Stefan Bornhofen

Marten Düring
email: marten.during@uni.lu

Exploring Dynamic Multilayer Graphs for Digital Humanities

Keywords: Visual analytics, network visualization, dynamic multilayer networks, digital humanities

The paper presents Intergraph, a graph-based visual analytics platform for the exploration and study of content in Digital Humanities document collections. The designed prototype is motivated by a practical use case on a corpus of circa 15.000 digitized resources about European integration since 1945. The corpus allowed generating a dynamic multilayer network which represents different kinds of named entities appearing and co-appearing in the collections. To our knowledge, Intergraph is one of the first interactive tools to visualize dynamic multilayer graphs for content in digital collections. Graph visualization and interaction methods have been designed for users without a strong background in network science, and to compensate for common flaws with the annotation of named entities. Users work with a structured and understandable amount of currently relevant data by interacting with a scene of small graphs which can be added, altered and compared. This allows an interest-driven navigation in the corpus and the discovery of the interconnections of its entities across time.

Introduction

In recent years vast amounts of the human cultural records have been digitized, further described with metadata and made available in form of collections. To-day, collections within the cultural heritage and digital humanities domains typically consist of digitized multimedia objects with a strong bias towards unstructured text, metadata in various levels of detail and completeness and often a layer of named entity annotations. Scholars in the humanities and related domains struggle to critically assess the value of and the biases inherent in such collections [START_REF] Putnam | The Transnational and the Text-Searchable: Digitized Sources and the Shadows They Cast[END_REF]. To this end they need to comprehend how it is organized and need to be able to search for and find relevant content in an exploratory manner without following predefined tasks [START_REF] Van Ham | Search, Show Context, Expand on Demand: Supporting Large Graph Exploration with Degree-of-Interest[END_REF][START_REF] Brown | RePAH: a user requirements analysis for research portals in the arts and humanities[END_REF]. This requires novel search and discovery tools which enhance well-established techniques such as faceted search and keyword search [START_REF] Windhager | Visualization of Cultural Heritage Collection Data: State of the Art and Future Challenges[END_REF].

Interactive graph visualizations have been considered useful for these requirements [START_REF] Jänicke | On Close and Distant Reading in Digital Humanities: A Survey and Future Challenges[END_REF][START_REF] Guido | histograph. Graph-based exploration, crowdsourced indexation[END_REF][START_REF] Moretti | Knowledge-Based Systems ALCIDE : Extracting and visualising content from large document collections to support humanities studies[END_REF][START_REF] Warren | Six Degrees of Francis Bacon. A Statistical Method for Reconstructing Large Historical Social Networks[END_REF][START_REF] Düring | Gleanings from applications for the graph-based exploration of cultural heritage collections[END_REF][START_REF] Jessop | Digital visualization as a scholarly activity[END_REF][START_REF] Boukhelifa | Supporting Historical Research Through User-Centered Visual Analytics[END_REF]. Network data is often generated automatically by means of Named Entity Recognition (NER) such as e.g. persons, locations and organizations, paired with the manual or computational extraction of relations between them. While most applications today use unipartite or bipartite graphs, multilayer graphs allow for more complexity in the exploration of named entities, documents and the relations they share with each other [START_REF] Mcgee | Towards Visual Analytics of Multilayer Graphs for Digital Cultural Heritage[END_REF]. In order to benefit from the analysis of interconnections within such corpora, humanists need to adapt and adjust their workflows. Most of the target users do not have a strong background in advanced data analysis but value very highly an at least basic comprehension of the inherent logic of the tools they work with [START_REF] Bach | NetworkCube: Bringing Dynamic Network Visualizations to Domain Scientists[END_REF][START_REF] Katifori | Supporting Research in Historical Archives: Historical Information Visualization and Modeling Requirements[END_REF]. Moreover, imperfections within the data may cause significantly skewed results and therefore need to be taken into account. Such imperfections may stem from automated processing of digitized materials e.g. by OCR or NER but also from manual curation of e.g. metadata as well as intrinsic ambiguities of the source material. Since data cleaning is typically too costly, we observe a strong need for systems which let users cope with data-inherent imperfections. These requirements present interesting challenges and opportunities for the design of innovative tools for visual analytics. This paper presents the concepts of the visual analytics platform Intergraph and reports the results of a first expert user testing. Intergraph is being developed as part of the BLIZAAR project, a French-Luxembourgish funded research project with the objective to develop visual analytics techniques for complex data modeled as dynamic multilayer graphs for domain experts in history and biology. Its principal use case consists of a collection of 15.000 digitized documents on European Integration since 1945. The next section reviews the state of the art in the visualization of dynamic multilayer networks. Section three presents the data structure followed by an overview of Intergraph's main features in section four. Section five gives an account of the conducted user tests. Finally, section six concludes the paper with a discussion and an outlook to future work.

State of the art

Network visualizations offer a unique way to understand and analyze complex data by enabling users to inspect and comprehend relations between individual units and their properties [START_REF] Rossi | Towards effective visual analytics on multiplex and multilayer networks[END_REF]. Some scientific fields have been using network visualizations for a long time, most notably systems biology where purpose-built visualizations are being developed for more than twenty-five years [START_REF] Mendes | GEPASI: a software package for modelling the dynamics, steady states and control of biochemical and other systems[END_REF][START_REF] Shannon | Cytoscape: a software environment for integrated models of biomolecular interaction networks[END_REF][START_REF] Pavlopoulos | Arena3D: visualization of biological networks in 3D[END_REF]. In Digital Humanities research we observe two types of network visualizations: (1) Manually compiled datasets based on network theory-and question-driven models of complex social relationships created to be analyzed by researchers [START_REF] Düring | HNR Bibliography[END_REF], (2) Applications for the distant reading of graph visualizations of larger datasets which were created typically using methods borrowed from Natural Language Processing. Such applications encourage an audience with an interest in the respective topics to explore the data [START_REF] Düring | Gleanings from applications for the graph-based exploration of cultural heritage collections[END_REF].

A preceding study by the BLIZAAR project on visual analytics requirements for research in digital cultural heritage has been published in [START_REF] Mcgee | Towards Visual Analytics of Multilayer Graphs for Digital Cultural Heritage[END_REF]. The authors suggest that the data structures supporting the analysis of a complex digital corpus, in which people, organizations, places, multimedia documents and document collections are connected across time, should best be modeled as a dynamic multilayer network. Dynamic networks represent relationships between entities that evolve over time [START_REF] Beck | The state of the art in visualizing dynamic graphs[END_REF]. In multilayer networks, sub-networks are represented on independent layers, but they can also interact with each other [START_REF] Kivelä | Multilayer networks[END_REF]. Multilayer networks can have multiple types of node [START_REF] Ghani | Visual analytics for multimodal social network analysis: A design study with social scientists[END_REF], with different attributes [START_REF] Kerren | Multivariate network visualization[END_REF], and different types of relationships [START_REF] Singh | Visual mining of multimodal social networks at different abstraction levels[END_REF]. The particularities of dynamic multilayer networks and their importance for real-world applications have recently come to attention in network science. This led to increased work on their definition, analysis and visualization. In the last years, two European collaborative projects were entirely dedicated to this topic.

