Noe Gaumont
email: noe.gaumont@lip6.fr

Clémence Magnien

Matthieu Latapy

Noé Gaumont

N Gaumont

Finding remarkably dense sequences of contacts in link streams

Keywords: stream, temporal network, density, face-to-face interaction, dense subgraphs

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Introduction

In this paper, we deal with link streams, i.e. sequences of quadruplets (b, e, u, v) meaning that a link exists between u and v from time b to time e. Link streams model many realworld situations like contacts between individuals, connections between devices, and others [START_REF] Casteigts | Time-varying graphs and dynamic networks[END_REF][START_REF] Cazabet | Detection of Overlapping Communities in Dynamical Social Networks[END_REF][START_REF] Holme | Modern temporal network theory: a colloquium[END_REF][START_REF] Holme | Temporal Networks. Understanding Complex Systems[END_REF][START_REF] Saramäki | From seconds to months: an overview of multi-scale dynamics of mobile telephone calls[END_REF]]. An illustration is given in Figure 1.

The problem of finding dense sub graphs has been extensively studied in the static case. Indeed, detecting cliques and dense groups [START_REF] Balalau | Finding Subgraphs with Maximum Total Density and Limited Overlap[END_REF][START_REF] Samudrala | A graph-theoretic algorithm for comparative modeling of protein structure[END_REF] allows finding particularly important sets of nodes in graphs. Some community detection methods [START_REF] Ahn | Link communities reveal multiscale complexity in networks[END_REF][START_REF] Falkowski | DENGRAPH: A density-based community detection algorithm[END_REF] also use density in order to obtain a high level description of a graph.

The notion of density has been extended to link streams and has been used to study complex networks [START_REF] Gaumont | Analysis of the temporal and structural features of threads in a mailing-list[END_REF]. It measures to which extent all pairs of nodes are connected all the time. We use this density measure to find relevant groups. This makes it possible to characterize partially the link stream by highlighting the most relevant groups of links.

Such groups should have a high density but this is not sufficient. Above all, they should have a density that is higher than their neighbour groups because, just like in graphs, the value of density in itself is not sufficient to evaluate a group. Therefore, a group is meaningful if it has a higher density than its neighbourhood, both structurally and temporally. For example, a group which has a low density may be considered relevant if the neighbouring link stream is empty. Conversely, a dense group may be considered irrelevant if it is included in a larger dense group. An example of which groups should be captured is given in Figure 1.

In order to find relevant groups, we proceed as follows:

-We build a projection of the link stream into a graph where each link is mapped to a node in the graph; -We apply a community detection algorithm on the projection and obtain a partition of links in the link stream; -From the resulting partition, we keep only the relevant groups, i.e. the ones which are denser than their neighbourhood and are large enough; we feel that very small groups have limited interest in terms of description of the link stream.

To prove the efficiency of the process, we apply our method on several real world networks and we argue that the groups Fig. 1: Example of a link stream. The nodes are on the vertical axis and time is on the horizontal axis. In the example, there is a link between nodes d and f from time 1 to 2. Three dense groups of links are identified by colour (red, green or blue).

found are meaningful and could not have been retrieved by static approaches. The remainder of this paper is organized as follows. The decomposition and validation method are explained in Section 2. The data sets we use and the associated results are presented in Section 3 and 4. In Section 5, the state-of-theart in dense groups detection is described and then we conclude and draw some perspectives in Section 6.

Method

Our method uncovers meaningful groups of links in a link stream. To this end, we first compute a link partition of the link stream. Then, we propose several criteria to evaluate each group of the partition and retrieve the most meaningful ones.

Definitions and notations

A link stream is defined as a triplet: L = (T,V, E), where T = [α, ω] is a time interval, V a set of nodes and E ⊆ T × T × V × V a set of links. Links of E are quadruplets (b, e, u, v), meaning that the pair (u, v) is continuously linked in the time interval [b, e] ⊆ [α, ω].

If, for all (b, e, u, v) ∈ E, u = v and for all (b, e, u, v) ∈ E and (b , e , u, v) ∈ E, [b, e] ∩ [b , e ] = / 0, then L is simple. In the following, L will always be considered to be simple. Also, we do not consider link orientation, i.e. (b, e, u, v) and (b, e, v, u) are equivalent.

An extension of the density notion to link streams has been proposed by Viard et al. [START_REF] Viard | Identifying roles in an IP network with temporal and structural density[END_REF], in the case where b = e. It measures to which extent all pairs of nodes are connected all the time. We adapt it to the general case of links with durations. The density of a set of nodes, V ⊆ V , in a time interval [t,t + δ ], is expressed as follows:

d(V ,t, δ ) = 1 |V | • (|V | -1) ∑ (u,v)∈V ×V , u =v τ t,δ (u, v) δ , (1)
where Notice that this is a natural extension of density because if all existing links in V ×V last for the whole time interval [t,t + δ ], i.e. ∀u, v ∈ V τ t,δ (u, v) = δ , then static and temporal densities are equal.

τ t,δ (u, v) = ∑ (b,e,u,v)∈E |[b, e] ∩ [t,t + δ ]|
In a graph, the density is the probability that two randomly chosen nodes are linked together. In a link stream, the density in a given time interval is the probability that two randomly chosen nodes are linked together at a randomly chosen time. Both densities have values in [0, 1]. For example in Figure 1, nodes a, b, c, d and e in the time interval [START_REF] Cazabet | Detection of Overlapping Communities in Dynamical Social Networks[END_REF][START_REF] Eagle | Inferring Social Network Structure using Mobile Phone Data[END_REF] have a density of 0.05 because this node set is poorly connected in this time interval. On the other hand, the same node set in the time interval [0, 1.5] has a much higher density because it is much more connected.

As in the case of graphs, density in link stream is very sensitive to the node set size. For example in Figure 1, d(V \ {a}, 8, 2) is much denser than d(V, 8, 2). Furthermore, the duration δ also has a huge impact on the density. If the duration is expanded and no additional link occurs, then the density decreases quickly, e.g. d({e, f }, 2, 2) is denser than d({e, f }, 2, 3) in Figure 1.

This definition holds for a group of nodes in a time interval. For a given group of links E ⊂ E, let α(E ) = min (b,e,u,v)∈E (b) and ω(E ) = max (b,e,u,v)∈E (e) denote respectively the beginning and the end of E and δ E = ω(E )α(E ) denote its duration. The density of E is then the density of the induced nodes

V E = {u, ∃(b, e, u, v) ∈ E } in the time interval [α(E ), ω(E )]: d(E ) = d(V E , α(E ), δ E ). (2)
With this formulation, all links in E are considered in the computation of the density. However, other links might also contribute to the density. For instance in Figure 1 the density of plain black links is computed, all nodes are induced by those links, thus V = V , the beginning equals 2 and the duration equals 9. Therefore in the computation of d(V, 2, 9), all black links are considered but red and blue links are also taken into account.

Discovering candidate groups of links

We propose a transformation of a link stream into an unweighted undirected graph that we call the link graph. Each link in the link stream is represented by a node in the link graph. Two different links (b, e, u, v) and (b , e , u , v ) are connected in the link graph if they share a node and if their time intervals are overlapping, i.e. {u, v} ∩ {u , v } = / 0 and [b, e] ∩ [b , e ] = / 0, see Figure 2. Therefore, a link in the link graph represents both a temporal and structural connection between two links in the link stream. We tested a variation with a weighted link graph where the weight is equal to the duration of the time intersection. However, the results are very similar to the unweighted version and therefore omitted.

Dense groups in the link graph therefore represent groups of closely interconnected links in the link stream, both structurally and temporally. To detect those groups, we apply one of the most used methods to detect communities: the Louvain method 1 [START_REF] Blondel | Fast unfolding of communities in large networks[END_REF]. The output of the algorithm is a partition where each community is a candidate relevant group of links. However, there are several reasons why some candidates may not be relevant. First, the candidates uncovered by community detection method usually have heterogeneous sizes and some are very small. As we do not consider very small candidates as relevant, we discard them. Second, as the Louvain algorithm greedily optimizes the modularity in the link graph, the partition in the link stream might also contain candidates which are irrelevant in a link stream context. For example in Figure 1, the links in the time interval [START_REF] Bogdanov | Mining Heavy Subgraphs in Time-Evolving Networks[END_REF][START_REF] Eagle | Inferring Social Network Structure using Mobile Phone Data[END_REF] form a connected component in the link graph and are considered as a community by the Louvain method. However, this candidate should not be considered as relevant because it is less dense than the links in [0, 4] or even [START_REF] Crofoot | Data from: Shared decision-making drives collective movement in wild baboons[END_REF][START_REF] Falkowski | Community dynamics mining[END_REF]. 1 Other community detection methods can be applied.

Therefore, we need a method to validate or discard each candidate.

Selecting relevant candidates

Density in itself is not sufficient to evaluate a candidate's relevance. Indeed, the optimum value is trivially obtained for a group of two nodes in the time interval when a link between them exists. This is why we consider as relevant the candidates which are denser than their neighbourhoods in the link stream. To define neighbourhoods, we observe that the density, defined by Eq. 1, depends on three aspects: the group of nodes V , the start time t and the duration δ . To take into account these three aspects, we consider groups which differ from the considered candidate in only one of these aspects, which we call neighbour groups. We propose to evaluate the relevance of a candidate by comparing its density to that of the corresponding three kinds of neighbours. The higher its density is compared to the one of its neighbour groups, the better the candidate is.

Neighbourhood definition

For the start time (resp. duration) aspect, we consider all possible values of start time (resp. duration) in a given interval. Each of these values defines neighbour groups with the same set of nodes, duration (resp. start time) as the candidate group and with the considered start time (resp. duration). We then compute the resulting density values of these neighbours by varying the start time (resp. duration) in a continuous fashion. Let I and I be intervals and L ⊆ E be a candidate. The density values of its start time neighbours are thus defined by d(V L , y, δ L ) with y ∈ I. The density values of its duration neighbours are defined by d(V L , α(L), z) with z ∈ I .

