Fan Yang

Zhigang Chen

Guifang Shao

Huazhen Wang

Distance Metric Learning-based Conformal Predictor

Keywords:

In order to improve the computational efficiency of conformal predictor, distance metric learning methods were used in the algorithm. The process of learning was divided into two stages: offline learning and online learning. Firstly, part of the training data was used in distance metric learning to get a space transformation matrix in the offline learning stage; Secondly, standard CP-KNN was conducted on the remaining training data with a nonconformity measure function defined by K nearest neighbors classifier in the transformed space. Experimental results on three UCI datasets demonstrate the efficiency of the new algorithm.

Introduction

In previous studies, K nearest neighbors (KNN) classifier was often used to design the nonconformity measure function for CPs, which is known as CP-KNN algorithm [START_REF] Papadopoulos | Regression Conformal Prediction with Nearest Neighbours[END_REF]. There are some disadvantages in CP-KNN [START_REF] Yang | Optimized Kernel-Based Conformal Predictor for Online Fault Detection[END_REF]. Firstly, the nonconformity measure function of CP-KNN is designed in the original space, but the distance metric in the original space can't adapt to most of the practical problems. Secondly, the distance metric is difficult to determine, and Euclidean distance and other distance are not good for many classification problems. Thirdly, it needs to store large amounts of historical data, and frequently search and access the database, so it will cost a lot of time. Especially, when the data sets are huge, the calculation is intolerable in many practical applications.

There are some existing versions of CPs aiming to improve its computational efficiency, e.g. offline learning transductive confidence machine [START_REF] Stijn | Off-line learning with transductive confidence machines: an empirical evaluation[END_REF], which is conducted in an offline manner. However, in offline learning, the calibration of CPs can not be guaranteed theoretically. In [START_REF] Wang | An online Algorithm with confidence for Real-Time Fault Detection[END_REF][START_REF] Yang | Using random forest for reliable classification and cost-sensitive learning for medical diagnosis[END_REF], Wang HZ and Yang F et al. proposed a hybrid compression CP which used random forest to learn a proximity matrix on part of training data and apply CP-KNN in an online learning manner on the remaining data in the sample space defined by the random forest proximity matrix. Hence the compu-tational efficiency was improved through the transfer of the online learning computational cost to the offline learning. Further, Yang F et al. propose to use adaptive kernel learning on part of the training data and also got both high predictive efficiency and computation efficiency on a fault detection dataset [START_REF] Yang | Optimized Kernel-Based Conformal Predictor for Online Fault Detection[END_REF]. Different from [START_REF] Balasubramanian | Kernel Learning for Efficiency Maximization in the Conformal Predictions Framework[END_REF], which use Multiple Kernel Learning (MKL) methodology to maximize efficiency in the CP framework, the above work mainly focused on improving the learning framework of CPs by dividing the learning process into two parts: offline learning and online learning. And this learning strategy can also be viewed as Mondrian CPs according to [START_REF] Vovk | Algorithmic learning in a random world[END_REF].

In this paper, we further present the distance metric learning based Conformal Predictor. Identically, the learning process was divided in to two stages. In the offline learning section, we used part of the training data sets to get a space transformation matrix by distance metric learning methods [START_REF] Kilian | Distance Metric Learning for Large Margin Nearest Neighbor Classification[END_REF][START_REF] Peltonen | Fast discriminative component analysis for comparing examples[END_REF][START_REF] Masashi | Dimensionality Reduction of Multimodal Labeled Data by Local Fisher Discriminant Analysis[END_REF], and then design the nonconformity measure function with KNN and apply online CP-KNN in the new space.

Conformal Predictor

Conformal predictor (CP) is a transductive confidence machine (TCM) based on Kolmogorov randomness theory and conducted in online scheme. When one testing example is coming, we assume the example belongs to every possible class, and get several new test sequences. Randomness test is then applied to every test sequence. If the randomness level of a new sequence is relatively high, the corresponding class may be the true label of the testing example. CP treats all the classes whose randomness levels are greater than the specified risk level as prediction results. So CP is region prediction rather than point prediction of the traditional machine learning algorithms [START_REF] Vovk | Algorithmic learning in a random world[END_REF].The key problem of the CP algorithm is the design of nonconformity measures for examples, which is the degree of a testing example consistent with each class's distribution.

Distance Metric Learning Algorithms

The KNN rule works well in the design of nonconformity measure in CPs. However the performance of KNN depends crucially on the distance metric. The performances of the KNN could vary greatly on different distance metrics. Usually, Euclidean distances are used as a similarity measure, which is not always the case in most applications. And the distance metric should adapt to the particular applications. We expected that the nonconformity measure with KNN could be more effective in a space learned from the training set. In this paper, we used three distance metric learning methods to get the space transformation matrix. The methods are Large Margin Nearest Neighbors Classifier (LMNN) [START_REF] Kilian | Distance Metric Learning for Large Margin Nearest Neighbor Classification[END_REF], Discriminative Component Analysis (DCA) [START_REF] Peltonen | Fast discriminative component analysis for comparing examples[END_REF] and Local Fisher Discriminant Analysis (LFDA) [START_REF] Masashi | Dimensionality Reduction of Multimodal Labeled Data by Local Fisher Discriminant Analysis[END_REF].

Distance Metric Learning-based Conformal Predictor Algorithm

In this paper, the process of learning is divided into two stages: offline learning and online learning. And the training data set is also randomly divided into two parts: compressed data set and calibration data set.

(i) Offline learning. In the original space, the compressed data set is used with Distance Metric Learning methods (LMNN, LFDA and DCA) to get a space transformation matrix (M). The purpose of this stage is to reduce storage size and the online computational cost by compressing part of the training data into knowledge.

(ii) Online learning. We get a new data space from offline learning stage. The transformation matrix not only increases the class separability of the compressed data set, but also increases the class separability of the calibration data set and the testing data set. The nonconformity measure function which is designed by KNN in the new space will be more effective.

The nonconformity measure function can be defined in the new space as: ) ], ,..., ([ : 1 -,..., 1 ), ], ,..., , ,..., ([ :

1 - 1 1 1 - 1 M Z Z A n i M Z Z Z Z A n n n n i i i i = = = + α α (1)
where n Z is a testing example and M is the linear transformation matrix. i A is the nonconformity measure function.

And the output of the prediction:

} /n | ) : 1,..., ( | : { , ,..., n 1 - 1 ε α α ε > ≥ + = = ∈ = Γ i k n n n m i p Y y x Z Z ) ( (2)
The nonconformity measure score was calculated as:

i j n m i k k j y ij k j y ij i ≠ + = ∑ ∑ = = = , 1,..., , / 1
) ( ) ( 1 - 1 - 1 1 , ,..., , n n y x y x
, testing data n x , k, and the risk level ε ;

Output: the region prediction ε Γ of n x .

Step 1. The compressed data set is used with Distance Metric Learning methods to get a space transformation matrix (M);

Step 2. The calibration data set is put into the new space by the space transformation matrix (M);

Step 3. Initialize the region prediction set and the calibration data set:

Φ = Γ ε , } { 1 - 1 - 1 1 , ,..., , ) ( ) (

Experiment Results

We call the Distance Metric Learning-based Conformal Predictor Algorithms as CP-LMNN, CP-LFDA and CP-DCA respectively. We compared our new algorithms with CP-KNN on three UCI data sets, i.e., SPAM E-mail Database, the Pen-Based Recognition of Handwritten Digits and the Thyroid disease [START_REF] Frank | UCI Machine Learning Repository[END_REF]. Four evaluation indicators are used, i.e., certain prediction rate, certain and correct prediction rate, empty prediction rate and exact calibration. The certain prediction rate means the rate of the region predictions which only have one class label. The certain and correct prediction rate denotes the rate of the region predictions which only have one label and the label is just the true class label. The empty prediction rate denotes the rate of the region predictions which have no elements.