Plexmath

The Plexmath project (2012)(2013)(2014)(2015) [25] aimed at formulating a new mathematical framework for the analysis of multi-level time-dependent complex networks. Several visualization methods have been published in the scope of this project. Pymnet [26] is a prototype to visualize graph data specifically described in compliance with Kivelä's general definition for multiplex and multilayer networks [START_REF] Kivelä | Multilayer networks[END_REF]. After loading the graph, the user can draw customized network images and save them in vector or raster formats. MuxViz [START_REF] De Domenico | MuxViz: a tool for multilayer analysis and visualization of networks[END_REF] is an open-source platform for the exploration and interactive visualization of dynamic multilayer networks. In particular, the software provides a collection of algorithms for multilayer network analysis.

Multiplex

The objective of the Multiplex project (2012-2016)[28] was understanding the functioning of multi-level complex systems. Just as in Plexmath, a number of novel visualization methods have been conceived. Multinets.io [29] is a web-based visualization platform which has been designed and implemented at ETH Zurich for demonstrative purposes. The software illustrates a set of universal functionalities that are pertinent to the visualization of dynamic multi-layered graphs. Multinets [START_REF] Piškorec | MultiNets: Web-Based Multilayer Network Visualization[END_REF] is a library consisting of reusable HTML components which provide functions to easily integrate the visualization of multilayer network data in a web page.

All of these applications, stand-alone or web-based, are primarily designed to either demonstrate concepts, or to render universal visualizations for (dynamic) multilayer graphs. However they are not directly applicable to visual analytics purposes in that they do not provide adequate functionality for domain-specific user tasks. After loading and visualizing a graph, interactivity is typically limited to node inspection, layout rearrangement and camera movement. In particular, the applications process complete networks without much possibility to query subnetworks or to create other visualizations for further exploration. While such kind of overall view might be adapted for relatively small sample data, it is not appropriate for larger real-world use cases.

Dataset and Requirements

The data is derived from resources on the European integration since 1945 collected by Centre Virtuel de la Connaissance sur l'Europe (CVCE) [31], a former research and documentation center which in 2016 was integrated into the University of Luxembourg. CVCE created a multilingual collection of ca. 25.000 digitized documents organized in 29 hierarchically organized thematic corpora. The documents differ significantly in nature: among them are newspaper articles, diplomatic notes, personal memoirs, audio interview transcripts, cartoons and photos with descriptive captions. The histograph project [START_REF] Guido | histograph. Graph-based exploration, crowdsourced indexation[END_REF] processed a subset of circa 15.000 of these documents with named entity recognition (NER) and -disambiguation and stored co-occurrence links between entities and documents in a Neo4j graph database. This dataset was made available to and further processed by the BLIZAAR project for the development of more advanced graph exploration tools.

Figure 1 shows the used histograph data structure with their nodes and relationships. On the one hand, resources are part of one or more collections, from the highest logical unit of thematic corpora (ePublications) down to the corresponding hierarchical units and subunits, which is modeled by the "is part of" relationship. On the other hand, named entities (persons, locations, themes, institutions) have been extracted using Named-Entity Recogni- tion software such as YAGO [START_REF]Max-planck-institut fur informatik: YAGO[END_REF] and TextRazor [START_REF]The natural language processing API[END_REF]. This process allowed generating the "appears in" relationship. Entities "co-appear" in resources, and collections "share" resources, by bipartite network projection [START_REF] Zweig | A systematic approach to the one-mode projection of bipartite graphs[END_REF]. Finally, a collection "mentions" an entity, and accordingly the entity "is mentioned in" the collection, if the collection contains at least one resource where the entity appears. Table 1 gives an idea of the size of the dataset.

The data structure is a dynamic multilayer network:

-Nodes can be considered on two layers, an entity layer and a collection layer, and they have different relationships; -Nodes of each layer have types: entities can be persons, locations, institutions or themes, collections can be epublications, units or subunits; -Resources are time-stamped by their historic publication date. Therefore, the network changes depending on the considered time period.

In workshops and regular exchanges domain experts identified content retrieval and insights concerning the representation and interconnections of entities in a corpus as main objectives, by drafting the following user story: "I would like to have an overview of how a specific person, institution or location is represented in the corpus, and of the other entities with whom they are mentioned. I would like to compare entities and explore where they share links. This helps me to decide which documents I want to study in greater detail". To achieve this within a graph-based environment users need to:

1. Create manageable subgraphs from the master graph 2. Compare multiple graphs 3. Observe temporal changes 4. Filter for node and resource properties 5. Maintain a straightforward link to the underlying resources 6. Handle inherent data imperfections As a matter of fact, a specific problem due to the automatic generation of the network are data Most commonly we observe fragments which were wrongly identified as entities, duplicate entities which have not been disambiguated correctly, and entities which have been disambiguated wrongly and linked to homonyms ("Robert Schuman"). An effort to rectify all of the abovementioned flaws is too costly and therefore unrealistic for this and comparable corpora. Functionalities moderating those flaws were therefore considered to be the most promising strategy in this case.

Intergraph

The visual analytics tool Intergraph offers a novel approach to exploring Digital Humanities corpora by means of an iterative search and discovery workflow. Written in javascript, Intergraph runs in a web browser and communicates with a node.js server which queries the data from a Neo4j database. The front-end client renders the graphs using the Three.js graphics library.

Given the size of the histograph dataset, an overall visualization of the corpus is neither suitable nor desirable for exploration. Users are rather interested in creating and inspecting subnetworks with entities relevant to their current research interest. Therefore, the main idea of Intergraph is to begin the exploration from one or more known start nodes. Following the expand-ondemand principle [START_REF] Van Ham | Search, Show Context, Expand on Demand: Supporting Large Graph Exploration with Degree-of-Interest[END_REF], the user will encounter new relevant nodes and pursue their exploration by conveniently creating additional graphs stemming from the existing ones. This path of exploration yields a sequence of linked subgraphs (user requirement 1).

Figure 2 shows a global screenshot of the Intergraph interface. Graphs can be dynamically added to and deleted from the scene. Following the VisLink approach [START_REF] Collins | VisLink: Revealing Relationships Amongst Visualizations[END_REF], they are rendered on free-floating planes which can be arbitrarily translated, oriented and scaled using familiar transformation widgets. Depending on the user tasks and preferences, the scene can be viewed in a 2D or a 3D perspective. The default 2D view is known to be most efficient for visual data exploration and analytics, since 3D visualizations tend to suffer from occlusion, overlapping and distortion, and they often require increased viewpoint navigation to find an optimal perspective [START_REF] Shneiderman | Why not make interfaces better than 3D reality?[END_REF]. 3D scenes allow however to stack planar graph layers in space and to create so-called 2.5D visualizations, which can have their virtue for understanding complex networks [START_REF] Ware | Designing with a 2 1/2D Attitude[END_REF].

