TABLE OF CONTENTS
Abstract
1.  Introduction
2.  Methods
3.  Tunnelling effect vs. Van der Walls contacts
     in the cytochrome f-plastocyanin complex
     ( i)  Structure-function model I
     (ii)  Structure-function model II
4.  Concluding remarks
References
Acknowledgements

A study was undertaken of the molecular pathways of electron transfer in the cytochrome f-plastocyanin (cyt f-Pc ) complex.  Between the Fe-atom in cyt f and the the Cu-atom in Pc, the calculated centre-to-centre distances of electron transfer distances (De) are 7.2 Å from the Fe-atom to tyrosine 1 (Y1) in cyt f, and De = 5.9 Å from Y1 to the copper atom (Pc).  Within Pc, De = 7.0 Å between cysteine 84 (C84) and serine 85 (S85) and 5.2 Å between S85(OH) and tyrosine 83 [Y83(OH)].  A calculated alternative route of electron transfer in Pc is between C84(SH) and the pi-electron system in Y83 where De is  ~7.3 Å.  On the other hand, the electron transfer distance between the Cu-atom and C84(SH) is approximately 2.6 Å, i.e., the coordination distance from the copper atom to the SH group in C84.  De =  2.6 Å is clearly quite small in relation to the 5 to ~7 Å determined for the various electron transfer pathways in cyt f-Pc.  In this respect, it is noted first that electron transfer distances higher than about 5 Å are in general a good indication of electron transfer occurring by tunnelling efffect, that is, by a quantum jump from one electronic state to another.  On the contrary, it is reasonable to assume that electron transfer reactions at distances as small as 2.6 Å might simply take place via Van der Waals contacts.  This is a convincing argument to suggest the coexistence of different molecular mechanisms of electron transfer in the cyt f-Pc complex. Such coexistence of molecular states has far reaching consequences so far as it presupposes the function in cyt f-Pc of adiabatic and non-adiabatic electron transfer processes which have different temperature dependence, or requirements.

   Electron transfer between redox proteins is of fundamental importance in living cells and organisms such as the chloroplasts of green plants and algae.  This question presents also a practical interest in the construction of efficient batteries for solar energy conversion into chemical or electrical energy.  Nevertheless, these devices are often plagued with difficulties inherent to energy losses due to back reactions.  In natural systems, however, this question has apparently been solved with a complex, yet elegant system of molecular pathways leading to a remarkably efficient transfer of electrons through molecular distances that are often very long, e.g., ~ 20-25 Å or more (see data discussed in [1]).  In this perspective, the electron transfer mechanisms in the photosynthetic membrane of the chloroplast made the object of a large number of works (see, e.g., [2-4]).  In spite of this, the molecular pathways of the photosynthetic electron transfer are not yet clearly understood.  In this study, we discuss first the most relevant pathways of electron transfer in the cytochrome f-plastocyanin complex.  Secondly, we shall try to characterize the molecular pathways of electron transfer by tunnelling effect and via Van der Walls contacts that may be at the origin, and coexistence,  of non-adiabatic and adiabatic electron transfer in cyt f-Pc.
 

2. Methods
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   The molecules used in this work were obtained from the Protein Data Bank [5], that is, 5pcy.pdb [plastocyanin (Pc)] and 1ctm.pdb [cytochrome f (cyt f)].  The cyt f-Pc complex was modelled [6] using the computer graphics program TURBO-FRODO [7,8], and the structures were further refined with the X-PLOR program (version 3.1) for the energy minimization (see details in [9]).  The atomic distances and other molecular details in the in Pc and the cyt f-Pc complex were determined with the WebLab ViewerPro software from Molecular Simulations Inc. (San Diego, CA).  Other calculations were performed with Maple (version V) from Waterloo Maple Inc. (Waterloo, ON), and Origin (version 5) from Microcal Software, Inc. (Northampton, MA).

(i) Structure-function model I

   In higher plants chloroplasts the cytochrome b6f (cyt b6f) complex transfers electrons between the photosystem II complex and the P700 reaction center in the photosystem I (PSI) complex.  From cytochrome f (cyt f) in cyt b6f to PSI, the electrons are shuttled by the mobile redox carrier plastocyanin (Pc) [10-13].  Fig. 1 shows a detail of the electron transfer interface in the cyt f-Pc complex obtained from molecular modelling of the cyt f-Pc interaction [6].  In short, electron tranfer between the Fe-atom in the cyt f heme and the tyrosine 83 (Y83) in plastocyanin starts with the oxidation of the Fe-atom and electron transfer directly to the OH group or the pi-electron system of tyrosine 1 (Y1) in cyt f, or through an intermediate pyrrole ring in the cyt f heme macrocycle.  From there, the electron transfer route goes through the Cu-coordination centre (see details in Fig. 2) following most likely one or several molecular pathways.  A few prossible routes are discussed in greater detail in Figs. 2-4.
 
 

   A schematic representation of the distances between the amino acid residues that most likely participate in electron transfer in the cyt f-Pc complex is given in Fig. 2.  The figure shows that the distance from the Fe-coordination centre to Y1 is approximately 7.2 Å and 5.9 Å from Y1 to the Cu-ion.  From C84(SH) to S85(OH) and from S85(OH) to Y83(OH) the electron transfer distances are respectively about 7.0 Å and 5.2 Å.  The figure indicates also that another possible electron transfer route is between C84(SH) and the pi-electron system in Y83 with an interaction distance of the order of 7.3 Å.   This presents a considerable interest since it has been quite often emphasized in past discussions (see, e.g., [1,14]) that electron transfer distances higher than about 5 Å are a reliable indication of electron transfer occurring by tunnelling efffect, that is, by a quantum jump from one electronic state to another.
 

