A comparative structural and functional analysis of cytochrome cM cytochrome c6 and plastocyanin from the cyanobacterium Synechocystis sp. PCC 6803

Cytochrome cM is a new c-class photosynthetic haem protein whose physiological role is still unknown. It has been proposed previously that cytochrome cM can replace cytochrome c6 and plastocyanin in transferring electrons between the two membrane complexes cytochrome b6-f and photosystem I in organisms growing under stress conditions. The experimental evidence herein provided allows us to discard such a hypothesis. We report a procedure to overexpress cytochrome cM from the cyanobacterium Synechocystis sp. PCC 6803 in Escherichia coli cells in mg quantities. This has allowed us to perform a comparative laser flash-induced kinetic analysis of photosystem I reduction by the three metalloproteins from Synechocystis. The bimolecular rate constant for the overall reaction is up to 100 times lower with cytochrome cM than with cytochrome c6 or plastocyanin. In addition, the redox potential value and surface electrostatic potential distribution of cytochrome cM are quite different from those of cytochrome c6 and plastocyanin. These findings strongly indicate that cytochrome cM cannot be recognised by and interact with the same redox partners as the other two metalloproteins.     

Site-directed mutagenesis of cytochrome c6 from Synechocystis sp. PCC 6803. The heme protein possesses a negatively charged area that may be isofunctional with the acidic patch of plastocyanin

This paper reports the first site-directed mutagenesis analysis of any cytochrome c6, a heme protein that performs the same function as the copper-protein plastocyanin in the electron transport chain of photosynthetic organisms. Photosystem I reduction by the mutants of cytochrome c6 from the cyanobacterium Synechocystis sp. PCC 6803 has been studied by laser flash absorption spectroscopy. Their kinetic efficiency and thermodynamic properties have been compared with those of plastocyanin mutants from the same organism. Such a comparative study reveals that aspartates at positions 70 and 72 in cytochrome c6 are located in an acidic patch that may be isofunctional with the well known "south-east" patch of plastocyanin. Calculations of surface electrostatic potential distribution in the mutants of cytochrome c6 and plastocyanin indicate that the changes in protein reactivity depend on the surface electrostatic potential pattern rather than on the net charge modification induced by mutagenesis. Phe-64, which is close to the heme group and may be the counterpart of Tyr-83 in plastocyanin, does not appear to be involved in the electron transfer to photosystem I. In contrast, Arg-67, which is at the edge of the cytochrome c6 acidic area, seems to be crucial for the interaction with the reaction center.     

Frontal gel chromatography of interacting systems: theoretical and experimental evaluation of the shapes of elution profiles for systems of the type A + B in equilibrium C

A theoretical and experimental study has been made of the advancing elution profile in frontal gel chromatography of interacting systems for which the elution volume of the complex is smaller than that of the larger reactant. First, Gilbert-Jenkins theory is used to delineate the form of the elution profile from the magnitudes of the elution volumes and concentrations of reacting species. This procedure resulted in the detection of a misinterpretation of certain patterns obtained in a gel chromatographic study of the interaction between myoglobin and ovalbumin. Second, a numerical computational procedure, which incorporates both axial dispersion and concentration-dependence of species elution volumes, is used to establish the influence of these two factors on boundary shapes for such systems. Third, frontal gel chromatography on Sephadex G-75 is used to compare experimental behavior with theoretical profiles predicted for the electrostatic interaction between cytochrome c and soybean trypsin inhibitor (pH 6.8, I 0.01). Results of these experiments serve as a guide for future conduct of experiments aimed at characterization of biologically important, reversible complex formation between proteins and/or other macromolecules.     

Solutions to axon equations

The solutions to a general class of axon partial differential equations proposed by FitzHugh which includes the Hodgkin-Huxley equations are studied. It is shown that solutions to the partial differential equations are exactly the solutions to a related set of integral equations. An iterative procedure for constructing the solutions based on standard methods for ordinary differential equations is given and each set of initial values is shown to lead to a unique solution. Continuous dependence of the solutions on the initial values is established and solutions with initial values in a restricted (physiological) range are shown to remain in that range for all time. The iterative procedure is not suggested as the basis for numerical integration.     