Since target users are not necessarily experts in network science, Intergraph forgoes advanced graph concepts and metrics like clustering coefficients or betweenness. Node colors reflect the node type, and sizes indicate the number of underlying resources. A click on a node or edge gives immediate access to these resources (user requirement 5). New graphs are typically produced by querying 1.5D ego-networks of existing nodes, via easy-to-communicate operations such as -All entities co-appearing with a given entity -All collections mentioning a given entity -All entities mentioned in a given collection -All collections sharing resources with a given collection If the same node appears on two or more graphs of the scene, interedges are drawn (see Figures 2 and3). This approach of user-driven network generation was partly inspired by "citation-chaining", one of the most commonly used search strategies for literature among historians [START_REF] Ellis | A behavioural approach to information retrieval system design[END_REF][START_REF] Buchanan | Information Seeking by Humanities Scholars[END_REF]. Intergraph applies the citation chaining principle to documents and the entities mentioned in them. This allows users to create their own interest-driven search and discovery paths across the dataset.

With regard to the imperfect data, the most frequent flaw encountered with entity disambiguation are multiple recognized entities where in reality only one was mentioned. For example, the Named-Entity Recognition yielded three separate nodes for "East Berlin". If the user wants to consider these three nodes as one in order to create an ego-network, it is possible to multiselect a number of nodes, and to query "All entities co-appearing with a given entity (union)" meaning that the result will be the list of nodes co-appearing with at least one of the selected nodes. The user can then define a unique groupnode for "East Berlin" and draw a meaningful graph (user requirement 6). It is also possible to query "All entities co-appearing with a given entity (intersection)". This operation returns the list of entities co-appearing in the corpus with all selected nodes and can be used to merge multiple nodes e.g. if understood as representatives of a social group.

Results to new queries first appear in the form of a table in the left pane. This first kind of visualization, itemizing only the nodes without the edges, may in some cases already be sufficient to work with. The table lets users decide whether it is worth generating the graph or to recompile the list of nodes, in case of missing nodes or nodes which should be excluded from the graph. A graph of a given node table, or a part of it, can be generated on demand, and it is added to the canvas on the right side of the interface.

The scene can be submitted to a filter which operates on resource type and time (user requirement 4). Subgraphs of a given resource type can provide a better understanding of its distribution within the corpus. Subgraphs considering the resources of a specific time window allow assessing the relevance and interconnections of entities during a considered period. The user can shift the time window and get an animated representation of the dynamic graph (user requirement 3). If time-to-time mapping, i.e. animation, is not convenient to analyze the evolution of a network over time, time-to-space mapping is also possible. For this purpose the user can clone and "freeze" a graph of the scene, meaning that its current filter is fixed. By this means, several graphs with the same nodes but distinct time periods can be juxtaposed (2D) or superimposed (3D) in space [START_REF] Beck | The state of the art in visualizing dynamic graphs[END_REF]. As an example, Figure 3 illustrates the dynamics of two related ego networks: Willy Brandt, former chancellor of the Federal Republic of Germany, and his advisor Egon Bahr. The graphs are filtered and frozen for three consecutive time periods (before 1964, 1964-1987, after 1987) and reveal how the co-occurrence networks evolve and overlap (user requirement 2).

User test results

A formal user evaluation was held at the Luxembourg Center for Contemporary and Digital History (C2DH), in order to assess how well the previously identified user story has been implemented in Intergraph. The tests were conducted with a group of four scholars, all of whom were former employees of CVCE. The selection criteria were familiarity with the underlying corpus on European integration, as well as with the application of digital tools and methods. Both criteria were put in place to ensure that, for one, users could turn their attention to the interaction with the prototype with only minimal reminders of the underlying data model and content, and for another, they were qualified to judge the pertinence of Intergraph's output.

After a brief introduction to the functionalities of the platform, users were invited to use Intergraph for themselves and to begin their session with an elementary keyword search for an entity they knew was mentioned in the corpus. From this starting point, they were free to perform more synoptic tasks, such as finding relevant collections and resources, searches for co-appearing entities and comparison of their corresponding networks, in order to get a comprehensive view of how the investigated element is represented, positioned and linked in the corpus. Throughout the session, users were encouraged to continuously verbalize their train of thoughts and actions following the thinking aloud approach [START_REF] Boren | Thinking aloud: reconciling theory and practice[END_REF].

Following the 45 minute testing period users were asked to give verbal feedback and to complete a questionnaire. Concerning verbal feedback, users appreciated the ease of navigating through the corpus, the flexibility and freedom to combine different elements, the links across canvases, the management of duplicate entities as well as the ability to drill down to the underlying resources. In the questionnaire, users were invited to rate on a scale of 1 to 7 the utility of Intergraph with view to all aspects of the initially defined user story. As a result, Figure 4 shows a high general acceptance. In particular, all users declared that for the given user story they would prefer to use Intergaph over the other available tools (CVCE homepage search and CVCE backend search).

Conclusion & future work

This paper presented Intergraph, a visual analytics platform dedicated to the effective navigation through the content of Digital Humanities corpora. The work is inspired by recent advances in the visualization of dynamic multilayer networks, and has been enhanced and optimized for humanists and their domain-specific workflows. The conducted user tests showed a high acceptance of the tool with respect to the original requirements.

Given the exploratory nature of Intergraph, future work will concentrate on additional ways to suggest related nodes, and to create pertinent graphs out of existing ones, for example by applying recommendation algorithms [START_REF] Bobadilla | Recommender systems survey[END_REF]. The multilayer character of the data should be leveraged by adding other types of interlayer edges, such as those indicating the "mentions" relationship between collections and entities. Finally, it is important to observe that the used data structure is highly generic. As a matter of fact, entities identified in collections of timestamped resources are likely to be found in a huge number of digital corpora. Therefore, it is planned to open the existing platform to other data sets, so that it can evolve into a valuable visualization and exploration tool for many scholars working in the field of Digital Humanities.

