Electron Transfer in Ferredoxin: Are Tunneling Pathways Evolutionarily Conserved?

Iraj Daizadeh1, Dmitry M. Medvedev and Alexei A. Stuchebrukhov

*Department of Molecular and Cellular Biology, Harvard University, Cambridge
{dagger}Department of Chemistry, University of California, Davis


    Abstract
 TOP
 Abstract
 Introduction
 Materials and Methods
 Results and Discussion
 Note added in proof
 Acknowledgements
 References
 
A theoretical study of electron transfer (ET) pathways in a recently crystallized Clostridium acidurici ferredoxin is reported. The electronic structure of the protein complex is treated at the semiempirical extended Hückel level, and the tunneling pathways are calculated with the rigorous quantum mechanical method of tunneling currents. The model predicts two pathways between the two [4Fe-4S] cubanes: a strong one running directly from Cys14 to Cys43 and a weaker one from Cys14 via Ile23 to Cys18, whereas other amino acids do not play a significant role in the electron tunneling. The cysteine ligands conduct almost all of the current when Ile23 is mutated to valine in silico, so that there is no appreciable change in the ET rate. The calculated value of the transfer matrix element is consistent with the experimentally determined rate of transfer. Results of the sequence analysis performed on this ferredoxin reveal that Ile23 is a highly variable amino acid compared with the cubane-ligating cysteine amino acids, even though Ile23 lies directly between the donor and acceptor complexes. We further argue that the homologous proteins with a [3Fe-4S] cofactor, which does not have one of the four cysteine ligands, use the same tunneling pathways as those in this ferredoxin, on the basis of the high homology as well as the absolute conservation of Cys14 and Cys43 which serve as the main tunneling conduit. Our results explain why mutation of amino acids around and between the donor and acceptor cubane clusters, including that of Ile23, does not appreciably affect the rate of transfer and add support to the proposal that there exist evolutionarily conserved electron tunneling pathways in biological ET reactions.


    Introduction
 TOP
 Abstract
 Introduction
 Materials and Methods
 Results and Discussion
 Note added in proof
 Acknowledgements
 References
 
With the solution of X-ray crystallographic structures of small, naturally occurring iron-sulfur [4Fe-4S], electron transfer (ET) proteins (for example, see Duce et al. 1994), it now becomes possible to conduct investigations of factors that regulate the ET rate in these proteins in a rigorous and systematic fashion (Huber, Moulis, and Gaillard 1996Citation ; Kyritis et al. 1997Citation ). Moreover, even though these proteins are small, they make ideal models for the analysis of ET reactions in more complex [4Fe-4S]-containing systems, such as the NADH-ubiquinone oxidoreductase of the mitochondrial respiratory chain (Walker 1992Citation ), various hydrogenases (Quinkal et al. 1994Citation ), and photosystem I (Krauss et al. 1996Citation ), because of structural similarities of the intervening protein medium and the similar distances between the donor and acceptor cubane clusters in these systems. These natural systems, together with the Ru-modified proteins (Langen et al. 1995Citation ), provide an ideal testing ground for modern theories of biological ET (Skourtis and Beratan 1999Citation ).

In a recent study, the rate constants and possible tunneling pathways for intramolecular ET between two [4Fe-4S] clusters in a series of native and genetically engineered Clostridia ferredoxins were reported (Kyritis et al. 1997Citation ). This ferredoxin is a small (55 amino acids) monomeric protein, which contains two redox centers—[4Fe-4S] cubane clusters—each ligated by four cysteine sulfurs. The lengths of the cubane edges are roughly 2.3 Å; the shortest distance between two atoms on different cubanes is 8.5 Å, whereas the shortest distance between two sulfur atoms ligating different cubanes (sulfur on Cys14 and that on Cys43) is 6.2 Å. It was found that the structural changes introduced around and between the two cubane clusters via site-directed mutagenesis had no major affect on the ET rate constant. In the same study, it was also found that the ET rate constant was independent of temperature in the range of 283–310 K.