Calculations of the spatial distribution of charge density in the environment of DNA

A technique for modeling the structured environmental charge distribution about isolated polyions of arbitrary geometry is presented and applied to B-DNA. It describes the three-dimensional variation of the continuous space charge and allows estimation of local electrostatic potentials and fields that the electrolytic environment induces at nuclei of the polyion. Calculations involve an iterative solution to the set of equations coupling electrostatic potential and average charge density in space. By dividing the region around a DNA segment into finite volume elements, sets of numerically stable atmospheric charge densities have been obtained over a range of concentrations of added monovalent salt. Results are in good agreement with those of Poisson-Boltzmann calculations on comparable systems and are consistent with findings from Monte Carlo simulations of DNA.     

Electrostatic orientation of the electron-transfer complex between plastocyanin and cytochrome c.

To understand the specificity and efficiency of protein-protein interactions promoting electron transfer, we evaluated the role of electrostatic forces in precollision orientation by the development of two new methods, computer graphics alignment of protein electrostatic fields and a systematic orientational search of intermolecular electrostatic energies for two proteins at present separation distances. We applied these methods to the plastocyanin/cytochrome c interaction, which is faster than random collision, but too slow for study by molecular dynamics techniques. Significant electrostatic potentials were concentrated on one-fourth (969 A2) of the plastocyanin surface, with the greatest negative potential centered on the Tyr-83 hydroxyl within the acidic patch, and on one-eighth (632 A2) of the cytochrome c surface, with the greatest positive potential centered near the exposed heme edge. Coherent electrostatic fields occurred only over these regions, suggesting that local, rather than global, charge complementarity controls productive recognition. The three energetically favored families of pre-collision orientations all directed the positive region surrounding the heme edge of cytochrome c toward the acidic patch of plastocyanin but differed in heme plane orientation. Analysis of electrostatic fields, electrostatic energies of precollision orientations with 12 and 6 A separation distances, and surface topographies suggested that the favored orientations should converge to productive complexes promoting a single electron-transfer pathway from the cytochrome c heme edge to Tyr-83 of plastocyanin. Direct interactions of the exposed Cu ligand in plastocyanin with the cytochrome c heme edge are not unfavorable sterically or electrostatically but should occur no faster than randomly, indicating that this is not the primary pathway for electron transfer.     

Kinetics of intracomplex electron transfer and of reduction of the components of covalent and noncovalent complexes of cytochrome c and cytochrome c peroxidase by free flavin semiquinones

The kinetics of reduction of free flavin semiquinones of the individual components of 1:1 covalent and electrostatic complexes of yeast ferric and ferryl cytochrome c peroxidase and ferric horse cytochrome c have been studied. Covalent cross-linking between the peroxidase and cytochrome c at low ionic strength results in a complex that has kinetic properties both similar to and different from those of the electrostatic complex. Whereas the cytochrome c heme exposure to exogenous reductants is similar in both complexes, the apparent electrostatic environment near the cytochrome c heme edge is markedly different. In the electrostatic complex, a net positive charge is present, whereas in the covalent complex, an essentially neutral electrostatic charge is found. Intracomplex electron transfer within the two complexes is also different. For the covalent complex, electron transfer from ferrous cytochrome c to the ferryl peroxidase has a rate constant of 1560 s-1, which is invariant with respect to changes in the ionic strength. The rate constant for intracomplex electron transfer within the electrostatic complex is highly ionic strength dependent. At mu = 8 mM a value of 750 s-1 has been obtained [Hazzard, J. T., Poulos, T. L., & Tollin, G. (1987) Biochemistry 26, 2836-2848], whereas at mu = 30 mM the value is 3300 s-1. This ionic strength dependency for the electrostatic complex has been interpreted in terms of the rearrangement of the two proteins comprising the complex to a more favorable orientation for electron transfer. In the case of the covalent complex, such reorientation is apparently impeded.(ABSTRACT TRUNCATED AT 250 WORDS)     

The negative cooperativity in cytochrome c oxidase redox reactions: the electrostatic effect

The electrostatic interaction of two hemes is calculated on the basis of the data on the cytochrome c oxidase structure. The interaction energy corresponds to the positive shift by approximately greater than 100 mV of the redox potential of one of the hemes when the other is oxidized. This effect seems to be the most likely reason of the negative cooperativity in the redox behavior of cytochrome c oxidase.     

