sera. It was hypothesized that ACE activity is masked by an endogenous inhibitor, which dissociates from the ACE when its concentration decreases upon dilution. ACE activity was measured by FAPGG hydrolysis first. The specific (dilution corrected) enzyme activities significantly increased by dilution of human serum samples (23.2±0.7 U/L at 4-fold dilution, 51.4±0.3 U/L at 32-fold dilution, n = 3, p = 0.001), suggesting the presence of an endogenous inhibitor. In accordance, specific enzyme activities did not changed by dilution when purified renal ACE was used, where no endogenous inhibitor was present (655±145 U/L, 605±42 U/L, n = 3, p = 0.715, respectively). FAPGG conversion strongly correlated with angiotensin I conversion suggesting that this feature is not related to the artificial substrate. Serum samples were ultra-filtered to separate ACE (MW: 180 kDa) and the hypothesized inhibitor. Filtering through 50 kDa filters was without effect, while filtering through 100 kDa filters eliminated the inhibiting factor (ACE activity after <100 kDa filtering: 56.4±2.4 U/L, n = 4, control: 26.4±0.7 U/L, n = 4, p<0.001). Lineweaver-Burk plot indicated non-competitive inhibition of ACE by this endogenous factor. The endogenous inhibitor had higher potency on the C-terminal active site than N-terminal active site of ACE. Finally, this endogenous ACE inhibition was also present in mouse, donkey, goat, bovine sera besides men (increasing of specific ACE activity from 4-fold to 32-fold dilution: 2.8-fold, 1.7-fold, 1.5-fold, 1.8-fold, 2.6-fold, respectively). We report here the existence of an evolutionary conserved mechanism suppressing circulating ACE activity, in vivo, similarly to ACE inhibitory drugs.     

KINETICS OF THE BIOLUMINESCENT REACTION IN CYPRIDINA. II

1. The decay curve of the light produced in the course of the luminescent reaction in Cypridina is, after the first second, in complete agreement with the theoretical expectation for a monomolecular reaction, if light intensity at any instant is assumed to be proportional to reaction velocity at that instant. It is shown that for such a reaction log I = - kt + log Ak and that the experimental values satisfy this equation. 2. The first second or two of the reaction is characterized by a brilliant initial flash, whose value is much too high to accord with the succeeding intensities and with the above formula. It is suggested that this initial high reaction velocity is an indication of a heterogeneous system. 3. Identical solutions run simultaneously give decay curves which check within the limits of the photographic error. 4. Stirring does not affect the reaction velocity or the form of the decay curve. 5. Reaction velocity is proportional to enzyme concentration, over the range of concentrations used in the study. 6. Changes in the concentration of the substrate do not affect the value of k, when all other factors are held constant. A diminution of luciferin concentration results only in a decrease in the value of the y-intercept, Log Ak, the two straight line plottings for two different concentrations being parallel. 7. The temperature coefficient is high, being about 4.5 for the 15–25° interval, and 3.0 for the 25–35° interval.     

THE SPECIFIC INTERACTION OF S-100 PROTEIN WITH SYNAPTOSOMAL PARTICULATE FRACTIONS. SITE-SITE INTERACTIONS AMONG S-100 BINDING SITES1

