Thermodynamics and kinetics of co-operative protein-nucleic acid binding: II. Studies on the binding between protamine and calf thymus DNA

Unspecific binding of a protamine, namely fluorescein-labelled clupeine Z, to double-stranded calf thymus DNA was studied using fluorescence titration methods and chemical relaxation techniques. Both equilibrium and kinetic data have been analysed using general theoretical approaches discussed in the accompanying paper. The results agree well with the predictions made on the basis of a standard co-operative binding model.Basic parameters evaluated are the co-operative binding constant (K), the coefficient measuring co-operative interaction between nearest neighbours (q), the number of nucleotides occupied by one protamine molecule (n) and the rate constant of dissociation at the ends of bound ligand sequences (K_D). Values obtained at 20 °C, pH 7.5 and 0.4 m-NaCl were K = 5.8 × 10⁷m^?1, q = 1700, n = 20 and K_D = 0.29 s^?1. They have been found to be sensitive to the concentration of added salt (NaCl). This effect apparently reflects the essentially electrostatic nature of the binding process. The results can be satisfactorily described in terms of competitive binding of sodium ions.     

Solvent isotope effects on α-glucosidase

The solvent kinetic isotope effects (SKIE) on the yeast α-glucosidase-catalyzed hydrolysis of p-nitrophenyl and methyl-d-glucopyranoside were measured at 25 °C. With p-nitrophenyl-d-glucopyranoside (pNPG), the dependence of k_cat/K_m on pH (pD) revealed an unusually large (for glycohydrolases) solvent isotope effect on the pL-independent second-order rate constant, ^DOD(k_cat/K_m), of 1.9 (±0.3). The two pK_as characterizing the pH profile were increased in D₂O. The shift in pK_a2 of 0.6 units is typical of acids of comparable acidity (pK_a=6.5), but the increase in pK_a1 (=5.7) of 0.1 unit in going from H₂O to D₂O is unusually small. The initial velocities show substrate inhibition (K_is/K_m～200) with a small solvent isotope effect on the inhibition constant [^DODK_is=1.1 (±0.2)]. The solvent equilibrium isotope effects on the K_is for the competitive inhibitors d-glucose and α-methyl d-glucoside are somewhat higher [^DODK_i=1.5 (±0.1)]. Methyl glucoside is much less reactive than pNPG, with k_cat 230 times lower and k_cat/K_m 5×10⁴ times lower. The solvent isotope effect on k_cat for this substrate [=1.11 (±0. 02)] is lower than that for pNPG [=1.67 (±0.07)], consistent with more extensive proton transfer in the transition state for the deglucosylation step than for the glucosylation step.     

On the acquisition and analysis of microscale thermophoresis data

A comprehensive understanding of the molecular mechanisms underpinning cellular functions is dependent on a detailed characterization of the energetics of macromolecular binding, often quantified by the equilibrium dissociation constant, K_D. While many biophysical methods may be used to obtain K_D, the focus of this report is a relatively new method called microscale thermophoresis (MST). In an MST experiment, a capillary tube filled with a solution containing a dye-labeled solute is illuminated with an infrared laser, rapidly creating a temperature gradient. Molecules will migrate along this gradient, causing changes in the observed fluorescence. Because the net migration of the labeled molecules will depend on their liganded state, a binding curve as a function of ligand concentration can be constructed from MST data and analyzed to determine K_D. Herein, simulations demonstrate the limits of K_D that can be measured in current instrumentation. They also show that binding kinetics is a major concern in planning and executing MST experiments. Additionally, studies of two protein–protein interactions illustrate challenges encountered in acquiring and analyzing MST data. Combined, these approaches indicate a set of best practices for performing and analyzing MST experiments. Software for rigorous data analysis is also introduced.     