Fig. 1 :

 1 Fig. 1: histograph/BLIZAAR data structure (nodes and relationships)

Fig. 2 :

 2 Fig. 2: Intergraph, global screenshot.

Fig. 3 :

 3 Fig. 3: Co-evolution of two dynamic networks over consecutive time periods.

Fig. 4 :

 4 Fig. 4: User test questionnaire results.

Table 1 :

 1 Histograph dataset magnitudes.

	Item	Approximate count
	Resources	15.000
	Collections	4.000
	Identified entities	36.000
	Entity appearances	300.000
	Entity co-occurrences 7.000.000

Acknowledgments

This work was funded by the ANR grant BLIZAAR ANR-15-CE23-0002-01 and the FNR grant BLIZAAR INTER/ANR/14/9909176.


domain: sdv chim

text:
Mitsuo Shoji

Yukihiro Abe

Mauro Boero

Yasuteru Shigeta

Yoshiaki Nishiya

Reaction mechanism of N -cyclopropylglycine oxidation by monomeric sarcosine oxidase

Introduction

Amine oxidation is an essential process for the metabolism of a wealth of microorganisms. All the amine oxidoreductases (AOs) in both the prokaryotic and eukaryotic forms contain covalently bound flavins. This common character seems to be due to intrinsic properties of flavin, which possesses a redox potential sufficiently high to oxidize a wide range of biological molecules. 1 The main oxidation reaction operated by the AOs is the conversion of a CN single bond of the substrates (mostly amino acids and amines) into a double bond. After hydrolysis of the CN double bond species (Schiff bases), the release of ammonium and the cleavage of the amines generate primary and secondary amines, respectively. In particular, monomeric sarcosine oxidase (MSOX) catalyzes the oxidation of sarcosine (Nmethylglycine) and secondary amino acids. 2 MSOX is widely used in clinical diagnostics with creatininase and creatinase to test the renal function. 3 The reaction mechanism of the MSOX has been extensively investigated by spectroscopic measurements, crystal structural analyses and molecular modeling approaches. 4,5 Closely related members of the AO family, as, for instance, monoamine oxidase (MAO) and Damino acid oxidase (DAAO), were also the focus of intense research activities. [6][7][8][9][START_REF] Mattevi | Proc. Natl. Acad. Sci[END_REF][START_REF] Kurtz | [END_REF][12] Nonetheless, the reaction mechanisms of the AOs have not been fully understood and multiple reaction mechanisms have been proposed as plausible. 9,[13][14][15] To date, at least four different mechanisms have been proposed: Two variants of a single electron transfer (SET) mechanism, a polar mechanism and a hydride transfer one. 9 For each possible mechanism, different intermediates are expected. The SET mechanism proceeds through a one-electron transfer from the substrate amine to the flavin. Support has been provided to this SET mechanism by the reaction with the N-(cyclopropyl) glycine (CPG), 4,16 motivated by the fact the SET is the more straightforward way to explain the formation of a covalent flavin-substrate adduct in the case of the CPG substrate. Scheme 1. Catalytic cycle of MSOX for CPG. 15 a. Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan. E-mail: mshoji@ccs.tsukuba.ac.jp b. JST-PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan. The afore mentioned two variants of the SET mechanism differ in the subsequent one-proton and one-electron transfer processes occurring either simultaneously or in a stepwise way. The polar mechanism, instead, involves the formation of a covalent flavin-substrate intermediate (4a-flavin adduct), whereas the polar mechanism is triggered by thiol substrates forming 4a-flavin adducts, 17 although the monothiol adduct does not promote the formation of a two-electron-reduced flavin. The hydride transfer mechanism proceeds through the direct hydride transfer from a substrate to the flavin N5. The majority of former experimental and theoretical results suggested a hydride transfer mechanism for most of the AOs. 9,18 The cyclopropyl group of CPG is expected to be easily converted into radical intermediates, since the cyclopropylmethyl has been used to trap radical species in various enzymatic reactions. 19 Former studies indicated that the hydride transfer mechanism is unlikely to occur in CPG, because the C1 proton (H1) cannot be easily donated. The polar mechanism was also expected to be difficult to realize, because the CPG adducted intermediate binding at the N atom of CPG is unstable. 16 Given this scenario, the SET mechanism remains as the more viable route. J. M. Kim et al. reported that both the polar and SET mechanisms are possible for the MAOs. 20 Scheme 2. Proposed CPG states in MSOX. 16 In a previous work, we have shown that the reaction mechanism of MSOX with sarcosine is a hydrogen-atom-coupled electron transfer (HACET), 5 which can be roughly categorized into a hydride transfer, meaning that the proton and electron simultaneously transfer from the substrate to the flavin. We termed this process HACET because the electron transfer via the  orbital interaction between the substrate and flavin is essential for an efficient reaction and, in this respect, "hydride" is not an accurate definition of the actual proton state. A single electron transfer and 4a-flavin adduct states were found to be unstable and characterized by activation barriers higher than the ones for the HACET mechanism. The study presented here is a thorough analysis of the reaction mechanism of MSOX with CPG. To this aim we resort to well-assessed computational approaches to investigate and unravel all the possible reaction pathways and intermediate states. The quantum mechanics/molecular mechanics (QM/MM) method used here is essential, since the inclusion of the explicit electronic structure is crucial to rationalize the electronic structure, especially when charge transfer processes occur, and to search for unforeseen protonation states and conformations, which can affect both the relative energetic stabilities of the intermediate states and the activation barriers. UV/Vis spectra calculations provide additional support to validate or discard the intermediate states.