Abstract— The Scatchard plot of the specific binding of the brain-specific S-100 protein to synaptosomal particulate fractions (SYN) is curvilinear, concave upwards. This could indicate the existence either of multiple classes of sites with different but fixed affinities, or of site-site interactions of the type defined as negative cooperativity among a single class of sites. To discriminate between these possibilities, the dissociation test described by De Meyts et al. (1976) for demonstrating negative cooperativity among insulin binding sites of human lymphocytes or liver membranes, was applied to the interaction of S-100 with SYN. The results show that the dissociation of the ¹²⁵I-labelled S-100-site complex is faster due to an ‘infinite’(100-fold) dilution of the complex plus an excess of unlabelled S-100 than due to dilution only, the effect of unlabelled S-100 being specific and dose-dependent. ¹²⁵I-IabeIIed S-100 dissociation is time, temperature, and Ca^{2 +}-dependent. The effect of unlabelled S-100 is more evident at a low site occupancy than at a high one, suggesting that at high site occupancies ¹²⁵I-labelled S-100 binding sites could be already negatively cooperating. It can be reasonably excluded that the effect of unlabelled S-100 is due to inhibition of rebinding of the dissociated tracer. Na⁺ and K⁺ stimulate the dissociation even at physiological concentrations. At low pH ¹²⁵I-labelled S-100 dissociates very little, while at high pH dissociation is greatly stimulated. Finally, the protein denaturating reagent urea accelerates the dissociation even at concentrations as low as 1m. These data suggest that negative cooperativity occurs among S-100 binding sites, but do not exclude other possibilities. Together with previously reported findings, they further support the view that S-100 binds to highly specific sites in nervous membranes.     

FURTHER STUDIES ON THE INDUCTION OF THE DRUG-HYDROXYLATING ENZYME SYSTEM OF LIVER MICROSOMES

Further studies of the induction of the liver microsomal drug-hydroxylating enzyme system by pretreatment of rats with various drugs are presented. The phenobarbital-induced increase in the microsomal content of CO-binding pigment and in the activities of TPNH-cytochrome c reductase and the oxidative demethylation of aminopyrine is proportional, within certain limits, to the amount of phenobarbital injected. Removal of the inducer results in a parallel decrease in the levels of CO-binding pigment, TPNH-cytochrome c reductase, and aminopyrine demethylation. Other inducing drugs have been investigated and shown to act similarly to phenobarbital. The early increase in these enzymes is found in the microsomal subfraction consisting of rough-surfaced vesicles, whereas repeated administration of the inducing drug results in a concentration of the enzymes in the smooth-surfaced vesicles. The phenobarbital-stimulated formation of endoplasmic membranes is reflected in increased amounts of the various microsomal phospholipid fractions as revealed by thin layer chromatography. There is no significant difference between the stimulated rates of P_i³² incorporation into phospholipids of the two different microsomal subfractions in response to phenobarbital treatment. The drug-induced enzyme synthesis is unaffected by adrenalectomy.     

PHOSPHATE ION AS A PROMOTER CATALYST OF RESPIRATION

The active component of phosphate solutions, in relation to promoter action on oxidising enzymes, is the PO₄ ^'''''' ion. This is shown by the demonstration of a hyperbolic relationship between per cent production of CO₂ (of Elodea) and pPO₄, the measure of the phosphate ion potential. This is consistent with the rate of respiration as affected by changing pPO₄ through change of total phosphate concentration while pH is kept constant. The equation for this relationship is (CO₂ – a) (pPO₄ – b)ⁿ = K where a, b, n, and K are constants and n = 1. The same relationship to phosphate ion concentration, expressed by the equation (Activity of enzyme) (pPO₄)ⁿ = K, where n and K are constants and n varies from 1 to 6 under different conditions, appears to hold for some other enzyme actions, including those of peroxidase and pancreatic lipase.     

Buffer-dependent variations in assay of tyrosine aminotransferase holoenzyme

Homogenization of rat liver in Hepes (N-2-hydroxyethylpiperazine-N′-2-ethane-sulfonic acid), MOPS (2-[N-morpholino]ethanesulfonic acid), Na phosphate, Pipes (piperazine-N,N′-bis[2-ethanesulfonic acid]), TEA (triethanolamine), TES (N-tris[hydroxymethyl]-methyl-2-aminoethanesulfonic acid), Tricine (N-tris-[hydroxymethyl]methylglycine), or Tris (tris[hydroxymethyl]aminomethane), and subsequent assay for supernatant total and holo tyrosine aminotransferase activity using these buffers yields apparent enzyme concentrations which vary depending upon the buffer composition, the ionic strength, and the fold-dilution of the supernatant. A precipitous decrease in the apparent holoenzyme concentration results from a slight dilution of the supernatant with most of the buffers. Some of the dilution effects may be due to dissociation of pyridoxal phosphate from the apoenzyme or to competition between the buffer and pyridoxal phosphate for association with the enzyme. The percentage of the apparent total enzyme which exists as holoenzyme varies from 3% for supernatant prepared in Na phosphate buffer up to 94% for that prepared in Hepes. Inactivation of total enzyme activity occurs to a similar extent resulting from incubation of liver homogenates prepared with Na phosphate, Hepes, or Pipes. The residual apparent holoenzyme activity observed when assayed in the presence of Na phosphate may be due to reaction of an enzyme other than tyrosine aminotransferase. The data provide a basis for explaining the large variation in reported percentage holoenzyme and should also serve as a warning for other holoenzyme assays which use pyridoxal phosphate as a cofactor.     