Implications of the progressive self-association of wild-type human factor H for complement regulation and disease

Factor H (FH) is a major regulator of complement alternative pathway activation. It is composed of 20 short complement regulator (SCR) domains and is genetically associated as a risk factor for age-related macular degeneration. Previous studies on FH suggested that it existed in monomeric and dimeric forms. Improved X-ray scattering and analytical ultracentrifugation methodology for wild-type FH permitted a clarification of these oligomeric properties. Data at lower concentrations revealed a dependence of the X-ray radius of gyration values on concentration that corresponded to the weak self-association of FH. Global sedimentation equilibrium fits indicated that a monomer-dimer equilibrium best described the data up to 1.3 mg/ml with a fitted dissociation constant K_D of 28 μM and that higher oligomers formed at increased concentrations. The K_D showed that about 85-95% of serum FH will be monomeric in the absence of other factors. Size-distribution analyses in sedimentation velocity experiments showed that monomeric FH was the major species but that as many as six oligomeric forms co-existed with it. The data were explained in terms of two weak dimerisation sites recently identified in the SCR-6/8 and SCR-16/20 fragments of FH with similar K_D values. These observations indicate a mechanism for the progressive self-association of FH and may be relevant for complement regulation and the formation of drusen deposits that are associated with age-related macular degeneration.     

Impact of hapten presentation on antibody binding at lipid membrane interfaces

We report the effects of ligand presentation on the binding of aqueous proteins to solid supported lipid bilayers. Specifically, we show that the equilibrium dissociation constant can be strongly affected by ligand lipophilicity and linker length/structure. The apparent equilibrium dissociation constants (K_D) were compared for two model systems, biotin/anti-biotin and 2,4-dinitrophenyl (DNP)/anti-DNP, in bulk solution and at model membrane surfaces. The binding constants in solution were obtained from fluorescence anisotropy measurements. The surface binding constants were determined by microfluidic techniques in conjunction with total internal reflection fluorescence microscopy. The results showed that the bulk solution equilibrium dissociation constants for anti-biotin and anti-DNP were almost identical, K_D(bulk) = 1.7 ± 0.2 nM vs. 2.9 ± 0.1 nM. By contrast, the dissociation constant for anti-biotin antibody was three orders of magnitude tighter than for anti-DNP at a lipid membrane interface, K_D = 3.6 ± 1.1 nM vs. 2.0 ± 0.2 μM. We postulate that the pronounced difference in surface binding constants for these two similar antibodies is due to differences in the ligands’ relative lipophilicity, i.e., the more hydrophobic DNP molecules had a stronger interaction with the lipid bilayers, rendering them less available to incoming anti-DNP antibodies compared with the biotin/anti-biotin system. However, when membrane-bound biotin ligands were well screened by a poly(ethylene glycol) (PEG) polymer brush, the K_D value for the anti-biotin antibody could also be weakened by three orders of magnitude, 2.4 ± 1.1 μM. On the other hand, the dissociation constant for anti-DNP antibodies at a lipid interface could be significantly enhanced when DNP haptens were tethered to the end of very long hydrophilic PEG lipopolymers (K_D = 21 ± 10 nM) rather than presented on short lipid-conjugated tethers. These results demonstrate that ligand presentation strongly influences protein interactions with membrane-bound ligands.     

Concentration equations for the diffusion of a reversibly reacting substance in gel-like media

The concentration of a diffusible substanceA(x, t) in a semi-infinite geometry is studied for the set of reversible reactionsA+B _i ?C _i ;i=1...n, whereB _i andC _i are assumed to be associated with non-diffusible biological structures. Assuming chemical equilibrium prevails throughout for each reaction, it is shown that a single uncoupled partial differential equation is sufficient to specifyA(x, t) and indirectlyB _i (x, t) andC _i (x, t) as well: $$\left[ {1 + \sum\limits_i {\frac{{K_i \beta _i }}{{\left( {1 + K_i A} \right)^2 }}} } \right]\frac{{\partial A}}{{\partial t}} = D_A \frac{{\partial ^2 A}}{{\partial x^2 }}$$ whereK _i is the chemical equilibrium constant of theith reaction, β₁ is concentration of binding sites of theith species (i.e.B _i+C _i) andD _A is the usual diffusion constant forA. Numerical solutions for boundary conditions amenable to the Boltzman transformation are presented and the range of parameters established over which the uniqueness and convergence of the solutions can be proven.     

