Bastien Cazaux
email: cazaux@lirmm.fr

Thierry Lecroq
email: thierry.lecroq@univ-rouen.fr

Eric Rivals
email: rivals@lirmm.fr

Construction of a de Bruijn Graph for Assembly from a Truncated Suffix Tree

Keywords: Stringology, Text Algorithms, Indexing Data Structures, de Bruijn Graph, Assembly, Space Complexity, Dynamic Update

In the life sciences, determining the sequence of bio-molecules is essential step towards the understanding of their functions and interactions inside an organism. Powerful technologies allows to get huge quantities of short sequencing reads that need to be assemble to infer the complete target sequence. These constraints favour the use of a version de Bruijn Graph (DBG) dedicated to assembly. The de Bruijn Graph is usually built directly from the reads, which is time and space consuming. Given a set R of input words, well-known data structures, like the generalised suffix tree, can index all the substrings of words in R. In the context of DBG assembly, only substrings of length k + 1 and some of length k are useful. A truncated version of the suffix tree can index those efficiently. As indexes are exploited for numerous purposes in bioinformatics, as read cleaning, filtering, or even analysis, it is important to enable the community to reuse an existing index to build the DBG directly from it. In an earlier work we provided the first algorithms when starting from a suffix tree or suffix array. Here, we exhibit an algorithm that exploits a reduced version of the truncated suffix tree and computes the DBG from it. Importantly, a variation of this algorithm is also shown to compute the contracted DBG, which offers great benefits in practice. Both algorithms are linear in time and space in the size of the output.

Introduction

The de Bruijn Graph (DBG) serves in bioinformatics and genomics to assemble the sequence of large molecules from a huge set of short sequencing reads. In this context, only the substrings of length, say k, of the reads form the nodes of the DBG (unlike in the original DBG). These substrings are termed k-mers in biology or k-grams in computer science. An arc links two k-mers whenever they overlap by (k -1) symbols at (necessarily) successive positions in a read. The assembly DBG is then traversed searching for long paths, which will form the contigs, i.e. the sequence of sub-regions of the molecule. However, in non repetitive regions, the layout of the reads dictate a single path of k-mers without bifurcations. Any simple path between an in-branching node and the next out-branching node, can then be contracted into a single arc without loosing any information on the graph structure. The sequence of such simple paths are called unitigs (the contraction from unique and contigs). The version of the DBG where all such "non-branching" paths are condensed into an arc is termed the Contracted DBG (CDBG).

Given the extreme throughput delivered by nowadays sequencing machines, it is crucial to enable fast construction of the CDBG. It is also desirable to build the DBG or its contracted version directly from space efficient indexing data structures, since the read set has often been filtered and mined for patterns representing errors prior to assembly using such data structures. It occurs for instance in a preprocessing phase of sequencing errors removal using a generalised suffix tree of the reads [START_REF] Salmela | Correction of sequencing errors in a mixed set of reads[END_REF]. The use of an indexing data structure (or index for short) also allows to compute and store additional information into the nodes of the DBG: the coverage of a k-mer, i.e. the number of reads in the layout covering that k-mer. Unexpected variations of the coverage permits to detect sequencing errors, to distinguish between classes of point mutations [START_REF] Philippe | CRAC: an integrated approach to the analysis of RNA-seq reads[END_REF], but also to disentangle repetitive sequence regions. Indeed, the reads coming from the distinct but similar copies of a repeat tend to collapse into a single assembly region and increase abnormally the local coverage. Actually, the DBG is itself used as a data structure to seek graph patterns representing mutation, large insertions/deletions, or chromosomal rearrangements [START_REF] Rizk | Mindthegap: integrated detection and assembly of short and long insertions[END_REF].

In a first attempt towards constructing the DBG from an index, Cazaux et al. gave recently two algorithms for building it from either a Generalised Suffix Tree (GST) or a generalised Suffix Array [START_REF] Cazaux | From Indexing Data Structures to de Bruijn Graphs[END_REF]. Indeed, a subset of the suffix tree nodes represent either exactly one k-mer or its shortest extension; hence, this subset is isomorphic to the set of nodes of the DBG. Moreover, following a suffix link and then going down the tree at most once allows to traverse from one node to its neighbours in the DBG. Hence, the arcs of the DBG can be simulated on the GST or computed using it. This summarises the basis of the DBG construction algorithms, which require linear time in the input length (i.e. the cumulated sum of the read lengths). Importantly, it was also shown that the contraction of the arcs in the DBG can be computed in linear time during the construction: this gave the first linear time CDBG construction algorithm [START_REF] Cazaux | From Indexing Data Structures to de Bruijn Graphs[END_REF].

However, in practice the size of the Generalised Suffix Tree remains prohibitive for large read sets. In the light of these algorithms, it is clear that many nodes of the GST among those having a string depth either larger than the order k or strictly smaller than k -1 are useless. Truncated Suffix Trees (TST) have been introduced to index only a subset of factors below a certain string depth [START_REF] Na | Truncated suffix trees and their application to data compression[END_REF][START_REF] Schulz | The generalised k-truncated suffix tree for time-and space-efficient searches in multiple DNA or protein sequences[END_REF]. TST avoid storing strings longer than a limit length k, but still include all suffixes shorter than k. In practice, when the reads are numerous and short, which occurs in a majority of large sequencing applications, the memory wasted for such nodes is important. With an Illumina sequencing experiment, the typical number of reads n := 10 8 , the read length is 100 and several values are used for k up to 64. In such a case, one stores n × (k -2) useless nodes. We set out to first find an algorithm for a reduced version of the TST that avoids those nodes, second to show that the DBG and CDBG can both be built in time and space that are linear in the size of the DBG, rather than in the cumulated length of the reads. The paper is organised as follows. Below we list related works. In Section 2, we define a simple condition that a set of input strings must satisfy to allow building a generalised index and sketch a modification of McCreight's algorithm [START_REF] Mccreight | A space-economical suffix tree construction algorithm[END_REF] for doing so. In Section 3, we introduce the reduced truncated suffix tree and specialise the previous algorithm for constructing it efficiently. Finally, in Section 4 we show how to construct both the de Bruijn Graph and its contracted version in optimal time from the reduced truncated suffix tree. We then conclude mentioning lines of future work.

Related Works

Suffix trees are well-known indexing data structures that enable to store and retrieve all the factors of a given string. They can be adapted to a finite set of strings and are then called generalised suffix trees (GST). They can be built in linear time and space. They have been widely studied and used in a large number of applications (see [START_REF] Apostolico | The myriad virtues of suffix trees[END_REF][START_REF] Gusfield | Algorithms on strings, trees and sequences: computer science and computational biology[END_REF]). In some applications it is not required to consider the full set of suffixes, since one may only be interested in factors of length bounded by a given constant. These factors are actually prefixes of suffixes. In 2003, Na et al. [START_REF] Na | Truncated suffix trees and their application to data compression[END_REF] introduced the truncated suffix trees which only stores the factors of length at most k in a context of lossless data compression. They gave linear time algorithms for directly constructing truncated suffix trees. They present experimental results showing that on various kinds of strings and different values of k that truncated suffix trees have much less nodes than suffix trees. Truncated suffix trees have been generalised to set of strings and use for performing efficient pattern matching in biological sequences [START_REF] Schulz | The generalised k-truncated suffix tree for time-and space-efficient searches in multiple DNA or protein sequences[END_REF].

DBGs are heavily exploited for genome assembly in bioinformatics [START_REF] Pevzner | An Eulerian path approach to DNA fragment assembly[END_REF], where several compact data structures for storing DBGs have been developed [START_REF] Conway | Succinct data structures for assembling large genomes[END_REF][START_REF] Bowe | Succinct de Bruijn Graphs[END_REF] including probabilistic ones [START_REF] Chikhi | Space-efficient and exact de Bruijn graph representation based on a Bloom filter[END_REF]. The emphasis is placed on the practical space needed to store the DBGs in memory. Moreover, some recent assembly algorithms put forward the advantage of using for the same input, multiple DBGs with increasing orders [START_REF] Peng | IDBA -A Practical Iterative de Bruijn Graph De Novo Assembler[END_REF], thereby emphasising the need for dynamically updating the DBGs.

From now on, the input of our problem consists of an integer k > 0 and R = {w 1 , . . . , w n } a set of n finite words over a finite alphabet. We will consider indexing the substrings of words in R; hence, all indexes used are generalised indexes [START_REF] Gusfield | Algorithms on strings, trees and sequences: computer science and computational biology[END_REF]. For simplicity, we may omit this adjective.

Set of Chains of Suffix-dependant Strings and Tree

Here, we introduce the notion of suffix dependence between strings, and the notion of chain of suffix-dependant strings in order to define a unified index that generalises both the suffix tree [START_REF] Mccreight | A space-economical suffix tree construction algorithm[END_REF] and the truncated suffix tree [START_REF] Na | Truncated suffix trees and their application to data compression[END_REF]. First, we introduce a notation on strings.

Notation on Strings

We consider finite strings (also termed words or sequences) over a finite alphabet Σ. For a string w, |w| denotes the length of w. For any integers i and j such that i ≤ j, [i, j] denotes the interval of integers between i and j. For any i ≤ j in [1, |w|], w[i, j] is the substring of w beginning at position i and ending at position j.