In this paper, we determine the electron tunneling pathways and calculate rate constants in the recently recrystallized Clostridium acidurici ferredoxin (Dauter et al. 1997Citation [The structure used for this paper was obtain from the Protein DataBank (www.rcsb.org): PDB code 2FDN]) as well as a mutant, using the rigorous quantum mechanical method of tunneling currents. We find that there is a main tunneling pathway running directly from Cys14 to Cys43 and a weaker pathway running from Cys14 via Ile23 to Cys18, whereas other amino acids do not play a significant role in the electron tunneling. In silico mutation of Ile23 to valine did not significantly affect the ET rate constant, in agreement with the experimental findings. This is because of the prominent Cys14 to Cys43 pathway.

We have also performed a molecular evolutionary study of this protein; it was found that Ile23 is a highly variable amino acid compared with the donor- or acceptor-ligating cysteines. Sequence analysis was performed on this ferredoxin, homologous sequences were found in species representing all the three domains (Woese 1982Citation ), including metazoans and members of the deepest part of the tree of life (Lazcano and Miller 1996Citation ). As this protein predates the prokaryote and eukaryote divergence date of around 2 billion years (Nealson and Conrad 1999Citation ) and is ubiquitous because of its role in important biological functions, we propose that the evolutionary constraints have been placed on the cysteine amino acids not only for the purpose of setting the redox potentials of the cubanes for which these amino acids serve as ligands but also as electron tunneling mediators. These results not only rationalize experiment but also add support to the hypothesis that there exists evolutionarily conserved electron tunneling pathways in biological ET reactions (Medvedev, Daizadeh, and Stuchebrukhov 2000)Citation .


    Materials and Methods
 TOP
 Abstract
 Introduction
 Materials and Methods
 Results and Discussion
 Note added in proof
 Acknowledgements
 References
 
Electron Transfer Theory and the Method of Tunneling Currents
According to the theory of nonadiabatic ET, the rate of reaction in the limit of classical motion of nuclei is given by (Kuznetsov 1995Citation ; Marcus and Sutin 1985Citation ):


Here, {Delta}G0 is the standard free energy of the reaction (the driving force), {lambda} is the reorganization energy, and TDA is the transfer matrix element.

Here we describe the electronic structure of the system within the extended Hückel approximation (Yates 1978Citation ; Whangbo et al. 1987Citation ). Extended Hückel parameters are listed in table 1 ; the diagonal elements of the Hamiltonian of the system are the empirically determined ionization potentials. The nondiagonal matrix elements are given by the Wolfsberg-Helmholtz equation:


with K = 1.75.


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Table 1 Here the Parameters Used for the Extended Hückel Calculations Are Shown. The Valence Shell Ionization Potentials (Hii) Are in eV. Slater Exponents ({zeta}) in a.u., and {zeta}1 and {zeta}2 Are Slater Exponents for Double-{zeta}–type Orbitals of Iron. Coefficients of Corresponding Single-{zeta} Orbitals Are Given in Parentheses

 
The coupling between the donor and acceptor electronic states |D> and |A> with overlap SDA is given by the transfer matrix element (Newton 1991Citation ; Daizadeh, Gehlen, and Stuchebrukoh 1997bCitation ),


TDA is the half energy splitting between two delocalized eigenstates |{psi}+> and |{psi}-> which result from diagonalization of the Hamiltonian of the system in a configuration when the states |D> and |A> are in resonance and have common energy E. When there is no resonance, the |D> and |A> states can be approximated by two corresponding eigenstates of the entire system. These two eigenstates are identified by projecting all the eigenstates of the system onto the zeroth-order donor and acceptor states, |d> and |a>, which are obtained by diagonalization of the isolated donor and acceptor complexes, respectively. The donor and acceptor complexes are predefined sets of atoms on which the states |D> and |A> are likely to be localized. Usually, the overlap of only one of the eigenstates of the entire system with the zeroth-order state |d> or |a> is close to unity, whereas all other eigenstates have nearly zero overlaps.

