Orientational steering in enzyme-substrate association: Ionic strength dependence of hydrodynamic torque effects

The effect of hydrodynamic torques on the association rate constants for enzyme-ligand complexation is investigated by Brownian dynamics simulations. Our hydrodynamic models of the enzyme and ligand are composed of spherical elements with friction forces acting at their centers. A quantitative measure of hydrodynamic torque orientational effects is introduced by choosing, as a reference system, an enzyme-ligand model with the same average hydrodynamic interactions but without orientational dependence. Our simple models show a 15% increase in the rate constant caused by hydrodynamic torques at physiological ionic strength. For more realistic hydrodynamic models, which are not computationally feasible at present, this effect is probably higher. The most important finding of this work is that hydrodynamic complementarity in shape (i.e. like the fitting together of pieces of a puzzle) is most effective for interactions between molecules at physiological ionic strength. Correspondence to: J.M. Briggs     

Computer modeling of electrostatic steering and orientational effects in antibody-antigen association.

Brownian dynamics simulations are performed to investigate the role of long-range electrostatic forces in the association of the monoclonal antibody HyHEL-5 with hen egg lysozyme. The electrostatic field of the antibody is obtained from a solution of the nonlinear Poisson-Boltzmann using the x-ray crystal coordinates of this protein. The lysozyme is represented as an asymmetric dumbell consisting of two spheres of unequal size, an arrangement that allows for the modeling of the orientational requirements for docking. Calculations are done with the wild-type antibody and several point mutants at different ionic strengths. Changes in the charge distribution of the lysozyme are also considered. Results are compared with experiment and a simpler model in which the lysozyme is approximately by a single charged sphere.     

Task-specific association of photoreceptor systems and steering parameters in Drosophila

Visual motion processing enables moving fruit flies to stabilize their course and altitude and to approach selected objects. Earlier attempts to identify task-specific pathways between two photoreceptor systems (peripheral retinula cells 1-6, and central retinula cells 7 + 8) and three steering parameters (wingstroke asymmetry, abdomen deflection, hindleg deflection) attributed course control and object fixation to peripheral retinula cells 1-6-mediated simultaneous reactions of these parameters. The present investigation includes first results from fixed flying or freely walking ninaE17 mutants which cannot synthesize the peripheral retinula cells 1-6 photoreceptor-specific opsin. Retention of about 12% of the normal course control and about 58% of the object fixation in these flies suggests partial input sharing for both responses and, possibly, a specialization for large-field (peripheral retinula cells 1-6) and small-field (central retinula cells 7 + 8) motion. Such signals must be combined to perceive relative motion between an object and its background. The combining links found in larger species might explain a previously neglected interdependence of course control and object fixation in Drosophila. -Output decomposition revealed an unexpected orchestration of steering. Wingstroke asymmetry and abdomen deflection do not contribute in fixed proportions to the yaw torque of the flight system. Different steering modes seem to be selected according to their actual efficiency under closed-loop conditions and to the degree of intended turning. An easy experimental access to abdominal steering is introduced.     

Electrostatic effects in divalent ion binding to tRNA.

The binding of Mn²⁺ to yeast tRNA^Phe at 25°C is measured by esr, and found to depend strongly on the concentration of monovalent cations, showing the importance of electrostatic effects. In low sodium (<15mM/l.), the affinity is high and the Scatchard plots are distinctly curved. In high sodium (>50mM/l.), the affinity and the curvature are reduced. In a limited range of sodium concentrations (15–30mM/l.), the folding of tRNA which is induced by the divalent ions results in cooperative binding, leading to upwards convexity of the Scatchard plot. An electrostatic model is developed, based on a single type of binding site which we take to be the phosphates, with a binding constant for Mn²⁺ in the range of that found for ApA, 10 l./M. We compute the change in the binding constant due to the electrostatic potential of the distant charges (other phosphates and counterions), using a single set of parameters for all sodium concentrations. The model predicts that the plots in low sodium are curved, and a good fit to the experimental results is obtained: it is therefore not legitimate or necessary to interpret these results in terms of two types of binding sites. In high salt, the model gives plots that are only slightly curved, corresponding to weaker electrostatic effects. This shows that a search for sites with a special binding mode should be done in high salt. The computed plots are in good agreement with the data, except for slight differences concerning the first bound ions, which give a possible indication in favor of special binding. Given the observation of one special site for Mg²⁺ at 4°C in high sodium [Stein, A. & Crothers, D. M. (1976) Biochemistry 15 , 157–160] in E. coli tRNA^fMet, we have measured the binding of Mn²⁺ at lower temperature. At 12°C, in both yeast tRNA^Phe and E. coli tRNA^fMet, the plots clearly indicate special binding. A site found in high sodium is on a very different footing from the four to six so-called strong sites unduly derived from low-salt binding plots.     

