Regina Pikalyova

Yuliana Zabolotna

Dragos Horvath

Gilles Marcou

Alexandre Varnek

The development of DNA-encoded library (DEL) technology introduced new challenges for the analysis of chemical libraries. It is often useful to consider a chemical library as a standalone chemoinformatic object�represented both as a collection of independent molecules, and yet an individual entity�in particular, when they are inseparable mixtures, like DELs. Herein, we introduce the concept of chemical library space (CLS), in which resident items are individual chemical libraries. We define and compare four vectorial library representations obtained using generative topographic mapping. These allow for an effective comparison of libraries, with the ability to tune and chemically interpret the similarity relationships. In particular, property-tuned CLS encodings enable us to simultaneously compare libraries with respect to both property and chemotype distributions. We apply the various CLS encodings for the selection problem of DELs that optimally "match" a reference collection (here ChEMBL28), showing how the choice of the CLS descriptors may help to fine-tune the "matching" (overlap) criteria. Hence, the proposed CLS may represent a new efficient way for polyvalent analysis of thousands of chemical libraries. Selection of an easily accessible compound collection for drug discovery, as a substitute for a difficult to produce reference library, can be tuned for either primary or target-focused screening, also considering property distributions of compounds. Alternatively, selection of libraries covering novel regions of the chemical space with respect to a reference compound subspace may serve for library portfolio enrichment. 47 mixture containing millions of compounds in a few simple and 48 easily automatable steps. A variety of encoding methods have 49 been developed, enabling the recording of specific reaction 50 rules and building block (BB) combinations defining a 51 mixture. 1 Affinity selection combined with decoding techni-52 ques allowed for the simultaneous biological screening of ultra-53 large compound collections contained within a single 54 Eppendorf tube. It is from the background of these 55 advancements that DNA-encoded library (DEL) technology 56 emerged and recently became an attractive tool for hit 57 identification successfully applied at the early stages of drug 58 discovery. 2,3 DEL technology enables much faster and cheaper 59 identification of potential hits as opposed to widely used but 60 quite expensive high-throughput screening. DEL technology is 61 associated with various challenges�both experimental and 62 computational. One of them is related to the fact that a library 63 of DNA-encoded molecules is synthesized and tested as a 64 whole. It can, of course, be designed by thorough choice of its Chemical Library Space: Definition a nd D NA-Encoded Library Comparison Study Case

INTRODUCTION

Chemical library design and evaluation have always been one of the central aspects of computer-aided drug design. Over the last decades, the main efforts in chemoinformatics were directed toward different ways of chemical structure encoding, various approaches for chemical space representation, visualization, and efficient ways to characterize the chemical composition of analyzed collections. Considering that at the time medicinal chemists were operating with only a few compound collections, a given library (in-house stock or preferable supplier catalog) was a space of exploration, and underlying compounds were the objects in this analysis. Later on, advances in organic chemistry (e.g., parallel synthesis) increased significantly the number of distinct chemical collections, and the compound population in those libraries exploded, especially so for tangible libraries. However, the association of a given molecule to a "classical" compound library was still somewhat arbitrary�one collection could be enhanced using compounds from the other or even a new library could be created by cherry-picking compounds from numerous different collections. Moreover, considering that each compound was synthesized and biologically tested separately, it was logical to only evaluate libraries at the level of individual molecules.

With time, combinatorial chemistry has advanced to the point that it is now possible to simultaneously synthesize a BBs or pooling multiple DELs together�but, once the mixture is produced, it cannot be broken down to individual molecules any longer. This means, it is impossible to exclude or replace some of the compounds from the DEL once the synthesis is completed. Hence, it is no longer sufficient to analyze it only on the level of individual molecules, but a global representation of a compound library is needed.

Here, we wish to formalize the concept of chemical library space (CLS)�a vector space in which residing items are entire chemical libraries. The key point here is the chemically meaningful definition of libraries as mappable objects�a generalization of standard chemical cartography. Several approaches of the representation and comparison of chemical libraries were proposed so far. For example, in the approach of Fourches et al., 4 each library was represented as a similarity graph (chemical space network) where two nodes�individual compounds�are connected if the similarity between them is higher than a given threshold. To compare two libraries, connectivity indices are calculated for the corresponding graphs, allowing discrimination between similar versus dissimilar pairs of datasets. However, the explicit pairwise compound-tocompound similarity calculations limit the application of this approach to rather small datasets. To solve this problem, modification of the fingerprint-based similarity metrics for library comparison, avoiding calculation of the entire similarity matrix, was introduced by Miranda-Quintana et al. 5 Proposed extended similarity coefficients were then applied for the visualization of the similarity relationships between libraries via chemical library networks [START_REF] Dunn | Diversity and Chemical Library Networks of Large Data Sets[END_REF] by analogy to above-mentioned chemical space networks.

The aforementioned methods, however, do not intuitively explain why some libraries are said to be similar. Indeed, a visual pairwise inspection of compounds in the connected nodes of chemical space networks answers the question for individual molecules, but not for compound libraries. One of the methods that address this problem is a consensus diversity plot where library position in the CLS is defined by the pair of diversity values�(i) the median of the pairwise Tanimoto scores over intra-library compound pairs and (ii) the fraction of scaffolds retrieving 50% of the library. [START_REF] González-Medina | Consensus diversity plots: a global diversity analysis of chemical libraries[END_REF] The relative size of the collection is represented by the size of the circle representing a data point, while its color is defined by the third diversity metric�the mean of the intra-set Euclidean distance of six physicochemical properties. Such plots are easily interpretable, as each of the values in the vector has a particular chemical meaning. However, the comparison of the internal diversity of libraries instead of the similarity between them is much less informative: a library can be internally highly diverse but have a very similar chemical composition to another equally diverse library. In another library representation by a Database Fingerprint (DFP), proposed by Fernańdez-de Gortari et al., [START_REF] Fernández-De Gortari | Database fingerprint (DFP): an approach to represent molecular databases[END_REF] the on-bits correspond to the most frequent fragments occurring in numerous molecules from the analyzed library. Even though the DFP allows the incorporation of the main structural information of the library, it ignores finer differences between the collections that might lie in the distribution of the less frequent structural fragments or mutual occurrence and rearrangements of several fragments in different groups of compounds. There is also no possibility to include property information along with the structural one into the comparison using DFPs.

To solve the foregoing limitations of existing methods, here we introduce and test several more complex vector-based Different types of GTM landscapes can be created for the 244 same library, where properties of the compounds projected 245 onto each node are rendered using a color code. Three major 246 types of landscapes were used in this study:

(1) Density landscape�created by coloring the GTM in accordance with the quantitative distribution of compounds over the nodes (2) Library-comparative landscape�obtained by coloring the GTM by a proportion of compounds of the analyzed library in the node's overall population (populated by both analyzed and reference library molecules)

(3) Property landscape�obtained by coloring the GTM by responsibility weighted average of compound property values for each node Using these landscapes, GTM can be applied for chemical space analysis, library comparison, or even virtual screening. [START_REF] Zabolotna | Chemography: Searching for Hidden Treasures[END_REF][START_REF] Casciuc | Virtual screening with generative topographic maps: how many maps are required?[END_REF] In the present work, the first Universal GTM (UGTM) [START_REF] Sidorov | Mappability of drug-like space: towards a polypharmacologically competent map of drug-relevant compounds[END_REF][START_REF] Casciuc | Virtual screening with generative topographic maps: how many maps are required?[END_REF] was used for the analysis of the 2497 DELs and filtered ChEMBL28. It was built using ISIDA atom sequence counts with the length of 2-3 atoms labeled by CVFF force field types and formal charge status as descriptors. [START_REF] Ruggiu | ISIDA Property-Labelled Fragment Descriptors[END_REF] Since this map was trained to predict the biological activity of molecules against 236 targets, it is suitable for the analysis of biologically relevant chemical space. It can serve not only for predictions of bioactivity but also for the analysis of large chemical libraries in the context of medicinal chemistry. 15 3.2. Chemical Library Space. The conventional way of library analysis consists of a detailed investigation of its compound space where each compound is defined by molecular descriptors�in our case ISIDA fragment counts. [START_REF] Ruggiu | ISIDA Property-Labelled Fragment Descriptors[END_REF] These fragments composed of elements of the molecule and their combinations define molecular properties. However, the structural fragment level is too detailed for characterizing the whole library. It makes little sense to build a cumulated count of all fragments seen in the members of a library because this vector loses the key information on how those fragments were initially distributed in individual compounds. In order to generalize the structural information of the library, one way would be to somehow encode the "chemotype" counts�the number of compounds of a particular "chemotype" present in a library. However, the detailed structural analysis of the large compound collection can be very computationally demanding, and the notion of "chemotype" is intrinsically vague and context-dependent.

Hence, in this work, we propose several methods of chemical library encoding derived using GTM. Since the latter preserves the topology of the initial space upon the dimensionality reduction, it is considered for the analyzed library: (i) zones of the map are associated with predominant "chemotypes" [START_REF] Zabolotna | Chemography: Searching for Hidden Treasures[END_REF][START_REF] Horvath | Generative topographic mapping in drug design[END_REF] as implicitly defined by the highly relevant fuzzy clustering mechanism of the GTM approach (ii) cumulated density for those zones implicitly reflect the chemotype distribution, without the need to explicitly predefine "chemotypes".