The transfer matrix element is calculated with the method of tunneling currents (Stuchebrukhov 1996, 1996a, 1997Citation ). In this method, the matrix of interatomic tunneling currents is defined by


Here, cD and cA are the molecular orbital expansion coefficients of the donor and acceptor states, respectively, and E is the tunneling energy, which is defined to be the average of the donor and acceptor state energies. The elements Jpi·qj and Jp·q describe the probability flux between the atomic orbitals |pi> and |qj> and the respective atoms p and q during the electron tunneling process. The tunneling matrix element is related to the total tunneling flux through a dividing surface SD by:


The dividing surface here is chosen as a sphere around the donor complex, with a radius sufficiently large so that it includes most of the electron density in the donor state, but excludes most of the electron density in the acceptor state. For this relatively small protein (739 atoms) diagonalization of the Hamiltonian of the whole system is possible.

The geometric structure used for these calculations was the original crystallographic structure as determined from the experiment. In certain cases, such as conformational or energetic studies, it is advisable to equilibrate such structures by molecular dynamics or molecular mechanics simulations when the protein coordinates experience appreciable differences from those of the crystal structure. Thus, taking into account the theoretical arguments and the fact that in these systems the closest distance between the donor and acceptor complex is within 9 Å with rigid substructures including covalently bound cysteine mediated donor and acceptor complexes, no equilibration was performed. Lastly, we should mention that, as the results will show, the calculated matrix element agrees well, within the approximations used in our calculations, with that of the experimental values, thus adding an additional level of confidence in our approach.

Lastly, we note that quantum theory and simulations of the ET rate constant have shown that the matrix element becomes a sensitive function of the atomic coordinates between the donor and acceptor when the distance between the donor and acceptor complexes becomes appreciably long (Daizadeh, Medvedev, and Stuchebrukhov 1997aCitation ). For the average intramolecular ET protein, with donor and acceptor distance around 14 Å (Page et al. 1999Citation ), such coordinate corrections to the calculation of the matrix element are not relevant. Indeed, the discovery that the matrix element is a function of coordinate configurations was a recent theoretical finding from our group (Daizadeh, Medvedev, and Stuchebrukhov 1997aCitation ; Daizadeh, Gehlen, and Stuchebrukhov 1997bCitation ). Because of the close proximity between the donor and acceptor cubanes and the closeness of our calculations with that of the experimental values for the rate constant, these additional quantum mechanical simulations were not performed.

In order to calculate the donor and acceptor states, we construct the donor (acceptor) complex by taking all eight atoms of the cubane and S{gamma}, Cß, H1ß, H2ßatoms on the four ligating cysteine amino acids: Cys8 (Cys18), Cys11 (Cys37), Cys14 (Cys40), and Cys47 (Cys43). The C{alpha} atoms on these amino acids are treated as hydrogen atoms and included in the donor and acceptor complexes, in order to eliminate the influence of dangling bonds on the zeroth-order donor and acceptor states. The coordinates of these hydrogen atoms are the same as those of C{alpha} atoms in the crystallographic structure.

Molecular Evolutionary Study
The entire C. acidurici primary sequence was used in the search against the nonredundant, highly curated SwissProt database using the web-version of BLAST (Madden, Tatusov, and Zhang 1996Citation [The web service can be found at http://www.ncbi.nlm.nih.gov/BLAST. The SwissProt database provided by NCBI was posted on December 2, 1999 and contained 82,258 sequences [Bairoch A., and R. Apweiler. 1997. Nucl. Acids Res. 25:31–36.] The default BLAST parameters were used in the calculations: gap-penalties: Existence: 11, Extension: 1, with a Lambda ratio of 0.85; a low complexity filter and the BLOSUM62 scoring matrix were also used.]); 80 pairwise alignments with E-value scores less than 0.001 were harvested from the output file (the original sequence was also retrieved). The set of pairwise alignments was then multiply aligned with MULTALIGN (Corpet 1988Citation [Version 5.3.2 was used with the following parameters: scoring matrix = Blosum62, gap penalty = -1, gap length = -1, exremity gap penalty = no penalty, scoring method = absolute, conservation for uppercase letter in consensus = 90 for lowercase letter in consensus = 50 via the world wide web at: http://npsa-pbil.ibcp.fr/cgi-bin/npsa_automat.pl?page=npsa_multalin.html]). Because of the small number of residues that comprise this protein (55 amino acids), the sequence was shuffled, changing the order of the amino acid randomly without disturbing the overall amino acid frequency, and used to search the database. No sequences below an E-value of 0.001 were retrieved from these randomized sequences, thus adding confidence that the sequences retrieved in the search procedure using the C. acidurici primary sequence were indeed biological homologues. (In fact, in many searches no sequences were found with E-values less than 10.0; in several, E-values more than 2.0 were retrieved.)