The interval considered is [α, ωδ L ] for the start time aspect. For the duration aspect, the interval considered is [0.8 δ min , 1.2 δ max ], where δ min (resp. δ max ), is the smallest (resp. largest) candidate duration in the partition. We use this interval for two reasons. First, it contains all reasonable durations when applied to our data sets. Second, we also tested the interval [1, ωα] which is much larger. It changes the evaluation quantitatively but not qualitatively. Indeed, groups with a duration of ωα have a density close to zero and therefore are always less relevant than candidate groups.

For the nodes aspect, it is impossible to consider all possible node sets as there are too many of them: 2 |V | . Moreover, most of the node sets will mostly be disconnected if the link stream is sparse. Therefore, if V L contains k nodes, then we consider all the sets of nodes of size k which share k -1 nodes with V L . Therefore, only similar groups are taken into account. This comparison is therefore stricter but also fairer than the one to all sets of nodes or to randomly chosen set of nodes. A lower number of shared nodes could be used but was not considered because of computational tractability. Indeed, there are already k(|V |k) set of nodes considered for a single candidate with our current method. We end up for each aspect with several density values. For the node aspect, we have k(|V |k) density values. For the start time (resp. duration) aspect, we have a function of the start time (resp. duration) to density.

Score definition

We evaluate a candidate by comparing its density to the density values in each aspect. If a candidate is truly meaningful, then it should have a higher density than most values in each aspect. From experiments, the density values do not seem to follow the same probability density function for all candidates. As an illustration, Figure 3 presents the cumulative distribution of the density for the duration aspect for 3 candidates in the Socio Pattern data set and 3 in the Rollernet data set (these data sets are described in Section 3). If they were following, for instance, a normal law, we could have computed the z-score to check if candidates have a density significantly larger than expected. Here the distributions do not seem to follow a common law. Hence, we use percentiles that quantify what fraction of the values are smaller than the considered candidate's density. For the node aspect which is represented by a set of density values S, the score of a given candidate L is:

p node (L) = ∑ d i ∈S 1 d i <d(L) |S| , ( 3
)
where 1 is the indicator function. For the start time and duration aspects which are represented by functions, the scores p t and p δ of a given candidate L are:

p t (L) = 1 ω -δ L -α ω-δ L α 1 d(V L ,z,δ L )<d(L) dz , (4)
p δ (L) = 1 1.2δ max -0.8δ min 1.2δ max 0.8δ min 1 d(V L ,α(L),z)<d(L) dz . (5)
A low score means that the candidate's density is smaller than most densities in the aspect and for this reason the candidate should be discarded.

To sum up, a candidate is evaluated by a triplet consisting of its score for each aspect, and should be discarded if one of them is low, i.e lower than a given threshold. The definition of what is a low value is non-trivial and depends on the purpose of the study and the characteristics of the link stream. For these reasons, we set no a priori thresholds and instead choose them a posteriori based on the observations made on the studied data set, as described in Section 4.

Data sets

We apply our method on four data sets. Table 1 lists the number of nodes (|V |), the number of links (|E|) and the duration (ωα) of each data set.

Socio Pattern [START_REF] Fournet | Contact patterns among high school students[END_REF] 2 contains the temporal network of contacts between students in a high school in Marseilles, France. It gives the contacts between 180 students of 5 classes during 9 days (from a Monday to the Tuesday of the following week) in Nov. 2012. The class of each student is known.

Rollernet [START_REF] Tournoux | The Accordion Phenomenon: Analysis, Characterization, and Impact on DTN Routing[END_REF] was collected during a rollerblade tour in Paris in August 2006. The tour is a weekly event and gathers approximately 2500 participants. Among these, 62 were equipped with wireless sensors recording when they are at a communication distance from one another. The data set therefore contains the proximity links between the persons carrying the sensors. We know the role of each person, e.g. staff member at the front or association member.

Reality Mining [START_REF] Eagle | Inferring Social Network Structure using Mobile Phone Data[END_REF] contains the temporal network of contacts between 94 persons at the MIT Media Laboratory between September 2004 and June 2005. Of these 94 subjects, 68 were colleagues working in the same building on campus (90% graduate students, 10% staff) while the remaining 26 subjects were incoming students at the university's business school. These data set was recorded by Bluetooth on loaned mobile phones.

Baboon [START_REF] Crofoot | Data from: Shared decision-making drives collective movement in wild baboons[END_REF][START_REF] Strandburg-Peshkin | Shared decision-making drives collective movement in wild baboons[END_REF] contains the position of 28 wild olive baboons (Papio anubis) at Mpala Research Centre in Kenya between 5 a.m. and 5 p.m. during 2 weeks. These 28 baboons represent around 80% of a troop. Each baboon was fitted with a custom-designed GPS collar that recorded its location every second. We transform this data into a link stream by creating a link between two baboons when the distance separating them is less than 1.5 meter and make each link last at least 10 seconds to smooth potential GPS inaccuracy.

Even if all these data sets are face-to-face interactions networks, they are quite different in their dynamics. For example, the Rollernet data set has roughly the same number of links as Socio Pattern but it lasts only 3 hours compared to 9 days for Socio Pattern. To visualize the data sets' sparse temporal dimension, the number of active links in time are plotted in Figure 4 for the Socio Pattern data set. As there are at most 40 links present at the same time between the 180 students, a graph representing a network at a specific time is mostly empty. The figures for the other data sets are in appendix ( Figures 12,17 and 22). They also present a very sparse temporal dimension.

Results

For each data set, we apply our method to uncover relevant groups of contacts. As presented in Section 2, the first step is to uncover a partition P of links. The basic statistics of each found partition such as the number of candidates |P|, the median number of links |L| , and the median node size |V | are listed in Table 2. The first striking fact in this table is that there are a lot of candidates in the partitions and most of them are very small in terms of number of links and nodes. There are however larger candidates in the Rollernet data set. This difference might be caused by the short link streams duration -3 hours compared to several days -and the high number of links which makes the link stream denser than other data sets. In order to get a more precise picture of the Socio Pattern data set, the inverse cumulative distributions of the number of nodes, the number of links, durations and density are presented in Figure 5. The distributions are all heterogeneous, except for the density distribution. The steps observed for the density are caused by small candidates; typically a group with 2 links between 3 nodes will have a density of 0.33 and candidates with 1 link3 will have a density of 1. The figures for the other data sets are in appendix (Figures 13, 18 and 23). For those data sets, we also observe heterogeneous distributions for the number of links, the number of nodes and the duration and steps in the density distribution.

As small candidates have a very limited interest in terms of description of link streams, we begin by discarding groups having less than 10 links. This leaves us with many candidates in all data sets, and we need to distinguish the relevant ones from the others.

Groups validation

To separate relevant candidates from others in the partition, we set thresholds on the scores. A candidate is considered as relevant if all its scores are above the thresholds. Notice that decreasing the thresholds will increase the number of candidates kept without removing any candidates previously kept. Therefore, the thresholds can be chosen a posteriori. As we do not have any knowledge for the thresholds selection, we 0 .9 9 7 0 0 .9 9 7 5 0 .9 9 8 0 0 .9 9 8 5 0 .9 9 9 0 0 .9 Inv. cdf (b) Duration: p δ 0 .9 6 5 0 .9 7 0 0 .9 7 5 0 .9 8 0 0 .9 8 5 0 .9 9 0 0 .9 [START_REF] Epasto | Efficient Densest Subgraph Computation in Evolving Graphs[END_REF] study the inverse cumulative distribution of scores for each aspect to fix these thresholds. They are presented for the Socio Pattern data set in Figure 6 (a-c). For this data set, the vast majority of scores are very high, i.e. close to 1, regardless of the aspect. We also observe for each aspect a sharp bend in the inverse cumulative distribution of score and use the corresponding value as threshold. We use for the start time, duration and node aspect the following values: 0.998, 0.85 and 0.98. For other data sets see Figures 15,20 and 25 in appendix; the scores are similar except for the Rollernet data set which has lower scores, which may be caused by the denser underlying link stream. Finally, Table 3 gives the threshold we used for each aspect and data set.

A candidate is discarded when at least one score is below the corresponding threshold. Therefore, we study if the aspects discard different candidates. The correlation between start time and duration scores is plotted in Figure 6 (d). Both aspects discard different candidates and therefore are not redundant. The same observation holds with the node aspect and for other data sets (see Figures 15 (d We present a manual analysis for two candidates captured in the Socio Pattern and Rollernet data sets respectively, thus illustrating the notions of scores defined in Section 2 and showing the relevance of the method. We chose these candidates for manual checking because their respective data sets contain information on either the participants or the usual schedule, which helps in evaluating the relevance of groups.

In the Socio Pattern data set, we know the participants' class; we also know when the lectures start in the morning and, when the breaks happen. The group we consider con- tains 50 links, 17 nodes and lasts for almost 15 minutes and is one of the largest candidates. As this group starts at 7:44 am, this is likely a group of friends gathering before the first lecture of the day which takes place at 8:00 am. Moreover, all of them except one are in the same class, thus making the possibility of a small class gathering even more likely. This simple qualitative evaluation is a first step but we might have missed a bigger structure. The underlying gathering behind this group of links might have started earlier, lasted longer or even impact other persons. As for all candidates, we have computed its score for each aspect.

Node aspect. For this aspect, the group has a score of 0.98. This means that of all adjacent node sets, the group has almost the highest density and therefore we are sure that this specific node set is indeed important at this period.

Start time aspect. For this aspect, the function start time to density is presented in Figure 7 (a). The circadian cycle is clearly visible along with the week-end. Moreover the group, with a density of 0.04, is denser than all its neighbours for the start time aspect. Therefore the group has a score of 1 which indicates that the start time of the group is relevant.

Duration aspect. For this final aspect, the group has a score of 0.98 which means that the group has also almost the best duration. The function duration to density is presented in Figure 7 (b). The group density is a bit higher if a shorter duration is considered, which is not unexpected because the duration affects the density. Moreover, this is still a very high score because a broad interval of durations is considered in the duration aspect, including durations that do not correspond exactly to any group of links. Indeed, for a given node set V , duration δ and start time t, some links may be only partially considered, i.e. ∃u, v ∈ V , (b, e, u, v)

∈ E s.t. 0 < |[b, e] ∩ [t,t + δ ]| ≤ |[b, e]|.
In this case, the neighbour groups considered cannot be recovered by a group of links, and their density is not reachable by a group of links. Therefore, a group of links with a perfect score of 1 would be very surprising. Notice that even when increasing the interval for the considered values of duration and exploring d(V L , y, z) for y ∈ [α; ωδ L ] and z ∈ [0.8g min ; 1.2g max ], the candidate is still often the best. This emphasizes even more greatly the peculiarity of this candidate.