Chemical Library Encoding Methods. Several ways

to use GTM responsibilities for library encoding are described in more detail below�responsibility pattern fingerprints (Γ), responsibility pattern count vectors (Γ w ), and several types of modified CRVs (Φ, Λ and Ω).

Responsibility Pattern Fingerprints (Γ) and Vectors (Γ w ).

Due to the probabilistic nature of GTM, a position of a compound on the map is defined by a probability distribution over the nodes, which, in turn, could be encoded by a responsibility vector. Therefore, two different yet similar compounds may not have exactly the same responsibility vector. However, similar compounds still are projected onto the map in a similar manner�according to a RP 20 representing discretized responsibility vector according to eq 1

= [ × + ] r rp 10 0.9 ik ik (1)
where [] means truncation, rp ik is the RP value for compound i in the node k, and r ik is responsibility value for compound i in the node k It follows from eq 1 that responsibility values smaller than 0.01 are reassigned to zero, and all others�to integer numbers from 1 to 10. Molecules situated close to each other in Ndimensional descriptor space and having slightly different responsibility vectors may have the same RP. These compounds usually share the same scaffold or substantial (connected or disconnected) maximum common substructure, or pharmacophore. [START_REF] Kayastha | From bird's eye views to molecular communities: two-layered visualization of structure-activity relationships in large compound data sets[END_REF] Thus, in a way, an RP could be associated with a prevalent "chemotype".

To encode a compound library using RPs, a library responsibility pattern fingerprint (Γ) and RP count vector (Γ w ) are suggested. Γ is a binary vector encoding the presence or absence of a particular reference RP in the analyzed library, and Γ w is a vector with numerical values corresponding to the number of reference library compounds associated with each common RP present in both libraries. A schematic f1 representation of the Γ and Γ w calculation is given in Figure 1.

Normalized CRVs (Φ).

A CRV = (c 1 ,c 2 ,...,c k ) is the vector encoding a library by the sum of responsibility values over all molecules of the library in each node of the map, as shown in eq 2. In other words, to some degree, this vector allows the encoding of a library by the number of compounds associated with each node of the corresponding GTM plot. Thus, the CRV mathematically describes compound distribution over the 2D map and consequently over the chemical space of the library that this map visualizes. Considering that each area of the map is populated by a particular prevailing chemotype, the CRV is a crude indirect way of assessing the occurrences of different chemotypes in the library without actually defining them. When aiming to maximize representation and coverage of the reference collection by the analyzed library, the ideal case would be an Λ with = 0 k for the fully empty nodes and = 1.5 k (corresponding to equal representation of both reference and analyzed libraries) in all occupied ones. This "ideal" vector can thus be used as a reference in Tanimoto calculations for ranking libraries based on Λ.

Property-Modulated CRV (Ω).

If the analysis of CLS should be performed in the context of some property or biological activity of underlying compounds for each library, the property-modulated CRV (Ω) can be used. Ω is composed of the mean property values for each node calculated according to eq 5.

= • = P r c k i N i ik k 1 (5)
where Ω k is the mean property value in the node k and P i is the property value for the compound i f2

Figure 2 shows a simplified scheme describing links between modified CRVs and related GTM landscapes. As soon as the compounds are projected on the map, the three types of landscapes�density, library comparative, and property land-scapes�are generated, followed by preparation of related vectors Φ, Λ, and Ω using, respectively, the density, libraries ratio or mean property value in each node. Each of these vectors allows encoding a chemical library as an object in the high-dimensional CLS. Notice that both coverage and weighted coverage scores 431 were used in our previous work 10 for the comparison of virtual 432 DEL collections with the ChEMBL database.

Similarity Relationships between

433

For the CRV-based representations (Φ, Λ, Ω), a pairwise 434 Tanimoto coefficient is a reasonable estimation of libraries' 435 similarity (8) 437 Here, v is a chosen CRV-based representation (v = Φ, Λ, Ω), 438 and K is the total number of nodes.

= + • Tc a r v a v r v a v r v a v r ( , ) ( ) ( ) ( ) ( ) ( ) ( ) k K k k k K k k K k k K k k 2 2 436

RESULTS AND DISCUSSION

439 The herein proposed library encoding vectors Φ, Λ, Ω, 440 ,and i w provide different views of the CLS. To investigate 441 their usefulness, the pool of 2.5k previously generated DELs 10 442 was used. Three case studies were performed. First, we 443 analyzed how proposed encodings and similarity metrics 444 handle the comparison of a large 88 M DEL with its 1 M 445 representative subset. The second case study addresses the 446 selection of the "optimal" DEL for the primary screening when 447 no or little information about the biological target is known. 448 The goal was to identify a DEL that covers "biologically 449 relevant" space (represented by ChEMBL) to the highest 450 extent. For this purpose, 2.5k DELs were compared to 451 ChEMBL (as a reference collection) in the CLS defined by 452 Γ, Γ w , Φ, and Λ. In the third case study, the property-focused 453 analysis of the libraries was performed using the Ω encodings. In our 456 previous study, 10 representative sets of each of the 2.5k DELs 457 were generated using random sampling of BBs in the 458 eDesigner [START_REF] Martin | Navigating the DNA encoded libraries chemical space[END_REF] tool and not the full libraries. Such a sub-library 459 should be very similar to the entire DEL and cover virtually all 460 of its chemical space. Therefore, overlap analysis of a 461 representative DEL subset with respect to its parent library is 462 a baseline case for illustrating how well each of the encodings 463 reflects its close relationship.

464

For this purpose, a 3BB DEL2568 based on the aldehyde 465 reductive amination, Migita thioether synthesis, and amine 466 guanidinylation was selected. The coverage of the entire 88M 467 DEL2568 by its representative subset or its similarity was 468 calculated using each of the selected encodings (Γ, Γ w , Φ, and From Table 1, it appears that coverage based on Γ is very low�only 9% of RPs present in the entire DEL library are covered by the 1M representative set. However, Γ w coverage shows that those 9% of RPs correspond to 87% of molecules, which means that the subset lacks very rare (but numerous) RPs, all while covering "mainstream" chemotypes from the full collection. It is interesting to witness a combinatorial library (sharing a common "scaffold" defined by the underlying chemistry) concentrating 87% of its members into 9% of the spanned chemical space. This is not unexpected�combinations of relatively "exotic" and rare BBs result in "exotic" but rare products.

The similarity between those two collections was also calculated using CRV-based representations�Φ and Λ. In the latter case, the Λ vector of the 1M subset was created by calculating the ratio of molecules from the representative subset with respect to the reference (full 88M collection) in each node of the map. It was then compared to the "ideal" Λ where each node occupied by the reference 88M library has a value Λ k = 1.5, which corresponds to the perfect representation of the full library by the subset (see details in the Methods section). Tanimoto coefficients calculated for CRV-based representations are given in Table 1. Those values being close to the maximum illustrate expected (and observed in In the case of Λ-based similarity, the Tc values are spread 543 within a narrow range: from 0.8 to 0.92 (Figure 4D). The Λ-544 based similarity spectrum is intrinsically different from those 545 calculated using other encodings. Since vectors for all libraries 546 are modulated with the CRV of the same reference collection, 547 the similarity value between two Λ is always higher than that in 548 the case of Φ, for example. However, the position of DEL2568 549 and DEL271 in Figure 4D is similar to the other three cases. Thus, even though being shifted toward higher values, similarity distribution in the CLS defined by Λ follows the same trends as in other library spaces.

For further analysis of the similarity relationships in the four proposed representations of CLS, all DELs were ranked with respect to the coverage of (or similarity to) ChEMBL. To simplify the analysis, here we analyze only five DELs: ranked the first, 50th, 100th, 1000th, and 2497th with respect to ChEMBL. For each of these five DELs, a density landscape showing compound distribution in the chemical space of the f5 library was created (see Figure 5). This figure shows that each of the representations ranks libraries differently�none of the libraries were selected as the best one by more than one representation. However, DELs having the same rank in different spaces (landscapes forming columns in Figure 5) still have very similar compound distribution over the map. Failure to consensually score one DEL as the best match for ChEMBL, in any CLS, is due to the fact that there are several DELs that might claim this title, and no single one is undoubtedly outstanding in terms of sharing related chemotypes with ChEMBL. Looking at the problem through the prism of multiple CLS definitions is evidencing this important aspect, that is, allowing for more flexibility in experimental setups. In this scenario, there is no particular reason to pick either of the DELs of column no 1 in Figure 5�a case in which extraneous parameters (availability, facility of synthesis, and cost) may be 576 applied by the user to select either of these. Should a 577 consensual winner emerge from this analysis, selecting it at 578 higher costs over the others may make sense. Practically, 579 however, visual inspection shows that the first few hundred 580 DELs have similar density landscapes to the top-ranked 581 landscapes corresponding to the 100th or even 500th-ranked 582 library still match the landscapes in column 1 quite well. 583 Finally, yet importantly, within the top 100 DELs chosen by 584 each of the encodings, there are 32 DELs common to all four 585 encodings; within the top 500, this value rises to 273, and for 586 the top 1000 DELs, it reaches 713, which shows how well the 587 ranking by coverage or Tc based on four encodings correspond 588 to each other. For more details, see Figure S1 of Supporting 589 Information.