A high-resolution (1.80 Å resolution) X-ray structure of sarcosine oxidase (PDB ID: 1EL5) was used as the starting structure in our simulations. 21 Crystallographic unavailable hydrogen atoms were added using the Reduce program. 22 Unsolved residues located before and after Gly3 and Glu386 at the N and C terminals were capped with acetyl and Nmethylamine groups, respectively. CPG was initially replaced by N,N-dimethylglycine in the crystal structure. The carboxy group of the CPG was assumed to be in the deprotonated form, according to results reported for a sarcosine substrate. 23 All the MM and MD simulations reported in this work were done using the AMBER 11 program package. [START_REF] Case | AMBER 11[END_REF] The parameters of the force fields Amber ff99SB, GAFF and TIP3P were used for the enzyme, the CPG and the solvating water, respectively. The atomic charges of the CPG and Cys315-FAD adduct were calculated at the DFT level (B3LYP/6-31G*) using the RESP method as implemented in the Amber Tools 1.4 and Gaussian package. [START_REF] Frisch | Gaussian 03[END_REF] The monomer of MSOX was placed at the center of an orthorhombic simulation box of size equal to 88 x 89 x 109 Å 3 , and the solvating water at ordinary liquid conditions completed the system. Periodic boundary conditions were applied to the simulation box for all simulations. The charge neutrality of the whole system was ensured by the addition of 21 sodium counter cations. Direct Coulomb interactions were computed using a 10 Å cut-off, and the remaining long-range interactions were evaluated via the PME method. To equilibrate the system, an initial energy minimization of the system treated as fully classical (MM) was performed, followed by a 50-ps heating phase from T = 0 K to 300 K via MD in the canonical NVT ensemble. Subsequently, a 50-ps NPT simulation was done at room temperature (T = 300 K) and at a constant pressure (P = 1 bar). In these simulations, positional constraints were applied to the solute molecules. A 20 ns MD simulation was performed in the same NPT ensemble upon activation of the SHAKE algorithm. This equilibration phase was then followed by a 0.5 ns MD simulation in which the temperature was gradually decreased from T = 300 K to 0 K. A spherical model of 45 Å radius from the N10 atom of FAD was then extracted from the final configuration, comprehensive of the protein and all the sodium atoms. This spherical structure was the one used Please do not adjust margins Please do not adjust margins to start the hybrid QM/MM simulations (Figure 1(A)), done with the NWChem 6.5 program suite. [START_REF] Valiev | [END_REF] The QM subsystem, shown in Figure 1(B), includes the CPG substrate, two water molecules and the side chains of the residues FAD, Cys315, Lys265, Lys347. The thiol link of Cyr315 was explicitly included in the QM region, since the covalent bond has a direct effect in the increase of the reduction potential of FAD by E ~ 120mV. 27 The selection of the most appropriate QM region has been done by considering various sizes including or excluding additional atoms and side chains residues. This benchmark analysis is reported in ESI † . The total charge of this QM region is equal to zero. The QM driver is the DFT functional in which the exchange-correlation interaction is computed at the B3LYP level complemented by the Grimme's D3 dispersion (UB3LYP-D3). 28 A 6-311G** basis set (TZVP) is used for all the atoms. The force field for the MM subsystem was the Amber ff99 one. The electronic embedding scheme was adapted for describing the QM-MM nonbonded interactions and the Coulomb interactions were explicitly computed without cut-off in the total energy calculations. To saturate the chemical bonds crossing the QM-MM interface, hydrogen link atoms were used, and the QM subsystem was optimized at the selected DFT level while keeping fixed the MM embedding region. Reaction pathways were sampled with the nudged elastic band (NEB) algorithm, and the transition states were further refined by a saddle point search point search to verify if single imaginary vibrational mode exists. Free energies were evaluated upon inclusion of the enthalpy corrections and entropy evaluation estimated from the frequency calculations in the optimized intermediate and transition states. For the UV/Vis absorption calculation, time dependent DFT (TDDFT) calculations were performed at the B3LYP/6-311++G** level (B3LYP/6-311++G**|Amber ff99) using a reduced QM region in which the thiol link (CH2-S-CH2) bridging the Cys315 and the FAD was kept in the MM embedding part to reduce the computational cost. The reported absorption spectra for the MSOX wild type and C315Ala mutant are rather similar with the absorption peak centered at ~454 nm. 27,16 The B3LYP functional has been shown to be the most reliable one in terms of accuracy of the absorption spectra of riboflavin with respect to both MPWB1K and PBE0. The TD-B3LYP/6-311+G(2d, 2p) approach still suffers from deviations from the experimental values by 40-50 nm. 29 Yet, this computational set-up has been extensively used to compute with appreciable accuracy the spectra of the flavin chromophores. 30,31 All the molecular structures shown in the figures were drawn using the visual molecular dynamics (VMD) program. 32

Results and discussion

Reaction Mechanism

All the intermediate states identified along the reaction pathways and their related free energy profiles are shown in Figures 2, 3 and4. The optimized structures of the transition states are sketched in Figure S1 (ESI † ). The atomic coordinates of all the intermediates and transition states are given in ESI † . In the following sections, the intermediate states (1-5) are thoroughly discussed, and in the following section the UV/Vis spectra of the intermediate states are analyzed. Finally, the reaction pathway is discussed and its atomic-level mechanism in MSOX is unravelled.

MSOX-CPG complex (state 1)

The first state on which we focused is an enzyme-substrate complex. In this state, hereafter indicated as state 1, the CPG is located in proximity of the flavin ring of FAD. The carboxy group of CPG is tightly anchored by two base residues, Arg52 and Lys347. Compared to the binding position of the sarcosine substrate, analyzed at an analogous QM/MM level, 5 the hydrogen-bond (H-bond) between the carboxy group of the substrate and the guanidine group of Arg52 are different. Namely, at the CPG binding, the carboxy group of CPG rigidly interacts with Arg52 via bidentate H-bonds, and the position of CPG shifts toward the N3 side of the flavin ring. Thus, the N atom of the CPG amine and the C (C) atom of the CPG cyclopropane turn out to be the closest ones to the flavin C4 and C4a atoms, respectively, and their distances in the state 1a are R(N CPG , C4 FAD )= 2.81 Å and R(C3 CPG , C4a FAD )=3.68 Å. On the other hand, at the sarcosine binding state, the N atom of the sarcosine amine and the CM atom of the sarcosine are closest ones to the C4a and N5 atoms of flavin, respectively, as the carboxy group of the CPG interacts with the side chain of Arg52 via a monodentate hydrogen bond, and the position of the sarcosine shifts to the C7 atom of the flavin. These different positions depend on the substrates relative to the FAD flavin, and are considered to be crucial to trigger different amine Please do not adjust margins Please do not adjust margins oxidation (H-elimination) reactions; for instance, in sarcosine, the C1 hydrogen is transferred to the FAD, whereas in CPG, the C2 hydrogen is the one transferred to the FAD. The search for stable CPG conformers in the state 1 allowed us to identify four different conformers, 33 hereafter denoted as the states 1a-1d. The most stable conformer is 1a (Figure 2), followed by a conformer with the rotated cyclopropane head of CPG (state 1b). Their relative stability locates the 1b above 1a by G =1.4 kcal mol -1 . The other two conformers of state 1, 1c and 1d, present a rotated amine group pointing toward the opposite and same side, respectively, of the O4 atom of FAD. Both 1c and 1d are energetically located above 1a by G = 6~9 kcal mol -1 . However, in these amine conformations (1c and 1d), the distances of (C2 CPG , N5 FAD ) and (C3 CPG , C4a FAD ) shrink to about 3 Å (Table S1, in ESI † ). As discussed in detail in the following sections, such a parallel orientation of the C2 CPG -C3 CPG bond and N5 FAD -C4a FAD bond in the 1c and 1d states play a central role in the oxidation of CPG promoted by FAD. From a

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Please do not adjust margins geometric standpoint, in 1a, only the C CPG atom is close to the N5 FAD and C4a FAD atoms, whereas in state 1b, only the C2 CPG atom is close to the N5 FAD and C4a FAD atoms (Table S1). The activation barriers of all the states 1, such as G(TS(1a,1b)) and G(TS(1a,1c)), are characterized by values G ≠ ≤ 13.3 kcal mol - 1 . Such a relative low activation barrier is a clear indication of the fact that the conformers of state 1 (1a-1d) can be easily interconverted.