Electrostatic and hydrophobic effects in affinity chromatography

A semi–quantitative theory is developed to explain the nonspecific binding of proteins to substituted affinity chromatography supports due to electrostatic and hydrophobic interactions. The equilibrium constant for the absorption of an enzyme to a solid support, and the rate of desorption of the enzyme are studied as functions of ionic strength. Experimental measurements were taken of the adsorption equilibrium constant and rate of desorption of E. coli β–galactosidase on Sepharose 4B substituted with 3, 3,-diaminodipropylamine in batch systems. It was found that the enzyme adsorption exhibits a hysteresis effect as the ionic strength is increased and then decreased. Furthermore, the adsorption of theenzyme becomes more reversible at the lower ionic strengths, while at the higher ionic strengths it is essentially irreversible. Using the measured equilibrium constants, and knowing the region of ionic strength where the adsorption becomes reversible, we were able to predict the desorption of enzyme in a continuous stirred tank as a function of time when a decreasing linear gradient of ionic strength was introduced into a slurry. It was found that the presence of another protein, hemoglobin, does not affect these results, and therefore can be separated from the enzyme.     

Electrostatic rate enhancement and transient complex of protein-protein association

The association of two proteins is bounded by the rate at which they, via diffusion, find each other while in appropriate relative orientations. Orientational constraints restrict this rate to approximately 10(5)-10(6) M(-1) s(-1). Proteins with higher association rates generally have complementary electrostatic surfaces; proteins with lower association rates generally are slowed down by conformational changes upon complex formation. Previous studies (Zhou, Biophys J 1997;73:2441-2445) have shown that electrostatic enhancement of the diffusion-limited association rate can be accurately modeled by $k_{\bf D}$ = $k_{D}0\ {exp} ( - \langle U_{el} \rangle;{\star}/k_{B} T),$ where k(D) and k(D0) are the rates in the presence and absence of electrostatic interactions, respectively, U(el) is the average electrostatic interaction energy in a "transient-complex" ensemble, and k(B)T is the thermal energy. The transient-complex ensemble separates the bound state from the unbound state. Predictions of the transient-complex theory on four protein complexes were found to agree well with the experiment when the electrostatic interaction energy was calculated with the linearized Poisson-Boltzmann (PB) equation (Alsallaq and Zhou, Structure 2007;15:215-224). Here we show that the agreement is further improved when the nonlinear PB equation is used. These predictions are obtained with the dielectric boundary defined as the protein van der Waals surface. When the dielectric boundary is instead specified as the molecular surface, electrostatic interactions in the transient complex become repulsive and are thus predicted to retard association. Together these results demonstrate that the transient-complex theory is predictive of electrostatic rate enhancement and can help parameterize PB calculations.     

Electrostatic effects in proteins: comparison of dielectric and charge models.