590

Even though each of the analyzed representations offers a 591 different DEL as the closest to ChEMBL (DEL2970, 592 DEL2568, DEL1847, and DEL845), they all appear to be 593 quite similar. Interestingly, all these libraries are three-cycled 594 DELs that were designed exclusively based on robust coupling 595 reactions�aldehyde reductive amination (all four libraries), 596 Ullmann-type N-aryl coupling (DEL2970 and DEL845), Migita thioether synthesis from thiophenols and arylbromides (DEL1847 and DEL2568), and carboxylic acid/amine condensation (DEL1847 and DEL845) (see Figure S2 of Supporting Information). The size of the full DELs is also very similar for those four libraries�slightly above 80M compounds. The reason for the high diversity of those collections and thus high coverage of (and similarity to) ChEMBL is due to the abundance and diversity of the purchasable BBs required for those reactions�amines, aldehydes, arylhalides, and carboxylic acids. 10,[START_REF] Zabolotna | A close-up look at the chemical space of commercially available building blocks for medicinal chemistry[END_REF] Libraries with the lowest rank�DEL1216, DEL271, DEL2266, and DEL3703�also have some design features in common. Their full size is much lower (between 1M and 5M), and they all have at least two heterocyclization steps in their design�aminothiazole and Larock indole synthesis were combined to form DEL1216, imidazole and Larock indole synthesis were used in DEL271 generation, and three heterocyclization steps (oxadiazole, triazole, and aminothiazole synthesis) were used both in DEL2266 and DEL3703 (see Figure S3 of Supporting Information). As is visible from Figure 5, those collections have one (maximum two) density peak, 618 which means that their diversity is much lower, and those 619 DELs can be considered as focused libraries containing very 620 similar compounds. This is explainable by the fact that 621 employing two heterocyclization steps in DEL synthesis means 622 that all compounds possess at least two identical hetero-623 cycles�a consequently large scaffold�with diversity being 624 introduced only via their "ornaments", by contrast to, say, an 625 amide formation in which everything but the -C(�O)NH-626 moiety is variable.

627

The use of only heterocyclizations is convenient for 628 "focused" DEL synthesis, as the common scaffold generated 629 by the reaction represents a common signature of all library 630 members, which vary in terms of scaffold substituents only. [START_REF] Dickson | Chemical composition of DNAencoded libraries, past present and future[END_REF] 631 This provides an excellent library for extracting structure-632 activity relations and fine-tuning lead molecules, provided, of 633 course, that the focus around the chosen heterocyclic core 634 matches the actual chemical space zone favored by the target. 635 However, if the goal is to produce general-purpose DELs, it is a 636 safer option to use building-block-rich coupling reactions 637 instead because abundant BB classes exist. Many BBs already 638 contain necessary heterocyclic moieties, [START_REF] Oksiuta | Heterocyclization vs Coupling Reactions: A DNA-Encoded Libraries Case[END_REF] albeit not necessarily 639 connected to each other in a same way as they would be linked

In-Depth Analysis and Interpretability of Library

Overlap. Overlap scores are useful for the rapid processing and ranking of large sets of candidate libraries, but a real understanding of overlap must go down to individual compound structure levels. The strength of this protocol is that the mapping used to define CLS vectors can implicitly support this approach. To illustrate that, the density landscape for DEL1847 that is the closest to ChEMBL according to Φ ranking was compared to the density landscape of ChEMBL f6 (Figure 6). DEL1847 is a three-step library based on aldehyde reductive amination with the NH 2 group of the headpiece (2652 aldehydes), followed by the condensation of the same Figure 6. Interpretation of the similarity between ChEMBL and DEL1847 via structural analysis of the density landscapes of those libraries. Areas A1-A8 (labeled in white) correspond to the peaks of high density in ChEMBL space that were reproduced in DEL1847. Areas A9-A12 (labeled in red) represent mismatched zones.

662 amino-group with 21 bifunctional carboxylic acids containing 663 thiol group that on the third cycle reacts with 1630 664 arylbromides to form thioether bonds. The total size of the 665 library is around 90M.

666

In Figure 6, most of the density peaks of ChEMBL (A1-A8) 667 were reproduced in DEL1847. These areas contribute to the 668 similarity of those two libraries and make DEL1847 the most 669 highly scored by the Tanimoto coefficient (Tc = 0.38) 670 calculated based on Φ. Indeed, areas A1-A4 are covered by 671 both libraries, containing molecules of similar structural 672 features, even though DEL1847 compounds also have 673 thioether and amide groups in their structures. Nevertheless, 674 this similarity value is far from perfect, which can be explained 675 by mismatched density peaks between ChEMBL and 676 DEL1847. Namely, areas A9 and A11 are heavily populated 677 in the ChEMBL landscape, but rather moderately occupied in 678 DEL1847. The former area is populated by 2-aminothiazole-679 containing compounds and is expectedly underrepresented in 680 DEL1847, as only 14 BBs used for its enumeration contain this 681 structural moiety (0.3% of all BBs). The same applies to area 682 A11, which is highly populated by pyridazinone/oxadiazolone-683 containing amides in ChEMBL and underpopulated in the case 684 of DEL1847. Regions A10, A12 in ChEMBL are empty in 685 DEL1847. This is because these areas are populated by 686 complex natural products, 10 and thus cannot be reproduced by 687 herein considered DELs.

688

The same analysis was performed for the most dissimilar one 689 to the ChEMBL library by Φ�DEL2266. This library is based 690 on three heterocyclization reactions�oxadiazole, triazole, and 691 aminothiazole synthesis�that provide 1.3M compounds in 692 total. As a result, each compound of the library contains the 693 same three cycles, which makes this library structurally highly 694 focused. However, there are no molecules in filtered f7 695 ChEMBL28 of similar chemotypes. In Figure 7, highly 696 populated areas A1 and A2 in the DEL2266 landscape are 697 almost empty on the ChEMBL map, and the two libraries 698 almost do not overlap at all, which explains close to zero 699 similarity between them.

Thus, by analyzing density landscapes for the selected pairs of libraries, it is possible to explain the similarity behavior in the CLS defined by Φ. The interpretation of the CLS defined by Λ can be performed by analyzing pairwise comparative landscapes featuring reference collection against each of the analyzed libraries.

Property-Sensitive Library Comparison.

A conventional way to analyze compound collections in terms of a particular physicochemical property is to build a frequency plot (histogram) showing the distribution of this property for all library molecules. [25][26][27][28] This approach though has several drawbacks. First of all, there is a complete disconnection of such plots from the chemotype composition of the analyzed f8 collection. Figure 8 shows that both libraries closest and farthest to ChEMBL according to Γ w ranking (DEL2568 and DEL271, respectively) have a very similar distribution of log P values, even though they strongly diverge in terms of composition. Moreover, compounds with a given property value (e.g., log P = 4) may be spread all over the map�they do not have to be similar simply because they share the same property value (Figure 8 In contrast, DEL630 (Figure 9C) selected as the most similar to ChEMBL using HAC-Ω representation has a significantly larger colored surface which means higher chemotype similarity to ChEMBL (Tc(Φ) = 0.34). Furthermore, the local property distribution in this collection is much closer to ChEMBL than that in DEL2189. Indeed, there are many areas

CONCLUSIONS

In this work, we reported the development of several types of vector-based encodings for characterizing libraries of various sizes and compositions as a function of the relative distribution of molecules in the GTM-based chemical space. These representations constitute a new way of the analysis of combinatorial mixtures, such as DELs, that should be considered not only as an ensemble of compounds, but also as unified entities�mixtures whose composition cannot be easily changed once synthesized. Of course, the methodology generally applies in contexts where any library�cherrypickable or not�needs to be regarded as a stand-alone entity, rather than a collection of individual molecules. With the encodings introduced here, it becomes possible to clearly define CLS where each collection is considered as a data point.

Classical chemoinformatics allows for the management of a portfolio of compounds forming a core library (comparison to other compound sets, directed enrichment in new compounds, focused subset extraction for screening, etc.), whereas this methodology enables the management of a portfolio of libraries (selection of the best suited one for a screening campaign, enrichment with novel libraries�overlapping or not, etc.). with respect to their similarity to ChEMBL. Therefore, any of the proposed representations can be used for selecting an optimal DEL for a particular task if the reference collection can be defined. Here, ChEMBL was used to represent the drugrelevant chemical space, and it was assumed that the ultimate goal in general diversity library design is mimicking the chemical space covered by it. This is of course debatable�in real applications, experts may define reference libraries based on much stricter and project-specific criteria. The present work outlines a novel methodology for library selection and comparison, which was shown to be senseful in all respects concerning the analysis of herein considered DELs, but must yet be proven useful in prospective library design�a goal unfortunately way beyond the resources of many academic research teams.

To analyze libraries with respect to the featured chemotypes without paying attention to their population the best choice would be Γ. If the population of the matched chemotypes in only one of the libraries (reference collection) is important� the coverage score based on the Γ w should be used, thereby ensuring that the candidate library matches the often-seen patterns in the reference collection, and not its atypical "singletons". In case the compound distribution over the chemical space of all analyzed collections is important, CLS should be defined by the Φ, whereas Tanimoto similarity should be used for library ranking. This strategy can also be used in order to select a library that maximally reproduces compound distribution from the chemical space of the reference collection (e.g., selection of the optimal representative subset). Λ-based encoding is particularly useful when one wants to compare a coverage of a reference dataset by some other libraries. In this case, each library is encoded considering its relative compounds distribution with respect to the reference collection, so a special accent is placed on the differences between the relative proportion of compounds coming from analyzed and reference libraries without taking into consideration the absolute popularity of each node. Moreover, in case the accent of the analysis is placed on the particular calculated or measured property, Ω can be used to encode libraries with respect to both chemotype and property distribution in the chemical spaces of these collections. In contrast to classical property histograms that describe the global distribution of the property values among compounds of the whole library, Ω encodes local property distribution among compounds belonging to different chemotypes and populating particular areas of the chemical space.