CPG bound states (states 2)

By searching the possible reactions from the state 1, 33 a C4a adduct formation of CPG to FAD was found to be a plausible candidate. This pathway includes the cleavage of a C3-C1 bond in CPG, accompanied by the formation of a new C3-C4a bond between CPG and FAD. Two unique features characterize this reaction pathway. The first one is the fact that only the 1c and 1d states can give rise to C4a adducts (states 2b and 2a) with a low activation barrier. The free energy barriers to the states 2a and 2b result rather similar and sufficiently low G(TS(1c,2b)) ≈ G(TS(1d,2a)) ≈ 16kcal mol -1 ) to make this reaction pathway realizable. The second feature is that the C3 CPG -C CPG bond cleavage and the C3 CPG -C4a FAD bond formation occur at the different faces, in a way similar to what is observed in an SN2 reaction. If the reaction proceeds in the same face as an SN1 reaction, then C3 CPG -C1 CPG bond cleavage occurs before the formation of the C3 CPG -C4a FAD bond. At the transition state, the C3 CPG radical is formed, and the radical species is expected to undergo a rotation bringing the system from the C CPG atom direction to the C4a FAD one. The activation barrier for this pathway turns out to be G ≈28 kcal mol -1 , and this relatively large value can be ascribed to the fact that a C3 CPG radical has to be generated to rotate the methylene terminal (-C3H2). Conversely, in the SN2like pathway, the C3 CPG radical rotation is not necessary and the motion of the CH2 moiety in CPG is negligible, since the C CPG -C1 CPG bond elongates, and the C3 CPG -C4a FAD bond shrinks. Thus, this reaction channel (1d -> 2a and 1c -> 2b) is the one realizing the minimum energy pathway not to form a C3 CPG radical species during the C4a adduct formation. We also checked whether or not an alternative C atom (C2 CPG ) of the CPG moiety can react with C4a FAD . This inspection has shown that the formed product is the state 2c. Nonetheless, this state 2c and its associated transition state are energetically less stable (G(2c) = 18 kcal mol -1 and G(TS(1d,2c)) = 45 kcal mol - 1 ), hence the C2 CPG atom is unlikely to become an alternative reactive side with respect to C4a FAD . Among the C4a adduct states of states 2, the conformation identified as state 2a is the most stable. In the state 2b, the amine NH of CPG points away from the FAD flavin ring, and this state 2b is energetically higher than 2a by 9 kcal mol -1 . In Figure 4, the green and blue colors identify the amine conformation in CPG along the reaction pathway. Among the states 1, the one labeled as 1d is energetically higher than 1c by G = 3 kcal mol - 1 , and this same state can revert easily to 2a as the direction of the CPG amine is identical in both cases. Similarly, state 1c can be converted into 2b by the CPG binding. Since in this case the energetic order of the states 1 and 2 is reversed, the relative energy at which the transition state is located turns out to be similar, i.e. G(TS(1c,2b)) ≈ G(TS(1d,2a)) ≈ 16 kcal mol -1 . Please do not adjust margins

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We did also a thorough inspection of the states realized by the SET mechanism. Since the SET mechanism can realize a diradical structure, namely a CPG radical form and a flavin radical, the QM subsystem assumes a triplet spin state electronic configuration. Our calculations show that SET in state 1 is still unstable, being characterized by G (1SET) = 16 kcal mol -1 , and the second one expected as stable, presenting a ring-opened cyclopropane group (2SET) is equally unlikely in view of its higher energy G (2SET) = 18 kcal mol -1 . We remark that this energy is when higher than the one characterizing the TS(1d,2a) in the radical formation step. The transition state for the C3-C1 bond cleavage in the SET mechanism is energetically slightly higher (G (TS(1SET, 2SET)) = 20 kcal mol -1 ). The molecular structures of these states in the SET mechanism are reported in Figure S2 (ESI † ). This energetically demanding pathway indicates that the SET mechanism is unfavorable compared to the polar mechanism via the nonradical nucleophilic attack by the C CPG atom.

CPG H transferred states (states 3)

In the hydrogen transfer process, we observed that one proton (H + ) binding to the C CPG atom in state 2 (HC) is transferred to the N5 FAD atom in state 3. The relative stability in terms of energy difference between states 2a and 2b (G(2b) -G(2a) = 9 kcal mol -1 ) is barely affected by the process, since upon overcoming the transition states (G(TS(2b, 3b)) -G(TS(2a,3a)) = 7 kcal mol -1 ) the realized products are still separated by an identical energy difference (G(3b) -G(3a) = 9 kcal mol -1 ). In these products, the conformers a and b differ only in the trans-and cis-configuration of the C CPG -N CPG bond. The state 3a results much more stable in comparison with states 1 and 2 (G(3a) = -10 kcal mol -1 ). The transition state TS(2a,3a) is, in turn, less energetically demanding than the TS(1d, 2a), although the transition state TS(2b, 3b) is still high in energy, and, as such, comparable to TS(1d,2a). Hence, a reaction channel passing across TS(2b, 3b) is relatively unfavorable compared to the reaction via TS(2a,3a).

Imine intermediates (states 4)

The state 3 can realize an alternative protonation state, the imine state, in which the proton of the CPG amine is transferred to the FAD N5. This imine state is slightly more stable than the state 3a (G(4a) -G(3a) = -1.5 kcal mol -1 ). We can infer that water molecules are prone to access freely the CPG. In this respect, the water molecules indicated as Wat1 and Wat2 in Figure 1(B) can play an active role in the mechanism, if they can be positioned in the proper active places. This can occur, for instance, as a consequence of the incoming of additional water molecules forcing at least two of them to form the needed Hbond network. Water molecules in proximity of the CPG might mediate the proton transfer to the state 4, although we could not clearly determine such a reaction pathway with the present model without including additional water molecules. In the state 3b, the corresponding imine state (4b) is the more stable one (G(4b) -G(3b) = -6 kcal mol -1 ). In the reduction step of L-proline in MSOX, a deprotonation of the amino group is required. 34 This suggests that a proton transfer is possible for the amine group of the substrate upon binding to the active site. Therefore, the enamine-imine tautomerization of 3 -> 4 is a viable process at the active site of MSOX.

Product states (states 5)

After the C4a CPG -C CPG bond cleavage occurring in the state 3a, a secondary amino acid product, ethenyl amino acetic acid, is formed in the state 5a. Compared to the initial substrate of CPG, this amino acid product is two-electron oxidized as the HC - moiety was transferred to the FAD flavin from CPG. The state 5a turns out to be less stable in comparison with states 3a and 4a (G(5a)-G(4a) = 5 kcal mol -1 ), and the activation barrier for accessing the 5a state from the 3a is rather modest (G(5a) -G(3a) = 7 kcal mol -1 ). These two facts, taken together, suggest that the reaction from 3a to 5a does not occur spontaneously because the reverse reaction (5a -> 3a) is faster compared to the forward reaction (3a -> 5a). It should be noted that the product amino acid is still bound to the active site. The conclusion that can be drawn is that a dissociation of the product amino acid is essential to revert to the initial oxidized flavin (EFADox) by reaction with O2. The transition state TS(3b, 5b) is highly unfavored energetically (G(TS(2b, 3b)) = 20 kcal mol -1 ) mainly because the terminal CH2 moiety in CPG should undergo a large rotation of approximately 90º in the 3b -> 5b reaction.