The effect of complex formation upon the reduction rates of cytochrome c and cytochrome c peroxidase compound II

The effect of complex formation between ferricytochrome c and cytochrome c peroxidase (Ferrocytochrome-c:hydrogen peroxide oxidoreductase, EC 1.11.1.5) on the reduction of cytochrome c by N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD), reduced N-methylphenazonium methosulfate (PMSH), and ascorbate has been determined at low ionic strength (pH 7) and 25 degrees C. Complex formation with the peroxidase enhances the rate of ferricytochrome c reduction by the neutral reductants TMPD and PMSH. Under all experimental conditions investigated, complex formation with cytochrome c peroxidase inhibits the ascorbate reduction of ferricytochrome c. This inhibition is due to the unfavorable electrostatic interactions between the ascorbate dianion and the negatively charged cytochrome c-cytochrome c peroxidase complex. Corrections for the electrostatic term by extrapolating the data to infinite ionic strength suggest that ascorbate can reduce cytochrome c peroxidase-bound cytochrome c faster than free cytochrome c. Reduction of cytochrome c peroxidase Compound II by dicyanobis(1,10-phenanthroline)iron(II) (Fe(phen)2(CN)2) is essentially unaffected by complex formation between the enzyme and ferricytochrome c at low ionic strength (pH 6) and 25 degrees C. However, reduction of Compound II by the negatively changed tetracyano-(1,10-phenanthroline)iron(II) (Fe(phen)(CN)4) is enhanced in the presence of ferricytochrome c. This enhancement is due to the more favorable electrostatic interactions between the reductant and cytochrome c-cytochrome c peroxidase Compound II complex then for Compound II itself. These studies indicate that complex formation between cytochrome c and cytochrome c peroxidase does not sterically block the electron-transfer pathways from these small nonphysiological reductants to the hemes in these two proteins.     

Iterative algorithms for processing experimental data

The need to solve linear and nonlinear integral equations arise, e.g., in recovering plasma parameters from the data of multichannel diagnostics. The paper presents an iterative method for solving integral equations with a singularity at the upper limit of integration. The method consists in constructing successive approximations and calculating the integral by quadrature formulas in each integration interval. An example of application of the iterative algorithm to numerically solve an integral equation similar to those arising in recovering the plasma density profile from reflectometry data is presented.     

Probing electrostatic interactions in cytochrome c using site-directed chemical modification.

This communication reports the generation of an electrostatic probe using chemical modification of methionine side chains. The alkylation of methionine by iodoacetamide was achieved in a set of Saccharomyces cerevisiae iso-1-cytochrome c mutants, introducing the nontitratable, nondelocalized positive charge of a carboxyamidomethylmethionine sulfonium (CAMMS) ion at five surface and one buried site in the protein. Changes in redox potential and its variation with temperature were used to calculate microscopic effective dielectric constants operating between the probe and the heme iron. Dielectric constants (epsilon) derived from deltadeltaG values were not useful due to entropic effects, but epsilon(deltadeltaH) gave results that supported the theory. The effect on biological activity of surface derivatization was interpreted in terms of protein-protein interactions. The introduction of an electrostatic probe in cytochrome c often resulted in marked effects on activity with one of two physiological partners: cytochrome c reductase, especially if introduced at position 65, and cytochrome c oxidase, if at position 28.     

Investigating protein-protein interaction surfaces using a reduced stereochemical and electrostatic model

A method of calculating the electrostatic potential energy between two molecules, using finite difference potential, is presented. A reduced charge set is used so that the interaction energy can be calculated as the two static molecules explore their full six-dimensional configurational space. The energies are contoured over surfaces fixed to each molecule with an interactive computer graphics program. For two crystal structures (trypsin-trypsin inhibitor and anti-lysozyme Fab-lysozyme), it is found that the complex corresponds to highly favourable interacting regions in the contour plots. These matches arise from a small number of protruding basic residues interacting with enhanced negative potential in each case. The redox pair cytochrome c peroxidase-cytochrome c exhibits an extensive favourably interacting surface within which a possible electron transfer complex may be defined by an increased electrostatic complementarity, but a decreased electrostatic energy. A possible substrate transfer configuration for the glycolytic enzyme pair glyceraldehyde phosphate dehydrogenase-phosphoglycerate kinase is presented.     

On computational approaches for size-and-shape distributions from sedimentation velocity analytical ultracentrifugation

Sedimentation velocity analytical ultracentrifugation has become a very popular technique to study size distributions and interactions of macromolecules. Recently, a method termed two-dimensional spectrum analysis (2DSA) for the determination of size-and-shape distributions was described by Demeler and colleagues (Eur Biophys J 2009). It is based on novel ideas conceived for fitting the integral equations of the size-and-shape distribution to experimental data, illustrated with an example but provided without proof of the principle of the algorithm. In the present work, we examine the 2DSA algorithm by comparison with the mathematical reference frame and simple well-known numerical concepts for solving Fredholm integral equations, and test the key assumptions underlying the 2DSA method in an example application. While the 2DSA appears computationally excessively wasteful, key elements also appear to be in conflict with mathematical results. This raises doubts about the correctness of the results from 2DSA analysis.     

