Ancestral gene synteny reconstruction improves extant species scaffolding
 Yoann Anselmetti^{1, 3},
 Vincent Berry^{2},
 Cedric Chauve^{5},
 Annie Chateau^{2},
 Eric Tannier^{3, 4} and
 Sèverine Bérard^{1, 2}Email author
https://doi.org/10.1186/1471216416S10S11
© Anselmetti et al.; 2015
Published: 2 October 2015
Abstract
We exploit the methodological similarity between ancestral genome reconstruction and extant genome scaffolding. We present a method, called ARtDeCo that constructs neighborhood relationships between genes or contigs, in both ancestral and extant genomes, in a phylogenetic context. It is able to handle dozens of complete genomes, including genes with complex histories, by using gene phylogenies reconciled with a species tree, that is, annotated with speciation, duplication and loss events. Reconstructed ancestral or extant synteny comes with a support computed from an exhaustive exploration of the solution space. We compare our method with a previously published one that follows the same goal on a small number of genomes with universal unicopy genes. Then we test it on the whole Ensembl database, by proposing partial ancestral genome structures, as well as a more complete scaffolding for many partially assembled genomes on 69 eukaryote species. We carefully analyze a couple of extant adjacencies proposed by our method, and show that they are indeed real links in the extant genomes, that were missing in the current assembly. On a reduced data set of 39 eutherian mammals, we estimate the precision and sensitivity of ARtDeCo by simulating a fragmentation in some well assembled genomes, and measure how many adjacencies are recovered. We find a very high precision, while the sensitivity depends on the quality of the data and on the proximity of closely related genomes.
Keywords
Introduction
Knowledge of genome organization (gene content and order) and of its dynamics is an important question in several fields such as cancer genomics [1–3], to understand gene interactions involved in a common molecular pathway [4], or evolutionary biology, for example to establish a species phylogeny by comparative analysis of gene orders [5].
On one side, studying genome organization evolution, and in particular proposing gene orders for ancestral genomes, requires well assembled extant genomes, while, on the other side, the assembly of extant genomes can in return benefit from evolutionary studies. This calls for integrative methods for the joint scaffolding of extant genomes and reconstruction of ancestral genomes.
The reconstruction of ancestral genome organization is a classical computational biology problem [6], for which various methods have been developed [7–13]. The rapid accumulation of new genome sequences provides the opportunity to integrate a large number of genomes to reconstruct their structural evolution. However, a significant proportion of these genomes is incompletely assembled and remains at the state of contigs (permanent draft) as illustrated by statistics on GOLD [14]. To improve assemblies, methods known as scaffolding were developed to order contigs into scaffolds. Most scaffolding methods use either a reference genome, or the information provided by pairedend reads, or both [15–22]. We refer to Hunt et al. [23] for a detailed comparative analysis of recent scaffolding methods.
In recent developments, scaffolding methods taking into account multiple reference genomes and their phylogeny have been proposed [24–27]. It suggests a methodological link with ancestral genome reconstructions: if ancestral genes are considered as contigs, scaffolding extant or ancestral contigs in a phylogenetic context differs only in the location of the considered genome within the phylogeny (leaf or internal node). This link has been observed [28] and exploited to develop a method for combining scaffolding and ancestral genomes reconstruction [29]. However, the latter, due to the computational complexity of the ancestral genome reconstruction problem, is currently limited to a few genomes and to singlecopy universal genes.
We propose to overcome this computational complexity by considering independent ancestral gene neighborhood reconstructions [12] instead of whole genomes, which allows to scale up to dozens of whole genomes and to use as input data genes with complex histories. We develop a method that scaffolds ancestral and extant genomes at the same time. The algorithm improves over previous methods of scaffolding by the full integration of the inference of evolutionary events within a phylogenetic context.
The principle of our method is imported from DeCo [12]. So we call it ARtDeCo for Assembly Recovery through DeCo. DeCo is an algorithm for ancestral synteny reconstruction. It is a dynamic programming scheme on pairs of reconciled gene tree, generalizing the classic dynamic programming scheme for parsimonious ancestral character reconstructions along a tree. It computes a parsimonious set of ancestral gene neighborhoods, the cost being computed as the weighted sum of gains and losses of such neighborhoods, due to genome rearrangements. In addition to DeCo, ARtDeCo considers a linkage probability for each couple of genes in extant genomes, that is included in the cost function in order to be able to propose gene neighborhoods in extant as well as in ancestral genomes.
