Bart Lamiroy
email: bart.lamiroy@loria.fr

Tao Sun

Precision and Recall Without Ground Truth

In this paper we present a way to use precision and recall measures in total absence of ground truth.

Precision and Recall

1.1 General Definitions and Notation

Precision P r and Recall Rc (and often associated F-measure or ROC curves) are standard metrics expressing the quality of Information Retrieval methods [START_REF] Van Rijsbergen | Information Retrieval[END_REF]. They are usually expressed with respect to a query q (or averaged over a series of queries) over a data set ∆ such that:

P r ∆ q = P ∆ q ∩ R ∆ q R ∆ q
(1)

Rc ∆ q = P ∆ q ∩ R ∆ q P ∆ q (2)
where P ∆ q is the set of all documents in ∆, relevant to query q, and where R ∆ q is the set of documents actually retrieved by q. Although we can make a safe assumption by considering R ∆ q known (i.e the query q can actually be executed, and returns a known, manageable set of results), the same assumption does not always hold for P ∆ q , as will be shown later. For ease of reading we will refer to respectively P r, P Rc, and R, when there is no ambiguity on ∆ and q.

Often both are combined in the F β measure, where

F β = 1 + β 2 P rRc β 2 P r + Rc (3)

Other Interpretations and Frameworks

Precision, Recall and the F-measure can also be defined with respect to true positives τ p , false positives φ p , true negatives τ n and false negatives φ p . In that case, the corresponding formulas are:

P r = τ p τ p + φ p (4)
Rc = τ p τ p + φ n (5)
F β = 1 + β 2 τ p (1 + β 2 ) τ p + β 2 φ n + φ p (6)
Here again, it is necessary to know the values of τ p , φ p , τ n and φ p (as, previously, the sets P and R) in order to be able to do the computations.

It is also possible to give probabilistic interpretations to P r and Rc. In that case, P r would be the probability that a random document retrieved by the query is relevant, and Rc that a random relevant document be retreived by the query (taking as assumption that documents have uniform distributions). This is the interpretation we are going to use in the next sections.

Absence of Ground Truth

Previously enumerated metrics all made the assumption that the returns of queries can, in some way be qualified as "good" or "bad". Most often, there even is the assumption that this can actually be quantified: belonging to set P, τ p , etc. This implies that there is some absolute knowledge of ground truth or an oracle function available for the assessment of these quantities. While it is very convenient to rely on established truth to further train or evaluate methods, it is often very costly to obtain in many cases, and even impossible in others. Furthermore, it generally requires some human intervention or validation of some sorts, which makes the ground-truthing process both difficultly scalable and error prone, and therefore costly.

This paper presents a way to estimate precision and recall using a probabilistic model, allowing either to compare algorithms operating on the same data, without the requirement of establishing ground truth, or, to leverage crowdsourcing to establish ground truth in presence of noise, errors and mistakes. In order to achieve this, we shall first establish the underlying assumptions to our approach, in section 2.1, defining the context in which we have conceived our model. We then develop the mathematical foundations an tools in section 2.2.1.

General Assumptions

In what follows we are assuming that the following general conditions and notations apply:

1. We are considering generic system S that, given a query q, partitions 1 a set of documents ∆ = {δ i } i=1...d into S q+ and S q-. The partitioning function S q is defined as

S q : ∆ → {+, -} δ i → S q (δ i ) (7)
S q+ (resp. S q-) is defined as the inverse image of {+} (resp. {-}).

2. Other systems, similar to S q exist and their partitioning results are available. It is assumed that these systems operate in the same semantic context, and therefore aim to achieve the same partitioning as S q . We shall refer to the set of these systems as Σ q = {S q i } i=1...s In what follows, and where it is obvious, parameter q will be omitted. Table 1 gives an example overview of what three different systems could produce for a given query over a particular document set ∆.

∆ S 1 S 2 S 3 δ 1 + + + δ 2 + + + δ 3 - + - δ 4 + - - δ 5 + - - δ 6 - - + δ 7 - - - S + 1 = {δ 1 , δ 2 , δ 4 , δ 5 } S - 1 = {δ 3 , δ 6 , δ 7 } S + 2 = {δ 1 , δ 2 , δ 3 } S - 2 = {δ 4 , δ 5 , δ 6 , δ 7 } S + 3 = {δ 1 , δ 2 , δ 6 } S - 3 = {δ 3 , δ 4 , δ 5 , δ 7 }
Table 1: Example of query systems S i operating on document set ∆

Performance Evaluation

The question that arises now is how to compare different S i and decide which one performs best. Traditionally, one would take an evaluation test set ∆ ⋆ for which the ground truth of a query q ⋆ is known and available. We shall refer to this ground truth as ∆ + ⋆ and ∆ - ⋆ (i.e. ∆ + ⋆ is the partition of ∆ ⋆ containing the documents corresponding to q ⋆ , ∆ - ⋆ its complement). This knowledge then allows to compute precision and recall values, as described in Section 1, for all S i and establish a performance metric adapted to the context under consideration.

When ∆ + ⋆ and ∆ - ⋆ are unavailable, it is less obvious to compare the results of the different S i . One well documented approach is to use statistical estimators by considering each S i (∆) as the outcome of some random variable. What we are going to develop here, is very similar, but particularly focused on the expression of precision and recall.

Simplified Case

First we're making the assumption that all S i are of equal importance, and that there is no a priori knowledge available allowing to presume some of the systems are more reliable than others. This assumption will be alleviated in later work. We also assume all documents have equal frequency and occurrence probability.

For the arguments developed next, we need to introduce two "virtual" query systems, S ⊤ and S ⊥ . S ⊤ always returns all documents for any given query, S ⊥ never returns any. In other terms,

S + ⊤ = ∆, S - ⊤ = ∅ (8)
S + ⊥ = ∅, S - ⊥ = ∆ (9)
We are also slightly reconsidering the partitioning function defined in equation [START_REF] Smith | An overview of the tesseract ocr engine[END_REF], such that it returns values in {1, 0} rather than in {+, -}.

Under these hypotheses, the probability that a document

δ i belongs to ∆ + ⋆ is P (δ i ) = 1 s + 2 k=1...s,⊥,⊤ S k (δ i ) (10)
The results of the application of this to the example in Table 1, is represented in Table 2.

∆ P (δ i ) S ⊤ S 1 S 2 S 3 S ⊥ δ 1 0.8 1 1 1 1 0 δ 2 0.8 1 1 1 1 0 δ 3 0.4 1 0 1 0 0 δ 4 0.4 1 1 0 0 0 δ 5 0.4 1 1 0 0 0 δ 6 0.4 1 0 0 1 0 δ 7 0.2 1 0 0 0 0 Table 2: Example
Given the hypothesis of equidestribution of all documents δ i in ∆ and given the probabilistic definition of precision in Section 1.2, stating that P r "is the probability that a random document retrieved by a query is relevant", we can now define P r (S k ):

P r (S k ) = i=1...d P (δ i ) S k (δ i ) i=1...d S k (δ i ) (11)
Similarly, Rc was defined as "the probability for a random relevant document to be retrieved by the query". In our case, however relevancy has no longer a binary value, but has been replaced by P (δ i ). By reformulating this conditional probability and using Bayes' theorem (and using the fact that the inverse conditional of Rc is P r), things smooth out elegantly.

Rc (S k ) = P rob retrievedBy S k (δ i ) isRelevant (δi) = P rob isRelevant (δ i ) retrievedBy S k (δi) P rob retrievedBy S k (δ i ) P rob (isRelevant (δ i )) = P r (S k ) 1 d i=1..d S k (δ i ) 1 d i=1..d P (δ i ) = i=1...d P (δ i ) S k (δ i ) i=1...d S k (δ i ) i=1..d S k (δ i ) i=1..d P (δ i ) = i=1...d P (δ i ) S k (δ i ) i=1..d P (δ i ) (12)
It is interesting to notice the resemblance between equations (1) and ( 11) as well as between ( 2) and (12). Table 3 shows the values obtained when applied to the examples of Table 2.

∆ P (δ i ) S ⊤ S 1 S 2 S 3 S ⊥ δ 1 0.8 1 1 1 1 0 δ 2 0.8 1 1 1 1 0 δ 3 0.4 1 0 1 0 0 δ 4 0.4 1 1 0 0 0 δ 5 0.4 1 1 0 0 0 δ 6 0.4 1 0 0 1 0 δ 7 0.

