Electrostatic contributions to the binding of Ca2+ in calbindin mutants. A Monte Carlo study

Monte Carlo simulation is used to calculate the free energy of binding of calcium ions to the native and several mutant forms of bovine calbindin D(9K) in salt solution. The simulations are performed in the canonical ensemble wherein free energies are calculated with a modified Widom method. The protein is modelled as a set of fixed hard spheres of fractional or unit charge with the surrounding solution as a dielectric continuum containing counterions and added salt particles. The interior of the protein is assumed to have the same dielectric permittivity as the solvent, which turns out to be an excellent approximation. Indeed, this simple model is able to predict accurately experimentally measured shifts in the calcium binding constants of up to five orders of magnitude, due to mutations and added salt.     

Interpreting protein/DNA interactions: distinguishing specific from non-specific and electrostatic from non-electrostatic components

We discuss the effectiveness of existing methods for understanding the forces driving the formation of specific protein-DNA complexes. Theoretical approaches using the Poisson-Boltzmann (PB) equation to analyse interactions between these highly charged macromolecules to form known structures are contrasted with an empirical approach that analyses the effects of salt on the stability of these complexes and assumes that release of counter-ions associated with the free DNA plays the dominant role in their formation. According to this counter-ion condensation (CC) concept, the salt-dependent part of the Gibbs energy of binding, which is defined as the electrostatic component, is fully entropic and its dependence on the salt concentration represents the number of ionic contacts present in the complex. It is shown that although this electrostatic component provides the majority of the Gibbs energy of complex formation and does not depend on the DNA sequence, the salt-independent part of the Gibbs energy--usually regarded as non-electrostatic--is sequence specific. The CC approach thus has considerable practical value for studying protein/DNA complexes, while practical applications of PB analysis have yet to demonstrate their merit.     

Fluorescence energy transfer in one dimension: Frequency-domain fluorescence study of DNA–fluorophore complexes

The theory for the salt dependence of the free energy, entropy, and enthalpy of a polyelectrolyte in the PB (PB) model is extended to treat the nonspecific salt dependence of polyelectrolyte–ligand binding reactions. The salt dependence of the binding constant (K) is given by the difference in osmotic pressure terms between the react ants and the products. For simple 1-1 salts it is shown that this treatment is equivalent to the general preferential interaction model for the salt dependence of binding [C. Anderson and M. Record (1993) Journal of Physical Chemistry, Vol. 97, pp. 7116–7126]. The salt dependence, entropy, and enthalpy are compared for the PB model and one specific form of the preferential interaction coefficient model that uses counterion condensation/limiting law (LL) behavior. The PB and LL models are applied to three ligand–polyelectrolyte systems with the same net ligand charge: a model sphere–cylinder binding reaction, a drug–DNA binding reaction, and a protein–DNA binding reaction. For the small ligands both the PB and limiting law models give (ln K vs. In [salt]) slopes close in magnitude to the net ligand charge. However, the enthalpy/entropy breakdown of the salt dependence is quite different. In the PB model there are considerable contributions from electrostatic enthalpy and dielectric (water reorientation) entropy, compared to the predominant ion cratic (release) entropy in the limiting law model. The relative contributions of these three terms in the PB model depends on the ligand: for the protein, ion release entropy is the smallest contribution to the salt dependence of binding. The effect of three approximations made in the LL model is examined: These approximations are (1) the ligand behaves ideally, (2) the preferential interaction coefficient of the polyelectrolyte is unchanged upon ligand binding, and (3) the polyelectrolyte preferential interaction coefficient is given by the limiting law/counterion-condensation value. Analysis of the PB model shows that assumptions 2 and 3 break down at finite salt concentrations. For the small ligands the effects on the slope cancel, however, giving net slopes that are similar in the PB and LL models, but with a different entropy/enthalpy breakdown. For the protein ligand the errors from assumptions 2 and 3 in the LL model do not cancel. In addition, the ligand no longer behaves ideally due to its complex structure and charge distribution. Thus for the protein the slope is no longer related simply to the net ligand charge, and the PB model gives a much larger slope than the LL model. Additionally, in the PB model most of the salt dependence of the protein binding comes from the change in ligand activity, i.e. from nonspecific anion effects, in contrast to the small ligand case. While the absolute binding is sensitive to polyelectrolyte length, little length effect is seen on the salt dependence for the small ligands at 0.1M salt, and for lengths > 60 Å. Almost no DNA length dependenceis seen in the salt dependence of the protein binding, since this is determined primarily by the protein, not the DNA. © 1995 John Wiley & Sons, Inc.     