To compare the amino acids implicated in the ET pathways by the theory summarized above and by experiment to those by sequence analysis, we developed the following heuristic approach: From the multiple alignment, the number of amino acid differences with respect to the amino acid sequence obtained from the C. acidurici PDB file (Dauter et al. 1997Citation ) were determined columnwise. These corresponding numbers of mutations were then normalized with respect to the number of sequences in the multiple alignments (80) (see caption of fig. 4 for complete details). These numbers were then used as a basis for a coloring scheme for an image of the three-dimensional coordinates of the molecule (MSI User Guide 1995Citation [Figures 1 and 2 were produced by using the charge color submodule in the InsightII program with the following criterion: redness of atom p = - 2.5 x {Sigma}q|Jp·q|/|TDA where intensity of color is maximum when redness is less than or equal to 0.5. Figure 5 was produced in a similar way where blueness of an amino acid is proportional to the degree of the conservation shown in fig. 4 ]) to qualitatively compare the results from the theory.



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Fig. 4.—Amino acid conservation is determined as the ratio of the number of sequences with amino acids different from C. acidurici ferredoxin divided by the number of sequences. Algebraically this takes the form: {Omega}i = {Gamma}i/{Theta} where {Gamma} corresponds to the number of amino acid differences with respect to the amino acid sequence for which the three-dimensional structure was used for the theoretical tunneling pathways calculations (Dauter et al. 1997Citation ) at position i and {Theta} is the total number of sequences in the multiple sequence alignment, respectively

 


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Fig. 1.—General picture of the tunneling currents in the Clostridium acidurici ferredoxin. Directions of major interatomic currents, except for those inside donor or acceptor complexes, are shown with black arrows (MSI User Guide 1995Citation )

 


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Fig. 5.—Amino acid conservation with respect to C. acidurici ferredoxin. Here, the results of the amino acid conservation index shown in figure 3 have been superimposed on an image of the ferredoxin crystal structure. Alanines 22 and 51 are not shown; they lie roughly 4 Å from their respective donor/acceptor cubane cysteine ligands and are not involved in the pathway picture. The depth of color is proportional to the variability (as calculated from fig. 3 ); a darker color implies increase of amino acid variability at that amino acid position (MSI 1995Citation )

 

    Results and Discussion
 TOP
 Abstract
 Introduction
 Materials and Methods
 Results and Discussion
 Note added in proof
 Acknowledgements
 References
 
Electronic Structure of Donor and Acceptor Complexes
The charge of the donor complex is -3 and that of the acceptor complex is -2. Because of the geometrical similarity of the donor and acceptor complexes, their electronic structures are very close to one another. In the extended Hückel approximation, the semioccupied molecular orbital (SOMO) of the complex with charge -3 (reduced cluster) and the two next unoccupied orbitals are separated by less than 0.1 eV, whereas the SOMO of the reduced cluster and the highest occupied molecular orbital (HOMO) of the complex with charge -2 (oxidized cluster) are separated by about 0.8 eV. The HOMO -1 of the oxidized complex is located within 0.04 eV of the HOMO.