Experimental Validation

In order to experimentally validate the model developed we have taken two contexts. One consists in taking the results of experiments reported in [START_REF] Santosh | Spatio-structural symbol description with statistical feature add-on[END_REF] related to comparing standard symbol recognition techniques. A second is related to evaluation of binarization algorithms on downstream treatment.

Symbol Recognition

In this section we use the experimental results reported in [START_REF] Santosh | Spatio-structural symbol description with statistical feature add-on[END_REF]. In this paper, the authors compare 5 different symbol recognition methods on a set of electrical wiring diagrams. Since their dataset has no know ground truth, they use a panel of human annotators to select and determine which ground truth corresponds to which query. [START_REF] Santosh | Spatio-structural symbol description with statistical feature add-on[END_REF].

Since the authors in [START_REF] Santosh | Spatio-structural symbol description with statistical feature add-on[END_REF] report retrieval efficiency, as defined in [START_REF] Kankanhalli | Cluster-based color matching for image retrieval[END_REF], we have resampled their raw experimental data to extract precision and recall.

The results, with respect to the human-defined ground-truth reported by the authors is given in Tables 4 and5. These data are also presented graphically in Figure 1.

Figure 2 reproduces the precision and recall values obtained using our method on the exact same data. It is interesting to note that, with one noteworthy exception, the ordering of the tested methods, with respect to precision or recall (i.e. when ordering methods from high precision/recall to low) is respected. Although not reproduced here, this also holds for the F-measure. What is even more compelling, is that the methods 'SC' and 'GFD' maintain their similarity in both cases, with and without consideration of ground truth.

The one exception is the 'ARG' method. While considered as a tie with 'SC' and 'GFD' with our method, it significantly outperforms all other approaches according to the ground truth. This is a very interesting result, and is currently under investigation.

Document Binarization

The data used in this second study are the historical images collected from the Library of Congress on-line data set [1]. A total of 60 TIF format images Figure 1: Precision and Recall as reported in [START_REF] Santosh | Spatio-structural symbol description with statistical feature add-on[END_REF] Figure 2: Precision and Recall as computed without ground truth with a resolution of 300 dpi. Various genres from official documents to private letters are included. The degraded quality of these images, such as uneven illumination, bleeding-through, handwritten marks, etc, are be a great challenge for recognition algorithms. In this case, we are going to try and use our approach to evaluating binarization quality to downstream recognition. The document image analysis pipeline consists of three stages: Binarization is the first stage, and three thresholding methods are used in this stage respectively. They are Otsu [START_REF] Otsu | A threshold selection method from gray-level histograms[END_REF], Sauvola [START_REF] Jaakko | Adaptive document image binarization[END_REF] and Wolf [START_REF] Wolf | Binarization of low quality text using a markov random field model[END_REF]. Otsu's method is a global thresholding method while the latter two are local thresholding methods. After all the images are converted into binary images, the resultant binary images were converted to ASCII texts by Tesseract-3.00 [START_REF] Smith | An overview of the tesseract ocr engine[END_REF] open source software package in the second stage. Finally, Stanford Named Entity Recognizer [START_REF] Finkel | Incorporating non-local information into information extraction systems by gibbs sampling[END_REF] is used in the third stage. To sum up, we have three different pipelines this way.

Although our method aims to calculate precision and recall without ground truth, we still need ground truth to evaluate if our method can achieve the goal proposed in Section 2.2. Since the groundtruth of the historical images are not directly available, we generate the groundtruth ourselves by manual typing the text and carefully proofreading. Since the three different pipelines depend on three different thresholding methods, we use the names of them to stand for the three pipelines, respectively. The calculation of average precision and recall is based on the outputs of these pipelines, which are the named entity extraction results. When evaluating our method, we use two different ways to process the outputs of the three pipelines. Method I considers all the recognized named entities as "bagof-words", so they are organized in an alphabetical way. While Method II use the multiple sequence alignment algorithm to align the three outputs first, the original positions of these named entities are kept this way. The experiment results are shown in the following tables. From Table 6 we can see that Sauvola and Wolf beat Otsu thresholding method. The reason is obvious. Only one threshold is determined for the whole image by Otsu, while for the other two methods, different thresholds are calculated according to the grey distribution of their corresponding local windows. Table 7 and Table 8 show the results of our method under two methods. We can see again the performance of Sauvola and Wolf is better than that of Otsu, while recognition accuracies between Sauvola and Wolf are similar. Both of them indicate that even if without ground truth, the precision and recall computed by our method is similar to those computed with ground truth.

Conclusion and Future Work

In this study we have presented how to compute precision and recall without presence of formally identified ground truth. Results indicate that this measure is coherent with real, ground truth based precision and recall measures.

Further work and development will consist in establishing:

1. how to rank or take into account user-contributed "partial" ground truth, especially considering "yes/no/unknown" information ?

2. What if we use confidence measures instead of binary values on the algorithm outcomes ?

3. What if we attach more weight or confidence to particular algorithms ?

Table 3 :

 3 Example of precision and recall computations without established ground truth.

		2	1	0	0	0	0
	Sum	3.4	7	4	3	3	0
	P S k		3.4	2.4	2	2	0
	P r		0.49	0.6	0.67 0.67 ∞
	Rc		1	0.71 0.59 0.59	0

Table 4 :

 4 Precision measures as reported in[START_REF] Santosh | Spatio-structural symbol description with statistical feature add-on[END_REF].

	k	Radon	GFD	zernike	SC	ARG
	1 1.00000 1.00000 1.00000 1.00000 1.00000
	2 0.59524 0.93023 0.72727 0.90698 0.97674
	3 0.43548 0.80000 0.60000 0.82813 0.92188
	4 0.34940 0.70930 0.49412 0.75581 0.83333
	5 0.30769 0.66038 0.44762 0.69811 0.81905
	6 0.28226 0.58730 0.41600 0.62698 0.75397
	7 0.26712 0.53061 0.37838 0.56164 0.72789
	8 0.23952 0.49102 0.35714 0.51205 0.68452
	9 0.21925 0.45455 0.35106 0.47059 0.65263
	10 0.20290 0.41546 0.33173 0.43269 0.61321
	k	Radon	GFD	zernike	SC	ARG
	1 0.05699 0.05699 0.05699 0.05699 0.05699
	2 0.06476 0.10362 0.08290 0.10103 0.10880
	3 0.06994 0.13471 0.10103 0.13730 0.15284
	4 0.07512 0.15803 0.10880 0.16839 0.18134
	5 0.08290 0.18134 0.12176 0.19170 0.22279
	6 0.09067 0.19170 0.13471 0.20466 0.24611
	7 0.10103 0.20207 0.14507 0.21243 0.27720
	8 0.10362 0.21243 0.15544 0.22020 0.29792
	9 0.10621 0.22020 0.17098 0.22797 0.32124
	10 0.10880 0.22279 0.17875 0.23316 0.33678

Table 5 :

 5 Recall measures as reported in

Table 6 :

 6 Average Recognition Accuracies with Ground Truth

	1. Binarization;
	2. OCR;
	3. Named Entity Recognition
		Otsu	Sauvola	Wolf
	Precision 0.6223	0.7715	0.7533
	Recall	0.5915	0.7281	0.7230

Table 7 :

 7 Method I: Average Recognition Accuracies without Ground Truth

		S ⊤	Otsu	Sauvola	Wolf	S ⊥
	Precision 0.4000 0.6327	0.6757	0.6722 ∞
	Recall	1.0000 0.5153	0.5660	0.5662	0

Table 8 :

 8 Method II: Average Recognition Accuracies without Ground Truth

		S ⊤	Otsu	Sauvola	Wolf	S ⊥
	Precision 0.5733 0.6035	0.6450	0.6416 ∞
	Recall	1.0000 0.6550	0.6988	0.6957	0

For the absent-minded reader, "partitioning" ∆ into S + and S -entails that ∆ = S + ∪S - and S + ∩ S -= ∅

Acknowledgements

The authors would like to acknowledge Santosh K.C. for having provided the experimental data, used in Section 2.3.1.

* Bart Lamiroy was a visiting scientist at Lehigh University in 2010-2011. This work was conducted at the Computer Science and Engineering Departent at Lehigh University and was supported in part by a DARPA IPTO grant administered by Raytheon BBN Technologies.

