Chakib Fettal

Lazhar Labiod

Mohamed Nadif

Scalable Attributed-Graph Subspace Clustering

Over recent years, graph convolutional networks emerged as powerful node clustering methods and have set state of the art results for this task. In this paper, we argue that some of these methods are unnecessarily complex and propose a node clustering model that is more scalable while being more effective. The proposed model uses Laplacian smoothing to learn an initial representation of the graph before applying an efficient self-expressive subspace clustering procedure. This is performed via learning a factored coefficient matrix. These factors are then embedded into a new feature space in such a way as to generate a valid affinity matrix (symmetric and nonnegative) on which an implicit spectral clustering algorithm is performed. Experiments on several real-world attributed datasets demonstrate the cost-effective nature of our method with respect to the state of the art.

Introduction

An attributed-graph is a type of graph that contains two information sources, a topology or structure and node-and/or edge-level features. Under different approaches, they are used to model a wide variety of structured data (Fettal, Labiod, andNadif 2023, 2022b), with applications in the fields of recommender systems [START_REF] Fan | Graph Neural Networks for Social Recommendation[END_REF][START_REF] Yang | Graph convolutional neural networks for web-scale recommender systems[END_REF], computer vision [START_REF] Satorras | Few-Shot Learning with Graph Neural Networks[END_REF][START_REF] Yang | Graph convolutional neural networks for web-scale recommender systems[END_REF], Natural language processing [START_REF] Marcheggiani | Encoding Sentences with Graph Convolutional Networks for Semantic Role Labeling[END_REF] and physical systems [START_REF] Hoshen | VAIN: Attentional Multi-agent Predictive Modeling[END_REF].

With the advent of the Graph Convolutional Network (GCN) [START_REF] Defferrard | Convolutional neural networks on graphs with fast localized spectral filtering[END_REF][START_REF] Kipf | Semi-supervised classification with graph convolutional networks[END_REF], graph related tasks such as graph representation learning [START_REF] Wu | Simplifying graph convolutional networks[END_REF][START_REF] Zhu | Simple Spectral Graph Convolution[END_REF] and graph clustering (Anton Tsitsulin and Müller 2020) have received a lot of attention. We observe, however, that for the task of graph clustering, few approaches [START_REF] Cai | Graph convolutional subspace clustering: A robust subspace clustering framework for hyperspectral image[END_REF] based on the subspace clustering principle have been proposed despite it being, at first sight, well-suited to attributedgraph data. We argue that this is mostly due to subspace clustering models suffering from high spatial and/or computational complexity. In a nutshell, the goal of subspace clustering is to group data points according to the subspaces in which they lie within a dataset. For example, subspace clustering models that use the self-expressive property, whereby every data point can be represented as an approximate linear combination of other points, have to learn a square matrix called the coefficient or self-representation matrix. This coefficient matrix has a size that is quadratic in the number of points. Once this matrix is learned, an affinity matrix is constructed from it and spectral clustering is performed on said affinity matrix. We can see the classical subspace clustering pipeline in figure 1.

In this paper, we argue that subspace clustering is wellsuited to attributed-graph representations generated with GCN-based models due the neighborhood averaging making the data points closer and thus helping with the selfexpressiveness of the data points. To leverage this property and in order to avoid the complexity problems associated with traditional subspace clustering, we propose an efficient variant to learn an initial representation of the graph before applying an efficient self-expressive subspace clustering procedure via learning a factored coefficient matrix and then projecting these factors into a new feature space in such a way as to generate a valid affinity matrix (symmetric with non-negative entries) on which to perform implicit spectral clustering. A schema for our model is available in figure 3. To showcase the efficacy and efficiency of our proposal, we perform extensive experimentation on six widely used attributed-networks. We can see a preview of the results in figure 2, these are the clustering results of our model on the Arxiv open graph benchmark, our model yields a 14% improvement over the second best model in terms of performance and 16% improvement in terms of speed. Code for our paper can be found in 1 .

This paper is organized as follows: Section 2 reviews related works. Section 3 presents the necessary previous work. Section 4 is devoted to the proposed model and its computational complexity study. In section five, we carry out our experimental study. Finally we present our conclusion in section 6.

Related Work

Subspace Clustering

Subspace clustering methods based on the self-expressive property are commonly used on image data and have set state-of-the-art results on the task of image clustering. One of the earlier approaches was the Least-Square Regression subspace clustering (LSR) that leverages a grouping effect in the data. Newer models that make up the state-of-theart include the Elastic-net Subspace Clustering (EnSC) (You et al. 2016) that uses a mix of l1-and l2-norm regularization, and the Subspace Clustering through the Orthogonal Matching Pursuit (SSC-OMP) (You, Robinson, and Vidal 2016) which possesses a subspace-preserving affinity under broad conditions. There are also deep learning approaches like the deep Subspace clustering network [START_REF] Ji | Deep subspace clustering networks[END_REF] and but these models have received some critique to the effect that their good performances are the result of an ad-hoc post processing step instead of the actual self-representation learning process [START_REF] Haeffele | A Critique of Self-Expressive Deep Subspace Clustering[END_REF]. More recently, a new efficiency trend has appeared, and some scalable models have also been proposed e.g. k-Factorization Subspace Clustering (k-FSC) [START_REF] Fan | Large-Scale Subspace Clustering via k-Factorization[END_REF]) which was put forward as a scalable subspace clustering model that factorizes data into subsets via structured sparsity.

Attributed-Graph Clustering

In this paper, attributed-graph clustering refers to the process of grouping nodes into clusters according to the graph topology and node features. We can classify attributed-graph clustering models into two subsets. A first one, where the goal is to learn graph representations and then use traditional clustering models such as k-means. Examples of models that use this approach include Simplified Graph Convolution (SGC) [START_REF] Wu | Simplifying graph convolutional networks[END_REF]) which proposes a neighborhood averaging process that corresponds to a fixed low-pass filter, and the Simple Spectral Graph Convolution (S²GC) which uses a new method for the aggregation of K-hop neighborhoods that is a trade-off of low-and high-pass filter bands. [START_REF] Zhu | Simple Spectral Graph Convolution[END_REF]. On the other hand, the second class of attributed-graph clustering models proposes to include the clustering objective into the representation learning process to learn better results, e.g., Graph InfoClust (GIC) (Mavromatis and Karypis 2021) which generates clusters by maximizing mutual information between nodes contained in the same cluster, and Graph Convolutional Clustering (GCC) (Fettal, Labiod, and Nadif 2022a) that performs clustering by minimizing the difference between convolved node representations and their reconstructed cluster representatives.

Preliminaries

Let G = (V, E, A, X) be an undirected attributed-graph where V is the vertex set consisting of nodes {v 1 , . . . , v n }, E is the set of edges that connects the nodes, A ∈ R n×n is a symmetric adjacency matrix where a ij denotes the edge weight between nodes v i and v j , if a ij = 0 then there is no edge between v i and v j , and X ∈ R n×d is a node-level feature matrix. Our goal is to partition this graph into k independent subsets in an unsupervised manner.

Graph Convolutional Networks

The graph Convolutional Network consists in a sequence of propagation layers. It can be formalized recursively as

H (l+1) ← σ D-1/2 Â D-1/2 H (l) W (l) with H (0) = X (1)
where  = A + I is the adjacency matrix with added selfloop the, D is its diagonal matrix of degrees, σ is some activation function and W (l) is the weight matrix of the l-th layer. These weight matrices are optimized for some downstream task like semi-supervised classification, link prediction, etc.

Simplified Graph Convolutional Networks

Authors in [START_REF] Wu | Simplifying graph convolutional networks[END_REF]) argued that the non-linearities in the GCN are superfluous and that most of its performance comes from the feature propagation. With this, the recursive We have as input an attributed-graph characterized by an adjacency matrix A and a feature matrix X. An initial representation H of the attributed-graph is learned through neighborhood propagation. Then, subspace clustering is performed using a latent factor matrix U where C = UU ⊤ is the subspace coefficient matrix that we project using a quadratic kernel feature map Φ so that M = Φ(U)Φ(U) ⊤ ≥ 0. With this we obtain the final partition by using the k-means algorithm on Z, the first k singular vectors (not counting the first one) of

D -1/2 Φ(U) ⊤ . definition of a p-layer GCN collapses into H ← S p XW where S = D-1/2 Â D-1/2 is called the propagation matrix.
Here, we can see how the weights matrices collapsed into a single weight matrix W while the graph propagation steps collapsed into the p-th power of the propagation matrix S.

Subspace Clustering

The goal of subspace clustering is to group data points according to the subspaces that support them. A popular formulation uses the self-expressive property where it is assumed that a data point can be written as a linear combination of the data points that belong to the same subspace. A possible formulation is

min C∈C ∥X -CX∥ 2 + Ω(C) (2)
where X ∈ R n×d is a matrix of d-dimensional data points, C ∈ R n×n is known as the self-representation or coefficient matrix, Ω(C) is a regularization term introduced to establish certain properties for C e.g. to avoid trivial solutions (such as C = I), and C is the feasible region. Once a solution C is found, an affinity matrix is generated based on the magnitudes of the entries of C, a popular choice for this is (|C| + |C ⊤ |)/2. Finally, a clustering of the data points is obtained using some graph clustering algorithm such as the spectral clustering algorithm [START_REF] Shi | Normalized cuts and image segmentation[END_REF].

Proposed Approach

In this paper, we propose the following generic formulation for the attributed-graph subspace clustering problem

min C∈C ∥agg(A, X) -C agg(A, X)∥ 2 + Ω(C) (3)
where agg is an aggregation function whose role is to merge the two information sources the topology information and the feature information present in the graph.

Simple Graph Convolutional Encoder

We propose to use a GCN-based encoder. More particularly, we use the convolution operation proposed in the simplified graph convolutional network along with the normalization of the adjacency matrix used in (Fettal, Labiod, and Nadif 2022a)

min C∈C ∥S p X -C S p X∥ 2 + Ω(C). (4)
Now that we have our initial graph representation, we can present our clustering step.

Efficient Subspace Clustering

Learning the implicit coefficient matrix We set constraints on C in order to obtain a decomposition of C into the Gramian product UU ⊤ where U ∈ R n×k is a semiorthogonal matrix i.e. U ⊤ U = I. This will allow us to significantly speed up the subspace clustering process. Thus, our problem becomes

min U ∥S p X -UU ⊤ S p X∥ 2 such that U ⊤ U = I.
(5) As we can see, we have no need for any form of regularization. This problem can be efficiently solved through a singular value decomposition of the convolved features S p X. With this we obtain a solution C which corresponds to a subspace coefficient matrix from which we can derive a clustering of the nodes.