UV/Vis spectra

Accurate spectroscopic measurements have been reported for MSOX 16,35 and these can provide a solid benchmark on which theoretical approaches can be tested. In the absence of CPG, the MSOX exhibits an intense absorption band at max=454 nm ascribed to an unmodified oxidized flavin. 16 Upon CPG addition, a charge transfer band was observed in the 500-700 nm range, 35 accompanied by a shift of the absorption tomax = 422 nm. Under aerobic conditions, the species with max = 422 nm accumulates and acts as a mechanism-based inhibitor for MSOX. This inactivated species is assigned to a CPG-modified flavin. 16 Under anaerobic conditions, MSOX carrying the CPG substrate show that the absorption spectra changes to broadband over the 400-500 nm range, which is assigned to the formation of a 1,5-dihydro-FAD (EFADH2). Thus, the MSOX catalytic cycle becomes trapped at the final oxidation step which, in turn, regenerates the unmodified oxidized state (EFADox). In order to verify the experimental UV/Vis spectra assignments for our simulated model, TDDFT calculations were done for all the intermediates identified in the present work. The results for the major states 0, 1a, 3a, 4a and 5a are shown in Figure 5. For the sake of completeness, the UV/Vis spectra for all the intermediate states are reported in Figure S3 (ESI † ). The state Please do not adjust margins Please do not adjust margins labeled as 0 is the unmodified MSOX without the CPG substrate. The calculated absorption peak for 0 is 0= 476 nm, which is overestimated by 22 nm with respect to the experimental value, a fact not entirely surprising in TDDFT approaches. In the CPG binding MSOX, the state 1a, the computed absorption peak is located at 1a= 443 nm, qualitatively consistent with the peak shift toward shorter wavelengths. Inactive species candidates with adsorption spectra peaked at max = 422nm are two states 3a and 4a. The calculated absorption peaks for 3a are 3a= 515 nm and 450 nm. We remark that also the 3b state is characterized by adsorption peaks in the same range, namely 3b= 586 nm and 451 nm. These wavelength absorptions are anyhow longer than 1a= 443 nm for 1a and, as such, inconsistent with the experimental results. Nonetheless, our computed absorption peaks for the states 3a, within the limitations of the TDDFT approach, are perfectly reasonable and corroborated by the observation that strong  orbital interactions between the FAD flavin and CPG unsaturated part (-CH=CH-NH-) have been found for the HOMO and LUMO orbitals in the states 3a and 3b. These interactions can reduce the HOMO-LUMO gap and thus shift the transitions between these two states to lower frequencies. The calculated absorption peak for the state 4a, the protonated tautomer of the state 3a, is located at 4a= 430 nm. From a free energy standpoint, the state 4a is more stable than 3a. In an attempt at getting a comprehensive scenario, we considered also a protonated state of 4a (4a+H + ), but in this case we obtained a substantially longer wavelength absorption peak (4a+H + = 524 nm). State 4b, a conformer of 4a, is also characterized by a similar absorption band peaked at 4b= 418 nm. Therefore, we can identify the state 4a, the imine state, as the experimentally observed inactivated species. In state 5a (green line in Figure 5) the absorption spectrum shows a long tail spreading in the wavelength range up to 500 nm. This feature is very similar to the experimental one for final state before the FAD oxidation. A broad absorption spectrum is found also for a model lacking the CPG oxidized product (EFADH -state). One additionally protonated state, the EFADH2 state without the CPG oxidized product, exhibits a low absorption peak centered at EFADH2= 482 nm. These calculated UV/Vis spectra in the absence of a substrate are reported in Figure S4 (ESI † ). On these grounds, the EFADH2 state can be ruled out as a possible final metastable state. The energy profile of Figure 4 shows that state 5a can be rapidly converted into the inactive state 4a, being the activation barrier for 5a -> TS(3a, 5a) -> 3a as low as G = 2 kcal mol -1 . Therefore, we expect that the final metastable state before the FAD oxidation (EFADH2 state in Schemes 1 and 2) can be assigned to the reduced FAD in the absence of the CPG substrate (EFADH -state), where O2 can easily react with flavin to produce hydrogen peroxide (H2O2) and an oxidized flavin (EFADox).

Reaction mechanism of the CPG oxidation by MSOX

The insight into the reaction mechanism of CPG in MSOX provided by the present study is the major focus of this section. The first step of this mechanism is the binding of CPG to the FAD flavin ring, a process that proceeds through the nucleophilic attack of the CPG C3 atom occurring simultaneously with the C3-C2 bond cleavage. This reaction can also be interpreted as a bond switch between the pristine C1-C3 bond in CPG and a newly formed CPG C3FAD C4a bond. This reaction step, which passes through the most unstable state TS(1d, 2a), is deeply different from the previously proposed single electron transfer process, in which a one-electron transfer occurs to CPG from the FAD flavin, and the cyclopropyl group opens forming a radical state. We have already shown that the radical intermediate states in SET are higher in energy than the TS(1d, 2a). We recall also that a rotation of the amino group in CPG via state 1d is crucial and has to be realized before the CPG adduct production in the state 2a. Based on the reaction rate kinetics, the first slow step in Scheme 1 gives k3 = 0.10 min -1 , 16 corresponding to G ≠ = 21.3 kcal mol -1 in terms of free energy. This activation barrier is comparable to the one calculated for the TS(1d,2a), namely G(TS(1d,2a)) = 16.2 kcal mol -1 . The second feature worthy of note is that the inactive species spectroscopically observed and having a spectrum peaked at max=422nm is assigned to an imine state 4a, and not to the amine state 3a. The states 4a and 3a are related to the imineenamine tautomers, and only the position of one proton is different. Their UV/Vis spectra are significantly different, and their adsorption peaks are centered on 3a= 515 nm and4a= 430 nm. Hence, there is no room for doubt: The imine state 4a is the inactive species. We remind that the intermediate state 4a is the most stable among all the intermediate states 1-5 identified in this study, and the inactive species is positioned in such a way that it screens completely the active site (C4a and N5) which becomes inaccessible to O2. The existence of this stable intermediate state of 4a is consistent with the observation that the species 4a is accumulated under aerobic conditions and the CPG acts as a mechanism-based inhibitor. The third remarkable feature is that the following slow process EFADred-X -> EFADH2 is expected to include not only the dissociation of the CPG oxidized product (3a -> 5a), but also the release of the product from the active site (5a ->). As shown in the free energy profile of Figure 4, the bond cleavage (3a -> TS(3a, 5a) -> 5a) does not correspond to the high activation barrier of G ≠ = 22.7 kcal mol -1 , expected from the reaction rate kinetics (k4=0.01 min -1 in scheme1). 16 By looking at Figure S4, the UV/Vis spectra for the reduced flavin in states 5a, 5b and Please do not adjust margins Please do not adjust margins EDADH -are not affected by the presence of the product in the active site. Thus, the last metastable state realized before the FAD oxidation process (EFADH2 species in Schemes 1 and 2) is represented by the EFADH -state, where the oxidized CPG product is released from the active site. Since the product amino acid is tightly anchored to the surrounding base residues, Lys347 and Arg52, because of their strong electrostatic interactions, an additional activation barrier must be overcome in the product release process. The negatively charged flavin (EFADH -) is well suited to release the substrate product with a negatively charged carboxy group. The reaction mechanism we propose for the CPG oxidation in MSOX