1


Filipe Folgosa

Cristina M Cordas

Joana A Santos

Alice S Pereira

José J G Moura

Pedro António

Brito Tavares

Isabel Moura

Pedro Tavares
email: pedro.tavares@dq.fct.unl.pt

New spectroscopic and electrochemical insights on a class I superoxide reductase: Evidence for an intramolecular electron transfer pathway

Keywords: Electron transfer, Non-mediated electrochemistry, Reactive Oxygen Species, Superoxide reductases, Biochemical

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Oxygen is one of the most abundant elements in biology. In its ground state, O 2 is a triplet, while most of reactants are singlets leading to spin forbidden processes. Thus, reactions between molecular oxygen and other molecules should be kinetically unfavorable, requiring large activation energies [START_REF] Elstner | Oxygen Activation and Oxygen-Toxicity[END_REF]. Over the years, biology overcame this problem by using transition metals, such as iron, for pairing electrons on a process called "oxygen activation" [START_REF] Bollinger | Stalking intermediates in oxygen activation by iron enzymes: motivation and method[END_REF][START_REF] Costas | Dioxygen activation at mononuclear nonheme iron active sites: enzymes, models, and intermediates[END_REF][START_REF] Korendovych | Dioxygen activation at non-heme iron: insights from rapid kinetic studies[END_REF][START_REF] Decker | Dioxygen activation by copper, heme and non-heme iron enzymes: comparison of electronic structures and reactivities[END_REF]. This complementarity enables oxygen to participate in biological cycles but can lead also to the formation of reactive oxygen species (ROS). Due to this behavior a large protection mechanism is required in order to overcome the possible lethal effects of the reactive species formed on the cell. Since the early 90's several reports of new classes of non-heme iron proteins isolation and characterization have been published [START_REF] Zhang | Crystal structure of Thermotoga maritima 0065, a member of the IclR transcriptional factor family[END_REF][START_REF] Tavares | Spectroscopic properties of desulfoferrodoxin from Desulfovibrio desulfuricans (ATCC 27774)[END_REF][START_REF] Moura | Characterization of three proteins containing multiple iron sites: rubrerythrin, desulfoferrodoxin, and a protein containing a six-iron cluster[END_REF][START_REF] Chen | A blue non-heme iron protein from Desulfovibrio gigas[END_REF][10][START_REF] Jenney | Neelaredoxin from Pyrococcus furiosus is a novel type of superoxide dismutase[END_REF][12][START_REF] Abreu | Oxygen detoxification in the strict anaerobic archaeon Archaeoglobus fulgidus: superoxide scavenging by neelaredoxin[END_REF][START_REF] Rodrigues | Superoxide reduction by Archaeoglobus fulgidus desulfoferrodoxin: comparison with neelaredoxin[END_REF][START_REF] Yeh | Structures of the superoxide reductase from Pyrococcus furiosus in the oxidized and reduced states[END_REF][START_REF] Jovanovic | Neelaredoxin, an iron-binding protein from the syphilis spirochete, Treponema pallidum, is a superoxide reductase[END_REF]. However, only in 1999 the real function of some of these proteins was assigned [START_REF] Jenney | Anaerobic microbes: oxygen detoxification without superoxide dismutase[END_REF]. The so-called superoxide reductases (SOR) reveled a new way to reduced, by one electron, the superoxide anion to hydrogen peroxide (eq. 1), instead of the well known reaction of dismutation (eq. 2), performed by the superoxide dismutases (SOD) [START_REF] Jenney | Anaerobic microbes: oxygen detoxification without superoxide dismutase[END_REF][START_REF] Mccord | Superoxide dismutase: the first twenty years (1968-1988)[END_REF].

O 2 -+ 2H + + e -→ H 2 O 2 (SOR) Eq. 1 2O 2 -+ 2H + → O 2 + H 2 O 2 (SOD) Eq. 2
This capability has an enormous biological relevance if we consider that the majority of these SOR proteins were first purified from anaerobes, giving them the skills to survive to small amounts of both oxygen and its reaction products [START_REF] Tavares | Spectroscopic properties of desulfoferrodoxin from Desulfovibrio desulfuricans (ATCC 27774)[END_REF][START_REF] Chen | A blue non-heme iron protein from Desulfovibrio gigas[END_REF]10]. SORs are usually divided into three classes, according to the number of iron centers (two irons per protein monomer for class I and one iron per monomer for class II and III SORs) and primary structure (presence of an extra N-terminal domain) [START_REF] Pereira | Superoxide reductases[END_REF]. Center I contains an iron atom coordinated by four cysteine residues ([Fe(S-Cys) 4 ]) in a way similar to the one identified in desulforedoxin [20,[START_REF] Archer | Crystal structure of desulforedoxin from Desulfovibrio gigas determined at 1.8 A resolution: a novel non-heme iron protein structure[END_REF] while center II has an iron atom coordinated by four histidine residues in the equatorial plane and one cysteine in the axial plane ([Fe(S-Cys)(N-His) 4 ]) [START_REF] Chen | A blue non-heme iron protein from Desulfovibrio gigas[END_REF]10,[START_REF] Pereira | Superoxide reductases[END_REF][START_REF] Devreese | Primary structure of desulfoferrodoxin from Desulfovibrio desulfuricans ATCC 27774, a new class of non-heme iron proteins[END_REF]. Class I SORs were first isolated by Moura et al. from the sulfate and nitrate reducing bacteria Desulfovibrio desulfuricans ATCC 27774 [10]. This dimeric protein (2x14 kDa) can have three different oxidation states, fully reduced (both centers in the reduced form), half-reduced (center I in the oxidized form and center II in the reduced form) and fully oxidized (both centers in the oxidized form). The UV/Visible spectrum of the halfreduced form is dominated by maxima at 495, 368 and 279 nm, while in the fully oxidized form UV/Visible spectrum shows additional bands at 335 and 635 nm. The fully reduced form has no absorption bands in the visible region of the spectrum. The EPR spectrum of the half-reduced form shows a set of resonances (g=7.7, 5.7, 4.1 and 1.8) characteristic of a high-spin ferric ion (S=5/2) with an E/D value of 0.08, while the fully oxidized form has additional resonances at g=4. In a different attempt, Kurtz and co-workers, reported a 2Fe-SOR mutant, C13S from D. vulgaris Hildenborough. This protein revealed spectroscopic features similar to the previously described for the class I SOR's center II. Besides, this mutant also revealed similar behavior when reacted with superoxide, indicating that rubredoxin efficiently donates electrons to center II. However, such as in DfxC, the C13S mutant is also less stable than the wild type form [30].

In this work we propose to characterize not only the biological relevance of center I in the class I SORs (as a putative redox center) but also its role in the enzyme mechanism. The iron atom located at center I was replaced by a zinc atom making it unavailable for electron transfer. We aim to demonstrate the differences in catalytic activity of the protein when only one, or both centers are present, and also to characterize the direct electron transfer pathway between the SOR and the common accepted physiological electron donor, rubredoxin [START_REF] Auchere | Overexpression and purification of Treponema pallidum rubredoxin; kinetic evidence for a superoxide-mediated electron transfer with the superoxide reductase neelaredoxin[END_REF][START_REF] Rodrigues | Rubredoxin acts as an electron donor for neelaredoxin in Archaeoglobus fulgidus[END_REF][START_REF] Auchere | Kinetics studies of the superoxide-mediated electron transfer reactions between rubredoxintype proteins and superoxide reductases[END_REF]. Several techniques such as UV-Visible, Stopped-Flow, EPR and also direct electrochemistry were used to accomplish the biochemical and spectroscopic characterization. Overexpression and purification of recombinant D. vulgaris Hildenborough rubredoxin D. vulgaris Hildenborough rubredoxin was overexpressed and purified to homogeneity following a protocol (see supplementary information) modified from the one previously published [START_REF] Auchere | Overexpression and purification of Treponema pallidum rubredoxin; kinetic evidence for a superoxide-mediated electron transfer with the superoxide reductase neelaredoxin[END_REF][START_REF] Auchere | Kinetics studies of the superoxide-mediated electron transfer reactions between rubredoxintype proteins and superoxide reductases[END_REF].

Overexpression and purification of recombinant D. gigas desulforedoxin D. gigas desulforedoxin was overexpressed and purified to homogeneity following a protocol (see supplementary information) modified from the one previously published [20].