Results on SPAM E-mail Database are showed in Fig. 1. The results on the other two datasets are similar to Fig. 1. And the certain and correct prediction rate are shown in Table 1.The experiments were performed on a laptop machine with a 2.1 GHz core 2 processor. In order to compare the computational efficiency, the CPU time for each experiment is listed in Table 2.

Table 1 shows that the certain and correct prediction rate of the new methods are better than CP-KNN at most confidence levels. The rate of region predictions which only have one label is improved, and most of the predictions are just the true class labels of the testing data. And the average degree of similarity of certain and correct prediction rate and certain prediction rate are also better.

From Table 2 we can see that the time costs of our method on all data sets are less than CP-KNN. Note that, the larger of the compressed data set, the CPU times of CP-LMNN will be less. The compressed data is used in offline learning and would not influence the computation efficiency of online learning. In contrast, as the number of historical data increases, CP-KNN will be very time-consuming. So the new algorithm is suitable for the online learning of huge data sets.

Conclusions

In this paper we propose a distance metric learning based conformal predictor. The new algorithm works well in improving the computational efficiency of CP. And at the same time, the predictive efficiency is also improved by some degree.

θ

  denotes the proximity sum of the k nearest neighbors whose class la- bel are not y, and ∑ y ij θ denotes the proximity sum of the k nearest neighbors whose class label are y. Algorithm 1. Distance Metric Learning-based Conformal Predictor Input:

4 . 5 .

 45 For test example n x , assume every class label c} {1,2,..., ∈ y as its label, and calculate the nonconformity score of each assumption with Eq. (15). If the random level (p) of the nonconformity scores sequence is larger than the risk level ( ε ), Get the true class label ( n y ) of n x , and add n x to the calibration data set

Fig. 1 .

 1 Fig. 1. The predictive efficiency on Spam E-mail Database, (a)CP-LMNN (b)CP-DCA (c)CP-LFDA (d)CP-KNN

Table 1 .

 1 The Comparison of the predictive efficiency*

		CL(%)	0.1	0.3	0.5	0.7	0.8	0.9	Cc/c
		KNN	3.6	19.49	30.6	43.37	53.86	69.86	86.58
	Spam	LMNN	10.77	25.99	42.71	60.44	73.32	87.04	96.46
	E-mail	LFDA	6.81	20.53	36.68	61.74	75.12	58.25	89.66
		DCA	9.11	27.56	47.4	67.67	62.82	43.83	79.41
		KNN	4.33	27	46.53	66.8	75.93	86.4	99.95
	Hand-	LMNN	11.67	33.73	53.47	72.8	82.73	91	99.86
	written	LFDA)	10.07	31.87	55.47	75.47	84.2	92.2	99.32
		DCA	10.8	31.13	52.2	71.8	82.2	92.33	99.41
	Thyroid

Table 2 .

 2 The Comparison on the Time Cost*(s) the number of examples used in the experiments; CM (compressed): the number of training data used for distance metric learning; CA (calibration): number of remaining training data used for online learning. TE :the test data.

	Dataset	N	CM	CA	TE	Attribute LMNN LFDA DCA	KNN
	E-mail	4601 1000 1000 2601	58	4697	4139	3987	7409
	Hand-written	4500 2000 1000 1500	17	5849	6257	6437 15778
	Thyroid 4534 1150 1150 2234	22	9126	8833	9442 16873
	*N :

This work was partially supported by the Fundamental Research Funds of China for the Central Universities under Grant No. 2010121065 and the Research Grant Council of Huaqiao University with Project No.09BS515.


Guillaume Mercy

Julien Mozziconacci

Vittore F Scolari

Kun Yang

Guanghou Zhao

Agnès Thierry

Yisha Luo

Leslie A Mitchell

Michael Shen

Yue Shen

Roy Walker

Weimin Zhang

Yi Wu

Ze-Xiong Xie

Zhouqing Luo

Yizhi Cai

Junbiao Dai

Huanming Yang

Ying-Jin Yuan

Jef D Boeke

Joel S Bader

Héloïse Muller
email: heloise.muller@curie.fr

Romain Koszul
email: romain.koszul@pasteur.fr.

3D organization of synthetic and scrambled chromosomes

While the design of the synthetic yeast genome Sc2.0 is highly conservative regarding gene content, the deletion of several classes of repeated sequences and the introduction of thousands of designer changes may affect genome organization and potentially alter cellular functions. We report here the Hi-C determined 3D conformations of Sc2.0 chromosomes. While the absence of repeats leads to a smoother contact pattern and more precisely tractable chromosome conformation, the large scale genomic organization is generally globally unaffected by the presence of synthetic chromosome(s). An exception is synIII which lacks the silent mating type cassettes, and synXII from which the rDNA has been moved to another chromosome. We also exploit the contact maps to detect rearrangements induced in SCRaMbLE strains.

Introduction

Genes of the budding yeast Saccharomyces cerevisiae genome are non-randomly distributed along its 16 chromosomes. For instance, centromere-and telomere-proximal regions are enriched in families of co-regulated genes (1)(2)(3)(4). Chromosome 3D organization has been studied through imaging and genetic studies (5)(6)(7)[START_REF] Taddei | Structure and function in the budding yeast nucleus[END_REF], revealing a characteristic "Rabl-organization" (9). Four main factors drive the overall organization: i) 16 centromeres tethered and clustered at the spindle pole body (SPB, the yeast microtubule organizing center), ii) telomeres forming smaller groups tethered at the nuclear envelope (NE), iii) a single nucleolus across the nucleus from the SPB where the rDNA is sequestered from other chromosomes, and iv) chromosomal arm lengths. In addition to these factors, several sequences have been shown or suggested to influence the organization. For instance, tRNA genes were proposed to influence chromosome folding through re-positioning in the vicinity of either the SPB or the nucleolus [START_REF] Thompson | Nucleolar clustering of dispersed tRNA genes[END_REF][START_REF] Haeusler | Genome organization in three dimensions: thinking outside the line[END_REF].