Learning the implicit affinity matrix Once we have a coefficient matrix C = UU ⊤ , we have to derive a nonnegative matrix that reflects the magnitudes of the entries of C. As already mentioned the common way is to compute (|C| + |C ⊤ |)/2 but this will result in a spectral clustering step which has a quadratic complexity in the number of nodes. In this paper, we propose to use a nonnegative kernel with feature map Φ to embed U into its feature space explicitly

M = Φ(U)Φ(U) ⊤ ≥ 0. (6)
Here the feature map is applied row-wise, for example, in our experiments, we used the quadratic kernel

M = C •2 = (m ij ) = (c 2 ij ). (7)
It is also possible to introduce a bias term b to the kernel such as

m ij = (c ij + b) 2 .
Hence, we have implicitly derived a Gramian decomposition through Φ(U) similarly to what was done for C. This will allow us to efficiently perform the last step which corresponds to spectral clustering. Note that M is symmetric by construction.

Spectral clustering the implicit affinity matrix Through the previous step we can now efficiently perform the NJW spectral clustering [START_REF] Ng | On spectral clustering: Analysis and an algorithm[END_REF] on matrix M by:

• Projecting the factor U using feature map Φ, i.e., Q ← Φ(U)

• Computing Q ← QD -1 2
where D is a diagonal matrix such that d ii is the sum of M i-th row.

• Constructing Z using the left singular vectors corresponding to the second to k + 1-largest singular values of Q. • Performing a clustering of the rows of Z and assigning node i to cluster j if the i-th row of Z was assigned to cluster j.

Complexity Analysis

Our overall algorithm is presented in algorithm 1. In what follows, we will analyze the computational complexity of our proposal

Graph representation learning step To compute the p-th order graph convolution, we need O(p|E|d) operations.

Learning the implicit coefficient matrix Getting the left singular values of the convolved data requires O(nd log(k)) operations using the randomized singular value decomposition [START_REF] Halko | Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions[END_REF]. . In other cases, when wishing to use nonnegative infinite dimensional kernels such as the RBF kernel or higher order polynomial kernels, feature map approximation techniques such as Nyströem method [START_REF] Zhang | Improved Nyström low-rank approximation and error analysis[END_REF] or the polynomial count sketch [START_REF] Pham | Fast and scalable polynomial kernels via explicit feature maps[END_REF]) can be used and m becomes a variable hyperparameter.

Learning the implicit affinity matrix

In table 1, we can see how the complexity of our algorithm compares with that of the other models. Despite our model being using subspace clustering, it is significantly more efficient than the other subspace clustering models both in terms of computational and spatial complexity. When comparing with the SOTA attributed-graph clustering models, we can see that when m ∈ O(d) then our model has the same complexity as them. Which means that when taking a smaller m, e.g., m ∈ O(k), then our model should be more computationally efficient.

Algorithm 1: Scalable Attributed-Graph Subspace Clustering (SAGSC).

Input : X data matrix, S propagation matrix, p propagation order, k number of clusters, Φ nonnegative kernel feature map. Output: π partition of the nodes. 1 H ← S p X; 2 Form the matrix U containing the first k left singular vectors of H in its rows;

3 Q ← Φ(U); 4 r ← Q ⊤ 1; 5 D ← diag(Qr); 6 Q ← QD -1
2 ; 7 Form the matrix Z containing left singular vectors corresponding to the second to k + 1-th largest singular values of Q in its rows; 8 Apply a clustering algorithm on the rows of Z to obtain π a partition of the data;

Experiments

In this section, we conduct experimentation to showcase the effectiveness and efficiency of our SAGSC model.

Datasets and Metrics

In our experiments, We use six commonly used benchmark datasets to compare the different models including three citation network datasets (ACM, DBLP [START_REF] Wang | Heterogeneous graph attention network[END_REF]; PubMed [START_REF] Sen | Collective classification in network data[END_REF]; and Wiki [START_REF] Yang | Network Representation Learning with Rich Text Information[END_REF]), an Amazon sales dataset (Computers) [START_REF] Shchur | Pitfalls of graph neural network evaluation[END_REF]) and one large scale dataset (OGBN-arXiv) [START_REF] Hu | Open graph benchmark: Datasets for machine learning on graphs[END_REF]. The summary statistics of the datasets are shown in table 2. We adopt three popular clustering evaluation metrics: clustering accuracy (CA), normalized mutual information (NMI) [START_REF] Strehl | Cluster ensembles-a knowledge reuse framework for combining multiple partitions[END_REF], adjusted rand index (ARI) [START_REF] Hubert | Comparing partitions[END_REF].

Baseline Models and algorithms

The following are the baselines we used in our experiments:

• k-Means will serve as the simplest baseline.

Table 1: Complexity of the different models. For k-FSC, m referes to the dimension of subspaces. For k-FSC, many possible complexities are possible depending on the chosen algorithm, please see [START_REF] Fan | Large-Scale Subspace Clustering via k-Factorization[END_REF] for a discussion on its complexity. For simplicity, we suppose that the embedding dimension in SGC, S²GC and GCC is in O(k).

Method

Time complexity Space complexity • LSR is a subspace clustering model with an l2-norm regularization. • EnSC is a subspace clustering model with an elastic net regularization (mix of l1-and l2-norm regularization). • SSC-OMP has a subspace-preserving affinity under broad conditions. • k-FSC is a scalable subspace clustering model that factorizes model in subsets via structured sparsity. • SC refers to the classical spectral clustering algorithm applied on the original adjacency matrix of the graph. • SGC proposes a neighborhood averaging process that corresponds to a fixed low-pass filter. • GIC generates clusters by maximizing mutual information between nodes contained in the same cluster. • S²GC proposes a new method for the aggregation of Khop neighborhoods that is a trade-off of low-and highpass filter bands. • GCC performs clustering by minimizing the difference between convolved node representations and their reconstructed cluster representatives.

k-means O(ndk) O(n(k + d)) LSR O(n 2 k) O(n 2 ) EnSC O(n 2 k) O(n 2 ) SSC-OMP O(n 2 k) O(n 2 ) SGC O(p|E|d + ndk) O(n(k + d)) S²GC O(p|E|d + ndk) O(n(k + d)) GCC O(p|E|d + ndk) O(n(k + d)) SAGSC O p|E|d + n(d + m) log(k) + nk 2 O (n(k + d + m))
We use the implementations of the authors when possible.

Experimental Settings

All experiments were implemented in TensorFlow and conducted on a standard computer with a 12GB memory GPU an a RAM of 12GB. In all experiments, we ran the models ten times, and report the average performance along with the corresponding standard deviation. We use the implementations of the authors when possible but optimized them to run on GPU. We used hyper-parameters prescribed by authors when possible. For fairness, for the remaining hyperparameters, we ran grid searches and reported the results corresponding to the best accuracy for all models. For k-FSC, we use the LARGE implementation. All results are the averages of ten runs.

For our model, we use a quadratic kernel feature map with a bias term equal to 1 √ 2 . This leads to the following kernel feature map:

φ : R k → R k+2 2 x → ⟨x 2 k , . . . , x 2 1 , x k x k-1 , . . . , x k x 1 , x k-1 x k-2 , . . . , x k-1 x 1 , . . . , x 2 z 1 , x k , . . . , x 1 , 1 √ 2 ⟩ (8)
for the power hyper-parameter, similarly to the other benchmarks, we use a grid search over the accuracy and report the best results. We do however propose a heuristic to adaptively select this hyper-parameter.

Node Clustering Results

Performance Clustering performances of the different methods are reported in tables 3 and 4. Best performances are highlighted in bold while second best results are underlined. In table 3, there is a general trend that the methods that use both A and X perform better than those that use A or X individually, except on DBLP where they perform well. Our model has the best performance over the three datasets with respect to all three metrics. The GCC has the second best results in all but one case, i.e., ARI on Wiki where it is outperformed by S²GC. In table 4, the three datasets are of larger sizes, our model has the best results in eight out of nine cases k-means X 87.8 ± 0.9 61.7 ± 1.5 67.4 ± 2.1 67.9 ± 0.0 37.3 ± 0.0 31.5 ± 0.1 47.6 ± 1.4 48.6 ± 0.2 26.6 ± 0.2 LSR X 78.6 ± 0.0 43.1 ± 0.0 48.3 ± 0.0 69.4 ± 0.1 34.7 ± 0.1 36.4 ± 0.2 17.8 ± 0.5 2.8 ± 1.7 0.3 ± 0.2 EnSC X 83.8 ± 0.0 53.0 ± 0.0 58.6 ± 0.0 30.0 ± 0.1 0.8 ± 0.2 0.1 ± 0.0 47.5 ± 0.0 45.2 ± 0.2 30.2 ± 0.1 SSC-OMP X 82.1 ± 0.0 49.4 ± 0.1 55.3 ± 0.0 29.4 ± 0.1 0.4 ± 0.1 -0.1 ± 0.0 37.8 ± 8.5 34.4 ± 9.1 21.2 ± 7.9 k-FSC X 59.7 ± 7.2 25.2 ± 7.1 27.2 ± 7.2 51.3 ± 11.1 17.4 ± 7.3 17.3 ± 9.6 38.2 ± 5.1 35.6 ± 3.9 17.7 ± 4.4 SC A 36.5 ± 0.2 1.0 ± 0.2 0.7 ± 0.1 91.0 ± 0.0 73.0 ± 0.1 78.3 ± 0.1 30.7 ± 1.1 24.0 ± 0.8 6.0 ± 0.2 SGC A, X 83.7 ± 0.0 55.7 ± 0.0 58.8 ± 0.0 88.8 ± 0.0 69.5 ± 0.0 73.2 ± 0.0 51.9 ± 0.8 49.6 ± 0.2 28.6 ± 0.1 GIC A, X 90.1 ± 0.3 68.2 ± 0.6 73.2 ± 0.6 90.2 ± 0.2 72.4 ± 0.4 77.4 ± 0.3 48.0 ± 0.7 48.4 ± 0.3 31.0 ± 0.3 S²GC A, X 84.1 ± 0.1 56.8 ± 0.1 59.6 ± 0.2 88.3 ± 0.0 69.2 ± 0.0 71.9 ± 0.0 52.1 ± 1.0 52.2 ± 0.1 33.0 ± 0.4 GCC A, X 91.3 ± 0.0 71.2 ± 0.1 76.0 ± 0.1 91.8 ± 0.0 74.5 ± 0.0 80.5 ± 0.0 53.7 ± 1.4 53.5 ± 0.5 31.6 ± 1.1 SAGSC A, X 93.3 ± 0.1 75.1 ± 0.2 80.9 ± 0.1 93.1 ± 0.1 78.1 ± 0.2 83.2 ± 0.2 56.0 ± 2.1 53.5 ± 1.2 34.1 ± 2.7 65.5 ± 0.0 52.2 ± 0.0 45.7 ± 0.0 69.6 ± 0.0 29.3 ± 0.0 29.9 ± 0.0 34.6 ± 0.4 39.2 ± 0.1 25.2 ± 0.6 GIC A, X 46.8 ± 2.2 47.5 ± 0.9 31.3 ± 3.5 64.5 ± 0.4 26.2 ± 0.3 23.8 ± 0.4 16.0 ± 0.8 17.9 ± 0.5 5.8 ± 0.2 S²GC A, X 65.4 ± 0.0 55.4 ± 0.0 49.5 ± 0.0 71.0 ± 0.0 32.9 ± 0.0 33.7 ± 0.0 41.9 ± 0.3 45.9 ± 0.1 36.9 ± 0.5 GCC A, X 67.6 ± 0.0 56.0 ± 0.0 46.5 ± 0.0 70.5 ± 0.0 32.2 ± 0.0 33.1 ± 0.0 40.5 ± 1.7 46.8 ± 0.2 35.1 ± 2.0 SAGSC A, X 69.0 ± 1.0 58.2 ± 0.4 48.2 ± 1.8 71.1 ± 0.0 32.9 ± 0.0 34.1 ± 0.0 47.8 ± 1.7 47.1 ± 0.5 38.4 ± 1.6 Analysis Overall, our model is as fast as the fastest attributed-graph clustering models while consistently yielding the best overall performance on all six datasets. This shows the cost-effective nature of our model with respect to the state of the art. We see that our model achieves the best rank, and is alone in the best performing group. We can also see the formation of two other groups.