However, the SOMO of the reduced complex and the next two highest orbitals were not considered donor or acceptor states in our calculations. Electron density in these states is localized mainly on the cubane iron (40%–45% of Mulliken population) and sulfur atoms (50%–55% of Mulliken population), with a small contribution from the cysteine ligand atoms. However, density functional theory (DFT) calculations performed on this system (Mouesca et al. 1994Citation ) show that both Mulliken and electrostatic potential charges of cysteine sulfurs change appreciably (by 10%–15%) on each sulfur atom upon reduction of the oxidized cluster, whereas charges of iron atoms change less significantly. This shows that the donor and acceptor orbitals in our calculations should have a significant electron density on the cysteine sulfur atoms. The orbitals which satisfy this criterion are HOMO and HOMO -1 of the oxidized complex. They have 45%–55% of the electron density on the cysteine sulfurs, mainly on their p orbitals, 30%–35% of electron density on the iron atoms, mainly on their d orbitals, and a small contribution from other atoms. This is not in exact agreement with the results of the DFT calculations, but the discrepancy of populations of the cubane atoms is expected to affect the value of the matrix element less significantly than that of the populations of the cysteine sulfurs. The reason is that if the population on the cysteine ligands is adequately described, then the degree of delocalization of the donor and acceptor wave functions, which is crucial for the value of matrix element, is correct.

Matrix Element and Tunneling Currents
The picture of tunneling currents in the case when both donor and acceptor states are represented by the HOMO of the oxidized complex is presented in figures 1 and 2 . Tunneling currents in the case when donor or acceptor state, or both, is represented by the HOMO -1 of the oxidized complex are similar. The larger intensity of red in the figures corresponds to a larger amount of total current (the sum of incoming and outgoing currents) passing through the atom. In both the figures, the atoms with total current larger than the whole current in the system are shown with maximal color intensity. All protein atoms and directions of major interatomic currents are shown in figure 1 . In figure 2 only those amino acids with observable currents are shown; here the interatomic currents are presented in greater detail. Interatomic currents that are larger than 30% of the whole current in this system are shown with solid black arrows, whereas some of the weaker interatomic currents are depicted with dotted black arrows. Currents inside donor and acceptor complexes, except for those between atoms of the cysteine ligands, are not shown.



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Fig. 2.—A more detailed picture of the tunneling currents found in figure 1 . Interatomic currents large than 30% of the whole current are shown with black arrows; some of the weaker currents are shown with long dashed arrows. Currents inside donor or acceptor complexes are not shown

 
One can see from the figures that very few amino acids of the entire protein participate in the ET reaction. These are the cubane-ligating cysteines, Ile23, Ala44, and Pro52. Most of the current flows directly from Cys14 (a donor cubane ligand) to Cys43 (an acceptor cubane ligand). There is also a weaker current conduit (shown in fig. 2 with dotted arrows) that runs through Cys14 to the {delta} methyl group of Ile23 and then to Cys18 (an acceptor cubane ligand). The closest distance between atoms of Cys14 and those of Ile23 is about 3.0 Å and between Ile23 and Cys18 is roughly 2.5 Å. The closest distance between Cys14 and Cys43 is also roughly 2.5 Å.

There is a strong and complicated system of circular currents involving Cys14, Cys43, and to a smaller extent the {delta} methyl group of Ile23. Another strong system of circular currents involves Cys18, Ile23, and some of the atoms of the acceptor cubane. On the other hand, Ala44 and Pro52, together with Cys47 (a donor cubane ligand) are involved in a weak system of circular currents and hence are not important for the ET. Current from the sulfur of Cys47, which has a significant amount of electron density on it flows mainly to the donor cubane and then to the acceptor via the main pathways. There are also strong circular currents inside donor and acceptor cubanes which are not shown.

