Mathematical analysis of ligand-induced monomerization and dimerization in the monomer dimer equilibrium of proteins. Application to D-amino acid oxidase.

We have mathematically analyzed ligand-induced monomerization and dimerization in a protein monomer-dimer equilibrium system, in which the monomer has one and the dimer two binding sites. These dimer sites have the same binding constants for the first ligand but may cooperatively interact when one of them is occupied by a ligand molecule. In this system, the apparent dimerization constant and the apparent molecular weight are functions of free ligand concentration, and depend on the intrinsic binding constants of the ligand molecule to the monomer and the dimer. The behavior of these functions is classified into 17 cases according to the values of the three intrinsic binding constants, and some calculated examples are shown graphically for selected parameters. The theory was also applied to D-amino acid oxidase [EC 1.4.3.3], a flavoprotein, and the pH dependence of the apparent dimerization constant and the apparent molecular weight in the presence of ligand, p-aminobenzoate, were studied theoretically using parameters obtained in our previous experiments (5).     

Effects of chemical modification of Anabaena flavodoxin and ferredoxin-NADP+ reductase on the kinetics of interprotein electron transfer reactions.

The influence of chemical modification of arginine residues (using phenylglyoxal) in ferredoxin-NADP+ reductase (FNR), and of carboxyl groups (using glycine ethyl ester) in flavodoxin (Fld), on the kinetics of electron transfer between FNR and Fld, and between ferredoxin (Fd) and FNR, was examined using laser flash photolysis methods. All proteins were obtained from the cyanobacterium Anabaena PCC7119. Reduction by laser-generated 5-deazariboflavin semiquinone of the FAD moiety of phenylglyoxal-modified FNR occurred with a second-order rate constant 2.5-fold smaller than that obtained for reduction of native FNR, indicating either a small degree of steric hindrance of the cofactor, or a decrease in its redox potential, upon chemical modification. In contrast, no changes were found in the kinetics of reduction of the FMN cofactor of Fld modified by glycine ethyl ester as compared with the native protein. The observed rate constants for reoxidation of Fdred (reduced Fd) by FNRox (oxidized FNR) were dramatically decreased (approximately 100-fold) when phenylglyoxal-modified FNR was used. In contrast to the reaction involving the native proteins, no ionic strength effects on kobs values were found. These results, and those obtained upon varying the protein concentration, indicate that the rate constant for complex formation and the attractive electrostatic interaction between the two proteins were greatly diminished by chemical modification of arginine residues of FNR. When phenylglyoxal-modified FNRsq (FNR semiquinone) was used to reduce Fldox (oxidized Fld), similar inhibitory effects were observed. In this case, the limiting first-order rate constant for Fldsq (Fld semiquinone) formation via intracomplex electron transfer from FNRsq was approximately 12-fold smaller than that obtained for the native FNR (600 s-1 vs 7000 s-1). Again, ionic strength effects were diminished. The glycine-ethyl-ester-modified Fld yielded a limiting first-order rate constant for intracomplex electron transfer from FNRsq to Fldox which was approximately 7-fold smaller (1000 s-1) than that obtained with native Fld, and ionic strength effects were again diminished. These results indicate that complex formation can still occur between modified FNR and native Fld, and between native FNR and modified Fld, but that the geometry of these complexes is altered so as to decrease the effectiveness of interprotein electron transfer. The results are discussed in terms of the specific structural features of the proteins involved.     

Kinetic evidence for the PsaE-dependent transient ternary complex photosystem I/Ferredoxin/Ferredoxin:NADP(+) reductase in a cyanobacterium.

A mutant of Synechocystis PCC 6803, deficient in psaE, assembles photosystem I reaction centers without the PsaE subunit. Under conditions of acceptor-side rate-limited photoreduction assays in vitro (with 15 microM plastocyanin included), using 100 nM ferredoxin:NADP(+) reductase (FNR) and either Synechocystis flavodoxin or spinach ferredoxin, lower rates of NADP(+) photoreduction were measured when PsaE-deficient membranes were used, as compared to the wild type. This effect of the psaE mutation proved to be due to a decrease of the apparent affinity of the photoreduction assay system for the reductase. In the psaE mutant, the relative petH (encoding FNR) expression level was found to be significantly increased, providing a possible explanation for the lack of a phenotype (i.e., a decrease in growth rate) that was expected from the lower rate of linear electron transport in the mutant. A kinetic model was constructed in order to simulate the electron transfer from reduced plastocyanin to NADP(+), and test for possible causes for the observed change in affinity for FNR. The numerical simulations predict that the altered reduction kinetics of ferredoxin, determined for the psaE mutant [Barth, P., et al., (1998) Biochemistry 37, 16233-16241], do not significantly influence the rate of linear electron transport to NADP(+). Rather, a change in the dissociation constant of ferredoxin for FNR does affect the saturation profile for FNR. We therefore propose that the PsaE-dependent transient ternary complex PSI/ferredoxin/FNR is formed during linear electron transport. Using the yeast two-hybrid system, however, no direct interaction could be demonstrated in vivo between FNR and PsaE fusion proteins.     