To back up this claim statistically, we use the Nemenyi post-hoc test [START_REF] Nemenyi | Distribution-free multiple comparisons[END_REF]) to find groups of models that perform similarly in a statistically meaningful manner, to do this we rank the performances of the different models w.r.t to each metric (CA, NMI, ARI, and clustering F1-score) for each dataset. This yields 24 different rankings. We then carry-out the Nemenyi test with a confidence level of 90%. Results are illustrated in figure 5. We see the formation of three groups. The first one containing the best performing model, SAGSC; a second one, containing GCC, S²GC and SGC; and a third one containing SGC and GIC.

Selection of the Power Hyper-Parameter

The selection of the power parameter is integral to the performance of our model. A power that is too small can lead to not enough neighborhood information being propagated and a power that is too large can lead to the oversmoothing phenomenon [START_REF] Chen | Measuring and relieving the over-smoothing problem for graph neural networks from the topological view[END_REF]. Since in the unsupervised context, it impossible to know for certain which power will lead to the best performance, several heuristics for the selection of this hyper-parameter have been proposed, e.g., in [START_REF] Zhang | Attributed Graph Clustering via Adaptive Graph Convolution[END_REF], authors proposed to use internal criteria based on the information intrinsic to the data while in (Fettal, Labiod, and Nadif 2022a,b) authors proposed to choose a cutoff threshold on the change of their loss function between successive powers. Here, we propose to use an approach similar to the elbow method [START_REF] Ketchen | The application of cluster analysis in strategic management research: an analysis and critique[END_REF] which is used for the selection of number of clusters in the k-means algorithm. We start by choosing an interval for the powers we wish to consider e.g. the multiples of five plus one between one and a hundred i.e. {1, 6, . . . , 96}. Then we choose the power that precedes the appearance of the first pronounced 'elbow' in the graph. if there is no elbow, we choose the upper bound of the interval.

For example, in figure 4, we have can see a clear elbow for ACM, DBLP when the power is equal to six so we the power to one. In the case of Pubmed, no such elbow appears and so we set the power 96. We see that with very simple rule, we reach an accuracy that almost the same as the best one. For DBLP, we retrieve the best power, while for ACM and PubMed, the differences between the accuracy of the power we retrieved and the best one are 0.23 and 0.02, respectively, which is negligible. Of course, after this initial selection, a more granular selection needs can be performed since here we used an interval with a crude spacing of five between consecutive powers. Note that this selection process can be easily automated.

Conclusion

In this paper, we leveraged subspace clustering for attributed-graphs through the means of an efficient algorithm whereby after learning an initial representation of the graph through a simple yet effective neighborhood propagation step. We learn a factored coefficient matrix through orthogonal constraints, these factors are then embedded into a new feature space in such a way as to create a symmetric and nonnegative affinity matrix on which an implicit spectral clustering algorithm is performed. We additionally showed how this overall clustering process corresponds to an implicit subspace clustering algorithm. The experimentation we conducted showed the effectiveness and efficiency of our proposal with respect to the state of the art attributed-graph clustering algorithms.

In future work, we plan to learn factor matrices through other ways than the orthogonality constraints and extend this approach to co-clustering (Fettal, Labiod, and Nadif 2022b).

Figure 1 :

 1 Figure 1: The traditional subspace clustering pipeline. A coefficient matrix C is initially learned. An affinity matrix M is then generated based on the magnitudes of C, e.g., a common choice is M = (|C| + |C ⊤ |)/2. Finally, a partition of the data is created via applying spectral clustering on M.

Figure 2 :

 2 Figure2: Clustering accuracy scores (%) plotted against the execution time (s) for our method and the state-of-theart attributed-graph clustering models on the OGBN-arXiv dataset.

Figure 3 :

 3 Figure3: Diagram of our proposal. We have as input an attributed-graph characterized by an adjacency matrix A and a feature matrix X. An initial representation H of the attributed-graph is learned through neighborhood propagation. Then, subspace clustering is performed using a latent factor matrix U where C = UU ⊤ is the subspace coefficient matrix that we project using a quadratic kernel feature map Φ so that M = Φ(U)Φ(U) ⊤ ≥ 0. With this we obtain the final partition by using the k-means algorithm on Z, the first k singular vectors (not counting the first one) of D -1/2 Φ(U) ⊤ .

  The projection of the data using a feature kernel of dimensionality m takes O(nm). The computation of the diagonal matrix D and its multiplication with Q takes O(nm) operations. The truncated singular value decomposition of Q is in O(nm log(k)). Finally, the k-means algorithm applied on Z costs roughly O(nk 2 ). The overall computation time of this step O(nm log(k) + nk 2 ). Overall complexity. The totality of our algorithm cost O p|E|d + n(m + d) log(k) + nk 2 . Generally, we have that k << d. The dimension m generally depends on k, for example in the case of the quadratic kernel m = k+2 2 = (k+2)(k+1) 2

Figure 4 :Figure 5 :

 45 Figure 4: Plot of the clustering accuracy (%) and the Davies-Bouldin index (Davies and Bouldin 1979) against the propagation power.

Table 2 :

 2 The datasets statistics. The imbalance is quantified via the ratio between the majority and minority classes.

	Dataset	Nodes	Edges	Features Classes Imbalance
	ACM	3025	16,153	1870	3	1.1
	Wiki	2405	14,001	4973	17	45.1
	DBLP	4057	2,502,276	334	4	1.6
	Amazon Computers 13,381	259,159	767	10	17.5
	Pubmed	19,717	64,041	500	3	1.9
	OGBN-arXiv	169,343 1,327,142	128	40	942.1

Table 3 :

 3 Clustering performance of the different models over ACM, DBLP and Wiki. Best results are highlighted in bold font and second best results are underlined.

	Method	Input	ACM			DBLP			Wiki
		CA	NMI	ARI	CA	NMI	ARI	CA	NMI	ARI

Table 4 :

 4 Clustering performance of the SOTA models over the larger networks; Amazon Computers, Pubmed and OGBN-arXiv. Best results are highlighted in bold font and second best results are underlined.

	Method Input	Amazon Computers		PubMed			OGBN-arXiv
			CA	NMI	ARI	CA	NMI	ARI	CA	NMI	ARI
	SGC	A, X

Table 5 :

 5 Execution time of all methods in seconds. Best results are highlighted in bold.

	Method	ACM	DBLP	Wiki		Pubmed Computers OGBN-arXiv
	k-means	4.29 ± 0.7	6.05 ± 0.7	24.25 ± 0.3	-	-	-
	LSR	20.14 ± 0.26	5.2 ± 0.64	46.55 ± 1.61	-	-	-
	EnSC	590.31 ± 63.93 120.66 ± 0.28 232.58 ± 3.04	-	-	-
	SSC-OMP 201.78 ± 34.8	37.1 ± 2.87	293.78 ± 9.63	-	-	-
	k-FSC	3.72 ± 0.87	8.45 ± 0.73	34.29 ± 1.86	-	-	-
	SC	2.15 ± 0.32	18.54 ± 1.30	2.86 ± 0.44	-	-	-
	SGC	0.56 ± 0.13	0.19 ± 0.04	1.68 ± 0.14	1.18 ± 0.39	1.00 ± 0.11	37.30 ± 2.66
	GIC	3.67 ± 0.16	268.96 ± 63.17	5.96 ± 0.66	12.0 ± 1.50 22.38 ± 1.51	155.7 ± 13.34
	S²GC	0.44 ± 0.04	0.23 ± 0.06	1.56 ± 0.10	0.82 ± 0.10	1.33 ± 0.28	42.98 ± 3.10
	GCC	1.73 ± 2.96	0.33 ± 0.10	1.66 ± 0.14	1.26 ± 0.11	1.92 ± 0.13	62.45 ± 6.40
	SAGSC	0.40 ± 0.05	0.18 ± 0.05	1.07 ± 0.09	0.79 ± 0.05	0.88 ± 0.12	35.64 ± 2.41
	although our model has the second best result on the remain-	than other subspace clustering models including the more
	ing case (ARI over Amazon Computers), note that for NMI	efficient ones like k-FSC. Second, our model is as fast the
	over PubMed we have a tie between S²GC and our model.	SOTA attributed-graph clustering models despite it being
	On the largest dataset OGBN-arXiv, our model shows a 14%	based on subspace clustering which is know to be compu-
	improvement over the second best model, S²GC.		tationally heavy.
	Efficiency In table 5, we report the training times of all
	the baselines over ACM, DBLP and Wiki, and report those
	of the SOTA over PubMed, Computers and OGBN-arXiv.
	Our model is the fastest one on all datasets. Two main obser-
	vations can be made. First, our model is significantly faster