Then, w[1, i] is called a prefix of w, while w[i, |w|] is a suffix of w. For a set of strings A, the norm of A, denoted ||A||, is ||A|| = ∑ a∈A |a|.
Now, let us define the concept of suffix-dependant strings and of chains of suffixdependant strings.

Definition 1. 1. A string x is said to be suffix-dependant of another string y if x [2..|x|] is prefix of y. 2. Let w be a string and m be a positive integer smaller than |w| -

1. A m-tuple of m strings (x 1 , . . . , x m ) is a chain of suffix-dependant strings of w if x 1 is a prefix of w and for each i ∈ [2, m], x i is a prefix of w[i, |w|] such that |x i | ≥ |x i-1 | -1.
For a set of strings R = {w 1 , . . . , w n } , let S = {C 1 , . . . ,C n } be a set of tuples such that

for each i ∈ [1, n], C i is a chain of suffix-dependant strings of the string w i . For i ∈ [1, n] and j ∈ [1, |C i |], C i [ j] is the j th string of the tuple C i . Let be S = { C 1 , . . . , C n } the set of tuples such that for each i ∈ [1, n] and j ∈ [1, |C i |], C i [ j] = |C i [ j]|, i.e. S contains tuples of lengths.
With S and R, we can easily compute S. In the sequel, we use S to demonstrate our results, and S to state the complexities of algorithms. Indeed, in the case where C i is the tuple of each suffix of w i , the size of

C i is linear in |w i | 2 but C i is linear in |w i |.
Let w be a string; w may occur in distinct tuples of S. Thus, we define N(w) the set of (i, j) such that w = C i [ j]. In other words, N(w) is the set of coordinates of the elements of S that are equal to w.

We define a contracted version of the well-known Aho-Corasick tree [START_REF] Gusfield | Algorithms on strings, trees and sequences: computer science and computational biology[END_REF]. In fact, we apply nearly the same contraction process that turns a trie of a word into its compact Suffix Tree [START_REF] Gusfield | Algorithms on strings, trees and sequences: computer science and computational biology[END_REF]. Consider the Aho-Corasick tree of R, in which each node represents a prefix of word in R. We contract the non-branching parts of the branches except that we keep all nodes representing a word that belongs to a tuple in S. From now on, let T (S ) denote this contracted version of the Aho-Corasick tree of R.

N and L denote respectively the set of nodes and the set of leaves of T (S ). Furthermore, we define for each node v of T (S ) two weights:

s(v) is the number of times that an element of a tuple of S is equal to the word represented by v (i.e. s(v) := |N(v)|).

t(v) is the number of times that the first element of a tuple of S is equal to the word

represented by v (i.e. t(v) := |{(i, 1) ∈ N(v) | i ∈ [1, n]}|).
Let w be a string, we put Succ(w) = {(i, j) | (i, j -1) ∈ N(w) and j ≤ |C i |}. We define F as the subset of L such that:

F := {u ∈ L | ∃C ∈ S and j < |C| such that u = C[ j]} It is equivalent to say that F = {u ∈ L | Succ(u) is not empty}. A mapping m from F to N is called possible link if for each node v in F , ∃(i, j) ∈ Succ(v) such that m(v) = C i [ j].
Below we present an algorithm that constructs T (S ), and computes for each node v in N , the weights s(v) and t(v) and a possible link P 0 .

Algorithm to Construct the T (S ): Now, we give an algorithm to construct T (S ). We use the version of McCreight's algorithm given by Na et al. [START_REF] Na | Truncated suffix trees and their application to data compression[END_REF] on our input and we build for each leaf v, s(v), t(v) and P 0 (v). For building T (S ), we start with a tree that contains only the root. Then, for each word w in every chain C, we create or update (if it exists) the node w as follows. Assume that we keep in memory the node v that has been processed just before w.

If w is the first word of C, we go down from the root by comparing w to the labels of the tree. If we create the node w, s(w) and t(w) are initialised to 1, and P 0 (w) to nil. If w already exists on the tree, we increment s(w) and t(w) by 1.

If w is not the first word of C, we start from v, and as in McCreight's algorithm, we create or arrive on the node representing w. If we need to create this node, s(w) is initialised to 1, t(w) to 0, and P 0 (w) to nil. Otherwise, we add 1 to s(w). We set P 0 (v) = w.

The loop continues with the next word until the end, and we obtain T (S ). Clearly, the construction algorithm of T (S ) computes both weights s(.) and t(.), and the possible link P 0 (.) correctly. For the complexity, for each chain of suffix-dependant C i of S, the length of the traverse path on the tree is equal to |w i |, thanks to the use of the suffix links. Thus as in McCreight's algorithm, the complexity is in O(||R||). Now, we are equipped with an algorithm that builds T (S ) for any set of chains of suffix-dependant strings. Let us review some instances of sets S, for which T (S ) is in fact a well-known tree.

-If C := ∪ w∈R {tuple of suffixes of w}, then T (C) is the Generalised Suffix Tree of R (see Figure 1a). We have that the restrained mapping sl(.) is an example of a possible link.

-If B k := ∪ w∈R {tuple of k-mer of w and suffixes of length k < k of w}, then T (B k )

is the generalised k-truncated suffix tree of R, as defined in [START_REF] Schulz | The generalised k-truncated suffix tree for time-and space-efficient searches in multiple DNA or protein sequences[END_REF] (which generalizes the k-truncated suffix tree of Na et al. [START_REF] Na | Truncated suffix trees and their application to data compression[END_REF]). -If A k := ∪ w∈R {tuple of k + 1-mer of w and suffixes of length k of w}, then T (A k ) is the truncated suffix tree that we define below in Section 3 (see Figure 1b).

Our Truncated Suffix Tree

First, let us introduce a notation about trees that index strings and whose edges are labelled with strings.

Definition 3. For a node v of a tree, f (v) denotes the parent node of v, and Children(v) its set of children. The depth of v is the length of the unique path between the root and v in the tree. Each represent a unique word: that made up by the concatenation of the label of edges along this path. The notion of node and the word it represents are confounded (we used one for the other). For a T (S ) and a word w, w is the node v with the shortest depth of the T (S ) such that w is a prefix of v. If this node does not exist, w does not exists. For a node u of the T (S ), sl(u) is the node u [2, |u|] .

For a set of words R = {w 1 , w 2 , . . . , w n } and an integer k > 0, we define the following notation.

Definition 4.

1. F k (R) is the set of substrings of length k of words of R. 2. Suff k (R) is the set of suffixes of length k of words of R. 3. For all i ∈ [1, |R|] and j ∈ [1, |w i | -k + 1],
A k,i denotes the tuple such that its j th is defined by

A k,i [ j] := w i [ j, j + k] if j ≤ |w i | -k w i [ j, |w i |] otherwise.

and finally A k is the set of these tuples: A

k := n i=1 A k,i . Proposition 5. 1. A k,i is a chain of suffix-dependant strings of w i . 2. Moreover, {w ∈ A k,i | A k,i ∈ A k } = F k+1 (R) ∪ Suff k (R). Proof. 1. For all j ∈ [1, |A k,i | -k], it is easy to see that A k,i [ j] is a suffix-dependant string of A k,i [ j + 1]. 2. For the second point {w ∈ A k,i | A k,i ∈ A k } = n i=1 ( |w i |-k+1 j=1 {A k,i [ j]}) = n i=1 ( |w i |-k j=1 {A k,i [ j]} {A k,i [|w i | -k + 1]}) = n i=1 (F k+1 ({w i }) Suff k ({w i })) = F k+1 (R) ∪ Suff k (R)
By applying the algorithm described in Section 2 to the set A k (Definition 4), and by using Theorem 2, we get the following result. Corollary 6. We can construct T (A k ) in O(||R||) time and space.

Experimental Results

We tested the two data structures GST and TST on real biological data. We considered a set of 2249632 Illumina reads of yeast of length 101 and performed tests for subsets of size 100, 1000, 10000, 100000, 1000000 and for the whole set. We counted the number of nodes of the GST and of the TST for various values of k (5, 10, 20 and 40). We used the gsuffix1 of [START_REF] Schulz | The generalised k-truncated suffix tree for time-and space-efficient searches in multiple DNA or protein sequences[END_REF]. It should be noted that their implementation of the TST stores all the suffixes shorter than k producing thus more nodes than our TST. Table 1 show the results. It can be seen that for small sets, TSTs do not save many nodes compare to the GST except for very small values of k but that for large sets TSTs save a lot of nodes for small values of k, they save more than two third of nodes for k = 20 and almost half of the nodes for k = 40. We also performed experiments with longer reads from Pacific Biosciences technology (not shown here). In this case, as expected, TSTs save less nodes than for Illumina reads.

De Bruijn Graph via the Truncated Suffix Tree

Here, we describe an algorithm that builds the de Bruijn Graph of a set of words R starting from the generalised truncated suffix tree of R. Note that this DBG differs from the original graph as defined by de Bruijn in the field of word combinatorics [START_REF] De Bruijn | On bases for the set of integers[END_REF]. The DBG studied here serves for genome assembly and for approximating the well-known Shortest Superstring problem [START_REF] Golovnev | Approximating shortest superstring problem using de bruijn graphs[END_REF].