In the Rollernet data set, we know the role of some participants (staff member, a group of friends, ...). The group we consider contains 38 links, 9 nodes and lasts for almost 5 minutes. The start time is just at the beginning of the roller tour and 8 of the group members are labelled as staff members that should be at the rear of the tour. The last member is labelled as a front member. This group might indicate a quick talk before the beginning of the tour. Again we computed its score for each aspect.

Node aspect. For this aspect, the group has a score of 0.99 which highlights the relevance of the node set at this start time and for this duration.

Start time aspect. For this aspect, the group has a score of 0.85, see Figure 8 (a). As the Rollernet data set is denser than the other data sets, the function start time to density is more stable and other start times achieved higher density. However the group still captures a local maxima of density.

Duration aspect. For this aspect, the group has a score of 0.86 for the duration aspect, see Figure 8 (b).

Even if these scores are not optimal, they are above the thresholds and this is why the group is considered as relevant.

Altogether, there are 136 groups considered as relevant from the 12532 in the Socio Pattern data set. These groups are selected because they have a high score. Most of them have scores that are close but no equal to 1 meaning that some neighbours are still denser. Finally for each aspect, we check how far the group density is from the maximum density. The group density is, for 75% of all groups, on average only 20% smaller than the maximum density in the aspect. Therefore, groups are dense parts of the link stream and have a density close to the maximal density.

Finally, the execution time for each data set is presented in Table 3. The code has been run on a laptop with 8 Go of RAM and an Intel core-i7 processor without any parallelization. The code in C + + to compute the scores is available online 4 . In order to study to which extent the detected groups offer a global description for the data set, we now study how they cover the nodes and the time interval of the link stream.

Concerning node coverage, the distribution of the number of groups per node for the Socio Pattern data set is shown in Figure 10. Notice that all the nodes are in at least one group while some nodes belong to more than 20 groups. With an average of 7.4 groups per node, the uncovered groups form a highly overlapping cover. For other data sets, see Figures 14,19 and 24. For all data sets, we found that the structure is highly overlapping, especially for the baboon data set; this is because a lot of groups are captured for only 28 nodes in the link stream. One could argue that this structure could also have been obtained by a method computing overlapping communities in a graph. To check this, we construct the aggregated graph G = (V, E ) of L = (T,V, E) such that there is an edge (u, v) ∈ E in G if and only if ∃(b, e, u, v) ∈ E. The edge weight is the sum of the durations of each corresponding link in the link stream. We test the bigclam method proposed by Yang et. al [START_REF] Yang | Overlapping community detection at scale[END_REF] which captures overlapping groups of nodes in a graph. This method considers only unweighted static graphs. Since edge weights are heterogeneous, we need to find a way to take them into account. As no natural weight separation appears in the link's weight distribution, we use a simple rule such that an edge is present in the unweighted graph if it has a weight strictly greater than at least λ % links, λ being a given threshold. Thus even if the graph is unweighted, we still keep some weight information. We then use the Jaccard index to compare the nodes of a community found by bigclam and the nodes induced by a group uncovered by our method in the original link stream. For each group L captured and its induced nodes V L , we com-

λ = 0.05 λ = 0.1 λ = 0.2 λ = 0.3 λ = 0.5 λ = 0.
pute J(L) = max C∈C |C ∩V L | |C ∪V L |
, the maximum Jaccard index among all communities C ∈ C found by bigclam. Table 4 presents the median and maximum Jaccard indexes of J(L) for different data sets and thresholds λ . According to this table, uncovered groups and communities found by bigclam are different (the median Jaccard index is low). Some groups are nevertheless present in both structures as reflected by a high maximum Jaccard index. This happens in the Rollernet and Baboons data sets for only very few groups and specific link removal thresholds. These high Jaccard indexes might by correlated to the high number of uncovered groups for these data sets because more uncovered groups induce a higher probability to find a matching community.

Overall, our method has highlighted groups of nodes which would not have been uncovered by this static method.

For the temporal aspect, we also look for the time overlap of groups. We compute the time proportion where no captured group is present. For all data sets except the Rollernet data set, there is no group present between 82% and 95% of the time. For Rollernet, this proportion drops to 15%. This difference is likely caused by the very short duration of the link stream. Indeed, the Socio Pattern, Reality Mining and Baboons data sets span nights, during which activity is lower.

While most of the time there is no active group in the link stream, at some times several groups are active at once. This result is very different from the structural aspect. Indeed, the groups form a cover of nodes but they are covering only a small fraction of the time. In the Socio Pattern data set, the groups are typically before the first lecture, during the breaks and lunch, and after the last lecture. Therefore, our method is able to recover important time intervals in link streams, which further show its relevance. Notice however that isolating important time intervals could be done in a simpler way, by observing the activity. To illustrate this, the number of active groups over time is presented in

Related Work

In recent years, significant efforts have been devoted to finding subgraphs in a temporal context. Subgraphs have mainly been studied in two ways: either as communities in graph snapshots or as dense sub-parts in evolving networks. These approaches are related but not equivalent. The former finds a whole partition of a network while the latter captures a single group. As they optimize different metrics and respect different constraints, it is difficult to compare the two approaches. See for instance these surveys and the references therein [START_REF] Falkowski | Community dynamics mining[END_REF][START_REF] Hartmann | Clustering evolving networks[END_REF][START_REF] Wang | Communities in evolving networks: definitions, detection and analysis techniques[END_REF] that describe community detection methods in graph snapshots. The results of these methods are partitions of nodes for each snapshot. In most of them, a group of nodes in a specific snapshot is tracked in the next snapshot to follow its evolution. These methods suffer from instability between two snapshots and from the construction of the snapshot in which some information is lost. For example, a group of nodes in a snapshot could be mistakenly captured because the aggregation method makes it seem like a relevant group. Symmetrically, a relevant group in the link stream could be ignored if it is split between two snapshots.

Several models keeping all the temporal information have been proposed and used in different contexts to gain meaningful insights. For example, the methods in [START_REF] Mitra | Intrinsically dynamic network communities[END_REF][START_REF] Speidel | Community detection in directed acyclic graphs[END_REF] aim at detecting communities in diachronic networks, i.e. links extremities are associated with possibly distinct timestamps. A diachronic network is modelled as a graph, G = (V, E), defined upon a set of time-labelled nodes, V = {(u i ,t i )}, and a set of links, E = {((u i ,t i ), (u j ,t j ))}. This accurately models citation networks where an author A publishing a paper at time t 1 is represented by the node (A,t 1 ). The link ((A,t 1 ), (B,t 2 )) exists if B has published a paper at time t 2 in which the paper from A published at time t 1 is cited. Thus, the link ((A,t 1 ), (B,t 2 )) in the diachronic network has a different meaning than the link (t 1 ,t 2 , A, B) in a link stream and both models represent intrinsically different objects.

The problem of finding the densest sub-part in evolving networks and temporal networks has also been studied. The method in [START_REF] Bogdanov | Mining Heavy Subgraphs in Time-Evolving Networks[END_REF] considers graphs where the weights on the edges vary between -1 and 1, which is rather different from link streams. Also, it recovers a subset of nodes on a time interval such that it maximizes the sum of the weight. Thus, some temporal information is lost because of the time aggregation.

Epasto et al. [START_REF] Epasto | Efficient Densest Subgraph Computation in Evolving Graphs[END_REF] recover the densest sub-graph in evolving networks. An evolving network is a network that changes according to a sequence of updates, namely edge additions or removals. It maintains at each time a single group of nodes which maximizes the average degree at this specific time. Therefore, the method is relevant only when a relevant network structure exists after each update, which is not necessarily the case for link streams, as we have seen.

Rozenshtein et al. [START_REF] Rozenshtein | Discovering Dynamic Communities in Interaction Networks[END_REF] designed a method to find the densest sub-graph in temporal networks. The method captures a group of nodes and potentially several time intervals. The maximum number of time intervals and the maximum sum of the duration of time intervals are parameters of the method, thus the results are very dependent on the parameter choice. Also, the notion of density used is the average degree in the graph aggregated over the chosen time intervals and therefore some temporal information is lost.

Viard et al. [START_REF] Viard | Computing maximal cliques in link streams[END_REF] consider link streams where links do not have durations and use a similar notion of density relying on a parameter, ∆ , emulating link duration. With this notion of density, they define maximal ∆ -cliques (in terms of nodes or time interval) as sets of nodes having a ∆ -density of one in a given time interval. ∆ -cliques are a great way to decompose a link stream. However, the ∆ -cliques are typically very small in size and duration. On the the Socio Pattern data, the interactions are captured with a time precision of 20 seconds therefore, when ∆ equals to 20 seconds, ∆ -density and density are equal. With ∆ = 20s, the biggest ∆ -cliques contains only 5 nodes and 10 links. As the relevant groups can have any density (see Figure 9(b)), we are able to detect bigger groups and build more coarse description of link streams.

Sekara et al. [START_REF] Sekara | Fundamental structures of dynamic social networks[END_REF] study a rich data set of approximately 1000 students during 36 months at a large European university. They use the temporal network of face-to-face interactions measured via Bluetooth. They study gatherings which are represented by sets of nodes and time intervals. Gatherings are captured by first transforming the temporal network into snapshots of small duration and computing the connected components in each snapshot. A gathering is then a matching of connected components across snapshots using a hierarchical clustering based on the Jaccard index [START_REF] Greene | Tracking the Evolution of Communities in Dynamic Social Networks[END_REF]. In the method, a gathering is considered only if it lasts at least 20 minutes. The definition of gathering relies on three intricate parameters which are set a priori: the snapshots duration, a threshold for connected component matching and the minimum duration of each gathering. Moreover, the notion of gathering is defined specifically to detect meeting of students, which explains the high minimum duration. Our method is able to detect groups of diverse durations (see Figure 9(a)).