We implemented ARtDeCo and tested it on several data sets. First we reproduced the experiment of [29] on 7 tetrapod genomes limited to universal unicopy genes, with comparable accuracy. Then we used all genes from 69 eukaryotic genomes from the Ensembl database [30]. The program runs in about 18 h and is able to propose ancestral genome structures and thousands of extant scaffolding linkages. We examine in details one of them, chosen randomly on the panda genome, and show why it seems reasonable to propose it as an actual scaffolding adjacency. Then on a reduced data set of 39 whole mammalian genomes, we tested the precision and sensitivity of the scaffolding performed by ARtDeCo by simulating artificial fragmentation of the human or horse genomes, removing up to 75% of the known gene neighborhoods of these well assembled genomes, and comparing the removed adjacencies with the ones proposed by ARtDeCo. We measure a >95% precision, while sensitivity, as expected, depends on the quality of the data and on the presence of closely related extant genomes. This denotes the domain of efficiency of our method: a vast majority of proposed adjacencies can be considered with confidence, but the final resulting scaffolding is still incomplete.
Ancestral and extant adjacencies
Input
The input of the method is

A species tree with all considered genomes and their descent pattern; We suppose the number of chromosomes of each extant genome is known.

A set of genes for all considered genomes, clustered into homologous families; for each family a rooted gene tree depicts the descent pattern of the genes.

A set of adjacencies, i.e., pairwise relations between neighboring genes AB on extant chromosomes. Genes A and B are called the extremities of the adjacency AB. We consider as neighbors two genes that are not separated by another gene present in the dataset, but a relaxed definition can be used with no impact on the method itself.
Internal nodes of the species tree are labeled with ancestral species (we always consider ancestral species at the moment of a speciation) and leaves are labeled with extant species. Gene trees are reconciled with the species tree: all ancestral genes are labeled by the ancestral species they belong to, so the input yields a gene content for all ancestral species. Genes and species are partially ordered by the descent relation, so we may speak of a last, or lowest, or most recent common ancestor. Here, as in [12], we use a reconciliation minimizing the number of duplications and losses of genes.
A module of ARtDeCo is able to produce a suitable input from the raw Ensembl Compara [30] gene tree files and a species tree if needed. Once the input is given, two preliminaries are necessary: partitioning extant adjacencies and computing an a priori adjacency probability for each extant species. They are detailed in the two following subsections.
A partition of extant adjacencies
The goal of this step is, without loss of generality, to reduce the analysis of the whole data set to the independent analysis of pairs of gene trees and adjacencies, each having an extremity in each of the gene trees. Moreover, we want that the roots of the two gene trees correspond to ancestral genes mapping to the same ancestral species.
The partition is realized thanks to a necessary condition for two adjacencies to share a common ancestor. Two adjacencies A_{1}B_{1} and A_{2}B_{2}, for genes A_{1}, A_{2}, B_{1}, B_{2}, may have a common ancestor AB only if A_{1} and A_{2} (respectively B_{1} and B_{2}) are in the same gene family, so have a common ancestor A (respectively B), and such that A and B belong to the same species. In other words, the ancestral adjacency has the possibility to exist only when the genes of this adjacency are present in a same ancestral species.
It is easy to check that this relation is an equivalence relation, which then partitions adjacencies into equivalence classes. Each equivalence class C can be represented by two ancestral genes: they are the most ancient distinct A and B genes involved in the twobytwo comparisons of adjacencies A_{1}B_{1} and A_{2}B_{2} in this class. Necessarily every adjacency in this class has a gene which is a descendant of A, and another which is a descendant of B. A and B are in the same species (ancestral or extant), and cannot be the descendant one of another.
For a node N of a gene tree T , T (N ) is the subtree of T rooted at N . Consider the two disjoint subtrees T (A) and T (B). All adjacencies in the equivalence class C have one extremity which is a leaf of T (A) and the other which is a leaf of T (B). So each equivalence class may be treated independently from the other, and the input can be restricted, without loss of generality, to T (A) and T (B).
