Ernesto Estrada

Generalized walks-based centrality measures for complex biological networks

Keywords: centrality indices, subgraph centrality, protein-protein interactions, complex networks, matrix functions

A strategy for zooming in and out the topological environment of a node in a complex network is developed. This approach is applied here to generalize the subgraph centrality of nodes in complex networks. In this case the zooming in strategy is based on the use of some known matrix functions which allow focusing locally on the environment of a node. When a zooming out strategy is applied new matrix functions are introduced, which give a more global picture of the topological surrounds of a node. These indices permit a modulation of the scales at which the environment of a node influences its centrality. We apply them to the study of 10 protein-protein interaction (PPI) networks. We illustrate the similarities and differences between the generalized subgraph centrality indices as well as among them and some classical centrality measures. We show here that the use of centrality indices based on the zooming in strategy identifies a larger number of essential proteins in the yeast PPI network than any of the other centrality measures studied.

Introduction

E-mail addresses: ernesto.estrada@strath.ac.uk. interactions and transformations, such as in transcription networks, protein-protein interaction networks and metabolic networks [START_REF] Barabási | Network biology: Understanding the cell's functional organization[END_REF]. Complex networks are also valuable in representing ecological systems, such as in the case of food webs [START_REF] Jordán | Network ecology: topological constraints on ecosystems dynamics[END_REF]. In both contexts the use of graph theoretic invariants to characterize the local and global topology of these networks is of tremendous importance for extracting useful biological information from such networks [START_REF] Costa | Characterization of complex networks: a survey of measurements[END_REF][START_REF] Jordán | Topological keystone species: measures of positional importance in food webs[END_REF][START_REF] Jordán | Quantifying positional importance in food webs: a comparison of centrality indices[END_REF].

Among the graph theoretic invariants characterizing biological networks, centrality indices ranking the relevance of nodes in the network have received great attention in recent years [START_REF] Costa | Characterization of complex networks: a survey of measurements[END_REF][START_REF] Jordán | Quantifying positional importance in food webs: a comparison of centrality indices[END_REF][START_REF] Junker | Exploration of biological network centralities with CentiBiN[END_REF]. In general the notion of node centrality comes from its use in social networks (Chapter 5 in [START_REF] Wasserman | Social Network Analysis: Methods and Applications[END_REF]. Intuitively, it is related to the ability of a node to communicate directly with other nodes, or to its closeness to many other nodes or to the quantity of pairs of nodes which need a specific node as intermediary in their communications. These ideas have materialized in some well-known centrality measures such as degree centrality (DC), closeness centrality (CC), eigenvector centrality (EC) and betweenness centrality (BC) [START_REF] Wasserman | Social Network Analysis: Methods and Applications[END_REF]. Some of these measures describe the local environment around a node, e.g., degree centrality, and others characterize more globally the position of a node in the network, e.g., eigenvector centrality. An intermediate ⎯ neither local nor global ⎯ characterization of the node centrality has been claimed as a necessity for the study of biological networks [START_REF] Jordán | Searching for keystones in ecological networks[END_REF][START_REF] Jordán | Topological keystone species: measures of positional importance in food webs[END_REF]). In such "meso-scale" view node centrality should takes into account that the strength of indirect effects decreases with the length of the pathway. In such a way an index accounting for node importance should be between the local and the global scales reflecting far reaching effects but only to smaller and smaller extent [START_REF] Jordán | Searching for keystones in ecological networks[END_REF][START_REF] Jordán | Topological keystone species: measures of positional importance in food webs[END_REF].

A c c e p t e d m a n u s c r i p t

3

Here we propose a strategy that permits to zooming in and out the topological environment of a node in order to characterize its centrality. This strategy is based on the use of matrix functions which permit to characterize the centrality of a node by taking into account its participation in network's walks. Our strategy permits to give more or less weight to the walks of different lengths producing the desired zooming of the topological environment of the node.

Despite the theoretical approaches described here can be applied to different network descriptors we have selected the subgraph centrality [START_REF] Estrada | Subgraph centrality in complex networks[END_REF] of a node for illustrating the applications of this local-global focus strategy in complex biological networks. By studying 10 protein-protein interaction (PPI) networks we show that the generalized subgraph centrality indices capture different topological information of the environment of a node. Such information can be useful in making predictions about network-independent functional data of PPI networks. As an example we show here that some of the indices obtained by zooming in the subgraph centrality are able to identify in silico more essential proteins in the yeast PPI network than any other centrality measure.

Preliminary definitions

Let

( )

E V G , =
be a network with n V = nodes and m E = links without loops and multiple edges. A walk of length k is a sequence of (not necessarily different) nodes

k k v v v v , , , , 1 1 0 - such that for each k i , 2 , 1 = there is a link from 1 - i v to . i v Let A G
( )= A be the adjacency matrix of the network. Then, the moment

( ) ( ) pq k k q p A = , μ
gives the number of walks of length k starting at the node p and ending at the node q . If q p = the moment ( )

p k μ
gives the number of walks starting and ending at the same node, which are known as a self-returning or closed walks (CWs).

The total number of CWs in a network is given by the trace of the corresponding power of the adjacency matrix, ( )

k k tr A = μ . It is known that if n λ λ λ , , , 2

A

.

(1)

Every CW is related to a given subgraph in a network. For instance, the number of CWs of length two for node i equals the degree of node i . CWs of length three are related to the number of triangles and CWs of length four are related to links, paths of length two and squares in the network. Then, the spectral moments of the adjacency matrix are the basis of several structural invariants used for networks in different environments. One of these invariants was introduced to quantify the degree of folding of protein chains [START_REF] Estrada | Characterization of 3D molecular structure[END_REF] in which a weighted graph is used to represent the adjacency between dihedral angles in the protein backbone. This index was later generalized to any complex network as a way to quantify the content of subgraphs in the network.

It is defined by the Taylor expansion of the spectral moments of the form [START_REF] Estrada | Characterization of 3D molecular structure[END_REF][START_REF] Estrada | Subgraph centrality in complex networks[END_REF] ( )

+ + + + + + = ! ! 3 ! 2 3 2 1 0 k G EE k μ μ μ μ μ , (2)
which has the following closed form in terms of the graph spectrum [START_REF] Estrada | Characterization of 3D molecular structure[END_REF]Estrada and Rodríguez-Velázquez, 2005a)

( ) ( ) A e tr e G EE n j j = = ∑ =1 λ , (3)
where the exponential adjacency matrix is defined as

+ + + + + + = ! ! 3 ! 2 3 2 k e k A A A A I A . ( 4
)
The number of CWs of length 2, which are accounted by 2 A , are counted twice for every link in the network. Similarly, the CWs of length 3, which are accounted by 3 A , are counted six times for every triangle. This can give the false impression that the penalization scheme used in ( 4) is based on this fact. That is, that CWs of length 2 are penalized by 2! and CWs of length 3 are penalized by 3!, because these are the number of repetitions of these CWs for links and triangles, A c c e p t e d m a n u s c r i p t 5 respectively. However, these is not true for other powers of the adjacency matrix beyond 3 A . For instance, for 4 A every link contributes twice, every path of length 2 contributes four times and every square contributes eight times, which is not equal to 4!. In the next section we are going to explain what are the conditions that the penalization used need to fulfill in order to produce appropriate descriptions of the subgraph centrality.

The index ( )

G EE
was proposed as a subgraph centralization of the network and it is nowadays referred to as the Estrada index of a graph (de la [START_REF] De La Peña | Estimating the Estrada index[END_REF][START_REF] Carbó-Dorca | Smooth function topological structure descriptors based on graph-spectra[END_REF][START_REF] Deng | The Estrada Index[END_REF].

The subgraph centrality of the node p is given by ( ) pp e A and it has the following spectral formula [START_REF] Estrada | Subgraph centrality in complex networks[END_REF],

( ) ( ) ( ) ( ) [ ] j e p e k p p EE n j j pp k k λ φ μ ∑ ∑ = ∞ = = = = 1 2 0 ! A , (5)
where

( ) ( ) pp k k p A = μ
is the number of CWs starting (and ending) at node p , ( )

p j φ
is the p th entry of the j th orthonormal eigenvector j φ associated to the eigenvalue j λ .

Recently [START_REF] Estrada | Network properties revealed through matrix functions[END_REF] proposed a general formulation for the invariants based on Taylor series expansion of spectral moments

( ) ∑ ∞ = = 0 , k k k c c G EE μ . (6)
This general formulation was applied to complex networks by considering the following invariant

( ) ( ) ∑ ∞ = - = 0 1 1 , k k k n c G EE μ , (7)
which eventually converges to the trace of the resolvent of the adjacency matrix [START_REF] Estrada | Network properties revealed through matrix functions[END_REF], ( ) ( ) c G EE , is very similar to the degree centrality of a node making it a very local index in comparison with the subgraph centrality. As we have explained before our aim here is to produce a method that permit us to zooming in and out the topological environment of a node in such a way that we can obtain indices in between the local-global characterization of node centrality, i.e., to obtain a sort of "meso-scale" centrality indices.

1 1 1 1 1 1 1 , - = - ∑ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - - = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - - = n j j n n tr c G EE λ A I . ( 8

On walk-based network measures

The concept of node centrality in networks was introduced in the beginning of the 50's when [START_REF] Bavelas | A mathematical model for group structure[END_REF][START_REF] Bavelas | Communication patterns in task oriented groups[END_REF] and [START_REF] Leavitt | Some effects of certain communication patterns on group performance[END_REF] used this concept in communication networks.

Freeman introduced the degree centrality in social networks in 1979 [START_REF] Freeman | Centrality networks: I. Conceptual clarifications[END_REF], which can be written in matrix form as

( ) i i k Au = , ( 9
)
where u is a unit column vector.

Instead of using only the adjacency matrix, [START_REF] Katz | A new index derived from sociometric data analysis[END_REF] proposed to use the different powers of it multiplied by certain coefficients, which can be considered the first walk-based characterization of nodes in a network

( ) [ ] { } i T i K u I A I - - = -1 α , ( 10
)
where I is the identity matrix and

1 1 λ α < .
Then, a quantum leap appears when [START_REF] Bonacich | Factoring and weighting approaches to status scores and clique identification[END_REF][START_REF] Bonacich | Power and centrality: a family of measures[END_REF] introduced the definition of eigenvector centrality in which nodes' centrality is a function of the centrality values of adjacent nodes, ( ) φ are the Perron-Frobenius eigenvalue and eigenvector or A , respectively. The reader can find more details about centrality measures in the excellent review of [START_REF] Borgatti | A graph-theoretic perspective on centrality[END_REF] as well as in the Chapter 5 of the book by [START_REF] Wasserman | Social Network Analysis: Methods and Applications[END_REF].

i i ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = 1 1 1 1 Aφ λ φ , (11)
The walk-based centrality measures can be expressed by the general formula ( )u

A f
, where the matrix function ( )

A f is given by ( ) ∑ ∞ = = 0 k k k c f A A . ( 12
)
It is straightforward to realize that the degree, eigenvector and subgraph centrality can be considered as walk-based characterizations of the nodes in complex networks. For instance, in this context the Bonacich eigenvector centrality in vector form can be written as,

( )u

A A A A φ ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + + + = + - - - ∞ → 1 1 3 2 1 2 1 1 1 1 lim k k k k λ λ λ . ( 13
)
The only conditions that the coefficients k c needs to fulfill can be resumed as follows: (i) the coefficients need to make the series (12) convergent; (ii) the coefficients need to give more weights to shortest walks than to longer ones; (iii) the indices produced need to be real-positive numbers.