De Bruijn Graph

Let k be a positive integer and R := {w 1 , . . . , w n } be a set of n words. We use the definition of a de Bruijn graph stated in [START_REF] Cazaux | From Indexing Data Structures to de Bruijn Graphs[END_REF].

Definition 7 (de Bruijn graph). The de Bruijn graph of order k for R, denoted by dBG + k , is a directed graph, whose vertices are the k-mers of words of S and where an arc links u to v if and only if u and v are two successive k-mers of a word of R.

Another slightly different definition is sometimes used in which the k-mers must overlap by (k -1) symbols, but must not necessarily occur in the same read. This relaxed definition introduces "false" arcs, but is easier to build and store in memory. All our results can easily be adapted to that definition. Proposition 8 states that there does not exist any leaf in T (A k ) representing a word strictly shorter than k.

Proposition 8. Let v be a leaf of T (A k ). Then |v| = k or |v| = k + 1. Proof. For all w i ∈ R and j ∈ [1, |w i | -k + 1], |A k,i [ j]| = k or k + 1. We set Init R,k = {v ∈ V T (A k ) | |v| ≥ k and | f (v)| < k}.
For a possible link P 0 , we define the mapping P from F to N . F , N and L have the same definition as before, but applied to the T (A k ). F can be seen in this case as the set of leaves of length k + 1 of T (A k ). We define the mapping P as follows:

P : F -→ N v → P 0 (v) if P 0 (v) ∈ Init R,k f (P 0 (v)) otherwise
The mapping P can be constructed in linear time in O(||R||). In fact, for each v ∈ F , P(v) can be constructed in O(1) because in this case,

P 0 (v) ∈ Init R,k ⇔ | f (P 0 (v))| = k.
(v) = f (P 0 (v)) ∈ Init R,k .
According to the definitions of a possible link P, and of A k , for any node v in L, P(v) is the shortest node of T (A k ) such that v is a prefix of P(v). Hence,

P(v) = sl(v).
Let us define, E + k , a set of arcs. Two cases arise depending on whether the starting node v represents a word of length k or k + 1. 2 illustrates the alternative cases in the definition of E + k , which is the union of these cases.

E + k = ∪ |v|=k+1 (v, P(v)) ∪ ∪ |v|=k ∪ u∈Children(v) (v, P(u)) with v ∈ Init R,k . Figure
Proposition 10. (Init R,k , E + k ) is isomorphic to dBG + k of R.
Proof. The proof is identical to that of [START_REF] Cazaux | From Indexing Data Structures to de Bruijn Graphs[END_REF]Theorem 1]. Figure 3 shows an example of de Bruijn graph of order 2 built from T (A 2 ).

Proposition 11. The size of T (A k ) is linear in the size of dBG + k .

Proof. Let b be the application from

F to E + k such that b(v) = (v, P(v)) if | f (v)| = k ( f (v), P(v)) if | f (v)| = k. By Proposition 10, b is a bijection. As |L \ F | ≤ |R|, |L| is linear in the size of dBG + k .
From R, we first build the reduced TST, and then build dBG + k from it. By Proposition 11, we get the following theorem.

A Contracted de Bruijn Graph

Let e an arc of dBG + k , e = (x, y) is said to be reducible if the outdegree of x and the indegree of y are at most 1.

Definition 13. Let k be a positive integer and R := {w 1 , . . . , w n } be a set of n words. The contracted de Bruijn graph of order k for R, denoted by CdBG + k , is the de Bruijn graph of order k where each reducible arc is contracted.

Let z be a word, Support R (z) is the set of pairs (i, j), where z is the substring Instead of using T (A k ) to build dBG + k or CdBG + k , we could have taken T (B k+1 ). Indeed, T (B k+1 ) is the tree T (A k ) with additional leaves representing all suffixes shorter than (k -1) of the words in R. These leaves make T (B k+1 ) linear in ||R||, but not in the size of dBG + k .

w i [ j, j + |s| -1]. Support R (z) is called the support of z in R.

Conclusion

First, we provided a unified version of the construction of a generalised index for a set of input words. It only requires that the elements of the chain are suffix-dependant. This general framework was applied to build a reduced version of a Truncated Suffix Tree (TST), which given a parameter k does not contain any node representing a string smaller than k -1 compared to the TST of [START_REF] Na | Truncated suffix trees and their application to data compression[END_REF][START_REF] Schulz | The generalised k-truncated suffix tree for time-and space-efficient searches in multiple DNA or protein sequences[END_REF]. Our algorithm does not build those nodes and thus does not need to remove them afterwards, as would be the case with the TST of [START_REF] Na | Truncated suffix trees and their application to data compression[END_REF][START_REF] Schulz | The generalised k-truncated suffix tree for time-and space-efficient searches in multiple DNA or protein sequences[END_REF]. This feature is crucial since otherwise, the index data structure could not be linear in the size of the de Bruijn Graph of order k. Moreover, it is not trivial to modify the algorithm of [START_REF] Na | Truncated suffix trees and their application to data compression[END_REF] to avoid building those nodes, because it uses their suffix links during construction. A natural question arise: does our framework remain valid if one relaxes the assumption of suffix-dependency? Second, we show that the de Bruijn Graph (DBG) that is heavily exploited in the context of genome assembly can be directly constructed from the reduced TST in a time and a space linear in the size of the output. This part builds upon our earlier work, which addressed the question of DBG construction from a Suffix Tree and Suffix Array [START_REF] Cazaux | From Indexing Data Structures to de Bruijn Graphs[END_REF]. Moreover, we provide an algorithm to build the contracted DBG, which is used in practice and directly yields as a by-product of the contraction, a class of reliable contigs, called the unitigs 2 . Starting from the reduced truncated tree ensures that the index encodes as much nodes as the output DBG. However, as information on nodes representing substrings of length < k -1 are missing, one looses the dynamicity obtained in [4, Section 6]: our reduced TST cannot support the DBG construction for both order k and k -1. Nevertheless, as our algorithms remain valid for the original TST [START_REF] Na | Truncated suffix trees and their application to data compression[END_REF][START_REF] Schulz | The generalised k-truncated suffix tree for time-and space-efficient searches in multiple DNA or protein sequences[END_REF], which stores all the information for any substrings ≤ k, we can dynamically update the DBG for any order < k. Both the questions of 1/ dynamically updating the de Bruijn Graph when the order changes by more than one unit, and of 2/ constructing the DBG from compressed indexes make thrilling lines of future work.

Theorem 2 .

 2 For a set of chain of suffix-dependant strings S, we can construct T (S ) in O(||R||) time and space. Proof. To begin with, let us to prove that T (S ) is in O(||R||) space. Its number of leaves equals ∑ C∈S |C|. Hence, its number of nodes is at most 2 ∑ C∈S |C| -1 ≤ 2||R||, and its number of edges is at most 2||R||. Thus the size of T (S ) is in O(||R||).

Fig. 1 .

 1 Fig. 1. (a) The generalised suffix tree for the set of words {bacbab, bbacbaa, bcaacb, cbaac, cbabcaa}. The part above the green line corresponds to the TST T (A 2 ), which is shown in (b). (b)The truncated suffix tree T (A 2 ) for the same set of words.

Fig. 2 .Proposition 9 .

 29 Fig. 2. The different cases of the definition of E + . For a node v (in green), the curved solid arrows are the arcs of E + , the dashed arrows are the suffix links of the nodes, the dashed nodes are nodes of Init R,k . (a) and (b) correspond to the first part of the definition while (c) corresponds to the second part. As |F | ≤ ||R||, we can construct P for all elements of F in O(||R||). Indeed, It is enough to look the length of the parent of P 0(v) to decide if P 0 (v) is in Init R,k . Proposition 9. Le be v ∈ L, P(v) ∈ Init R,k and P(v) = sl(v) if sl(v) exists. Proof. Let be v ∈ L. If v ∈ F and P 0 (v) / ∈ Init R,k , | f (P 0 (v))| = k and thus P(v) = f (P 0 (v)) ∈ Init R,k .According to the definitions of a possible link P, and of A k , for any

Theorem 12 .

 12 For a set of words R, we can construct dBG + k in O(||R||) time and in O(size(dBG + k )) space.

1 Fig. 3 .

 13 Fig.3. The de Bruijn graph of order 2 built on T (A 2 ). The solid curved arrows are the edges corresponding to the first part of the definition of E + k , while those in blue correspond to the second part.

Proposition 14 .

 14 For each leaf v of T (A k ), s(v) is the size of the support of v in R and t(v) is the size of the set Support R (v) ∩ {(i, 1) | 1 ≤ i ≤ n} .Hence, we obtain the following theorem. Theorem 15. For a set of words R, we can construct CdBG + k in O(||R||) time and in O(size(dBG + k )) space.

Table 1 .

