New direct dynamic models of protein interactions coupled to photosynthetic electron transport reactions

Abstract

This review covers the methods of computer simulation of protein interactions taking part in photosynthetic electron transport reactions. A direct multiparticle simulation method that simulates reactions describing interactions of ensembles of molecules in the heterogeneous interior of a cell is developed. In the models, protein molecules move according to the laws of Brownian dynamics, mutually orient themselves in the electrical field, and form complexes in the 3D scene. The method allows us to visualize the processes of molecule interactions and to calculate the rate constants for protein complex formation reactions in the solution and in the photosynthetic membrane. Three-dimensional multiparticle computer models for simulating the complex formation kinetics for plastocyanin with photosystem I and cytochrome bf complex, and ferredoxin with photosystem I and ferredoxin:NADP⁺-reductase are considered. Effects of ionic strength are featured for wild type and mutant proteins. The computer multiparticle models describe nonmonotonic dependences of complex formation rates on the ionic strength as the result of long-range electrostatic interactions.

Keywords: Complex formation; Computer model; Electrostatic interaction; Photosynthesis; Protein interaction.

Fig. 1

Schematic view of photosynthetic electron transport. Two thylakoid membranes and the luminal space between them are shown. Multiprotein complexes photosystem 1 (PSI), photosystem 2 (PSII), and cytochrome bf (cyt bf) are embedded in the membrane. Mobile electron carrier protein plastocyanin (Pc) diffuses in the lumen. The arrows denote electron transport. The connection with the Calvin cycle is carried out by mobile carriers Fd or Fld via FNR. Inside the multienzyme complexes of PSI, PSII, and cyt bf complex, the electron follows the “electron pathway” via a fixed sequence of carriers in the multienzyme complexes

Fig. 2

Ellipsoid of revolution

Fig. 3

Description of plastocyanin (Pc) and cytochrome f (cyt f) by ellipsoids of revolution for the calculation of the viscous friction coefficients of the molecules. Reprinted from (Kovalenko et al. 2006) with permission from IOP Publishing

Fig. 4

Approximation of the cytochrome f (a) and plastocyanin (b) molecules by sets of spheres (shown in blue)

Fig. 5

Approximation of the multisubunit complex photosystem I by sets of spheres. The spheres are shown in blue, the atoms are red. The surface of the parts of PSI protruding from the membrane are approximated in high detail (Abaturova et al. 2008)

Fig. 6

Equipotential surfaces, −6.5 mV (red) and +6.5 mV (blue), for the reduced cytochrome f (Cyt f) and oxidized plastocyanin [Pc, wild-type (WT) and mutant E59K/E60Q], calculated using Poisson-Boltzmann equation. Ionic strength is 100 mM, pH = 7, ε _sol = 80, ε _prot = 2. Reprinted from (Kovalenko et al. 2006) with permission from IOP Publishing. The lines connect the amino acids on Pc and cyt f used in the simulation to calculate the distance between the proteins. For mutant Pc, the blue points represent atoms with charges changed as compared to the wild-type. The values for distances between contacting amino acid residues are given in Table 1 in (Kovalenko et al. 2006)

Fig. 7

Equipotential surfaces, −6.5 mV (red) and +6.5 mV (blue), for the reduced wild-type Fd (a) and oxidized wild-type FNR (b), calculated by the Poisson-Boltzmann equation. Ionic strength is 100 mM, pH = 7, ε _sol = 80, ε _prot = 2 (Kovalenko et al. 2008b). As the docking distance r we chose the distance between Fe1 atom of the [2Fe-2 S] cluster on Fd and C8M atom of FAD on FNR

Fig. 8

The logarithm of second-order protein binding rate constant k dependence on the root square of the ionic strength I for the wild-type and mutant Pc and cytochrome f. a Experimental data from (Kannt et al. and Crowley et al. 2004). b Simulation results (Kovalenko et al. 2006). k is in (М·s)^–1, the ionic strength I is in М. Reprinted from (Kovalenko et al. 2006) with permission from IOP Publishing

Fig. 9

Equipotential surfaces, −6.5 mV (red) and +6.5 mV (blue), for flavodoxin. Green points are atoms of the molecule; the arrow points to the FMN cofactor. a Ionic strength is 0 mM. b Ionic strength is 80 mM (Abaturova et al. 2008)

Fig. 10

Equipotential surfaces, −6.5 mV (red) and +6.5 mV (blue), for PSI. The luminal side is on the bottom, the stromal side is on the top. a Ionic strength is 0 mM. b Ionic strength is 80 mM (Abaturova et al. 2008)

Fig. 11

a Experimental dependence of the observed rate constant for PSI-Fld reaction on the solution ionic strength. Reprinted from (Medina et al. 1992) with permission from Elsevier and the author. b Calculated dependence of the second-order rate constant at docking distance r = 22 Å and docking probability p = 0.025 (Abaturova et al. 2008)

Fig. 12

The model scene visualization (the thylakoid lumen bounded by the thylakoid membranes) with proteins plastocyanin (Pc) and cytochrome f (Cyt f)

Fig. 13

Dependence of the protein binding rate constant of the Pc-cyt f reaction divided by cyt f concentration in the thylakoid lumen on the distance z between the membranes at constant number of molecules (Kovalenko et al. 2008a)