Silvia Voci

Bertrand Goudeau

Giovanni Valenti

Andreas Lesch

Milica Jović

Stefania Rapino

Francesco Paolucci

Stéphane Arbault

Neso Sojic

Near-field Electrochemiluminescence Microscopy of Cell Membranes

Herein is reported a near-field microscopy based on electrochemiluminescence (ECL) which allows to image the plasma membrane of single cells at the interface with an electrode. By analyzing photoluminescence (PL), ECL and AFM images of mammalian CHO cells, we demonstrate that, in contrast to the wide-field fluorescence, ECL emission is confined to the immediate vicinity of the electrode surface and only the basal membrane of the cell becomes luminescent. The resulting ECL microscopy reveals details which are not resolved by classic fluorescence microscopy, without any light irradiation and specific setup. The thickness of the ECL-emitting regions is ~ 500 nm due to the unique ECL mechanism which involves short-lifetime electrogenerated radicals. In addition, the reported ECL microscopy is a dynamic technique which reflects the transport properties through the cell membranes and not only the specific labeling of the membranes. Finally, disposable transparent carbon nanotube (CNT)-based electrodes inkjet-printed on classic microscope glass coverslips, were used to image cells in both reflection and transmission configurations. Therefore, our approach opens new avenues for ECL as a near-field microscopy to develop single cell assays and to image the dynamics of biological entities in cells or in membranes.

Introduction.

The cell membrane is an electrical and physical barrier integrating diverse and complex structures (e.g. proteins, phospholipids, sugars) where the cell interacts with the environment and responds to local biological or physicochemical variations. Imaging single cell membranes and detecting specific membrane protein biomarkers is mandatory for developing early diagnosis in medicine and for investigating fundamental issues in biology. [1][2][3][4][5] For example, the selective measurement of overexpressed membrane proteins on tumor cells is critical for diagnosis and dedicated disease treatment. 3,[6][7][8] These proteins are of great interest, particularly because they constitute targets for antibodies in immunoassays and immunohistochemistry. The study of protein transport and trafficking is required to understand the function and organization of the cell. Imaging these processes at single cells with high spatiotemporal resolution is challenging but also rewarding and a large variety of optical and electrochemical techniques have been developed on this purpose.

Fluorescence microscopy, especially confocal laser fluorescence microscopy, total internal reflection fluorescence (TIRF) microscopy and single molecule microscopies, are widely used to image specific protein localizations and various functions like effector-receptor interactions, membrane fusion, channel activities, etc. 2,4 However, autofluorescence of the sample (from flavins at least) is an intrinsic limitation of such techniques that can be avoided or minimized with methods based on other physical principles. For example, electrochemical methods based on micro/nanoelectrodes also provide high spatiotemporal resolution and excellent local sensitivity allowing to investigate complex biological processes at the single cell level such as the release of species during exocytosis or oxidative stress. [9][10][11][12][13][14][15] Scanning single cells with a microelectrode in SECM mode was reported for the study of cell respiration 16,17 and metabolic processes, [18][19][20] molecular uptake, 21 or morphological variations. 15,22 In spite of many successful applications, the major limitation of SECM is its temporal resolution related to the requirement to scan the sample in order to reconstruct an image of the "electrochemical" activity or topography of the cells, even if arrays of soft microelectrodes constitute a promising approach. [23][24][25] Zu et al. reported a near-field scanning optical microscopy (NSOM) with an ECL light source produced at a nanoelectrode tip. 26 This ECL nanoprobe was scanned over the substrates (typically, interdigitated electrode arrays and samples containing submicrometer holes) using the shear force mode. In this overall context, developing novel ultrasensitive imaging methods for the analysis of cellular and subcellular events 27,28 is still a very active research area.

In order to broaden the strategies available for studying the topology or activities of cell membranes, we report here the design and application of a new class of near-field microscopy, which combines electrochemical and luminescence methodological principles. We propose to involve electrochemiluminescence (ECL) as a readout mechanism to image the plasma membrane including its passive transport properties. ECL is an electrochemically triggered process that leads in fine to photon emission. 29,30 The excited state of the luminophore is reached by a homogeneous exergonic electron-transfer reaction between electrogenerated species. Then the excited luminophore relaxes to the ground state and emits light. Thus, ECL intimately combines orthogonal steps: electrochemistry and photochemistry, which govern the initiation and termination steps of the process, respectively. The electrochemical stimulation allows controlling very precisely the location and the duration of the ECL-emitting region whereas the optical readout makes the method extremely sensitive. In addition, ECL has the advantage of not requiring an excitation light source unlike photoluminescence (PL) techniques (i.e. fluorescence or phosphorescence). It results in an extremely low background, high sensitivity detection and a simple instrumentation that can be coupled to microscopy. 31 By exploiting these remarkable characteristics, clinical ECL-based analyzers are commercialized for a large number of immunoassays, such as for cardiac and infectious diseases, thyroid and tumor markers, etc. [32][33][34] Model systems providing high ECL efficiency in biological fluids (e.g. urine or serum) consist of a ruthenium polypyridine luminophore, [Ru(bpy)3] 2+ , with tripropylamine (TPA) as a sacrificial coreactant species. This latter is oxidized at the electrode surface and generates highly-reactive radicals that diffuse over short distances and react with [Ru(bpy)3] 2+ to produce its excited state. Therefore, depending on the chemical stability of the radicals, ECL emission occurs in the coreactant reaction layer at the vicinity of the electrode surface. [35][36][37] For imaging applications, ECL was used previously to visualize single entities such as nanowires, 27 beads for immunoassays, 36,38,39 collisions of attoliter droplets, 28 graphene oxide nanoparticles, 40 and Janus metallic nanoparticles 41 . At the single cell level, effluxes of hydrogen peroxide were observed with luminol ECL. [42][43][44][45] Recently, we reported the ECL imaging of single cells exploiting the reactivity of the tandem [Ru(bpy)3] 2+ /TPA system. 46 However, since the plasma membrane was not permeable to the coreactant, only the cell borders were observed and the rest of the plasma membrane (i.e. central regions of the cells) remained dark. It is a major constraint, which limits drastically the development of ECL for cell imaging. On the other hand, when considering that ECL is based on an initial electrochemical reaction occurring directly at the electrode surface, it has the potential to offer not only the imaging of labeled cell components but also to study their structural dynamics by giving access to transport properties through the membranes. Investigating original strategies to overcome this biological barrier due to the initial electrochemical step and the hindered diffusion of the coreactant is therefore of paramount importance to expand ECL abilities at the level of cells, for example, in ultrasensitive single cell imaging assays. [47][48][49] In addition, the spatial characteristics of such an ECL-based near-field microscopy with enhanced vertical resolution have never been reported, even more for the imaging of cells and their plasmic membranes.

Herein, we show the efficient generation of ECL at the level of the entire basal membrane of single cells (Scheme 1). In contrast to the classic wide-field fluorescence microscopy, we demonstrate that the ECL emission is confined to the immediate vicinity of the electrode surface and generated only at the level of the basal membrane. The limited extension of the ECL-emitting region, comparable to the ECL wavelength but much smaller than the thickness of a diffusion field, is defined by the short lifetimes of the electrogenerated TPA radicals. Conceptually, this feature of ECL is reminiscent of TIRF microscopy where the optical signal is restricted within a few hundred nanometers from the surface. Finally, cell membranes were imaged by ECL microscopy in reflection configuration on GC electrodes as well as in transmission configuration (Scheme 1a) with disposable transparent CNT-based electrodes that were inkjetprinted on classic glass coverslips. Therefore, our wide-field approach expands the applicability of ECL to diverse optical microscopies by imaging biological entities with near-field features. Scheme 1. Schematic principle of the near-field ECL microscopy of labeled cells (i) in reflection configuration with the GC electrode or (ii) in transmission configuration through the transparent CNT inkjet-printed electrodes. a) SA@Ru labels were attached to the biotinylated proteins of the cellular membrane. b) Influence of the membrane permeabilization step on the ECL responses of (left) fixed and (right) permeabilized cells. It illustrates the effects of the permeabilization step on the TPA diffusion through the cell membrane and on the resulting localization of the ECL-emitting regions.

Experimental section.

Materials. Tripropylamine (TPA), 2-(dibutylamino) ethanol (DBAE), phospate buffered saline (PBS) solution (pH 7.4), streptavidin from Streptomyces avidinii, bis(2',2-bipyridine)-4'-methyl-4-carboxybipyridine-ruthenium Nsuccinimidyl ester-bis(hexafluorophosphate) [Ru(bpy)2 (mcbpy-O-Su-ester)(PF6)2] and paraformaldehyde (PFA) were from Sigma-Aldrich and used without any further purification. Triton X-100 was from Acros Organic. Iscove's modified Dulbecco's medium, fetal bovine serum, PBS1x, trypsin and penicillin / streptomycin 100 U/ mL were from Gibco. Biotin X was from Fisher Scientific. DMSO was from Invitrogen. Phosphate buffer solution (PBS) 0.1 M (pH = 7.4) was obtained by mixing 0.1 M of sodium phosphate monobasic monohydrate (NaH2PO4•H2O) and 0.1 M sodium phosphate dibasic heptahydrate (Na2HPO4•7H2O), both from Sigma-Aldrich and used as received.

Cell culture, labeling and permeabilization. CHO-K1 cells were from Public Health England (HPA) Culture Collections and supplied by Sigma (85051005). Iscove's modified Dulbecco's medium (IMDM) supplemented with 10 % fetal bovine serum and penicillin/ streptomycin 100 U/ mL were used to grow cells in an incubator. CHO-K1 cells were trypsinized, plated on glassy carbon electrode or in a Petri dish containing CNT electrode and incubated 48 h with culture medium at 37 °C, 5% CO2. A solution of 100µL of ruthenium complex (10 mg/ mL) in anhydrous DMSO, 100µL of streptavidin (1 mg/ mL in PBS), and 800µL PBS was prepared. The solution was vortexed for 4 h at 4 °C and dialyzed overnight under stirring at 4 °C. Before ECL experiment, CHO-K1 cells were fixed 10 min with PFA 4%, permeabilized 10 min with Triton X-100 0.1%, labeled with biotin X 11 µM and streptavidin-ruthenium complex solution SA@Ru (0.1 mg/mL).