It is worth mentioning that several other successful centrality measures are not based on walks, such as the closeness, betweenness, and information centrality [START_REF] Borgatti | A graph-theoretic perspective on centrality[END_REF]).

Here we propose to generalize these invariants by using a new strategy that allows the definition of new centrality measures containing structural information on biological networks which is not duplicated by other measures. The duplication of information is analyzed by considering the strength of correlation among these measures, which indicates how much overlap exists among their information content.

Strategy for generalization

A c c e p t e d m a n u s c r i p t 8

The motivation for introducing the subgraph centralization and centrality was to count the participation of a node in all the subgraphs existing in the graph. This was accomplished by considering the number of closed walks in which a node takes place giving larger weights to shorter closed walks. For the sake of simplicity let us consider the graph illustrated in Figure 1.

The subgraph centrality clearly identifies the node 5 as the most central one in the graph followed by the node 7. The main difference between these two nodes is given by their participation in paths of length two (2-paths) as they take part in the same number of triangles and squares. Node 5 appears six times as the centre and six times as an end point of a 2-path. However, node 7 appears three times as a centre and five times as an end point of a 2-path. Node 1 is ranked fourth by the subgraph centrality after the equivalent nodes 2 and 4. This node takes part only in one triangle (1-2-4) instead of two (5-8-7, 5-6-7). However, it appears seven times as an end point of a 2-path and three times as its centre.

Insert Fig. 1 about here.

2-paths can be very relevant in clustered networks as the one represented by the graph in Fig. 1. For instance, the two nodes taking part in the largest number of 2-paths are nodes 1 and 5, which here form a bridge between the two clusters in the network. On the other hand, because the number of 1-paths in which a node takes place is the degree of the node, the number of 2-paths can be seen as the next step in extending such centrality. The same reason can be generalized to

consider m -paths ( 2 ≥ m
). A strategy for giving more weights to these fragments is to decrease the penalization imposed to the smaller spectral moments in the original definition of the subgraph centrality. For instance, let us use the following expression to calculate a modified subgraph centrality:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + + + + + + + + + ! 3 ! 2 8 7 6 5 4 3 2 1 0 i i i i i i i i i μ μ μ μ μ μ μ μ μ
Then, the new ranking of the nodes places node 1 as the second most central in the graph following node 5 and preceding node 7. The differences in the ranking are more evident if we We can generalize this idea by considering positive and negative rescaling of the expression

(5). By positive (negative) rescaling we mean moving forward (backward) the numerators (spectral moments) respect to the denominators (factorials) in the expression (2) as illustrated below positive rescaling:

+ + + ⇒ + + + ! 3 ! 2 ! 1 ! 2 ! 1 ! 0 2 1 0 2 1 0 μ μ μ μ μ μ
negative rescaling:

+ + + ⇒ + + + ! 1 ! 0 ! 2 ! 1 ! 0 2 1 0 2 1 0 μ μ μ μ μ μ
If we consider the CWs accounted for by both kinds of rescaling we can see that the positive rescaling corresponds to zooming in of the environment of a node. That is, by penalizing more the longest walks we concentrate more in the local environment of the corresponding node.

On the other hand, the negative rescaling corresponds to a zooming out of the surrounds of the corresponding node. In this case we allow long walks to contribute to the index in such a way that we obtain more global information about the environment of the node under study.

Zooming in by positive rescaling

By moving forward one step the spectral moments respect to the factorial denominators we obtain the following Taylor series

+ + + + + + + = ! 1 ! 4 ! 3 ! 2 3 2 1 0 1 k G EE k μ μ μ μ μ . ( 14
)
Then the index ( )

G EE 1
has the following spectral formula only in the case when no eigenvalue is equal to zero

( ) ∑ = - = n j j j e G EE 1 1 1 λ λ . ( 15
)
It is straightforward to realize that ( )

G EE 1
can be obtained as the trace of the ( ) [START_REF] Higham | Function of Matrices[END_REF],

A 1 ψ matrix function
( ) ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - = = A I A A e tr tr G EE 1 1 ψ . ( 16
)
where A is a non-singular matrix. The function ( )

A 1 ψ
appears in the exact solution of ordinary differential equations [START_REF] Hochbruck | Exponetial integrators for large systems of differential equations[END_REF]. Hamiltonian is simply the negative adjacency matrix [START_REF] Estrada | Statistical-mechanical approach to subgraph centrality in complex networks[END_REF]. Then, the first order index is related to the solutions of the nonlinear Schrödinger equation using exponential integrators [START_REF] Hochbruck | Exponential integrators for quantum-classical molecular dynamics[END_REF].

The index ( )

G EE 1
can be obtained by means of the following recurrence relation:

∑ ∞ = - + - = 1 0 1 ! 1 1 k k k k G EE G EE μ , ( 17
)
where the second member of the RHS of this expression converges as follow when no eigenvalue is equal to zero

( )( ) ∑ ∑ = ∞ = + - = - + n j j j k k j j e e k k 1 1 1 ! 1 1 λ λ μ λ λ . ( 18
)
The application of this power sum to the adjacency matrix of the graph gives rise to a new matrix function, which when A is non-singular can be expressed as ( )( )

A I A A A A + - = - + ∑ ∞ = e e k k k k 1 ! 1 1 .
We can extend the positive rescaling approach to generate a series of indices characterizing a graph in terms of the spectral moments of the adjacency matrix weighted by inverse factorials. The general formulation for these indices is given below

( ) ( ) ∑ ∞ = + = 0 ! k k t t k G EE μ . ( 19
)
The generalized ( )

G EE r
index has the following spectral formula when no eigenvalue is equal to zero:

( ) ( ) ( ) ∑ ∑ = = - - - = n j t j t s s t j t s t e G EE j 1 1 ! λ λ λ . ( 20
)
These indices are also related to matrix functions through the trace formula ( ) ( )

A t t tr G EE ψ = , ( 21
)
where the ( ) [START_REF] Higham | Function of Matrices[END_REF] have the following integral formula

A t ψ matrix functions
( ) ( ) ( ) ∫ - - - = 1 0 1 1 ! 1 1 dx x e t t t t A A ψ . ( 22
)
The following recurrence formula is known for these matrix functions [START_REF] Higham | Function of Matrices[END_REF])

( ) ( ) ( )( ) ∑ ∞ = + - + + + - = 1 1 ! 1 1 k k t t t k t k G EE G EE μ , ( 23
)
where the Taylor series in second member of the RHS of this expression converges as follow when no eigenvalue is equal to zero

( )( ) ∑ ∑ ∑ = + = + ∞ = ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ - + - = - + + + n j t j r s s j t j j k k s e e t k t k j j 1 1 2 1 1 1 1 ! 1 1 λ λ λ λ μ λ λ . ( 24
)
It should be mentioned that the functions ( )

A t ψ
are entire and they can always be calculated despite some eigenvalues of the adjacency matrix are equal to zero or the matrices are singular, because they can be represented as a power series which converges compactly. There are several numerical approaches to address the calculation of these functions which have been reported in the literature and the reader is referred to it for details [START_REF] Higham | Function of Matrices[END_REF].

Zooming out by negative rescaling

In the negative rescaling approach we are interested in not penalizing the closed walks of the smallest length in the graph. In the original ( )

G EE 0
the spectral moments of length zero and one are not penalized by dividing them with any factor. Suppose we are interested in extending this idea to the second spectral moments, such that we have the following power sum

! 3 ! 2 4 3 2 1 0 μ μ μ μ μ + + + + ,
or to the third ones in such a way that we have

! 3 ! 2 5 4 3 2 1 0 μ μ μ μ μ μ + + + + + .
In general, we can define the following negatively rescaled indices

( ) ( ) ( )( ) ∑ ∞ + = + - - - - + - + = 1 1 ! 1 1 t k k t t t k t k G EE G EE μ , ( 27
)
where the Taylor series in the second member of the RHS converges as follow

( )( ) ( ) ∑ ∑ = - ∞ + = - + = - - + - n j j t j t k k j j e e t k t k 1 1 1 1 ! 1 1 λ λ λ λ μ . ( 28
)
By applying this Taylor series to the adjacency matrix of a graph we can obtain a new matrix function, which is given by ( )

A A A I A e e t - + . ( 29
)

Study of protein-protein interaction networks

We study here 10 protein-protein interaction (PPI) networks in which nodes represent proteins and links represent interactions between pairs of proteins. These PPI networks correspond to Archaeglobus fulgidus [START_REF] Motz | Elucidation of an archaeal replication protein network to generate enhanced PCR enzymes[END_REF], Kaposi sarcoma-associated herpes virus (KSHV) [START_REF] Uetz | [END_REF], varicella-zoster virus (VZV) [START_REF] Uetz | [END_REF], Bacillus subtilis (Noirot and [START_REF] Noirot | Protein interaction networks in bacteria[END_REF][START_REF] Hoebeke | SPiD: a subtilis protein interaction dataset[END_REF], Escherichia coli [START_REF] Butland | Interaction network containing conserved and essential protein complexes in Escherichia coli[END_REF]), malaria parasite Plasmodium falciparum [START_REF] Lacount | A protein interaction network of the malaria parasite Plasmodium falsiparum[END_REF], the worm Caenohabditis elegans (Li et al., 2004),

Helicobacter pylori [START_REF] Rain | The protein-protein interaction map of Helicobacter pylori[END_REF], Sacchoromyces cereviciae [START_REF] Von Mering | Comparative assessment of large-scale data sets of protein-protein interactions[END_REF][START_REF] Bu | Topological structure analysis of the yeast protein-protein interaction network of budding yeast[END_REF], and Homo sapiens [START_REF] Rual | Towards a proteome-scale map of the human protein-protein interaction network[END_REF]. Here we consider the main connected component of these networks in which interactions between proteins are taken to be undirected and no selfinteractions are considered. Consequently, the corresponding networks are undirected and do not contain self-loops.

A c c e p t e d m a n u s c r i p t 14

We study here the subgraph centrality of the protein i in a PPI network, which is given by ( ) ( ) ii e i EE A = 0 . The subgraph centrality has been previously applied to the identification of essential proteins in proteomic maps (Estrada, 2006a;2006b;[START_REF] Zotenko | Why do hubs in the yeast protein interaction network tend to be essential: re-examining the connection between the network topology and essentiality[END_REF][START_REF] Lin | Hubba: hubs objects analyzer-a framework of interactome hubs identification for network biology[END_REF][START_REF] Gursoy | Topological properties of protein interaction networks from a structural perspective[END_REF] and the characterization of malignant tissues [START_REF] Platzer | Characterization of protein-interaction networks in tumors[END_REF]. It has also been applied to the study of weighted graphs to account for the degree of folding of protein chains (see for instance [START_REF] Estrada | Characterization of the folding degree of proteins[END_REF][START_REF] Estrada | Characterisation of the amino-acids contributions to the folding degree of proteins[END_REF] as well as to describe the molecular structure of drug-like and environmentally relevant organic compounds (for a review see [START_REF] Estrada | Recent advances on the role of topological indices in drug discovery research[END_REF].