The interpretability of the proposed vectors merits a special mention here. Being GTM-based, Φ, Ω, and Λ can be visualized as compound density, property, or comparative landscapes for each library on a separate plot. By analyzing landscapes of the selected pairs of libraries, the similarity behavior in particular CLS can be investigated and interpreted. For example, in the case of Φ-defined CLS, by comparing the highest peaks on the density landscapes of two libraries it is easy to identify which common chemotypes positively contributed to the similarity, and which mismatched areas of the chemical space decreased the Tanimoto value. Now, when the performance of the proposed encodings and the similarity behavior of libraries (objects) in corresponding CLS are analyzed and described, it should be last but not least noted that this CLS may also be visualized, like any "classical" chemical space. In perspective, the meta-GTM approach 29 is 896 perfectly suited for the dimensionality reduction and visual-897 ization of CLS.

  128 representations for compound libraries that allow us to 129 compare numerous large collections (in our case DELs) 130 from different perspectives and produce intuitive visualizations 131 of the CLS. They all are based on generative topographic 132 mapping (GTM)�a probabilistic dimensionality reduction 133 method.[START_REF] Bishop | The generative topographic mapping[END_REF] For each mapped item of the initial, high-134 dimensional descriptor space, GTM provides a vector R 135 ("responsibility vector") rendering its fuzzy levels of assign-136 ment to the k nodes of the 2D map grid. The sum of R vectors 137 over all members of the library provides a cumulated 138 responsibility vector (CRV), a "baseline" representation of 139 the library/mixture as a whole. Different refinements of this 140 vector are introduced here: 141 (i) Normalized CRV (Φ), as a library-size independent 142 library descriptor 143 (ii) Library-modulated CRV (Λ)�representing a library 144 with respect to its overlap with a reference collection 145 (iii) Property-modulated CRV (Ω)�introducing property-146 centered library representation considering both chemo-147 type and property distributions over the chemical space. 148 In the present article, these vectors were used to encode the 149 previously generated 2.5k different DELs. 10 The ability of each 150 of the vectors to accurately represent and identify DELs closest 151 to the reference library was evaluated and compared to 152 previous results obtained using responsibility patterns (RPs). 10 153 Based on the values from each of the introduced library vectors 154 (Φ, Λ and Ω), GTM landscapes (described in detail in the 155 Methods section) were created enabling visualization of the 156 chemical space of a particular library from different 157 perspectives�either from structural or property point of 158 view and which allowed us to chemically interpret the 159 similarity ranking results. 160 In more general terms, this work showcases how to exploit 161 the flexibility of GTM technology to define inter-library

  is responsibility value of the molecule i in the node k 349 The CRV is intrinsically dependent on the size of the library 350 it encodes. Therefore, when collections of different sizes are 351 compared in a context in which size differences are not 352 relevant, c k must be normalized by library size N according to 353 eq 3. The resulting normalized CRV (Φ) encodes relative 354 compound distribution over the chemical space of the analyzed 3. Library-Modulated CRV (Λ). So far, the CRV and Φ 358 consider all the chemical space zones (nodes) to be equally 359 important in describing the library. However, some nodes may 360 be more important�for example, the ones found to be highly 361 populated by reference library compounds. For this purpose, 362 the CRV of the analyzed library (a) can be modulated with 363 respect to the compound distribution of another reference 364 collection (r). The resulting library-modulated CRV (Λ) can 365 be computed from the Φ of both collections, by calculating the 366 fraction of compounds of the analyzed library in the total 367 population of each node, as shown in eq 4. In Λ, a value Λ k = 0 368 is assigned to all empty nodes in both analyzed and reference 369 libraries, whereas for all non-empty nodes 1 ≤ Λ k ≤ 2 vary as a 370 function of the fraction of compounds from the analyzed 371 library in a given node. Nodes populated exclusively by 372 compounds from r and a have value = have values in the range 1 < Λ k < 2. Λ k is Λ value in a given non-empty node k for analyzed 377 library a, whereas Φ k (a) and Φ k (r) are normalized cumulated 378 responsibilities in the node k for the analyzed and reference 379 library, respectively.

Figure 1 .

 1 Figure 1. Summary of the RP-based library representations. The Γ values for a particular library are assigned based on the presence or absence of a certain RP in the reference library, and the Γ w values represent the counts of reference library compounds covered by this RP.

  Libraries in the CLS. To define similarity relationships between libraries in the 407 CLS, various scores based on RP-based representation can be 408 suggested. A score assessing the coverage of a reference library 409 r by a candidate library a can be defined in terms of the binary 410 Γ as the fraction of RPs of a reference library also present in a. 411 Considering the binary nature of Γ, the coverage score is the 412 number of on-bits common for two libraries divided by the 413 total number of on-bits in the reference collection; see eq 6. simply stands for the total number of 416 RPs encountered in the reference and Γ i (a) is a value (1 or 0) 417 in the Γ of the analyzed library corresponding to the i-th RP. 418 However, this coverage score does not account for the 419 number of compounds corresponding to each RP, although 420 different RPs can be populated differently. This means that the 421 high RP coverage does not necessarily imply high compound 422 coverage. To solve this problem, a weighted RP coverage score 423 can be defined as the fraction of compounds of a reference 424 library that corresponds to the RPs present in both analyzed 425 and reference libraries. Γ wi (r) is the number of compounds from the reference 428 library r corresponding to i-th RP and N r is the total number of 429 compounds in the reference library r.

Figure 2 .

 2 Figure 2. Scheme depicting how each of the introduced herein library encodings (Φ, Λ, and Ω) are derived from the GTM for a particular compound library.

4544. 1 .

 1 Representative DEL Subset vs Its Parent Library: 455 A Test Study of Expected Near-Perfect Overlap.

  Figure 3 provides a visualization of the chemical space of 470 those two libraries. Relative compound distribution over the 471 maps is almost identical, which backs up the claim of 472 representation of the subset.

  t1

Figure 3 )

 3 Figure 3) high similarity between compound distribution in the chemical spaces of those libraries. Both CRV-based representations provide close to the maximum similarity values between the library and its representative subset, as expected. RP-based representations, on the other hand, provide a stricter comparison with an accent on the missing reference RPs (chemotypes) in the analyzed library. This example demonstrates the importance of using both the Γand Γ w -based coverage scores. While the first one shows how many "chemotypes" are covered, the second one puts this number into the perspective of their compound population and provides a compound-weighted coverage of the chemical space.

4. 2 .Figure 3 .

 23 Figure 3. Density landscapes of the entire 88M DEL2568 and its 1M representative subset.

Figure 4 .

 4 Figure 4. Pairwise comparison of 2.5k DELs with ChEMBL using different representations and metrics: distribution of ChEMBL coverage scores calculated using Γ (A) and Γ w (B), and distribution of Tc between ChEMBL and each DEL calculated using Φ (C) and Λ (D).

Figure 5 .

 5 Figure5. Density GTM landscapes of ChEMBL28 and selected DELs ranging from the most similar to the least similar to ChEMBL. DELs were selected and ranked either by coverage scores (in the case of Γ and Γ w ) or Tanimoto similarity coefficients (in the case of Φ and Λ). Values of either coverage or Tc are provided in red on each landscape. For all landscapes, the same color scale corresponding to the density distribution of ChEMBL was used.

  up in a heterocyclization synthesis-based DEL. Another option might be to use only one heterocyclization step combined with two coupling synthetic cycles. In this way, the diversity coming from coupling reactions can partially compensate for the presence of the same heterocycle in each molecule. An example of such design is DEL2806 (1000th library by Γ)�it combines imidazole synthesis with guanidine group formation from amines and Ullmann-type N-aryl coupling. All other DELs featuring from 1st to 500th in Figure 5 are based only on coupling reactions.

  on the right). By contrast, property-modulated Ω has two key advantages: being focused on specific chemical space zones populated by similar chemotypes, it does account for the chemistry "behind" the property values. The second key feature is that propertyrelated information is provided via GTM property landscapes, thus it is directly associated with chemical space zones. In this way, Ω representation allows for dual libraries' analysis and comparison where the most similar to the reference library collection simultaneously demonstrates both chemotype and property similarity. To further illustrate the advantages of Ω over the property histograms, the DELs most similar to ChEMBL were selected and compared using both approaches. First, each classical bar chart for H-bond acceptor count was encoded by a ncomponent vector, whose length corresponded to the number of bars in the property histogram. Then, based on these vectors, Tanimoto coefficients were calculated between each DEL and ChEMBL, and the most similar DEL2189 was f9 selected (see Figure 9A) with Tc = 0.95. The same was done by calculating the Tanimoto coefficient between each DEL and ChEMBL using the respective Ω, which led to the selection of DEL630 as the most similar one (Figure 9C) with Tc = 0.78. The Tc values for both DEL2189 and DEL630 calculated either based on the Ω or H-bond acceptor counts distribution vectors with respect to the filtered ChEMBL database are given t2 in Table 2. From Figure 9 it is visible that even though having similar global property distributions (illustrated in histograms), the local distribution of H-bond acceptor counts in each area of the chemical space of DEL2189 (Figure 9A) is dissimilar compared to the ChEMBL property landscape (Figure 9B)� there are almost no zones containing compounds with more than eight hydrogen bond acceptor atoms on the DEL2189 landscape. Moreover, there are lots of ChEMBL areas that are empty on the DEL2189 landscape, thus the chemotype similarity of this library to ChEMBL is low (Tc(Φ) = 0.13).