EmrE dimerization depends on membrane environment

The small multi-drug resistant (SMR) transporter EmrE functions as a homodimer. Although the small size of EmrE would seem to make it an ideal model system, it can also make it challenging to work with. As a result, a great deal of controversy has surrounded even such basic questions as the oligomeric state. Here we show that the purified protein is a homodimer in isotropic bicelles with a monomer–dimer equilibrium constant (K_MD^2D) of 0.002–0.009 mol% for both the substrate-free and substrate-bound states. Thus, the dimer is stabilized in bicelles relative to detergent micelles where the K_MD^2D is only 0.8–0.95 mol% (Butler et al. 2004). In dilauroylphosphatidylcholine (DLPC) liposomes K_MD^2D is 0.0005–0.0008 mol% based on Förster resonance energy transfer (FRET) measurements, slightly tighter than bicelles. These results emphasize the importance of the lipid membrane in influencing dimer affinity.     

A mathematical theory of enamel solubility and the onset of dental caries: II. Some solubility equilibrium considerations of hydroxyapatite

Equilibrium solubility considerations are presented based on the assumption that equating the kinetic expressionq, developed in part I, to zero can describe the equilibrium or steady state between hydroxyapatite and salt solutions. From this expression is derived Hodge's empirical equilibrium equation,C=KH. Further, a lograithmic transformation of this equation results in an expression that accounts for the equilibrium calcium, phosphorus andpH relation found by Levinskas and Neuman. Finally, it also shows the relation between log (C·P) andpH necessary for typical artificial carious lesions as found by Coolidge, Besic and Jacobs. A discussion of a recent theory of hydroxyapatite solubility of LaMer reveals calculation errors that vitiate his results. It is shown that logK ₁ (K ₁ is the ratio of the rate constants inq and can serve as a solubility equilibrium constant for hydroxyapatite) varies by only 1.2 units when calculated from three diverse sets of data. This variation is less than that reported by LaMer (when the errors of calculation in that work are corrected) and considerably less than the range of 11 among attempts to calculate a conventionalpK _sp , as summarized by Hodge. Literature list is found at the end of the last part, this issue, pp 462–464.     

Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting in vivo potency

We consider the relationship between the target affinity of a monoclonal antibody and its in vivo potency. The dynamics of the system is described mathematically by a target-mediated drug disposition model. As a measure of potency, we consider the minimum level of the free receptor following a single bolus injection of the ligand into the plasma compartment. From the differential equations, we derive two expressions for this minimum level in terms of the parameters of the problem, one of which is valid over the full range of values of the equilibrium dissociation constant K_D and the other which is valid only for a large drug dose or for a small value of K_D. Both of these formulae show that the potency achieved by increasing the association constant k_on can be very different from the potency achieved by decreasing the dissociation constant k_off. In particular, there is a saturation effect when decreasing k_off where the increase in potency that can be achieved is limited, whereas there is no such effect when increasing k_on. Thus, for certain monoclonal antibodies, an increase in potency may be better achieved by increasing k_on than by decreasing k_off.     

Characterization of binding of [3H]PD 128907, A selective Dopamine D3 receptor agonist ligand,to CHO-K1 cells

PD 128907 [4a R, 10 b R-(+)-trans- 3, 4, 4a, 10 b - tetrahydro - 4- n-propy12 H,5H-[1] benzopyrano[4,3-b]1,4-oxazin-9-ol.], a selective dopamine (DA) D3 receptor agonist ligand exhibits about a 1000-fold selectivity for human D3 receptors (K_i, 1 nM) versus human D₂ receptors (K_i, 1183 nM) and a 10000-fold selectivity versus human D₄ receptors (K_i, 7000 nM) using [³H]spiperone as the radioligand in CHO-K1-cells. Studies with [³H]PD 128907, showed saturable, high affinity binding to human D₃ receptors expressed in CHO-K1 cells (CHO-K1-D₃) with an equilibrium dissociation constant (K_d) of 0.99 nM and a binding density (B_max) of 475 fmol/mg protein. Under the same conditions, there was no significant specific binding in CHO-K1-cells expressing human D₂ receptors (CHO-K1-D₂). The rank order of potency for inhibition of [³H]PD 128907 binding with reference DA agents was consistent with reported values for D₃ receptors. These results indicate that [³H]PD 128907 is a new, highly selective D₃ receptor ligand with high specific activity, high specific binding and low non-specific binding and therefore should be useful for further characterizing the DA D₃ receptors.     

