The linkage between oxygenation and subunit dissociation in human hemoglobin. Consequences for the analysis of oxygenation curves.

For human hemoglobin, a pronounced dependence of oxygenation curves upon protein concentration can be demonstrated experimentally in the range between 10(-4) and 2 X 10(-6) M heme. The effects of such protein concentration dependence upon analysis of saturation curves have been explored using a model-independent linkage analysis which incorporates the dissociation of tetramers to dimers. We have carried out stimulations of oxygenation curves representing a variety of energy distributions designed to cover a wide range of values which are relevant to known hemoglobin systems and experimental conditions. The resulting simulated oxygenation curves were analyzed by least-squares minimization procedures in terms of the tetramer binding isotherm to yield the four apparent Adair constants. These derived constants were compared with the originally assumed values used in the simulation in order to assess the extent to which their values may be altered by the presence of dimer. For each energy distribution the analysis has been carried out over a wide range of protein concentration. We have found that the presence of even small amounts of dimer that are necessarily present at the low protein concentrations commonly employed may have a devastating effect upon the reliability of Adair constant determinations. In addition to these simulated cases, we have analyzed two sets of highly precise experimental data from the literature in order to assess the degree to which constants obtained may have been influenced by the presence of dimer.     

Theory for modeling the copolymerization of tubulin and tubulin-colchicine complex

Substoichiometric concentrations of tubulin-colchicine complex (TC) inhibits microtubule assembly through a copolymerization reaction between tubulin and TC. We have determined the rates and extent of TC incorporation into bovine brain microtubules and developed a theory that models copolymerization. Our analysis suggests that while the apparent association rate constants for tubulin and TC are similar, the apparent dissociation rate constants for TC are a factor of five or more larger than those of tubulin. Copolymer composition showed only slight changes during assembly despite changes in the solution phase and showed little dependence at high TC upon the initial tubulin concentration. The theory was based on coupled Oosawa-Kasai equations that allow for the co-assembly of two components, tubulin and TC. An expression was derived that relates copolymer composition to reaction mixture composition and to the affinity of microtubule ends for tubulin and TC. This expression predicts copolymer composition at TC concentrations less than 10 microM and correlates composition with assembly inhibition. We perceive copolymerization as a facilitated incorporation of TC requiring the presence of tubulin. TC incorporation was dependent on the ratio of total tubulin to the dissociation constant for TC bound to microtubule ends. The copolymerization reaction is thus characterized by an interplay of two effects (a) where tubulin facilitates the incorporation of TC into the microtubule, and (b) where TC inhibits the assembly of tubulin into microtubules.     

Polyelectrolyte effects on site-binding equilibria with application to the intercalation of drugs into DNA

A theory of polyelectrolyte effects on site-binding equilibria is generalized to multivalent ligands, multivalent supporting salt, intercalation, and multiple-site exclusion. The theory, which contains no adjustable parameters, except the number of sites excluded by a bound ligand, gives the dependence of the equilibrium constant on the binding fraction and the salt concentration. The theory is compared with prior experimental data for the dissociation of poly(acrylic acid), the binding of magnesium to polyphosphate, and the binding of ethidium and actionomycin D to DNA. The theory predicts the binding fraction dependence of the dissociation constant of poly(acrylic acid) well. The theory predicts the binding fraction dependence of the association constant of the binding of Mg²⁺ to polyphosphate well, if either one or two phosphates are bound by a magnesium ion. We conclude that polyelectrolyte effects on drug-DNA equilibria must be substantial. It follows that an incorrect estimate of the number of sites excluded by a bound drug molecule (because of its size or some other nonpolyelectrolyte effect) can be obtained from binding data if polyelectrolyte effects are ignored. The estimate is also within the context of, and subject to the validity of, the model used to describe the nonpolyelectrolyte contribution to binding. Our results suggest that, subject to these conditions, the anticooperativity of the binding of ethidium to DNA might be explained solely in terms of polyelectrolyte effects, and without reference to multiple-site exclusion, if sequence-specificity effects can be safely ignored. Our results also suggest that as few as two base pairs might be excluded by an actinomycin molecule. The theory gives fairly good agreement for the salt-concentration dependence of the association constant of all of the systems studied, including the complex of the neutral drug actinomycin with DNA.     