STUDIES ON THE AMOUNT OF LIGHT EMITTED BY MIXTURES OF CYPRIDINA LUCIFERIN AND LUCIFERASE

1. A photometric method was devised for measuring the intensities of light emitted per cc. of hiciferin solution and calculating the amount of light emitted per gm. of dried Cypridina powder. A total of 128 runs was made and the data are incorporated in this report. 2. The maximum amount of light emitted from 1 gm. of powder under the experimental conditions was 0.655 lumens. Different samples of powder vary greatly in amount of light production. 3. When the concentration of substrate is doubled, nearly twice as much light is emitted, or an average ratio 2C/C of 1.86. Calculations of total light emissions per gm. of powder at different concentrations indicate that slightly more light is produced from the smaller concentrations. The maximum amount of light was produced by the solutions made with neutral sea water and averaged 0.445 lumens. The least light was obtained from solutions in distilled water saturated with hydrogen. The technique allows too rapid spontaneous oxidation prior to the saturation with hydrogen. The maximum amount of light from such experiments was only 0.077 lumens. Acid sea water solutions subsequently neutralized gave an average maximum of 0.386 lumens per gm. of powder per second. 4. When the concentration of enzyme is doubled, approximately the same amount of light is produced by both concentrations, although the stronger concentrations are slightly less effective than weaker ones. This undoubtedly is due to the colloidal nature of the enzyme and is a function of surface rather than of mass. In dilute solutions greater dispersion probably allows for greater adsorption to the surface of the enzyme. The average maximum amount of light produced in the series of enzyme experiments is of the magnitude 0.56 lumens per gm. of powder.     

The theoretical analysis of kinetic behaviour of "hysteretic" allosteric enzymes. IV. Kinetics of dissociation-association processes of allosteric enzymes.

The kinetics of equilibration of dissociating enzyme system

$\text{2}\text{p}\text{?}\text{k ? 0}\text{k + 0}\text{P}$

(P is enzyme oligomer which is able to dissociate reversibly forming two identical halves p) is analysed after changes in storage conditions or after addition of allosteric ligands. The expressions for changes in the proportions of p and P forms with time and the expressions for dependence of initial rate of dissociation-association processes and half-life time on enzyme concentration or allosteric ligand concentration are deduced. It is shown that the dependences of intial rate of dissociation-association processes on allosteric ligand concentration has co-operative character at definite values of kinetic parameters. The graphic methods of determination of the first-order rate constant for dissociation (k_?0) and the second-order rate constant for association (k₊₀) are developed. The experimental kinetic data of dissociation of L-threonine dehydratase, glycogen phosphorylase a and aspartic-β-semialdehyde dehydrogenase are used for illustration of applicability of deduced expression.     