Carboxyl pKa Values and Acid Denaturation of BBL

The protein BBL undergoes structural transitions and acid denaturation between pH 1.2 and 8.0. Using NMR spectroscopy, we measured the pK_a values of all the carboxylic residues in this pH range. We employed ¹³C direct-detection two-dimensional IPAP (in-phase antiphase) CACO NMR spectroscopy to monitor the ionization state of different carboxylic groups and demonstrated its advantages over other NMR techniques in measuring pK_a values of carboxylic residues. The two residues Glu161 and Asp162 had significantly lowered pK_a values, showing that these residues are involved in a network of stabilizing electrostatic interactions, as is His166. The other carboxylates had unperturbed values. The pH dependence of the free energy of denaturation was described quantitatively by the ionizations of those three residues of perturbed pK_a, and, using thermodynamic cycles, we could calculate their pK_as in the native and denatured states as well as the equilibrium constants for denaturation of the different protonation states. We also measured ¹³C^α chemical shifts of individual residues as a function of pH. These shifts sense structural transitions rather than ionizations, and they titrated with pH consistent with the change in equilibrium constant for denaturation. Kinetic measurements of the folding of BBL E161Q indicated that, at pH 7, the stabilizing interactions with Glu161 are formed mainly in the transition state. We also found that local interactions still exist in the acid-denatured state of BBL, which attenuate somewhat the flexibility of the acid-denatured state.     

Impedance analysis of phosphatidylcholine membranes modified with valinomycin

The effect of the ion carrier valinomycin on the electrochemical features of the phosphatidylcholine membrane was investigated by electrochemical impedance spectroscopy. Phosphatidylcholine and valinomycin were chosen for the study because they fulfil essential functions in lively organisms. The experimental impedance values obtained in the presence of different amounts of carrier, studied with several potassium ion concentrations, were used for the research ability of valinomycin to form a 1:1 potassium ion complex on the lipid bilayer/electrolyte solution interface. Based on derived mathematical equations, the heterogeneous equilibrium constant (K _h), association rate constant of the complex (k _R) and dissociation rate constant of the complex (k _D) were calculated. The result of the investigation is the proposal of a new method for the determination of the parameters used to describe the chemical reaction at the interface between a carrier molecule from the membrane and a monovalent ion from the aqueous phase.     

Cooperativity in viral fusion

A simple model for membrane fusion mediated by vial spike glycoproteins is presented. The viral proteins are considered to be allosteric proteins that undergo concerted conformational transitions when they bind the ligand. The ligand in this case is H⁺. The effect of the conformational transition is to bring membranes together and induce their fusion. An equation is derived for the dependence of fusion rates on ligand concentration, for a given dissociation constant (K _d), equilibrium constant for the conformational change (L), and number of cooperating subunits (n). Curves generated by this equation provide a reasonable fit to data on the rates of fusion of Vesicular Stomatitis virus with cells for a pK _d of 6.3,L=1000 andn=6.     

Decrease or increase in cardiac muscarinic cholinergic receptor number in rats treated with methacholine or atropine

The effects of chronic treatment of the rat with methacholine and atropine on the cardiac muscarinic cholinergic receptors were investigated. [³H]Quinuclidinyl benzilate ([³H]QNB) was used to directly estimate the number and affinity of the receptors in the heart ventricular membrane. Methacholine treatment decreased, in a dose-related and time-dependent manner, the specific binding of [³H]QNB by 34% as compared to the control. Atropine treatment, on the other hand, resulted in a dose-related increase (28 to 66%) in the number of the receptors. The equilibrium dissociation constant (K_D) of the receptors for the ligand was the same (about 200 pM) for the control and the methacholine treated groups of rats, whereas a dose-related increase (39 to 105%) in the K_D was noted for the atropine treated rats. Similarly, the concentration of acetylcholine causing a 50 percent inhibition (IC₅₀) of the [³H]QNB binding was unaltered for the methacholine treated rats (4 μM), but it was increased 43% for the atropine treated rats.     