Telomeric repeats may also play a role in telomere clustering and anchoring to the NE [START_REF] Taddei | Structure and function in the budding yeast nucleus[END_REF][START_REF] Schober | Controlled exchange of chromosomal arms reveals principles driving telomere interactions in yeast[END_REF]. Sc2.0 genome design specifies strong conservation of gene content and arrangement with respect to the native yeast genome [START_REF] Richardson | Design of a synthetic yeast genome[END_REF]. However, synthetic chromosomes encode thousands of designer changes intended to improve genetic stability and increase genetic flexibility [START_REF] Richardson | Design of a synthetic yeast genome[END_REF]. For instance, tRNA genes were deleted during design of Sc2.0 chromosomes, to be relocated to a separate 'neochromosome' [START_REF] Richardson | Design of a synthetic yeast genome[END_REF], while subtelomeric regions were substantially altered as well, with large repeated sequences corresponding either to Y' or genes families deleted. Further, loxPsym sites encoded by Sc2.0 chromosomes enable inducible evolution by 'SCRaMbLE' [START_REF] Dymond | Synthetic chromosome arms function in yeast and generate phenotypic diversity by design[END_REF][START_REF] Dymond | The Saccharomyces cerevisiae SCRaMbLE system and genome minimization[END_REF] to generate combinatorial genomic diversity through rearrangements [START_REF] Shen | SCRaMbLE generates designed combinatorial stochastic diversity in synthetic chromosomes[END_REF]. Several synthetic chromosomes are now built [START_REF] Dymond | Synthetic chromosome arms function in yeast and generate phenotypic diversity by design[END_REF][START_REF] Shen | Deep functional analysis of synII, a 770 kb synthetic yeast chromosome[END_REF][START_REF] Annaluru | Total synthesis of a functional designer eukaryotic chromosome[END_REF][START_REF] Xie | Perfect" designer chromosome V and behavior of a ring derivative[END_REF](20)[START_REF] Wu | Bug mapping and fitness testing of chemically synthesized chromosome X[END_REF][START_REF] Zhang | Engineering the ribosomal DNA in a megabase synthetic chromosome[END_REF]; it is thus possible to experimentally address whether or not Sc2.0 modifications affect the overall chromosome organization in strains carrying synthetic chromosomes.

Genomic chromosome conformation capture approaches (e.g. Hi-C; [START_REF] Dekker | Capturing chromosome conformation[END_REF][START_REF] Lieberman-Aiden | Comprehensive mapping of long-range interactions reveals folding principles of the human genome[END_REF]), which provide access to the average 3D chromosome organization from a population of cells, highlighted the Rabl organization of the S. cerevisiae and other fungi genomes (Fig. 1A; [START_REF] Duan | A three-dimensional model of the yeast genome[END_REF][START_REF] Marie-Nelly | Filling annotation gaps in yeast genomes using genome-wide contact maps[END_REF]). In a Hi-C experiment, ligation frequencies between DNA restriction fragments are quantified through deep sequencing, reflecting contacts within the nuclear space and presumably their averaged respective positions in populations of cells. These frequencies are usually represented as 2D heat maps (fig S1) and can be processed and visualized as 3D representations to facilitate their interpretation (Fig. 1A; [START_REF] Lesne | Mozziconacci, 3D genome reconstruction from chromosomal contacts[END_REF]). To investigate Sc2.0 chromosome organization, Hi-C contact maps (bin=5kb) and 3D representations (see Material and Methods for interpretation of such structures) of synII, synIII, synV, synVI, synIXR, synX and synXII were generated from daughter cells synchronized through elutriation (Fig. 1B, C andD; fig S2 -10; tables S1-2; movies S1-10; [START_REF] Cournac | Generation and Analysis of Chromosomal Contact Maps of Yeast Species[END_REF]).

Results

Trajectories of synthetic chromosomes in the nuclear space

To determine whether individual or combinations of Sc2.0 chromosomes influence the overall genome organization, the contact map of the subset of invariant (i.e. native) chromosomes was generated for each strain. Euclidean distances between these maps were then computed and revealed that the presence of one or more Sc2.0 chromosomes did not dramatically affect the overall structure of the remaining genome (fig S11). The 3D representations also allow for the qualitative comparison of native and syn sequences, revealing that the average trajectories of individual Sc2.0 chromosome did not appear significantly altered compare to their native counterparts, with syn chromosomes neighboring the same chromosomes as the native ones (Fig. 1 and fig S2-10 for side by side comparisons). To quantitatively compare the internal folding of Sc2.0 chromosomes with their native counterparts, we computed the contact frequency decay as a function of the increasing genomic distance for all pairs of loci. No substantial changes between synthetic and native chromatin were detected (Fig. 1E), suggesting that the redesigned sequence has little if no effect on the internal folding of the chromosome beyond a ~5-10% shortening through the removal of repeats.

Sc2.0 design improves mappability

A comparison of Sc2.0 maps with their native counterparts nevertheless revealed remarkably "smoother" contact patterns in the designer chromosomes, as shown by the quasi-absence of white lines in syn contact maps. This stems from the intentional deletion of repeated elements relative to the native sequence, which leads to improved "mappability" along the length of the synthetic chromosome (Fig. 1E andF ). In addition, the normalized contact frequencies between synVI subtelomeres appear to be much higher than in the WT counterpart (fig S13). This variation results directly from the improved mappability of subtelomeric regions following the removal of subtelomeric repeats. On the other hand, subtelomeric contacts are underestimated in native chromosome because of these repetitive sequences. These observations highlight the conceptual advance brought by bottom-up chromosome design and synthesis to investigate fundamental questions, as scientists can now design at unprecedented levels of refinement experimental systems making complex questions easier to address experimentally. For instance, investigating the elusive regulatory influences of repeated sequences in mammalian genomes could benefit from similar techniques.

SynIII conformation is modified by the design

Specific contacts between the duplicated HML and HMR silent mating-type loci that bridge the two arms of chromosome III have been identified [START_REF] Dekker | Capturing chromosome conformation[END_REF][START_REF] Miele | Yeast silent mating type loci form heterochromatic clusters through silencer protein-dependent long-range interactions[END_REF]. The deletion of these cassettes led to a loss of contacts on synIII (Fig. 2A,B). Moreover, chr III shows a mating-type specific conformation that depends on the integrity of a recombination enhancer sequence (RE) [START_REF] Belton | The Conformation of Yeast Chromosome III Is Mating Type Dependent and Controlled by the Recombination Enhancer[END_REF].

Despite the presence of the RE in synIII, the mating-type specific conformation is lost (fig S14).

We speculate that the deletion of the silent loci in synIII underlies this result, but additional experiments are required to discriminate this possibility from other changes in the sequences.

Note that synIII still exhibits enriched contacts between its subtelomeres, a feature characteristic of the small metacentric chromosomes I, III, and VI [START_REF] Schober | Controlled exchange of chromosomal arms reveals principles driving telomere interactions in yeast[END_REF][START_REF] Bystricky | Chromosome looping in yeast: telomere pairing and coordinated movement reflect anchoring efficiency and territorial organization[END_REF].

Re-positioning the rDNA locus affects the global 3D structure of the genome

The rDNA locus on the right arm of chromosome XII consists of a cluster (100-200) of ~9kb rDNA units, each containing two ribosomal precursor genes. This cluster assembles in the nucleolus, a discrete, crescent shaped nuclear compartment that occupies ~1/3rd of the total nuclear space and is positioned opposite to the SPB. Two versions of the synXII chromosome were designed, with and without the rDNA cluster. When not located on synXII, the rDNA was positioned either on the multicopy 2µ plasmid (one unit per plasmid) or reintegrated as an array within the right arm of the small chromosome III [START_REF] Zhang | Engineering the ribosomal DNA in a megabase synthetic chromosome[END_REF]. Chromosome organization was investigated in these strains. Because of their repetitive nature, rDNA unit reads cannot be uniquely mapped, and the rDNA cluster on the 3D reconstruction thus appears as an empty space flanked by the closest regions that can be mapped unambiguously (Fig. 1A and Fig. 3A, B andC). In strains without the rDNA locus on synXII (JDY446, JDY448 and JDY449), the continuity of the two regions flanking the original insertion site was clearly visible on the contact map and 3D representations of the right arm (Fig. 3A, B andC and fig S5 -6). The presence of 2µ plasmids carrying rDNA unit (strain JDY446) did not result in a large reorganization of the genome (fig S5), suggesting that the plasmids do not form large discrete heterochromatic structures, in agreement with the studies reporting the formation of multiple small clusters [START_REF] Zhang | Engineering the ribosomal DNA in a megabase synthetic chromosome[END_REF][START_REF] Oakes | Mutational analysis of the structure and localization of the nucleolus in the yeast Saccharomyces cerevisiae[END_REF]. On the other hand, the insertion of the rDNA array in the middle of the right arm of chromosome III (strains JDY448 and JDY449) resulted in substantial reorganization of the genome (Fig. 3C andfig S6). The right arm of chromosome III now appears split into two non-interacting regions by the rDNA cluster, an arrangement similar to the native chromosome XII structure [START_REF] Duan | A three-dimensional model of the yeast genome[END_REF].