Overexpression and purification of recombinant D. vulgaris Hildenborough 2Fe-SOR Production of recombinant D. vulgaris Hildenborough 2Fe-SOR followed a protocol modified from the one previously published [29,[START_REF] Auchere | Kinetics studies of the superoxide-mediated electron transfer reactions between rubredoxintype proteins and superoxide reductases[END_REF]. In this case, the cell culture was allowed to grow at 310.15 K at 230 rpm until its O.D. at 600 nm was near 0.8 in M9 media containing 0.1 mg/mL ampicillin and 0.1 mM FeCl 2 . At this time 1 mM IPTG and 0.1mM FeCl 2 were added and the culture was able to grow for approximately 14 hours at room temperature (between 293.15 and 298.15 K) at 230 rpm. The fraction containing the 2Fe-SOR was collected as described for Dv rubredoxin. Two consecutive ion-exchange chromatographic steps (DEAE-Sepharose FF® and Q Speharore FF® from GE HealthCare®) were applied. The collected fractions were analyzed by UV-Visible and SDS-PAGE and pooled according to their purity. With this procedure it was possible to collect a final fraction containing SOR with a purity ratio of 6.2 (Abs 280 /Abs 490 ). All this purification steps were performed at 277.15 K and pH 7.6.

Overexpression and purification of recombinant D. vulgaris Hildenborough Zn/Fe-SOR The procedure was similar to the one described for the 2Fe-SOR. Though, in this case, both at the beginning and at the time of induction, 0.1 mM FeCl 2 and 0.1 mM ZnCl 2 were added to the culture. Following, the same chromatographic steps used for the 2Fe-SOR were applied and it was possible to collect a final fraction containing pure Zn/Fe-SOR form with a purity ratio of 21 (Abs 280 /Abs 644 ).

Metal Content and Protein quantification

Metal content was determinated by inductively coupled plasma emission (Lab. de Análises, Dept. Química, CQFB/REQUIMTE, FCT/UNL). Protein determination was performed using Lowry assay with BSA as protein standard [START_REF] Lowry | Protein measurement with the Folin phenol reagent[END_REF]. A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

The concentration of protein solutions were also determined spectrophotometrically using the reported molar extinction coefficients, ε 490nm =6.9 mM -1 cm -1 for Dv rubredoxin, ε 502 nm =4.3 mM -1 cm -1 for Dv SOR Fe(III)-Fe(II) , ε 645nm =1.9 mM -1 cm -1 for Dv Zn/Fe-SOR, and ε 502nm =4.6 mM -1 cm -1 for Dg desulforedoxin.

Direct electron transfer experiments

Stopped-Flow experiments were performed using a Bio-Logic SFM-300/S apparatus coupled with a MOS-250 optical system. All the experiments were performed in anaerobic conditions in a glove box (UNILab, MBraun, less than 1 ppm). All assays were performed in 50 mM phosphate buffer at pH 7.6 with 0.1 mM EDTA at 283.15 K. To perform the experiments both rubredoxin and SOR were degassed in a Schlenk line before transfer to the glove box. Rubredoxin was then reduced with a slight excess of sodium dithionite. The SOR Fe(III)-Fe(II) form was obtained by incubating as-purified SOR with a slight excess of ascorbic acid. The SOR Fe(III)-Fe(III) and Zn/Fe-SOR forms were prepared with an excess of sodium hexachloroiridate (IV) in order to obtain the fully oxidized form. The excess of reagents (oxidants and reductants) were removed using a 5 mL Hitrap™ (GE Healthcare®) desalting column. The data was best fitted with a second order rate constant with [Rd] 0 = [SOR] 0 , where is the amount of oxidized rubredoxin, [Rd] 0 and [SOR] 0 are the initial concentration of reduced rubredoxin and oxidized SOR, respectively and k'=k [Rd red ] 0 , were k is the second order rate constant [START_REF] Rodrigues | Rubredoxin acts as an electron donor for neelaredoxin in Archaeoglobus fulgidus[END_REF][START_REF] Wisitruangsakul | Redox-linked protein dynamics of cytochrome c probed by timeresolved surface enhanced absorption spectroscopy[END_REF].

Eq. 3

Spectroscopic and kinetic characterization

Absorption spectra were collected with a Shimadzu UV-2101PC spectrophotometer, connected to a computer. Superoxide mediated electron transfer assays were performed as in a similar way (see supplementary information) that the previously published by Auchère et al. at 296.15 K with a Hewlett-Packard 8452A diode-array spectrophotometer [START_REF] Auchere | Kinetics studies of the superoxide-mediated electron transfer reactions between rubredoxintype proteins and superoxide reductases[END_REF]. Data was fitted assuming that the reaction rate was proportional to the concentration of the reagents and a kinetic constant k. The concentration of both rubredoxin and superoxide used were significantly larger than SOR and so, considered constant at t=0. The obtained equation was as follows:

v 0 = k' [SOR]
Eq. 4

where k' is

k' = k [Rd] [O 2 .-] Eq. 5
The value for v 0 was obtained directly from the experimental data and plotted versus the correspondent amount of SOR.

[ ]

t κ' 1 0 red Rd 0 ] red [Rd ] ox [Rd × + - = Biochemical Journal

Electrochemical Studies

The potentiodynamic measurements were performed with a Potenciostat / Galvanostat µAUTOLAB Type II. Glassy carbon (GC) disk (4 mm diameter) and a gold disk (3 mm diameter) were the working electrodes. The counter electrode was a Pt wire and a saturated calomel electrode (SCE) was used as reference. The working electrodes were previously polished with 1.0 and 0.3 µm alumina and immersed in Millipore water in ultra-sound bath for 5 min and finally thoroughly rinsed with Millipore water. The proteins were immobilized on the electrode using a cellulose membrane (Spectra/Por dialysis membrane, 3500 Da cut-off) that was fitted to the electrode with an o-ring, to obtain a thin layer regime. The supporting electrolyte was 10 mM Tris-HCl buffer pH 7.6, 0.1 M KNO 3 , 20 mM MgCl 2 . The proteins concentration ranged from 150 to 300 µM. For each assay 10 µL of protein solution was used. In the membrane, together with the protein solution, 2 µL of 2 mM neomycin sulfate was added for the assays with GC electrode. The gold electrode was previously conditioned for 5 min in 1 mM 4,4'dithiodipyridine solution.

9

RESULTS

Spectroscopic characterization

Figure 1 shows a UV-Vis spectrum of the SOR Zn(II)-Fe(III) . The features presented by this new form of D. vulgaris Hildenborough SOR protein are very similar to those already known for class II and III SORs. The absorption spectrum has three main features, at 280 nm (ε 280 =28650 M -1 cm -1 ), 314 nm (ε 314 =6089 M -1 cm -1 ) and 644 nm (ε 644 =1746 M -1 cm -1 ). This 644 nm absorption band was previously assigned to center II from D. vulgaris Hildenborough SOR and also for the oxidized form of the C-terminal domain, DfxC, of the recombinant SOR from D. vulgaris Hildenborough which contains only center II [START_REF] Tavares | Spectroscopic properties of desulfoferrodoxin from Desulfovibrio desulfuricans (ATCC 27774)[END_REF]29,[START_REF] Verhagen | On the two iron centers of desulfoferrodoxin[END_REF]. The shoulder around 314 nm should correspond to the cysteine-iron charge transfer band, also present in other proteins with similar iron centers [START_REF] Tavares | Spectroscopic properties of desulfoferrodoxin from Desulfovibrio desulfuricans (ATCC 27774)[END_REF]10,29,[START_REF] Verhagen | On the two iron centers of desulfoferrodoxin[END_REF]38]. Further spectroscopic characterization of SOR Zn(II)-Fe(III) was performed by EPR in order to compare to the signals obtained for the iron only form, SOR Fe(III)-Fe(III) . Figure 2 shows the EPR spectra of SOR Zn(II)-Fe(III) recorded at 4.2 K. This spectrum is very similar to the one obtained with both SOR Fe(III)-Fe(III) center II and DfxC protein [START_REF] Tavares | Spectroscopic properties of desulfoferrodoxin from Desulfovibrio desulfuricans (ATCC 27774)[END_REF]29]. The dominant features at g=8.93, g=4.76 and g=4.30 are indicative of the presence of a ferric ion with a S=5/2 and E/D approximately 1/3 [START_REF] Tavares | Spectroscopic properties of desulfoferrodoxin from Desulfovibrio desulfuricans (ATCC 27774)[END_REF][START_REF] Chen | A blue non-heme iron protein from Desulfovibrio gigas[END_REF]10,29].