The influence of electrostatic interactions on partition in aqueous polyethylene glycol/dextran biphasic systems: Part II

In aqueous polyethylene glycol/dextran two-phase systems, the hydrophobicity, free volume, surface tension, and interfacial tension of the phases in equilibrium were measured as a function of pH and ionic strength. These parameters were found to change with pH, but the pattern and magnitude cannot explain the unusual partition of charged macromolecules, observed previously. The electrostatic potential difference was determined by a new experimental approach based on the measurement of the pH difference between the phases at equilibrium. In polyethylene glycol/dextran systems containing sodium chloride as ionized species, the electrostatic potential is not constant in the pH range 2 to 11. The partition behavior of charged macromolecules and its dependence on pH can be explained by the combined action of charge and phase potential. This conclusion was tested with poly-L-glutamate, which partitioned as predicted and in a pattern opposite to positively charged macro- molecules. (c) 1995 John Wiley & Sons, Inc.     

Electrostatic potential of macromolecules measured by pKa shift of a fluorophore. 1. The 3' terminus of 16S RNA

We have investigated the use of the pH-sensitive fluorescein label as a probe for electrostatic potential in macromolecules. The practicality of this technique is demonstrated by its application to the 16S RNA molecule. The dependence of the electrostatic potential upon ionic conditions and upon the presence of ribosomal proteins and the state of the RNA was studied. The combination of electrostatic and anisotropy data emphasizes the r?le of the 30S ribosomal proteins, rather than of the renaturation of the 16S RNA or the presence of the 50S subunit, in shaping the environment of the 3' terminus of the 16S RNA in the active ribosome.     

Activity of cyclic-AMP phosphodiesterase in permeabilised cells of Bakers'' yeast

1. Pulse-radiolysis experiments were performed in the presence of methyl viologen and cytochrome c3. After the pulse, methyl viologen radicals are formed and the kinetics of these radicals with cytochrome c3 are studied, The reaction between cytochrome c3 and methyl viologen radicals (MV+) is diffusion controlled. The ionic strength dependence and the pH-dependence of this reaction were studied. From the ionic strength dependence (at pH 7.8) we found that the net charge of the fully oxidized cytochrome c3 molecule was Z = + 4.7 +/- 0.7. 2. After the pulse an equilibrium is reached for the reaction of MV+ with cytochrome c3. From this equilibrium an apparent midpoint potential can be obtained. The apparent midpoint potential of this multihaem molecule was found to depend on the degree of reduction, alpha. With the help of the Nernst equation an empirical equation is obtained to describe this dependence of the midpoint potential: E0 = - 0.250 - 0.088 alpha (in V). 3. An estimation is made of the energy of interaction between the haems due to electrostatic interactions (delta epsilon less than 32 mV) and due to ionic strength effects (- 12 mV less than delta epsilon less than 26 mV). The results suggest that the redox properties of the individual haems in the cytochrome c3 molecule are dependent on the degree of reduction of the other haems in the molecule. 4. The reaction of cytochrome c3 with MV+ or with ethanol radicals (EtOH) has been compared with the reactions of horse-heart cytochrome c and of metmyoglobin with the same radicals. The reaction of MV+ or EtOH with horse-heart cytochrome c is found to be diffusion controlled; the reactions with metmyoglobin on the other hand are most probably controlled by an activation energy.     

The Application of Electromagnetic Theory to Electrocardiology: II. Numerical Solution of the Integral Equations

In an earlier paper exact integral equations were derived for the surface potentials resulting from sources within an irregularly shaped inhomogeneous body. These exact equations cannot usually be solved. In this paper a discrete analogue is constructed which is not straightforward to solve, but which can be treated by careful mathematical methods. In particular a deflation procedure greatly facilitates the iterative solution of the problem and overcomes the divergence encountered by other authors. Numerical solutions obtained for simple geometries are compared to the exact analytic solutions available in such cases. The necessary convergence of the solutions of the discrete analog towards the solution of the continuous problem is shown to occur only if the coefficients of the discrete analogue are carefully evaluated. Calculations are then presented for realistic thoracic geometries, typical results being presented as surface potential maps. Finally the important effect of the internal regional inhomogeneities, particularly a realistic cardiac blood mass, is demonstrated by obtaining vector loops with and without these effects.     