Relocating the rDNA to a short chromosomal arm imposes new constraints on the genome: the nucleolus is now trapped between short and long chromosome arms, forming a physical barrier between them as shown by reduced contacts between these arms (Fig. 3C). In addition, contacts between the rDNA and subtelomeric regions are increased overall (Fig. 3D), as a result of the greater proximity of the nucleolus to the entire set of chromosomal extremities. Also, the IIIR subtelomere in this strain is now contacting long arms subtelomeres (blue arrow on Fig. 3C). No growth rate defects were detected in these strains, suggesting that the position of the rDNA locus has little effect on fitness in laboratory growth conditions tested here. However, given the observed constraints, it would be informative to run long-term cultures to see if the rDNA locus spontaneously re-localizes, and if so, where.

Hi-C analysis of SCRaMbLE chromosomes

All synthetic chromosomes carry the "synthetic chromosome rearrangement and modification by LoxP mediated evolution" or SCRaMbLE system, a chromosome-wide expansion of the Cre/lox site specific recombination assay exploited to measure local DNA concentrations in genomes (5,[START_REF] Hildebrandt | Comparison of recombination in vitro and in E. coli cells: Measure of the effective concentr ation of DNA in vivo[END_REF]. The Sc2.0 design includes the integration of hundreds of loxPsym sites all along chromosomes, at the end of every non-essential gene and at specific landmarks. Upon activation of the Cre recombinase, two loxPsym will recombine if they encounter each other in the nuclear space, leading to a structural variant (SV). The hundreds of sites therefore hold a large combinatory potential, leading to rapid and complex structural changes of synthetic chromosomes. Previous analysis of synIXR SCRaMbLE strains has revealed a large variety of cis events ranging from simple duplications, inversions and deletions to highly reorganized structures [START_REF] Dymond | Synthetic chromosome arms function in yeast and generate phenotypic diversity by design[END_REF][START_REF] Shen | SCRaMbLE generates designed combinatorial stochastic diversity in synthetic chromosomes[END_REF]. We took the opportunity offered by strains carrying two Sc2.0 chromosomes to explore further the power of the SCRaMbLE recombination assay in trans [START_REF] Dymond | Synthetic chromosome arms function in yeast and generate phenotypic diversity by design[END_REF][START_REF] Dymond | The Saccharomyces cerevisiae SCRaMbLE system and genome minimization[END_REF]. The Cre recombinase was induced for 48h in strain yLM539 carrying synIII and synIXR (Fig. 4A; fig S15). Independent clones were sampled during the time course experiment and two clones, HMSY029 (T2 = 2h) and HMSY030 (T8 = 8h), were retained for in-depth analysis. Genomewide Hi-C contact data were recently shown to provide a convenient way to identify and solve chromosomal rearrangements (fig S16; [START_REF] Marie-Nelly | High-quality genome (re)assembly using chromosomal contact data[END_REF][START_REF] Kaplan | High-throughput genome scaffolding from in vivo DNA interaction frequency[END_REF][START_REF] Flot | Contact genomics: scaffolding and phasing (meta)genomes using chromosome 3D physical signatures[END_REF][START_REF] Burton | Chromosome-scale scaffolding of de novo genome assemblies based on chromatin interactions[END_REF]). We therefore applied Hi-C to investigate the consequences of genome structural alterations in these two isolates. The contact maps identify gross chromosomal rearrangements (GCRs) in both SCRaMbLE strains, with each strain exhibiting deletion and translocation events, the latter representing a class of trans SCRaMbLE events not previously observed (Fig. 4B). The resolution of the contact map (~2 to 5 kb) allowed identification of relatively large scale rearrangements, but loxPsym sites are often more closely spaced. To address this, a refined analysis of the reads coverage was performed (table S3; fig S17), unveiling multiple short-scale modifications of loxPsym flanked segments (summarized in Fig. 4C; see fig S18 for details). These results highlight the potential of the SCRaMbLE design to generate GCRs, with more rearrangements being achieved after longer induction times.

Incidentally, Hi-C analysis of Sc2.0 strains identified several chromosomal rearrangements that spontaneously arose during chromosome assemblies such as aneuploidy, duplication or translocation events outside of the synthetic chromosome of interest (table S1, fig S19; ( 17)). Hi-C is therefore a convenient way to validate the assembly and subsequent processing of strains carrying synthetic chromosomes.

Conclusion

Overall, this large dataset represents a resource that will be exploited in future studies exploring the power of the SCRaMbLE system. By showing that the spatial organization of the Sc2.0 genome is not significantly altered, this work pioneers future studies addressing the influence of genome-wide engineering approaches on essential features of living systems.

Materials & Methods

Media

Yeast were grown either in YPD [1% (w/v) Bacto peptone (Difco) 1% (w/v) Bacto yeast extract (Difco), 2% (w/v) glucose and 2% (w/v) Bactoagar] or in selective SC media [0.67% Yeast Nitrogen Base without amino acids (Difco), supplemented with an amino acid mix minus those whose prototrophy is selected for, 2% (w/v) glucose and 2% (w/v) Bactoagar].

Strains

All strains used in the study are described in Table S1.

Culture conditions

Cells were inoculated and grown overnight in 10 ml YPD. Overnight cultures were then diluted and grown to exponential phase in 500 ml YPD for ~15h at 30°C. For SCRaMbLE and mating-type specific organization experiments, Hi-C libraries were generated from asynchronous cultures (see Table S2). For all other Sc2.0 strains, Hi-C libraries were generated from daughter cells recovered using elutriation and restarted for 30 min in YPD at 30°C [START_REF] Guidi | Spatial reorganization of telomeres in long-lived quiescent cells[END_REF].

Generation of Hi-C libraries

Hi-C libraries were generated with a protocol adapted from [START_REF] Dekker | Capturing chromosome conformation[END_REF] with introduction of a biotin-ligation step [START_REF] Lieberman-Aiden | Comprehensive mapping of long-range interactions reveals folding principles of the human genome[END_REF]. Briefly, aliquots of 1-3 x 10 9 cells were cross-linked for 30 minutes with fresh formaldehyde (3% final concentration) and quenched with glycine for 15 min. Pelleted cells were dissolved in 10 ml sorbitol 1M and incubated for 30 minutes with DTT 5mM and Zymolyase 100T (CFinal=1 mg/ml). Spheroplasts were washed first with 5 ml sorbitol 1M, then with 5 ml 1X restriction buffer (DpnII NEB buffer), and suspended in 3.5 ml of 1X restriction buffer. Cells were split into aliquots (V=500µL) and incubated in SDS (3%) for 20 minutes at 65°C. Crosslinked DNA was digested at 37°C overnight with 150 units of DpnII restriction enzyme (NEB). The digestion mix was subsequently centrifuged 20 minutes at 18000 g and the supernatant discarded. Pellets were suspended and pooled into 400 µL of cold water. DNA ends were repaired in the presence of 14-dCTP biotin (Invitrogen), and crosslinked complexes incubated for 4 hours at 16°C in presence of 250 U of T4 DNA ligase (Thermo Scientific, 12.5 mL final volume). DNA purification was achieved through an overnight incubation at 65°C in presence of 250µg/mL proteinase K in 6.2mM EDTA followed by a precipitation step and RNAse treatment.