The calculated value of the matrix element is between 3.7 and 6.7 cm-1. The driving force of this reaction is small, -6 and 15 meV between the two [4Fe-4S] cubane groups in C. acidurici and in Clostridium pasteuranium, respectively (Kyritis et al. 1997Citation ). Calculated values of the matrix element correspond to the range of the rate of ET (assuming {Delta}G0 = 0) from 2.2 x 105 s-1 to 7.4 x 105 s-1 with {lambda} = 1 eV and from 4 x 107 s-1 to 1.3 x 108 s-1 with {lambda} = 0.5 eV (at room temperature). This range of values of the matrix element is in reasonable agreement with the experimentally defined rate of transfer of 6.5 x 106 s-1 (Kyritis et al. 1997Citation ), given the crude nature of the underlying extended Hückel parameterization used in the model.

The experimental mutant, I23V, in the homologous C. pasteurianum ferredoxin did not affect the value of the ET rate significantly, there was only a marginal decrease to 5.3 x 106 s-1 from 6 x 106 s-1 (Kyritis et al. 1997Citation ). We performed an in silico site-directed mutagenic experiment, computationally transforming Ile23 to a valine using the program SCRWL (Bower, Cohen, and Dunbrack 1997Citation [The SCRWL program can be obtained from: http://www.fccc.edu/research/labs/dunbrack/scwrl/]) and calculated the matrix element for the C. acidurici system. The SCRWL program was used because in our previous calculations on cytochrome c oxidase (Medvedev, Daizadeh, and Stuchebrukhov 2000)Citation and photolyase (Cheung et al. 1999Citation ), the program, which replaces side chains onto the protein backbone based on predefined parameters defined from a backbone-dependent rotamer library, is a computationally nonintensive alternative to the computational procedure of replacement of amino acids followed by minimization of conformational energies, while producing the same qualitative results with respect to our electronic structure calculations. Upon this substitution, the matrix element did not change by more than a factor of 1.8; this again is in good agreement with the experiment. Examination of the tunneling currents shows that in this case almost all the current flows from Cys14 to Cys43. This shows that Ile23 is not important for the ET, but may be important for protein stability (Kyritis et al. 1997Citation ).

We have also performed calculations using the SOMO of the reduced cluster and two next orbitals as donor and acceptor states. As expected, the matrix element was too small (not more than 0.3 cm-1) to account for the observed rate of transfer, assuming that the reorganization energy is within a usual range, which for proteins is typically taken to be between 0.5 and 1 eV. However, the amino acids participating in the electron tunneling were found to be the same—cysteine ligands of cubanes, Ile23, Ala44, and Pro52. This observation adds further confidence to our results.

Sequence Analysis
Here, we present the results of the sequence analysis study of the C. acidurici ferredoxin. The homologous sequences of this ferredoxin belong to species from the three domains, which include the eukaryotes (10 sequences), bacteria (54 sequences), and the archaea (16 sequences) and span the full gamut of evolutionary distances from mammals to the green sulfur bacteria. The 10 eukaryotic sequences were composed of three Metazoa (two mammals, one nematode), three Viridiplantae, one Fungi, one Rhodophyta, one Reclinomonas, and one Entomoebidae. The 54 bacterial sequences were composed of 32 Proteobacteria, 18 Firmicutes, 3 Green-sulfur bacteria, and 1 Thermo/Deinococcus group. The 16 archaeal sequences constituted 15 Euryarchaeota and 1 Crenarchaeota. Thus the protein is an ancient protein predating the prokaryotic and eukaryotic divergence around 2 billion years ago.

The proteins, which contain regions of homology with the 55 amino acid sequence from C. acidurici ferredoxin, are associated with ET, but from a wide range of biological functions in natural systems; from an examination of the annotations for the sequences extracted from the database, we find the following distribution using the annotation support provided within SwissProt documentation: 34 ferredoxin (24 ferredoxin, 5 FDI, 4 FDII, 1 seven-iron ferredoxin fragment), 8 NADH-ubiquinone oxidoreductase 9 hydrogenases/hydrogenlyases (3 coenzyme F420 hydrogenase gamma subunits [8-hydroxy-5-deazaflavin-reducing]), 2 periplasmic hydrogenase large subunit, 1 formate hydrogenlyase subunit 6 [hydrogenase-3 component F], 2 hydrogenase-4 [including component A and H], [1 NADH-dehydrogenase I chain I], 2 DMSO reductase iron-sulfur subunit anaerobic dimethyl sulfoxide reductase chain B), and 1 RNA polymerase (DNA-directed RNA polymerase subunit D). The remaining 25 sequences correspond to sequences annotated with keywords, such as probable, putative, ferredoxin-like, or hypothetical. A complete list of accession numbers as well as the details for the multiple alignments is shown in figure 3 .