 1 Number of nodes of the GST vs the TST for k = 5, 10, 20, 40 and the percentage compare to the GST for Illumina reads of length 101.

	reads	100	1000	10000
	ST	14382	135558	1320811
	TST (k = 5)	1352 (9.40%)	1365 (1.00%)	1365 (0.10%)
	TST (k = 10)	14100 (98.03%) 120602 (88.96%)	677153 (51.26%)
	TST (k = 20)	14347 (99.75%) 133204 (98.26%) 1263803 (95.68%)
	TST (k = 40) 14382 (100.00%) 134316 (99.08%) 1291685 (97.79%)
	reads	100000	1000000	2249632
	ST	12354838	103555389	216725799
	TST (k = 5)	1365 (0.01%)	1365 (0.001%)	1365 (0.0006%)
	TST (k = 10) 1315886 (10.65%) 1396675 (1.34%)	1397752 (0.64%)
	TST (k = 20) 10549607 (85.38%) 49389538 (47.69%) 69248532 (31.95%)
	TST (k = 40) 11337038 (91.76%) 69375578 (66.99%) 117282522 (54.11%)

http://gsuffix.sourceforge.net/gsuffix-docs/main.html

Usually the result of an assembly is not the complete sequence, rather a set of assembled sequences called contigs

This work is supported by ANR Colib'read (http://colibread.inria.fr) (ANR-12-BS02-0008) and by Défi MASTODONS SePhHaDe (http://www.lirmm.fr/mastodons) from CNRS.


Long

Mélanie Alberich

François André

Cécile Menez

Roger K Prichard

Anne Lespine
email: anne.lespine@inrae.fr

the development of the dog heartworm is highly sensitive to sterols which activate the orthologue of the nuclear receptor DAF-12

prevention therapy against Dirofilaria immitis in companion animals is currently threatened by the emergence of isolates resistant to macrocyclic lactone anthelmintics. Understanding the control over developmental processes in D. immitis is important for elucidating new approaches to heartworm control. The nuclear receptor DAF-12 plays a role in the entry and exit of dauer stage in Caenorhabditis elegans and in the development of free-living infective third-stage larvae (iL3) of some Clade IV and V parasitic nematodes. We identified a DAF-12 ortholog in the clade III nematode D. immitis and found that it exhibited a much higher affinity for dafachronic acids than described with other nematode DAF-12 investigated so far. We also modelled the DimDAF-12 structure and characterized the residues involved with DA binding. Moreover, we showed that cholesterol derivatives impacted the molting process from the iL3 to the fourth-stage larvae. Since D. immitis is unable to synthesize cholesterol and only completes its development upon host infection, we hypothesize that host environment contributes to its further molting inside the host vertebrate. Our discovery contributes to a better understanding of the developmental checkpoints of D. immitis and offers new perspectives for the development of novel therapies against filarial infections.

 . They typically bind small lipophilic molecules, resulting in their activation, which allows the receptor to recruit coregulators of expression of specific genes 5 . Because of their central role in critical metabolic processes, including development, NRs are relevant targets for drug discovery 2 . It is estimated that 10-20% of the pharmaceutical market targets these receptors in humans 5 .

 . In contrast, in unfavorable conditions, DAs are not synthesized and the DAF-12 apo-receptor interacts with a co-repressor, preventing target gene expression and resulting in arrest of development at dauer diapause larvae, a non-feeding, non-reproducing, stress-resistant, open

the C-terminus and appears more divergent between NRs [START_REF] Mangelsdorf | The nuclear receptor superfamily: the second decade[END_REF] . It contains the ligand binding pocket (LBP) where ligands, co-activators or co-repressors bind to modulate the receptor activity. DimDAF-12 LBD shares only 43% sequence identity to CelDAF-12 but more than 52% with parasitic SstDAF-12, AceDAF-12 and AcaDAF-12. Taken together, the analysis of the sequence showed that DimDAF-12 was a typical NR and structurally related to the DAF-12 NR family.

Dafachronic acids activate recombinant DimDAF-12.

Based on the high sequence homologies between DimDAF-12 and the other nematode DAF-12 (Fig. 1), we explored whether DAs, known ligands and activators of CelDAF-12 [START_REF] Motola | Identification of ligands for DAF-12 that govern dauer formation and reproduction in C. elegans[END_REF][START_REF] Gerisch | A bile acid-like steroid modulates Caenorhabditis elegans lifespan through nuclear receptor signaling[END_REF] , can also activate DimDAF-12. Using a transactivation assay based on mammalian NIH3T3 cells co-transfected with a gene encoding a chimeric protein Gal4-DimDAF-12_LBD and the luciferase gene reporter, we found that both Δ4-DA and Δ7-DA activate the recombinant Gal4-DimDAF-12_LBD protein in a dose-dependent manner (Fig. 2), with EC 50 of 0.21 and 0.65 nM respectively for Δ7-DA and Δ4-DA whereas the EC50 for activation of CelDAF-12 was 16 and 81 nM respectively.

Analysis of DimDAF-12 ligand-binding domain structure. To characterize the molecular basis of DA binding mode to DimDAF-12, we constructed a structural model of DimDAF-12_LBD using the coordinates of AceDAF-12 (PDB: 3up0; 1.6 Å) and SstDAF-12 (3gyt; 2.4 Å) LBD crystal structures, for which Dim- C. elegans (Cel; NP_001024547), S. stercoralis (Sst; AAD37372), A. ceylanicum (Ace; EPB79655) and A. caninum (Aca; RCN38687). The cysteine residues involved in the coordination of zinc atoms are conserved and shown with an asterisk (*) below the sequence. The conserved arginine that is responsible for high affinity DNA binding is shown with a hash mark (#). P-box and D-box are underlined. B Sequence alignment of the LBD. The secondary structures delimited above the sequence are based on the crystal structure of SstDAF-12. H α-helix, B β-sheet. The residues that were previously shown as critical for the binding of dafachronic acids are indicated by hash marks (#) below the sequence. Amino acid residues are indicated on the right. Residues that are identical are highlighted in black and similar sequences in grey. Multiple sequence alignment was performed with BioEdit 7.2 ClustalW Multiple alignment (https ://bioed it.softw are.infor mer.com/). DAF-12 shares respectively 55 and 53% of identity [START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] . The alignment of DimDAF-12_LBD with 3up0 and 3gyt crystal structure sequences revealed that several helices were conserved such as helix H3, H3′, H4, H5, H6, and H8 (Fig. 1).

Inside the LBD, the LBP contains 30 key residues in CelDAF-12 and SstDAF-12, including mainly hydrophobic residues that can enclose the hydrophobic steroid core of DAs and few polar residues that maintain electrostatic interactions with ligand oxygen atoms (Fig. S1) [START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF][START_REF] Alvarez | The Caenorhabditis elegans DAF-12 nuclear receptor: structure, dynamics, and interaction with ligands[END_REF] . DimDAF-12_LBD shares 22 identical residues with AceDAF-12_LBD in the LBP, while three are replaced by similar amino acids and three present major modifications (F478 to L620, T548 to V690, R574 to G716) (Table S1; Fig. S1). DimDAF-12_LBD shares 23 identical residues in the LBP with SstDAF-12_LBD, four are replaced by similar amino acids and two present major modifications (V603 to R678, A725 to S801) (Fig. S1; Table S1). Remarkably, the DimDAF-12 LBP contains all the conserved key residues involved in the binding of DAs that have been previously identified in the crystal structures (see Supplementary Table S1). In addition, the residue R640 (R564, R498, R565, respectively in Cel/ Ace/SstDAF-12) which favors DA binding by forming a lid to entrap the ligand in both Ace and SstDAF-12 structures [START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] is also fully conserved.

In silico prediction of high-affinity binding of DAs on DimDAF-12_LBD model. Based on the high sequence similarity in the LBP shared by DimDAF-12 with AceDAF-12 and SstDAF-12, DimDAF-12 might adopt a similar binding mode for DAs. This was investigated by docking experiments. The crystal structures of AceDAF-12 and SstDAF-12 were solved as a complex with respectively, Δ7-DA and Δ4-DA, and we constructed 100 DimDAF-12_LBD apo models using Modeller program and the coordinates of ligand-depleted AceDAF-12 and SstDAF-12 structures. Two models of DimDAF-12_LBD showed the highest accuracy and very similar scores for quality evaluation (Table S2). The model DimDAF-12_LBD_94, which corresponded to the best DOPE score, displayed the maximum number of residues in the allowed regions of the Ramachandran plot and was thus selected for further studies (Table S2). DimDAF-12 adopts a similar LBP as AceDAF-12 and SstDAF-12 (Figs. 1,3).

We evaluated in silico the binding mode of different conformers of Δ4-and Δ7-DA to the model Dim-DAF-12_LBD_94 (Fig. 4). For all the docking calculations, all the conformers of DAs bound to the LBP with similar binding points and orientations. Δ4-DA and Δ7-DA both possess polar groups at their extremities that are determining for ligand recognition (Fig. 4B): oxygen atoms from the C3 ketone (arrow) and the C27 carboxyl groups (arrowhead) can form H-bonds and/or salt bridges with polar and charged side chains of various residues.

As a result of the docking calculations, the best docking poses in the predicted complex DimDAF-12_LBD/ DA involved a slightly different network of interactions compared to the crystal structures of the templates. For all conformers of DAs, the best solution of lowest energy cluster (binding energy score: -13.3 and -13.5 kcal/ mol for Δ4-DA and Δ7-DA, respectively) (Table S3) revealed two salt bridges established between the ligand carboxylate group and two arginine sidechains (R674 and R640), for both Δ4-and Δ7-DA, whereas only one was detected in the crystal structures, involving the arginine residue equivalent to R674. However, the H-bond interaction involving DAs carboxylate group and threonine residues in the templates (T495 and T562 in Ace and SstDAF-12 respectively) was also found in our best scored conformations with the conserved T637 residue. By contrast, on the opposite moiety of the ligand molecule, our models did not predict any interaction between the C3 ketone group of Δ4-or Δ7-DA and surrounding side chains of DimDAF-12_LBD.