Calbindin D28k exhibits properties characteristic of a Ca2+ sensor

Calbindin D(28k) is a member of the calmodulin superfamily of Ca(2+)-binding proteins and contains six EF-hands. The protein is generally believed to function as a Ca(2+) buffer, but the studies presented in this work indicate that it may also act as a Ca(2+) sensor. The results show that Mg(2+) binds to the same sites as Ca(2+) with an association constant of approximately 1.4.10(3) m(-1) in 0.15 m KCl. The four high affinity sites in calbindin D(28k) bind Ca(2+) in a non-sequential, parallel manner. In the presence of physiological concentrations of Mg(2+), the Ca(2+) affinity is reduced by a factor of 2, and the cooperativity, which otherwise is modest, increases. Based on the binding constants determined in the presence of physiological salt concentrations, we estimate that at the Ca(2+) concentration in a resting cell calbindin D(28k) is saturated to 40-75% with Mg(2+) but to less than 9% with Ca(2+). In contrast, the protein is expected to be nearly fully saturated with Ca(2+) at the Ca(2+) level of an activated cell. A substantial conformational change is observed upon Ca(2+) binding, but only minor structural changes take place upon Mg(2+) binding. This suggests that calbindin D(28k) undergoes Ca(2+)-induced structural changes upon Ca(2+) activation of a cell. Thus, calbindin D(28k) displays several properties that would be expected for a protein involved in Ca(2+)-induced signal transmission and hence may function not only as a Ca(2+) buffer but also as a Ca(2+) sensor. Digestion patterns resulting from limited proteolysis of the protein suggest that the loop of EF-hand 2, a variant site that does not bind Ca(2+), becomes exposed upon Ca(2+) binding.     

Some characteristics of protein precipitation by salts

The solubilities of lysozyme, alpha-chymotrypsin and bovine serum albumin (BSA) were studied in aqueous electrolyte solution as a function of ionic strength, pH, the chemical nature of salt, and initial protein concentration. Compositions were measured for both the supernatant phase and the precipitate phase at 25 degrees C. Salts studied were sodium chloride, sodium sulfate, and sodium phosphate. For lysozyme, protein concentrations in supernatant and precipitate phases are independent of the initial protein concentration; solubility can be represented by the Cohn salting-out equation. Lysozyme has a minimum solubility around pH 10, close to its isoelectric point (pH 10.5). The effectiveness of the three salts studied for precipitation were in the sequence sulfate > phosphate > chloride, consistent with the Hofmeister series. However, for alpha-chymotrypsin and BSA, initial protein concentration affects the apparent equillibrium solubility. For these proteins, experimental results show that the compositions of the precipitate phase are also affected by the initial protein concentration. We define a distribution coefficient kappa(e) to represent the equilibrium ratio of the protein concentration in the supernatant phase to that in the precipitate phase. When the salt concentration is constant, the results show that, for lysozyme, the protein concentrations in both phases are independent of the initial protein concentrations, and thus kappa(e) is a constant. For alpha-chymotrypsin and BSA, their concentrations in both phases are nearly proportional to the initial protein concentrations, and therefore, for each protein, at constant salt concentration, the distribution coefficient kappa(e) is independent of the initial protein concentration. However, for both lysozyme and alpha-chymotrypsin, the distribution coefficient falls with increasing salt concentration. These results indicate that care must be used in the definition of solubility. Solubility is appropriate when the precipitate phase is pure, but when it is not, the distribution coefficient better describes the phase behavior. (c) 1992 John Wiley & Sons, Inc.     

Biophysical characterization of the influence of salt on tetrameric SecB.