Figure 7 .

 7 Figure 7. Interpretation of the similarity between ChEMBL and DEL2266 via structural analysis of the density landscapes of these libraries.

Figure 8 .

 8 Figure 8. (Left) Density landscapes of filtered ChEMBL, DEL2568, and DEL271; (center) classical bar chart visualization of calculated log P distribution for all compounds from analyzed libraries; (right) compounds with log P = 4 (black dots) projected on the corresponding density landscapes.

Figure 9 .

 9 Figure 9. Hydrogen bond acceptor count (HAC) landscapes for (A) DEL2189 (selected by property distribution similarity), (B) reference libraryfiltered ChEMBL28, and (C) DEL630 [selected by Tc(HAC-Ω) similarity].

From

  the example of ChEMBL vs DEL comparison, it was shown that all proposed CLS representations�responsibility pattern fingerprints (Γ), responsibility count vectors (Γ w ), normalized CRVs (Φ), library-modulated CRVs (Λ), and property-modulated CRVs (Ω)�are able to efficiently encode key information about the "chemotype" distribution of analyzed libraries, where "chemotypes" are implicitly defined by the intrinsic neighborhood compliance of GTMs. "chemotypes", in this sense, may be common scaffolds including or not common key "ornaments", common topological pharmacophores, or more loosely defined compound clusters of molecules with a specific global charge or outstanding size, etc. Similarity relationships in all five CLSs seem reasonable and chemically meaningful and allow adequate sorting of DELs

Figure 10 .

 10 Figure 10. First row: On the left: QED landscape of filtered ChEMBL28. On the right: QED landscapes of DELs ranging from the most similar to the least similar to ChEMBL sorted by their Tanimoto coefficients calculated based on their QED-Ω with respect to ChEMBL (in black). Second row: On the left: density landscape of the filtered ChEMBL. On the right: corresponding density landscapes for selected DELs with their Φ similarity values with respect to ChEMBL (in red).

  is available free of charge at 901 https://pubs.acs.org/doi/10.1021/acs.jcim.3c00520. 902 Venn diagrams comparing several DELs, density land-903 scapes of selected DELs, and distributions of some 904 physicochemical parameters of selected DELs (PDF) Laboratory of Chemoinformatics, 908 University of Strasbourg, Strasbourg 67081, France; 909 orcid.org/0000-0003-1886-925X; Phone: +33 910 368851560; Email: varnek@unistra.fr

Table 1 .

 1 Coverage and Similarity of the Full DEL2568 by Its Representative Subset

	CLS encoding	coverage of the full DEL2568 by the 1M subset
	Γ	0.09
	Γ w	0.87
	CLS	Tanimoto similarity between the full DEL2568 and 1M
	encoding	subset
	Φ	0.99
	Λ	0.98

Table 2 .

 2 Tanimoto Values for DEL2189 and DEL630 Calculated Either Using HAC-Ω or H-Bond Acceptor Count Distribution Vectors with Respect to the Filtered ChEMBL28 Database

		Tc(HAC-Ω)	Tc(property distribution)
	DEL2189	0.34	0.95
	DEL630	0.78	0.67


Mihai Deleanu

Jean-François Hernandez

Hervé Cottet

Joseph Chamieh

Taylor dispersion analysis discloses the impairment of Aβ peptide aggregation by the presence of a fluorescent tag

Taylor dispersion analysis discloses the impairment of Aβ peptide aggregation by the presence of a fluorescent tag

Introduction

Alzheimer's disease (AD) is a neurodegenerative pathology inducing damage to the patient's brain and translating in memory loss and behavioural impairment. One of the main hallmarks of AD is the presence of amyloid β peptide (Aβ) plaques in the brain of patients and several evidence points that Aβ peptides are one of the main reasons behind the symptoms of AD either in its oligomeric form (thought to be neurotoxic) [START_REF] Selkoe | The amyloid hypothesis of Alzheimer's disease at 25 years[END_REF][START_REF] Lambert | Diffusible, nonfibrillar ligands derived from Aβ1-42 are potent central nervous system neurotoxins[END_REF] or in its fibrillary form [START_REF] Hardy | Alzheimer's disease: the amyloid cascade hypothesis[END_REF].

In all cases, there is a necessity to better understand the aggregation mechanism of Aβ peptides.

However in vitro studies are often hampered by the detection limits of the used methods which often impose the use of concentrations (µM range) several tens of times higher than the in vivo ones (nM range [START_REF] Lazarevic | Physiological Concentrations of Amyloid Beta Regulate Recycling of Synaptic Vesicles via Alpha7 Acetylcholine Receptor and CDK5/Calcineurin Signaling[END_REF]). Studying the aggregation process of amyloid peptides in detail is a challenging task especially at concentrations in the order of magnitude of physiological ones.

For that, the use of selective and sensitive detection methods such as fluorescence based ones is highly desirable to study peptides at lower concentrations [START_REF] Rice | Illuminating amyloid fibrils: Fluorescence-based singlemolecule approaches[END_REF]. This strategy implies a modification of the peptide structure by adding a label often on its N-terminal end. However, the attached tag may affect the physical and chemical properties of the amyloid peptides [START_REF] Wägele | How Fluorescent Tags Modify Oligomer Size Distributions of the Alzheimer Peptide[END_REF] and their propensity to form beta-sheets and thus fibrillar structures. Wägele et al. [START_REF] Wägele | How Fluorescent Tags Modify Oligomer Size Distributions of the Alzheimer Peptide[END_REF] studied by fluorescence correlation spectroscopy (FCS) the effect of four fluorescent tags (HLyte 647, HiLyte 488, Atto 655 and Atto 488) on the oligomer distribution of both Aβ and Aβ . They concluded that HiLyte 647 and Atto 655, compared to the other two tags, had high peptide-tag interactions which promoted the formation of the high molecular weight oligomers of Aβ and consequently the fibrillation step. In this experiment, Atto 488 seemed to be the most suitable as no significant interaction was noted. Quinn et al. [START_REF] Quinn | Real-time probing of β-amyloid self-assembly and inhibition using fluorescence selfquenching between neighbouring dyes[END_REF] demonstrated that HiLyte fluor 555-labelling of Aβ peptides on its N-terminus did not alter the self-assembly kinetics or the resulting aggregated structures. On the contrary, Taverna et al. demonstrated that a fluorescent tag (Fluoprobe 488 NHS Ester) attached on a side-chain of amyloid Aβ(1-42) (on the amines of Lys-16, Lys-28 and/or N-terminus Asp residues) inhibited the aggregation [START_REF] Taverna | Méthode de stabilisation d'un peptide[END_REF]. In another study by Zheng et al. [START_REF] Zheng | The effects of fluorescent labels on Aβ42 aggregation detected by fluorescence correlation spectroscopy[END_REF], the effect of five different dyes introduced in the form of N-hydroxysuccinimidyl esters (BP, RB and 5-SFX) or as isothiocyanates (RITC and 5-(6)-FITC) was evaluated. The authors concluded that 5-SFX and 5-(6)-FITC inhibited the aggregation, since no change in the Rh was observed during the incubation period of 4 h, while the other three promoted it. However, this study showed limitations as a concentration of 5 µM in peptide was used and the aggregation was monitored for only few hours at 25 °C.

Under these conditions the aggregation of the Aβ peptides would take a few days (even weeks) [START_REF] Hu | Amyloid seeds formed by cellular uptake, concentration, and aggregation of the amyloid-beta peptide[END_REF] to start and it seems difficult to judge on the inhibition effect of these dyes. In our opinion, in order to study the aggregation process of amyloid peptides at relevant physiological concentrations one might consider the use of preformed seeds known to accelerate the aggregation process at such low concentrations [START_REF] Sowade | Seed-induced acceleration of amyloid-β mediated neurotoxicity in vivo[END_REF]. Eventhough, when labelled peptides are used, it is important to understand if the attached label is not introducing a bias in the aggregation process.

Amyloid peptides exist under different isoforms, the most common ones being Aβ(1-40) and Aβ(1-42), which differ from the former by two extra amino acids at the C-terminus, making it more hydrophobic. These co-existing isoforms aggregate differently when separate [START_REF] Wang | Different Aggregation Pathways and Structures for Aβ40 and Aβ42 Peptides[END_REF][START_REF] Deleanu | Unraveling the Speciation of beta-Amyloid Peptides during the Aggregation Process by Taylor Dispersion Analysis[END_REF].