Interaction of effecting ligands with lac repressor and repressor-operator complex.

The equilibrium association constants for the binding of a wide variety of effecting ligands of the lac repressor were measured by equilibrium dialysis. Also, detailed investigations of the apparent rate of dissociation of repressor-operator comples as a function of ligand concentration were carried out for several inducers and anti-inducers. The affinity of repressor-ligand comples for operator DNA was evaluated from the specific rate constants at saturating concentrations of effecting ligand. By fitting the experimental data depicting the functional dependence of the rate of dissociation upon ligand concentrations to calculated curves, assuming simple models of the induction mechanism, the equilibrium association constant for the binding of effecting ligand to repressor-operator comples was determined. Inducers reduce the affinity of lac repressor for operator DNA by a factor of approximately 1000 under standard conditions; the extent of destabilization depends on Mg2+ ion concentration. Anti-inducers increase the affinity of repressor for operator at most a factor of five. Only one neutral ligand, which binds to repressor without altering the stability of repressor-operator comples, was found. No homotropic or heterotropic interactions in the binding of effecting ligands either to repressor or to repressor-operator complex are evident.     

Pressure-jump studies of the folding/unfolding of trp repressor.

The dimeric protein, trp apo-repressor of Escherichia coli has been subjected to high hydrostatic pressure under a variety of conditions, and the effects have been monitored by fluorescence spectroscopic and infra-red absorption techniques. Under conditions of micromolar protein concentration and low, non-denaturing concentrations of guanidinium hydrochloride (GuHCl), tryptophan and 8-anilino-1-naphthalene sulfonate (ANS) fluorescence detected high pressure profiles demonstrate that pressures below 3 kbar result in dissociation of the dimer to a monomeric species that presents no hydrophobic binding sites for ANS. The FTIR-detected high pressure profile obtained under significantly different solution conditions (30 mM trp repressor in absence of denaturant) exhibits a much smaller pressure dependence than the fluorescence detected profiles. The pressure-denatured form obtained under the FTIR conditions retains about 50 % alpha-helical structure. From this we conclude that the secondary structure present in the high pressure state achieved under the conditions of the fluorescence experiments is at least as disrupted as that achieved under FTIR conditions. Fluorescence-detected pressure-jump relaxation studies in the presence of non-denaturing concentrations of GuHCl reveal a positive activation volume for the association/folding reaction and a negative activation volume for dissociation/unfolding reaction, implicating dehydration as the rate-limiting step for association/folding and hydration as the rate-limiting step for unfolding. The GuHCl concentration dependence of the kinetic parameters place the transition state at least half-way along the reaction coordinate between the unfolded and folded states. The temperature dependence of the pressure-jump fluorescence-detected dissociation/unfolding reaction in the presence of non-denaturing GuHCl suggests that the curvature in the temperature dependence of the stability arises from non-Arrhenius behavior of the folding rate constant, consistent with a large decrease in heat capacity upon formation of the transition state from the unfolded state. The decrease in the equilibrium volume change for folding with increasing temperature (due to differences in thermal expansivity of the folded and unfolded states) arises from a decrease in the absolute value for the activation volume for unfolding, thus indicating that the thermal expansivity of the transition state is similar to that of the unfolded state.     

Effects of ionic strength on the regulation of Na/H exchange and K-Cl cotransport in dog red blood cells

Dog red cell membranes contain two distinct volume-sensitive transporters: swelling-activated K-Cl cotransport and shrinkage- activated Na/H exchange. Cells were prepared with intracellular salt concentration and weight percentage of cell water (%cw) varied independently by transient permeabilization of the cell membrane to cations. The dependence of transporter-mediated Na and K influxes upon %cw and upon extracellular salt concentration (c(ext)) was measured in cells so prepared. It was found that the critical value of %cw at which transporters are activated, called the set point, is similar for the two transporters, and that the set points for the two transporters decrease similarly with increasing extracellular salt concentration. These findings suggest a common mechanism of regulation of these two transporters. Cellular Na, K, and Cl concentrations were measured as functions of %cw and c(ext). Using these data together with data from the literature for other solute concentrations, empirical expressions were developed to describe the dependence of the intracellular concentrations of all significant small molecule electrolytes, and therefore the intracellular ionic strength, upon %cw and c(ext). A mechanistic model for the dependence of the set point of an individual transporter upon intracellular ionic strength is proposed. According to this model, the set point represents a critical extent of association between the transporter and a postulated soluble regulatory protein, called regulator. Model functions are presented for the calculation of the thermodynamic activity of regulator, and hence extent of regulator- transporter association, as a function of total intracellular protein concentration (or %cw) and ionic strength. The experimentally observed dependence of set point %cw on c(ext) are simulated using these functions and the empirical expressions described above, together with reasonable but not uniquely determined values of model parameters.     