To sum up, some methods [START_REF] Bogdanov | Mining Heavy Subgraphs in Time-Evolving Networks[END_REF][START_REF] Epasto | Efficient Densest Subgraph Computation in Evolving Graphs[END_REF][START_REF] Rozenshtein | Discovering Dynamic Communities in Interaction Networks[END_REF] seek the densest node set in evolving networks. However, the criteria they use do not take time into account as they rely on classical graph metrics which might not be relevant for temporally sparse data sets. Also, they recover only the densest node set while we uncover several groups of links.

Other methods [START_REF] Sekara | Fundamental structures of dynamic social networks[END_REF][START_REF] Viard | Computing maximal cliques in link streams[END_REF] detect node sets during time intervals in link stream. However, the groups uncovered with these methods have strict characteristics tailored to the object of study: cliques or long duration. Our method is able to detect more diverse groups. Finally, our method can be tuned by parameters set a posteriori.

Conclusion

In this paper, we consider the problem of uncovering dense groups in link streams where each link has a duration. As opposed to some existing methods, we take full advantage of the temporal information thanks to the link stream formalism which does not use any aggregation. This shift is important as it eases the definition of algorithms and metrics that mix structural and temporal information. The extension of density for link streams that we propose is such an example. Moreover, we do not consider a group as a combination of a node set and a time interval but simply as a group of links existing for a given time interval.

To uncover dense groups of links, we propose a method that first transforms a link stream into a static, unweighted and undirected graph where links of the link stream become nodes in the graph. Two nodes in the graph are connected if there is a temporal and a structural connection between the corresponding links in the link stream. Thus looking for communities in the graph is a way to find a set of candidate groups. To do this, we use an existing community detection method, namely the Louvain method.

To assess the relevance of the candidates in the found partition of links, we propose to study several aspects. Each aspect defines and builds neighbour groups from a given candidate in the time or topological dimension. We use each aspect to compute a score that compares the candidate density to neighbourhood densities. Once the scores of each candidate are computed, the relevant ones are the one having scores above thresholds that are set a posteriori using the scores distributions. Changing the thresholds does not interfere in the set of candidate but on the candidates selection.

We apply our detection method to 4 real world data sets. All of them are face-to-face interaction networks. However, they come from drastically different contexts. Two of them are networks of students, one is a network of roller blade tour participants in Paris and the last one is a network of baboons in wild life. Also, the duration of each data set is drastically different: from a few hours to several months. In all data sets, we find groups having a very high density compared to their neighbour groups.

There is no known ground truth in the used data sets, however some metadata are known for two of them. In this way we are able to analyze manually some of the uncovered groups. We find that the groups correspond to relevant events in the data and they have empirical justification such as students gathering before the first class or for lunch. More generally, we also studied the distribution of groups in time and over the nodes. We find out that the groups are highly overlapping over the nodes but concern only a small fraction of time.

To test the novelty of our results, we apply a method that detect overlapping communities on static graphs: the bigclam method. We find that just very few groups were recovered by the bigclam method. Therefore by using time information, we are able to uncover new structures that might hardly be detected by a static method.

Perspectives

Our method relies on a static graph, a classical community detection algorithm, a minimum group size, and some thresholds set a posteriori. An automatic selection of the thresholds used is a promising direction, for example by detecting inflection points in the scores distributions. Classification methods could also be used on the groups based on their three scores. However, we need to apply this method in more diverse contexts to understand how reliable an automatic method could be.

It would also be interesting to detect relevant groups without relying on the transformation into a graph for two main reasons. First, the density in the link stream cannot be deduced from the static graph we created. Second, we might have missed groups by using the Louvain algorithm on the link graph.

Our method detects groups of links in link streams while the literature is mainly focused on community structure in graph snapshots. Communities in graph snapshots are related to dense groups, yet they are different. It would be interesting to study the interplay between the two objects. One way to do this could be to find appropriate time windows and build graph snapshots from link streams and then to use existing methods on the snapshots.

Finally, another promising direction is to build generative models of link streams with some constraints on density. This would be beneficial to test the accuracy of our method but also to design new algorithms applied to community detection in link streams. 0 .9 5 0 .9 6 0 .9 7 0 .9 8 0 . 0 .9 3 0 .9 4 0 .9 5 0 .9 6 0 .9 7 0 .9 8 0 .

Fig. 2 :

 2 Fig. 2: Transformation of a simple link stream with 4 nodes (a-d) and 6 links into its link graph.

Fig. 3 :

 3 Fig. 3: Cumulative distribution of density rescaled to [0, 1] in the duration aspect for several candidates. Full (resp. dashed) lines are candidates from the Rollernet (resp. Socio Pattern) data set.

Fig. 4 :

 4 Fig. 4: Number of active links (left axis) and average number of active links per node (right axis) as a function of time on the Socio Pattern data set.

Fig. 5 :

 5 Fig. 5: Inverse cumulative distributions of the number of links, nodes and duration (a) and density (b) for the candidates found by the Louvain method on the Socio Pattern data set.

  (d) Correlation between start time and duration aspects.

Fig. 6 :

 6 Fig. 6: Inverse cumulative distribution of scores for each aspect for the data set Socio Pattern.

  ), 20 (d) and 25 (d)).

Fig. 7 :

 7 Fig. 7: Plain lines: the function d(V L , z, δ L ) in (a) and d(V L , α(L), z) in (b) for a group L in the Socio Pattern data set. Dashed lines: density of L.

Fig. 8 :

 8 Fig. 8: Plain lines: the function d(V L , z, δ L ) in (a) and d(V L , α(L), z) in (b) for a group L in the Rollernet data set. Dashed lines: density of L.

Fig.Fig. 10 :

 10 Fig. Inverse cumulative distributions of the number of links, nodes and duration in (a) and density in (b) for the candidates captured by our method on the Socio Pattern data set.

  Figure 11 along with the number of links for the first day of the Socio Pattern data set.

Fig. 11 :

 11 Fig. 11: Number of active links (plain line) and number of active groups (red dashed line) as a function of time for the first day of the Socio Pattern data set.

Fig. 12 :Fig. 13 :

 1213 Fig. 12: Number of active links (left axis) and average number of active links per node (right axis) as a function of time on the Rollernet data set.

Fig. 15 :Fig.Fig. 17 :Fig. 18 :

 151718 Fig. 15: Inverse cumulative distribution of scores for each aspect for the data set Rollernet.

Fig. 19 :

 19 Fig. 19: Inverse cumulative distribution of the number of groups captured per node for the Baboon data set.

  Correlation between start time and duration aspects.

Fig. 20 :Fig. 21 :Fig. 22 :Fig. 23 :

 20212223 Fig. 20: Inverse cumulative distribution of scores for each aspect for the data set baboon.

Fig. 24 :

 24 Fig. 24: Inverse cumulative distribution of the number of groups captured per node for the Reality Mining data set.

  Correlation between start time and duration aspects.

Fig. 25 :Fig. 26 :

 2526 Fig. 25: Inverse cumulative distribution of scores for each aspect for the data set Reality Mining.

Table 1 :

 1 number of nodes |V |, number of links |E| and duration ωα for each data set.

		Data sets	|V |	|E|	ω -α
		Socio Pattern	180 19774	9 days
		Rollernet	62	15803	3 hours
		Reality Mining	94	44975 9 month
		Baboon		28	95616	14 days
	0 0 5 10 15 20 25 30 35 40 # links	2	4 Time in days 6	8	10 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 # links per node

Table 2 :

 2 Median of some characteristics for each data set partition. The value in parentheses corresponds to the value for candidates with at least 10 links only.

Table 3 :

 3 Threshold used, number of groups captured and execution time for each data set. p node ,p t ,p δ and N c are respectively the node aspect threshold, the start time aspect threshold, the duration aspect threshold and the number of group captured.

	Data sets	p node	p t	p δ	N c	execution
	Socio Pattern	0.98	0.998 0.85	136	2 min
	Rollernet	0.9	0.7	0.6	37	4 min
	Reality Mining	0.97	0.98	0.8	394	1h
	Baboon	0.95	0.99	0.85 1023	52 min
	4.2 Group characteristics
	To get a more precise picture for the groups captured, the
	inverse cumulative distributions of the number of nodes, the
	number of links, durations and density are presented in Fig-
	ure 9 for the Socio Pattern data set. The duration, node size
	and link size distributions are again heterogeneous. The fig-
	ures for the other data sets are in appendix (Figures 16,21
	and 26).

Table 4 :

 4 Median (and maximum) Jaccard index between the groups uncovered and the communities found by bigclam in the aggregated graph where a proportion of λ edges having the smallest weight have been removed. Values which are above 0.8 are in bold.

		10 0
	Inv. cdf	10 -1
			duration
			# nodes
		10 -2	# links
			10 1	10 2	10 3
				x

http://www.sociopatterns.org

Candidates with one link represent 83% of all candidates.

https://bitbucket.org/nGaumont/densityanalysis/

This research was supported by a DGA-MRIS scholarship, by a grant from the French program "PIA -Usages, services et contenus innovants" under grant number 018062-44430 and by the CODDDE project ANR-13-CORD-0017-01.


Zhenghong Gao

Juan A Varela

Laurent Groc

Brahim Lounis

Laurent Cognet
email: laurent.cognet@u-bordeaux.fr

Toward the suppression of cellular toxicity from single-walled carbon nanotubes

In the multidisciplinary fields of nanobiology and nanomedicine, single-walled carbon nanotubes (SWCNTs) have shown great promises due to their unique morphological, physical and chemical properties. However, understanding and suppressing their cellular toxicity is a mandatory step before promoting their biomedical applications. In the light of flourishing recent literature, we provide here an extensive review on SWCNT cellular toxicity and attempt to identify the key parameters to be considered in order to obtain SWCNT samples with minimal or no cellular toxicity.