Instrumentation. The ECL/PL microscopies were performed in a PTFE (Teflon) homemade electrochemical cell. The ECL imaging cell was used in a three-electrode configuration, in which glassy carbon or CNT electrode acted as working electrode, Ag/AgCl (KCl, 3M) as reference electrode and a Pt wire as counter electrode. For ECL experiments, the potential applied to the working electrode was 1.4 V vs. Ag/AgCl (KCl, 3M). For microscopic imaging, an epifluorescence microscope from Leica (DMI6000, Leica Microsystems) equipped with ultrasensitive Electron-Multiplying Charge Coupled Device camera (EM-CCD 9100-13 from Hamamatsu, Hamamatsu Japan) was used with an inverted 63x microscope objective from Leica (63x/1.2, 0.2mm). The integrated system also included a potentiostat from AUTOLAB (µAUTOLAB, type II) suitable to provide the required potential to generate ECL. Atomic Force Microscopy. AFM experiments were performed with a Veeco MultiMode 8.

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Fabrication and characterization of the inkjet-printed CNT electrodes. The CNT electrodes were fabricated first on polyethylene terephthalate sheets (PET, 125 µm thick) and then on glass microscope coverslips (VWR, 631-1573, 0.13-0.16 mm thickness) following our previously established inkjet-printing protocols 50 and by using an X-Serie CeraPrinter (Ceradrop) with piezoelectric Dimatix Q-class Sapphire QS-256-80pL print-heads and disposable DMC-11610 cartridges. The Ceraprinter was combined with a PulseForge 1300 photonic curing system (Novacentrix) and a FireEdge FE300 380-420nm UV LED (Phoseon Technology) for rapid flash light-induced thermal and photochemical postprocessing, respectively. In brief, Jettable nano silver Silverjet DGP-40LT-15C (w/w 30-35%, Sigma Al-drich) was printed and photonic cured as electrical connection layer. The CNT dispersion BSI.B16171_A (Brewer Science) was printed and photonic cured to generate the transparent CNT working electrode and the jettable insulator EMD6201 (Sun Chemical) was printed and quasi-simultaneously polymerized as insulation layer. For each printing process, essential printing parameters, such as piezoelectric actuation, jetting frequency, etc. were optimized and after printing all layers the electrodes were ready to use. The transmittance of a 1 cm 2 CNT layer on glass was measured with an 8453 UV-visible spectroscopy system (Agilent Technologies). The inkjet-printed CNT pattern was characterized using a Fei Teneo scanning electron microscope (SEM).

Results and discussions.

To develop ECL microscopy of cell membranes, mammalian Chinese Hamster Ovary (CHO) cells were grown first on glassy carbon (GC) electrodes. These adherent cells were fixed and then labeled with a prototypical ECL agent, i.e.

[Ru(bpy)3] 2+ , using the biotin-streptavidin interactions (Scheme 1a). Biotinylation of the membranes was performed by incubating the cells with biotin X, which reacts with primary amino groups of cell surface proteins. Such biotinylation method is classically used in biology to label specifically extracellular proteins of the membrane, whereas intracellular proteins remain unlabeled. Streptavidin-modified [Ru(bpy)3] 2+ labels (noted SA@Ru or SA@[Ru(bpy)3] 2+ ) were then attached to the biotinylated proteins of the cellular membrane. 51 The PL signal reflects the sites of the immobilized ruthenium labels on the plasma membrane and the PL image (Figure 1) shows that the whole plasma membrane was labeled by SA@Ru. When applying 1.4 V to the GC electrode in presence of TPA, the SA@Ru labels react with the electrogenerated TPA radical species. We selected this potential value because it leads to strong and stable ECL signals on labeled cells (Figure S1). In this first series of experiments, cells were fixed without further modification (Figure 1a). ECL spatial distribution recorded in reflection configuration (Scheme 1a) reveals that light emission is restricted to the external cell borders. 46 It is also clearly visible on the right part of Figure 1a where 4 cells are in close contact and only their periphery is ECL-active. This is due to the hindered diffusion of TPA through the plasma membrane, from the cell upper part or from sides at its basis, toward the electrode surface (Scheme 1b, left). Therefore, TPA cannot be oxidized at the electrode surface in the central part of the cell and these regions remain dark. Only the cell borders close to the electrode surface are exposed to the concentration gradients of TPA radicals (i.e. TPA reaction layer) 36,46 and local SA@Ru labels emit ECL light. As a result, the localization of the ECL-emitting regions depends not only on the labeling step but also on the transport properties of the coreactant species near or through the membrane. To push further the imaging abilities offered by ECL at cell membranes, it was essential to overcome this important limitation due to the cell barrier. For that, we applied a standard biological procedure used to permeabilize lipid bilayers and cell membranes. The cells were thus incubated with Triton X-100 as classically performed in immunofluorescence or Western blot techniques. 52,53 Triton X-100, a nonionic surfactant, is widely exploited to permeabilize the cell membranes, including the nuclear membrane, for DNA transfection or further labeling steps. Indeed, permeabilization provides access to intracellular or organelle proteins. Thus, Figure 1b shows the compared PL and ECL images of a single cell after incubation with Triton X-100. One can clearly observe that ECL emission occurs now at the whole cell membrane facing the electrode (Figure 1b), and not only from the cell borders (Figure 1a). Such a significant result proves unambiguously that TPA diffusion through the membranes, at least through the plasma membrane, is essential for a global imaging of the cell (Scheme 1b, right). Moreover, ECL light is also detected in the nucleus region, which illustrates that even the nucleus membrane has become permeable to TPA following this procedure. A detailed observation of both PL and ECL images (Figure 1b) shows that 2 nucleoli are present in the nucleus. However, they remain dark because they have not been permeabilized and they block the TPA diffusion from the bulk to the electrode surface. Thus, diffusion of TPA through the membranes governs the location of the ECLemitting regions within the cell as well as the proximity to the electrode surface. Consequently, such ECL microscopy does not reflect only the spatial distribution of the labels and the structure of the plasma membrane but reveals also the passive transport properties through the membranes. Therefore, our approach may allow investigating the transport and trafficking across the cell membranes.

DBAE is an environmentally friendly co-reactant, which gives stronger ECL intensity than TPA when the [Ru(bpy)3] 2+ luminophores are free in solution (not immobilized as in the present case on cells). 54 We tested its performance on the SA@Ru labelled cells (Figure S2). But we have not been able to record any ECL image of the cells using DBAE. The ECL intensity was below the detection limit. In a previous work, 36 ECL emission was also extremely low at the level of SA@Ru-modified beads. Such a behavior might be attributed to the intervention of a very unstable intermediate and/or to the inadequate potential of the DBAE •+ radical, which is unable to populate the excited state by reaction with SA@[Ru(bpy)3] + (reaction 4).

To demonstrate the near-field feature and the vertical resolution of the presented ECL-based microscopy, we analyzed and compared both PL and ECL images in different focal planes (Figure 2). When considering resolution in optical microscopy, in addition to the lateral resolution, the main characteristic is the vertical resolution. 55,56 For instance, in wide-field fluorescence microscopy, the excitation wavelength provokes the entire object to fluoresce and, in usual conditions, more than 90% of the collected fluorescence signal is out-of-focus emission. that can completely mask the in-focus details. 55 Vertical resolution is determined by the depth of field so that a thin section of the cell can be imaged. 55,56 The depth of field may be defined as the distance from the nearest object plane in focus to that of the farthest plane also simultaneously in focus. [START_REF] Keller | Handbook of Biological Confocal Microscopy[END_REF] Figure 2 shows PL and ECL images of the same region of interest presenting 2 adherent cells on the GC electrode. These images have been recorded in the reflection configuration (Scheme 1a) with a high numerical aperture (1.2) 63x objective in different focal planes. The depth of field of the objective is 400 nm. By adjusting the focus in the PL mode (Figure 2a), the cell and nucleus membranes are clearly imaged as well as the pseudopods, which adhere to the electrode surface. The excitation source was then turned off and the ECL image recorded while applying a sufficiently positive potential to the GC electrode in presence of TPA. In this PL focal plane, the resulting ECL image appeared blurry, out-of-focus (Figure S3). Well-defined ECL imaging of the cell (Figure 2c), actually of its plasma membrane, was obtained when moving the focal plane of the objective 1.2 µm below the previous PL focus, i.e. closer to the electrode surface. If we recorded the PL image in this adequate focal plane for ECL, PL image of the cells appeared blurry, not well-defined (Figures 2b andS4). It means that the focal PL and ECL planes are distinct and not located at the same distance from the electrode surface. The mean average distance between PL and ECL focal planes has been evaluated as 1.2 ± 0.4 µm (n ≥ 30 CHO cells). In other words, the ECL focal plane is located 1.2 ± 0.4 µm closer to the electrode surface in comparison to the PL focal plane. This conclusion appears fully logic since PL is acquired in far-field mode and provides a whole cell image of all SA@Ru labels present on membranes from the apical (top) to the basal (down) planes of the cell. Otherwise, ECL emission only occurs from SA@Ru labels reacting with TPA electrogenerated radicals, meaning in the TPA reaction layer (Scheme 1b) between the electrode surface and basal cell membranes. In order to characterize better the topology and thickness of CHO cells, we performed AFM analyses on CHO cells (~70% confluent) grown on a GC surface (Figure 3a). Typical dimensions of the cells were about 30-70 μm in diameter, similarly to when observed in usual culture conditions. On the AFM images, characteristic brighter regions corresponding to higher parts in the central region of the cells (Figure 3a) are attributed to the nucleus areas. The zones surrounding the nuclei correspond to the cytoplasm, which becomes progressively thinner at the pseudopods ensuring the adhesion on the surface. Typical profiles for two cells are represented on Figure 3b. Nuclei regions appeared about 1.5-2 µm in height whereas cell borders are about 1 µm. These AFM results are in good agreement with similar topographic studies also performed on CHO cells. [START_REF] Puntheeranurak | [END_REF] Considering the cell morphology and thickness, the PL focal plane is located in the middle of the cell, as schematized on Figure 3c. Since the ECL focal plane is 1.2 ± 0.4 µm below the PL focal plane, ECL is truly emitted from a cell zone in the immediate vicinity of electrode surface, i.e. in the TPA reaction layer (Scheme 1b). In other words, ECL emission is confined to the basal cell membrane (Figure 3c).