Rate constants for binding, dissociation, and internalization of EGF: effect of receptor occupancy and ligand concentration

We measured the kinetic parameters for interaction of epidermal growth factor (EGF) with fetal rat lung (FRL) cells under two sets of experimental conditions and applied sensitivity analysis to see which parameters were well-defined. In the first set of experiments (method 1), the kinetics of internalization and dissociation of radiolabeled EGF were measured with a temperature-shift protocol in medium initially devoid of free ligand. The initial concentration of radiolabeled EGF bound to the cell surface corresponded to levels of receptor occupancy ranging from approximately 200 receptors per cell to approximately 18,000 receptors per cell, a level at which EGF binding approaches saturation. In the second set of experiments (method 2), carried out at a constant temperature, we began with no surface-bound or internalized ligand. The initial free ligand concentration was varied from 0.2 to 50 ng/mL. In both sets of experiments, we measured surface-bound, internalized, and free 125I-EGF as functions of time and evaluated the parameters of a mathematical model of endocytosis. Sensitivity analysis showed that three rate constants were well-defined in this combination of two experimental approaches: ke, the endocytic rate constant; ka, the association rate constant; and kd, the dissociation rate constant. The endocytic parameter ke was found to be independent of initial surface receptor occupancy (method 1); there was some indication that it increased with initial free ligand concentration in method 2. Neither kd nor ka was found to change with extent of initial surface receptor occupancy or initial free ligand concentration, respectively, a finding of significance, since diffusion theory predicts these parameters will vary with surface receptor occupancy.(ABSTRACT TRUNCATED AT 250 WORDS)     

Kinetics of gonadotropin binding by receptors of the rat testis. Analysis by a nonlinear curve-fitting method.

The kinetics of the reaction between human chorionic gonadotropin (hCG) and specific gonadotropin receptors in the rat testis were determined at 24 and 37 degrees, over a wide range of hormone concentrations. Hormone concentrations were corrected for the binding activity of the (-125I)hCG tracer preparations. Analysis of the experimental data was performed with an interactive nonlinear curve fitting program, based upon the second-order chemical kinetic differential equation. The mean values for the association rate constant (k1) were 4.7 x 10-7 M-1 min-1 at 24 degrees, and 11.0 x 10-7 M-1 min-1 at 37 degrees. At both temperatures, the values of kl were independent of hormone concentration. Initial dissociation rates were consistent with first order kinetics, with dissociation rate constant (k2) of 1.7 x 10 minus -3 and 4.6 x 10 minus -3 min minus -1 at 24 and 37 degrees, respectively. When studied over longer periods at 24 degrees, the dissociation process appeared to be multiexponential. The kinetics of degradation of (-125I)hCG and receptors were determined at both temperatures, and a mathematical model was developed by modification of the second-order chemical kinetic differential equation to take these factors into account. The application of such a model to hCG kinetic binding data demonstrated that reactant degradation had little significant effect on the derivation of the association rate constant (k1), but caused significant overestimation of the dissociation rate constant (k2) values derived from association experiments. The model was also applied by computer simulation to a theoretical analysis of the effects of degradation of free hormone and receptor sites upon kinetic and steadystate binding data. By this method, the initial velocities of hormone binding were shown to be less affected by degradation than the steady-state levels of hormone-receptor complex. Also, reactant degradation in simulated steady-state experiments caused an underestimate of the apparent equilibrium association constant, but had relatively less effect on the determination of binding site concentration.     

Concentration dependence of the subunit association of oligomers and viruses and the modification of the latter by urea binding.