Electrostatic interaction of cytochrome c with cytochrome c1 and cytochrome oxidase

The reactions of horse heart cytochrome c with succinate-cytochrome c reductase and cytochrome oxidase were studied as a function of ionic strength using both spectrophotometric and oxygen electrode assay techniques. The kinetic parameter Vmax/Km for both reactions decreased very rapidly as the ionic strength was increased, indicating that electrostatic interactions were important to the reactions. A new semiempirical relationship for the electrostatic energy of interaction between cytochrome c and its oxidation-reduction partners was developed, in which specific complementary charge-pair interactions between lysine amino groups on cytochrome c and negatively charged carboxylate groups on the other protein are assumed to dominate the interaction. The contribution of individual cytochrome c lysine amino groups to the electrostatic interaction was estimated from the decrease in reaction rate caused by specific modification of the lysine amino groups by reagents that change the charge to 0 or -1. These estimates range from -0.9 kcal/mol for lysines immediately surrounding the heme crevice of cytochrome c to 0 kcal/mol for lysines well removed from the heme crevice region. The semiempirical relationship for the total electrostatic energy of interaction was in quantitative agreement with the experimental ionic strength dependence of the reaction rates when the parameters were based on the specific lysine modification results. The electrostatic energies of interaction between cytochrome c and its reductase and oxidase were nearly the same, providing additional evidence that the two reactions take place at similar sites on cytochrome c.     

Brownian dynamics study of the influences of electrostatic interaction and diffusion on protein-protein association kinetics.

A unified model is presented for protein-protein association processes that are under the influences of electrostatic interaction and diffusion (e.g., protein oligomerization, enzyme catalysis, electron and energy transfer). The proteins are modeled as spheres that bear point charges and undergo translational and rotational Brownian motion. Before association can occur the two spheres have to be aligned properly to form a reaction complex via diffusion. The reaction complex can either go on to form the product or it can dissociate into the separate reactants through diffusion. The electrostatic interaction, like diffusion, influences every step except the one that brings the reaction complex into the product. The interaction potential is obtained by extending the Kirkwood-Tanford protein model (Tanford, C., and J. G. Kirkwood. 1957. J. Am. Chem. Soc. 79:5333-5339) to two charge-embedded spheres and solving the consequent equations under a particular basis set. The time-dependent association rate coefficient is then obtained through Brownian dynamics simulations according an algorithm developed earlier (Zhou, H.-X. 1990. J. Phys. Chem. 94:8794-8800). This method is applied to a model system of the cytochrome c and cytochrome c peroxidase association process and the results confirm the experimental dependence of the association rate constant on the solution ionic strength. An important conclusion drawn from this study is that when the product is formed by very specific alignment of the reactants, as is often the case, the effect of the interaction potential is simply to scale the association rate constant by a Boltzmann factor. This explains why mutations in the interface of the reaction complex have strong influences on the association rate constant whereas those away from the interface have minimal effects. It comes about because the former mutations change the interaction potential of the reaction complex significantly and the latter ones do not.     

Kinetics of flavin semiquinone reduction of the components of the cytochrome c-cytochrome b5 complex

The kinetics of flavin semiquinone reduction of the components of the 1:1 complex formed by cytochrome c with either cytochrome b5 or a derivative of cytochrome b5 in which the heme propionates are esterified (DME-cytochrome b5) have been studied. The rate constant for the reduction of horse heart cytochrome c by the electrostatically neutral lumiflavin semiquinone (LfH) is unaffected by complexation with native cytochrome b5 at pH 7. However, complex formation with DME-cytochrome b5 (pH 7) decreases by 35% the rate constant for cytochrome c reduction by LfH. At pH 8, complex formation with native cytochrome b5 decreases the rate constant for cytochrome c reduction by LfH markedly, whereas the rate constant for cytochrome c reduction, either unbound or in the complex formed with DME-cytochrome b5, is increased 2-fold relative to pH 7. These results indicate that the accessibility of the cytochrome c heme is not the same in the complexes formed with the two cytochrome b5 derivatives and that the docking geometry of the complex formed by the two native cytochromes is pH dependent. Binding of horse heart and tuna cytochromes c to native and DME-cytochromes b5 decreases the rate constants for reduction of cytochrome c by the negatively charged flavin mononucleotide semiquinone (FMNH) by approximately 30% and approximately 40%, respectively. This finding is attributed to substantial neutralization of the positive electrostatic potential surface of cytochrome c that occurs when it binds to either form of cytochrome b5.(ABSTRACT TRUNCATED AT 250 WORDS)