An a prioriprobability for all adjacencies
Given two extant genes v_{1} and v_{2} from the same extant genome G, we give an a priori probability that there is an adjacency between v_{1} and v_{2}. If the genome G is perfectly assembled, then this probability is given by the input, that is, it is 1 if there is an adjacency in the input and 0 otherwise. But if the genome G is not perfectly assembled, then this probability depends on the quality of the assembly. It will allow the program to propose more adjacencies in extant genomes that are more fragmented.
We note n the number of contigs in an extant genome (which is the number of genes minus the number of adjacencies if all contigs are linear arrangements of genes), and p the number of chromosomes. We always have n ≥ p >0. All contigs are assumed to have two distinct extremities.
We call a solution of the scaffolding problem a set of n − p adjacencies between the extremities of contigs, which forms p chromosomes from the n contigs. The number of different solutions for given n and p is denoted by f (n, p).
where ρ is a correction function which is equal to 4 if v_{1} and v_{2} are the only genes in their contigs, 2 if one of v_{1} v_{2} is the only gene in its contig but not the other, and 1 otherwise. If n = p, we have P (v_{1} ~ v_{2}) = 0 if the adjacency v_{1}v_{2} is not in the data, and P (v_{1} ~ v_{2}) = 1 otherwise.
For the computation of P (v_{1} ~ v_{2}) we use the following formula for f (n, p).
Proof First remark that the formula f (n, p) can be extended to the case where p > n and to the case where n ≥ 1 and p = 0, by setting its value to 0 in those cases (there is no possible way to transform n contigs into p chromosomes). In those cases, the equality is still true, since $\left(\begin{array}{c}n1\\ p1\end{array}\right)$ is then equal to 0. Thus, in all what follows, we use this extension of definition when needed.
We proceed now by induction on n ≥ 1.
Base case: n = 1, it is straightforward since $f\left(1,1\right)=1=\frac{1!}{1!}{2}^{0}\left(\begin{array}{c}0\\ 0\end{array}\right)$, and for p >1, we have $f\left(1,p\right)=0=\frac{1!}{p!}{2}^{1p}\left(\begin{array}{c}n1\\ p1\end{array}\right)$, since the binomial coefficient is equal to 0 in this case.
Where $\frac{1}{p}$ is used to avoid couting the same solution several times. ${2}^{x1}\frac{\left(n+1\right)!}{\left(n+1x\right)!}$ can be written ${2}^{x1}x!\left(\begin{array}{c}n+1\\ x\end{array}\right).\phantom{\rule{0.3em}{0ex}}x!$ representing the number of possibilities to sort x contigs, 2^{x−1 }allows to take into account contig orientations and $\left(\begin{array}{c}n+1\\ x\end{array}\right)$ represents the number of possibilities to pull x contigs of n + 1.
which concludes the proof.
We define $p\left(S\right)=\frac{np}{2n\left(n1\right)}$ the part of this formula that does not depend on v_{1} and v_{2}, as an assembly fragmentation measure for genome S.
A Dynamic programming scheme
We largely refer to DeCo [12] for a full description of the dynamic programming scheme, and only describe the overall principle and the differences we introduce. Adjacencies are constructed between ancestral genes (equivalently internal gene tree nodes), and propagate along gene trees. For two nodes v_{1} and v_{2} defining genes belonging to the same (ancestral or extant) species, we define a solution as a descent pattern of ancestral and extant adjacencies explaining the input extant adjacencies that have an extremity in T (v_{1}) and another in T (v_{2}). So a solution is a set of ancestral adjacencies and descent relations linking ancestral and extant adjacencies. The cost of a solution is the cumulative cost of gains and breakages of adjacencies (due to rearrangements) in the descent pattern, according to an individual cost for gains (Gain) and breakages (Br).
More precisely we define two costs c_{0}(v_{1}, v_{2}) (respectively c_{1}(v_{1}, v_{2})), which are the minimum cost previously mentioned, given that there is an (respectively there is no) adjacency between v_{1} and v_{2} in a solution. All c_{0} and c_{1}, for every couple v_{1} and v_{2}, can be computed by the dynamic programming scheme described in [12]. ARtDeCo and DeCo have the same time complexity, that is O(g^{2} × k^{2}) where g is the number of gene trees in the input and k be the maximum size of a tree.