However, in vivo these isoforms coexist and it is not clear how they influence each other. In fact, it was found that the amyloid plaques in the brains of AD patients were mainly, and sometimes exclusively, constituted of Aβ(1-42) [START_REF] Roher | beta-Amyloid-(1-42) is a major component of cerebrovascular amyloid deposits: implications for the pathology of Alzheimer disease[END_REF], despite that Aβ(1-40) concentration is several-fold higher than Aβ(1-42) one. The co-aggregation of these two isoforms was intensively studied over the last decade [START_REF] Gokce | The ratio of monomeric to aggregated forms of Abeta40 and Abeta42 is an important determinant of amyloid-beta aggregation, fibrillogenesis, and toxicity[END_REF][START_REF] Cukalevski | The Aβ40 and Aβ42 peptides self-assemble into separate homomolecular fibrils in binary mixtures but cross-react during primary nucleation[END_REF]. Some authors claimed that the peptide mixing only influences the elongation phase by seeding the fibrillation but no heteromolecular fibrils are formed [START_REF] Cukalevski | The Aβ40 and Aβ42 peptides self-assemble into separate homomolecular fibrils in binary mixtures but cross-react during primary nucleation[END_REF]. But other reports suggested that mixed fibrils could be formed [START_REF] Gokce | The ratio of monomeric to aggregated forms of Abeta40 and Abeta42 is an important determinant of amyloid-beta aggregation, fibrillogenesis, and toxicity[END_REF][START_REF] Cerofolini | Mixing Aβ(1-40) and Aβ(1-42) peptides generates unique amyloid fibrils[END_REF].

In previous works, we showed the potential of Taylor dispersion analysis (TDA) to speciate the aggregation process of Aβ(1-40) and Aβ(1-42), as pure or mixed peptide solutions [START_REF] Deleanu | Unraveling the Speciation of beta-Amyloid Peptides during the Aggregation Process by Taylor Dispersion Analysis[END_REF][START_REF] Deleanu | Taylor Dispersion Analysis and Atomic Force Microscopy Provide a Quantitative Insight into the Aggregation Kinetics of Aβ (1-40)/Aβ (1-42) Amyloid Peptide Mixtures[END_REF].

In this work we present the use of TDA coupled with simultaneous UV and LEDIF detections to study the influence of the fluorescent tag FITC on the Aβ peptide aggregation and to unravel if heteromolecular species are formed along the aggregation course.

Materials and methods

Materials

Aβ(1-40) was prepared by fast conventional SPPS using a Fmoc orthogonal strategy, as described elsewhere [START_REF] Deleanu | Unraveling the Speciation of beta-Amyloid Peptides during the Aggregation Process by Taylor Dispersion Analysis[END_REF]. Aβ(1-42) (batch number 100002591, >95% purity by HPLC), were purchased from Bachem (Bubendorf, Switzerland). Both FITC peptides were tagged on their N-terminal side, and the molar mass of the tagged peptides was confirmed by MALDI-MS (provider) and HPLC-ESI-MS in this work (4790 g/mol and 5016 g/mol for tagged Aβ and tagged Aβ(1-42) respectively). Sodium dihydrogeno phosphate and sodium hydroxide were purchased from Sigma Aldrich (France). All buffers were prepared using ultrapure water obtained from a MilliQ system (Millipore, France).

Peptide pretreatment and sample preparation

Both native (nAβ) and tagged (tAβ) peptides were pretreated independently using the protocol previously described [START_REF] Deleanu | Unraveling the Speciation of beta-Amyloid Peptides during the Aggregation Process by Taylor Dispersion Analysis[END_REF][START_REF] Brinet | An improved capillary electrophoresis method for in vitro monitoring of the challenging early steps of Aβ(1-42) peptide oligomerization: Application to anti-Alzheimer's drug discovery[END_REF]. Briefly, the peptides were first dissolved at a concentration of 2 g/L in an ammonium hydroxide solution (NH4OH) which concentration differed between the two studied peptides (0.10 % (m/v) for Aβ(1-40), 0.16 % (m/v) for Aβ(1-42)). The peptide solutions were then incubated for 10 minutes at room temperature, then aliquoted and freezedried. The stock aliquots contained 10 nmol of peptide, and lyophilized peptide aliquots were stored at -20 °C until use. The pure tagged or native peptide solutions were prepared directly from the aliquoted fractions and dissolved in the adequate amount of buffer to reach the desired final peptide concentrations of 1, 10 and 100 µM.

The mixed aliquots containing both native and tagged Aβ were prepared so that the final sample contained either 7% of tAβ(1-40) or 10% of tAβ . First stock aliquot of native or tagged peptides was dissolved in 100 µL of 0.16% (m/v) NH4OH, then appropriate volumes were used to obtain the desired combinations having a total Aβ content of 10 nmol, as detailed in table 1.

Study of Aβ aggregation by Taylor dispersion analysis

TDA was performed using an Agilent 7100 (Waldbronn, Germany) capillary electrophoresis system with bare fused silica capillary (Polymicro technologies, USA), having 60 cm × 50 µm i.d. dimensions and a UV detection window at 51.5 cm from the inlet end. The system was coupled with a Zetalif light-emitting diode induced fluorescence (LEDIF) detector (Picometrics, Toulouse, France) with a window at 33 cm from the inlet end. The capillary was conditioned with the following flushes: 1 M NaOH (30 min) followed by a flush with ultrapure water (30 min). Between each analysis, the capillary was rinsed with a 20 mM sodium phosphate buffer at pH 7.4 for 2 min. Samples were injected hydrodynamically on the inlet end of the capillary (44 mbar, 4 s) and the injected volume was about 6.5 nL, corresponding to 1% of the capillary volume to the LEDIF detection point and 0.64% with respect to the UV detection window. In the case of the 1µM, 10 µM and 100 µM tAβ(1-42) samples, the solutions were injected hydrodynamically by applying for 3 s a pressure of 33, 55 and 6 mbar respectively. The injection volumes were modified to prevent detector saturation.

Experiments were performed at a mobilization pressure of 100 mbar. The temperature of the capillary cartridge was set at 37 °C and the vial carrousel was thermostated using an external circulating water bath 600F from Julabo (Germany). The solutes were simultaneously monitored by UV with an absorbance measured at 191 nm and by fluorescence with an excitation at 480 nm. Emission light was collected through a ball lens and a high-pass filter in the wavelength range from 515-760 nm. The proportion of tagged peptide in the mixtures was chosen so that the obtained LEDIF signal was as high as possible without saturating the detector. The higher fluorescence intensity observed for tAβ(1-40) presumably stems from the presence of unreacted FITC during synthesis, as observed for these samples from the taylorgrams (see supporting information to 1300 nL (0.87 and 1.3 µL). Finally, to prevent sample evaporation, the vial cap was changed three times a day. All taylorgrams were recorded using Agilent Chemstation software and then exported to Microsoft Excel for subsequent data processing. The data obtained from the UV signal were treated on the right side of the taylorgram to avoid the spikes detected on the left part, as described elsewhere [START_REF] Deleanu | Unraveling the Speciation of beta-Amyloid Peptides during the Aggregation Process by Taylor Dispersion Analysis[END_REF][START_REF] Deleanu | Taylor Dispersion Analysis and Atomic Force Microscopy Provide a Quantitative Insight into the Aggregation Kinetics of Aβ (1-40)/Aβ (1-42) Amyloid Peptide Mixtures[END_REF].

Results and discussion

Influence of the peptide concentration

The effect of the peptide concentration on the kinetics of the aggregation process was first investigated by TDA at different tagged peptide (tAβ(1-42)) concentrations ranging from 1 to 100 µM. As can be seen from Figure 1A, the total peak area, obtained by integrating the taylorgrams from the LEDIF detection, did not evolve significantly in the case of the lowest concentrations (1 and 10 µM), over the whole studied incubation time (352 h for the 1µM sample and 162 h for the 10 µM sample), suggesting that the kinetics of the aggregation at these concentrations is very slow, as shown in the literature the kinetics of the aggregation increase with increasing concentration [START_REF] Lattanzi | Solubility of Aβ40 peptide[END_REF]. The normalization of the peak area in Figure 1A was realized for the sake of comparison and was obtained by dividing each peak area of each run by the peak area obtained at tag = 0 h.

In the case of the highest concentration (i.e. 100 µM), the peak area decreased to reach a plateau after ~3 h of incubation. The comparison with a sample having the same 100 µM total peptide concentration but with a mixing of 90 µM nAβ(1-42) with 10 µM of tAβ(1-42), demonstrated similar kinetics of aggregation from the LEDIF peak area. In addition, Figure 1.B shows the average Rh obtained for the 100 µM samples by integration of the LEDIF elution profiles as described elsewhere [START_REF] Chamieh | Comparison of single and double detection points Taylor Dispersion Analysis for monodisperse and polydisperse samples[END_REF]. At tag = 0 h and during the first hour of incubation the average Rh was around 1.9 nm (corresponding to the size of the Aβ(1-42) monomer and small oligomer population, in good agreement with previously published works [START_REF] Deleanu | Unraveling the Speciation of beta-Amyloid Peptides during the Aggregation Process by Taylor Dispersion Analysis[END_REF][START_REF] Deleanu | Taylor Dispersion Analysis and Atomic Force Microscopy Provide a Quantitative Insight into the Aggregation Kinetics of Aβ (1-40)/Aβ (1-42) Amyloid Peptide Mixtures[END_REF]). After about 1 h, the Rh value decreased to reach a plateau around 0.8 nm, which most likely corresponds to the free fluorescent tag or free tagged aminoacids (FITC, theoretical Rh obtained from modelization [START_REF] Deleanu | Unraveling the Speciation of beta-Amyloid Peptides during the Aggregation Process by Taylor Dispersion Analysis[END_REF] using HydroPro software [START_REF] Ortega | Prediction of Hydrodynamic and Other Solution Properties of Rigid Proteins from Atomic-and Residue-Level Models[END_REF] on a energy minimized 3D structure is 0.64 nm). In the case of the low concentration samples, the Rh at tag = 0 h was of 1.95 and 1.85 nm for the 1 µM and the 10 µM samples respectively. The average Rh value decreased very slowly with the appearance of the small sized population (Rh ~ 0.8 nm) and reached the plateau after two weeks for the 1 µM sample (see supporting information figure SI.9). Eventhough it is theoretically possible to follow the aggregation process at these two low concentrations and for a relatively long period of time, it is not possible to do a control run without the fluorescent tag at these concentrations because of the low sensitivity of the UV detection as compared to fluorescence.