A theoretical model is presented that accounts for the facilitation of the pressure dissociation of R17 phage, and for the partial restoration of the concentration dependence of the dissociation, by the presence of subdenaturing concentrations of urea. As an indifferent osmolyte urea should promote the stability of the protein aggregates under pressure, and the decrease in pressure stability with urea concentration demonstrates that such indirect solvent effects are not significant for this case, and that the progressive destabilization is the result of direct protein-urea interactions. By acting as a "homogenizer" of the properties of the phage particles, urea addition converts the pressure-induced deterministic dissociation of the phage into a limited stochastic equilibrium. The model establishes the origin of the uniform progression from the stochastic equilibrium of dimers, to the temperature-dependent and partially concentration-dependent association of tetramers, to the fully deterministic equilibrium observed in many multimers and in the virus capsids.     

Kinetics and thermodynamics of ouabain binding by intact turkey erythrocytes: effects of external sodium ion, potassium ion, and temperature

The kinetics of association and dissociation for the ouabain-Na+,K+- dependent ATPase complex have been studied in intact turkey erythrocytes as a function of external Na+ concentration, K+ concentration, and temperature. At free ligand concentrations substantially exceeding the concentration of available binding sites, the association reaction exhibits pseudo-first-order kinetics with an association rate constant (k1) that is conveniently determined over a wide range of temperatures (5-37 degrees C). The dissociation reaction exhibits strict first-order kinetics with a dissociation rate constant (k-1) that has the unusual property, in the turkey cell, of being sufficiently great to permit its direct determination even at temperatures as low as 5 degrees C. Values for the equilibrium binding constant for the ouabain-ATPase complex (KA) predicted from the ratio of the association and dissociation rate constants agree closely with independently measured values of KA determined directly under conditions of equilibrium binding. KA is a sensitive function of the composition of the external ionic environment, rising with increasing Na+ concentration and falling with increasing K+ concentration. These changes in KA are shown to be quantitatively attributable to changes in the rate constant k1, k-1 in contrast being unaffected at any given temperature by even very large changes in Na+ or K+ concentration. Arrhenius plots of k1 and k-1 both yield straight lines over the entire temperature range corresponding to activation energies for association and dissociation of 29.5 and 24.2 kcal/mol, respectively. These observations have made it possible to calculate the following standard values for the ouabain binding reaction in the presence of 150 mM Na+: delta G degree = -9.8 kcal/mol; delta H degree = +5.3 kcal/mol; delta S degree = +48.7 cal/degree/mol. The large positive value of delta S degree presumably reflects a highly ordered configuration of the ouabain-free ATPase molecule that is lost upon ouabain binding and that "drives" the reaction despite the positive value of delta H degree.     

Physical chemical studies of short-chain lecithin homologues. IV. A simple model for the influence of salt and the alkyl chain length on the micellar size

A simplified association model for micellisation is presented. In this model two features are incorporated; (a) There is an optimum for the change of the standard free energy per monomer upon micellisation at a certain association number. (b) At higher association numbers this free energy change becomes constant. The resulting equations for the dependence of the average micellar weight on the concentration are used to explain the experimetitally observed effects of a salting-out agent (NaCl) and of the alkyl chain length of dihexanoyl-, diheptanoyl- and dioctanoyl-lecithin.     

1H NMR study of the base-pairing reactions of d(GGAATTCC): salt effects on the equilibria and kinetics of strand association

Previously, we examined the imino proton relaxation of d(GGAATTCC) in order to characterize salt and polyamine effects on the base-pair opening kinetics of this oligonucleotide [Braunlin, W. H., & Bloomfield, V. A. (1988) Biochemistry 27, 1184-1191]. Here, we report salt-dependent measurements of the NMR behavior of the nonexchangeable base proton resonances of d(GGAATTCC). From chemical shift measurements, we find an unexpectedly large salt dependence of Ka, the equilibrium constant for helix association. A total of 1.8 +/- 0.3 sodium ions are thermodynamically released upon dissociation of the octamer duplex. Most of the salt dependence of the equilibrium constant can be traced to a large salt dependence of the association rate. Thus, 1.4 +/- 0.2 sodium ions associate during the rate-limiting step of helix association. In agreement with our previous imino proton results, we also find a significant salt dependence of the duplex dissociation rate. Activation energies for helix association are very small, and possibly negative; most of the temperature dependence of the association equilibrium can be traced to a large activation energy (approximately 50 kcal/mol) for duplex dissociation.     