The main difference is that in [12] extant genomes were supposed to be perfectly assembled and in particular, if v_{1} and v_{2} are extant genes (or equivalently gene tree leaves, which corresponds to Case 1 in [12]), then DeCo would use the following scoring rules:
c_{0}(v_{1}, v_{2}) = ∞ and c_{1}(v_{1}, v_{2}) = 0 if v_{1}v_{2} is an adjacency in the data, otherwise c_{0}(v_{1}, v_{2}) = 0 and c_{1}(v_{1}, v_{2}) = ∞.
Here we modify these rules (it is the only case different from the dynamic programming equations given in [12] and Additional file 1) and propose instead that
These formulas define a cost system which is consistent with the previous one: when n = p (perfectly assembled genomes) it gives the same result. When it is not the case, the costs are between 0 and ∞ as the probabilities go from 0 to 1.
Exploration of the solution space
The dynamic programming scheme of DeCo allows the quantitative exploration of the whole solution space. This has been developed, in the DeCo model, in [31], where it was shown how to explore all solutions (i.e. evolutionary histories for adjacencies) under a Boltzmann probability distribution defined as follows: for a given instance (pair of gene trees and set of extant adjacencies) with solution space S, the parsimony score of an adjacency history h is denoted by s(h), and the Boltzmann probability of h is defined as ${e}^{s\left(h\right)/kT}/{\sum}_{g\in S}{e}^{S\left(g\right)/kT}$. Here kT is a constant that can be used to skew the probability distribution: when kT is small, parsimonious histories dominate the distribution, while a large kT leads to a more uniform distribution over the whole solution space.
This allows to associate to a feature of a solution (here an ancestral adjacency) a support defined as the ratio between the sum of the probabilities of the solutions that contain this feature and the sum of the probabilities of all solutions. This approach has been implemented in the DeClone software [31]. We integrated this possibility to ARtDeCo and thus associate a support to both extant and ancestral adjacencies. Computations were run with a value of the kT constant equal to 0.1 to ensure that the Boltzmann distribution is highly dominated by optimal and slightly suboptimal solutions. This value was chosen after preliminary tests on a subset of instances that showed that scenarios sampled with this value of kT were in very large majority optimal scenarios.
Results
We tested ARtDeCo on three data sets. The first one is composed of 7 tetrapod species with only universal unicopy genes, and aims at comparing our method with the method of Aganezov et al. [29]; on this data set, we obtain comparable results. Then we ran ARtDeCo on the complete Ensembl Compara [30] database, including 69 eukaryotic species and 20,279 gene families with arbitrary numbers of duplications and losses. This shows that ARtDeCo scales up and can process large data sets of whole genomes; for this data set we examine carefully one scaffolding adjacency proposed by ARtDeCo in the poorly assembled panda genome and provide evidence it is likely a true scaffolding adjacency. The third data set we consider is the restriction to the 39 eutherian mammals genomes of the previous data set. The computational efficiency of ARtDeCo allows to reproduce the computation many times with simulated missing adjacencies, and replicates to obtain empirical error bars on the measures. We performed all experiments with fixed costs for adjacency gains (Gain) and breakages (Br), respectively set to 3 and 1. There are several reasons for this discrepancy: first the actual number of adjacencies is very low compared to the space of possible adjacencies, which makes more probable to break a particular one $\left(p=\frac{1}{\#adj}\right)$ than to gain a particular one $\left(p=\frac{2}{\#genes\times \left(\#genes1\right)}\right):$ there is a huge unobserved space of possible solutions that should affect the costs; second it has been remarked that good statistical estimates of genomic distances when genomes are coded by the presence or absence of adjacencies are obtained with a state of possible adjacencies 3 times larger than the number of adjacencies [32].
Seven tetrapods  comparison with the method of Aganezov et al. [29]
By querying Biomart [33], we produced a data set similar to the one described in Aganezov et al. [29]: it consists in 8,818 universal unicopy gene families from Human, Chimp, Macaque, Mouse, Rat, Dog and Chicken. The latter was not present in the data set of Aganezov et al. [29], and we included it here because of a fundamental difference between the two methods: our method works with rooted phylogenies whereas Aganezov et al. [29] is not sensitive to the position of the root. This means that our method cannot scaffold an outgroup species, simply because, for any adjacency absent from the outgroup, it is more parsimonious to assume it is gained in all ingroup species. So we just added a distant outgroup to scaffold the 6 species used in [29].