Introduction

Over the past two decades, nanoscience and nanotechnology have been largely impacted by the development of carbon-based nanomaterials, such as fullerenes, 1 nanodiamonds, 2,3 graphene, 4 and carbon nanotubes. 5,6,7 Carbon nanotubes are attractive due to their outstanding electrical, 8 optical, 9 mechanical, 10 thermal properties. [START_REF] Jianwei | III[END_REF] Apart from applications in material science, electronics or photonics, 12 carbon nanotubes also have multiple promising applications in biomedicine, serving as biosensors, 13,14 bioprobes, 15,16 drug carriers, 17 photothermal therapy enhancers 18 and molecular imaging contrast agents. 19 SWCNTs distinguish themselves from double-walled carbon nanotubes 20 and multi-walled carbon nanotubes 5 by their single-layer cylindrical sidewall structure, provides them more finely tuned physical and chemical properties for applications as compared to other carbon structures. Due to their ultra-small diameter, high curvature and large surface area (1315 m 2 /g), 21 they possess highly reactive surfaces 22 and they can interact with biomolecules present in biological systems, like proteins, 23 DNA 24 and lipids 25 by weak interactions (e.g. van de Waals, π-stacking, hydrophobic interactions, and hydrogen bonds). Reactive surfaces of SWCNTs may offer vast opportunities for surface modification and have potential for a variety of applications. 26,27 Conversely, direct interactions of SWCNTs with biomolecules might make them deleterious to the integrity of cells and organs. In this regard, SWCNTs impact on human health is a rising concern within the scientific, industrial, and public communities. 28,29 Cell-based experiments are considered the preliminary test for assessing the biological safety of nanoparticles before practical applications in biology and medicine. Toxicity of nanoparticles to cells can be evaluated at different levels, ranging from evaluation of the plasma membrane integrity to the activation of late intracellular proteolytic cascades and DNA fragmentation. Typical tests include the examination of cell growth, cell viability, membrane permeability, mitochondrial activity, metabolic activity, oxidative stress, immune response, DNA fragmentation, DNA repairing enzymes cleavage, etc. Over the past years, a high number of studies have been performed to understand SWCNTs cellular toxicity. Many published results are however contradictory and the full knowledge concerning nanotube cellular toxicity remains to be established.

The purpose of this article is to review the current knowledge of SWCNTs cellular toxicity, which differs from that of their multiwall counterparts. Previous review articles 30 generally addressed the toxicity of carbon nanotubes regardless of their type (single versus multi walled). Our aim is to attempt to identify the critical parameters to be taken into account to understand and further minimize SWCNTs cellular toxicity. We will consider several aspects of SWCNT sample properties (see Figure 1); among them, nanotube synthesis and purification processes will first be discussed. Generally, as-produced SWCNT samples are a heterogeneous mixture of nanotubes with impurities (mainly metal catalysts and carbon by-products) 31 and multiple step post-synthesis purification procedures are commonly employed to remove such impurities. 32 In addition, SWCNTs do not consist of single molecular species, but instead different chiral angles and diameters provide them distinct molecular structures. This can induce specific species-related physical properties and (bio)chemical molecular affinities 33,34,35 which could further result in distinct cellular toxicity. [START_REF] Nilos | General, Applied and Systems Toxicology[END_REF][START_REF] Skandani | [END_REF] Vast improvements of sorting techniques have arisen over recent years, 38,39,40 which could greatly help in the understanding of SWCNT cellular toxicity. Furthermore, the strong inter-tube van de Waals interactions among pristine SWCNTs can be up to 500 eV/µm, 41,42 which renders pristine nanotubes insoluble in common physiological media. 43 In order to overcome this issue, nanotube encapsulation using amphiphilic molecular moieties (commonly called surfactants) is generally used to individualize and solubilize SWCNT in aqueous media. 43 Cellular toxicity arising from surfactants rather than nanotubes themselves must also be considered. An alternative route for solubilizing SWCNTs consists of functionalizing the nanotube surface, thus creating defects on the pristine SWCNT backbone structures. 44,45 The contribution of these functional groups on SWCNT cellular toxicity will also be discussed in this review.

Effect of Synthesis and Impurities

Several synthesis methods are commonly used for producing SWCNTs, such as chemical vapor deposition (CVD), 46 laser-ablation 47 and arc-discharge. 48 Different types of metal particles are used as catalysts in the synthesis formulations in order to reduce activation energy barriers of the chemical reaction and/or to control nanotube growth orientation.

The most commonly used metals are Fe, Ni, Co, Mo and Y, 49 which can therefore be present in as-produced nanotube samples. In addition, carbonaceous by-products may also be produced, such as nanocrystalline graphite, amorphous carbon, and fullerenes. 50 As a result, as-produced SWCNT samples not only contain nanotubes but also many impurities which depend on the synthesis formulations. Impurities can be embedded within the inner channels of nanotubes making them difficult to be removed completely (see Figure 2a andb). 51 They might therefore interfere with the pristine properties of SWCNTs and affect the interplay between nanotubes and cells. 52 Indeed, metal elements commonly co-exist with many proteins/enzymes and also participate in various biological pathways. 53 Loading metal particles in cells may cause multiple type of toxicity, 54,55 such as gene silencing and hypoxia signals induction, 56 ion channel inhibition, 57 production of reactive oxygen species (ROS), 58 lipid peroxidation 59 and formation of massive mitochondrial and nuclear DNA adducts. 60 The impact of carbonaceous particles on cell integrity might also be significant. 61,62 In order to reduce the influence of impurities, as-produced SWCNTs samples might require thorough purification through various chemical and physical treatments, 63 such as harsh acid washing, 64 low temperature oxidation, 65 polymer wrapping extraction, 66 in combination with ultracentrifugation or other sorting techniques. Applications of such strategies depend on the SWCNT synthesis methods as will be discussed below.

CVD SWCNTs

CVD methods allow large-yield production of SWCNTs. CVD commonly produces nanotubes through carbon monoxide (CO) disproportionation either under high-pressure (HiPco sample) 67 or with Co-Mo as supported catalysts (CoMoCAT sample). 68 The former technique produces nanotubes with interesting pristine optical properties for biological imaging. 69 The latter allows narrow nanotube chirality distributions. We discuss below the impact of the impurities contained in HiPco and CoMoCAT nanotube samples on cellular toxicity.

HiPco SWCNTs

HiPco samples contain a mixture of nanotubes with different chiralities. 70 They can also contain various metal catalysts used during the synthesis process. A number of studies that focused on the interplay between SWCNTs and cells employed unpurified nanotube samples, and such impurities played a critical role on cellular toxicity. 71,72,73 Maria et al.

studied the impact of HiPco SWCNTs containing 10 wt% Fe on primary human lung epithelial cells (A549) 74 , as lung exposure is a primary pathway for human contract with nanoparticles. After 24 hours exposure at a dosage of 800 µg/mL, low acute toxicity was reported but apparent changes in cell morphology were visualized with transmission electron microscopy (TEM). No individual SWCNTs were observed inside cells, while an increased number of multi lamellar and vesicular bodies were observed, which was hypothesized to arise from a defensive response of lung cells. A549 and human bronchial epithelial cells (NHBE) further showed suppressed inflammatory and increased oxidative stress responses after exposure to the same nanotubes coated with dipalmitoylphosphatidylcholine (DPPC). 75,76 DPPC coating improves the individualization degree of SWCNTs in cell culture medium and led to increased toxicity in A549 cells after 48 hours exposure but no had no effect on NHBE cells. This induced toxicity can be attributed to impurities (10 wt% in this study) released from DPPC-coated nanotubes when incubated with A549 cells. 77 This observation also indicates that SWCNT toxicity depends on the cell type. To also address another important pathway of nanoparticle body penetration, Murray et al. 78 studied the effect of unpurified nanotubes on skin cells. Cell oxidative and inflammatory effects were evaluated on EpiDerm-FT engineered skin of murine epidermal cells (JB6 P+) through administration of unpurified HiPco SWCNTs containing 30 wt% Fe and their purified counterparts containing only 0.23 wt% Fe. 78 A significant induction of activator protein 1 (a transcription factor regulating gene expression in responses to various stimulus) 79 was observed upon exposing unpurified HiPco SWCNTs to JB6 P+ cells, but no activation was observed using purified HiPco nanotubes. Further topical exposure of unpurified HiPco nanotubes to immune-competent hairless SKH-1 mice after 5 days at daily dosage of 40 µg/mouse led to increased oxidative stress, depletion of glutathione, oxidation of protein thiols and carbonyls, and elevated myeloperoxidase activity, thereby resulting in an increase of dermal cell numbers and thickening of the animal skin. In an attempt to obtain bio-compatible nanotube samples by coating them with biomolecules, Patrick et al. 80 used bovine serum albumin (BSA), a bioactive blood protein widely used as blocking reagents for reducing non-specific bindings, as an encapsulating macro-molecule. The authors reported the cellular uptake of HiPco SWCNTs (containing 5 wt% carbonaceous and 0.3 wt% metallic impurities) by murine macrophage-like cells (J774A.1) and NIH-3T3 cells. 80 BSA-coated SWCNTs reduced cell proliferation in a dose-dependent manner and increased cell sizes at a dosage level of 30 µg/mL, most likely due to increased amounts of impurities. More recently, Holt and coworkers reported that BSA-coated SWCNTs were taken up by human mesenchymal stem cells and HeLa cells without apparent acute effects. 81 Altogether the investigations mentioned above suggest that the impurity content in HiPco nanotube samples and the role of encapsulating agents are important parameters in cellular toxicity. Sample purification might be employed to reduce impurities and therefore toxicity. The impact of encapsulating compounds will be detailed in section 3.1.2.