Anomalous pressure dissociation of large protein aggregates. Lack of concentration dependence and irreversibility at extreme degrees of dissociation of extracellular hemoglobin

The effects of hydrostatic pressure on the extracellular hemoglobin of Glossoscolex paulistus were investigated by studies of light scattering, intrinsic protein fluorescence, filtration chromatography, and oxygen binding. Pressure promoted a large decrease of light scattering consistent with the dissociation of the hemoglobin. Pressures up to 1.7 kbar caused dissociation with reversibility of the light scattering and fluorescence properties after return to atmospheric pressure. Higher pressures provoked additional dissociation with increasing loss of reversibility. After complete dissociation by incubation at 2.5 kbar followed by decompression, the protein continued mostly dissociated. The dissociated forms were distributed in two populations as based on size exclusion chromatography, one corresponding to small dissociated units (average Mr = 33,000) and the other population corresponding to the one-twelfth subunit (260,000 Mr). The pressure dissociation curves showed no significant dependence on protein concentration suggesting that the native hemoglobin population exists in a distribution of free-energies of association. Both the decrease of concentration dependence and the loss of ability to reassemble seem to increase with the complexity and size of the protein aggregate. These findings permit the conclusion that increased heterogeneity of free-energies of association with the size of the aggregate may result in the molecular individuality of large protein complexes such as subcellular particles and viruses.     

Determination of dependence of binding parameters on receptor occupancy

Measurements of the binding of ligand to receptors that are macromolecules, either free or components of biomembranes, often show deviation from what is expected of a simple reaction described by an association and a dissociation rate constant. A more versatile model and more discriminating experiments are required for a satisfactory explanation. This paper is based on a general model of the binding reaction in which the rate constants and equilibrium constant are dependent upon occupancy of receptors. The analysis of the model leads to three kinds of experiments: (1) equilibrium measurements which permit quantitative determination of a dissociation equilibrium parameter as a function of receptor occupancy; (2) measurements prior to equilibrium which yield the same information; and (3) measurements prior to equilibrium which reveal quantitatively the dependence of both association and dissociation rate parameters separately, on occupancy.     

Analysis of the dynamic equilibrium of histone oligomers in a solution. The nature of forces stabilizing the (H2A-H2B-H3-H4)2 octamer structure

Dynamic equilibrium analysis of the (H2A-H2B-H3-H4)2 histone octamer with lower oligomers was performed in 2 M NaCl. Calculated data on the relative content of histone oligomers upon changing protein concentration in solution are given. The red shift of lambda max for histone tyrosine fluorescence spectra is shown to be due to hydrogen bond formation by tyrosyl OH-groups. Analysis of free energy changes of histone oligomers upon association (delta G = -17,37 +/- 0,14 kcal/mole) as well as the effect of urea on histone octamer dissociation made it possible to conclude that virtually all tyrosyls in octamer form hydrogen bonds. Intermolecular hydrogen bonds formed by tyrosyls contribute substantially to octamer stabilization. The (H2A-H2B) dimer positive cooperativity in association with the (H3-H4)2 tetramer was found. This cooperativity is caused by interaction between association sites with a two order increase in an apparent constant of dimers with tetramer association. The histone octamer was determined to be of asymmetric structure due to unequivolency of the two binding sites for the (H2A-H2B) dimers.     

Kinetics and mechanism of dissociation of cooperatively bound T4 gene 32 protein-single-stranded nucleic acid complexes. 2. Changes in mechanism as a function of sodium chloride concentration and other solution variables