The plasma membrane is usually separated from the substrate (i.e. in our case, the electrode surface) by ~100-150 nm via the formation of extracellular matrices-integrin-cytoskeleton linkages, as demonstrated by TIRF and SPR microscopies. 59,60 Therefore, since the cell membrane has been biotinylated and labeled with the SA@Ru, ECL emission is intrinsically confined next to the electrode surface and it arises from the basal cell membrane. Consequently, such ECL imaging offers a near-field vertical resolution of biological structures at distances below the emission wavelength of the ruthenium fluorophore (615 nm). This is emphasized by the comparison of PL and ECL images (Figures 2a and2c), which shows also that ECL allows the imaging of a significantly larger spatial extension of the cell borders. The parts of the plasma membrane that reside closer to the electrode surface produce stronger ECL and they are revealed by ECL microscopy whereas they remain dark with PL. The contrast is indeed much improved in comparison to PL images. This means that different but complementary information are provided by classic fluorescence microscopy and the ECL-based microscopy. Conceptually, the limited extension of the probed space is equivalent to TIRF microscopy, which is an optical technique confined to the observation interface, due to the nonpropagating properties of the evanescent electromagnetic field. Indeed, the evanescent wave decays exponentially into the sample within few hundreds of nanometers, typically ∼300 nm from the surface. Thus, only the fluorophores located in this space are photo-excited and may contribute to the fluorescence signal.

For the ECL microscopy, the limited extension of the ECL-emitting region results from the unique mechanism of TPA coreactant with SA@Ru labels. 35,36 TPA was selected as a sacrificial "oxidative-reduction" coreactant because it can "electro-excite" the ECL labels at a submicrometric distance from the electrode surface, by reaction of immobilized SA@Ru with the diffusing electrogenerated TPA radicals (Scheme 1b). As demonstrated in bead-based immunoassays, the resulting heterogeneous ECL emission has been rationalized considering the following reaction mechanism: 35 This item was downloaded from IRIS Università di Bologna (https://cris.unibo.it/)

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TPA -e D TPA •+

(1)

TPA •+ D TPA • + H + (2) TPA • + SA@[Ru(bpy)3] 2+ D P + SA@[Ru(bpy)3] + (3)
TPA •+ + SA@[Ru(bpy)3] + D TPA + SA@[Ru(bpy)3] 2+ * (4)
SA@[Ru(bpy)3] 2+ * " SA@[Ru(bpy)3] 2+ + hνECL (5) where P is the product of the homogeneous TPA • oxidation.

Since the SA@Ru labels are immobilized on the plasma membrane, the luminophores might not be oxidized directly at the electrode surface in this mechanistic pathway. We checked this point by recording differential pulse of the GC electrodes on which CHO cells were grown and we have not observed any measurable current at the oxidation potential of the ruthenium complex (Figure S5). In the present scheme, only TPA is oxidized at the electrode (reaction 1) and it generates the cation radical TPA •+ , which deprotonates rapidly to form the strong reducing neutral radical TPA • (reaction 2). This latter reduces SA@[Ru(bpy)3] 2+ to SA@[Ru(bpy)3] + (reaction 3). Then TPA •+ oxidizes SA@[Ru(bpy)3] + to populate the excited state of the label (reaction 4). Finally, it deactivates to the ground state and emits a photon (reaction 5). In the present mechanism, ECL generation requires only the TPA oxidation at the electrode surface to produce simultaneously both TPA radicals at the same location (i.e. TPA reaction layer) and to form the excited state of SA@Ru. In the reaction scheme 1-5, the key kinetic parameter is the rate constant for the deprotonation of the TPA •+ radical, leading to a half-life time of ~0.24 ms. 35,36 Taking into account the overall mechanistic scheme for TPA (reactions 1-5), simulations in bulk configuration have shown that maximum ECL intensity occurs at 0.5 µm from the electrode surface and then decays exponentially until 1 µm. 35,36,46 The extension of this ECL layer might even be smaller within or in the cell-electrode interspace in comparison to the bulk situation. Therefore, this finite ECL reaction layer, which results from the reactivity of the TPA radicals, provides the near-field vertical feature for generation and observation of ECL luminophores. In other words, TPA reactivity limits the light emission over the basal region of the cell membrane. SA@Ru labels located further, i.e. on the apical cell membrane, are not electrochemically excited by the TPA radicals and do not contribute to the ECL signal. The submicrometric extension of the ECL reaction layer, where the labels are excited by a cascade of redox reactions, is conceptually similar to the evanescent wave in TIRF microscopy, which photo-excites the luminophores. Finally, since the thickness of this "evanescent" ECL reaction layer depends on the lifetimes of the cation coreactant radicals, we envision that its extension could be modulated, i.e. increased or reduced by using other coreactants possessing different lifetimes of the electrogenerated radicals. Therefore, various heights and regions of the substrates or cells could be imaged by ECL microscopy by adapting this strategy.

The last part of this work was devoted to widen the applicability of the above ECL microscopy by using innovative electrode supports. In the experiments above, we used first GC as the electrode surface because carbon-based materials give strong ECL signals due to their efficient TPA oxidation and a low fouling by biomolecules. 61 However, since GC is opaque, ECL microscopy on such electrode is limited to the reflection configuration (Schema 1a). In addition, GC materials cannot be used routinely for traditional optical microscopies since it requires several preparations steps (cleaning, polishing). Ideal electrode materials for ECL microscopy should associate high electrical conductivity, excellent electrochemical stability and high optical transparency. Transparent metal oxide electrodes, such as indiumdoped tin oxide (ITO) and fluorine-doped tin oxide (FTO), are currently the standard materials for transparent electrodes. 61 But the rather limited stability of these oxides restricts the electrochemical potential window and their low efficiency for TPA oxidation leads to very low ECL intensity compared to carbon-based materials. To extend our ECL-based approach to the transmission configuration and to develop more practical disposable devices for microscopy, CNT-based transparent electrodes were fabricated by inkjet-printing first on polyethylene terephthalate sheets and then on microscope glass coverslips (Figure S6). This inkjet-printing technology approaches progressively the industrial production level at reasonable costs for thin layer materials. In the transmission PL configuration, the PET layer induces some optical distortions probably related to the different refractive index of PET (Figure S7). Then we used classic microscope glass coverslips (0.13-0.16 mm thickness) on which the CNT layers were printed (Figure 4). Such glass coverslips are ideal for biologists and for researchers working with microscopy because it is a standard object in their field. An inkjet-printed silver Ag pattern served as electrical connection for the printed CNT layer just by minor overlapping these two layers (Figure S6). The heart of the printed electrode is a stand-alone CNT layer on the glass coverslip ("CNT/glass", Figure 4a). An inkjet-printed insulation layer ("Insu/CNT/glass") defined precisely the stand-alone CNT working electrode area and protected the Ag from the solution ("Insu/Ag/glass"). The SEM image shows a uniform surface coverage of the glass substrate by the CNT (Figure 4b). The oxidation of TPA occurs efficiently on such CNT electrode surfaces and their electrochemical performances are indeed comparable to GC electrodes giving an ECL emission ten times higher compared with standard transparent ITO electrode. 39 The CNT-printed electrodes were quasi-transparent allowing ~90% of transmission (Figure 4d) at the emission wavelength of [Ru(bpy)3] 2+ (i.e. 615 nm). Further, CHO cells were cultured on the inkjet-printed CNT electrodes as illustrated by the PL image (Figure 4c). Cell viability on the CNT layer was comparable to a glass substrate, as reported previously. 46 Figure 5a shows the PL image of the CHO cells in the transmission configuration through the CNT layer (Schema 1a). Cells appeared relatively separated when observed in the PL mode. Then, we imaged the same region of interest in ECL with the transmission configuration (Figure 5b). ECL light is generated at the level of the basal cell membrane (vide supra), transmitted through the CNT layer and the coverslip, and collected by the microscope objective (Scheme 1a).

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When citing, please refer to the published version. The cells were previously permeabilized and one can observe the entire cell area by ECL microscopy. As a result, they appear much closer than in PL (Figure 5c), similarly to images recorded in the reflection configuration with GC electrodes. As already discussed above, ECL allows the observation of a larger fraction of the plasma membrane with CNT-electrodes, in comparison to PL, because ECL is a surface-confined imaging technique. The regions of the labeled membrane located in the immediate vicinity of the electrode surface are clearly visible in ECL whereas they are not distinguished in PL. ECL microscopy allows observing membrane details, which are difficult to resolve by classic PL microscopy.

Conclusions.

In this work, we developed a near field-type microscopy based on ECL to image plasma membranes at the single cell level. By comparing PL, ECL and AFM images of the cells, we have demonstrated that, in contrast to classic fluorescence microscopy, the ECL emission is confined to the immediate vicinity of the electrode surface. Thus, only the basal membrane generates ECL light and ECL microscopy reveals details, which are hardly resolved by classic farfield fluorescence microscopy. The limited extension of the ECL-emitting region results from the ECL mechanism and the short lifetimes of the coreactant radicals. Conceptually, this subwavelength vertical resolution is reminiscent of TIRF microscopy with a restricted propagation depth of the evanescent wave. By using other coreactants presenting different radical lifetimes, we envision that the extension of the ECL-emitting regions can be modulated allowing to image different heights in substrates or in cells by ECL. Since ECL emission requires the oxidation of the coreactant at the electrode surface, the reported ECL microscopy is a dynamic technique. It does not visualize only the plasma membrane structures but it reflects also their passive transport properties. The presented strategy may allow investigating the transport and trafficking properties through the cell membranes. Finally, ECL microscopy is performed for the first time in both reflection and transmission configurations owing to disposable transparent CNTbased electrodes inkjet-printed on standard glass coverslips for microscopy. Therefore, our approach using such standard biological objects expands the possibilities of ECL to diverse microscopy fields by imaging globally the dynamics of biological entities. The presented near-field ECL microscopy offers exciting opportunities to study the dynamic properties of the cell membranes and promising applications in ultrasensitive cell imaging assays.

Figure 1 .