Two approaches for calculating electrostatic effects in proteins are compared and ana analysis is presented of the dependence of calculated properties on the model used to define the charge distribution. Changes in electrostatic free energy have been calculated using a screened Coulomb potential (SCP) with a distance-dependent effective dielectric permittivity to model bulk solvent effects and a finite difference approach to solve the Poisson-Boltzmann (FDPB) equation. The properties calculated include shifts in dissociation constants of ionizable groups, the effect of annihilating surface charges on the binding of metals, and shifts in redox potentials due to changes in the charge of ionizable groups. In the proteins considered the charged sites are separated by 3.5-12 A. It is shown that for the systems studied in this distance range the SCP yields calculated values which are at least as accurate as those obtained from solution of the FDPB equation. In addition, in the distance range 3-5 A the SCP gives substantially better results than the FDPB equation. Possible sources of this difference between the two methods are discussed. Shifts in binding constants and redox potentials were calculated with several standard charge sets, and the resulting values show a variation of 20-40% between the 'best' and 'worst' cases. From this study it is concluded that in most applications, changes in electrostatic free energies can be calculated economically and reliably using an SCP approach with a single functional form of the screening function.     

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.     

Electrostatic effects in short superhelical DNA

We present Monte Carlo simulations of the equilibrium configurations of short closed circular DNA that obeys a combined elastic, hard-sphere, and electrostatic energy potential. We employ a B-spline representation to model chain configuration and simulate the effects of salt on chain folding by varying the Debye screening parameter. We obtain global equilibrium configurations of closed circular DNA, with several imposed linking number differences, at two salt concentrations (specifically at the extremes of no added salt and the high salt regime), and for different chain lengths. Minimization of the composite elastic/long-range potential energy under the constraints of ring closure and fixed chain length is found to produce structures that are consistent with the configurations of short supercoiled DNA observed experimentally. The structures generated under the constraints of an electrostatic potential are less compact than those subjected only to an elastic term and a hard-sphere constraint. For a fixed linking number difference greater than a critical value, the interwound structures obtained under the condition of high salt are more compact than those obtained under the condition of no added salt. In the case of no added salt, the electrostatic energy plays a dominant role over the elastic energy in dictating the shape of the closed circular DNA. The DNA supercoil opens up with increasing chain length at low salt concentration. A branched three-leaf rose structure with a fixed linking number difference is higher in energy than the interwound form at both salt concentrations employed here.     

Electrostatic effects on the kinetics of bound enzymes.

1. The effect of the interaction between the charged matrix and substrate on the kinetic behaviour of bound enzymes was investigated theoretically. 2. Simple expression is derived for the apparent Km. 3. The apparent Km can only be used for the characterization of the electrostatic effect of the ionic strength does not vary with the substrate concentration. 4. The deviations from Michaelis-Menton kinetics are graphically illustrated for cases when the ionic strength varies with the substrate concentration. 5. The inhibition of the bound enzyme by a charged inhibitor at constant ionic strength is characterized by an apparent Ki. 6. When both the inhibitor concentration and the ionic strength change there is no apparent Ki, and the inhibition profile is graphically illustrated for this case. 7. Under certain conditions the electrostatic effects manifest thenselves in a sigmoidal dependence of the enzyme activity on the concentration of the substrate or inhibitor.     

Electrostatic effects in the control of glycogen phosphorylase by phosphorylation.

Electrostatic effects are important in the initial activation mechanism of glycogen phosphorylase by phosphorylation. Analysis of the electrostatic surface potential of glycogen phosphorylase with the program GRASP shows that in the unphosphorylated state, the N-terminal 20 residues, which include a number of basic amino acids, are located close to a position on the surface of the molecule that is highly acidic. Upon phosphorylation by phosphorylase kinase at Ser 14, the N-terminal residues change their position and conformation so that the Ser-P is directed away from the acidic patch and to an intersubunit site where 2 arginines bind the phosphate. This recognition site is created through tertiary and quaternary structural changes that accompany the activation mechanism.     