We are interested in comparing this index with the generalized subgraph centrality indices defined by using positive and negative rescaling, which are given by the following expressions, respectively

( ) ( ) [ ] ii t t i EE A ψ = , ( ) ii t t s s t e i EE ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = ∑ - = - A A A 1 0 ,
where the matrix functions ( )

A t ψ
were previously defined.

First we analyze the intercorrelation between all subgraph centrality indices obtained here for 10 10 ≤ ≤ t . It is easy to realize that ( )

i EE t - diverges as . ∞ → t
On the other hand,

( ) 0 A = ∞ → t t ψ lim
, where 0 is an all-zeros matrix, and consequently ( )

i EE t tends to zero as ∞ → t .
We have observed that for the PPI networks analyzed here this already happens for 8 ≥ t

. Then, we exclude these values from our analysis. As a non-parametric measure of correlation between the indices we use the Kendall τ statistics [START_REF] Kendall | A new measure of rank correlation[END_REF], which represents the difference between the probability that the observed data are in the same order for the two variables versus the probability that the observed data are in different orders for the two variables. In Table 1 we give the values of the intercorrelation measures between the subgraph centrality indices for the PPI networks studied here. As can be seen there are relatively large intercorrelations between the indices defined here, which is expected from the fact that they are measuring the same topological properties of nodes, i.e., their subgraph centrality. Most of this intercorrelation arises from the indices which are obtained using the same strategy, i.e., positive or negative rescaling. We have used factor analysis for studying the subgraph centrality indices for the nodes of the PPI network of C. elegans. In Fig. 2A it can be seen that the first two factors divide the walk-based indices into two clusters corresponding to the positively and negatively rescaled indices, respectively. Similar patterns are also observed in the correlation matrices for this (see Fig. 2B) and the other PPI networks studied.

Insert Table 1 andFig

( ) i EE 10
there is no penalization for walks of length between one and eleven. It is known that for non-bipartite connected graphs as the ones studied here, the eigenvector centrality of a node is proportional to the number of walks of length k starting at this node as

∞ → k
, which explains the empirical correlation obtained. The second interesting observation is that the correlation between the degree centrality and the generalized subgraph centralities increases as the values of t increases. That is, negatively rescaled indices are less correlated with the degree than the positively rescaled ones. This observation is easily explained by the fact that in the positively rescaled indices we penalize very much long walks.

Consequently, walks of length two, which are equal to the degree of the node, have a large influence of these indices explaining the observed empirical correlations. Finally, the closeness centrality displays a similar behavior to the eigenvector centrality and the betweenness centrality is more similar to the degree in their correlations with the generalized subgraph centrality indices.

Based on these empirical findings we can conclude that the negatively rescaled subgraph centrality indices represent a zooming out which describe more globally the environment around a node due to their small penalization of the longer walks. On the other hand, the positively rescaled subgraph centrality measures are describing more local characteristics of the surrounds of a node due to the heavy penalization of long walks.

Insert Fig. 3 about here.

In order to have a closer look to the differences between the walk-based indices introduced here and the subgraph centrality we are going to study the PPI network of A. fulgidus in more indentifies proteins AF0335 and AF0382 as the most central ones in this proteome. These two proteins are also the most connected ones. The first of them is involved in tethering polymerases to DNA and the second one in replication. The ranking is followed by AF1195 (replication factor), AF1347

(unknown function), AF1692 (endonuclease III) and AF0699 (DNA-specific exonuclease).

Insert Fig. 4 about here.

The indices

( ) i EE t
are in general strongly correlated to

( ) i EE 0
with Kendall τ indices higher than 0.90. However, a looking glass analysis reveals certain differences. For instance, we can see that the first 6 proteins ranked by the index . For this value of t the protein AF1558/SMC-1 (chromosome segregation protein) has moved from the 13 th position in the original ranking to the 10 th . These two proteins only have degree two, but they are indeed connected to the hubs of the network, i.e., AF0335 and AF0382. Consequently, these two proteins AF0780/RPA-36 and AF1558/SMC-1 are present in a large number of fragments, which include the two hubs of the network. These fragments are in general large, but the negative rescaling approach does not penalize them very much, which implies that their participation in the centrality is significant enough.

In summary, we have seen in this example that the subgraph centrality of a node, e.g.

protein, can be zoomed in and out in order to extract information which differs in the participation of the nodes in the different structures of the network. In this way, the use of positively rescaled indices zooming in the environment of a node by maximizing the participation of a node in small subgraphs, such as 2-paths, due to the heavy penalization of large spectral moments. These small subgraphs can be important for the communication of different parts of the (protein) networks. On the other hand, when negatively rescaled indices are used a zooming out of this environment takes places because the participation of a node in large subgraphs is not so heavily penalized, which means that potentially important large substructures of the network are considered for the centrality of a node. In a previous work we compared the performance of several centrality measures in identifying essential proteins in this version of the yeast PPI network (Estrada 2006a). Our strategy consisted in selecting the top top 1%, top 5%, etc. of proteins, and determining how many of these are essential in the yeast PPI network. We showed that the subgraph centrality identifies the largest percentage of essential proteins in comparison with the degree, betweenness, closeness, eigenvector and information centrality. For instance for the top 5% of proteins selected the subgraph centrality identifies 56.4% of essential proteins while a random selection identifies only 25.3% and the degree centrality identifies 41.8%.

Here we use an identical strategy as in our previous work by ranking the proteins in the yeast PPI network according to their values of the walk-based centrality measures introduced here. Then, we select the top 5%, 10%, 15% and 20% and count the number of essential proteins according to each rank. We take the difference between the number of proteins identified by the new indices to the one identified by the subgraph centrality

Conclusions

We have developed a general strategy for zooming in and out the topological environment of a node using a walk-based description of complex networks. Using this approach we generalize the subgraph centrality of nodes in complex networks, which is then applied to study PPI networks.

  ubiquitous in biological sciences. They can represent molecular

  1 denote the eigenvalues of the adjacency matrix A of G , then the k th spectral moment of A can be expressed as follows

  this index largely penalize long closed walks in the graph. As a consequence,

  of removing the most central nodes according to the original subgraph centrality and the modified one. Removing node 7 does not affect the connectivity of the graph while removing node 1 produces the same effect as the removal of node 5, which separates the graph into two disjoint components. This example illustrates how by modulating the penalization of the spectral moments we can change the ranking of the nodes in a graph according to the relevance of different structural elements in which they participate.

  exact solution of this equation when the square matrix A and the column vector b are independent of t , a network obtained by solving the Schrödinger equation in which the

  obtained by means of the following recurrence relation:

  obtained by means of the following recurrence relation:

.

  of concordant and discordant pairs of data points, respectively, such that Then the Kendall τ index is defined as[START_REF] Kendall | A new measure of rank correlation[END_REF] τ for every pair of index are represented as a correlation matrix C . Then we use the first eigenvalue 1 ε of C normalized by the number of data points p as a measure of the global intercorrelation between the indices studied. Note that 1

  . 2 about here.The second part of this global analysis of the generalized subgraph centrality indices is devoted to compare them with some of the best known centrality indices. These "classical" centrality indices are the degree (DC), closeness (CC), betweenness (BC), and the eigenvector centrality (EC). The reader is referred to the Chapter 5 of the book of[START_REF] Wasserman | Social Network Analysis: Methods and Applications[END_REF] to obtain details about these indices. While the degree and eigenvector centrality are clearly walk-based centrality indices, the closeness and betweenness are based on the concept of shortest path distance.

  show the Kendall indices for the non-parametric correlations between the generalized centrality indices and the four classical centrality indices studied. The first interesting observation is that the negatively rescaled subgraph centrality indices are highly correlated with the eigenvector centrality and these correlations decay when the value of t increases. Such strong correlations can be explained by the fact that the negatively rescaled indices do not penalize so heavily long walks. For instance, in the index

  exactly the same as the ones appearing in the ranking due to ( ) i EE 0 . Now, in the ranking produced by ( ) i EE 0 the seventh to tenth proteins are AF1790, AF1722 and AF0780, while in the one produced by and AF0472. These differences are quite significant from the topological point of view. For instance, the deletion of the protein AF1790 ranked as the seventh by other topological change in the protein interaction network. However, removing protein AF1194, which is ranked seventh by( ) i EE 3produces the disconnection of four other proteins. Among these four proteins are the three histidine kinases present in this proteome AF0103 (HisK-1), AF1332 (HisK-2) and AF1452 (HisK-3). Similar results are obtained if we compare the removal of the proteins ranked eighth and ninth by the two indices. While the removal of those proteins ranked by ( ) i EE 0 has no further changes in the topology of the network the deletion of those ranked by three entries of the ranking using these indices are the same as the one using ( ) i EE 0 . However, the order of the other proteins in the top ten list change respect to the original index. The most that protein AF0780/RPA-36 (replication protein A) jumps from the 10 th place in the original ranking to the 4 th when 4 -= t

  Despite the new indices clearly identify new topological features of the proteins in the PPI networks it is necessary to illustrate whether these indices are useful in explaining or predicting network-independent functional data. In order to conduct this experiment we consider the essentiality of proteins in the PPI network of S. cereviciae. The essentiality of a protein defines the functional significance of a gene at its most basic level. Essential genes are those upon which //bioinfo.mbb.yale.edu/genome/), we checked for all proteins in the main cluster of the yeast PPI network for essentiality. An illustration of this PPI network and the essential proteins in it is given in Fig.4.Insert Fig.4about here.

  any difference in the number of essential proteins identified in comparison with the subgraph centrality ( ) i EE 0 . However, for the positively rescaled indices the number of essential proteins identified is significantly larger than the ones identified by ( ) i EE 0 . In Fig. 5 we illustrate the number of essential proteins identified by these indices in excess of that identified by the subgraph centrality. For instance, for the top 5% of proteins selected the index ( ) i EE 7 identifies 5 essential proteins more than ( ) i EE 0 . This index identifies 9, 12 and 17 essential proteins more centrality indices (degree, betweenness, closeness, eigenvector, information, subgraph) in identifying essential proteins in the yeast PPI network studied here. Insert Fig. 5 about here.

Fig. 1 .

 1 Figure caption

Fig. 2 .

 2 Fig. 2. Protein interaction network of the archaebacterium A. fulgidus.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Statistical analysis of the intercorrelation among the generalized subgraph centrality

Fig. 5 .

 5 Fig. 5. The principal connected component of the yeast PPI studied here. Red circles represent

Fig. 6 .

 6 Fig. 6. The number of essential proteins identified by the generalized subgraph centrality indices

  Fig. 1

Table 1 .

 1 Intercorrelation between the generalized subgraph centrality indices networks. The number of proteins (N), the number of interactions (E) and the first eigenvalue of the correlation matrix based on the Kendall τ indices ( 1 ε ) normalized by the number of observations ( p ) are given.

	t EE ,	-	10	≤	t	≤	7	,
							27

Acknowledgements

The author thanks Prof. N.J. Higham (Manchester) for introducing him to the Psi matrix functions. We also thanks the comments and suggestions of two anonymous referees, which contributed to a better presentation of the results in this paper. This work is partially supported by the Principal of the University of Strathclyde through the New Professor's Fund.