CoMoCAT SWCNTs

CoMoCAT nanotube samples have a narrow chirality distribution, generally enriched in (6.5) nanotubes. 68 CoMoCAT formulation involves the use of Co-Mo bi-metallic catalysts supported on a SiO 2 substrate. 82 83 Nanotubes were suspended in Dulbecco's modified eagle medium (DMEM) containing fetal bovine serum (FBS) 5 v/v% (DM-SWCNTs). MitoRox TM Red assay suggested that superoxide levels in mitochondria were similar for both incubations, with and without nanotubes. HeLa cell morphology and proliferation showed no apparent change after exposure to DM-SWCNTs compared with unexposed cells over 4 days. This investigation indicated that DM-SWCNTs were not inherently toxic because the impurities were efficiently removed. CoMoCAT samples with low number of impurities (Co-Mo 1.8 wt%, dosage of 10 µg/mL) similarly showed low cellular toxicity to E. coli K12 cells after 1 hour exposure. 84 The cellular toxicity of CoMoCAT coated with biomolecules was investigated by Bertulli et al., assessing the long-term effects of BSA-coated CoMoCAT SWCNTs, purified by low temperature oxidation and acid treatments 200-300 nm in length, dosage of 8 µg/mL on macrophages. 85 No significant difference in cell proliferation and viability was observed between cells exposed to reference and BSA-coated SWCNTs during 65 hours (corresponding to three cell division cycles). This result supports the observations made on HiPCO nanotubes suspended in BSA where toxicity was primarily attributed to sample impurities. 80 Ge and coworkers further examined the cellular toxicity of SWCNTs (Co as catalysts) coated by different blood proteins, including bovine fibrinogen (BFG), gamma globulin, transferrin, and BSA in human acute monocytic leukemia (THP-1) and human umbilical vein endothelial cells (HUVECs). 86 Interestingly, BFG-coated SWCNTs showed the lowest toxicity, which might be due to the tighter binding of BFG proteins to nanotubes preventing direct contacts of the nanotube backbone with cellular components.

These results suggest that blood proteins can be promising candidates for coating SWCNTs by reducing interactions between nanotubes and cellular components. They might also suggest that bare nanotubes can adsorb proteins in the bloodstream, although the fate of nanotubes in the bloodstream is not yet understood.

Arc-Discharge SWCNTs

The synthesis of SWCNTs by arc-discharge utilizes a composite anode, usually placed in hydrogen or argon atmosphere. 87 The anode is made of graphite and a metal, such as Ni, Fe, Co, Pd, Ag, Pt, etc; or the mixture of Co, Fe, and Ni with other elements.

Arc-discharge SWCNTs have diameters of 1.4-2 nm and lengths of several µm. The reaction products include many metal catalyst residents and unexpected products such as MWCNTs and fullerenes. 48 Aditya et al. reported the influence of arc-discharge SWCNTs on 3T3 mouse fibroblasts. 88 As-produced (AP-SWCNT, Ni 0.73 wt%, Y 0.38 wt%), purified (Pur-SWCNT, Ni 0.07 wt%, Ni 0.04 wt%), and glucosamine-modified (GA-SWCNT, Ni 0.09 wt%, Y 0.03 wt%) arc-discharged nanotubes were incubated with 3T3 mouse fibroblasts for 3 days at concentrations up to 0.1 wt%. It was found that 3T3 cell viability and metabolic activity strongly depend on nanotube preparation, purification, and concentration. AP-SWCNTs showed the largest cellular toxicity, Pur-SWCNTs showed a mild toxicity while GA-SWCNTs showed the lowest cellular toxicity. These results demonstrated again that the impurity content of carbon nanotube samples significantly affects cellular toxicity for HiPco and CoMoCAT nanotubes.

Laser-Ablation SWCNTs

Laser-ablation formulation produces SWCNT samples containing a high content of carbon arc-materials and metal catalysts that require to be removed by extensive purification. 89 Ni/Co catalysts. 91 After 24 hours nanotube exposure to cells at a dosage of 100 µg/mL, no acute toxicity was reported on cell viability. In contrast, the use of unpurified commercial SWCNTs (CVD, Nanostructured & Amorphous Materials Inc., Los Alamos, USA) indicated a dose-and time-dependent increase of intracellular reactive oxygen species and a decrease of mitochondrial membrane potential in both NR8383 and A549 cell lines, revealing the impact of impurities in laser-ablation nanotube sample on cellular toxicity.

Comparison between SWCNT synthesis methods and toxicity mechanism

In order to gain insight into the cellular toxicity of different SWCNT formulations, The observations mentioned above suggest that regardless of the synthesis method, metal catalysts/impurities embedded in SWCNTs samples have a deep impact on cellular toxicity. A possible molecular mechanism of cytotoxicity induced by cell exposure to carbon nanotubes and leached metallic particles has recently been proposed. 71 The cellular toxicity of SWCNTs was suggested to be mediated by ROS and the related disorder of intracellular metabolic pathways. 92,93 As a first conclusion, the use of SWCNTs samples containing low metal impurities is important to obtain reduced cellular toxicity. The control of SWCNTs' cellular toxicity primarily requires a control on nanotube sample impurity contents through synthesis and purification processes.

Effect of nanotube length and aggregation

The impact of nanoparticles on living cells depends on several parameters such as their physical size, hydrodynamic volume, aggregation states, colloidal stability in physiological environment etc. 94 It is well known that SWCNTs in colloidal suspensions are relatively heterogeneous in length, and contain both individualized nanotubes and bundles. In this section, we summarize reported effects of nanotube lengths and aggregation states on cellular toxicity.

Length

SWCNTs have very large aspect-ratios (length-to-diameter), which complicates the understanding of size effects involved in cellular toxicity. The lengths of SWCNTs are believed to play essential roles in nanotubes internalization pathways, 95,96 cellular responses 97 and subcellular distribution. 98 Kang et al. reported the effect of SWCNT lengths (chitosan-coated nanotubes, dosage of 50 µg/mL) on cell internalization pathways 98 and suggested that 100-200 nm long nanotubes are internalized in cells through clathrin-coated vesicles and the caveolin-dependent pathways. In contrast, 50 nm short nanotubes could directly enter cells through an energy-independent pathway involving insertion and diffusion across the cell membrane. After internalization, 100-200 nm long nanotubes were found to localize mainly in the cytoplasm, while 50-100 nm short nanotubes were found to distribute closer to cell nucleus. Sato and coworkers' investigations indicated that cell toxicity caused by exposure to 220 nm long nanotubes was weaker than the toxicity induced by 825 nm long nanotubes. 99 protons and DNA molecules. 102 From a bio-safety point of view, these results imply that extremely short DOPC-SWCNT complexes may interfere with the structure and function of cell membranes.

Aggregation

The aggregation state of SWCNTs is also an important parameter for minimizing their cellular toxicity. 103 SWCNTs can form large aggregates (micrometers in diameter) in cell culture medium or inside the cell body. 104 From these studies, it clearly appears that aggregation of SWCNTs should be avoided and that nanotube individualization is a key parameter to minimize cellular toxicity.

Surface Modification of SWCNTs

As already suggested above, cellular toxicity of SWCNTs can also be influenced by nanotube surface exposure to cellular environment. 95,107,108 In this section, we now discuss the impact of diverse surface modification strategies (see Figure 3) used in biological studies to introduce nanotubes in biological samples.

Pristine SWCNTs are insoluble in water due to their hydrophobic surfaces and direct exposure of pristine nanotubes to biological systems might lead to interactions with various biomolecules. For examples, in the bloodstream, many proteins and biochemical species can adsorb onto nanotubes in an unspecific way. 109 In this sense, it is important to shield or modify the surface of pristine SWCNTs to make them inert to chemical and biological components of the cells. The surface of SWCNTs can also contain various defects and chemical groups 110 that might play a role in nanotube interactions with biological molecules. Conversely, certain covalently doped SWCNTs have been shown to provide new optical or chemical properties promising for bioimaging or sensing applications, 111,112,113 such that controlling nanotube surface exposure to their bio-environments might also be promising to retain their properties.

Encapsulation of nanotubes by hydrophilic moieties and chemical grafting of solubilizing agents on nanotube surfaces are the two commonly used approaches preparing nanotube aqueous solutions with solubility up to concentrations in the order of g/mL. 114 For bio-applications, many small biomolecules, polymers and surfactants have been used.

Among them, poly(ethylene glycol) (PEG) arose as the most widely used biocompatible moiety for modifying nanoparticle surfaces (termed as PEGylation) due to its proven biological inertness and hydrophilic properties. 115 PEG chains are relatively flexible in physiological environments and are able to undergo long-time circulation in blood due to the strong resistance against non-specific protein absorption. It was also suggested that PEG modified nanoparticles are promising for penetrating various biophysical barriers, such as the reticulo-endothelial system and blood-brain barriers. 116 This is essential for increasing the accessibility of nanoparticles and the specificity for in vivo targeting applications.

We summarize below the cellular toxicity of SWCNTs coated by either covalent or non-covalent approaches. We outline several widely employed surface coatings and put a particular focus on PEG-based strategies due to their wide applicability in biomedical usages.

Covalent Modification

Chemical modification of SWCNTs sidewalls is a widely used approach for solubilizing nanotubes in aqueous media. It is usually achieved by grafting functional moieties onto initially oxidized SWCNT sidewalls (see Figure 3). Using high concentration of 100 µg/mL during 24 hours exposure, linear PEG-modified SWCNTs were found to be much less toxic than non-modified counterparts (as indicated by water soluble tetrazolium reduction assay). Similarly, based on lactate dehydrogenase release assays, it was found that linear PEG-modified SWCNTs caused less cell membrane damage than non-modified nanotubes. The morphology of these cells was also differentially affected, as cells treated with oxidized SWCNTs had an elongated shape while linear PEG-modified nanotubes did not induce such morphological changes.

Dose-dependent ROS and significant glutathione depletion were found after 24 hours administration of both materials. However, linear PEG-modified SWCNTs showed considerably less effect to oxidative stress related genes in PC12 cells compared to non-modified nanotubes. Once again, these findings indicate that the cellular toxicity mechanism of nanotubes is associated with oxidative stress. Importantly, these results suggest that PEG modification reduces oxygen species generation induced by nanotube administration.

In order to study the effect of PEG structures on nanotube cellular toxicity, Heister et al.

compared HeLa cell viability after exposure to branched PEG-modified and non-modified SWCNTs. 125 Unlike non-modified SWCNTs which formed clusters/precipitates in cell culture media, branched PEG-modified nanotubes (10 kDa)

were more stable and disperse. In addition cell viability stayed at 100 % over the whole dosage range from 0.01 to 100 µg/mL after 4 days of incubation. This observation suggests that branched PEG-modified SWCNTs are able to isolate nanotube surfaces more efficiently from exposure to cellular components compared to linear PEG chains.