 1 Figure 1. PL (green), ECL (red) and overlay of both luminescence signals (from left to right) of CHO cells that were (a) labeled with SA@Ru or (b) permeabilized and then labeled with SA@Ru. Cells were grown on GC electrodes. SA@Ru labels were attached to the biotinylated proteins of the cellular membrane. Both PL and ECL images were recorded in the reflection configuration on the same regions of interest in the ECL focal plane. ECL was generated in PBS (pH = 7.4) containing 100 mM TPA by applying 1.4 V. Scale bar: 20 µm.

Figure 2 .

 2 Figure 2. PL images of the same CHO cells focused in the focal (a) PL or (b) ECL planes at different magnifications. (c) ECL images of the same region of interest recorded with the objective focused in the focal ECL plane (i.e. similar to b). Cells were grown on GC electrodes and then treated with Triton X-100 for 10 min. SA@Ru labels were attached to the biotinylated proteins of the cellular membrane. Both PL and ECL images were recorded in the reflection configuration. ECL was generated in PBS (pH = 7.4) containing 100 mM TPA. Scale bar: 10 µm.

Figure 3 .

 3 Figure 3. (a) Top and (c) side views of AFM images of CHO cells grown on a GC surface. The bright regions correspond to the nuclei region. (b) Cross-section profile of two adjacent cells along the white line materialized on Fig. 3a. On the side view, both mean PL (green) and ECL (red) focal planes are schematically represented. Scale bars: 10 µm.

Figure 4 .

 4 Figure 4. (a) Photograph of the inkjet-printed CNT electrodes on the microscope glass coverslips. b) SEM of the CNT electrode surface. c) PL images of the CHO cells grown on the inkjet-printed CNT electrodes. d) Transmission curve of the inkjet-printed CNT electrodes.

Figure 5 .

 5 Figure5. PL (a), ECL (b) and overlay of both luminescence images (c) of CHO cells that were obtained in the transmission configuration through the CNT inkjet-printed electrode. Cells adherently grown on the CNT electrodes were permeabilized and labeled with SA@Ru. ECL was generated in PBS (pH = 7.4) containing 100 mM TPA. PL and ECL images were both recorded in the ECL focal plane. Scale bar: 20 µm.

This item was downloaded from IRIS Università di Bologna (https://cris.unibo.it/)

ACKNOWLEDGMENT

We thank Bordeaux INP and the Agence Nationale de la Recherche (MOLY, ANR-15-CE19-0005-02; NEOCASTIP ANR-15-CE09-0015-03) for their financial supports.

This item was downloaded from IRIS Università di Bologna (https://cris.unibo.it/)

ASSOCIATED CONTENT

Supporting Information. ECL-potential curves. PL images of the CHO cells recorded at high magnifications in different focal planes. ECL microscopy with DBAE. DPV. Scheme and photograph of the inkjet-printed CNT electrodes on glass coverslips. Optical effects on the PET and glass coverslips.

AUTHOR INFORMATION

Corresponding Author * Neso.Sojic@enscbp.fr ORCID Neso Sojic: 0000-0001-5144-1015

Author Contributions

The manuscript was written through contributions of all authors.

Notes

The authors declare no competing financial interest.


Haidong Li

Adam C Sedgwick

Meng Li

Richard A R Blackburn

Steven D Bull

Stéphane Arbault

Tony D James
email: t.d.james@bath.ac.uk

Neso Sojic
email: neso.sojic@enscbp.fr

Selective Electrochemiluminescent Sensing of Saccharides using Boronic Acid-Modified Coreactant

We report a strategy for modulating the electrogenerated chemiluminescence (ECL) response by integrating a boronic acid to the chemical structure of coreactants. Excellent selectivity for Dglucose was achieved by tuning the linker length of a bis-boronic acid amine coreactant.

The discovery of electrogenerated chemiluminescence (ECL) in aqueous media has resulted from intense fundamental research on the mechanisms of the phenomenon [START_REF] Bard | Electrogenerated Chemiluminescence[END_REF][START_REF] Rubinstein | [END_REF] and has led eventually to important bioanalytical applications including commercialized immunoassays for clinical diagnostics. [3][4] The corresponding ECL process is based on a reaction cascade initiated at an electrode surface between a tandem system composed of a luminophore and a sacrificial coreactant species. The luminophore reaches the excited state by the highly exergonic reactions with the electrogenerated coreactant radicals. It relaxes then to the ground state by emitting ECL light which is the analytical signal. During the process, the luminophore is regenerated, whereas the coreactant is consumed by the electrochemical reactions. The amount of light generated directly depends on the concentration of the luminophore but also of the coreactant. The luminophore has been used as ECL labels in numerous bioassays 5 or as molecular probes with different receptor sites. [6][7][8][9][10][11] For example, ruthenium and iridium complexes have been modified with crown ether moiety to measure different metal cations. [6][7][8][9] In this case, the role of the coreactant is just to generate efficiently electrochemically suitable radicals with adequate redox potentials and life-times. Another enticing possibility is to detect and to quantify any ECL-active coreactant treated thus as an analyte as its concentration will directly influence ECL intensity. An example of the ECL detection of coreactants is the determination of oxalate and peroxydisulfate. Another class of analytes that may act as coreactants is amines. ECL assays for amine-based compounds find many analytical applications because amine groups are present in a large variety of pharmacologically important compounds such as antibiotics, anti-histamines, opiates, etc. 5,[12][13] However, a major limitation is that the analytes have to be electro-active and also able to generate strong reducing or oxidizing radicals to bring the luminophore to the excited state. So it limits strictly the nature of the possible molecules to detect.

Scheme 1 Chemical structures of the boronic acid based coreactants E0, E3 and E6 and Fluorescent boronic based saccharide sensors F0, F3 and F6. 14 As an alternative strategy, we propose to confer recognition properties to the coreactant by integrating a receptor site to its chemical structure (Scheme 1). The recognition of the target analyte would then modulate its electrochemical properties and the resulting ECL emission of the luminophore. Here, we develop an approach using a boronic acid as the receptor group. Model systems providing high ECL efficiency in water consist of the luminophore Ru(bpy) 3 2+ with coreactants such as tri-npropylamine (TPrA) or 2-(dibutylamino) ethanol. [16][17][18] The pursuit of efficient ECL reagents is an intense area of investigation and several groups have studied the ECL mechanism using amine coreactants. 19 In general, tertiary amines produce ECL emission more efficiently than secondary amines and primary amines, following this order. 5 Recently, it has been reported that increasing the electrochemical oxidation rate of amines leads to higher ECL efficiency. For instance, ECL emission is amplified with amines bearing electron-donating groups. 18 In addition, aromatic amines, such as the pyridine ring of NAD + , the coenzyme of the dehydrogenase enzyme class, do not produce chemiluminescence or ECL with the ruthenium luminophore. 20 By contrast, NADH, the reduced form of the coenzyme, may generate ECL emission because the aromaticity of the pyridine ring is destroyed and the aliphatic tertiary amine group undergoes ECL emission. Herein, inspired by the remarkable structure/reactivity relationship of this very efficient biomolecule, we designed and prepared a series of amine-based coreactants (E0, E3 and E6) integrating boronic acid function as receptor units (Scheme 1). For the first time, we demonstrated that the recognition of the saccharide modifies both the structure and the reactivity of the coreactant and thus the resulting ECL emission (Fig. 1). With the presented approach, ECL generation depends on target molecules that are electro-inactive and do not to change the conformation of the luminophore as classically performed with molecular probes. Moreover, differential selectivity for D-glucose and D-fructose is achieved by tuning the number of boronic acid groups and the spacer length.

To explore the usefulness of the above strategy, we selected the prototypical Ru(bpy) 3 2+ complex as a luminophore and modified tertiary amines as oxidative-reduction coreactants because such a model system leads very efficiently to strong ECL emission. 16 As a test case, we designed and prepared compound E0 which is similar to the TPrA structure but containing a boronic acid as recognition unit. E0 and the other coreactants shown in Scheme 1 (E3 and E6) were synthesised through the alkylation of their corresponding amine using 2-(2-(bromomethyl)phenyl)-4,4,5,5-tetramethyl-1,3,2dioxaborolane (Schemes S1 and S2).

Once isolated, E0 electrochemical and ECL properties were investigated by using cyclic voltammetry in PBS solution that contained 10 µM of Ru(bpy) 3 2+ and 0.2 mM of E0 (Fig. 2). The coreactant concentration was in excess in comparison to the luminophore, as very classically employed in ECL experiments because it is consumed during the ECL process. As shown in Fig. 2, irreversible oxidation of E0 occurred at 0.77 V vs. Ag/AgCl/KCl and the oxidation wave is shifted to less anodic potentials by 100 mV in comparison to the model TPrA reagent (Fig. S1a). It indicates that the phenylboronic acid group is a better donor than ethyl group. This donor effect makes the molecule much easier to oxidize and can also stabilize the radical cation by charge delocalization. ECL emission occurred at the oxidation potential of Ru(bpy) 3

2+

(Fig. 2c), as for TPrA in the same experimental condition (i.e. low Ru(bpy) 3 2+ concentration). It follows an oxidative-reduction mechanism where both the luminophore and the coreactant are oxidized (Fig. 1). After a deprotonation step, the cation radical gives a highly reducing neutral radical that react with the oxidized Ru(bpy) 3 3+ to generate the excited state of the luminophore. This one relaxes in fine to the ground state by emitting ECL light. In comparison to TPrA, ECL response with E0 is divided by a factor 2 (Fig. S1b). Indeed, the nature of substituents attached to nitrogen or α-carbon on the amine coreactant can also affect the ECL efficiency 5,21 and it has been reported that aromatic-substituted amines that can conjugate the radical intermediates consistently lead to lower ECL emission response. 22 The addition of D-glucose caused a notable effect on both the voltammetric wave and the ECL response (Fig. 2). It resulted in a dramatic decrease of the oxidation current along with its shift to more anodic potentials (Fig. 2b). Correspondingly, ECL intensity decreases progressively with the addition of Dglucose. Under these conditions, the effects of D-fructose were qualitatively similar to the ones of D-glucose but with a much stronger decrease of both anodic wave and ECL intensity for a given concentration (Fig. S2). Indeed, the oxidation wave almost vanished and the ECL peak decreased by 57% with 50 mM of D-fructose (Fig. 3a). The same limit values for the ECL intensity and for the current were reached with 200 mM of D-glucose than with 50 mM of D-fructose. Such a difference was expected because the complexation constant of phenylboronic acid with D-fructose is much higher than with D-glucose (110 dm 3 mol - 1 ). 15,23 Fig. 3 a) Variation of the normalized ECL peak intensity (triangles) and of the oxidation peak current (dots) for the system Ru(bpy) 3 2+ /E0 as a function of the concentration of D-glucose (red markers) or of D-fructose (blue markers). b) Correlation between the ECL signals and the peak current corresponding to the E0 oxidation for the addition of different concentrations of D-glucose or of D-fructose.