PhD FRCP Ammar Al-Chalabi
email: ammar.al-chalabi@kcl.ac.uk

M F Hanby Bsc

P N Leigh Fmedsci

Shaw Md Frcp

MD W Ye

PhD F Rijsdijk

Al-Chalabi

AN ESTIMATE OF AMYOTROPHIC LATERAL SCLEROSIS HERITABILITY USING TWIN DATA

Keywords: Twin study, amyotrophic lateral sclerosis, genetics, heritability, frontotemporal dementia

Causative gene mutations have been identified in about 2% of those with amyotrophic lateral sclerosis (ALS), often, but not always, when there is a strong family history. There is an assumption that there is a genetic component to all ALS, but genome-wide association studies have yet to produce a robustly replicated result. A definitive estimate of ALS heritability is therefore required to determine whether ongoing efforts to find susceptibility genes are worthwhile. We have performed two twin studies, one population and one clinic based. We used structural equation modelling to perform a meta-analysis of data from these studies and an existing twin study, to estimate ALS heritability. We identified 171 twin pairs in which at least one twin had ALS. Five monozygotic twin pairs were concordant affected and 44 discordant. No dizygotic twin pairs were concordant affected and 122 were discordant. The heritability of sporadic ALS was estimated as 0.61 (0.38, 0.78) with the unshared environmental component 0.39 (0.22, 0.62). ALS has high heritability and efforts to find causative genes should continue.

INTRODUCTION

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease of motor neurons with a median survival of about two years. The lifetime prevalence is about 1 in 400, [START_REF] Johnston | Amyotrophic lateral sclerosis in an urban setting: a population based study of inner city London[END_REF] but the appalling prognosis means the point prevalence is only 5 per 100,000 persons. [START_REF] Beghi | The epidemiology of ALS and the role of population-based registries[END_REF] In 95% of cases, there is no family history of ALS, but a study has found that the risk to siblings or offspring of a proband is elevated between nine and seventeen times. [START_REF] Fang | Familial aggregation of amyotrophic lateral sclerosis[END_REF] There is thus a familial tendency to ALS, which is best regarded as a complex disease.

There have been many genetic studies of ALS, [START_REF] Dion | Genetics of motor neuron disorders: new insights into pathogenic mechanisms[END_REF] but the only consistent findings have been the identification of six genes in which mutation predisposes to ALS, both in families and in sporadic cases, accounting for about 2% of ALS overall; these are SOD1, TARDBP, FUS, VAPB, ANG and OPTN. [START_REF] Rosen | Mutations in Cu/Zn superoxide dismutase gene are associated with familial amyotrophic lateral sclerosis[END_REF][START_REF] Sreedharan | TDP-43 mutations in familial and sporadic amyotrophic lateral sclerosis[END_REF][START_REF] Kabashi | TARDBP mutations in individuals with sporadic and familial amyotrophic lateral sclerosis[END_REF][START_REF] Vance | Mutations in FUS, an RNA processing protein, cause familial amyotrophic lateral sclerosis type 6[END_REF][START_REF] Kwiatkowski | Mutations in the FUS/TLS gene on chromosome 16 cause familial amyotrophic lateral sclerosis[END_REF][START_REF] Nishimura | A mutation in the vesicle-trafficking protein VAPB causes late-onset spinal muscular atrophy and amyotrophic lateral sclerosis[END_REF][11][START_REF] Maruyama | Mutations of optineurin in amyotrophic lateral sclerosis[END_REF] Genome-wide association studies have not resulted in independent replication of findings, although replication of a large study in a second large internal cohort has been successful [START_REF] Van Es | Genome-wide association study identifies 19p13.3 (UNC13A) and 9p21.2 as susceptibility loci for sporadic amyotrophic lateral sclerosis[END_REF]. There is, nevertheless, the assumption of a genetic component to all ALS. A twin study would help determine whether this assumption is reasonable by allowing an estimate of ALS heritability. The British Motor Neuron Disease (MND) Twin Study [START_REF] Graham | British motor neuron disease twin study[END_REF] made a start on this process by reporting the likely range in which the ALS heritability value would lie: 0.38 to 0.85. We have therefore collected twin data from two further sources: the Swedish Twin Registry [START_REF] Lichtenstein | The Swedish Twin Registry: a unique resource for clinical, epidemiological and genetic studies[END_REF] and the King's College Hospital Motor Neuron Disease Clinic Register. [START_REF] Wijesekera | Natural history and clinical features of the flail arm and flail leg ALS variants[END_REF] We have analyzed these two new data sets with the existing data used for the British MND Twin Study, independently but simultaneously in a meta-analysis framework, to generate for the first time an estimate of ALS heritability.

METHODS

Data collection

Data for the British MND Twin Study were extracted from the published manuscript. [START_REF] Graham | British motor neuron disease twin study[END_REF] Methods for the Swedish Twin Registry and King's Register have been previously described. [START_REF] Fang | Familial aggregation of amyotrophic lateral sclerosis[END_REF][START_REF] Wijesekera | Natural history and clinical features of the flail arm and flail leg ALS variants[END_REF] For the King's Register, pedigree records as obtained at the initial visit of each participant were used to identify twins. Zygosity status was self-reported, a method shown in the Swedish Twin Registry to be correct in 99% of twin pairs. [START_REF] Lichtenstein | The Swedish Twin Registry: a unique resource for clinical, epidemiological and genetic studies[END_REF] Concordance was defined as reported in the pedigree at the time of last follow-up. The two new studies were approved by the Research Ethics Committees of each institution.

Informed written consent to participate in research was obtained for all participants.

Familiality

Although the distinction between familial and sporadic ALS is to a large extent artificial, the population under study consists of two groups: those with a strong family history of ALS in whom we can assume a strong genetic component, and those without, in which the demonstration of a heritable component would be most useful. We therefore tested the effect of including and excluding individuals with a family history of ALS in a first degree relative. For the British MND Twin Study this information was provided in the published information. For the Swedish Twin Registry, data were linked to the Swedish Multi-Generational Register, which has family history information for those born after 1932 who were still alive in or after 1967, the Swedish Inpatient Register (1973 to 2004) and the Swedish Causes of Death Register (1961 to 2003) to identify relatives with ALS.

For the King's Register, pedigree structure and family history taken both at the initial visit and subsequent follow-up were used to identify families with affected first degree relatives.

Statistical methods

Genetic model-fitting is based on biometrical genetic theory where contributions of additive genetic (A), dominant genetic (D), shared environmental (C) and unshared environmental (E) effects on the trait are estimated by examining how often twins of different types correlate. MZ twins share all their genes, while DZ twins share only half on average. A trait that is strongly genetic would therefore be expected to strongly correlate between MZ twins, but show about half as strong a correlation between DZ twins. Calculation of correlations between twins for a continuous trait, such as height, is straightforward, but when the trait under study is discrete, as is ALS, a statistical measure called tetrachoric correlation is used, which assumes an underlying normal distribution of liability with a threshold effect determining if someone is affected or not. A DZ correlation which is less than half that of the MZ suggests the effect of dominance, whereas a DZ correlation which is higher than half that of the MZ suggests the effect of shared environment. [START_REF] Christian | Comparison of analysis of variance and maximum likelihood based path analysis of twin data: partitioning genetic and environmental sources of covariance[END_REF] As these two sources of variance are confounded, ACE and ADE models are fitted separately. Model fit is indicated by χ 2 statistics and related pvalues.

We performed a meta-analysis to maximize power. Twins of unknown zygosity were excluded from analysis. Tetrachoric correlations for ALS for monozygotic (MZ) and dizygotic (DZ) twins were calculated from contingency tables summarizing the number of concordant affected, concordant unaffected and discordant pairs, using the Mx program. [START_REF] Neale | Mx: Statistical Modeling. 6th ed: VCU Box 900126[END_REF] The calculations assume that the joint liability distribution is bivariate normal and a threshold determines affection or normality. Data for the British MND Twin Study and the King's Register were derived from local case register information on ALS, Al-Chalabi 6 6 rather than being direct population-based observations as is the case for the Swedish Twin Registry. The number of concordant unaffected pairs is therefore unknown, requiring ascertainment correction and the liability threshold to be fixed to the prevalence of ALS.

Population studies put the median age of onset of ALS at about 70 years of age, [START_REF] Chio | Epidemiology of ALS in Italy: a 10-year prospective population-based study[END_REF] so the prevalence of ALS was taken as about 1 in 740 (z-value threshold = 3.00), which is the approximate lifetime risk to this age. [START_REF] Johnston | Amyotrophic lateral sclerosis in an urban setting: a population based study of inner city London[END_REF] No such corrections were necessary for the Swedish data. The combined data were then used to estimate the overall MZ and DZ twin correlations. Because there were no concordant affected DZ twin pairs in any study, we also modelled the effect of the next DZ twin pair sampled being concordant affected. [START_REF] Bailey | Autism as a strongly genetic disorder: evidence from a British twin study[END_REF] Different sex twin pairs were included in the analysis, even though there is a differential risk for males and females with ALS, to avoid a loss of power and to allow comparison with the British MND Twin Study, which did not differentiate between twins by sex.

Al-Chalabi 7 7

RESULTS

Numbers studied

The British MND Twin Study examined 10,872 death certificates of people with MND, identifying 75 twin pairs for further study. It excluded seven twin-pairs where one of the pair had died before the proband developed disease, and also excluded one pair on the basis they were from a family with known familial ALS. It is arguable whether these are valid reasons for exclusion and therefore we did not exclude such pairs. Of 26 MZ probands identified, four were double twin pairs and therefore counted twice. Thus, the original study analysed 20 discordant and one concordant MZ pair, and 44 discordant and no concordant DZ pairs. We analysed 22 discordant and two concordant affected MZ pairs, and 51 discordant and no concordant affected DZ pairs overall, and excluded one MZ concordant pair for analysis of sporadic ALS.

The Swedish Twin Registry study examined 86,441 twin pairs, of which 14,824 were MZ, 43,070 DZ and 28,547 of unknown zygosity. Of the MZ pairs, 15 were discordant and two concordant for ALS. Of the DZ pairs, 58 were discordant and none concordant for ALS. For six twins, no family history data were available. For the remainder, no family history of ALS was identified in first degree non-twin relatives. The King's Register contained records of 1,502 individuals with ALS and 3,480 first degree relatives. There were 21 twin pairs in which at least one twin had ALS. There were eight MZ pairs, one concordant and seven discordant for ALS, and 13 DZ pairs, all discordant. The concordant MZ pair and one of the DZ pairs had a family history of ALS in a first degree relative and were excluded from the analysis of sporadic ALS.

well (χ 2

(2) = 3.16, P = 0.21), the heritability of ALS could not be meaningfully decomposed into additive and dominance genetic effects, most likely because of the lack of concordant affected DZ twins. To resolve this, we explored two alternative procedures.