Metal Analysis and N-Terminal sequence

The amount of iron per protein, as well as the screening of other metals in the protein was analyzed by induction-coupled plasma emission (Lab. de Análises, Dept. Química, CQFB/REQUIMTE, FCT/UNL). The analysis performed pointed to a 1:1 ratio (Zn and Fe atoms) and also doesn't reveal the presence of any other metal ions. The protein was also subjected to sequential Edman degradation on an automatic protein sequencer (Applied Biosystem model LC491) and the NH2-terminal sequence of the first amino acid residues was determined. This ensured that the recombinant protein did not suffer an unexpected mutation/deletion in one or more center I amino acid ligand. The analysis indicated that the first 21 amino acids had 100% identity when compared to the sequence predicted by the gene analysis.

Direct electron transfer measurements

Direct electron transfer between reduced rubredoxin and half-reduced form, SOR Fe(III)- Fe(II) , was measured. The stopped-flow experiments were performed in a 1:1 ratio for the two proteins and monitored at 500 nm in order to follow rubredoxin oxidation rate of (see experimental section for further details). The kinetic traces were best fitted with a second order kinetic rate constant with a k of (2.8±0.4)x10 7 M -1 s -1 , which corresponds to the electron transfer rate constant from rubredoxin to SOR Fe(III)-Fe(II) center I. The same experimental procedure was applied for the assay between reduced rubredoxin and the fully oxidized form, SOR Fe(III)-Fe(III) . In this case, the experiment was monitored at both 500 and 650 nm, near the absorption maxima of both oxidized rubredoxin and SOR Fe(III)-Fe(III) center II, respectively. The second order rate constants calculated for both wavelengths were (4.3±1.9)x10 6 M -1 s -1 and (1.9±0.5)x10 6 M -1 s -1 , for 500 and 650 nm respectively. These values were considered identical within the experimental error. Besides, they are also closed to the ones published for the electron transfer between Rd-1 and Rd-2 and 10 center II of class I SOR from A. fulgidus (1.9x10 6 M -1 s -1 and 2.4x10 6 M -1 s -1 respectively) [START_REF] Rodrigues | Superoxide reduction by Archaeoglobus fulgidus desulfoferrodoxin: comparison with neelaredoxin[END_REF] and for the reduction of the center II of the SOR mutant C13S from D. vulgaris Hildenborough, 1.2x10 6 M -1 s -1 [START_REF] Emerson | Kinetics of the superoxide reductase catalytic cycle[END_REF]. On the contrary, when Neelaredoxin (class II SOR) from A. fulgidus is reduced by Rd-1 and Rd-2, the authors report two second order rate constants of 1x10 7 M -1 s -1 and 6x10 7 M -1 s -1 , respectively [START_REF] Rodrigues | Rubredoxin acts as an electron donor for neelaredoxin in Archaeoglobus fulgidus[END_REF]. Nevertheless, in this case, and as described for the reduction of oxidized SOR from A. fulgidus [START_REF] Rodrigues | Superoxide reduction by Archaeoglobus fulgidus desulfoferrodoxin: comparison with neelaredoxin[END_REF], the absorbance measured at 500 nm, at the end of the experiment and considering the concentration of both proteins after mixing, was due to the contribution of both oxidized rubredoxin and SOR Fe(III)-Fe(II) , that was obtained after the one electron reduction. Two possibilities arise from this observation: a) electrons are donated by rubredoxin to center I and then, by a fast intramolecular electron transfer process will reduce center II which gives rise to an oxidized center I at the end of the experiment or; b) rubredoxin donated electrons directly to center II, keeping center I in the oxidized form, such as was proposed before [START_REF] Rodrigues | Superoxide reduction by Archaeoglobus fulgidus desulfoferrodoxin: comparison with neelaredoxin[END_REF]. However, this observation brings to the fore the question about the exact location where electron transfer occurs or even if there is some type of intramolecular electron transfer. To further understand the electron transfer process, a similar experiment was performed but with a 2:1 rubredoxin:SOR Fe(III)-Fe(III) ratio. The calculated second order rate constant values were (1.3±0.2)x10 6 M -1 s -1 and (1.7±0.3)x10 6 M -1 s -1 , at 500 nm and 650 nm respectively. In this case, the fully oxidized form of rubredoxin is achieved with the concomitant conversion of SOR to the reduced form, meaning that complete SOR reduction is possible within stopped-flow timescale when enough electrons are provided. Besides, the similarity of these two values is the first evidence of a possible intramolecular electron transfer since, a biphasic behavior would be expected at 500 nm if rubredoxin was able to donate electrons independently to center I or center II, considering the 10 fold difference between the obtained values in the previous experiments for reduction of center I in SOR Fe(III)-Fe(II) and center II in SOR Fe(III)-Fe(III) . The absence of this biphasic behavior supports the idea that when both SOR centers are oxidized the electrons follow a pathway that goes thru center I to center II. To calculate the electron transfer rate constant of the isolated center II the same experiments were repeated, but this time mixing reduced rubredoxin with oxidized SOR Zn(II)-Fe(III) in a 1:1 ratio between the two proteins. As a result, the calculated values at both wavelengths were (3.2±1.5)x10 6 M -1 s -1 and (2.9±0.4)x10 6 M -1 s -1 , for 500 nm and 650 nm respectively. Again, these values can be considered similar within the experimental error and they are also similar to the ones obtained for the SOR Fe(III)-Fe(III) (Figure 3). This experiment proves that reduced rubredoxin is able to reduce SOR's center II but at a lower rate constant that center I of the same protein.

ET measurements in the presence of superoxide anion Superoxide reductase activity Superoxide mediated electron transfer assay was performed in a way similar to the previously published by Auchère et al. (see experimental section for further details) [START_REF] Auchere | Kinetics studies of the superoxide-mediated electron transfer reactions between rubredoxintype proteins and superoxide reductases[END_REF]. In this experiment the initial reaction rate was used to differentiate the reaction A c c e p t e d M a n u s c r i p t constants obtained when different forms of SOR are used. As was previously described by Auchère et al [START_REF] Auchere | Kinetics studies of the superoxide-mediated electron transfer reactions between rubredoxintype proteins and superoxide reductases[END_REF], the results shows that, also in the superoxide mediated electron transfer process, a higher rubredoxin oxidation rate is obtained when SOR Fe(III)-Fe(II) form is used, (12.34±0.08) min -1 , while the reaction rates calculated when SOR Fe(III)-Fe(III) and SOR Zn(II)-Fe(III) are used are (9.72±0.06) min -1 and (8.98±0.04) min -1 , respectively (Figure 4). Despite the differences in the assays, as well as their different purpose, these observations point out the same trend as for the results obtained for direct electron transfer experiments. Thus, it is possible to speculate that the SOR Fe(III)-Fe(II) is not only able to receive electrons faster than the other forms but also it is catalytically more efficient. This effect could be related with the reduced state of center II in the beginning of the reaction. To test this observation a new experiment was performed, starting using both SOR Fe(II)-Fe(II) , SOR Zn(II)-Fe(II) forms. In this case, the calculated rate constants are comparable within each other (11.79±0.86) min -1 and (12.12±0.73) min -1 for SOR Fe(II)-Fe(II) , SOR Zn(II)-Fe(II) , respectively, and with the SOR Fe(III)-Fe(II) form. A summary of all the obtained values is presented in Table 2. The results of this last experiment suggest that when the catalytic reaction is assayed starting with center II in the reduced state, the presence of center I is not relevant for catalysis. The smaller reaction rate constants observed for the SOR Fe(III)-Fe(III) and oxidized SOR Zn(II)-Fe(III) forms are in accordance with this observation, since in both cases center II has to be reduced prior to the reaction with superoxide radical, leading to a slower initial reaction rate.