Characterization of the dimerization domain in the FNR transcription factor

The global anaerobic regulator FNR from Escherichia coli is a dimeric Fe-S protein that is inactivated by O(2) through disruption of its [4Fe-4S] cluster and conversion to a monomeric form. As a first step in elucidating the molecular interactions that control FNR dimerization, we have performed alanine-scanning mutagenesis of a potential dimerization domain. Replacement of many hydrophobic residues (Met-143, Met-144, Leu-146, Met-147, Ile-151, Met-157, and Ile-158) and two charged residues (Arg-140 and Arg-145) with Ala decreased FNR activity in vivo. Size exclusion chromatography and Fe-S cluster analysis of three representative mutant proteins, FNR-M147A, FNR-I151A, and FNR-I158A, showed that the Ala substitutions produced specific defects in dimerization. Because hydrophobic side chains are known to stabilize subunit-subunit interactions between alpha-helices, we propose that Met-147, Ile-151, and Ile-158 lie on the same face of an alpha-helix that constitutes a dimerization interface. This alignment would also position Arg-140, Met-144, and Asp-154 on the same helical face. In support of the unusual positioning of a negatively charged residue at the dimer interface, we found that replacing Asp-154 with Ala repaired the defects caused by Ala substitutions of other residues located on the same helical face. These data also suggest that Asp-154 has an inhibitory effect on dimerization, which may be a key element in the control of FNR dimerization by O(2) availability.     

Optimal temperature control policy for a two-stage recombinant fermentation process.

The optimal temperature control policy to be followed in the operation of a two-stage fermentation system in which gene expression is induced by a temperature-sensitive gene switching system was studied. A genetically structured model was used to describe product formation, and kinetic equations based on experimental data were used to quantify the specific gene expression rate and parameters that affect plasmid instability. A constant temperature control policy and temperature profiling control policy including temperature cycling were studied and compared. Maximum average production rate was obtained from a temperature control policy in which the second stage was operated initially at about 40.5 degrees C and the temperature decreased slightly to a constant value at 40.0 degrees C. The maximum average production rate, which corresponds to the optimal temperature control policy, for an operation of 180 h was 29.7 units of protein (mg of cells)-1 h-1.     

myo-inositol oxygenase from rat kidneys. Substrate-dependent oligomerization

myo-Inositol from rat kidneys, an oligomeric protein with apparent molecular mass of about 270 kDa can be dissociated under mild conditions to structured 16.8-kDa monomers. This dissociation can be reversed at high protein concentrations at room temperature. The corresponding apparent dimerization constant K2app = 1.38 x 10(5) M-1, the corresponding rate constant k2 = 350 s-1.M-1, and the apparent constant for the association of dimers, K4app = 2.7 x 10(6) M-1. Reassociation is significantly enhanced in the presence of the substrate and iron(II) (K2app = 9.8 x 10(5) M-1; K4app = 3.75 x 10(6) M-1, k2 = 1750 s-1.M-1, at 20 mM myo-inositol and 0.5 mM FeSO4). Under these conditions almost 100% of the original enzymatic activity was reconstituted. Monomers, with or without bound ligands, lack catalytic activity, whereas the dimer is likely to be the elementary active enzyme-building unit. The effects of myo-inositol on the dimerization lead to the conclusion that this step is both mediated and facilitated by the substrate.     

Laser flash photolysis studies of the kinetics of reduction of ferredoxins and ferredoxin-NADP+ reductases from Anabaena PCC 7119 and spinach: electrostatic effects on intracomplex electron transfer

The influence of electrostatic forces on the formation of, and electron transfer within, transient complexes between redox proteins was examined by comparing ionic strength effects on the kinetics of the electron transfer reaction between reduced ferredoxins (Fd) and oxidized ferredoxin-NADP+ reductases (FNR) from Anabaena and from spinach, using laser flash photolysis techniques. With the Anabaena proteins, direct reduction by laser-generated flavin semiquinone of the FNR component was inhibited by complex formation at low ionic strength, whereas Fd reduction was not. The opposite results were obtained with the spinach system. These observations clearly indicate structural differences between the cyanobacterial and higher plant complexes. For the complex formed by the Anabaena proteins, the results indicate that electrostatic forces are not a major contributor to complex stability. However, the rate constant for intracomplex electron transfer had a biphasic dependence on ionic strength, suggesting that structural rearrangements within the transient complex facilitate electron transfer. In contrast to the Anabaena complex, electrostatic forces are important for the stabilization of the spinach Fd:FNR complex, and changes in ionic strength had little effect on the limiting rate constant for intracomplex electron transfer. This suggests that in this case the geometry of the initial collisional complex is optimal for reaction. These results provide a clear illustration of the differing roles that electrostatic interactions may play in controlling electron transfer between two redox proteins.     