The resulting Hi-C libraries were sheared and processed into Illumina libraries according to manufacturer instructions (Paired-End DNA sample Prep Kit -Illumina -PE-930-1001) using custom-made versions of the Illumina PE adapters [START_REF] Cournac | Generation and Analysis of Chromosomal Contact Maps of Yeast Species[END_REF]. Fragments of sizes between 400 and 800 bp were purified on from 2% agarose gel, PCR amplified, and paired-end (PE) sequenced on an Illumina platform (HiSeq2000 or NextSeq500, Table S2).

Raw sequences are accessible on SRA database through the following accession number: SRP070421.

Generation and normalization of contact maps

Sequencing pair-end data was processed as follow. For each library, PCR duplicates were collapsed using the 6 Ns present on each of the custom-made adapters and trimmed. Reads were then aligned using Bowtie 2 in its most sensitive mode against the S. cerevisiae reference genome adapted with the synthetics sequences [START_REF] Langmead | Fast gapped-read alignment with Bowtie 2[END_REF]. An iterative alignment procedure was used:

for each read the length of the mapped sequence increases gradually from 20 bp until mapping becomes unambiguous (mapping quality > 30). Read pairs were aligned independently and assigned to a restriction fragment (RF). Religation and other unwanted events were filtered out, taking into account the orientation of the reads, as described [START_REF] Cournac | Generation and Analysis of Chromosomal Contact Maps of Yeast Species[END_REF][START_REF] Cournac | Normalization of a chromosomal contact map[END_REF]. Contact matrices were built for each strain by binning the aligned reads into units of single RF. Adjacent restriction fragments were then pooled into fixed size bins of either 2,000 or 5,000 base pairs. Bins exhibiting important contact frequencies variations (< or > 2 Standard deviation, SD were filtered out of the data, with the corresponding bin vectors either set to zero (white band on the contact maps) or removed from the picture (see Figure legend). Finally, binned contact maps were normalized following the "Sequential Component Normalization" (SCN) procedure described in [START_REF] Cournac | Normalization of a chromosomal contact map[END_REF].

3D Representation of contact maps

The 3D representations of the contact maps were generated using ShRec3D [START_REF] Lesne | Mozziconacci, 3D genome reconstruction from chromosomal contacts[END_REF] on the normalized contact maps filtered for low signal bins. These 3D structures are average representations and therefore do not represent the exact structure found in an individual cell. It must also be underlined that they are not polymer models and cannot be interpreted as such.

They have to be interpreted in light contact frequencies over a population of cells. For instance, on these 3D representations the telomeres loosely cluster together. In a single nucleus, telomeres would rather form smaller groups scattered all around the nuclear membrane. Since in different cells these group gather different partners, they are regrouped together in the average structure that reflects the population average of contacts. All the 3D structures presented here were rendered using VMD [START_REF] Humphrey | VMD: visual molecular dynamics[END_REF].

Similarity between contact maps

To assess for the similarity between different datasets, we proceeded as follows. First, normalized matrices of chromosomes I, IV, VII, VIII, XIII, XIV, XV and XVI were binned at 50 kb and quantile normalized. We then computed the Euclidean distance between all pairs of maps and performed a principal component analysis on the resulting distance matrix.

Genomic distance plot

Pairs of reads mapping in cis-(i.e. intrachromosomal) positions along the genome were partitioned by chromosome. Reads oriented towards different directions or separated by less than 1,500 bp were discarded. For each chromosome read pairs were log-binned in function of their genomic distance s (in kb) according to the following formula:

bin = ⌊log1.1(s)⌋.
The genomic distance plot is the weighted histogram computed from the sum of read pairs for each bin weighted with both the difference between the length of the chromosome and the genomic distance s (as a proxy for the number of possible events) and the bin-size 1.1 (1+bin) (because of the log-binning). To compare syn and native chromosome both distributions were normalized by their mean computed over the 70% of the curve at lower distances.

SCRaMbLE assay

Strain yLM539 (synIII, synIXR) was transformed with the plasmid pSCw11 CRE-EBD_HIS3, and grown in SC-HIS media [START_REF] Dymond | Synthetic chromosome arms function in yeast and generate phenotypic diversity by design[END_REF]. Cre expression was induced by adding 1µM final of estradiol, and samples of induced and non-induced cultures were analyzed at multiple time point during 48h. For each time point (T0, 1h, 2h, 4h, 5h, 6h, 24h, 48h), OD600 of a sample of each culture was recorded and then adjusted to OD600 = 0.05. Aliquots of 5µL of these cells and four 10-fold serial dilutions were spotted on YPD and SC-HIS agar plates. Growth curve and dilution dots experiments are shown in fig S15. Two clones, HMSY029 (T2=2h) and HMSY030 (T8=8h), were retained for sequencing and Hi-C analysis.

Genomic analysis of SCRaMbLE strains

Illumina paired-end short-reads were trimmed to remove adapter sequences and filtered to remove reads either shorter than 100 bp, and/or with unknown bases, and/or exhibiting 1 or more bases with a Phred-score under 7. The filtered reads were then mapped to the reference sequence using Bowtie2. The read coverage over the entire genome was computed, with a specific focus on the synthetic regions for which the copy number of each segment in-between loxPsym sites was assessed to detect deletions, duplications, and higher amplifications. To account for possible systematic experimental biases in the sequencing depth resulting from library preparation and mapping, we used an iterative algorithm developed previously to refine the copy number estimation and the potential bias [START_REF] Shen | SCRaMbLE generates designed combinatorial stochastic diversity in synthetic chromosomes[END_REF].

We then focused on the unmapped reads carrying a loxPsym site to characterize further potential SCRaMbLE rearrangements. The two segments flanking a loxPsym site defines a junction. We trisected unmapped reads into a loxPsym site and its two flanking extremities, then mapped each of the latter to the reference genome using EMBOSS water [START_REF] Rice | EMBOSS: the European Molecular Biology Open Software Suite[END_REF] to identify novel junction. The average depth of novel junctions for the 2h and 8h Cre-induced strains was 16.3 and 14.3, respectively. We combined novel junctions with a depth higher than 5 and the copy number of segments to characterize the SCRaMbLE induced rearrangements (Table S3).

That no off-target rearrangement occurred elsewhere in the genome was confirmed by analyzing unmapped reads without loxPsym site with EMBOSS water to detect potential recombination events.