Electrochemical measurements

The electrochemical features of the Desulfovibrio gigas desulforedoxin, Desulfovibrio vulgaris Hildenborough rubredoxin and native and modified forms of SOR proteins were observed by cyclic and square wave voltammetry. Both desulforedoxin and rubredoxin present well defined current peaks, in quasi-reversible behavior, due to a one electron transfer, at the redox center, [Fe(S-Cys) 4 ] 3+ / [Fe(S-Cys) 4 ] 2+ . Figure 5 shows the typical behavior of these two proteins at 288.15 K. The calculated values for the formal redox potential of these centers were -27±2 and +39±2 mV, for desulforedoxin and rubredoxin, respectively. The value calculated for rubredoxin is in accordance with previous published results obtained on graphite microelectrodes [START_REF] Correia Dos Santos | Electrochemical studies of rubredoxin from Desulfovibrio vulgaris at modified electrodes[END_REF]. The electrochemical pattern observed for 2Fe-SOR is not so straightforward. Although the structural similarities found between center I of this protein and both desulforedoxin and rubredoxin centers, its redox behaviour is more complex. In fact, different features are observed with slow and fast scan rates. Typically, at the range 10-20 mV/s or higher scan rates, two very close redox processes are visible, although with low definition. At lower scan rates, only one redox process is observed with the anodic and cathodic peaks possessing a large peak width, leading to the conclusion that redox processes become merged and are better seen at higher scan rate potentials. Also, with the temperature increase the merging of the processes is also observed at increasingly higher scan rate. A typical example of this different behavior at low temperature (278.15 K) and a better view of the merging of the two peaks at higher temperature (298.15 K) is shown on Figure 6. The proximity of the potential values at which these two apparent redox processes are observed and the merging with the change in the applied potential scan rate and temperature, seems to point that both processes are due to center I, corresponding to a single electron transfer process. An estimation of the number of electrons involved through the current peaks width at half height also points to this hypothesis. One possible explanation of this phenomenon is associated to different heterogeneous electron transfer constants for the same process. This was already reported by other authors, although in different systems and conditions [40]. In fact, superficial charge calculations performed with Accelrys DS Visualizer v2.0.1.7347, Accelrys Software Inc. shows that 2Fe-SOR does not have a preferential positive or negative superficial electrostatic charge, contrary to what is observed for desulforedoxin and rubredoxin proteins (see Figure 7). This may result in a non-preferential protein orientation towards the electrode surface, even with the addition of a positive charged promoter, which may originate different electronic pathways to the redox center and different heterogeneous electronic transfer constants, producing two apparent redox processes. Partial adsorption of the biomolecules could also contribute to this hypothesis of apparent dispersion of heterogeneous constant rates. However, the control experiments, performed following the assays at the same conditions, after the electrode was washed in Millipore® water and then immersed in the same electrolyte solution, without protein, have shown no apparent adsorption. Another hypothesis is related to the electrochemical mechanism of the 2Fe-SOR reduction. These two apparent redox processes can occur from two different electron transfer pathways in the SOR reduction, including an intramolecular step, with one electron transfer from center I to center II. This explanation is in agreement with center II data, from both 2Fe-SOR and Zn/Fe-SOR proteins, observed by fast electrochemical techniques and it will be discussed in more detail later. The formal potential of the three proteins, desulforedoxin, 2Fe-SOR and rubredoxin, was estimated in the range of 278.15 to 290.15 K in order to establish its temperature dependence (Figure 8). Both desulforedoxin and rubredoxin present lower slopes and considerable lower associated errors than 2Fe-SOR. The values used to evaluate the 2Fe-SOR formal redox potential of center I were taken from the assays where the two processes were merged, resulting in E 0 '=+32±11 mV for the temperature 288.15 K. This explains the larger dispersion of the values and so, the larger error, associated to this protein, on E 0 ' compared with the associated errors resulting from desulforedoxin and rubredoxin. Also, the 2Fe-SOR center I redox potential value is in agreement with the results obtained for the recombinant DfxN already published [29]. The Gibbs free energy of the electron transfer reaction can be estimated from the centers redox potential dependence on the temperature, and related with redox states conformational changes, amongst other factors, such as the bonding interaction at the metallic centers [START_REF] Moore | Factors Influencing Redox Potentials of Electron-Transfer Proteins[END_REF]. As the three proteins under study have the same type of metallic centers, the differences on the variations of the free energy, ∆G 0 ', are assumed to be mainly related to conformational changes (that occur with the redox state change) and it will be analyzed without discrimination of the different components of the Gibbs energy. The three proteins estimated ∆G 0 ' values, taken from the slopes of the E 0 ' vs T plot, were, for desulforedoxin, rubredoxin and 2Fe-SOR, 1.66, 2.41 and 5.25 kJmol -1 , respectively. From these values, and regarding the previous assumptions, it could be inferred that 2Fe-SOR is the one where more pronounced conformational changes occur. The electrochemical behaviour of Zn/Fe-SOR was studied by cyclic voltammetry and its behavior compared with 2Fe-SOR. The results are shown in Figure 9. As displayed, the Zn/Fe-SOR center I is redox inactive, which proves that zinc has been successfully incorporated in the protein but also that the redox signal observed close to 0 V vs NHE in 2Fe-SOR can be definitely indexed to center I, and is also in agreement with the DfxN behavior already published. Moreover, the electrochemical results are in accordance to the previously described which show that Zn/Fe-SOR sample is homogeneous. Differential pulse (DP) and Square wave (SW) voltammetry were used to test the behaviour of 2Fe-SOR, starting from different potentials values, corresponding to the initial protein oxidation states and same window of observation. The aim is to observe the existence of differences in the protein electrochemical patterns depending on the initial redox starting point. DPV assays, in the potential range between 0.352 to -0.254 V (cathodic direction), have confirmed the previous cyclic voltammetry results, showing the presence of center I on 2Fe-SOR (E 1/2 =13 mV vs NHE) and the absence of the correspondent signal on Zn/Fe-SOR. SWV technique revealed better results in the anodic scanning direction than DPV, allowing better comparison between the potential values obtained in each scanning direction. The results have shown some differences in the center I current peak positions, depending of the potential scanning direction. From the results, the E o ' of the 2Fe-SOR center I was estimated to be -25 mV and +79 mV vs NHE, when the potential scan was started at the cathodic and anodic direction, respectively, which correspond to the oxidized and reduced initial states of the protein (see Figure 10 and supplementary material). This may be indicative of the center I conformational changes between the reduced and oxidized states, and, consequently, to the difference in the observed redox potential [START_REF] Wisitruangsakul | Redox-linked protein dynamics of cytochrome c probed by timeresolved surface enhanced absorption spectroscopy[END_REF]42]. In addition, using SWV it was possible, for the first time, to observe the redox signal of 2Fe-SOR center II. Figure 10 shows the comparison between the 2Fe-SOR and the Zn/Fe-SOR, scanned in the anodic direction. Three signals observed in the 2Fe-SOR SW voltammograms were considered to be significant. Two of these signals were assigned as corresponding to the centers I and II, respectively, based on CV results for center I on both forms as shown in the Figure 9. For Zn/Fe-SOR only one signal is observed, that must correspond to center II. It should be emphasised that unlike center I, which presents a stable signal with time, center II is only possible to detect in the first scan and in the anodic direction. It seems that this center suffers an irreversible change after the potential sweep, and it is always needed to use a fresh preparation on the electrode to be able to observe this second process. The estimated values of the E o ' for the 2Fe-SOR and Zn/Fe-SOR center II are +255 mV and +167 mV, respectively. Previous published work with DfxC [29], also pointed to a signal due to center II of 247 mV which is in agreement with the present results with the all protein. A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

The third current peak observed in the potential range between processes I and II in 2Fe-SOR could result from the differences in the dispersion of the electron transfer rate constants, as discussed before for the 2Fe-SOR. However, in the present data, both 2Fe-SOR and Zn/FeSOR are being scanned in the same potential region, using the same technique and experimental conditions. If the dispersion of the electron constant rate, due to the proteins surface charge, is the cause of the observed signal, this should also be visible in the Zn/FeSOR data. Such phenomenon reinforces the hypothesis of an intramolecular electron transfer between center I and II. The electrochemical mechanism in accordance with these data implies not only the direct electron transfer between 2Fe-SOR and the electrode but also an intramolecular electron transfer. 3 From the data the electronic pathway must involve a first direct electrode electron transfer with the protein, to center I, promoting a transient SOR Fe(II)- Fe(III) state, followed by a partial intramolecular electron transfer between center I and center II, leading to a mixture of SOR Fe(II)-Fe(III) and SOR Fe(III)-Fe(II) states. A second electron reduction can occur directly either to center I or to center II. Though, the SOR Fe(III)-Fe(II) state will probably need a lower driving force to be interconverted in SOR Fe(II)-Fe(II) . This would cause a split in the center II peak, observed in Figure 10, and the appearance of a "pre-peak", corresponding to the redox state SOR Fe(II)-Fe(II) of the protein resulting from the intramolecular electron transfer. The continuous potential increase, by the direct electron transfer to the protein, directly to center II, will result also in the SOR Fe(II)-Fe(II) state, while the remaining molecular population is still in the SOR Fe(II)-Fe(III) redox state. Figure 11 represents a schematic presentation to simplify the described hypothesis, comparing the electronic pathways in 2Fe-SOR. Pathway 1 is observed in 2Fe-SOR data, corresponding, respectively to the current peaks named in Figure 10 as center I, "pre-peak" of center II and center II, where the "prepeak" is indeed the result of the reduction of the SOR Fe(II)-Fe(III) redox state resulting from the previous intramolecular electron transfer. 4 Pathway 2 is a simulation of a second reduction directly to center II, which is similar to the case of Zn/Fe-SOR electron transfer (in the Figure 10, refered as II) from the electrode to the protein center II. In this case, as Zn(II) is electrochemically inactive, at the experimental potential window, center I is not able to participate in any intramolecular electron transfer, therefore, with Zn/Fe-SOR, only one current peak is visible. A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

3 and 9 . 6 .