PetH is rate-controlling in the interaction between PetH, a component of the supramolecular complex with photosystem II, and PetF, a light-dependent electron transfer protein

Cyanobacterial PetH is similar to ferredoxin-NADP⁺ oxidoreductase (FNR) of higher plants and comprises 2 components, CpcD-like rod linker and FNR proteins. Here, I show that PetH controls the rate of the interaction with PetF (ferredoxin [Fd1]). Purified recombinant PetH protein, which cut off a CpcD-like rod linker domain, and Fd1 were used in detailed surface plasmon resonance analyses. The interaction between FNR and Fd1 chiefly involved extremely fast binding and dissociation reactions and the FNR affinity for Fd1 was stronger than the Fd1 affinity for FNR. The dissociation constant values were determined as approximately 93.65 μM (FNR) for Fd1 and 1.469 mM (Fd1) for FNR.     

Evolutionary optimization of the catalytic efficiency of enzymes.

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.     

Comparison of the kinetics of reduction and intramolecular electron transfer in electrostatic and covalent complexes of ferredoxin-NADP+ reductase and flavodoxin from Anabaena PCC 7119

The kinetics of reduction and intracomplex electron transfer in electrostatically stabilized and covalently crosslinked complexes between ferredoxin-NADP+ reductase (FNR) and flavodoxin (Fld) from the cyanobacterium Anabaena PCC 7119 were compared using laser flash photolysis. The second-order rate constant for reduction by 5-deazariboflavin semiquinone (dRfH) of FNR within the electrostatically stabilized complex at 10 mM ionic strength (4.0 X 10(8) M-1 s-1) was identical to that for free FNR. This suggests that the FAD cofactor of FNR is not sterically hindered upon complex formation. A lower limit of approximately 7000 s-1 was estimated for the first-order rate constant for intracomplex electron transfer from FNRred to Fldox under these conditions. In contrast, for the covalently crosslinked complex, a smaller second-order rate constant (2.1 X 10(8) M-1 s-1) was obtained for the reduction of FNR by dRfH within the complex, suggesting that some steric hindrance of the FAD cofactor of FNR occurs due to crosslinking. A limiting rate constant of 1000 s-1 for the intracomplex electron transfer reaction was obtained for the covalent complex, which was unaffected by changes in ionic strength. The substantially diminished limiting rate constant, relative to that of the electrostatic complex, may reflect either a suboptimal orientation of the redox cofactors within the covalent complex or a required structural reorganization preceding electron transfer which is not allowed once the proteins have been covalently linked. Thus, although the covalent complex is biochemically competent, it is not a quantitatively precise model for the catalytically relevant intermediate along the reaction pathway.     

Tetramer formation kinetics in the signaling state of AppA monitored by time-resolved diffusion

The photoreaction kinetics of the BLUF domain of AppA(5-125) was studied by monitoring time-dependence of an apparent diffusion coefficient (D) using the pulsed laser-induced transient grating technique. It was found that D of the photoproduct is time-dependent. From the concentration dependence of the reaction rate, it was concluded that the BLUF domain of AppA forms a dimer upon the photoexcitation. Since AppA exists as a dimeric form in the ground state, this dimerization reaction indicates the tetramer formation in the signaling state. From the slope of the plot of observed rate constants (k(obs)) against the AppA concentration, the second order rate constant is determined to be approximately 2.5 x 10(5) M(-1) s(-1), which is approximately 4 orders in magnitude lower than the diffusion controlled reaction. It indicates that a relative orientation of the protein molecules during the dimerization process causes additional constraints, which slow down the reaction rate.     

Photo-induced electron transfer from photosystem I to NADP(+): Characterization and tentative simulation of the in vivo environment

The photoproduction of NADPH in photosynthetic organisms requires the successive or concomitant interaction of at least three proteins: photosystem I (PSI), ferredoxin (Fd) and ferredoxin:NADP(+) oxidoreductase (FNR). These proteins and their surrounding medium have been carefully analysed in the cyanobacterium Synechocystis sp. PCC 6803. A high value of 550mg/ml was determined for the overall solute content of the cell soluble compartment. PSI and Fd are present at similar concentrations, around 500μM, whereas the FNR associated to phycobilisome is about 4 fold less concentrated. Membrane densities of FNR and trimeric PSI have been estimated to 2000 and 2550 per μm(2), respectively. An artificial confinement of Fd to PSI was designed using fused constructs between Fd and PsaE, a peripheral and stroma located PSI subunit. The best covalent system in terms of photocatalysed NADPH synthesis can be equivalent to the free system in a dilute medium. In a macrosolute crowded medium (375mg/ml), this optimized PSI/Fd covalent complex exhibited a huge superiority compared to the free system. This is a likely consequence of restrained diffusion constraints due to the vicinity of two out of the three protein partners. In vivo, Fd is the free partner, but the constant proximity between PSI and the phycobilisome associated FNR creates a similar situation, with two closely associated partners. This organization seems well adapted for an efficient in vivo production of the stable and fast diffusing NADPH.