Firstly, we interpreted an AE model. This fitted the data well (χ 2 (3) = 4.60, P = 0.20) with heritability estimated at 0.61 (0.38, 0.78). Secondly, we adopted an approach used by the British MND Twin Study and others: all studies were assumed to have a single Our analysis differs from the British MND Twin study in an important aspect. We used structural equation modelling. [START_REF] Karlin | Path analysis in genetic epidemiology: a critique[END_REF] This is a powerful likelihood based technique that allows an estimate of heritability despite the lack of concordant affected DZ twin pairs, without resorting to statistical workarounds. The British MND Twin study used an accepted method in which the next affected DZ twin observed is assumed to come from a concordant pair. [START_REF] Bailey | Autism as a strongly genetic disorder: evidence from a British twin study[END_REF] When we adopted this approach, the results were not very different from our unmodified analysis (Table 1). This is important as it suggests that a moderate increase in sample size designed to identify more twin pairs will not greatly change our results.

When familial samples were included in our analysis, the heritability estimate was, as expected, higher, but the overall findings are not greatly different from those for sporadic ALS whether or not we allowed for the next DZ twins identified to be concordant affected.

Al-Chalabi 11 11

We have previously estimated the heritability of age of onset of SOD1-mediated ALS as 0.29 (0-0.42) using a variance components approach in ALS pedigrees.

[22] This contrasts with the much higher estimate for susceptibility heritability we obtain here, indicating independent genetic effects on age of onset and susceptibility.

Co-morbidity of ALS and frontotemporal dementia, and pathological overlap is well recognised. No formal twin study has been performed for frontotemporal dementia, but in more than 41% of cases there is some family history, suggesting a high heritability. We did not distinguish between individuals with and without frontotemporal dementia concurrent with ALS, and our heritability estimate will therefore also have implications for frontotemporal dementia.

This study has important implications for sporadic ALS. Clinically, the knowledge of a significant genetic component means the question of why ALS has developed can be more confidently explained in terms of complex disease genetics. For research, despite the difficulties with replication of genome-wide association studies [START_REF] Dion | Genetics of motor neuron disorders: new insights into pathogenic mechanisms[END_REF], we can pursue more highly powered genome-wide association studies boldly, explore statistical methods for interactions and epistasis, and use techniques to find rare genetic variants, copy number variants, microsatellites, and epigenetic changes.

10 DISCUSSION

 10 concordant affected DZ twin pair as the next studied. In this situation the MZ and DZ twin correlations were 0.65 (0.42, 0.81) and 0.47 (0.27, 0.63) respectively, indicating shared environmental effects. Although the ACE model fitted the data well (χ 2 (2) = 3.65, P = 0.16), the 95% confidence interval for the shared environmental component included zero. The reduced AE model (dropping C) showed an additive genetic component of 0We estimate the heritability of sporadic ALS to be 0.61 (0.38, 0.78). The strength of this study lies in the extra power available from combining the two new studies and the previous British study in a meta-analysis. This has allowed us to independently but simultaneously model the different studies, despite their different designs. The value we obtain and the confidence interval lie within the range predicted by the British MND Twin Study. Although it can be difficult to estimate heritability in relatively rare diseases, our study combines data from 10,872 MND death certificates over a ten year period, a country-wide study of 86,441 twin pairs and a clinic-based study of 4,982 individuals with ALS or their family members, generating results from 171 ALS twin pairs.

Fogh I, Rijsdijk F, Andersen PM, et al. Age at onset in sod1-mediated amyotrophic lateral sclerosis shows familiality. Neurogenetics. 2007;8(3):235-236

ACKNOWLEDGEMENTS

We thank the NIHR Centre for Biomedical Research.

COMPETING INTERESTS

None.

FUNDING

FF and WY were supported by Bjorklunds Fond 2008-20892. MFH was supported by the British Geriatric Society. We thank the Medical Research Council (UK), the Wellcome Trust, the Motor Neurone Disease Association of Great Britain and Ireland, The American ALS Association, the ALS Therapy Alliance and the Angel Fund for support.

Model results

Results for all fitted genetic models are presented in Table 1.


Prof. Dr Tanja Fehm
email: tanja.fehm@med.unituebingen.de

Volkmar Müller

Bahriye Aktas

Wolfgang Janni

Andreas Schneeweiss

Elmar Stickeler

Claus Lattrich

Christian R Löhberg

Erich Solomayer

Brigitte Rack

Sabine Riethdorf

Christoph Klein

Christian Schindlbeck

Kerstin Brocker

Sabine Kasimir-Bauer

Diethelm Wallwiener

Klaus Pantel

HER2 status of circulating tumor cells in patients with metastatic breast cancer: a prospective, multicenter trial

Keywords: Breast cancer, circulating tumor cells, HER2, metastasis

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

Introduction

Human epidermal growth factor receptor 2 (HER2) is a transmembrane tyrosine kinase receptor encoded by a proto-oncogene located on chromosome 17q21. The HER2 proto-oncogene is amplified or overexpressed in approximately 20% of invasive primary breast cancers [START_REF] Coussens | Tyrosine kinase receptor with extensive homology to EGF receptor shares chromosomal location with neu oncogene[END_REF][START_REF] Schechter | The neu oncogene: an erbB-related gene encoding a 185,000-Mr tumour antigen[END_REF][START_REF] Slamon | Studies of the HER-2/neu proto-oncogene in human breast cancer and ovarian cancer[END_REF]. A positive HER2 status has been linked with aggressive tumor behavior and resistance to cytotoxic and endocrine therapy [START_REF] Slamon | Studies of the HER-2/neu proto-oncogene in human breast cancer and ovarian cancer[END_REF][START_REF] Konecny | Quantitative association between HER-2/neu and steroid hormone receptors in hormone receptor-positive primary breast cancer[END_REF][START_REF] Moliterni | HER2 overexpression and doxorubicin in adjuvant chemotherapy for resectable breast cancer[END_REF]. Patients with HER2 amplification and/or overexpression are eligible for HER2-targeted treatment [START_REF] Burstein | Neratinib, an irreversible ErbB receptor tyrosine kinase inhibitor, in patients with advanced ErbB2-positive breast cancer[END_REF][START_REF] Gianni | Open-label, phase II, multicenter, randomized study of the efficacy and safety of two dose levels of pertuzumab, a human epidermal growth factor receptor 2 dimerization inhibitor, in patients with human epidermal growth factor receptor 2-negative metastatic breast cancer[END_REF][START_REF] Baselga | Phase II trial of pertuzumab and trastuzumab in patients with human epidermal growth factor receptor 2-positive metastatic breast cancer that progressed during prior trastuzumab therapy[END_REF]. As a consequence, strategies for response prediction and monitoring are of high clinical relevance.

The methods used to select patients that are suitable for HER2-targeted therapy are based on the immunohistochemical (IHC) detection of HER2 protein overexpression and the demonstration of HER2 gene amplification by fluorescence in situ hybridization (FISH) in the primary tumor [START_REF] Wolff | American Society of Clinical Oncology/College of American Pathologists guideline recommendations for human epidermal growth factor receptor 2 testing in breast cancer[END_REF]. In recent years, there has been a growing body of evidence that the HER2 status of the primary tumor may be different from metastatic disease and changes might occur during treatment. A discrepancy between the primary tumor and distant metastases has been observed in 7% to 26 % of cases [START_REF] Vincent-Salomon | HER2 status of bone marrow micrometastasis and their corresponding primary tumours in a pilot study of 27 cases: a possible tool for anti-HER2 therapy management?[END_REF][START_REF] Zidan | Comparison of HER-2 overexpression in primary breast cancer and metastatic sites and its effect on biological targeting therapy of metastatic disease[END_REF][START_REF] Gancberg | Comparison of HER-2 status between primary breast cancer and corresponding distant metastatic sites[END_REF][START_REF] Regitnig | Change of HER-2/neu status in a subset of distant metastases from breast carcinomas[END_REF][START_REF] Edgerton | erbB-2 (HER-2) and breast cancer progression[END_REF][START_REF] Carlsson | HER2 expression in breast cancer primary tumours and corresponding metastases. Original data and literature review[END_REF][START_REF] Aitken | Quantitative analysis of changes in ER, PR and HER2 expression in primary breast cancer and paired nodal metastases[END_REF][START_REF] Tanner | Amplification of HER-2/neu and topoisomerase IIalpha in primary and metastatic breast cancer[END_REF][START_REF] Simmons | Does confirmatory tumor biopsy alter the management of breast cancer patients with distant metastases?[END_REF][START_REF] Liedtke | Prognostic impact of discordance between triple-receptor measurements in primary and recurrent breast cancer[END_REF].

In many patients with metastatic breast cancer, the re-evaluation of HER2 status by a tissue biopsy of the metastatic lesion is not feasible due to location of the metastatic site. In addition, HER2 status may vary between different metastatic sites and also change during treatment. Therefore, determination of the HER2 status of circulating tumor cells (CTCs) might be a strategy with potential clinical application.

So far, no large prospective studies have been reported comparing different methods for CTC detection and characterization.

The aim of this prospective multicenter trial was to compare the HER2 status of CTCs in 254 patients with metastatic breast cancer at the time of first diagnosis or disease progression obtained by the antibody-based CellSearch ® System and the real-time polymerase chain reaction (RT-PCR) approach, AdnaTest BreastCancer™, and to assess the concordance rate between these two techniques. The CellSearch assay is an automated, standardized, and FDA-approved method for detecting and enumerating tumor cells [START_REF] Riethdorf | Detection of circulating tumor cells in peripheral blood of patients with metastatic breast cancer: a validation study of the CellSearch System[END_REF][START_REF] Cristofanilli | Circulating tumor cells, disease progression, and survival in metastatic breast cancer[END_REF][START_REF] Budd | Circulating tumor cells versus imaging: predicting overall survival in metastatic breast cancer[END_REF]. AdnaTest BreastCancer is based on detection of three tumorassociated transcripts by RT-PCR after immunomagnetic enrichment of tumor cells [START_REF] Fehm | Detection and characterization of circulating tumor cells in blood of primary breast cancer patients by RT-PCR and comparison to status of bone marrow disseminated cells[END_REF][START_REF] Aktas | Stem cell and epithelial-mesenchymal transition markers are frequently overexpressed in circulating tumor cells of metastatic breast cancer patients[END_REF]. Both assays have been frequently used in studies evaluating CTC detection [START_REF] Liedtke | Prognostic impact of discordance between triple-receptor measurements in primary and recurrent breast cancer[END_REF][START_REF] Riethdorf | Detection of circulating tumor cells in peripheral blood of patients with metastatic breast cancer: a validation study of the CellSearch System[END_REF][START_REF] Cristofanilli | Circulating tumor cells, disease progression, and survival in metastatic breast cancer[END_REF][START_REF] Budd | Circulating tumor cells versus imaging: predicting overall survival in metastatic breast cancer[END_REF][START_REF] Fehm | Detection and characterization of circulating tumor cells in blood of primary breast cancer patients by RT-PCR and comparison to status of bone marrow disseminated cells[END_REF][START_REF] Aktas | Stem cell and epithelial-mesenchymal transition markers are frequently overexpressed in circulating tumor cells of metastatic breast cancer patients[END_REF][START_REF] Riethdorf | Detection and HER2 expression of circulating tumor cells: prospective monitoring in breast cancer patients treated in the neoadjuvant Geparquattro trial[END_REF][START_REF] Hauch | The clinical significance of circulating tumour cells in breast cancer and colorectal cancer patients[END_REF]. However, comparison between the two methods, notably for HER2 expression, has not been performed in a prospective, large, multicenter cohort to date.