Covalent PEG modifications can also be achieved through grafting PEG molecules onto -NH 2 groups. These groups are introduced on SWCNT surfaces by adding pyrrolidine rings to nanotubes via 1,3 dipolar cycloaddition reaction in azomethine ylides with subsequent thermal condensation in α-amino acids and aldehydes. 114 These PEG modified nanotubes are stable in various colloidal suspensions. They do not induce any complement reaction due to high structural stability. 126 Indeed, it was shown that the PEG chains on SWCNTs are unable to interact with the natural anti-PEG factor that is involved in the complement reaction induced by PEG molecules in biological systems.

Altogether, these studies indicate that PEG covalent grafting strategies dramatically reduce the cellular toxicity of oxidized SWCNTs. Branched PEG-modified SWCNTs appear to be more biocompatible than linear PEG-modified counterparts due to compact binding and large coverage of nanotubes, which limits the nanotube backbone exposure to cellular components. Yet, the effects of PEG density, length and branch degree are yet to be systematically investigated to fully understand their impact on cellular responses and toxicity.

Non-covalent encapsulation

The covalent modification of nanotube surfaces discussed above induces sp 3 hybridization bonds through the introduction of chemical groups. These modifications can have important detrimental implications on the mechanical, physical or chemical properties of nanotubes. For instance, heavy covalent nanotube functionalization generally suppresses the intrinsic near-infrared (NIR) photoluminescence properties of nanotubes 127 whereas many bio-applications of SWCNTs are based on these properties. 128 For such applications, non-covalent-based nanotube solubilization using biological compatible amphiphilic materials (soft polymers and biomolecules) is a widely used strategy (see Figure 3). 69 In general, cationic, anionic or nonionic charged surface coating can be used to encapsulate SWCNTs and to control the outer charge of the coated nanotubes. As the plasma membrane is negatively charged, the surface charge of encapsulated SWCNTs is a key parameter for controlling nanotube-cell membrane interactions, nanotube internalization pathways and intracellular fate. Usually, cationic nanoparticles interact more strongly with the cell membrane and therefore show higher uptake efficiency compared to anionic and neutral nanoparticles. 129 Negatively charged nanoparticles are also known to be taken up efficiently by pinocytosis or following membrane diffusion. 130,131,132 Keeping nanotube surfaces neutrally charged thus appears to be key for reducing nanotubes non-specific binding to cell membranes and serum proteins. In addition, nanoparticle hydrophobicity should also be controlled as it plays an important role in cellular uptake processes and subcellular fate. 133,134 More specifically, ionic detergents (such as sodium dodecyl benzene sulphonate, sodium dodecyl sulfate, cetyltrimethylammonium bromide, sodium cholate or sodium deoxycholate) are frequently used as excellent suspension agents of SWCNTs. 135,136 However, because of the well-known cytotoxicity of these ionic surfactants, they are not ideal for SWCNT biological applications. On the other hand, nonionic surfactants (e.g. pluronic) can also disperse SWCNTs and be used in cellular applications. 137,138 Low cellular toxicity of pluronic F108-coated nanotubes was previously reported, 139 however, recent developments illustrate that serum proteins in the bloodstream can replace F108 molecules and stick to SWCNT surfaces in physiological environments, which could restrict the performance of this surfactant. 140 Interestingly, collagen has also been used to suspend SWCNTs with no apparent effects on viability of bovine chondrocytes at a high dosage (15 µg/mL) after 15 days exposure. 141 Phospholipid-polyethylene glycol (PL-PEG), deserves a particular focus since it has become a widely used non-covalent suspension agent for bio-applications of SWCNTs both in vitro and in vivo. 69,142,143,144,145 The hydrophobic PL chains attach to the surface of nanotubes, with the hydrophilic PEG chains increasing the solubility and stability of nanotubes in high salts and serum containing environments. It is worth noting that 5 kDa linear PL-PEG-coated SWCNTs have been reported to trigger complement system reactions in vitro via the lection pathway, but neither acute nor chronic toxicity was observed for these materials both for in vitro and in vivo tests as a consequence of complement activation. 146 It was similarly found that PL-PEG incorporated into liposomes activates the complement system in human serum through an alternative pathway via interaction with naturally existent anti-PEG antibodies. 147 We note that BSA-, RNA-, glycolipid-, and non-coated SWCNTs were also reported to trigger complement activation. 126 However, recent studies suggested that complement activation reaction could be avoided by slightly modifying the chemical structure of the surfactants.

For example, complement activation by PL-PEG could be avoided by mutating anionic phosphate site into a methylated site 146 since it activation arises from the anionic phosphate site in the PL-PEG structure.

DNA molecules represent another class of biomolecules commonly used to solubilize

SWCNTs in the context of potential biomedical applications. 24 DNA is flexible biopolymer capable of adjusting its molecular geometry to wrap around the SWCNT outside walls by forming a helical structure. 24,35 This is achieved by non-covalent interactions (mainly π-stacking interactions) between SWCNT backbones and the aromatic nucleotides along the DNA perpendicular axis. This compact DNA wrapping can be SWCNT chirality selective depending on DNA sequences. 148 Interestingly, several studies have also explored peptide-PEG 152 and DNA-PEG 14 conjugations as new SWCNTs coatings. The impact of these surfactant-nanotube complexes on cellular toxicity remains to be investigated.

Surface coverage density

The density of chemical functionalities on the sidewall of SWCNTs significantly affects the surface properties of the nanotubes and their fate in biological systems. For instance, Sayes et al. examined the cellular toxicity of HiPco SWCNTs in human dermal fibroblasts (HDF) varying the density of phenyl-SO 3 X functional groups covalently grafted on the nanotubes (purified by acid treatment, containing 1 wt% impurities). 153 The average density of phenyl-SO 3 X groups was controlled by the carbon/phenyl-SO 3 X ratio (18, 41, and 80). This study indicated that SWCNTs were less cytotoxic as the degree of sidewall functional density increased.

Similar to covalently modified SWCNTs, non-covalently suspended carbon nanotubes showed improved solubility 69 Another study addressed the impact of PEG length and nanotube surface coverage density by monitoring protein adsorption on SWCNTs using either covalently grafted or non-covalently attached PEG moieties. 155 It was shown that PEG conformational transition from mushroom to brush state was key for reducing non-specific protein absorption, 155 which may help to reduce nanotube toxicity and prolong circulation lifetime in bloodstream. 156 For both covalent and non-covalent surface coverage, increasing PEG density and branched degree not only improved the solubility of SWCNTs in biological fluids, but also made nanotubes less toxic by reducing unspecific interactions with biological components, especially proteins. 125

Effect of SWCNT-Protein Corona

In biological fluids, binding of biomolecules onto nanoparticle surfaces might lead to the formation of supramolecular complexes, usually called the nanoparticle-biomolecule corona. 157 Knowledge of the dynamic rates, affinities, and stoichoimetry of nanoparticle-protein association/dissociation is fundamental for understanding the properties of these complexes. 158 In particular, these coronae directly impact the fate of nanoparticles in biological systems, in terms of pathophysiology, 159 biological performance, 160 and toxicity. 158,160 In this section, we focus on the impact of PEG-modified SWCNT-protein coronae on cellular toxicity. Indeed, PEG chains are used to minimize the formation of the protein corona, thus allowing a better control on nanoparticle fate in many applications.

Conclusions and Challenges

In this review, we presented recent advances in the understanding of SWCNTs cellular toxicity. We showed that SWCNTs cellular toxicity is related to many factors, such as nanotube synthesis, impurity content, surface modification, nanotube length, nanotube aggregation state and protein corona formation. In addition, the reliability and accuracy of the methods used for assessing the toxicity of the nanotubes may need to be considered. 165,166 Interdisciplinary knowledge on nano-bio interfaces in materials science, physics, chemistry, biology, and medical engineering, is thus required to understand SWCNT toxicity and move towards better control of nanotube impact on biological specimens.

We can attempt to draw a general strategy (although not a complete one) for minimizing SWCNT cellular toxicity (Figure 5). First, regardless of nanotube synthesis method, metallic impurities and carbon byproducts present in SWCNT samples need to be entirely removed by using dedicated purification processes. The cellular toxicity is also strongly associated with SWCNT properties (e.g. length, aggregation, and stability) in various suspensions. These need to be rationally controlled during preparation. Second, in order to reduce non-specific absorption of biomolecules, it is necessary to incorporate robust anti-fouling coatings on nanotube surfaces in order to isolate the nanotube backbone from biological environments and further minimize the formation of nanotube-protein corona.

It is key to achieve a full coverage of nanotube surfaces by incorporating a dense, compact, and biocompatible coating. Many natural biomolecules and synthetic polymers can be good candidates for nanotube coating but PEG surface modification (PEGylation) currently seems to provide the best option. PEG indeed gathers a combination of excellent properties: water solubility, low absorption to proteins, low toxicity, and long lifetime circulation. Third, the administration conditions (incubation approach, time, concentration etc.) need to be rationally chosen.

In this context, several challenges still remain to fully understand and minimize SWCNT cellular toxicity. A major challenge is certainly to produce high-purity and chirality-controlled nanotube samples. 167,168,169 Although PEG-nanotube complexes are widely used, new biocompatible surface coatings with ultra-low nonspecific protein absorption must be prepared when the use of PEG should be avoided. 170,171 More generally, one should emphasize that further studies on SWCNT clearance, removal, and degradation in living systems will be necessary in order to fully understand their fate. 172,173 The dosage and hydrodynamic size of nanotubes after binding plasma proteins need to be correctly monitored. 174,175,176 In addition there is no standard tool for assessing SWCNT cellular toxicity. 177 In many experiments, the chemical reagents used for assessing toxicity directly interact with nanotubes in the absence of cells and can lead to false results and misunderstanding 178 which hinder fair comparison between reports.

Finally, investigations at the molecular and genetic level will certainly be needed. This would allow the molecular mechanisms of nanotube induced genetic toxicity, such as DNA damage, 179,180 multiple poles in cell mitosis, 120 and interruption to chromosome 181 to be uncovered.

In spite of clear challenges, SWCNT-based biomedical materials and devices have shown spectacular progresses in recent years and as such they hold great promises for innovations in biology and medicine. 182

2 .