Analysis of rDNA contacts

Genome-wide rDNA contact frequencies were investigated in Sc2.0 strains carrying the rDNA either at its natural position on chromosome XII (datasets from strains YS031, yXZX538, yLM539, yLM896, HMSY012, yXZX573) on chromosome synXII (datasets from strains JDY465, JDY512, JDY452), on chromosome III (datasets from strains JDY448, JDY449), or on the 2μ plasmid (dataset from strain JDY446). For each dataset, pair-end reads were aligned on the reference genome of the corresponding strain lacking rDNA sequences and on an extra contig corresponding to a single rDNA unit (~9kb). Contact maps of trans interactions were generated (bin = 5 kb) and normalized [START_REF] Cournac | Normalization of a chromosomal contact map[END_REF]. To compare the contacts made by the rDNA contig with the rest of the genome between different datasets, the values in the corresponding vector were divided by their median to alleviate differences of coverage and/or number of rDNA units. Chromosomes III and XII, that carries the rDNA cluster in three out of four datasets, were removed from the analysis to allow comparison of the rest of the genome. For each dataset, the contacts made by the rDNA with the 28 subtelomeric regions (30 kb at the extremities of the 14 chromosomes investigated) and a central region of 30 kb in each arm were plotted using violin plot function from the "vioplot" R library.

Distribution of read coverage for syn and native chromosomes

The removal of repeated genetic elements in synthetic genomes relative to native counterparts leads to smother contact maps in the designed chromosomes. Indeed, the presence of repeated sequences in the genome prevent the non-ambiguous alignment of Hi-C reads against them, resulting in the corresponding vectors in the contact matrix to display low if not null number of contacts. Those empty vectors that appear as empty rows and columns in the contact maps are a source of noise and spurious contacts in the matrices after normalization. For this reason, these regions are filtered according to a threshold (see the Generation and normalization of contact maps paragraph). To quantify the improvement in the visibility of syn chromosomes all along their length, we compared the histogram of their coverage between the synthetic and the native dataset (fig S12). The histograms count the number of contacts made by each vector within the region of interest with the entire genome (histogram bin = 500 reads). The filtering threshold (median -2SD) was computed over the entire genome (reported on the fig S12

histograms as dotted lines). Top: normalized contact maps of the seven synthetic chromosomes (bin = 5kb). Normalized contact frequencies [START_REF] Oakes | Mutational analysis of the structure and localization of the nucleolus in the yeast Saccharomyces cerevisiae[END_REF] are indicated in a log10 scale ranging from white (few contacts) to dark red (many contacts). Filtered bins are set to zero (white vectors). Bottom: corresponding 3D representation of the contact maps displayed above, with synthetic chromosome and the set of natural chromosomes represented with colored and gray beads, respectively. (E) Distribution of the number of contacts as a function of the genomic distance for synV (pink) and native chromosomes V (black). (F) Vis à vis comparison of synII (strain YS031) and native chromosome II (strain BY4742) normalized contact maps. Non-mappable, repeated regions are highlighted with red arrowheads on the wild-type map.

Supplementary Materials:

Figures S1-S19

Tables S1-S3

Movies S1-S10 The number on top of the first bin of each histogram corresponds to the number of filtered vectors in the region. The lower the number, the smoother (and complete) the matrix. The histograms illustrate how synthetic matrices are now much less affected by the filtering step compared to native chromosomes. For each chromosome, the number and percentage of filtered bins are the following: II: 8 (5%) synII 0 (0%); III: 5 (8%), synIII: 1 (2%); IXR: 0 (0%), synIXR:1 (5%); V: 7 (6%), synV: 2 (2%); VI: 5 (9%), synVI: 0 (0%); X: 12 (8%), synX: 5 (4%); XII: 20 (9%), synXII: 6 (3%). analysis of intrachromosomal contacts made by the subtelomeric regions of the native chromosome VI (dark dots) and synVI (blue dots) using a bait chromosome capture approach. The contacts made by a 10kb window positioned either 20kb away from the left (top) or the right (bottom) telomere (dark gray areas) are displayed. Y-axis: contact frequencies. X-axis: distance (in kb) from the left and right telomere. Each point represents the mean contact frequency for the bait region with 5kb windows (bins) over the native and synVI chromosome, computed from three independent experiments. The Δ symbol points at the normalized contacts discrepancies between the left arm extremities of synVI and native chromosomes. Whereas the native chromosome end is "invisible" to the 3C assay, the telomere proximal region of the synthetic chromosome, which does not harbor repeated elements anymore, is now fully accessible and thus "visible". Because of DNA polymer nature, two fragments of DNA at close distance on the chromosome will collide more frequently than two fragments separated by a larger distance. In addition, two fragments positioned onto two different chromosomes will display, in general, even lower contacts. (A) If no rearrangement is observed, chromosomes appear as discrete domains composed of adjacent DNA segments frequently colliding with each other's within one chromosome. Two chromosomes (DNA molecules) will display less contacts between them than intrachromosomal contacts. (B) If a fragment is duplicated and the reference genome not modified to take into account this mutation, the signal will be doubled over the duplicated region, and therefore a cross will appear in the contact map at that position. (C) If a fragment is deleted, no reads corresponding to this fragment will be present in the data. A region without signal will therefore appear on the contact map. (D) If a fragment is inverted, the continuity of the signal will be altered intrachromosomally, with strong signal appearing at the extremities of the inverted region, away from the diagonal of the contact map. (E) If a fragment is translocated from one chromosome to another, a characteristic high interchromosomal contact will appear at the region involved in the translocation.

Fig. S17: Genomic analysis of SCRaMbLE strains

Number of reads remaining at each step of genomic analysis as described in M&M, for the parental strain yLM539 (T0) and the two SCRaMbLE strains HMSY029 (T2=2h) and HMSY030 (T8=8h).

  and fig S2-10). For instance, for chromosome II, eight bins (5% of the chromosome) appeared insufficiently covered in the WT when its synthetic counterpart had none (fig S2 and fig S12

Fig. 1 .

 1 Fig. 1. 3D genome organization of wild-type and synthetic chromosomes. (A) 3D

Fig. 2 .Fig. 1 .

 21 Fig. 2. Loss of subtelomeric contacts in synIII. (A) Normalized contact maps (bin = 5kb) of

Fig. 3 .

 3 Fig. 3. Repositioning of rDNA affects the overall genomic organization. (A -C) Top panel:

Fig. 4 .

 4 Fig. 4. SCRaMbLE induction of syn chromosomes results in multiple types of genome

  Fig. 1

Fig. 3 position

 3 Fig. 3

Fig. S11 :

 S11 Fig. S11: Correlation between contact maps (A) Euclidean distances between all pairs of contact maps for chromosomes I, IV, VII, VIII, XIII, XIV, XV and XVI. (B) Principal component analysis of the distance matrix (A).

Fig. S12 :

 S12 Fig. S12: Quantification of the increased visibility of syn chromosomesThe distribution of bin coverage was plotted for the contact matrix of each syn chromosome (top histogram) and their native counterpart (bottom histogram). In each of these comparisons, the colored histogram (top histogram) represents the sum of the elements for each column in the contact matrix in the syn chromosomes while the dark histogram (bottom histogram) represents the sum of the elements for each column in the native contact matrix, for the same region. The dashed lines represent the filtering threshold used for normalization purposes (M&M). The number on top of the first bin of each histogram corresponds to the number of filtered vectors in the region. The lower the number, the smoother (and complete) the matrix. The histograms illustrate how synthetic matrices are now much less affected by the filtering step compared to native chromosomes. For each chromosome, the number and percentage of filtered bins are the following: II: 8 (5%) synII 0 (0%); III: 5 (8%), synIII: 1 (2%); IXR: 0 (0%), synIXR:1 (5%); V: 7 (6%), synV: 2 (2%); VI: 5 (9%), synVI: 0 (0%); X: 12 (8%), synX: 5 (4%); XII: 20 (9%), synXII: 6 (3%).