Functional effects of heme orientational disorder in sperm whale myoglobin

The optical absorption and ligand binding properties of newly reconstituted sperm whale myoglobin were examined systematically at pH 8, 20 degrees C. The conventional absorbance and magnetic circular dichroism spectra of freshly reconstituted samples were identical to those of the native protein. In contrast, reconstituted azide or CO myoglobin initially exhibited less circular dichroism in the Soret wavelength region than native myoglobin. These data support the theory proposed by La Mar and co-workers (La Mar, G. N., Davis, N. L., Parish, D. W., and Smith, R. M. (1983) J. Mol. Biol. 168, 887-896) that protoheme inserts into apomyoglobin in two distinct orientations. The equilibrium and kinetic parameters for O2 and CO binding to newly reconstituted myoglobin were observed to be identical to those of the native protein. Thus, the orientation of the heme group has no effect on the physiological properties of myoglobin. This result is in disagreement with the preliminary report of Livingston et al. (Livingston, D. J., Davis, N. L., La Mar, G. N., and Brown, W. D. (1984) J. Am. Chem. Soc. 106, 3025-3026) which suggested that the abnormal heme conformation exhibited a 10-fold greater affinity and association rate constant for O2 binding. Significant kinetic heterogeneity was observed only for long-chain isonitrile binding to newly reconstituted myoglobin, and even in these cases, the rate constants for the abnormal and normal heme conformations differed by less than a factor of 4.     

Electrostatic analysis and Brownian dynamics simulation of the association of plastocyanin and cytochrome f.

The oxidation of cytochrome f by the soluble cupredoxin plastocyanin is a central reaction in the photosynthetic electron transfer chain of all oxygenic organisms. Here, two different computational approaches are used to gain new insights into the role of molecular recognition and protein-protein association processes in this redox reaction. First, a comparative analysis of the computed molecular electrostatic potentials of seven single and multiple point mutants of spinach plastocyanin (D42N, E43K, E43N, E43Q/D44N, E59K/E60Q, E59K/E60Q/E43N, Q88E) and the wt protein was carried out. The experimentally determined relative rates (k(2)) for the set of plastocyanin mutants are found to correlate well (r(2) = 0.90 - 0.97) with the computed measure of the similarity of the plastocyanin electrostatic potentials. Second, the effects on the plastocyanin/cytochrome f association rate of these mutations in the plastocyanin "eastern site" were evaluated by simulating the association of the wild type and mutant plastocyanins with cytochrome f by Brownian dynamics. Good agreement between the computed and experimental relative rates (k(2)) (r(2) = 0.89 - 0.92) was achieved for the plastocyanin mutants. The results obtained by applying both computational techniques provide support for the fundamental role of the acidic residues at the plastocyanin eastern site in the association with cytochrome f and in the overall electron-transfer process.     

Electrostatic association and donnan phenomena as mechanisms of ion accumulation

Excised roots of barley (Hordeum vulgare, var. Campana) were incubated for periods up to 24 hours in salt solutions of various concentrations and ion accumulation was determined at various time intervals. The data were consistent with the existence of 2 components of ion uptake, one accounting for ion uptake from solutions below 1 mm and both components contributing to uptake from solutions of concentrations higher than 1 mm.     

Saxitoxin and tetrodotoxin. Electrostatic effects on sodium channel gating current in crayfish axons.

The effects of extracellular saxitoxin (STX) and tetrodotoxin (TTX) on gating current (IgON) were studied in voltage clamped crayfish giant axons. At a holding potential (VH) of -90 mV, integrated gating charge (QON) was found to be 56% suppressed when 200 nM STX was added to the external solution, and 75% suppressed following the addition of 200 nM TTX. These concentrations of toxin are sufficiently high to block greater than 99% of sodium channels. A smaller suppression of IgON was observed when 1 nM STX was used (KD = 1-2 nM STX). The suppression of IgON by external toxin was found to be hold potential dependent, with only minimal suppression observed at the most hyperpolarized hold potentials, -140 to -120 mV. The maximal effect of these toxins on IgON was observed at hold potentials where the QON vs. VH plot was found to be steepest, -100 to -80 mV. The suppression of IgON induced by TTX is partially relieved following the removal of fast inactivation by intracellular treatment with N-bromoacetamide (NBA). The effect of STX and TTX on IgON is equivalent to a hyperpolarizing shift in the steady state inactivation curve, with 200 nM STX and 200 nM TTX inducing shifts of 4.9 +/- 1.7 mV and 10.0 +/- 2.1 mV, respectively. Our results are consistent with a model where the binding of toxin displaces a divalent cation from a negatively charged site near the external opening of the sodium channel, thereby producing a voltage offset sensed by the channel gating apparatus.     