We produced different sets of randomly fragmented genomes by considering n = 50 to n = 1050 random artificial breaks (or "fissions") in genomes, sticking to the described experiments in [29]. This means we simply removed n random adjacencies per genome from the data set. For each n, we replicated the experiment 30 times.
For each replicate with n random artificial adjacency breaks, let T P be the number of removed adjacencies that ARtDeCo retrieves and F P be the number adjacencies not in the removed ones but proposed by ARtDeCo.
Statistics on adjacencies recover by ARtDeCo on 7 tetrapods dataset with different number of simulated breaks
#Breaks (n)  50  150  250  350  450  550 

T P  283  829  1364  1895  2418  2922 
F P  14  16.5  21  24.5  32  40 
True positive  88.64%  89.98%  89.38%  89.00%  88.32%  87.35% 
False positive  4.40%  1.78%  1.39%  1.15%  1.18%  1.19% 
#Breaks (n)  650  750  850  950  1050  
T P  3431  3917  4398  4875  5338  
F P  46  57  63  73.566  83  
True positive  86.84%  85.87%  85.12%  84.38%  83.58%  
False positive  1.17%  1.25%  1.22%  1.27%  1.30% 
Thus, on small data sets and discarding gene families with complex histories, we obtain similar performance. The next experiments illustrate that the contribution of our method is then to be able to process much larger and much more complex data sets.
69 eukaryotes  a proof of scaling up
n = N umber of genes with degree >2
d_{ x } = N umber of degree of gene x
m = N umber of genes with degree = 1
On 43 species with nonlinear contigs, 23 have nonlinear contigs with only one extra branch. For the 20 remaining species, contigs are more branchy and few are circular.
This analysis also allowed to see a possible lack of data in Ensembl. As can be seen on the mouse lemur (Microcebus murinus) genome, there is no adjacency between CREG1 and RCSD1 because no RCSD1 gene has been annotated in Ensembl for this species. However, the gene content and order around CREG1 is very similar to that of close genomes (e.g., human). Moreover, Ensembl contains an incomplete DNA sequence for the equivalent position of CD247 and RCSD1 genes in mouse lemur. This implies that the genes CD247 and RCSD1 could be present in mouse lemur but are not annotated.
39 mammals  validity
We switched to a smaller dataset to measure the validity of the method, because the computing time don't allow too many replicates in the entire database. We selected all protein coding gene families from the 39 eutherian mammal genomes stored in the Ensembl database [30].
ARtDeCo proposes 1,056,418 ancestral adjacencies and 22,675 new adjacencies in extant genomes. A proportion of 95% of these adjacencies have a >0.9 support, meaning that they are present in over 90% of parsimonious solutions, computed as described in [31] for a kT value equal to 0.1 (chosen to ensure that the probability distribution over the solution space is highly dominated by optimal solutions).
Figure 8B is the analog of Figure 8A but for ancestral genomes: blue for the number of neighbors in the version of ARtDeCo without support (only one solution is given), and pink for the version of ARtDeCo with support. The several peaks of the graph illustrate that ancestral genomes are not in the shape of disjoint paths, as we would expect it from linear genomes. This was already remarked in [12], and is likely due to errors in gene trees in the Ensembl database [35, 36]. Additional computations show that ancestral species indeed contain a larger proportion of nonlinear contigs: only 91.2% contigs are linear for those species, among which contigs hosting only one gene are more represented than in extant genomes. Thus, a small part of the inferred adjacencies are incorrect, leading to some artificially treelike or cyclic contigs.
The bars with supports are more dispersed, as expected, because they take their values from non integer numbers. It puts the conflicts into perspective: when a gene has more than two neighbors, usually one adjacency is less supported.
We also performed experiments with artificial adjacency breaks as in the 7 tetrapods experiment. We removed from 1 to 75% input adjacencies from the human genome, and then from the horse genome. We chose the human and horse genome because of their phylogenetic position: one has many closely related genomes, while the other is rather distant from its closest neighbor inside the placentals. This allows us to measure the effect of the presence of closely related genomes in the given phylogeny. The two situations are very different because of the bias in taxonomic sampling around human. The presence of very close relatives in the data set makes the problem much easier for the human genome.
The complexity of the data is a real issue here. While in a prepared, filtered data set of 7 tetrapods the sensitivity was above 80% in all cases, here with all genes from 39 genomes including duplications and losses, it is much lower in all cases.