Several residues confer high-affinity binding of DAs to DimDAF-12_LBD.

To confirm the mode of interaction of DAs with DimDAF-12 as revealed by the model, we disrupted the putative H-bonds and ionic interactions by mutating the polar residues T637 and R674 predicted to be essential for binding Δ4-DA and Δ7-DA. We then tested variable mutants with two concentrations of DAs (0.01-0.1 µM corresponding to the concentration where the receptor is completely saturated) in cell-based transactivation assays. First, we found that the single mutation T637V (residue T637 mutated to a valine) had no consequence on the activity of DAF-12 with both DAs (Fig. 5A,C). However, the mutations R674K and R674M had distinct effects on DimDAF-12 activity when tested with either Δ4-or Δ7-DA. While the mutant R674K significantly decreased the Δ4-DAdependent activity of DimDAF-12 at 0.01 µM, it did not affect the Δ7-DA-dependent activity (Fig. 5A,C).

However, we found that the double mutant T637V/R674K was not active with any of DAs (Fig. 5B,D). In contrast, the activity of the double mutant T637V/R678V was conserved with Δ4-DA and even significantly increased with Δ7-DA (Fig. 5B,D). However, when both residues R674 and R678 were mutated respectively into a lysine and a valine, DimDAF-12 significantly lost DA-dependent activity (Fig. 5B,D) indicating that the H-bond formed by T637 is not crucial for the activity of DimDAF-12, and also confirming that the salt bridge formed with R640 can be disturbed by a repulsive effect of lysine group. This is supported by the absence of activity of R674K/R678V where T637 is intact but apparently not sufficient to activate DimDAF-12 (Fig. 5B,D). The triple mutant T637V/R674K/R678V completely abolished the activation of DimDAF-12 by Δ4-DA, whereas the activity of this triple mutant was significantly increased with Δ7-DA (Fig. 5).

Overall, the results revealed that DimDAF-12 responded differently to mutations compared with SstDAF-12 and other DAF-12s so far examined. To validate the model and confirm that the residue Q713 was not involved in H-bond formation with the C3 ketone of Δ4-DA or Δ7-DA, we also mutated the Q713 to glutamate (Q713E) or leucine (Q713L) and demonstrated that these mutations compromised the activity with Δ4-DA but not with Δ7-DA (Fig. 5A,C), with Q713L increasing the Δ7-DA dependent activity (Fig. 5C). This suggests the absence of a stabilizing H-bond interaction with Q713, and supports the docking computations.

Finally, we mutated the residue R640 to a cysteine residue, which is also conserved among DAF-12 orthologues and has been described as essential for the activity of CelDAF-12 and other parasitic DAF-12 [START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] . Dim-DAF-12_R640C had differential effects on DimDAF-12 activity: a significant decrease and increase respectively with 0.01 and 0.1 µM of Δ4-DA; and a significant increase with 0.01 µM of Δ7-DA suggesting that the residue R640 would be also important to maintain the activity, as shown by the salt bridge present in our best-scored docked conformations.

Dafachronic acids accelerate the molting process of D. immitis infective third-stage larvae (iL3) into L4.

To evaluate the effects of DAs in vitro on D. immitis iL3, we exposed the iL3 to 10 µM of either Δ7-DA or Δ4-DA, one day after recovery from mosquitoes and recorded under a microscope any developmental changes (relative to the molting process). The worms grew in size and stayed alive during the experiment and we did not see any killing effect of DAs. To assess whether DAs impacts the molting of iL3, we observed (1) the shedding of the iL3 cuticle, which corresponded to L3 larvae that had started to molt, and (2) the presence of free cuticles in the medium which was a sign that the molting of iL3 to L4 was completed (Fig. 6A). For Δ7-DA, the molting process started around day 3-4 in culture. Interestingly, we found that the number of free cuticles were significantly higher in Δ7-DA-treated worms than in the DMSO control, by day 4 and 5, suggesting that there were more L4 in Δ7-DA-treated conditions compared to DMSO-treated. This was confirmed by the low percentage of iL3 which had initiated but not completed the molt at day 5 or 6 in the medium containing Δ7-DA, compared to DMSO control demonstrating that Δ7-DA induced a rapid development of iL3 into L4. In the same way, we observed that Δ4-DA accelerates the molting process of iL3 with a significant higher percentage of iL3 that initiated the molting at day 4 and completed the molting at day 5, compared to DMSO (Fig. 6C,D).

Cholestenoic acid, a mammalian cholesterol metabolite, accelerates the development of iL3

probably through DimDAF-12. Since the recovery of iL3 development and molting of parasitic nematodes appear to be triggered by host environment, we evaluated whether mammalian cholesterol metabolites such as cholestenoic acid (CA), can display in silico binding affinity for the model of DimDAF-12. Cholestenoic acid is an endogenous cholesterol metabolite found in mammalian blood with a core structure similar to DAs that differs by the presence of two double bonds respectively at C2 and C5 of the steroid nucleus and a C3 hydroxyl group instead of a C3 ketone (Fig. 7A). In our structural model of DimDAF-12, we found that CA bound in the LBP with the same orientation and with a similar high binding affinity as DAs (scoring energy -13 kcal/mol vs. -13.5 with DAs) (Fig. 7B; Table S4). Consistently, the cell-based transactivation assay revealed that CA activates DimDAF-12 but at a lower potency (EC 50 = 178 nM) than DAs.

We then tested the effects of CA on the development of iL3 and found that the molting of iL3 started at day 3 when treated with CA, which was one day earlier than when iL3 were treated with DMSO (Fig. 8A). At day 4, the number of iL3 undergoing molting as well as the number of L4 were significantly higher with CA than DMSO (Fig. 8B).

Discussion

The developing stages from the iL3 and L4 larval stages of D. immitis are critically important for preventing clinical disease, as the target stages for chemoprophylaxis of heartworm disease by MLs. Nevertheless, the signaling pathways governing the molting of iL3 larvae inside the dog are poorly understood in D. immitis; but it is an essential process for the parasite to develop and maintain its life cycle. In this research, we have identified for the first time an ortholog of DAF-12 from a filarial parasite as a possible novel target to interrupt the parasite development and eliminate the heartworm parasite D. immitis. Interestingly, DimDAF-12 shares some close structural homologies with the previously described NR of C. elegans CelDAF-12 and DAF-12s from Clade IV and V parasitic nematodes which have bacteria-feeding free-living stages (more than 30% identity in the whole sequence) [START_REF] Antebi | DAF-12 regulates developmental age and the dauer alternative in Caenorhabditis elegans[END_REF][START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] . Particularly, the typical NR sequences are conserved in the DBD (more than 94%) and the ligandbinding domain (LBD) (more than 40% identity) (Fig. 1). Based on the crystal structures released for AceDAF-12 and SstDAF-12 (respectively, 3up0 and 3gyt), we proposed a model for the 3D structure of DimDAF-12_LBD and predicted the binding mode of different ligands (Figs. 3,4). DAs are the natural ligands of CelDAF-12 and have been shown to bind and activate SstDAF-12, AceDAF-12, AcaDAF-12, N. americanus DAF-12 and Haemonchus contortus DAF-12 [START_REF] Motola | Identification of ligands for DAF-12 that govern dauer formation and reproduction in C. elegans[END_REF][START_REF] Ma | Dafachronic acid promotes larval development in Haemonchus contortus by modulating dauer signaling and lipid metabolism[END_REF][START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] . We showed by combining docking calculations and in vitro cell-based transactivation assays that the two forms of DAs (Δ4-DA and Δ7-DA) also bind strongly to DimDAF-12 (Figs. 2, 3, 4, 5). Nevertheless, DAs bind to and activate differently DAF-12 according to nematode species. Interestingly, the two isomers of DAs bound with a markedly higher affinity (× 100) to DimDAF-12 from the filarial parasite D. immitis (Fig. 2), than to CelDAF-12 and the other Clade IV and V parasitic DAF-12s investigated so far (EC 50 = 0.21-0.65 nM for DimDAF-12 versus EC 50 = 16-81 nM and 25-294 nM respectively for CelDAF-12 and parasitic nematode DAF-12) [START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] suggesting than DimDAF-12 was much more sensitive to DAs than all the other nematode DAF-12. Regarding the binding of DAs on DimDAF-12, our models did not predict any interaction between the C3 ketone group of Δ4-or Δ7-DA and surrounding side chains of DimDAF-12_LBD, whereas in AceDAF-12 and SstDAF-12, a H-bond interaction was found involving glutamine residues Q571 or Q637, respectively [START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] . The equivalent residue Q713 in DimDAF-12 model was nevertheless found not far from the DA ketone group; however, at too long a distance for favoring an H-bond, but indicating a favorable polar environment. Interestingly, among the two biological assemblies of the AceDAF-12/Δ7-DA complex resolved in 3up0, one structure (chain A) did not show the direct H-bond interaction of Q571 with the ketone group of Δ7-DA, but interacted through a molecule of water bridge [START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] . Moreover, the residue R674 has shown to be important for Δ4-DA-dependent activity of DimDAF-12 but not the Δ7-DA-dependent activity. This residue has also been shown critical in the activity of AceDAF-12 and CelDAF-12 but not SstDAF-12 [START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] . It is also interesting that there is evidence of species specificity in the steroid biosynthetic pathways. In C. elegans, cytochrome P450 DAF-9 is a limiting enzyme for DA biosynthesis, for which a gene homolog has yet to be identified in the genomes of the parasitic nematode S. stercoralis and A. ceylanicum [START_REF] Wang | Global analysis of dauer gene expression in Caenorhabditis elegans[END_REF][START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] . Our analysis of the D. immitis genome also failed to identify a daf-9 homolog, suggesting that the natural ligand of DimDAF-12 in D. immitis might not be a DA. This could be in agreement with the inability of nematode parasites to synthesize their own ligands including DAs, as previously suggested [START_REF] Wang | Nuclear receptors: emerging drug targets for parasitic diseases[END_REF][START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] and their need to exploit host nutrients as triggers of their development. However, an orthologue of daf-9 has been recently identified in H. contortus with a role in the synthesis of Δ7-DA and larval development [START_REF] Ma | Dafachronic acid promotes larval development in Haemonchus contortus by modulating dauer signaling and lipid metabolism[END_REF] as previously described for C. elegans [START_REF] Gerisch | Hormonal signals produced by DAF-9/cytochrome P450 regulate C. elegans dauer diapause in response to environmental cues[END_REF] .