SecB is a tetrameric chaperone, with a monomeric molecular mass of 17 kDa, that is involved in protein translocation in Escherichia coli. It has been hypothesized that SecB undergoes a conformational change as a function of the salt concentration. To gain more insight into the salt-dependent behavior of SecB, we studied the protein in solution by dynamic light scattering, size exclusion chromatography, analytical ultracentrifugation, and small angle neutron scattering. The results clearly demonstrate the large influence of the salt concentration on the behavior of SecB. At high salt concentration, SecB is a non-spherical protein with a radius of gyration of 3.4 nm. At low salt concentration the hydrodynamic radius of the protein is apparently decreased, whereas the ratio of the frictional coefficients is increased. The protein solution behaves in a non-ideal way at low salt concentrations, as was shown by the analytical ultracentrifugation data and a pronounced interparticle effect observed by small angle neutron scattering. A possible explanation is a change in surface charge distribution dependent on the salt concentration in the solvent. We summarize our data in a model for the salt-dependent conformation of tetrameric SecB.     

Dynamic arrangement of ion pairs and individual contributions to the thermal stability of the cofactor-binding domain of glutamate dehydrogenase from Thermotoga maritima

The dynamics of a hyperthermophilic protein fragment in a water environment, as studied by performing molecular dynamics (MD) simulations at various temperatures, is compared to the dynamical behavior of a homologous mesophilic protein simulated under identical conditions. The effects on the stability of the spatial arrangement and mobility of the charged residues in solution were quantified by calculating free energy changes upon salt bridge formation in these proteins. Electrostatic free energy terms derived from a thermodynamic cycle were obtained by solving the linearized Poisson-Boltzmann equation for a series of protein conformations generated by MD simulations and placed subsequently in a continuum solvent medium. Our results show that the ion pairs are electrostatically stabilizing in most of the cases, but their individual contributions vary significantly. The greater contribution of the charged residues to the stability of the hyperthermophilic protein as compared with the mesophilic counterpart was evidenced only by the calculations that included conformations sampled at 343 and 373 K. The "dynamic" structure of the hyperthermophilic protein fragment simulated at elevated temperatures reveals an optimum placement of the ionizable residues within the protein structure as well as the role of their cooperative interactions in promoting thermal stability. The thermodynamic properties such as electrostatic free energy differences, configurational entropies, and specific heat capacities calculated in the dynamic context of the protein structure provided new insight into the mechanism of protein thermostabilization.     

Electrostatic contributions to the binding of Ca2+ in calbindin D9k

A set of accurate experimental data is provided for Ca2+ ion binding to calbindin D9k, a protein in the calmodulin superfamily of intracellular regulatory proteins. The study comprises both the role of protein surface charges and the effects of added electrolyte. The two macroscopic Ca2(+)-binding constants K1 and K2 are determined for the wild-type and eight mutant calbindins in 0, 0.05, 0.10, and 0.15 M KCl from titrations in the presence of Quin 2 or 5,5'-Br2BAPTA. The mutations involve replacement of surface carboxylates (of Glu17, Asp19, Glu26, and Glu60) with the corresponding amides. It is found that K1K2 may decrease by a factor of up to 2.5 x 10(5) (triple mutant in 0.15 M KCl as compared to the wild-type protein in 0 M KCl). Ca2(+)-binding constants of the individual Ca2+ sites (microscopic binding constants) have also been determined. The positive cooperativity of Ca2+ binding, previously observed at low salt concentration [Linse et al. (1987) Biochemistry 26, 6723-6735], is also present at physiological ionic strength and amounts to 5 kJ.mol-1 at 0.15 M KCl. The electrolyte concentration and some of the mutations are found to affect the cooperativity. 39K NMR studies show that K+ binds weakly to calbindin. Two-dimensional 1H NMR studies show, however, that potassium binding does not change the protein conformation, and the large effect of KCl on the Ca2+ affinity is thus of unspecific nature. Two-dimensional 1H NMR has also been used to assess the structural consequences of the mutations through assignments of the backbone NH and C alpha H resonances of six mutants.(ABSTRACT TRUNCATED AT 250 WORDS)     

Salt dependence of DNA structural stabilities in solution. Theoretical predictions versus experiments