Therefore in order to study the impact of the fluorescent tag it seems important to apply conditions were both native and tagged peptides could be followed simultaneously.

In conclusion of this first part, it was found that a high concentration of typically 100 µM was recommended to study the impact of the fluorescent tag on the aggregation process within a reasonnable time range (few days instead of weeks). Therefore, if fluorescent detection combined with a low peptide concentration (below 1 µM) seems hardly applicable for monitoring amyloid peptide aggregation because of slow kinetics, the impact of the fluorescent tag on the aggregation process may however be studied on mixed mixtures of native and tagged peptides, at 100 µM total peptide concentration. To increase the aggregation kinetics for low concentration samples, the use of preformed seeds might also be a suitable option.

Monitoring the aggregation process of Aβ peptides by TDA-UV

In this work, we used a proportion of tagged peptide between 7 and 10% (see pie charts in Figure 2), keeping constant the total peptide concentration at ~100 µM. Simultaneous UV and fluorescent detections could be compared using these mixed non-tagged and tagged mixtures.

The UV detection was used to determine the kinetics of aggregation which can be compared in presence or in absence of tagged peptide. In a recent work [START_REF] Deleanu | Unraveling the Speciation of beta-Amyloid Peptides during the Aggregation Process by Taylor Dispersion Analysis[END_REF], we showed by TDA that the products of Aβ peptide aggregation could be divided into four main populations differing by their size. The first population is that of monomeric and small oligomeric forms of the peptides having an Rh < 5 nm. The second population corresponds to higher molar mass oligomers with Rh between 4 and 50 nm. The third population shows Rh > 50 nm and corresponds to soluble protofibrillar structures. Finally the fourth one is that of insoluble fibrils which size is not accessible by TDA. Figure 3 In Figure 2 are presented the area of the monomer and small oligomers population obtained by deconvolution of the elution profile by UV detection over the whole aggregation process for all the studied systems. The evolution of this population was found to be representative of the aggregation kinetics [START_REF] Deleanu | Unraveling the Speciation of beta-Amyloid Peptides during the Aggregation Process by Taylor Dispersion Analysis[END_REF][START_REF] Deleanu | Taylor Dispersion Analysis and Atomic Force Microscopy Provide a Quantitative Insight into the Aggregation Kinetics of Aβ (1-40)/Aβ (1-42) Amyloid Peptide Mixtures[END_REF] via the consumption of the monomeric units. As can be seen from and its fibrillary structures adopt compacted conformations [START_REF] Barz | Compact fibril-like structure of amyloid β-peptide (1-42) monomers[END_REF], in which the N-terminus is supposedly water-shielded. In this work, the FITC tag can change in the hydrophilichydrophobic balance of the peptides, can induce steric hindrance or may change the peptide conformation, leading to a lower propensity for aggregation. For instance, it was reported in the literature that the N-terminally truncated amyloid peptides were more prone to aggregation than the full length ones [START_REF] Dunys | Are N-and C-terminally truncated Aβ species key pathological triggers in Alzheimer's disease?[END_REF][START_REF] Bouter | N-truncated amyloid β (Aβ) 4-42 forms stable aggregates and induces acute and long-lasting behavioral deficits[END_REF][START_REF] Rostagno | N-terminally truncated Aβ4-x proteoforms and their relevance for Alzheimer's pathophysiology[END_REF][START_REF] Bayer | N-Truncated Aβ Starting at Position Four-Biochemical Features, Preclinical Models, and Potential as Drug Target in Alzheimer's Disease[END_REF] because the truncated peptides would become more hydrophobic, which supports that an increase in hydrohilicity at the N-terminus region would impair the aggregation.

Figure 4 shows the hydrodynamic radii obtained for all studied samples and for all populations obtained by deconvolution of the UV elution profile. The monomers and low molar mass oligomers have an Rh of 1.60 -2.25 nm which was relatively constant during the whole aggregation process (Figure 4, monomers). According to our previous study, these values suggest that this population is mainly comprised of monomers and dimers [START_REF] Deleanu | Unraveling the Speciation of beta-Amyloid Peptides during the Aggregation Process by Taylor Dispersion Analysis[END_REF]. As for the higher mass oligomer population, it varied from ~4 to ~30 nm for all studied samples with an average value around 10 nm. Then the Rh of protofibrils ranged from 50 to 250 nm for all studied systems. These results suggest that the fluorescent tag did not influence the size of the different populations when compared to native samples.

When a deeper look is taken at the higher mass oligomer population for the 3:1 mixtures with and without tagged peptides (Figure 5), the following observations could me made: first, in the native peptides mixture, this population increased in proportion and reached a maximum value after 6h incubation and then decreased and reached a lower plateau after 15 h. Then, the addition of tAβ(1-40) did not seem to significantly influence the evolution of this population, which seemed to disappear after 24 h in both cases (with and without tAβ(1-40)). Finally, when tAβ(1-42) was added to the mixture, the bell shaped distribution extended from 0 h up till 60 h with a maximum reached around 30 h, suggesting that the oligomers are more stabilized under these conditions.

The comparison of the evolution of the monomer and small oligomer populations obtained from the elution profiles from the UV and the LEDIF detections (Figure 6), showed no difference in the pathway between the tagged peptide (selectively detected by LEDIF) and the total peptides (detected by UV; composed of tagged and non-tagged peptides), suggesting that the aggregation involves all the different peptides at all steps and that the formed assemblies might be heteromolecular (mixture of Aβ(1-40) and Aβ(1-42)). where the decrease of the monomer population in UV is observed as well.

Conclusion

In this work, we showed the ability of TDA to follow the aggregation process of labelled Aβ Peak area was normalized to obtain a better comparison of the species evolution by dividing the area of each data point to the total peak area obtained for the first run at tag = 0 h. The inserted pie charts denote the proportion of the nAβ and tAβ content in the studied samples.

Figures 1 ,

 1 Figures 1, 2 and 5 show pie charts with the proportion of the native and tagged peptides in the samples. The final aliquots were immediately subjected to freeze-drying and then stored at -20°C before being dissolved in 20 mM phosphate buffer at pH 7.4 to perform the aggregation study.

Table 1 :

 1 Peptide quantities (nmol) and proportions in the mixed native/tagged samples Peptide quantities (nmol) and (proportions) Sample nAβ(1-40) nAβ(1-42) tAβ(1-40) tAβ(1-42) Aβ(1-40) with tAβ(1-40)

  Figures SI.1 to SI.8). The mobile phase was a 20 mM sodium phosphate buffer (pH 7.4; viscosity at 37 °C: 0.7×10 -4 Pa.s). Peptide aliquots were first dissolved in 100 µL of a 20 mM sodium phosphate buffer solution (pH 7.4) to reach a final concentration of 100 µM and then immediately transferred to a vial to be incubated at 37°C in the capillary electrophoresis carrousel. The aggregation was conducted by injecting the sample (Vinj ≈ 7 nL) every 11 min for 100% Aβ(1-42) experiments, and each 30 min for all the experiments containing Aβ(1-40). The total average of TDA injections was between 124 and 185 TDA runs per sample, corresponding to a total sample volume consumption between 870

  displays one example of taylorgram deconvolution with the contributions of the different populations to the total UV signal. The residual trace shown in the upper part of Figure 3 (difference between the experimental data and the theoretical fit) represents the soluble fibril fraction.