Methods

Enumeration and characterization of CTCs

Detection of CTCs and assessment of HER2 status of CTCs was performed using both AdnaTest BreastCancer (Adnagen AG, Langenhagen, Germany) and the CellSearch assay (Veridex LLC, Raritan, NJ, USA) according to the manufacturers' instructions without modifications. Table 1 summarizes the technical features of each assay [START_REF] Riethdorf | Detection of circulating tumor cells in peripheral blood of patients with metastatic breast cancer: a validation study of the CellSearch System[END_REF][START_REF] Riethdorf | Detection and HER2 expression of circulating tumor cells: prospective monitoring in breast cancer patients treated in the neoadjuvant Geparquattro trial[END_REF][START_REF] Hauch | The clinical significance of circulating tumour cells in breast cancer and colorectal cancer patients[END_REF]. AdnaTest BreastCancer.

Two 5-ml EDTA blood samples were collected for CTC isolation using the AdnaCollect™ blood collection tubes (Adnagen AG) and stored at 4°C until further analysis. Establishment and validation of AdnaTest BreastCancer has been described in detail elsewhere [START_REF] Fehm | Detection and characterization of circulating tumor cells in blood of primary breast cancer patients by RT-PCR and comparison to status of bone marrow disseminated cells[END_REF][START_REF] Aktas | Stem cell and epithelial-mesenchymal transition markers are frequently overexpressed in circulating tumor cells of metastatic breast cancer patients[END_REF][START_REF] Hauch | The clinical significance of circulating tumour cells in breast cancer and colorectal cancer patients[END_REF]. In brief, blood samples were incubated with a ready-to-use antibody mixture (against GA 73. CellSearch assay.

Two 7.5-ml blood samples were collected into CellSave tubes (Veridex Inc.). The CellSearch Epithelial Cell Test (Veridex Inc.) was applied for CTC enrichment and enumeration. The method has been described in detail elsewhere [START_REF] Riethdorf | Detection of circulating tumor cells in peripheral blood of patients with metastatic breast cancer: a validation study of the CellSearch System[END_REF]. In brief, CTCs are captured from peripheral blood by anti-epithelial cell adhesion molecule (EpCAM)-antibody-bearing ferrofluid and subsequently identified by cytokeratin-positivity/negativity for the leukocyte common antigen CD45 and 4',6-diamidino-2phenylindole (DAPI) staining to ensure the integrity of the nucleus. A blood sample was positive when at least 5 CTCs were present based on the prognostically relevant cut-off as previously published [START_REF] Cristofanilli | Circulating tumor cells, disease progression, and survival in metastatic breast cancer[END_REF][START_REF] Budd | Circulating tumor cells versus imaging: predicting overall survival in metastatic breast cancer[END_REF]. HER2 expression of CTCs was characterized within the CellSearch assay by addition of a fluorescein isothiocyanate (FITC)-labeled anti-HER2 antibody (CellSearch tumor phenotyping reagent HER2, Veridex Inc.), as described previously [START_REF] Riethdorf | Detection and HER2 expression of circulating tumor cells: prospective monitoring in breast cancer patients treated in the neoadjuvant Geparquattro trial[END_REF][START_REF] Hayes | Monitoring expression of HER-2 on circulating epithelial cells in patients with advanced breast cancer[END_REF][START_REF] Meng | HER-2 gene amplification can be acquired as breast cancer progresses[END_REF]. To evaluate the intensity of HER2

immunostaining, approximately 500 breast cancer cells from cell lines with known HER2 status (MCF-7: no HER2 gene amplification, MDA-MB-453: 2-to 3-fold HER2 gene amplification, SK-BR-3 and BT474: 5-to 7-fold HER2 gene amplification) were spiked into 7.5 ml blood from healthy donors and were processed under identical conditions with the CellSearch assay. The intensity of the HER2specific immunofluorescence was categorized into negative (0), weak (1+), moderate (2+), and strong (3+). CTCs were considered HER2 positive if at least one CTC had strong HER2 staining (3+) based on the cut-off level published by Riethdorf et al. [START_REF] Riethdorf | Detection and HER2 expression of circulating tumor cells: prospective monitoring in breast cancer patients treated in the neoadjuvant Geparquattro trial[END_REF].

Determination of the HER2 status in the primary tumor

The HER2 status of the primary tumor was obtained from the patient's chart. In all participating centers, the HER2 status had been determined by the HercepTest™ (Dako, Glostrup, Denmark)

and/or the Pathvysion ® Kit (Vysis, Downers Grove, IL, USA). All pathology laboratories had participated in ring experiments and were certified laboratories for HER2 detection. A central review of the HER2 status of the primary tumor was therefore not performed. The cut-off level for HER2 positivity were based on the ASCO/CAP guidelines [START_REF] Wolff | American Society of Clinical Oncology/College of American Pathologists guideline recommendations for human epidermal growth factor receptor 2 testing in breast cancer[END_REF].

Statistical analysis

Primary endpoint of the study was the rate of HER2-positive CTCs with each method. Secondary endpoints were the concordance between the two methods in HER2-positive CTC detection. The study was performed in accordance with REMARK criteria [START_REF] Hayes | New guidelines for reporting of tumor marker studies in breast cancer research and treatment: REMARK[END_REF][START_REF] Mcshane | Statistics Subcommittee of the NCI-EORTC Working Group on Cancer Diagnostics: Reporting recommendations for tumor marker prognostic studies (REMARK)[END_REF]. Relationships between categorical variables were investigated using contingency tables. In case of independent data, Fisher's exact test

was

Results

Patient characteristics

A total of 254 patients with metastatic disease were enrolled between December 2007 and May 2009.

The clinical characteristics of the patients are summarized in Table 2 for the total cohort and the subgroups that were CTC positive by CellSearch assay and AdnaTest BreastCancer, respectively.

Detection of CTCs and determination of HER2 expression with the CellSearch assay

A total of 245 of 254 blood samples (two 7.5-ml blood tubes) could be analyzed for presence of CTCs by the CellSearch assay. Nine samples had to be excluded due to technical issues: test failure (n = 6), hemolysis of blood sample (n = 2), and insufficient blood volume (n = 1). At least one CTC was detected in 180 of 245 patients (73%) (Table 3). The average number of tumor cells was 177 cells per 7.5 ml (range, 1-6389; median, 4). Using the established cut-off level of 5 cells, 122 of 245 (50%) metastatic patients were considered CTC positive at the time of first diagnosis or disease progression.

Presence of CTCs was only associated with extent of metastatic disease (p < 0.05) (Table 2).

All CTCs were further characterized for HER2 expression within the CellSearch system by addition of an FITC-labeled anti-HER2 antibody. Cases were categorized as HER2-positive CTC if at least five CTCs were detected and at least one CTC showed strong immunostaining (3+) for HER2. Based on this definition, 72 (59%) of the 122 CTC-positive patients, were classified as HER2 negative and 50 (41%) as HER2 positive by immunofluorescence. Table 4 summarizes the distribution of combinations regarding HER2 immunostaining of CTCs in individual patients.

The mean ratio between number of HER2-positive CTCs and total number of CTCs was 0.31, ranging from 0.1 to 1 in HER2-positive blood samples. The percentage of HER2-positive CTCs was >10% in 64% of patients (32/50), >30% in 40% of patients (20/50) and >50% in 26% patients (13/50).

Correlation of HER2 status between CTCs and corresponding primary tumor was determined. Of those patients with detectable CTCs, primary tumors were HER2 negative in 78 patients and HER2 positive in 31 patients. HER2 status was unknown or inconclusive due to missing FISH analysis in 15

cases. HER2-positive CTCs in HER2-negative primary tumors were seen in 25 of the 76 patients (33%). Discordant HER2 expression was also found in patients with HER2-positive primary tumors, where 13 of 31 (42%) patients had exclusively HER2-negative CTCs. The correlation between HER2 status of CTC and corresponding primary tumor was fair (P = 0.02, = 0.23). Results are summarized in Table 5.

Detection of CTCs and determination of HER2 expression with AdnaTest BreastCancer

A total of 229 blood samples (two 5-ml blood tubes) could be analyzed for presence of CTCs by AdnaTest BreastCancer. Twenty-five blood samples had to be excluded, in most cases, due to insufficient blood volume (n = 12) followed by failure of the assay to pass quality control (n = 7), and time until processing >48 hours (n = 6). The overall detection rate for CTCs was 39% (90 of 229 patients). No correlations were observed between CTC positivity and any clinicopathological characteristic (Table 2).

A blood sample was considered as HER2-positive CTC, if the blood sample was considered CTC positive based on the cut-off-level described above and the transcript for HER2 was present. HER2positive CTCs were detected in 42 of 90 CTC positive patients (47%). Nine of these patients had a HER2-positive primary tumor, whereas 28 patients were initially HER2 negative based on the expression profile of the primary tumor (Table 5). There was no correlation between HER2 expression of CTCs and the corresponding primary tumor (P = 0.51, = -0.09).

Comparison between CellSearch assay and AdnaTest BreastCancer

Both methods could be performed successfully in 221 cases. A significant difference in CTC-positivity rates was observed. The CTC-positivity rate was 53% for the CellSearch assay compared to 40% for AdnaTest BreastCancer (P < 0.05). Concordance between the two assays was 64%. The correlation between the two assays was fair (P < 0.01, = 0.28). Sixty-two patients (28%) were CTC positive by both methods, whereas either the CellSearch assay or AdnaTest BreastCancer were exclusively positive in 24% (54/221) and 12% (26/221), respectively (Table 6).

Concordance between the HER2 status revealed by either the CellSearch assay or AdnaTest

BreastCancer could be only evaluated in the 62 patients who were CTC positive with both assays.

Concordant results were obtained in 50% of the patients (31/62) (P = 0.96, = -0.006,). Thirteen patients had HER2-positive CTCs by both assays. HER2-positive CTCs were only detected by the CellSearch assay in 15 patients (24%) and only by the AdnaTest BreastCancer in 16 patients (26%) (Table 6). Data are presented for different cut-off levels for the CellSearch assay including 1 and 2 cells, respectively, in Table 3.

Discussion

HER2 is the most prominent target for novel therapeutic approaches in breast cancer [START_REF] Burstein | Neratinib, an irreversible ErbB receptor tyrosine kinase inhibitor, in patients with advanced ErbB2-positive breast cancer[END_REF][START_REF] Gianni | Open-label, phase II, multicenter, randomized study of the efficacy and safety of two dose levels of pertuzumab, a human epidermal growth factor receptor 2 dimerization inhibitor, in patients with human epidermal growth factor receptor 2-negative metastatic breast cancer[END_REF][START_REF] Baselga | Phase II trial of pertuzumab and trastuzumab in patients with human epidermal growth factor receptor 2-positive metastatic breast cancer that progressed during prior trastuzumab therapy[END_REF]. Currently, HER2 status is determined at the time of initial disease diagnosis by analyzing primary tumor tissue.