From all data sets, we observe that the precision of ARtDeCo is always high, while the sensitivity varies according to the conditions. So we can see the method as a rather sure predictor of a small number of scaffolding linkages, without the pretension to reconstruct fully assembled genomes.
Discussion and Conclusion
Ancestral gene order reconstruction, when ancestral genes are given, can be seen as a scaffolding problem. Indeed ancestral genes may be seen as contigs, and finding an order between contigs is a similar problem in both extant and ancestral genomes. If this similarity had already been remarked and exploited in some way [24, 26, 37], a fully integrated approach has only recently been achieved by Aganezov et al. [29], with a method which was limited to universal unicopy genes and a small number of genomes. Extending DeCo [12], a software aimed at reconstructing ancestral genomes and scaling up to dozens of genomes with possibly complex histories, we implement the additional possibility of scaffolding extant genomes in the same process, by handling equally ancestral and ancient genomes, with known and unknown parts in genome structures.
We demonstrate the efficiency of this approach on several eukaryote genomes data sets. It runs fast enough, proposes many additional supported adjacencies in extant genomes, and from several investigations we think we can state that such links are very likely to exist in reality. We are able to detect the less likely ones by assigning a support on ancestral and extant adjacencies by the same principle.
The main computational difference with the approach of Aganezov et al. [29] is that adjacencies are supposed to evolve independently. It has several notable consequences. The first one is the running time, because we switch from an NPcomplete to a polynomial problem, and we are able to handle a large number of whole genomes. The second one is the shape of ancestral genomes. While methods modeling rearrangements [29] end up with bona fide genome structures, as linear arrangement of genes, our adjacency sets can be conflictual, both in ancestral and extant genomes. This means a gene can have more than two neighbors, unlike in real genomes. Whereas this can be seen as a serious drawback because genomes are not realistic, we would like to argue that it has several advantages, in addition to the running time. Indeed, the amount of conflicts can be a measure of uncertainty of the methods and data. It has been remarked many times that data sets, and in particular gene trees, are far from perfect. But better gene trees produce ancestral genomes with less conflicts [34]. Conflicts can point at problems that don't necessarily concern the method itself, but give an overview of the quality of the data. This overview is lost if we force the data to fit in a linear structure. But if a linear ancestral genome is really needed, linearization techniques exist [38], even if we would argue for linearization techniques that also put into question the input data.
Some limitations would be still to overcome. For example we don't handle the orientation of the genes. This would be desirable to have a finer account of ancestral and extant genomes, and to have a better fit between the a priori probability of an adjacency (computed in an oriented mode) and the reconstructed adjacencies. It would not be conceptually much complicated because adjacencies can be considered between gene extremities instead of between genes. But it would result in a loss of sensitivity because inversions of a single gene, which seem to be frequent, would fall into a rearrangement signal, increasing the probability to lose the traces of neighborhoods. We leave this open for a future work.
Another perspective is to be able to question extant adjacencies given in the input. In our framework they have probability 1, but a scaffolding is not necessarily only giving an order to the contigs. It can be inserting a contig inside another, or cutting a chimeric contig because a better arrangement can be proposed. Assembly errors are often numerous, not only because of a lack of information, but also because of false information [39]. It could be done by reassigning an a priori probability to each extant adjacency, and not only to the ones outside the contigs. Finally, following the idea introduced in RACA [26], it could be interesting to pair the predictions of ARtDeCo with sequence information such as matepairs or even physical or optical maps in order to integrate both evolutionary signal and sequencing data.
Declarations
Acknowledgements
This work and its publication is funded by the Agence Nationale pour la Recherche, Ancestrome project ANR10BINF0101.
ARtDeCo analyses benefited from the Montpellier Bioinformatics Biodiversity platform services. We thank Yann Ponty for technical help for patching DeClone to integrate the scaffolding and the exploration of the solution space.
This article has been published as part of BMC Genomics Volume 16 Supplement 10, 2015: Proceedings of the 13th Annual Research in Computational Molecular Biology (RECOMB) Satellite Workshop on Comparative Genomics: Genomics. The full contents of the supplement are available online at http://www.biomedcentral.com/bmcgenomics/supplements/16/S10.
Authors’ Affiliations
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