 2 Warheit et al. investigated the cellular toxicity of laser-ablation SWCNTs to pulmonary cells. SWCNT samples containing 30-40 wt% amorphous carbon and 5 wt% Ni and Co 90 were directly dispersed in phosphate-buffered saline (PBS) containing 1 wt% Tween80 and used in cells experiments without further purification. No significant change of cell proliferation was found compared to control samples following 24 hours cell exposure at a dosage of 5 µg/mL. SWCNTs samples used in this study were however rarely found as individualized nanotubes, but rather in agglomerated ropes. The effects of nanotube aggregation on cellular toxicity will be discussed in Section 4.Pulskamp et al. studied the responses of lung macrophages (NR8383) and A549 cells to the exposure of laser-ablation SWCNTs purified by acid treatment containing traces of

  Chowdhury et al. tested on bacteria the toxicity of SWCNTs produced by HiPco,CoMoCAT, and arc-discharge methods.84 SWCNTs were dispersed in water containing 2 wt% F108 copolymer, and their toxicity was determined by live/dead baclight bacterial viability tests. This study suggested that HiPco (Fe 6.52 wt%) nanotubes have greater impact on cell viability as compared to CoMoCAT (Co-Mo 1.80 wt%) and arc-discharge nanotubes (Y-Ni 0.21 wt%) at a same dosage of 10 µg/mL after 1 hour exposure.

  Umemoto and coworkers 105 reported that nanotube aggregates induced relocation of cell clathrin complexes in mast cells (RBL2H3) just after 10 min of exposure, and reduced the total clathrin level after 1 hour (NanoLabs, Detroit, USA. CVD, 5 wt% Fe impurities, 10 to 100 µg/mL). Further studies revealed striking membrane perturbations and rearrangements around nanotube aggregation zones in mast cells as a consequence of a strong disruption of the cortical actin cytoskeleton. Characterizations performed at the molecular level indicated that nanotube aggregations induced biphasic calcium response and phosphorylation of post-receptor kinases related to FCER1 receptors (a high affinity receptor for the Fc region of the immunoglobulin E). Altogether, these observations suggest that nanotube aggregates activate pro-inflammatory responses of mast cells. Peter et al.106 compared the cellular toxicity of well-dispersed SWCNTs (arc-discharged nanotubes with Ni and Y catalyst, polyoxyethylene sorbitan monooleate (PS80)-coated nanotubes, dosage of 50 µg/mL) as well as purified rope-like aggregated nanotubes (HCl treatment, 15 minute) and soot-like nanotubes-pellet fractions (centrifugation pellet) with commercial asbestos as a reference in human MSTO-211H cells. Cell morphology analyses suggested that well-suspended SWCNTs were less toxic than asbestos and that rope-like nanotube aggregates induced more pronounced toxicity than asbestos fibers at identical concentrations. Raja et al.104 examined the impact of SWCNTs (0.1 mg/mL HiPco, sonicated in a 3:1 (v/v) mixture of H 2 SO 4 and HNO 3 ) on rat aortic smooth muscle cells after 3.5 days of incubation. Unfiltered samples containing nanotube aggregates significantly decreased cell-growth rates compared to filtered ones.

  and reduced toxicity with an increasing coverage of coating molecules. For examples, Liu et al. studied the effect of PEG length and nanotube surface coverage density on the nanotube circulating lifetime and accumulation in live mice skin.154 It was found that poly(maleic anhydride-aIt-1octadecene)-poly(ethylene glycol) (C18PMH-PEG) coated SWCNTs showed the longest circulating lifetime (up to 20 hours) due to their compactness upon nanotube binding and large surface coverage. The same group reported that branched PEG chains could also be used. The extension of hydrophilic star-like PEG chains in biological surrounding allowed imaging the nanotubes for up to 10 hours in mice.

Figure 1 .

 1 Figure 1. Key parameters associated to SWCNT cellular toxicity.

Figure 2 .

 2 Figure 2. Typical electron microscopy micrographs of Ni-containing SWCNT samples

Figure 3 .

 3 Figure 3. Surface modification of SWCNTs for bio-applications. Covalent approaches

Figure 4 .

 4 Figure 4. PEG2k-SWCNTs interactions with human plasma proteins. (a)

Figure 5 .

 5 Figure 5. General strategy for minimizing SWCNT cellular toxicity.

  Donkor et al. reported that short SWCNTs (coated with 6-arm branched PEG) with length below 35 nm could efficiently deliver 4700 bp plasmid DNA molecules into HeLa cells in 24 hours to obtain transfected cells.100 Moreover, short nanotubes were reported to be less hazardous to DNA than their longer countparts.101 A very recent study suggested that short SWCNTs

	(1.5	nm	in	diameter,	10	nm	in	length,	coated	by
	1,2-dioleoyl-sn-glycerol-3-phosphocholine (DOPC) at a concentration of 10 mg/mL)

were able to spontaneously insert into the lipid bilayer of cell membranes. This leads to the formation of artificial 'molecule channels' capable of translocating water, ions,

  Therefore, oxidized SWCNTs without further surface modification should be used with caution for both in vitro and in vivo applications.

	In this context, it was shown that grafting anti-fouling polymers onto nanotube backbones
	provides an efficient approach for minimizing SWCNTs direct interactions with cellular
	components. For instance, PEG-modified SWCNTs are commonly used and are usually
	produced by amidation reaction of -COOH groups of oxidized nanotube with -NH 2
	groups of PEG. PEG-modified SWCNTs produced with this approach stabilize nanotubes
	as individual and/or small bundles in colloidal suspensions and are stable in high salt and
	serum containing environment.
	tubulin network disorganization, adhesion complex maturation and decrease of migration
	ability during multicellular alignment or migration after cellular exposure to oxidized
	SWCNTs. 119 Such oxidized SWCNTs were also reported to induce multipolar spindle
	and abnormal mitosis. 120 Luanpipong et al. reported that direct chronic exposure of
	oxidized SWCNTs to lung epithelial cells would induce the production of cancer stem
	cells with malignant properties 121 and that these cells could become aggressive and

117,118

Oxidation of nanotubes is performed using H 2 SO 4 and/or HNO 3 to create carboxylic groups. Importantly, oxidized SWCNTs used without further coating were reported to induce multiple toxic effects to cells. For example, Singh et al. reported cell chirality loss, centrosome disintegration, develop tumors. These nanotubes might thus be more toxic than pristine unpurified nanotubes, which reflects the impact of surface defects and chemical groups introduced by oxidation. 122 123 Zhang et al. investigated the toxic effects of linear PEG-modified SWCNTs and compared it to non-modified SWCNTs on PC12 cells.

124

  Importantly, DNA being naturally biocompatible, DNA-coated SWCNTs can be expected to show little cytotoxicity. Dong et al. demonstrated that low doses (GT) 15 -coated SWCNTs (0.8 µg/mL) have no detectable impact on human astrocytoma cell morphology, proliferation, or viability after 24 hours exposure, as opposed to nanotubes coated by SDBS or SDS.149 Accordingly, Jin et al. reported no apparent cytotoxicity in live NIH 3T3 cells exposed for several hours to (GT)15 -coated SWCNTs at the same dose. Such low SWCNTs doses are typically used in live cell experiment aiming at studying nanotube endocytosis and intracellular trafficking at the single nanotube level. 150,95 Indeed, DNA-coated nanotubes are usually found to strongly interact with cells and thus get internalized. The absence of cytotoxicity at higher doses of DNA-coated SWCNTs has yet to be determined. In addition, several studies have suggested that the adsorption of biomolecules present in cellular serums on DNA-coated SWCNTs and the nanotube cellular uptake might depend on DNA sequence, nanotube chirality 151 and length.107 Additional studies are required to fully understand the nature and stability of DNA-nanotube interactions and the interplay of DNA-coated SWCNTs with biological systems.

  161,162 However, PEG molecules do not completely prevent dynamic protein binding, especially when the PEG coverage of nanoparticle surface is not total.163 In addition, and as mentioned above, covalent and non-covalent approach can be used to coat SWCNT surfaces. Sacchetti et al. systematically investigated the protein corona properties of arc discharge SWCNTs surface coated with

	surface properties and proteins properties: fPEG2-SWCNTs mainly adsorbed coagulation
	proteins whereas cPEG2-SWCNTs mainly adsorbed immunoglobulin proteins (see
	Figure 4c and d). In addition, some plasma proteins were selectively enriched or
	depleted depending on the type of PEG coating used. The influence of PEG conformation
	was subsequently tested by in vivo distribution studies using PEG2k-SWCNTs 156
	confirming that surface modification (covalent vs non-covalent), size, and PEG
	conformation together influence the composition and dynamics of nanotube-protein
	corona. 164
	PEG-coated SWCNTs (terms as cPEG-SWCNTs) leaving open areas that extend up to
	tens of nanometers that could directly expose the nanotube surface to biological
	environments. In contrast, covalent PEG-functionalized SWCNTs (fPEG-SWCNTs)
	displayed a denser and more uniform PEG layer on nanotube surfaces. After removing
	unbound PEG, cPEG2-SWCNTs and fPEG2-SWCNTs showed respectively a PEG
	density of 0.1 mmol (PEG average height 1 nm, mushroom conformation) and 0.4 mmol
	(PEG average height 7 nm, mushroom-brush transition conformation) per gram of
	nanotubes. Analysis of human plasma proteins adsorbed on nanotubes were studied by
	mapping with 1D SDS-polyacrylamide gel electrophoresis combined with a mass
	spectrometry after incubating plasma with nanotubes. The results revealed clear
	differences in the composition of PEG2k-SWCNT coronae as a function of nanotube

2kDa PEG chains through either covalent or non-covalent approaches (see Figure

4a and b

).

156

In this study, non-uniform coating was observed on the sidewall of non-covalent

Acknowledgments

This work was supported by CNRS, Agence Nationale de la Recherche (ANR-RPIB-004-03), Conseil Régional d'Aquitaine (2011-1603009), the France-BioImaging national infrastructure (ANR-10-INBS-04-01) and IdEx Bordeaux (ANR-10-IDEX-03-02). JAV acknowledges Marie Curie Individual Fellowship 326442 funding. The authors gratefully acknowledge Lisa-Maria Needham for her constructive comments on the manuscript.