However, several studies have demonstrated that HER2 status may change during disease progression. CTCs may be an ideal tool for reassessment of predictive markers since the phenotype of CTCs reflect the phenotype of the metastatic load at different sites [START_REF] Hayes | Monitoring expression of HER-2 on circulating epithelial cells in patients with advanced breast cancer[END_REF][START_REF] Meng | HER-2 gene amplification can be acquired as breast cancer progresses[END_REF][START_REF] Hayes | New guidelines for reporting of tumor marker studies in breast cancer research and treatment: REMARK[END_REF][START_REF] Mcshane | Statistics Subcommittee of the NCI-EORTC Working Group on Cancer Diagnostics: Reporting recommendations for tumor marker prognostic studies (REMARK)[END_REF] .

In this study we used the CellSearch assay and AdnaTest BreastCancer because they are suitable for use in a multicenter setting due to a highly standardized procedure for CTC enrichment and detection [START_REF] Riethdorf | Detection of circulating tumor cells in peripheral blood of patients with metastatic breast cancer: a validation study of the CellSearch System[END_REF][START_REF] Fehm | Detection and characterization of circulating tumor cells in blood of primary breast cancer patients by RT-PCR and comparison to status of bone marrow disseminated cells[END_REF][START_REF] Riethdorf | Detection and HER2 expression of circulating tumor cells: prospective monitoring in breast cancer patients treated in the neoadjuvant Geparquattro trial[END_REF][START_REF] Hauch | The clinical significance of circulating tumour cells in breast cancer and colorectal cancer patients[END_REF].

The FDA-approved CellSearch assay is currently the most frequently used approach, particularly in on-going clinical trials. CTCs are isolated by immunomagnetic beads coated with antibodies against EpCAM and identified by cytokeratin-positivity, positive nuclear staining, and CD45 negativity [START_REF] Riethdorf | Detection of circulating tumor cells in peripheral blood of patients with metastatic breast cancer: a validation study of the CellSearch System[END_REF].

Using only EpCAM to enrich CTCs from blood is considered as one of the major limitations of this assay. EpCAM might be heterogeneously expressed by CTCs and be down-regulated as a consequence of the metastatic process [START_REF] Thurm | Rare expression of epithelial cell adhesion molecule on residual micrometastatic breast cancer cells after adjuvant chemotherapy[END_REF]. In addition, experimental data not confirmed in the clinical setting suggest that normal-like breast cancer cells are less efficiently captured by an EpCAM-based approach, which may reduce the sensitivity of this assay [START_REF] Sieuwerts | Anti-epithelial cell adhesion molecule antibodies and the detection of circulating normal-like breast tumor cells[END_REF].

Most prognostic studies have used the cut-off level for CTC positivity of five cells (in 7.5 ml blood) in metastatic breast cancer to distinguish patients with statistically significant clinical outcome [START_REF] Riethdorf | Detection of circulating tumor cells in peripheral blood of patients with metastatic breast cancer: a validation study of the CellSearch System[END_REF][START_REF] Cristofanilli | Circulating tumor cells, disease progression, and survival in metastatic breast cancer[END_REF][START_REF] Budd | Circulating tumor cells versus imaging: predicting overall survival in metastatic breast cancer[END_REF].

Based on this cut-off level, 50% of our patients had at least five CTCs at the time of first diagnosis or disease progression, which is in concordance with the reported positivity rates from 36% to 61% in other large studies [START_REF] Liedtke | Prognostic impact of discordance between triple-receptor measurements in primary and recurrent breast cancer[END_REF][START_REF] Riethdorf | Detection of circulating tumor cells in peripheral blood of patients with metastatic breast cancer: a validation study of the CellSearch System[END_REF][START_REF] Cristofanilli | Circulating tumor cells, disease progression, and survival in metastatic breast cancer[END_REF][START_REF] Budd | Circulating tumor cells versus imaging: predicting overall survival in metastatic breast cancer[END_REF][START_REF] Van Der Auwera | Circulating tumour cell detection: a direct comparison between the CellSearch System, the AdnaTest and CK-19/mammaglobin RT-PCR in patients with metastatic breast cancer[END_REF][START_REF] Hayes | Circulating tumor cells at each follow-up time point during therapy of metastatic breast cancer patients predict progression-free and overall survival[END_REF]. The determination of HER2 status of CTCs has been based on an immunofluorescence staining score established by Meng et al. [START_REF] Meng | HER-2 gene amplification can be acquired as breast cancer progresses[END_REF] and Riethdorf et al. [START_REF] Riethdorf | Detection and HER2 expression of circulating tumor cells: prospective monitoring in breast cancer patients treated in the neoadjuvant Geparquattro trial[END_REF]. FISH would be the optimal method for this task but the relocation of CTCs for FISH analysis may be difficult and does not currently seem feasible in a large clinical trial. A high concordance between immunofluorescence and FISH analysis has been demonstrated by Meng et al. [START_REF] Meng | HER-2 gene amplification can be acquired as breast cancer progresses[END_REF], Riethdorf et al.

[25], and Pestrin et al. [START_REF] Pestrin | Correlation of HER2 status between primary tumors and corresponding circulating tumor cells in advanced breast cancer patients[END_REF], suggesting that the immunofluorescence approach is accurate. However, in the study of Pestrin et al. the correlation between HER2 status of CTCs and primary tumor was higher using the FISH technique. An appropriate cut-off level for HER2 positivity of CTC-positive blood samples has not yet been established. Pestrin et al. [START_REF] Pestrin | Correlation of HER2 status between primary tumors and corresponding circulating tumor cells in advanced breast cancer patients[END_REF] defined CTC samples as HER2 positive if at least 50% of CTCs demonstrated HER2 expression. Meng et al. [START_REF] Meng | HER-2 gene amplification can be acquired as breast cancer progresses[END_REF] suggested that at least 10 CTCs are necessary for optimal HER2 evaluation but did not exclude the possibility that fewer CTCs may be sufficient to indicate that a patient is a candidate for HER2-targeted therapy. The cut-off level used in that study was also 50%. Riethdorf et al. [START_REF] Riethdorf | Detection and HER2 expression of circulating tumor cells: prospective monitoring in breast cancer patients treated in the neoadjuvant Geparquattro trial[END_REF] investigated the percentage of HER2-positive CTCs in a neoadjuvant setting using the threshold of one HER2-positive CTC; however, the number of CTCs in non-metastatic patients is much lower than in the metastatic setting.

In our trial, a case was defined as HER2-positive CTC when at least one CTC had a HER2 immunostaining score of 3+ and ≥5 CTCs were present (criterion for CTC positivity). Based on these definitions, 72 (59%) of the 122 CTC-positive patients were classified as HER2 negative and 50 (41%) as HER2 positive by immunofluorescence staining. HER2-positive CTCs in HER2-negative primary tumors were seen in 25 of the 78 patients (33%), which is in the range of conversion rates of 29% to 38% for initially HER2-negative patients reported in other, smaller studies [START_REF] Meng | HER-2 gene amplification can be acquired as breast cancer progresses[END_REF][START_REF] Pestrin | Correlation of HER2 status between primary tumors and corresponding circulating tumor cells in advanced breast cancer patients[END_REF][START_REF] Fehm | Determination of HER2 status using both serum HER2 levels and circulating tumor cells in patients with recurrent breast cancer whose primary tumor was HER2 negative or of unknown HER2 status[END_REF]. However, modification of the cut-off level for HER2 positivity may be necessary in the case of therapeutic decision-making.

AdnaTest BreastCancer was the other approach used in our current trial. Here, CTCs are isolated by immunomagnetic beads labeled with antibodies against MUC1 and EpCAM. After isolation of the mRNA, transcripts encoding epithelial-specific markers (GA 73.3, MUC1 and HER2) were amplified by a multiplex PCR and detected by microfluid gel electrophoresis. In contrast to RT-PCR approaches mRNA expression levels cannot be quantified, which would be desirable for therapy monitoring. In the present study, the overall detection rate for CTCs was 39%, which is within in the range of other published studies [START_REF] Van Der Auwera | Circulating tumour cell detection: a direct comparison between the CellSearch System, the AdnaTest and CK-19/mammaglobin RT-PCR in patients with metastatic breast cancer[END_REF][START_REF] Tewes | Molecular profiling and predictive value of circulating tumor cells in patients with metastatic breast cancer: an option for monitoring response to breast cancer related therapies[END_REF]. However, using the CellSearch assay, 50% of patients were CTC positive with ≥5 CTCs per 7.5 ml blood despite the fact that only EpCAM was used for CTC enrichment and RT-PCR approaches are supposed to be more sensitive [32].

Overall agreement between AdnaTest BreastCancer and the CellSearch assay was 64%, which is low given that both assays should detect HER2-positive CTCs. Only one other study has so far evaluated both techniques in a head-to-head comparison [START_REF] Van Der Auwera | Circulating tumour cell detection: a direct comparison between the CellSearch System, the AdnaTest and CK-19/mammaglobin RT-PCR in patients with metastatic breast cancer[END_REF]. The concordance rate was nearly 80% but another cut-off level (≥2 CTCs) was used for the CellSearch assay. In our study we analyzed the concordance rate between the assays using three different cut-off levels (1, 2, and 5 cells). The concordance rate was highest using the cut-off of 5 cells, which is mostly used for patients with metastatic breast cancer. Nevertheless, concordance rates of only 52-64% could be obtained (Table 3).

Patients with HER2-positive CTCs were observed in 41% and 47% of cases using the CellSearch assay and AdnaTest BreastCancer, respectively. However, no correlation was observed between these assays regarding HER2 evaluation of CTCs. Several explanations may account for this observation. The CellSearch assay evaluates the HER2 status of individual cells by immunofluorescence, which is important due to heterogeneity of circulating tumor cells. AdnaTest BreastCancer determines the average HER2 expression of all tumor cells. The test is not able to detect the heterogeneity in HER2 expression between different CTCs and to determine the percentage of HER2-positive CTCs. To define a gold standard in an ideal study setting, the HER2 status has to be reassessed by each method and compared to the HER2 status of the metastatic tissue. In our study, biopsy of the metastatic tissue was optional and all patients were encouraged to participate. One potential drawback of our study is that only 30 of 252 patients finally accepted a tissue biopsy. Since most of these patients were CTC negative, no meaningful comparison could be performed.

Should we use CTCs for HER2 assessment despite these caveats? Our findings and case reports from other studies suggest that: 1) initially HER2-negative patients can have HER2-positive CTCs;

and 2) HER2-positive CTCs are eliminated by HER2-targeted therapy, resulting in an objective clinical response in initially HER2-negative patients [START_REF] Hayes | Monitoring expression of HER-2 on circulating epithelial cells in patients with advanced breast cancer[END_REF][START_REF] Meng | HER-2 gene amplification can be acquired as breast cancer progresses[END_REF].

Our study is the largest to compare HER2 CTC testing with different methods. Advantages are the blinded data entry, technical performance of the assays, and the multicenter setting. To implement the HER2 status of CTCs as a stratification parameter in future clinical trials it will be necessary to define a gold standard for HER2 assessment. Since repeated tissue biopsies are not feasible, an alternative seems to investigate the clinical response to HER2-targeted therapy based on the changes in HER2- 1 HER2 positive if at least one cell is strongly stained for HER2 (3+).