Figure 2A, nAβ( 1 -

 1 Figure2A, nAβ showed a lag phase of about 18 h before a rapid decrease in the monomeric population to reach a final lower plateau after ~26 h. Aβ is thought to follow a secondary nucleation mechanism, where monomers add to already existing fibrils to produce larger fibrils, without going through intermediate states as discussed in the literature[START_REF] Lattanzi | Solubility of Aβ40 peptide[END_REF][START_REF] Arosio | On the lag phase in amyloid fibril formation[END_REF][START_REF] Chen | Distinct Early Folding and Aggregation Properties of Alzheimer Amyloid-β Peptides Aβ40 and Aβ42[END_REF]. Conversely, the nAβ(1-42) (Figure2C) decreased rapidly (less than 1h) without showing any lag phase. The 3:1 nAβ(1-40):nAβ(1-42) mixture showed a similar trend as for the nAβ(1-42) sample but with slower kinetics (the plateau was reached after 16 h). As displayed in Figure2D, the addition of 7% of tAβ(1-40) to nAβ(1-40) did not seem to affect the lag phase, however it affected the kinetics of the monomer consumption which reached a plateau after ~60 h instead of 26 h for the 100 % native sample. This observation suggests that the tagged peptide influenced the elongation phase of the aggregation mechanism but not the nucleation step. When the tAβ(1-42) (10%) was added to the nAβ(1-42) sample (see Figure2G), the kinetics of the aggregation decreased as well and the time to reach the final lower plateau changed from less than 1 h to about 3 h. Similarly, in the case of the 3:1 mixture of Aβ(1-40):Aβ(1-42), when 7% of tagged Aβ(1-40) were added to the sample, the aggregation pathway was not significantly changed compared to the native mixture. However slower kinetics were observed (lower plateau reached after 36 h instead of 16 h for the native mixture; see Figure2Ecompared to Figure2B). These results suggest that the nAβ(1-42) peptide is driving the aggregation process: it rapidly formed the nucleus (no lag phase) and the elongation step was slown by the tAβ(1-40). Likewise, when a fraction of tAβ(1-42) was added to the mixture the aggregation mechanism resembled to the aggregation mechanism of Aβ(1-40) solutions, i.e. a lag phase was observed up to about 30 h and then the monomer population proportion decreased until it reached a final plateau at about 60 h. These observations confirmed that the tAβ(1-42) delayed the formation of the Aβ(1-42) nucleus serving as a seed for the elongation of Aβ. In a study by Zheng et al.[START_REF] Zheng | The effects of fluorescent labels on Aβ42 aggregation detected by fluorescence correlation spectroscopy[END_REF], the effect of several fluorescent tags, among which FITC tag used in this work, on the aggregation process of tAβ(1-42) was investigated using fluorescence correlation spectroscopy. The authors concluded that the FITC tag decreased the propensity of oligomers to aggregate and they attributed this effect to the increase of the peptide hydrophilicity by the fluorescent tag. Further, it was reported that the native Aß(1-42) monomer

  Figure 6C helps supporting this claim since a rapid decrease of tAβ(1-42) is observed during the first hours of incubation, probably corresponding to the formation of a nucleus, followed by a plateau. Then, another decrease in the tAβ(1-42) fraction is observed after about 24 h suggesting the onset of the elongation phase with the participation of the Aβ(1-40) (predominantly present in the sample)

  peptides by fluorescence detection and to study the effect of the label on the aggregation propensity of amyloid peptides. It was found that at very low concentrations (lower than 10 µM) the aggregation kinetics were drastically decreased and the monitoring of the aggregation at these concentrations would be a long process (days or weeks). To increase the kinetics and the experimental throughput, the concentration was increased up to 100 µM with a certain proportion of fluorescent-tagged peptides. At this concentration, it was possible to monitor the aggregation process of Aβ peptide mixtures in a reasonable amount of time. Further, it was reported that the aggregation of Aβ(1-40) and Aβ(1-42) was affected by a small proportion of FITC label. The effect of the fluorescent tag was observed on the elongation phase rather than on the nucleation one. Further, in the case of Aβ(1-40):Aβ(1-42) mixtures, when the tagged peptide was Aβ(1-42), it was observed a higher influence of the FITC label on the aggregation mechanism than with the tagged Aβ(1-40). As a consequence, the formed oligomers in Aβ(1-40):Aβ(1-42) mixtures (with a proportion of tAβ(1-42)) had a substantial increase of their lifetime and potentially of their toxicity. Finally, the comparison of both detection modes allowed to assume that the aggregation mechanism was a heteromolecular process involving both peptide isoforms and both tagged and untagged peptides in the aggregates. In perspective, the study of seeding at low Aβ concentrations and the effect of the truncation on the aggregation process, monitored and speciated by TDA would be an important input into the huge amount of literature dealing with the aggregation of amyloïd peptides.

Figure 1 .

 1 Figure 1. (A) Evolution of the peak area (normalized with the peak area at tag = 0 h) obtained by integration of the elution profiles with the LEDIF detection for all analyzed incubation times for 100 % tAβ(1-42) solutions at 1 µM (squares), 10 µM (circles) and 100 µM (triangles), and for a 100 µM Aβ(1-42) solution constituted of 90% nAβ(1-42) and 10% tAβ(1-42) (inversed triangles). (B) Comparison of the average hydrodynamic radii (obtained by integrating the LEDIF elution profile as described in[21]) over the whole aggregation study for the 100 µM Aβ(1-42) solutions (100 % tAβ(1-42) (triangles) and the mixture of 90% nAβ(1-42) and 10% tAβ(1-42) (inversed triangles)).

Figure 2 .

 2 Figure 2. Peak area evolution of the monomer and small oligomer populations obtained for both nAβ + tAβ systems and 100 % nAβ experiments at 100 µM total peptide concentration (except for 3:1 native peptides mixture where the concentration was of 133 µM) as obtained from the analysis of the UV-TDA elution profile: (A) 100% nAβ(1-40), (B) 75% nAβ(1-40) + 25% nAβ(1-42), (C) 100% nAβ(1-42), (D) 93% nAβ(1-40) + 7% tAβ(1-40), (E) 68% nAβ(1-40) + 7% nAβ(1-40) + 25% nAβ(1-42), (F) 75% nAβ(1-40) + 15% nAβ(1-42) + 10% tAβ(1-42) and (G) 90% nAβ(1-42) + 10% tAβ(1-42). Peak area was normalized to obtain a better comparison of the species evolution, by dividing the area of each data point to the total peak area obtained for the first run at tag = 0 h. The inserted pie charts denote the proportion of the nAβ and tAβ content in the studied samples.

Figure 3 :

 3 Figure 3: Example of data processing of the experimental taylorgrams. The lower graph represents the experimental data (black) fitted with the sum of four Gaussian peaks (dashed orange) which are individually represented on the graph. The residuals plot in the upper part of the graphs is the difference between the experimental data and the theoretical fit. Experimental conditions: Sample: 100 µM of 3:1 Aβ(1-40):Aβ(1-42) mixture (68% nAβ(1-40) + 7% tAβ(1-40) + 25 % nAβ(1-42)) at tag = 16 h; 20 mM phosphate buffer pH 7.4. Incubation: quiescent conditions at 37 °C. Fused silica capillaries: 50 µm i.d. × 60 cm × 51.5 cm. Mobile phase: 20 mM phosphate buffer, pH 7.4. Mobilization pressure: 100 mbar. Injection: 44 mbar for 4 s. Analyses were performed at 37 °C. UV detection at 191 nm. Baseline treatment was performed in Microcal Origin. The experimental fitting of the taylorgrams was performed by using the sum of four Gaussian functions in Microsoft Excel.

Figure 4 .

 4 Figure 4. Hydrodynamic radius evolution of the species obtained for both nAβ + tAβ systems and 100 % nAβ experiments during the UV analysis: (A) 100% nAβ(1-40), (B) 3:1 Aβ(1-40):Aβ(1-42) -75% nAβ(1-40) + 25% nAβ(1-42), (C) 100% nAβ(1-42), (D) 93% nAβ(1-40) + 7% tAβ(1-40), (E) 3:1 Aβ(1-40):Aβ(1-42) -68% nAβ(1-40) + 7% tAβ(1-40) + 25 % nAβ(1-42), (F) 3:1 Aβ(1-40):Aβ(1-42) -75% nAβ(1-40) + 15% nAβ(1-42) + 10% tAβ(1-42), (G) 90% nAβ(1-42) + 10% tAβ(1-42). The species are represented as follows: monomer and low molar mass oligomers (squares, ■), higher molar mass oligomers (circles, •) and protofibrils (triangles, ▲). Experimental conditions: Sample: 100 µM total Aβ; 20 mM phosphate buffer, pH 7.4. Incubation: quiescent conditions at 37 °C. Fused silica capillaries: 50 µm i.d. × 60 cm × 51.5 cm. Mobile phase: 20 mM phosphate buffer, pH 7.4. Mobilization pressure: 100 mbar. Injection: 44 mbar for 4 s, Vi ≈ 7 nL (Vi/Vd ≈ 0.6 %). Analyses were performed at 37 °C. UV detection at 191 nm.

Figure 5 .

 5 Figure 5. Peak area evolution of the higher molar mass oligomer population obtained from the UV analysis of the TDA elution profile for 3:1 Aβ(1-40):Aβ(1-42) -75% nAβ(1-40) + 25% nAβ(1-42) (squares); 3:1 Aβ(1-40):Aβ(1-42) -68% nAβ(1-40) + 7% nAβ(1-40) + 25% nAβ(1-42) (circles); and 3:1 Aβ(1-40):Aβ(1-42) -75% nAβ(1-40) + 15% nAβ(1-42) + 10% tAβ(1-42) (triangles). Peak area was normalized, to obtain a better comparison of the species evolution, by dividing the area of each data point to the total peak area obtained for the first run at tag = 0 h.

Figure 6 .

 6 Figure 6. Comparison of the peak area evolution of the monomer and small oligomer populations obtained by UV detection (closed symbols) and LEDIF detection (open symbols) for nAβ + tAβ systems: (A) 93% nAβ(1-40) + 7% tAβ(1-40), (B) 3:1 Aβ(1-40):Aβ(1-42) -68% nAβ(1-40) + 7% nAβ(1-40) + 25% nAβ(1-42), (C) 3:1 Aβ(1-40):Aβ(1-42) -75% nAβ(1-40) + 15% nAβ(1-42) + 10% tAβ(1-42) and (D) 90% nAβ(1-42) + 10% tAβ(1-42).

Acknowledgments: The authors wish to thank Pr. Luca Cipelletti (L2C Montpellier) for the valuable discussions that helped shape this work.

Data availability statement: "The data that support the findings of this study are available from the corresponding author upon reasonable request."