 96 Mössbauer spectroscopy clearly indicated the presence of two high-spin iron centers, where the component Biochemical Journal Immediate Publication. Published on 17 Jun 2011 as manuscript BJ20110836 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110836A c c e p t e d M a n u s c r i p t attributed to centre II is characteristic of a high-spin ferric ion with E/D of approximately 1/3[START_REF] Tavares | Spectroscopic properties of desulfoferrodoxin from Desulfovibrio desulfuricans (ATCC 27774)[END_REF] 10]. Class II SOR, was first isolated and described by Chen et al. in 1994, from a sulfate reducing bacteria, Desulfovibrio gigas[START_REF] Chen | A blue non-heme iron protein from Desulfovibrio gigas[END_REF]. Such as class I SORs, this is also a dimeric protein with 14 kDa per monomer, however, in this case, these proteins only have one iron per monomer, similar to center II of class I SORs ([Fe(S-Cys)(N-His) 4 ]). Also, the Nterminal domain of this class of proteins does not present the cysteine motif that coordinates the iron atom in center I of class I SORs. The EPR spectrum of the oxidized form (S=5/2) of these proteins shows a pH dependence with E/D values of 0.06 for lower pH and more rhombic conformation, E/D≈0.33 for highest pH values. The UV-Visible spectrum exhibits pH dependent absorption bands with pKa≈9.6 and maxima ranging from 660 and 600 nm, from lowest to highest pH values[START_REF] Chen | A blue non-heme iron protein from Desulfovibrio gigas[END_REF][START_REF] Clay | Spectroscopic studies of Pyrococcus furiosus superoxide reductase: implications for active-site structures and the catalytic mechanism[END_REF]. An analysis of Treponema pallidum genome revealed a gene highly homologous to the class I SOR with two domains, named class III SOR. However, in this case, domain I lacked three of the four cysteine residues responsible for centre I iron binding site. The gene product, expressed in E. coli had ca. 14 kDa per monomer and the EPR and Mössbauer features are similar to the center II of class I SOR. Enzymatic studies revealed that this protein was able to reduce superoxide anion to hydrogen peroxide and that rubredoxin, isolated from the same organism is capable of donate electrons to SOR [12,[START_REF] Jovanovic | Neelaredoxin, an iron-binding protein from the syphilis spirochete, Treponema pallidum, is a superoxide reductase[END_REF][START_REF] Auchere | Overexpression and purification of Treponema pallidum rubredoxin; kinetic evidence for a superoxide-mediated electron transfer with the superoxide reductase neelaredoxin[END_REF]. Extensive studies on the catalytic mechanism of the three enzyme classes have been reported over the past 10 years, in particular on class I SORs isolated from many bacteria and archaea, such as Desulfovibrio vulgaris strain Hildenborough (D. vulgaris), Desulfovibrio desulfuricans ATCC27774 (D. desulfuricans), Desulfoarculus baarsii (D. baarsii) and Archaeoglobus fulgidus (A. fulgidus) [13, 14, 25-28]. In 2000, Ascenso et al. published the cloning of two engineered constructs, expressed separately in Escherichia coli. The N-terminal (DfxN) consisted of the first 39 amino acids from D. vulgaris Hildenborough SOR that resembles D. gigas desulforedoxin. The Cterminal domain consisted of the last 92 amino acids of D. vulgaris Hildenborough SOR (DfxC). Both recombinant fragments were able to bind iron, despite that, in the DfxC, the iron showed a labile behaviour. Biochemical and spectroscopic features of DfxN and DfxC have properties similar to desulforedoxin and center II of class I SORs, respectively. The authors also tested the reaction of DfxC with superoxide but, no evidence of reduction. This was related with the possible loss of iron in the catalytic center [29].

Biochemical

  Journal Immediate Publication. Published on 17 Jun 2011 as manuscript BJ20110836 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110836

  Immediate Publication. Published on 17 Jun 2011 as manuscript BJ20110836 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110836 A c c e p t e d M a n u s c r i p t 8 EPR Spectroscopy EPR spectra were recorded on a Bruker EMX spectrometer equipped with a dual-mode cavity and an Oxford Instruments continuous flow cryostat. The experimental conditions used were: temperature 4.1 K; microwave frequency 9.653 GHz; microwave power 2.002 mW; modulation amplitude 1 mT; receiver gain 1.26 x 10 5 .

Biochemical

  Journal Immediate Publication. Published on 17 Jun 2011 as manuscript BJ20110836 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110836

Biochemical

  Journal Immediate Publication. Published on 17 Jun 2011 as manuscript BJ20110836 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110836A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

Biochemical

  Journal Immediate Publication. Published on 17 Jun 2011 as manuscript BJ20110836 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110836

  . L., Li, H. and Raman, C. S. (1999) Heme-mediated oxygen activation in biology: cytochrome c oxidase and nitric oxide synthase. Curr Opin Chem Biol. 3, 131-137 46 Page, C. C., Moser, C. C., Chen, X. and Dutton, P. L. (1999) Natural engineering principles of electron tunnelling in biological oxidation-reduction. Nature. 402, 47-52 Biochemical Journal Immediate Publication. Published on 17 Jun 2011 as manuscript BJ20110836 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110836A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

Figure 1 .

 1 Figure 1. Absorbance spectrum oxidized form of the new Zn/Fe-SOR A) Absorbance spectrum, converted to extinction coefficient, of the oxidized form of the new Zn/Fe-SOR. B) Inset showing the absorption band around 650 nm, correspondent to ferric center II.

Figure 2 .

 2 Figure 2. EPR spectra of Zn/Fe-SOR A) as-purified form and B) Oxidized form (by incubation with sodium hexachloroiridate (IV)). The experimental conditions used were: temperature 4.1 K; microwave frequency 9.653 GHz; microwave power 2.002 mW; modulation amplitude 1 mT; receiver gain 1.26 x 10 5 .

Figure 3 .

 3 Figure 3. Stopped-flow kinetics of the reduction of SOR Zn(II)-Fe(III) and SOR Fe(III)-Fe(III)Comparison of stopped-flow kinetics of the reduction of SOR Zn(II)-Fe(III) by reduced rubredoxin (black line) and SOR Fe(III)-Fe(III) form by reduced rubredoxin (dashed line). The variation was measured by the absorbance changes at 650 nm and converted to concentration. Each trace was recorded in three integration time steps (0.01, 1 and 100 ms), in order to get better resolution at the beginning of the experiment.

Figure 4 .

 4 Figure 4. Representation of rubredoxin oxidation rate by superoxide-mediated electron transfer A) The squares ( ) stand for SOR Fe(III)-Fe(II) form, triangles ( ) for SOR Fe(III)-Fe(III) form and dots ( ) for the SOR Zn(II)-Fe(III) form. B) The squares stand for SOR Fe(II)-Fe(II) form and dots for the SOR Zn(II)-Fe(II) .

Figure 5 .

 5 Figure 5. Electochemical behavior of desulforedoxin and rubredoxinComparison between the typical cyclic voltammograms of desulforedoxin and rubredoxin at the same experimental conditions, using a glassy carbon working electrode; pH 7.6, T=288.15 K, v=20 mV/s.

Figure 6 .

 6 Figure 6. 2Fe-SOR electrochemical behavior 2Fe-SOR redox behaviour on glassy carbon electrode, showing the apparent merging of two redox processes at 278.15 K, indicated by the arrows. Inset: the same experiment at 298.15 K, 20 mV/s.

Figure 7 .

 7 Figure 7. Superficial charge calculated for SOR, rubredoxin and desulforedoxin Superficial charge calculated by Poisson-Boltzmann for: A) Desulfovibrio desulfuricans ATCC 27774 SOR; B) Desulfovibrio gigas desulforedoxin and C) Desulfovibrio vulgaris rubredoxin. The blue color stands for positive charges and the negative charges are represented by the red color. The calculations were performed using Accelrys DS Visualizer v2.0.1.7347, Accelrys Software Inc.