In contrast to threadworms and hookworms, D. immitis is an obligate parasite that is transmitted by the mosquito to the dog, which are two distinct, non-bacterial environments that might provide different ligands to regulate DimDAF-12 effects. DAF-9 has a similar function to mammalian CYP27A1, which synthesizes bile acid metabolites from cholesterol. Since D. immitis is auxotrophic for cholesterol [START_REF] Kurzchalia | Why do worms need cholesterol?[END_REF] , we speculate that the vertebrate host provides the DimDAF-12 ligand based on previous observations in other parasitic nematodes that lack a pathway for DA synthesis [START_REF] Wang | Nuclear receptors: emerging drug targets for parasitic diseases[END_REF][START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] . Indeed, the mammalian bile acid metabolite 3β-hydroxy-5-cholestenoic acid (CA) has previously been shown to weakly activate CelDAF-12 and rescue the dauer formation of daf-9 mutants [START_REF] Held | DAF-12-dependent rescue of dauer formation in Caenorhabditis elegans by (25S)-cholestenoic acid[END_REF] . Moreover, (25S)-diastereoisomer of CA has also been shown to stimulate the activity of AceDAF-12 and have a higher sensitivity to the receptor than DAs [START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] . The fact that the CA binds to the DimDAF-12 LBP, with a high affinity (Fig. 7B), and activates the receptor of D. immitis at a concentration for optimal binding (EC 50 = 178.7 nM, Fig. 7C) in the same range as that measured in circulating mammalian plasma (about 456 nM), suggests that CA of mammalian origin could be a natural ligand of DimDAF-12 (Fig. 7). This hypothesis is supported by our observation that CA also improves significantly the molting of iL3 into L4 (Fig. 8).

Since the ortholog of DAF-12 in D. immitis binds DAs with high affinity, this suggests the existence of a conserved DAF-12 downstream pathway [START_REF] Bethke | Nuclear hormone receptor regulation of microRNAs controls developmental progression[END_REF][START_REF] Hochbaum | DAF-12 regulates a connected network of genes to ensure robust developmental decisions[END_REF] . Interestingly, the analysis of the D. immitis genome revealed that genes known to be regulated by CelDAF-12 are also conserved in D. immitis. Among them, we identified an homolog of the serine threonine kinase lit-1, that might play an important role in the development or in amphid channel morphogenesis of D. immitis, as shown in C. elegans [START_REF] Shostak | Identification of C. elegans DAF-12-binding sites, response elements, and target genes[END_REF] . Furthermore, CelDAF-12 has been shown to regulate larval development by activating the transcription of let-7 family miRNAs (mir-84 and mir-241) in C. elegans [START_REF] Hammell | A feedback circuit involving let-7-family miRNAs and DAF-12 integrates environmental signals and developmental timing in Caenorhabditis elegans[END_REF][START_REF] Bethke | Nuclear hormone receptor regulation of microRNAs controls developmental progression[END_REF] . The family of let-7 miRNAs has been identified in Brugia pahangi, the causative agent of zoonotic filariasis, and the upregulation of several let-7 genes seems to correlate with the development of iL3 following host infection [START_REF] Winter | A novel member of the let-7 microRNA family is associated with developmental transitions in filarial nematode parasites[END_REF] . In the genome of D. immitis [START_REF] Godel | The genome of the heartworm, Dirofilaria immitis, reveals drug and vaccine targets[END_REF] , let-7 miRNA family is also conserved suggesting that DimDAF-12 could possibly regulate larval development in a similar way as in C. elegans [START_REF] Wang | Nuclear receptors: emerging drug targets for parasitic diseases[END_REF] .

Consistently, we showed that the Δ7-DA and Δ4-DA isoforms (Fig. 6) accelerates the molting of D. immitis from iL3 to L4 stage indicating that DimDAF-12 activation may play a key role in the development of this parasite. It is noteworthy that molting of iL3 to L4 in D. immitis is only possible in media supplemented with serum, suggesting that there might be a molecule in the serum that triggers the molting process by activating DimDAF-12 [START_REF] Abraham | Dirofilaria immitis: molting process of third-stage larvae[END_REF][START_REF] Lok | In vitro development of third-and fourth-stage larvae of Dirofilaria immitis: comparison of basal culture media, serum levels and possible serum substitutes[END_REF] . This is strengthened by our data showing that CA binds and activates DimDAF-12 LBP (Fig. 7) and contributes to the molting of iL3 into L4 (Fig. 8), suggesting that the host mammalian environment may be the trigger of this process. Indeed, since helminths, including D. immitis, are unable to synthesize cholesterol, they rely on host cholesterol for critical biological processes that could include their development and growth inside the host [START_REF] Kurzchalia | Why do worms need cholesterol?[END_REF] .

Methods

Amplification and cloning of DimDAF-12. Total RNA from male or female D. immitis worms and L3 larvae was isolated using the Trizol method (Invitrogen). cDNA was obtained by reverse transcription using Superscript III first strand (Invitrogen). The full length DimDAF-12 (nDi.2.2.2.t09652) was then amplified by High Fidelity Platinum Taq DNA polymerase (Invitrogen) using DimDAF-12Fw/DimDAF-12Rv primers (Table S4) encompassing the predicted initiation and stop codon of the respective ORF based on the D. immitis genome reference nDi.2.2.2 (https ://www.nemat odes.org/genom es/dirofi lari a_immit is/). The product was subcloned into a pCR4 vector (Invitrogen) and the exact sequence was then confirmed by sequencing (McGill University/Genome Quebec Innovation Centre). Two DimDAF-12 cDNA sequence encoding two different isoforms A Chemical structures of Δ4-dafachronic acid (Δ4-DA), Δ7-dafachronic acid (Δ7-DA) and 3β-hydroxy-5-cholestenoic acid (CA). B Predicted structures of the complexes of DimDAF-12 formed with Δ4-DA (green), Δ7-DA (pink) and with CA (magenta). In silico docking showed that the ligand binding pocket of DimDAF-12 accommodates CA. All images were generated using PyMol. C CA activates DimDAF-12 in a dose-dependent manner. NIH3T3 cells were co-transfected with Gal4-DimDAF-12_LBD and luciferase gene reporter construct. Recombinant cells were incubated with increasing concentrations of CA (up to 10 µM). The ligand binding and transactivation activity were assessed by measuring the luciferase activity, which was normalized by Renilla luciferase activity for transfection efficiency and expressed as relative light units (RLU). Data represent the average of normalized luciferase activity and the error bars correspond to the standard error of mean from a triplicate assay. The experiments were repeated at least two times in triplicate. The figure shows a representative experiment performed in triplicate using Prism 6.0 (Graph Pad Software, Inc.).

of DimDAF-12 have been deposited in the GenBank database and are available under the respective accession number MN449986 (long form, DimDAF-12a and short form, MK820661).

Constructs and cell-based transactivation assays.

To construct Gal4:DimDAF-12_LBD, the LBD of DimDAF-12 (DimDAF-12_LBD; residues 587-828) was PCR amplified with Platinum Taq DNA polymerase High Fidelity (Invitrogen) using DimDAF-12-LBD-SmaIFw and DimDAF-12-SmaIRv primers (Table S4), which were flanked by SmaI restriction sites. The PCR product was then cloned after digestion with SmaI (New England BioLabs) into a mammalian expression vector, CMX (gift from D. J. Mangelsdorf) [START_REF] Motola | Identification of ligands for DAF-12 that govern dauer formation and reproduction in C. elegans[END_REF] , downstream of the DNA-binding domain of the Gal4 yeast transcription factor (Gal4-DBD).

NIH3T3 cells (ATCC) were cultured in DMEM (Dulbecco's modified Eagle's medium) with L-glutamine supplemented with 10% (v/v) FBS containing 100 U/ml penicillin and 100 μg/ml streptomycin.