The predictions of currently available theories for treating DNA-diffuse ionic cloud free energy contributions to conformational stability have been tested against experimental data for salt induced B-Z and B-A transitions. The theories considered are (i) Manning's counterion condensation approach (CC), (ii) the idealized Poisson-Boltzmann approximation (PB), and (iii) the potentials of mean force (PMF) approach proposed by Soumpasis. As far as we can judge from comparison with the set of experimental data currently available, it is found that only the latter theory yields satisfactory quantitative results for the dependence of the B-Z and B-A relative stabilities on monovalent salt concentration. The correct application of the PB and CC theories does not yield very low salt Z-B transitions, in contradiction to earlier assertions. At low salt concentrations the PB theory is qualitatively correct in predicting that the B form is electrostatically more favorable than both the A and Z forms, whereas the CC theory is qualitatively wrong predicting that Z-DNA is more stable than both B and A DNA.     

Monte Carlo and Poisson–Boltzmann calculations of the fraction of counterions bound to DNA

The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson–Boltzmann (PB) methods. Two different definitions of the “bound” and “free” components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization—one in which monovalent cations in regions where the average electrostatic potential is ledd than ?kT are considered to be bound—provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B from of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observatiob is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicated by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylindera of varying lineat charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 Å hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the rediys enclosing the region in which the electrostatic potential is calculated studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than ?kT is advocated s a more suitable binding or condensation radius that enclosing the fraction of counterions given by (1 – ξ^?1). A comparsion of radii calculated using both of these definitions is presented. © 1994 John Wiley & Sons, Inc.     

Peptidyl-prolyl cis-trans isomerase does not affect the Pro-43 cis-trans isomerization rate in folded calbindin D9k

The calcium-binding protein calbindin D9k has previously been shown to exist in two folded forms only differing in the proline cis-trans isomerism of the Gly-42-Pro-43 amide bond. This bond is located in a flexible loop connecting the two EF-hand Ca2+ sites. Calbindin D9k therefore constitutes a unique test case for investigating if the recently discovered enzyme peptidyl-prolyl cis-trans isomerase (PPIase) can affect the cis-trans exchange rate in a folded protein. The 1H NMR saturation transfer technique has been used to measure the rate of interconversion between the cis and trans forms of calbindin in the presence of PPIase (PPIase:calbindin concentration ratio 1:10) at 35 degrees C. No rate enhancement could be detected.     

Salt Dependence of DNA Structural Stabilities in Solution. Theoretical Predictions Versus Experiments

Abstract

The predictions of currently available theories for treating DNA-diffuse ionic cloud free energy contributions to conformational stability have been tested against experimental data for salt induced B-Z and B-A transitions. The theories considered are (i) Manning's counterion condensation approach (CC), (ii) the idealized Poisson-Boltzmann approximation (PB), and (iii) the potentials of mean force (PMF) approach proposed by Soumpasis. As far as we can judge from comparison with the set of experimental data currently available, it is found that only the latter theory yields satisfactory quantitative results for the dependence of the B-Z and B-A relative stabilities on monovalent salt concentration. The correct application of the PB and CC theories does not yield very low salt Z-B transitions, in contradiction to earlier assertions. At low salt concentrations the PB theory is qualitatively correct in predicting that the B form is electrostatically more favorable than both the A and B forms, whereas the CC theory is qualitatively wrong predicting that Z-DNA is more stable than both B and A DNA.     

Protein Electrostatics: Rapid Multigrid-Based Newton Algorithm for Solution of the Full Nonlinear Poisson-Boltzmann Equation

Abstract

A new method for solving the full nonlinear Poisson-Boltzmann equation is outlined. This method is robust and efficient, and uses a combination of the multigrid and inexact Newton algorithms. The novelty of this approach lies in the appropriate combination of the two methods, neither of which by themselves are capable of solving the nonlinear problem accurately. Features of the Poisson-Boltzmann equation are fully exploited by each component of the hybrid algorithm to provide robustness and speed. The advantages inherent in this method increase with the size of the problem. The efficacy of the method is illustrated by calculations of the electrostatic potential around the enzyme Superoxide Dismutase. The CPU time required to solve the full nonlinear equation is less than half that needed for a conjugate gradient solution of the corresponding linearized Poisson-Boltzmann equation. The solutions reveal that the field around the active sites is significantly reduced as compared to that obtained by solving the corresponding linearized Poisson-Boltzmann equation. This new method for the nonlinear Poisson-Boltzmann equation will enable fast and accurate solutions of large protein electrostatics problems.     