B Tables

2 HER2 positive if a HER2 transcript has been detected. 3 Excluding those with unknown HER2 status.

PatientsA

  total of 254 patients with metastatic breast cancer from nine German university breast cancer centers [Düsseldorf (n = 4) Erlangen (n = 30), Essen (n = 46), Freiburg (n = 9), Hamburg (n = 79), Heidelberg (n = 18), Munich (n = 16), Regensburg (n = 2), and Tübingen (n = 50)] were enrolled in this prospective, open-label, non-randomized study. Inclusion criteria were: epithelial invasive carcinoma of the breast with distant metastatic disease (M1), age ≥18 years, the availability of primary tumor tissue results for ER, PR and HER2 and first diagnosis of metastatic disease or disease progression (before start of new treatment regimen). Blood was drawn before the start of a new line of therapy. This included any therapy including hormonal therapy and any line of treatment. All patients gave their informed consent for the use of their blood samples. A web-based databank was designed for data management and on-line documentation (www.detect-study.de). By the use of this interface, clinical investigators were blinded for results of CTC testing and the investigators performing CTC testing were blinded for the clinical data of the patients and the result of the CTC test results from the other centers. The study was approved by local institutional review boards (2007/B01). The trial was registered in the Current Controlled Trials Registry at http://www.controlled-trials.com (no. ISRCTN59722891).

  3 and MUC1) commercialized as AdnaTest BreastCancerSelect™ (Adnagen AG) according to the manufacturer's instructions. The labeled cells were extracted by a magnetic particle concentrator. Subsequently, mRNA isolation from lysed, enriched cells was performed with a Dynabeads mRNA DIRECT™ Micro Kit (Dynal Biotech GmbH, Hamburg, Germany). Sensiscript™ Reverse Transcriptase (QIAGEN GmbH, Hilden, Germany) was used for the reverse transcription in combination with oligo(dT) coupled Dynabeads ® of the mRNA DIRECT™ Micro Kit (Dynal Biotech GmbH) [26]. The analysis of tumor-associated mRNA isolated from CTC tumor cells was performed in a multiplex polymerase chain reaction (PCR) for three tumor-associated transcripts (HER2, MUC1, and GA733-2) and the housekeeping gene -actin. GA 73.3 refers to the EpCAM epitope and the GA733-2 transcript refers to EpCAM mRNA. The primers generate fragments of the following sizes: GA733-2, 395 base pairs (bp); MUC1, 293 bp; and HER2, actin, 114 bp.Visualization of the PCR fragments was carried out with a 2100 Bioanalyzer (Agilent Technologies Inc., Santa Clara, CA, USA) using DNA 1000 LabChips and the Expert Software Package (version B.02.03.SI307). The test was considered CTC positive if a PCR fragment of at least one tumor-associated transcript (MUC-1, GA 773-2, or HER2) and a fragment of the control gene -actin (internal PCR control) was clearly detected (peak concentration of >15 ng/µl) in both blood samples. CTCs were considered HER2 positive if a PCR fragment of the HER2 transcript (peak concentration of >15 ng/µl) was present.

  Sample preparation and analysis by

	that samples could be stored and transported (up to 72 hours) as well as examining the high inter-and
	intra-assay concordance of the results in a multicenter setting [20].
	Before the study was started, each breast cancer center was assigned to send its samples only to the
	designated laboratory for the CellSearch assay and AdnaTest BreastCancer, respectively. Blood
	samples for AdnaTest BreastCancer were shipped in cooled boxes at 4°C whereas samples for the
	CellSearch assay were sent at room temperature based on the manufacturer's recommendation. All
	blood samples were processed within 48 hours for AdnaTest BreastCancer and 96 hours for the
	CellSearch assay, or otherwise discarded. Both AdnaTest BreastCancer and the CellSearch assay
	were performed independently and the investigators were blinded to the results obtained by the other
	method.
	AdnaTest BreastCancer were performed by either of two centers (Departments of Gynecology and
	Obstetrics, Essen (SK-B) or Tübingen (TF); 173 and 81 tests, respectively). CTC analysis by the
	CellSearch assay was performed by either of two centers (Institute of Tumor Biology, University
	Medical Center, Hamburg-Eppendorf (KP) or Department of Gynecology, Munich (BR); 173 and 81
	tests, respectively). These centers have previously conducted a validation study and demonstrated

  used to evaluate the relationship, whereby P values <0.05 indicate statistically significance. When paired data were considered in terms of assessing the reliability of test results of the methods, agreement and consistency were regarded via Cohen's kappa ( ) and McNemar-test, respectively.

Statistical analysis was performed using SAS version 9.2.

Table 1 :

 1 Assay technical data for AdnaTest BreastCancer and the CellSearch assay

		CellSearch assay		AdnaTest BreastCancer
	Storage before processing	96 hours (room temperature)	1	48 hours (4°C)	2
	Immunomagnetic separation	Yes		Yes
	(IS)
	Antibodies for IS	EpCAM		MUC1, EpCAM
	Enrichment	10,000-100,000 times		~10,000 times
	Detection targets	CK CD45		EpCAM, HER2, MUC1
	Detection method	Immunofluorescence		RT-PCR
	Detection limit	1 cell per 5 ml		2 cells per 5 ml
	Specificity	95-100%		95%
	Quantitative	Yes		No
	Reference	Riethdorf et al. [20,25]		Hauch et al. [26]

1

Using CellSave tubes

2

Using AdnaCollect blood collection tubes

Table 2 :

 2 Clinical characteristics of patients and effect on CTC positivity rate according to assay used

				CellSearch CTC positive	AdnaTest CTC positive
				(n = 245)		(n = 229)
				No./total 1 (%)	P value	No./total 1 (%)	P value
	Total (N = 254)	122/245 (50)		90/229 (39)
	Menopausal status
	Pre (n = 82) Post (n = 172)	44/80 (55) 78/165 (47)	0.25	37/78 (47) 5/2151 (35)	0.07
	Histology
	Ductal (n = 203)	93/194 (48)		71/184 (39)
	Lobular (n = 25)	15/25 (60)	0.48	11/20 (55)	0.26
	Other (n = 26)	14/26 (54)		8/25 (32)
	ER status	2
	Negative (n = 77) Positive (n = 176)	33/74 (45) 89/170(52)	0.27	27/70 (39) 63/158 (40)	0.85
	PR status	2
	Negative (n = 102) Positive (n = 151)	47/99 (47) 75/145 (52)	0.51	36/91 (40) 54/137 (39)	0.98
	HER2 status	2,3
	Negative (n = 145)	76/139 (55)		57/126 (45)
	Positive (n = 77)	31/75 (41)	0.174	22/73 (30)	0.10
	Unknown (n = 32)	15/31 (48)		11/30 (37)
	Metastatic site
	Bone (n = 35)	14/35 (40)		8/30 (27)
	Visceral (n = 100)	39/96 (41)	0.07	34 / 91 (37)	0.19
	Both (n = 119)	69/114 (61)		48 / 108 (44)
	Metastatic site
	One site (n = 85) Multiple sites (n = 169)	34/84 (41) 88/161 (55)	0.03	24/75 (32) 66/154 (43)	0.11
	Disease-free interval
	≤12 months (n = 65) >12 months (n = 189)	32/61 (53) 90/184 (49)	0.63	22/57 (39) 68/172 (40)	0.90
	Therapeutic setting
	First line (n = 98)	48/94 (51)		37/88 (42)
	Second line (n = 68)	28/65 (43)	0.43	26/62 (42)	0.51
	≥Third line (n = 86)	46/86 (53)		27/79 (34)

Table 4 :

 4 Distribution of HER2 immunostaining score (0, 1+, 2+, and 3+) 1 combinations of CTCs analyzed by CellSearch assay in individual patient samples (n = 122)

	HER2 staining score of CTCs	Number of patients (%)
	CTC (0)			3 (3)
	CTC (1+)			31 (25)
	CTC (2+)			0
	CTC (1+ and 2+)		38 (31)
	CTC (3+)	2		2 (2)
	CTC (1+ and 3+)	2	8 (6)
	CTC (2+ and 3+)	2	2 (2)
	CTC (1+, 2+, and 3+)	2	38 (31)
	HER2 positive		50 (41)
	Total			122 (100)

Table 5 :

 5 HER2 status of CTCs determined by the assays and correlation with primary tumor HER2

	status
	No. (%)

Table 6 :

 6 Correlation for CTC positivity between CellSearch assay and AdnaTest BreastCancer

			No. (%)
			AdnaTest BreastCancer
	CellSearch assay		Negative	Positive	Total
	(A) CTC positivity (n = 221)	1
	Negative		79 (36)	26 (12)	105 (47)
	Positive		54 (24)	62 (28)	116 (53)
	Total		133 (60)	88 (40)	221 (100)
	(B) HER2 status of CTC positive samples (n = 62)	2
	Negative		18 (29)	16 (26)	34 (55)
	Positive		15 (24)	13 (21)	28 (45)
	Total		33 (53)	29 (47)	62 (100)
	1 p < 0.01 ( = 0.28);	2 p = 0.96 ( = -0.006).

positive CTCs in cancer patients[START_REF] Riethdorf | Detection and HER2 expression of circulating tumor cells: prospective monitoring in breast cancer patients treated in the neoadjuvant Geparquattro trial[END_REF]. Our present study is a step towards the implementation of HER2 CTC status determination as a novel biomarker for the use of HER2-targeted therapies.

Data missing for some patients.

ER,PR and HER2 status of the primary tumor ,

Negative, IHC 0/1+ or FISH negative, positive, IHC 3+ or FISH positive; unknown, not determined or IHC 2+ and FISH not performed.

CTCs: 0 = HER2 negative; 1+ = weakly stained;

2+ = moderate staining; 3+ = HER2 strongly stained.[START_REF] Schechter | The neu oncogene: an erbB-related gene encoding a 185,000-Mr tumour antigen[END_REF] Blood samples with HER2 positive CTCs based on the definition for HER2-positive CTCs (≥5 CTCs and ≥1 CTC with strong immunostaining (3+).

Acknowledgements

This work was supported by an unrestricted research grant of Roche Pharma AG, Germany.

Furthermore, this study was partly supported by Adnagen (Langenhagen, Germany). We thank Cornelia Coith, Susanne Hoppe, Sylke Krenkel, Oliver Mauermann, Malgorzata Stoupiec, and Silke Dürr-Störzer for excellent technical assistance. Our special thanks to Ute Hilcher for coordinating the study. In addition, we would like to thank all doctors (Michaela Becker, Julia Jüstock, Dina Mury, Mitras Tewes, and Julia Zeitz) for help with patients and data collection, Dr. Elke Heidrich-Lorsbach (Alcedis GmbH) for statistical analysis and data management, and Lee Miller from Miller Medical Communications for editing and reviewing the manuscript.

Abbreviations

CK, cytokeratin; CTC, circulating tumor cell; DAPI, 4',6-diamidino-2-phenylindole; FDA, Food and Drug Administration; HER2, human epidermal growth factor receptor 2; EpCam, epithelial cell adhesion molecule; ER, estrogen receptor; FISH, fluorescence in situ hybridization; FITC, fluorescein isothiocyanate; IHC, immunohistochemistry; MUC1, mucin 1; N/A, not available; PR, progesterone receptor; RT-PCR, real-time polymerase chain reaction.