Fig. S13 :

 S13 Fig.S13: Telomere interactions of synVI (A) Normalized contact maps (bin = 5 kb) of native (left; strain BY4742) and synVI (right; strain yLM896) chromosome VI. Same colorscale as in Fig.1. (B) Quantitative analysis of intrachromosomal contacts made by the subtelomeric regions of the native chromosome VI (dark dots) and synVI (blue dots) using a bait chromosome capture approach. The contacts made by a 10kb window positioned either 20kb away from the left (top) or the right (bottom) telomere (dark gray areas) are displayed. Y-axis: contact frequencies. X-axis: distance (in kb) from the left and right telomere. Each point represents the mean contact frequency for the bait region with 5kb windows (bins) over the native and synVI chromosome, computed from three independent experiments. The Δ symbol points at the normalized contacts discrepancies between the left arm extremities of synVI and native chromosomes. Whereas the native chromosome end is "invisible" to the 3C assay, the telomere proximal region of the synthetic chromosome, which does not harbor repeated elements anymore, is now fully accessible and thus "visible".

Fig. S14 :

 S14 Fig. S14: loss of mating-type specific conformation in synIIINormalized contact maps (bin = 10 kb) of chr III (top matrices) and synIII (bottom matrices) from MATa (A) and MATalpha (B) cells growing in asynchronous conditions. Contact frequencies are displayed in log2. (C) MATa/MATalpha differential contact maps of WT strains (top) and syn strains (bottom). Colorscale reflects contact enrichment in MATa (the more red, the more contacts in MATa) or in MATalpha (the more blue, the more contacts in MATalpha).

Fig. S15:

  Fig. S15: SCRaMbLE induction(A) Growth curve of strain yLM539 + pSCw11 in SC-HIS media in presence or absence of estradiol (+/-E). (B) Dilution dot experiment on YPD and SC-HIS agar plates during SCRaMbLE induction of strain yLM539 + pSCw11.

Fig. S16 :

 S16 Fig. S16: Hi-C contacts patterns resulting from various chromosomal rearrangementHi-C contacts maps allow the identification of chromosomal rearrangements compared to the reference genome. Because of DNA polymer nature, two fragments of DNA at close distance on the chromosome will collide more frequently than two fragments separated by a larger distance. In addition, two fragments positioned onto two different chromosomes will display, in general, even lower contacts. (A) If no rearrangement is observed, chromosomes appear as discrete domains composed of adjacent DNA segments frequently colliding with each other's within one chromosome. Two chromosomes (DNA molecules) will display less contacts between them than intrachromosomal contacts. (B) If a fragment is duplicated and the reference genome not modified to take into account this mutation, the signal will be doubled over the duplicated region, and therefore a cross will appear in the contact map at that position. (C) If a fragment is deleted, no reads corresponding to this fragment will be present in the data. A region without signal will therefore appear on the contact map. (D) If a fragment is inverted, the continuity of the signal will be altered intrachromosomally, with strong signal appearing at the extremities of the inverted region, away from the diagonal of the contact map. (E) If a fragment is translocated from one chromosome to another, a characteristic high interchromosomal contact will appear at the region involved in the translocation.

Fig. S18 :

 S18 Fig. S18: Genomic structure of SCRaMbLE clonesDetailed genetic maps of synIII and synIXR of strains yLM539 (A), HMSY029 (B), and HMSY030 (C). (A) For each synthetic chromosome carried by the parental strain yLM539, segments between two loxPsym sites (and telomeres and a loxPsym site) are numbered from left to right (1 to 100 for synIII, blue numbers; 1 to 45 for synIXR, pink numbers). Genetic elements along the chromosomes are indicated with symbols and colors according to figure legend. Names of genes at rearrangements borders are also indicated. Chromosome segments along the SCRaMbLEd synIII and synIXR chromosomes from stains HMSY029 (B) and HMSY030 (C) are numbered and colored according to their original location along the parental strain depicted in (A). The

Fig. S19 :

 S19 Fig. S19: Accompanying rearrangements generated during syn assembly, and identify through Hi-C(A) Genome wide contact map of Sc2.0 synII strain (YS031). A duplication and a translocation occurred between chromosomes XIII and XVI of this strain, highlighted with the black arrows. (B) Schematic representation of the rearrangements between chromosome XIII (yellow) and XVI (orange). Reciprocal translocation happened between the left arm of the chromosome XIII (coordinates 1-212,400 bp) and the right arm of chromosome XVI (850,341-924,431 bp). Additionally, a segment of chromosome XIII (184,000-212,400 bp; in red) has been duplicated on chromosome XVI. This kind of double-rearrangement is uncommon, but was reported before to occur spontaneously in the yeast genome(2). (C) Contact map of chromosomes XIII and XVI aligned with corrected reference sequences, including the reciprocal translocation. As duplicated sequences cannot be unambiguously mapped, the reference sequence contains the duplicated segment of chromosome XIII only in chromosome XVI for a clearer visualization. Read coverage shown in the lower panel allows to identify the duplication.

Fig

  fig S2

Table S1

 S1

	yLM422 HMSY030	synIII MATalph synIII LE_T8 SCRaMb synIXR -	MATalpha ura3Δ0 leu2Δ0 his3Δ1 lys2Δ0 synSUP61::HO::ura3, synIII, synIXR, SCRaMbLE lys2Δ0 hoΔ::synSUP61_KlURA3, MATalpha ura3Δ0 leu2Δ0 his3Δ1	duplication s	This work This work
		a	synIII
	HMSY012	MATa synIII	synIII lys2Δ0 synSUP61::HO::ura3, MATa ura3Δ0 leu2Δ0 his3Δ1		This work
	yYW0115	synX	met15Δ0, synX MATa ura3Δ0 leu2Δ0 his3Δ1		(5)
	yXZX573 synV synX	met15Δ0 LYS2, synV, synX MATa ura3Δ0 leu2Δ0 his3Δ1		This work
	JDY465	synXII	lys2∆0 Oj::HIS3, synXII MATalpha ura3∆0 leu2∆0 his3∆1		(6)
	yLM539	synIXR synIII	synIII, synIXR lys2Δ0 hoΔ::synSUP61_KlURA3, MATalpha ura3Δ0 leu2Δ0 his3Δ1		This work
	yLM896	synIXR synVI synIII	IXL-synIXR synIII, synVI SYN-WT.PRE4, lys2∆0 hoΔ::synSUP61::ura3, MATalpha ura3∆0 leu2∆0 his3∆1		(7)
			MATa/MATalpha ura3∆0 leu2∆0	duplication	This work
			his3∆1 lys2∆0 synLYS2	of chr III
	JDY512	synII synXII	synMET15 synOjΔ::HIS3 ZLP101-pRS316-	small rearrangem
			(tL(UAG)L1+tL(UAU)L+tL(UAG	ent in
			)L2)::natNT2, synII, synXII	synXIIa
	JDY452	synXII synIII	hoΔ::synSUP61, synIII, synXII lys2∆0 synMET15 synOjΔ::HIS3 MATalpha ura3∆0 leu2∆0 his3∆1		This work
	JDY446	pRDN synXII	U, synXII_ RDN∆∆ lys2∆0 rdn::NatMX4 + pRDN-wt-MATalpha ura3∆0 leu2∆0 his3∆1		(6)
	. Strain description synXII MATa ura3∆0 leu2∆0 his3∆1	duplication	(6)
	JDY448	ChrIII-	lys2∆0 rdn::NatMX4 ChrIII-	of chr XI
	strain name JDY449 BY4742 BY4741 YS031 HMSY029	descripti on rDNA_17 synXII ChrIII-WT rDNA_18 WT synII synIII LE_T2 SCRaMb synIXR -	genotype rDNA, synXII_RDN∆∆ MATalpha ura3∆0 leu2∆0 his3∆1 lys2∆0 rdn::NatMX4 ChrIII-MATalpha ura3∆0 leu2∆0 his3∆1 lys2∆0 rDNA, synXII_RDN∆∆ MATa ura3∆0 leu2∆0 his3∆1 met15Δ0 met15Δ0 synLYS2, synII MATa ura3Δ0 leu2Δ0 his3Δ1 synIII, synIXR, SCRaMbLE lys2Δ0 hoΔ::synSUP61_KlURA3, MATalpha ura3Δ0 leu2Δ0 his3Δ1	karyotype abnormali duplication of chr XI ties segmental XIIItXVI +	Original (6) description (3) (3) (4); This work