Slow,Reversible, Coupled Folding and Binding of the Spectrin Tetramerization Domain

Many intrinsically disordered proteins (IDPs) are significantly unstructured under physiological conditions. A number of these IDPs have been shown to undergo coupled folding and binding reactions whereby they can gain structure upon association with an appropriate partner protein. In general, these systems display weaker binding affinities than do systems with association between completely structured domains, with micromolar K_d values appearing typical. One such system is the association between α- and β-spectrin, where two partially structured, incomplete domains associate to form a fully structured, three-helix bundle, the spectrin tetramerization domain. Here, we use this model system to demonstrate a method for fitting association and dissociation kinetic traces where, using typical biophysical concentrations, the association reactions are expected to be highly reversible. We elucidate the unusually slow, two-state kinetics of spectrin assembly in solution. The advantages of studying kinetics in this regime include the potential for gaining equilibrium constants as well as rate constants, and for performing experiments with low protein concentrations. We suggest that this approach would be particularly appropriate for high-throughput mutational analysis of two-state reversible binding processes.     

SENSORY ADAPTATION AND THE STATIONARY STATE

1. Experiments are described which measure the sensitivity of animals exposed to continued illumination to which they have become adapted. It is shown that the amount of outside light energy necessary to stimulate an adapted animal increases with the intensity of the adapting illumination. 2. The data are analyzed quantitatively in terms of the reversible reaction S ⇌ P + A shown previously to account for the photic sensitivity of these animals. This analysis demonstrates that, though the amount of incident energy necessary for a minimal response varies with the adapting intensity, the actual amount of photochemical decomposition required to set off the sensory mechanism is a constant quantity. 3. The ability of these animals to come into sensory equilibrium with any sustained illumination is accounted for quantitatively by the presence of a stationary state in the reversible photochemical reaction S ⇌ P + A during which the concentrations of the three components are constant. 4. It is shown that the concentrations of these substances at the stationary state are automatically controlled by the outside intensity. Therefore, given the sensory mechanism as a basis, the adaptation of the animals to light and the consequent changes in sensitivity, are determined entirely by the light to which the animals are exposed. 5. Because of the properties of the stationary state, and of the constancy of photochemical decomposition for a minimal effect, it is suggested that the sensory system is not only the traditional receptor system, but is also a protecting layer which stabilizes and buffers the relation between the nervous system and the environment.     

Analysis of Biochemical Equilibria Relevant to the Immune Response: Finding the Dissociation Constants

This paper analyzes the biochemical equilibria between bivalent receptors, homo-bifunctional ligands, monovalent inhibitors, and their complexes. Such reaction schemes arise in the immune response, where immunoglobulins (bivalent receptors) bind to pathogens or allergens. The equilibria may be described by an infinite system of algebraic equations, which accounts for complexes of arbitrary size n (n being the number of receptors present in the complex). The system can be reduced to just 3 algebraic equations for the concentrations of free (unbound) receptor, free ligand and free inhibitor. Concentrations of all other complexes can be written explicitly in terms of these variables. We analyze how concentrations of key (experimentally-measurable) quantities vary with system parameters. Such measured quantities can furnish important information about dissociation constants in the system, which are difficult to obtain by other means. We provide analytical expressions and suggest specific experiments that could be used to determine the dissociation constants.     

Trans-membrane transport of n-octadecane by Pseudomonas sp. DG17

The trans-membrane transport of hydrocarbons is an important and complex aspect of the process of biodegradation of hydrocarbons by microorganisms. The mechanism of transport of ¹⁴C n-octadecane by Pseudomonas sp. DG17, an alkane-degrading bacterium, was studied by the addition of ATP inhibitors and different substrate concentrations. When the concentration of n-octadecane was higher than 4.54 μmol/L, the transport of ¹⁴C n-octadecane was driven by a facilitated passive mechanism following the intra/extra substrate concentration gradient. However, when the cells were grown with a low concentration of the substrate, the cellular accumulation of n-octadecane, an energy-dependent process, was dramatically decreased by the presence of ATP inhibitors, and n-octadecane accumulation continually increased against its concentration gradient. Furthermore, the presence of non-labeled alkanes blocked ¹⁴C n-octadecane transport only in the induced cells, and the trans-membrane transport of n-octadecane was specific with an apparent dissociation constant K _t of 11.27 μmol/L and V _max of 0.96 μmol/min/mg protein. The results indicated that the trans-membrane transport of n-octadecane by Pseudomonas sp. DG17 was related to the substrate concentration and ATP.