Figure 8 .

 8 Figure 8. Formal potential values dependence on the temperature From the obtained formal potential values, for the three proteins, desulforedoxin ( ), 2Fe-SOR ( ) and rubredoxin ( ) it was possible to estimate the Gibbs energy variation.

Figure 9 .

 9 Figure 9. Redox behavior comparison between the 2Fe-SOR and Zn/Fe-SOR Plot of the comparison between the electrochemical behaviour of 2Fe-SOR (black bold line) and Zn/Fe-SOR (grey bold line) for the same experimental conditions; room temperature, v=10 mv/s; dashed black line: control, glassy carbon.

Figure 10 .

 10 Figure10. Square wave voltammograms of the 2Fe-SOR and Zn/Fe-SOR Square wave voltammetry records of the SORFe-Fe and SORZn-Fe proteins scanned in the anodic direction. Experimental parameters: room temperature, gold working electrode, step pot. 5 mV, amp. 20 mV, freq. 8 Hz, v= 40 mV/s. The current peaks of center I and II are marked. A more anodic peak current, observed close to 0.4 V, is not related with the protein center and is due to interfering.

Figure 11 .

 11 Figure 11. Proposed mechanisms for the electron transfer pathway between 2Fe-SOR and rubredoxin Proposed mechanisms for the electron transfer pathway between 2Fe-SOR and its physiological redox partner, rubredoxin. Pathway 1 involves an intra-molecular electron transfer from center I to center II and then the entrance, to center I, of a second electron, resulting in a fully reduced SOR. Pathway II involves a second electron transfer directly to center II, resulting in a fully reduced SOR. Common to both pathways is the first electron transfer that occurs in center I.

Figure 1 Biochemical

 1 Figure 1

Figure 2 25

 2 Figure 2

Figure 3 Biochemical

 3 Figure 3

Figure 4 Biochemical

 4 Figure 4

Figure 5 BiochemicalFigure 6 Biochemical

 56 Figure 5

Figure 7 Biochemical

 7 Figure 7

Figure 8 Biochemical

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Figure 9 Biochemical

 9 Figure 9

Figure 11 Biochemical

 11 Figure 11

  DNAse and sodium hexachloroiridate (NaIrCl 6 ) were purchased from Sigma-Aldrich. All buffers were from Merck. Competent Escherichia coli BL21(DE3) cells were purchased from Stratagene®. All the reagents used were of analytical grade or higher.

		Biochemical Journal Immediate Publication. Published on 17 Jun 2011 as manuscript BJ20110836
		EXPERIMENTAL
		Chemicals
		Bovine Cu,Zn superoxide dismutase, bovine milk xanthine oxidase, xanthine, horse heart
		cytochrome	c,	Luria-Bertani	(LB)	medium,	ampicillin,	isopropyl-β-D-
	THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110836	A c c e p t e d M a n u s c r i p t thiogalactopyranoside (IPTG),
								6

Table 1 .

 1 Second order rate constants of electron transfer between reduced rubredoxin and the different SOR formsSecond order rate constant x 10 6 (M -1 .s -1 )

	Wavelength (nm)	SOR Fe(III)-Fe(II)	SOR Fe(III)-Fe(III) (1:1)	SOR Fe(III)-Fe(III) (2:1)	SOR Zn(II)-Fe(III)
	500	28±4	4.3±1.9	1.3±0.2	3.2±1.5
	650	-	1.9±0.5	1.7±0.3	2.9±0.4

Table 2 .

 2 Apparent rate constants, k', calculated for the superoxide-mediated electron transfer between rubredoxin and all SOR forms

	k' (min -1 )

Biochemical Journal Immediate Publication. Published on 17 Jun 2011 as manuscript BJ20110836 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110836

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© 2011 The Authors Journal compilation © 2011 Portland Press Limited

A first electron transfer to/or from the protein, direct to center I, promotes the conversion between redox states, for example, SOR Fe(III)-Fe(III) to SOR Fe(II)-Fe(III) , and a subsequent second direct electron transfer (to center II) leads to the conversion between SOR Fe(II)-Fe(III) and SOR Fe(II)-Fe(II) .

A small, more positive, current peak in the 2Fe-SOR scan is also visible, but this should correspond to some amino acid oxidation or some oxide formation and it is believed not to be related with the metal center of the protein.

FUNDING This work has been supported by Fundação para a Ciência e Tecnologia (FCT), project POCI/QUI/57475/2004, FF PhD grant, SFRH/BD/18905/2004 and CC PhD grant SFRH/BD/2917/2000. Biochemical Journal Immediate Publication. Published on 17 Jun 2011 as manuscript BJ20110836 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20110836

DISCUSSION

The new Zn/Fe-SOR form revealed some spectroscopic features similar to class II and III SORs, such as the UV-Visible and EPR spectra. On the other hand, primary structure analysis proved that this protein was identical to the native D. vulgaris Hildenborough SOR. The experiments performed focused on the direct electron transfer between rubredoxin and the three different forms of SOR (SOR Fe(III)-Fe(II) , SOR Fe(III)-Fe(III) and SOR Zn(II)-Fe(III) ) revealed the existence of electron transfer processes. The kinetic rate constants calculated for both SOR Fe(III)-Fe(III) and Zn/Fe-SOR forms were comparable to previously published data, but a 10 fold increase was observed in the SOR Fe(III)-Fe(II) form, suggesting an easier reduction of center I [START_REF] Rodrigues | Superoxide reduction by Archaeoglobus fulgidus desulfoferrodoxin: comparison with neelaredoxin[END_REF][START_REF] Rodrigues | Rubredoxin acts as an electron donor for neelaredoxin in Archaeoglobus fulgidus[END_REF][START_REF] Emerson | Kinetics of the superoxide reductase catalytic cycle[END_REF][START_REF] Rodrigues | Superoxide reduction mechanism of Archaeoglobus fulgidus one-iron superoxide reductase[END_REF][START_REF] Coulter | A role for rubredoxin in oxidative stress protection in Desulfovibrio vulgaris: catalytic electron transfer to rubrerythrin and twoiron superoxide reductase[END_REF]. In a first approach, this could mean that the preferential electron transfer pathway from rubredoxin to SOR is through center I. Nevertheless, the kinetic evidences obtained in this work could also point to a direct electron transfer to center II. This was supported by the similarity of the rate constants values found for the SOR Fe(III)-Fe(III) form at 500 nm (oxidation of rubredoxin) and 650 nm (reduction of SOR's center II), which were themselves similar to the calculated values for the Zn/Fe-SOR form (where center I is not redox active). An explanation for this apparent inconsistency can be found in the electrochemical data that strongly suggests the existence of two different pathways for the electron transfer processes in 2Fe-SOR. In such case, one exclusively due to the direct electron transfer between the electrode and the protein and a second one that can only be explained by an intramolecular electron transfer from center I to center II (which, as expected, is missing in the Zn/Fe-SOR form). Also, the electrochemical behavior points to probable conformational changes in the protein, possibly triggered by redox changes in center II. This type of long range (22 Å) intramolecular electron transfer, coupled to conformational change is not unique in Nature, being found in other examples like cytochrome c oxidase (CcO) [45,46]. One should also consider the fact that in the superoxide-mediated electron transfer assay, values of k' for forms with center II reduced (SOR Fe(III)-Fe(II) , SOR Fe(II)-Fe(II) and SOR Zn(II)-Fe(II) ) are of the same magnitude and significantly higher than k' values estimated for forms with an oxidized center II (SOR Fe(III)-Fe(III) and SOR Zn(II)-Fe(III) ). So, an enzyme with a reduced center II will have higher turnover rates, being also more able to stay in that state due to the possibility of an intramolecular electron transfer and to the enhanced rate of reduction of center I. Then it is possible to hypothesize that, when active, intracellular concentrations of SOR Fe(III)-Fe(III) form are negligible and that the enzyme is kept either in a "ready" SOR Fe(III)-Fe(II) state or in a fully reduced form, SOR Fe(II)-Fe(II) . Therefore, the existence of center I can be seen as a structural advantage to the enzyme, enabling it to be more efficient in the metabolic pathway and helping the cell to keep a pool of "ready" enzyme for catalysis [START_REF] Pereira | Superoxide reductases[END_REF]. The enzymes in question are isolated from microaerophilic Desulfovibrio species where an effective defence mechanism against ROS is essential for survival, and as such one would expect the enzyme to be adapted to the highest possible turnover rates.