Quantitative studies of the non-productive binding of lysozyme to partially N-acetylated chitosans: Binding of large ligands to a one-dimensional binary lattice studied by a modified McGhee and von Hippel model

This paper considers the non-productive (inhibitory) binding of chitosans to lysozyme from chicken egg white. Chitosans are linear, binary heteropolysaccharides consisting of 2-acetamido-2-deoxy-β-d-glucose (GlcNAc; A-unit) and 2-amino-2-deoxy-β-d-glucose (GlcN, D-unit). The active site cleft of lysozyme can bind six consecutive sugar residues in subsites named A–F, and specific binding of chitosan sequences to lysozyme occurs with A-units in subsite C. Chitosans with different fractions of A-units (F_A) induced nearly identical changes in the ¹H NMR spectrum of lysozyme upon binding, and the concentration of bound lysozyme could be determined. The data were analysed using a modified version of the McGhee and von Hippel model for binding of large ligands to one-dimensional homogeneous lattices. The average value of the dissociation constant for different sequences that may bind to lysozyme (K^ave_D) was estimated, as well as the number of chitosan units covered by lysozyme upon binding. K^ave_D decreased with increasing F_A-values at pH* 3 and 4.5, while the opposite was true at pH* 5.5. Contributions from different hexamer sequences to K^ave_D of the chitosans were considered, and the data revealed interesting features with respect to binding of lysozyme to partially N-acetylated chitosans. The relevance of the present data with respect to understanding lysozyme degradation kinetics of chitosans is discussed.     

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.     

Allowance for thermodynamic nonideality in the characterization of protein interactions by spectral techniques

Theory is developed for the characterization of protein interactions by spectral techniques, where the constraints of constant temperature and pressure demand that thermodynamic activity be defined on the molal concentration scale. The customary practice of defining the equilibrium constant (K) on a molar basis is accommodated by developing expressions to convert those experimental values (K_molar) to their thermodynamically more rigorous counterparts (K_molal). Such procedures are illustrated by reanalysis of published results for the effects of molecular crowding agents on the isomerisation of α-chymotrypsin and reversible complex formation between catalase and superoxide dismutase. Although those reanalyses have led to only minor refinements of the quantitative interpretation, it is clearly preferable to adopt thermodynamic rigor throughout future spectral studies by employing the molal concentration scale from the outset.     

ESR study of intercalation: quantitative evaluation of drug-DNA binding through competition with a spin-labeled 9-aminoacridine

Interaction of a spin-labeled 9-aminoacridine with DNA was studied by electron spin resonance spectroscopy. Accurate determination of the binding parameters, equilibrium dissociation constant (K_D), and total number of ligand-binding sites was obtained using Scatchard and Lineweaver-Burk plots. The competition between 9-aminoacridine and its spin-labeled derivative was examined by a similar analysis of the spin-label signals. The practical interest of this method lies in the fact that the precision and the simplicity of the measurements allow the quantitative determination of the binding capacity of any intercalative drug which interacts specifically with adenine/thymine bases of DNA.     

Allowance for antibody bivalence in the determination of association rate constants by kinetic exclusion assay

This investigation completes the amendment of theoretical expressions for the characterization of antigen–antibody interactions by kinetic exclusion assay—an endeavor that has been marred by inadequate allowance for the consequences of antibody bivalence in its uptake by the affinity matrix (immobilized antigen) that is used to ascertain the fraction of free antibody sites in a solution with defined total concentrations of antigen and antibody. A simple illustration of reacted site probability considerations in action confirms that the square root of the fluorescence response ratio, R_Ag/R_o, needs to be taken in order to determine the fraction of unoccupied antibody sites, which is the parameter employed to describe the kinetics of antigen uptake in the mixture of antigen and antibody with defined initial composition. The approximately 2-fold underestimation of the association rate constant (k_a) that emanates from the usual practice of omitting the square root factor gives rise to a corresponding overestimate of the equilibrium dissociation constant (K_d)—a situation that is also encountered in the thermodynamic characterization of antigen–antibody interactions by kinetic exclusion assay.