DimDAF-12_T637V, DimDAF-12_R674K/M, DimDAF-12_Q713E/L and DimDAF-12_R640C mutants were created by respectively modifying the residue threonine at position 637 to a valine, the arginine at position 674 to a lysine or methionine, the glutamine 713 to a glutamate or leucine and the residue arginine at the position 640 to a cysteine using QuickChange XL Site-Directed Mutagenesis (Agilent Technologies) and primers including the desired mutation (Table S4). Double mutants were obtained using the same strategy and the corresponding primers. The presence of a mutation was then verified by sequencing.

To perform the cell-based transactivation assays, firefly luciferase under the control of the Gal4 response element (UAS, upstream activation sequence) was used as a reporter construct. 5 × 10 3 NIH3T3 cells were seeded in 96-well plates and transiently transfected the following day in serum-free DMEM with 50 ng of DAF-12 receptors and 100 ng of reporter constructs using 2 µl of SuperFect Transfection Reagent (Qiagen). 10 ng of an additional reporter construct, Renilla luciferase was also co-transfected into cells and was used for normalization. C. elegans DAF-12 (CelDAF-12) (gift from D. J. Mangelsdorf) [START_REF] Motola | Identification of ligands for DAF-12 that govern dauer formation and reproduction in C. elegans[END_REF] and empty CMX vector were used respectively as positive and negative controls. At 3 h after transfection, serum-free medium was replaced by complete medium and ligands or vehicle control was added. After 24 h incubation, the cells were lysed and luciferase and renilla activities were successively measured using the Dual-Glo luciferase assay system (Promega). The ligands used were: Δ4-dafachronic acid (Δ4-DA) (Cayman Chemical) and (25S)-Δ7-dafachronic acid (Δ7-DA) (Santa Cruz Biotechnology), and 3β-hydroxy-5-cholestenoic acid (CA) (Santa Cruz Biotechnology), a mammalian bile acidlike metabolite that shares a core structure with DAs (Figs. 4B, C and7). The ligand stock solutions were dissolved in DMSO and the final concentration of DMSO was maintained at 0.1% in each well.

In order to draw a dose response curve, we first calculated the ratio of luminescence from the luciferase reporter to luminescence from the renilla reporter for each condition and replicate. The mean of this ratio was then calculated from triplicate or quadruplate assays and then the ratio of DimDAF-12-or CelDAF-12-transfected cells was normalized to empty vector-transfected cells that were treated under the same conditions. The curve was fitted using GraphPad Prism 6 using a sigmoidal, 4PL, standard curve type (four-parameter logistic curve). Data presented for the cell-based transactivation assays are representative experiments (shown as mean data ± SE from triplicate or quadruplicate replicates from one representative assay). The iL3 stage larvae were collected from mosquitos and treated with cholestenoic acid (CA) or DMSO (A). The developmental changes were observed daily under a microscope. The iL3 that completed the molting from iL3 to L4 (A) were scored as well as the iL3 that were still undergoing molting (B). The number of free cuticles (left panel) found in the wells corresponded to larvae that had completed the molt and were L4. The figure shows a representative experiment performed in quadruplate using Prism 6.0 (Graph Pad Software, Inc.). The statistical significance was evaluated with an unpaired t test (**p < 0.005; *p < 0.05).

Sequence alignment, homology model construction and validation. In the absence of a crystal structure, the 3D tertiary structure of D. immitis DAF-12_LBD was built by comparative modeling using Modeller 9.18 software [START_REF] Sali | Comparative protein modelling by satisfaction of spatial restraints[END_REF][START_REF] Webb | Comparative protein structure modeling using MODELLER[END_REF] and protocol previously described in David et al. [START_REF] David | Structural model, functional modulation by ivermectin and tissue localization of Haemonchus contortus p-glycoprotein-13[END_REF] . Suitable template structures upon which to model the DimDAF-12 tertiary structure were retrieved using BLAST-P (Basic Local Alignment Search Tool) program and the protein data bank (pdb) database. Blast searches predicted that the crystal structures of A. ceylanicum (AceDAF-12; PDB ID: 3up0, resolved at 1.60 Å) [START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF] and S. stercoralis DAF-12 (SstDAF-12; 3gyt, resolved at 2.40 Å) [START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF] were suitable templates with highest homology to DimDAF-12 (BLAST-bit score: 282, 274 respectively) and excellent residue conservation (55 and 53% sequence identity, respectively). The ligands Δ4-and Δ7-DAs initially bound to 3up0 and 3gyt were not included in the homology model reconstruction of LBD. A pairwise sequence alignment between both 3up0 and 3gyt sequences was generated by Modeller script salign and then improved using a knowledge based approach. A multiple sequence alignment between DimDAF-12 and the pairwise alignment of crystal structures was then achieved using align2D script and used as input for Modeller 9.18. From this alignment, 100 structural models were generated by satisfaction of spatial restraints calculated by Modeller, which were ranked based on their DOPE (Discrete Optimized Potential Energy) score and their molecular pdf value of the objective function of Modeller [START_REF] Shen | Statistical potential for assessment and prediction of protein structures[END_REF] . We selected two homology models, one with the best DOPE score and another one with the best objective function value, and assessed their quality using various online scoring function servers; in particular: QMEAN (Qualitative Model Energy ANalysis) scoring function [START_REF] Benkert | QMEAN server for protein model quality estimation[END_REF] as a statistical potential, ProSA-web (Protein Structure Analysis) for evaluating energy profile and assessing the overall quality of the structure in term of Z score [START_REF] Sippl | Recognition of errors in three-dimensional structures of proteins[END_REF][START_REF] Wiederstein | ProSA-web: interactive web service for the recognition of errors in three-dimensional structures of proteins[END_REF] , and PROCHECK for Ramachandran plots and listing the amino acids found in allowed and disallowed configurational regions (Table S2) [START_REF] Laskowski | PROCHECK: a program to check the stereochemical quality of protein structures[END_REF] . The model with maximum number of residues in allowed regions in the Ramachandran plot was selected for further studies.

Molecular docking studies. The in silico calculations for Δ4-DA, Δ7-DA and CA on the DimDAF-12 homology model were performed using the Autodock 4.2 program as previously described [START_REF] David | Structural model, functional modulation by ivermectin and tissue localization of Haemonchus contortus p-glycoprotein-13[END_REF][START_REF] David | In silico analysis of the binding of anthelmintics to Caenorhabditis elegans p-glycoprotein 1[END_REF] . All ligand structures were prepared using Marvin Suite (https ://www.chema xon.com/produ cts/marvi n/marvi nsket ch/), from which 10 conformers were generated under the MMFF94 force field with correct stereochemistry, protonation states, and ring conformations. After 3D-alignment of conformers and calculation of RMSD under PyMOL for clustering, three representative conformers were selected for further docking calculations with Autodock 4.2. This program predicts top ranking poses with best scores and consists in two main programs, AutoGrid, which computes a three-dimensional grid of interaction energy based on macromolecular coordinates and Autodock, which performs the docking search.

The grid built by Autogrid 4 included the whole LBD of the DimDAF-12 receptor with 126, 126, and 98 points in x, y and z directions, with a grid spacing of 0.375 Å, to allow a complete search in the LBD structure for binding of DAs. For each ligand representative conformer, 100 runs were performed using the Lamarckian genetic algorithm. All the other parameters were kept as default. The generated poses were scored based on an estimated free energy of ligand binding calculated by Autodock, which can be considered as a binding affinity score. They were then clustered according to the similarity of their positions and conformations, with RMSD set at 2.0 Å, and finally ranked by their binding score (in each cluster). For each lowest energy pose of selected clusters, the number and nature of interacting residues were analyzed within the complex DimDAF-12/DA. Among these, particular interest was given to residues involved in the ligand binding previously described in the crystals 3up0 and 3gyt [START_REF] Wang | Identification of the nuclear receptor DAF-12 as a therapeutic target in parasitic nematodes[END_REF][START_REF] Zhi | Structural conservation of ligand binding reveals a bile acid-like signaling pathway in nematodes[END_REF][START_REF] Alvarez | The Caenorhabditis elegans DAF-12 nuclear receptor: structure, dynamics, and interaction with ligands[END_REF] .

Development of D. immitis. D. immitis iL3 larvae (2005 Missouri strain) were obtained from FR3

Molecular Resources through BEI resources [START_REF] Michalski | The NIH-NIAID filariasis research reagent resource center[END_REF] . The iL3 were collected from infected mosquitoes as previously described [START_REF] Kurzchalia | Why do worms need cholesterol?[END_REF] and shipped overnight to McGill University. After several washes in PBS, the iL3 were incubated in RPMI-1640 with l-glutamine (Gibco) supplemented with 10% FBS, 0.1 mg/ml streptomycin, 100 U/ml penicillin, 0.04 mg/ml gentamycin, and 0.25 µg/ml amphotericin B. The next day, the iL3 were immediately transferred to a 24-well plate with 10-15 larvae per well and the medium replaced by fresh complete RPMI-1640 containing 10 µM of Δ7-DA or Δ4-DA or CA. Media was renewed every 2 days with fresh Δ7-DA. Animals were incubated at 37 °C and 5% CO 2 and were observed every 24 h for 9 days under a stereomicroscope for any appearance of sheath or free cuticle as a signature of the molting process. Molting from the iL3 to the L4 larvae was recorded by scoring the number of larvae which had initiated but not completed the molt and the number of free cuticles into the medium. The percentage of iL3 that did not complete the molt and the percentage of L4 were calculated as the mean of iL3 or L4 from a quadruplate assay/total number of larvae × 100.