(0 -> 1a -> 1d -> 2a -> 3a -> 4a -> 3a -> 5a -> EFADH --> 0) is summarized in Scheme 3.
The present QM/MM results clearly suggest that the reaction of MSOX with CPG can be categorized as a polar mechanism. The SET mechanism, for the reasons summarized in this work, can be ruled out the CPG oxidation reaction in MSOX. In our previous theoretical study, 5 we were able to show that sarcosine in MSOX proceeds through a HACET mechanism, which can be roughly categorized as a hydride transfer mechanism. In the HACET mechanism, sarcosine is needed to close to the flavin ring to form substantial orbital overlap between the amine orbital and flavin aromatic orbital. In particular, the approach of Namine and C4a atoms is essential to low the activation barrier in the sarcosine oxidation. Based on these considerations, the HACET mechanism can be reinterpreted: The hydride transfer of the sarcosine oxidation in MSOX is stabilized by a polar mechanism through the Namine-C4a interaction, although an amine adduct is not stably formed for the sarcosine substrate (E = 16.3 kcal mol -1 , E + = 44.9 kcal mol - 1 ). 5 Based on the similarities between the reactions in sarcosine and CPG substrates, a polar mechanism is likely to play a key role also for other amine substrates in MSOX.

Conclusions

By resorting to accurate QM/MM molecular modeling, we unravelled the reaction mechanism of CPG in MSOX. The CPG substrate is widely used to trap radical species in enzymatic reactions, and the CPG has been identified as a prototype example of the SET mechanism in MSOX. The amine group of CPG can take two conformations, resulting in the two alternative pathways. In the first one, the CPG NH amine points directly toward the O atom of flavin, whereas in the second one the CPG NH amine points away from this same O flavin atom. The former pathway has lower activation barriers for the transitions 2a -> 3a and 3a -> 5a compared to the latter one with higher activation barriers for the processes 2b -> 3b and 3b ->5b. On these grounds, we can infer that the most favorable reaction pathway is the one realizing the subsequent steps 1a -> 1d -> 2a -> 3a -> 4a -> 3a -> 5a. According to this mechanism, the rotations of the cyclopropyl and the CPG amine are crucial to trigger the 1a -> 1d step. From this point, the CPGflavin interaction proceeds through a nucleophilic attack of the C3 atom belonging to the cyclopropyl group to the C4a atom of the flavin ring, thus realizing the 1d -> 2a step. The related activation barrier is G(TS(1d, 2a)) = 16.1 kcal mol -1 , namely the first slow step in the overall catalytic cycle (G1 ≠ =21.4 kcal mol - 1 ). The radical states are located at energetically higher values than the TS(1d, 2a), which clearly suggests that the SET mechanism can be ruled out. After a proton transfer (2a -> 3a) and an enamine-imine transformation (3a -> 4a), the imine state (4a) is formed, identified in our simulations as the most stable intermediate state. Such a high stability of the intermediate state can be ascribed to the inhibition of the catalytic activity. The imine species turns out to be the only possible one possessing the characteristic absorption peaks in a wavelength range (4a= 430 nm, 4b= 418 nm) compatible with the experimental value max= 422nm. This allows us to identify the inactivated species as the imine state (4a). The second slow step after the formation of the inactivated species is a product release from the active site. This somehow escapes the capabilities of our QM/MM model. Nonetheless, the reaction steps 4a -> 3a -> TS(3a, 5a) -> 5a could be traced and investigated. Indeed, we found that the associated activation barrier, G =G(TS(3a,5a)) -G(4a) = 8.8 kcal mol - 1 , is too low to be compared with the analogous barrier estimated from the kinetic rate (G2 ≠ = 22.7 kcal mol -1 ). This indicates that something is missing and that there should be an additional activation barrier to be overcome to access the product release. One possible explanation is that the carboxy group of the product is strongly anchored to the two base residues of Arg52 and Lys347; these strong interactions have to be destabilized somehow to make the release from the active Please do not adjust margins Please do not adjust margins site feasible. The final intermediate state before the FAD oxidation has been identified as the EFADH -state in the absence of a substrate. This conclusion is supported by the computed UV/Vis spectra. We have formerly shown that the key interaction in the sarcosine oxidation is the approach of the N sarcosine and C4a flavin atoms. 5 This is comparable to the nucleophilic attack of C3 CPG to the C4a flavin atom evidenced in the present study. The explicit and implicit influences from the polar mechanism is expected to stimulate investigations in other amine oxidoreductases.

Figure 1 .

 1 Figure 1. (A) QM/MM system used in the present study. (B) Schematic illustration of the active site of the monomeric sarcosine oxidase (MSOX). Atoms in the QM region are shown in black, and the green parts represent fragments of the embedding MM system. Hydrogen bonds in the initial state (state 1) are drawn in red broken lines.

Figure 3 .

 3 Figure 3. Schematic illustration of the intermediate states. CPG moieties are colored blue for easy identification. The green curved arrows show the movement of electrons. The dashed arrows showing the direct proton transfer between C2 and N in the CPG moiety are only helpful guides to connect the states.

Figure 2 .

 2 Figure 2. QM/MM optimized structures of the intermediate states. The letter following each number in states indicates a specific conformer. For the sake of clarity, only the atoms of the QM subsystem are shown.

Figure 4 .

 4 Figure 4. Free energy profile calculated at the QM/MM (UB3LYP-D3/TZVP|AMBER99) theoretical level. The green and blue colors refer to the different amine conformation in CPG along the reaction pathway.

Figure 5 .

 5 Figure 5. Computed UV/Vis spectra as provided by TDDFT (B3LYP/6-311++G**) calculations.

Scheme 3 .

 3 Scheme 3. Reaction mechanism of CPG in MSOX derived from the present QM/MM calculations.

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00 , 1 -3 | 5

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Acknowledgements

This research was supported by JSPS KAKENHI ground numbers 16KT0055, 17H04866, 18H05154, 19H05781 and JST, PRESTO Grant Number JPMJPR19G6, Japan. Numerical calculations were carried out under the support of (1) Multidisciplinary Cooperative Research Program in CCS, University of Tsukuba, (2) HPCI system research project (project ID: hp19110) using the computational resource of CX400 provided by the Information Technology Center in Nagoya University. M.B. thanks the HPC Mesocentera at the University of Strasbourg funded by the Equipex Equip@Meso project (Programme Investissements d'Avenir) and the CPER Alsacalcul/Big Data, and the Grand Equipement National de Calcul Intensif (GENCI) under allocation DARI-A6 A0060906092.