To check that the observed decrease was related to the complexation of the saccharides by the phenylboronic acid from E0 and not to some photochemical or quenching effects, we recorded first the ECL spectra of Ru(bpy) 3

2+ with increasing concentrations of D-fructose (Fig. S3). Identical ECL and photoluminescent spectra were obtained showing that the photochemical properties of the luminophore were not affected neither by D-fructose nor D-glucose. Then we investigated the electrochemical and ECL signals of the model Ru(bpy) 3 2+ /TPrA in presence of D-fructose (Fig. S4) and the effects of D-fructose addition led to minute changes. Finally, to determine the rate controlling step in the global ECL process, we plotted the variations of the normalized ECL peak (i.e. final readout signal) as a function of the normalized peak current (i.e. first step in the ECL process) with increasing concentration of Dfructose or D-glucose (Fig. 3b). One can observe unambiguously that both signals are cross-correlated for both saccharides. Which demonstrates that the variation of the ECL intensity is governed by the oxidation of the coreactant. The electrochemical step, and more specifically the heterogeneous oxidation of E0, controls the efficiency of the ECL process. In other words, the decrease of the ECL intensity observed with increasing concentration of saccharides is due to the direct oxidation of the E0 at the electrode surface when it binds the saccharides.

The oxidation behavior of tertiary amines at glassy carbon electrodes has been examined in aqueous solutions. 17,[24][25][26] It is known that oxidation of a tertiary amine occurs when it is in the deprotonated form. 17 When protonation of the tertiary amines becomes important at acidic pH, its oxidation peak decreases in intensity and shifts toward more positive potentials. 17 As illustrated in Fig. 1, the complexation of the saccharide by E0 induces a solvent-inserted B-N bond which behaves in a very similar fashion to protonation of the nitrogen atom. 15,27 Therefore, heterogeneous oxidation of the coreactant in the presence of saccharide becomes a very inefficient process that limits drastically the ECL signal. However, even at high Dfructose concentrations where almost all the E0 is bound, we still observe an ECL signal. Since ECL is obtained at the oxidation potential of Ru(bpy) 3 2+ , the remaining ECL intensity resulted probably from the electrocatalytic mechanism where E0 is homogeneously oxidized by the electrogenerated Ru(bpy) 3 3+ .

To further assess our approach and to improve the selectivity, we designed and prepared new symmetric tertiary bis amino reagents bearing boronic acid end-groups and having linkers with different lengths (Scheme 1). Previous, research has demonstrated that saccharide selectivity can be achieved in systems with two boronic acid groups. [14][15] We investigated first the properties of the compound E6 with a hexyl linker between both amino groups. The cyclic voltammogram in Fig. S1a is dominated by the irreversible oxidation waves of the amino moieties at the same potential as TPrA. The peak current is increased by approximately 2.1-fold indicating that both amino groups are simultaneously oxidized. However, the ECL signal is 15% lower with E6 than with TPrA (Fig. S1b), even if two amino groups were oxidized and may participate to the ECL process. This low ECL response is probably related to the lower stability of the electrogenerated dication radicals. The addition of Dfructose or D-glucose induces the decrease of the oxidation current and the shift of the corresponding anodic wave, as reported for E0 (Fig. S5), which resulted in a decrease of the ECL response in the presence of both saccharides (Fig. S5-S6). To further investigate the properties of E6, additional competitive assays were performed. They clearly showed that D-fructose and D-glucose caused notable modification of the current and of the ECL signal (Fig. S7). The detection limits of D-glucose and of D-fructose for E6 were 20 µM and 10 µM, respectively (Fig. S8). Initially, it was somewhat surprising to us that E6 could not discriminate between D-fructose and D-glucose and detect them selectively. However, from our previous fluorescence work for F6 the measured binding constants for D-fructose and D-glucose are very similar 784±44 and 962±70 dm 3 mol -1 . 14 Further electrochemical experiments were performed on to investigate the influence of the linker length on the selective recognition of both saccharides. Fig. 4a presents the results obtained with E3 where the linker between both amino group and the phenylboronic acid moieties is shorter. The cyclic voltammogram showed that the oxidation process of E3 is more complex exhibiting a first anodic wave at 0.87 V vs. Ag/AgCl/KCl and a second at 0.95 V vs. Ag/AgCl/KCl (Fig. 4a). The fact that both waves are partially separated indicates that the electronic communication between both amino groups is not negligible, in contrast to what was observed for E6. Adding D-glucose induces the decrease of the current for both oxidation waves as well as the parallel decrease of the ECL response (Fig. 4b). Remarkably, an invatriant voltammetric signal and ECL response (Fig. 4 c-d) was observed for D-fructose, allowing discriminating between both saccharides (Fig. 5). While this result seems quite strange, our observations with similar fluorescence systems 14 can help explain the observed selectivity. Since, the binding of F3 with D-fructose is Please do not adjust margins Please do not adjust margins significantly impaired when compared with the model system F0 evidenced by a 4-fold reduction in binding for D-fructose from 395±11 dm 3 mol -1 for F0 to 95±9 dm 3 mol -1 for F3. However, for D-glucose the binding is enhanced 2-fold from 44±3 dm 3 mol -1 for F0 to 103±3 dm 3 mol -1 for F3. 14 The proportional decrease of the ECL readout signal with the Dglucose concentration allowed for facile quantification. Finally, the correlation of the ECL variation with the current for E3 confirmed that the oxidation step of the coreactant is the one determining the efficiency of the ECL process. ECL peak / a.u.

[saccharide] / mM In summary, we have developed a saccharide selective electrogenerated chemiluminescence (ECL) system that functions in aqueous media. To our knowledge this is the first report of a sensing strategy based on the recognition of the target analyte by the ECL coreactant which directly impacts the CL readout. We achieved excellent D-glucose selectivity by varying the linker length of a bis-boronic acid amine coreactant. Our approach allows manipulating the ECL readout signal with an additional parameter and not by playing only with the structure of the luminophore and the electrode potential. The simplicity of the system ensures that it will find many applications from biological and chemical sensing to incorporation in molecular logic circuits. HL and ML acknowledge the China Scholarship Council for their PhD scholarships. ACS thanks the EPSRC for a Studentship and RARB is grateful to the University of Bath faculty of science for a Scholarship. TDJ wishes to thank the University of Bath for support and the University of Bordeaux for an AMADEus invited Professorship.

Notes and references

Fig. 1

 1 Fig. 1 Influence of the binding equilibrium of phenylboronic acid to the saccharides (either D-fructose or D-glucose) on the ECL mechanism of the system Ru(bpy) 3 2+ /E0. Im + is the iminium product. [Under the measurement conditions the pinacol protecting group is removed.]

Fig. 2

 2 Fig. 2 Effect of D-glucose addition on electrochemical oxidation of E0 and on the corresponding ECL response. (a-b) Cyclic voltammetry and (c) ECL signal of a PBS solution (pH 7.4) containing 10 µM Ru(bpy) 3 2+ , 0.2 mM E0 and different concentrations of Dglucose. The arrow indicates increasing concentrations of D-glucose (0, 0.5, 1, 10, 50, 100 and 200 mM). Experiments were performed on glassy carbon (GC) electrode at a scan rate of 0.1 V s -1 .

4 |

 4 J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx

Fig. 4

 4 Fig. 4 Effect of (a-b) D-glucose or (c-d) D-fructose addition on electrochemical oxidation of E3 and on the corresponding ECL responses. Cyclic voltammograms and ECL signals of a PBS solution (pH 7.4) containing 10 µM Ru(bpy) 3 2+ , 0.1 mM E3 and different concentrations of D-glucose or of D-fructose. The arrow indicates increasing concentrations of D-glucose or of D-fructose (0, 0.5, 1, 10 and 50 mM). Experiments were performed on glassy carbon (GC) electrode at a scan rate of 0.1 V s -1 .

Fig. 5

 5 Fig. 5 Variation of the ECL peak intensity for the system Ru(bpy) 3 2+ /E3 as a function of the concentration of D-glucose or of D-fructose.

Bath data archive at http://


Mathilde Perray

Lucas Riegel

Djenebou Traore

Daniela Rojas Castro

Bruno Spire

Marion Mora

Adam Yattassaye

Marie Préau

The role of interpreter during qualitative data set collection in the context of the evaluation of the Gundo-So program

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

• The Gundo-So program is an intervention that aims to empower Malian women living with HIV (WLHIV) through supporting them in their decision-making process to disclose their serological status or not. She played a role in the meaning she communicated to the researchers of participants' discourses. She translates and adapted the questions to be understand Interpreters plays a key role in the comprehension and interpretation of patients' discourses. They are necessary in some contexts. They are also an advantage, as they bring greater cultural awareness and therefore greater understanding of the different issues at stake on the ground.  But they may be perceived as bringing bias to scientific studies. Acknowledgements :

To our interpreter Niakha Sissoko and all the Arcad Sida Santé plus's team.

She also proved to be a source of new information. In particular, she enhanced some participant responses with explanations about Malian cultural traditions, and changed some words to improve comprehension.

She was also sources of some bias during the interviews : asked some questions, guided the answer etc. She omitted or summarized some information depending on what she felt was important or not to communicate.

The interpreter's work filled different functions during the interviews:

Methods Context

Results

Conclusion

  The role of interpreter during qualitative data set collection in the context of the evaluation of the Gundo-So program Perray, M. 1 , Traore, D. 2 ,Riegel, L., 3 Rojas Castro,D. 3,4 ,Spire, B. 4 , Mora, M. 4 ,Yattassaye, A. 2 , Préau, M. 1 1 GRePS, Lyon 2 University, Lyon, France; 2 ARCAD Santé Plus, Bamako, Mali; 3 Laboratoire de recherche communautaire, Coalition PLUS, Paris, France; 4 Aix Marseille Université, Inserm, IRD, SESSTIM, Marseille, France mathilde.perray@univ-lyon2.fr