Electrostatic interactions in the association of proteins: an analysis of the thrombin-hirudin complex.

The role of electrostatic interactions in stabilization of the thrombin-hirudin complex has been investigated by means of two macroscopic approaches: the modified Tanford-Kirkwood model and the finite-difference method for numerical solution of the Poisson-Boltzmann equations. The electrostatic potentials around the thrombin and hirudin molecules were asymmetric and complementary, and it is suggested that these fields influence the initial orientation in the process of the complex formation. The change of the electrostatic binding energy due to mutation of acidic residues in hirudin has been calculated and compared with experimentally determined changes in binding energy. In general, the change in electrostatic binding energy for a particular mutation calculated by the modified Tanford-Kirkwood approach agreed well with the experimentally observed change. The finite-difference approach tended to overestimate changes in binding energy when the mutated residues were involved in short-range electrostatic interactions. Decreases in binding energy caused by mutations of amino acids that do not make any direct ionic interactions (e.g., Glu 61 and Glu 62 of hirudin) can be explained in terms of the interaction of these charges with the positive electrostatic potential of thrombin. Differences between the calculated and observed changes in binding energy are discussed in terms of the crystal structure of the thrombin-hirudin complex.     

Electrostatic effects play a central role in cold adaptation of trypsin.

Organisms that live in constantly cold environments have to adapt their metabolism to low temperatures, but mechanisms of enzymatic adaptation to cold environments are not fully understood. Cold active trypsin catalyses reactions more efficiently and binds ligands more strongly in comparison to warm active trypsin. We have addressed this issue by means of comparative free energy calculations studying the binding of positively charged ligands to two trypsin homologues. Stronger inhibition of the cold active trypsin by benzamidine and positively charged P1-variants of BPTI is caused by rather subtle electrostatic effects. The different affinity of benzamidine originates solely from long range interactions, while the increased binding of P1-Lys and -Arg variants of BPTI is attributed to both long and short range effects that are enhanced in the cold active trypsin compared to the warm active counterpart. Electrostatic interactions thus provide an efficient strategy for cold adaptation of trypsin.     

Electrostatic effects on polynucleotide transitions. II. Behavior of titrated systems

The theory developed in the previous paper to discuss changes in electrostatic free energies in polynucleotide order–disorder transitions is extended to cases where one or more of the participating species is titrated to some degree α. It is shown that, for any class of transition, the melting temperature T_m at constant pH is a linear function of the logarithm of the monovalent counterion concentration M, that at high salt the logarithm of the depression of the melting temperature by pH titration is proportional to the pH change, and that the stability of the ordered form as measured by its melting temperature at neutral pH, is a monotonic function of the quantity pH_m – pK, where pH_m and pK are the pH of melting and the monomer base pK, both measured under similar conditions of temperature and ionic strength. For the transition from double helix to coil, the dependences of T_m and dT_m/d log M on pH are determined experimentally and compared with the qualitative predictions of the theory. It is found that dT_m/dlog M, a measure of – ΔF?^el (the negative of the electrostatic free energy change in the transition), decreases with increasing pH. In acid solution, where the coil is more extensively prolonated than the helix, the change in electrostatic free energy in the transition is larger than at neutral pH. Conversely, in alkali the electrostatic five energy change is smaller than at neutral pH. Hence (dT_m/d log M)_acid > (dT_m/d log M _neutral) > (dT_m/d log M)_alkali. At Suffeciently high pH, dT_m/d log M is observed to become negative, indicating that the electrostatic free energy change is positive in the transition of this region. Date from the literature on the ionic strength dependence of the melting temperature for the acid helices of poly rA, poly rC, and poly dC are also considered from the standpoint of the theory.