   Fig. 2 indicates also that the distance Cu-C84(SH) is approximately 2.6 Å, i.e., the coordination distance from the Cu-ion to the SH group in C84.  This is a quite small electron transfer distance in relation to the 5 to 7 Å determined for the other pathways illustrated in Fig. 2.  At first, this is a convincing argument to suggest the co-existence of different molecular mechanisms of electron transfer in the Cyt f-Pc complex.  Secondly, an electron transfer distance of about 2.6 Å is a good indication that in the Cu-coordination centre, and maybe also in its molecular nearness, the electron transfer reaction originates in Van der Waals (VDW) contacts.  This question is discussed further in section (ii) below.
 

(ii) Structure-function model II

   Fig. 2 indicates that the Cu-ion in Pc is coordinated to the cysteine 84 (C84) thiol group, the methionine 92 (M92) thioether group, and the histidines 37 (H37) and 87 (H87) imidazole groups in a quite highly distorted tetrahedral configuration.  The corresponding coordination distances are given in the figure.  Such unstable three-dimensional configuration has partly its origin in differences of conformational strain energy (DHs) of the amino acid residues (see discussion in [15]) in the Cu-coordination centre.  That is, DHs = 0.08 (C84),  11.68 (M92) and 14.15 (H37, H87) kJ/mol.  This materializes in the almost identical coordination distances for Cu-H87 (2.42 Å), Cu-H37 (2.44 Å) and Cu-C84 (2.61 Å) as compared to the quite different Cu-M92 distance (3.22 Å) which gives thus rise to the distortion observed in the coordination tetrahedron (see Fig. 2).

   The distorted tetrahedral configuration of the Cu-coordination centre is obviously unstable from a thermodynamic viewpoint, inusmuch as the copper ion may adopt two different configurations;  that is, the configurations corresponding to the coordination numbers (CN) four or six (see, e.g., [16]).  It is worth noting at this point that a fifth and a sixth coordination partners corresponding to CN = 6 are predicted, in addition to the more common four coordination partners of the Cu-ion in Pc which are usually identified with the amino acid residues described above.  The implicit fifth and sixth coordination partners were not, however, correctly identified.  Nevertheless, this matter raises an interesting point.  In fact, the crystal radii for the Cu-ion being 0.74 Å for CN = 4 and 0.91 Å for CN = 6 [16], it becomes perceptible that any  molecular volume change in the Cu-centre should have functional consequences that  have not yet been determined, but which are certainly instrumental in influencing the electron transfer rate in cyt f-Pc, at least in the route from the Cu-ion to Y83.  This may take place, for example, by changing the arrangement and the reorganizational energy [1] of the Van der Waals contacts in the region comprising the H87 imidazole ring, the Cu-ion and the C84 thiol group (Fig 3).
 
 

   From the above considerations, it is reasonable to foresee that the transfer of an electron from Y1 (in cyt f) to the Cu-ion in plastocyanin, the bond lengths in the Cu-coordination centre must distort from their stable, or steady-state geometry, to another distorted geometry, or transition-state geometry, where lenghtening and contraction of bonds occur.  For this to take place, energy is expended prior to the return of the coordinnation centre to its equilibrium geometry.  This model is in accord with the Franck-Condon principle since the transfer of an electron is faster than the nuclear motions, thereby meaning that the nuclear positions are so to say 'frozen' in time during the electron transfer process.  A model to take into account these effects is presented in Fig. 4 where the 'Van der Waals route', that is, the Y1(cyt f)-->H87(Pc)-->Cu(Pc) molecular pathway, is shown in parallel with the 'tunnelling effect pathways' discussed above, i.e., (i) Fe(cyt f)-->Y1(cyt f), (ii) Cu(Pc)[or C84(Pc)]-->S85(Pc)-->Y83(Pc), and (iii) Cu(Pc)[or C84(Pc)]-->Y83[pi-electron system](Pc).
 
 

   First, the data shown in Figs. 2 and 4 indicate that different electron transfer mechanisms may take place in the same cyt f-Pc complex, that is, electron transfer by tunnelling effect and via Van der Waals contacts.  This may have far reaching consequences since, in a first approximation, it presupposes the parallel function of adiabatic and non-adiabatic electron transfer mechanisms, thereby implying the interplay of mechanisms with different temperature dependence, or requirements [1,14].  The coexistence of such processes may well constitute a means of control of the electron transfer activity not only in the cyt-Pc complex, but also between the cytochrome b6f complex and P700, the reaction center of photosystem I.

   Secondly, it is noted that two other questions still remain.  The first is the possibility that water molecules may provide an efficient pathway of electron transfer (see discussions in [17,18]).  In which the cyt f-Pc complex is concerned, the mediation or facilitation of electron transfer by interposed water molecules inside the protein complex is an assumption that, though attractive, has most probably to be ruled out on account of arguments discussed in computer simulations of water-plastocyanin interaction energies [19].  Another interesting matter is the effect of side chain movements on electron transfer through the 'electron transfer hole or tunnel' in the cyt f-Pc complex, which the molecular pathways delineated in Figs. 2 and 4 tacitly predict. A detailed examination of these questions shall be reported elsewhere.
 
 

ACKNOWLEDGEMENTS.  This work was supported by grant OGP0006357 from the Natural Science and Engineering Research Council of Canada and institutional grants from the Université du Québec à Trois-Rivières, and is the result of a collaboration with Dr. A. Kajava at the Institut Suisse de Recherches Expérimentales sur le Cancer (ISREC), Groupe de Bioinformatique, Epalinges s/Lausanne, Suisse.  I wish to thank Dr. A. Kajava and the Bioinformatics Group and Library staff at ISREC for the friendliness of their welcome and help, and Dr. I. Gabashvili for many interesting comments and suggestions.
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