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Fig. 3.—Multiple alignment of ferredoxin determined from querying the SwissProt database (Madden, Tatusov, and Zhang 1996Citation ). The query sequence was from taken from (Dauter et al. 1997Citation ) and is the first sequence in the alignment; all numbering schemes are based on the query sequence. See text for a complete description. The graphical image of the multiple alignment was made using BOXshade Version 3.31 C (beta, 970507). Currently there is no citation for this program but reference can be given to its writers: Kay Hofmann, Bioinformatics group, ISREC, CH-1066 Epalinges s/Lausanne, Switzerland. E-mail: khofmann@isrec-sun1.unil.ch; Michael D. Baron, Institute for Animal Health, Ash Road, Pirbright Surrey GU240NF, U.K. E-mail: michael.baron@bbsrc.ac.uk. An identity threshold of 0.50 was used. The BOXshade program was accessed via the World Wide at: http://bioweb.pasteur.fr/seqanal/interfaces/boxshade.html

 
We note that for the results presented in this paper, we have decided to keep all the sequences for the evolutionary study even though their functional annotations represent in one case a non-ET phenomena (polymerase) and in several without any known function. The reasons for this were mainly because the number of non-ET sequences was only one (polymerase) and would not affect the qualitative results of our calculations and that this sequence satisfied our predefined criteria: The first of which was a relatively stringent E-value cutoff criteria of 0.001 (keeping in mind the low sequence number represented in the SwissProt database as compared with that of the Genbank [Madden, Tatusov, and Zhang 1996Citation ]). The second is that the randomized query sequence (see above) did not find any sequences close to or less than 0.001. Our keeping of this sequence in the calculations also prevented it from being excluded simply on the basis of functional annotations which may be inaccurate.

Because of the ubiquity and age of this protein, as well as the presence of sufficient experimental data, this protein system makes an ideal candidate to study a speculation concerning the role of evolution in the formation of tunneling pathways. A comparison of the amino acids implicated in the tunneling process by the method of tunneling currents with that of the multiple alignment data reveals an interesting correlation. In figure 4 , we show the (normalized) number of mutations of amino acids which are different from those found in C. acidurici ferredoxin, and in figure 5 , we have represented this information graphically on an image of the X-ray crystallographic structure of the ferredoxin molecule. We find that the cysteine amino acids are the most conserved part of the protein (shown in white), whereas Ile23, even though its position in the three-dimensional structure is directly between donor and acceptor cubanes, is highly variable (shown in blue). Notice that in addition to the cysteines, prolines in positions 19 and 48 are also highly conserved; the cysteines and prolines are exposed to solution and may serve as regions for protein-protein interactions. (The isopolymorphic alanincs in positions 22 and 51 are located within 4 Å of the cubane cysteine ligands and may serve to stabilize the protein).

Evolutionary substitutions of Ilc at position 23 include the hydrophobic amino acids: 9 leucines, 5 phenylalanines, 3 valines, 2 methionines, and 1 histidine. Lastly and interestingly, roughly six homologous sequences did not have a cysteine at position 11 (Cys14, Cys18, Cys37, Cys43, and Cys17 showed no variability; the substitutions at position 8 and 40 were of the order of one or two and may be because of errors in the database). It is known that homologous proteins with a deficient cysteine ligand correspond to a substitution of [4Fe-4S] with the [3Fe-4S] cofactor (Betrand et al. 1995Citation ). Even though this substitution at position 11 will change the reduction potential, we argue that as Cys11 and Cys13 are present and it is highly likely that they are roughly the same distance apart (because of the high level of homology as it is known that sequence homologies on the order of 20%–30% yield almost identical three-dimensional structures [Holmes 1999]), the ET tunneling pathway will be the same.