Ion flow in the bath and flux interactions between channels.

We present an exact solution to the linearized Nernst-Planck-Poisson equation for spherically symmetric current flow. This solution differs from Levitt's solution (Levitt, D. G. 1992. Biophys. J., Eq. A5) by its dependence on an additional parameter, which is equal to the net ion flux for monovalent ion-selective channels. For ion-selective channels, this solution may provide better boundary conditions to modelling the flow in the channel pore itself, although only at low salt concentrations. We use the solution to estimate the effects of flux interaction between closely packed channels.     

Systematic interpolation method predicts protein chromatographic elution with salt gradients,pH gradients and combined salt/pH gradients

A methodology is presented to predict protein elution behavior from an ion exchange column using both individual or combined pH and salt gradients based on high‐throughput batch isotherm data. The buffer compositions are first optimized to generate linear pH gradients from pH 5.5 to 7 with defined concentrations of sodium chloride. Next, high‐throughput batch isotherm data are collected for a monoclonal antibody on the cation exchange resin POROS XS over a range of protein concentrations, salt concentrations, and solution pH. Finally, a previously developed empirical interpolation (EI) method is extended to describe protein binding as a function of the protein and salt concentration and solution pH without using an explicit isotherm model. The interpolated isotherm data are then used with a lumped kinetic model to predict the protein elution behavior. Experimental results obtained for laboratory scale columns show excellent agreement with the predicted elution curves for both individual or combined pH and salt gradients at protein loads up to 45 mg/mL of column. Numerical studies show that the model predictions are robust as long as the isotherm data cover the range of mobile phase compositions where the protein actually elutes from the column.     

Kinetics of melittin-induced fusion of dipalmitoylphosphatidylcholine small unilamellar vesicles

We have studied the kinetics of fusion of dipalmitoylphosphatidylcholine small unilamellar vesicles at 51 degrees C which is induced by bee venom melittin at a protein-to-lipid molar ratio of 1/60. This was done by following with a stopped-flow fluorometer the reduction in the ratio of the excimer to monomer fluorescence intensities of 1-palmitoyl-2-(10-pyrenyldecanoyl)-sn-glycero-3-phosphorylcholine that accompanies fusion. At a low melittin concentration and low ionic strength, for which case the protein is monomeric, the value of the rate constant for fusion is 0.006 s-1. This is much smaller than that of 0.06 s-1 obtained for a high melittin concentration at low ionic strength, i.e. for the protein in the tetrameric form which is not induced by a high salt concentration. The value of the rate constant for fusion for a low melittin concentration in the presence of 2 M NaCl, i.e. for the protein in the tetrameric form which is induced by a high salt concentration, is 0.12 s-1. This is twice as large as that for fusion induced by the tetramer in a low ionic strength solution. These findings show that the state of aggregation of the protein in solution and, to a lesser extent, electrostatic interactions play an important role in the kinetics of melittin-induced fusion of vesicles.     

Large-scale HPLC purification of calbindin D9k from porcine intestine

Two efficient procedures for large-scale purification of calbindin D9k from porcine intestine by HPLC were developed. Both protocols start with heat treatment of the intestinal tissue followed by acetic acid extraction, a capture with alginic acid, NaCl precipitation of other proteins, and a concentration step on Amberlite XAD-2. In the first method, a single reverse-phase HPLC step completes the purification and results in milligram quantities of pure calbindin. In the second method, an additional ion exchange HPLC step was introduced, followed by a reverse-phase HPLC resulting in 100 milligram-scale preparations of homogeneous calbindin in a 56% yield from the Amberlite step. Both methods yielded a homogeneous metal-free apoprotein with a molecular weight of 8838.0 +/- 8.8 as analyzed by MALDI TOF mass spectrometry corresponding to N-acetylated porcine calbindin. The isolated apocalbindin was fully reconstituted with 2 molar equivalents of Ca(2+) and the protein displayed UV and fluorescence spectra characteristic of those of native calbindin D9k.