The dissociation kinetics of bacteriophage T4 coded gene 32 protein-single-stranded nucleic acid complexes have been examined as a function of monovalent salt concentration, temperature, and pH in order to investigate the details of the dissociation of cooperatively bound protein. Fluorescence stopped-flow techniques were used, and irreversible dissociation was induced by a combination of [NaCl] jumps and mixing with excess nucleic acid competitor. This made it possible to directly investigate the irreversible dissociation process over a wide range of NaCl concentrations [e.g., from 50 mM to 0.60 M for the gene 32 protein-poly(A) complex], in the absence of reassociation. Over the entire salt range, the only dissociable species observed is the singly contiguously bound gene 32 protein which dissociates from the ends of protein clusters. However, the [NaCl] dependence of the dissociation rate constant suggests that two competing pathways exist for dissociation of cooperatively bound gene 32 protein from the ends of protein clusters. At high monovalent salt concentrations, dissociation is dominated by a single-step process, with log ke/log [NaCl] = 6.5 +/- 0.5; i.e., the dissociation rate constant increases with increasing NaCl concentration due to the uptake of approximately six monovalent ions upon dissociation. This indicates that singly contiguous protein dissociates directly into solution. However, at much lower [NaCl] the data suggest that gene 32 protein, when bound at the end of a protein cluster, dissociates by first sliding off the end to form a noncooperatively bound intermediate which subsequently dissociates. A quantitative model which incorporates the sliding pathway [Berg, O. G., Winter, R. B., & von Hippel, P. H. (1981) Biochemistry 20, 6929-6948] in the dissociation mechanism fits the data reasonably well and suggests that noncooperatively bound monomers of gene 32 protein may be capable of one-dimensional translocation along single-stranded nucleic acids as suggested by independent kinetic data on the association reaction [Lohman, T. M., & Kowalczykowski, S. C. (1981) J. Mol. Biol. 152, 67-109]. It is also observed that both the absolute dissociation rate constant for T4 gene 32 protein and its salt dependence are sensitive to the average molecular weight and polydispersity of the nucleic acid sample used. This is a general phenomenon exhibited by proteins that bind to nucleic acids in a highly cooperative manner.     

Length dependence of rate constants for end-to-end association and dissociation of equilibrium linear aggregates

A semi-quantitative analysis is given of the length dependence of the rate constant for association (annealing) of two long linear aggregates in solution. The equilibrium constant for this process, or its inverse (fragmentation or dissociation), is relatively easy to formulate from appropriate partition functions. From these two ingredients, the length dependence of the rate constant for spontaneous fragmentation can be deduced. Numerical examples are included.     

Direct measurement of actin polymerization rate constants by electron microscopy of actin filaments nucleated by isolated microvillus cores

We used actin filament bundles isolated from intestinal brush-border microvilli to nucleate the polymerization of pure muscle actin monomers into filaments. Growth rates were determined by electron microscopy by measuring the change in the length of the filaments as a function of time. The linear dependence of the growth rates on the actin monomer concentration provided the rate constants for monomer association and dissociation at the two ends of the growing filament. The rapidly growing ("barbed") end has higher association and dissociation rate constants than the slowly growing ("pointed") end. The values of these rate constants differ in 20 mM KCl compared with 75 mM KCl, 5 mM MgSO4. 2 microM cytochalasin B blocks growth entirely at the barbed end, apparently by reducing both association and dissociation rate constants to near zero, but inhibits growth at the pointed end to only a small extent.     

Oligonucleotide facilitators may inhibit or activate a hammerhead ribozyme.

Facilitators are oligonucleotides capable of affecting hammerhead ribozyme activity by interacting with the substrate at the termini of the ribozyme. Facilitator effects were determined in vitro using a system consisting of a ribozyme with 7 nucleotides in every stem sequence and two substrates with inverted facilitator binding sequences. The effects of 9mer and 12mer RNA as well as DNA facilitators which bind either adjacent to the 3'- or 5'-end of the ribozyme were investigated. A kinetic model was developed which allows determination of the apparent dissociation constant of the ribozyme-substrate complex from single turnover reactions. We observed a decreased dissociation constant of the ribozyme-substrate complex due to facilitator addition corresponding to an additional stabilization energy of delta delta G=-1.7 kcal/mol with 3'-end facilitators. The cleavage rate constant was increased by 3'-end facilitators and decreased by 5'-end facilitators. Values for Km were slightly lowered by all facilitators and kcat was increased by 3'-end facilitators and decreased by 5'-end facilitators in our system. Generally the facilitator effects increased with the length of the facilitators and RNA provided greater effects than DNA of the same sequence. Results suggest facilitator influences on several steps of the hammerhead reaction, substrate association, cleavage and dissociation of products. Moreover, these effects are dependent in different manners on ribozyme and substrate concentration. This leads to the conclusion that there is a concentration dependence whether activation or inhibition is caused by facilitators. Conclusions are drawn with regard to the design of hammerhead ribozyme facilitator systems.