Although our results do not provide a logical proof that conservation of Cys14 and Cys43 is exclusively because of their involvement in the tunneling process (It can be argued that these amino acids are conserved along with the other five cysteines as ligands for regulating the redox potentials. Recall, however, that one of the ligands, Cys11 is less conserved evolutionarily than the other respective amino acids [see fig. 4 ]), the conservation of amino acids making up tunneling paths is interesting and is in line with the hypothesis of evolutionary conservation of tunneling paths. Further analyses including domain-level sweeping of the database in search for other related ET is currently under investigation. This paper along with an analysis in cytochrome c oxidase (Medvedev, Daizadeh, and Stuchebrukhov 2000)Citation demonstrates that the union of rigorous quantum chemical theories based on crystallographic information, experiment and molecular evolution may serve together to clarify the nature of the biological ET tunneling process.


    Note added in proof
 TOP
 Abstract
 Introduction
 Materials and Methods
 Results and Discussion
 Note added in proof
 Acknowledgements
 References
 
Figures 1 and 2 were produced by using the charge color submodule in the Insight II program with the following criterion: atom color of atom p = -2.5 x {Sigma}q |Jp,q|/|TDA|, where intensity of color is maximum when color criterion is less than or equal to 0.5. Figure 5 was produced in a similar way, where color criterion of an amino acid is proportional to the degree of the conservation shown in figure 4.


    Acknowledgements
 TOP
 Abstract
 Introduction
 Materials and Methods
 Results and Discussion
 Note added in proof
 Acknowledgements
 References
 
The work at Davis was partially supported by a research grant from the National Institutes of Health (GM54052-02). Fellowships from the Sloan and Beckman Foundations to A.A.S. are gratefully acknowledged. Computer resources for this project were provided by the Jet Propulsion Laboratory Supercomputing Center NASA. We would also like to thank Dr. Peng-Liang Wang for directing us to reference (Mouesca et al. 1994Citation ), Dr. Xuehe Zheng for critical comments, and two anonymous reviewers for their constructive criticisms, including pointing out certain references. I.D. gratefully acknowledges Walter Gilbert for critical comments on this work and for postdoctoral support while at Harvard University. I.D. also extends his gratitude to Biobank, A Life Science Community for support during the latter stages of this work. I.D. and D.M.M. contributed equally to this work.


    Footnotes
 
Claudia Kappen, Reviewing Editor

Present address: Nautilus Biotech, Evry, France Back

Keywords: electron transfer evolution Clostridia ferredoxin sequence analysis Back

Address for correspondence and reprints: Alexei A. Stuchebrukhov, Department of Chemistry, University of California, Davis, California 95616. stuchebr{at}chem.ucdavis.edu Back


    References
 TOP
 Abstract
 Introduction
 Materials and Methods
 Results and Discussion
 Note added in proof
 Acknowledgements
 References
 

    Betrand P., O. Mbarki, M. Asso, L. Blanchard, F. Guerlesquin, M. Tegoni, 1995 Biochemistry 34:11070–11079.

    Bower M. J., F. E. Cohen, R. I. Dunbrack, 1997 Prediction of protein side-chain rotamers from a backbone-dependent rotamer library—a new homology modeling tool J. Mol. Biol 267:1268-1282[ISI][Medline]

    Cheung M. S., I. Daizadeh, A. A. Stuchebrukhov, P. F. Heelis, 1999 Pathways of electron transfer in Escherichia coli DNA photolyase: Trp306 to FADH Biophys. J 76:1241-1249[Abstract/Free Full Text]

    Corpet F., 1988 Multalin multiple sequence alignment with hierarchical clustering Nucleic Acids Res 16:10881-10890[Abstract]

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Accepted for publication October 9, 2001.





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