Table S2 . Number of pair-end reads of Hi-C libraries

 S2

	3.-73 synIII MATalpha 3.76	asynchronous 3.-72 3.74	45 716 748 1 13	31 088 161	5 337 666
	synIII synIXR -3.81 SCRaMbLE_T2 3.-82 synIII synIXR -SCRaMbLE_T8 9.11	asynchronous 3.-78 3.79 asynchronous 3.86	27 973 841 25 36 29 802 054 2	19 529 594 21 234 553	16 859 454 18 270 085
	3.-91		3.-89	21
	3.-92		3.92	1
	Table S3. Depth of novel junctions. 3.-96 3.-94	23
	Strain Novel junctions with depth more than 5 were used to identify SCRaMbLE Synchronization Total Reads Aligned Reads 3.02 3.99 2 rearrangements (highlighted in blue). 3.-05 3.99 1	Aligned reads after filtering
	WT BY4742 2h strain HMSY029	elutriated	39 064 198	26 992 227	22 642
	Junction 1 Movie S1A.	Junction 2	Depth
	3.-03	SynII	elutriated 3.99	29 338 003 5	20 242 978	18 055
	3.01		3.03	37
	SynIII MATa 3.21	elutriated 3.-05	46 516 034 1	32 428 055	27 106
	3.-22 3.-44	SynV	elutriated 3.22 3.-42	45 137 272 1 29	30 264 624	25 212
	3.42 SynV SynX 9.-12	elutriated 9.01 3.-85	39 075 196 1 39	25 690 540	20 354
	9.11	SynXII	elutriated 3.86	24 609 744 48	16 649 288	10 262
	9.34		9.-01	1
	SynXII pRDN 3.01	elutriated 9.-43	25 972 574 1	18 994 222	14 107
	SynXII ChrIII-rDNA_17 8h strain HMSY030 Junction 1	elutriated Junction 2	32 174 741 Depth	24 406 105	14 663
	SynXII ChrIII-rDNA_18 3.-03 3.01	elutriated 3.02 3.-02	60 793 665 22 10	47 785 032	33 074
	SynII SynXII 3.01	elutriated 3.03	46 479 888 2	33 765 768	28 424
	3.01		3.05	14
	SynIII SynXII 9.-32	elutriated 3.-05	40 325 041 19	28 353 744	24 186
	3.28		3.06	26
	SynIII SynIXR 3.26	elutriated 3.-18	34 986 055 8	23 192 750	21 097
	SynIII SynVI SynIXR 3.-21 3.-27	elutriated 3.19 3.-20	45 249 989 18 31	32 268 208	25 568
	WT BY4741 3.-27	asynchronous 3.-25	50 039 070 29	34 269 612	3 325
	9.-01		3.-27	1
	WT BY4742 9.31	asynchronous 3.29	47 799 156 16	34 494 832	3 229
	9.35		3.-33	28
	synIII MATa 3.-44	asynchronous 3.-42	50 190 359 8	34 235 518	4 056
	3.42		9.01	1

3D reconstruction of the WT strain BY4742 contact matrix (related to

Acknowledgments:

We thank Axel Cournac, Martial Marbouty and Luciana Lazar-Stefanita for fruitful discussions and advices. This research was supported by funding to R.K. from the European Research Council under the 7th Framework Program (FP7/2007-2013, ERC grant agreement 260822), from Agence Nationale pour la Recherche (MeioRec ANR-13-BSV6-0012-02), and from ERASynBio and ANR (IESY ANR-14-SYNB-0001-03). H.M. and V.S are partly supported by Pasteur-Roux Fellowships. J.D. was funded by National Science Foundation of China (31471254), Tsinghua University Initiative Scientific Research Program (2011Z02296), Ph.D. Programs Foundation of Ministry of Education of China (20110002120055) and Chinese Ministry of Science and Technology (2012CB725201). Y.J.Y. was supported by Natural Science Foundation of China 21621004 and 21390203. Y.C. was funded by a Chancellor's Fellowship from the University of Edinburgh, a startup fund from SULSA and BBSRC grants [BB/M005690/1; BB/M025640/1 and BB/M00029X/1]. This research was supported to Y.S. by the research grant from the Shenzhen Engineering Laboratory for Clinical Molecular Diagnostic Promotion (JZF No. [2016]884). This work was supported in part by funding from the United States National Science Foundation [grant MCB-0718846 and MCB-1026068 to J.D.B. and J.S.B., MCB-0546446 and MCB-1445545 to J.S.B.]. J.D.B. and J.S.B. are founders and directors of Neochromosome, Inc. J.D.B. serves as a scientific advisor to Recombinetics, Inc. and Sample6, Inc. These arrangements are reviewed and managed by the committees on Conflict of interest at NYU Langone Medical Center (J.D.B.) and Johns Hopkins University (J.S.B.).

FASTQ files of the reads were deposited in the SRA database under the accession number SRP070421.

Supplementary Materials 3D organization of synthetic and scrambled chromosomes

Guillaume Mercy et al.

Fig. S1. Contact map of the wild-type strain BY4742

Normalized contact map of all chromosomes of WT strain BY4742 (bin = 5 kb). Normalized contact frequencies ((1)) are indicated in a log scale from white (few contacts) to dark red (many contacts). Filtered bins were discarded from the map.

Figs. S2-10: Contact maps and 3D conformations of synthetic chromosomes

Normalized contact maps (with filtered bins set to zero) and corresponding 3D representation of the genome using ShRec3D (27) of each strain described in this study. Top panel: normalized contact maps of the synthetic chromosome(s) carried by each synthetic strain (right) and of the native chromosome(s) in the WT strain (left). Bottom panel: two views of the 3D representation of the contact maps of the corresponding genomes from the top panel, with chromosomes of interests highlighted. Each synthetic chromosome and its native counterpart in the WT chromosomal set is represented by a specific color (synII: cyan, synIII: yellow, synV: purple, synVI: blue, synIXR: pink, synX: orange, synXII: green).