Statistical analysis.

All experiments were performed at least twice with triplicate or quadruplicate replicates with consistent results between experiments. Data presented for the cell-based transactivation assays are representative experiments (shown as mean data ± SE from triplicate or quadruplicate replicates from one representative assay). The effects of DimDAF-12 mutants in cell-based transactivation assays were analyzed by two-way ANOVA with multiple comparisons without correction using Prism 6.0 (Graph Pad Software, Inc.). The significance of small molecule effects on iL3 molting were analyzed using Student's t test in Prism 6.0.

Figure 1 .

 1 Figure 1. Alignment of DimDAF-12 protein with a subset of known DAF-12 receptors in nematodes. A Sequence alignment of the DBD of D. immitis (Dim; accession no. MK820661), C. elegans (Cel; NP_001024547), S. stercoralis (Sst; AAD37372), A. ceylanicum (Ace; EPB79655) and A. caninum (Aca; RCN38687). The cysteine residues involved in the coordination of zinc atoms are conserved and shown with an asterisk (*) below the sequence. The conserved arginine that is responsible for high affinity DNA binding is shown with a hash mark (#). P-box and D-box are underlined. B Sequence alignment of the LBD. The secondary structures delimited above the sequence are based on the crystal structure of SstDAF-12. H α-helix, B β-sheet. The residues that were previously shown as critical for the binding of dafachronic acids are indicated by hash marks (#) below the sequence. Amino acid residues are indicated on the right. Residues that are identical are highlighted in black and similar sequences in grey. Multiple sequence alignment was performed with BioEdit 7.2 ClustalW Multiple alignment (https ://bioed it.softw are.infor mer.com/).

Figure 2 .

 2 Figure 2. Dafachronic acids activate DimDAF-12 in a dose-dependent manner. NIH3T3 cells were co-transfected either with Gal4-CelDAF-12_LBD (A) as control or with the wild-type construct Gal4-DimDAF-12_LBD (B) and luciferase gene reporter construct. Recombinant cells were incubated with increasing concentrations of Δ4-or Δ7-DA (respectively up to 5 or 6 µM). The ligand binding and transactivation activity were assessed by measuring the luciferase activity, which was normalized by Renilla luciferase activity for transfection efficiency and expressed as relative light units (RLU). Data represent the average of normalized luciferase activity and the error bars correspond to the standard error of mean from quadruplate assays. The experiments were repeated at least two times in triplicate or quadruplate. The figure shows a representative experiment using Prism 6.0 (Graph Pad Software, Inc.).

Figure 3 .

 3 Figure 3. Structure of DimDAF-12 ligand binding domain model. The model of DimDAF-12_LBD (A and B) was constructed using Modeller and the coordinates of the crystal from Ancylostoma ceylanicum DAF-12 (pdb:3up0) and Strongyloides stercoralis DAF-12 (3gyt). Similar to the other members of the nuclear receptor family, DimDAF-12 exhibits 13 helices and three β-strands, which are packed in a three-layer α-helical sandwich to create a ligand binding pocket, where the DAs were found to bind in the case of AceDAF-12 and SstDAF-12. α-helices were either shown in teal or marine to distinguish them, β-strands were colored in yellow and the loops in teal. All images were generated using PyMol 1.3 (https ://pymol .org/2/).

Figure 4 .

 4 Figure 4. Binding mode of dafachronic acids on model of DimDAF-12 ligand binding domain. A In silico docking of dafachronic acids (DAs) into the model of DimDAF-12 LBD was performed using Autodock. Δ4-DA and Δ7-DA bind inside the ligand binding pocket of DimDAF-12. The structures of Δ4-DA (B) and Δ7-DA (C) differ in the position of an unsaturated double bond respectively at C4 or C7 of the steroid nucleus. H-bonds are illustrated by yellow dashed lines with bond lengths noted in Å. All images were generated using PyMol 1.3 (https ://pymol .org/2/).

Figure 5 .

 5 Figure 5. Mutation of residues in DimDAF-12 ligand binding pocket abolishes the activity of the receptor. NIH3T3 cells were co-transfected with wild type Gal4-DimDAF-12_LBD or the corresponding mutants and luciferase gene reporter construct and then tested with 0.01 or 0.1 uM of Δ4-(A single mutant, B double mutants) or Δ7-(C single mutant, D double mutants) dafachronic acids (DAs). The ligand binding and transactivation activity were assessed by measuring the luciferase activity, normalized by Renilla luciferase activity for transfection efficiency and expressed as relative light units (RLU). Data represent the average of normalized luciferase activity and the error bars correspond to the standard error of the mean from a triplicate assay. The figure shows a representative experiment performed in triplicate. The significance of the effects of mutation on DimDAF-12 LBD activity was analyzed by two-way ANOVA with multiple comparisons without correction using Prism 6.0 (Graph Pad Software, Inc.) (***p < 0.0005; **p < 0.005; *p < 0.05) versus wild-type.

Figure 6 .

 6 Figure 6. Dafachronic acid accelerates the complete molting of infective third stage D. immitis larvae to L4. The iL3 stage larvae were collected from mosquitos and treated with Δ7-(Δ7-DA, A and B) or Δ4-dafachronic acid (Δ4-DA, C and D) at 10 µM or DMSO. The developmental changes were observed daily under a microscope. The iL3 that completed the molting from iL3 to L4 (left panel A and C) were scored as well as the iL3 that were still undergoing molting (right panel B and D). The number of free cuticles (left panel) found in the wells are directly related to the amount of larvae that had completed the molt and were L4. The figure represents the mean of two independent experiments performed in quadruplate from different pools of iL3s using Prism 6.0 (Graph Pad Software, Inc.). The statistical significance was evaluated with an unpaired t test (**p < 0.005; *p < 0.05).

Figure 7 .

 7 Figure 7. Cholestenoic acid binds and activates DimDAF-12. A Chemical structures of Δ4-dafachronic acid (Δ4-DA), Δ7-dafachronic acid (Δ7-DA) and 3β-hydroxy-5-cholestenoic acid (CA). B Predicted structures of the complexes of DimDAF-12 formed with Δ4-DA (green), Δ7-DA (pink) and with CA (magenta). In silico docking showed that the ligand binding pocket of DimDAF-12 accommodates CA. All images were generated using PyMol. C CA activates DimDAF-12 in a dose-dependent manner. NIH3T3 cells were co-transfected with Gal4-DimDAF-12_LBD and luciferase gene reporter construct. Recombinant cells were incubated with increasing concentrations of CA (up to 10 µM). The ligand binding and transactivation activity were assessed by measuring the luciferase activity, which was normalized by Renilla luciferase activity for transfection efficiency and expressed as relative light units (RLU). Data represent the average of normalized luciferase activity and the error bars correspond to the standard error of mean from a triplicate assay. The experiments were repeated at least two times in triplicate. The figure shows a representative experiment performed in triplicate using Prism 6.0 (Graph Pad Software, Inc.).

Figure 8 .

 8 Figure 8. Cholestenoic acid accelerates the complete molting of infective third stage D. immitis larvae to L4.The iL3 stage larvae were collected from mosquitos and treated with cholestenoic acid (CA) or DMSO (A). The developmental changes were observed daily under a microscope. The iL3 that completed the molting from iL3 to L4 (A) were scored as well as the iL3 that were still undergoing molting (B). The number of free cuticles (left panel) found in the wells corresponded to larvae that had completed the molt and were L4. The figure shows a representative experiment performed in quadruplate using Prism 6.0 (Graph Pad Software, Inc.). The statistical significance was evaluated with an unpaired t test (**p < 0.005; *p < 0.05).

Scientific RepoRtS |(2020) 10:11207 | https://doi.org/10.1038/s41598-020-67466-9

Acknowledgements

We wish to thank the NIH/NIAID Filariasis Research Reagent Resource Center (FR3) (www.filar iasis cente r.org) for distribution by BEI Resources for providing the following reagent: Stage L3 Dirofilaria immitis, Strain Missouri, Infective Larvae (Live), NR-48909. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA Grant Agreement No. PCOFUND-GA-2013-609102, through the PRESTIGE program coordinated by Campus France (T. L.). This study was also supported by Region Occitanie (T. L.) and INRAE, a Burroughs-Wellcome Fund Travel Award (T. L.), and a grant from the Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN-2017-04010) (R. K. P.). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. All experimental procedures were approved by McGill University in accordance with relevant guidelines and regulations. Stage L3 D. immitis were provided by FR3 Molecular Resources located at the University of Georgia; maintenance and handling of vertebrate animals were approved by the University of Georgia's Institutional Animal Care and Use Committee (IACUC).

Data availability

Accession codes: Genbank accession number MN449986 for DimDAF-12a and MK820661 for DimDAF-12b.

Received: 16 January 2020; Accepted: 7 May 2020

Author contributions

T. L., M. A., F. A, C. M, R. K. P and A. L. conceptualized and designed the experiments. T. L. and F. A. carried out experiments, and the experimental analysis. T. L. wrote the manuscript with input from all authors.

competing interests

The authors declare no competing interests.