Amartya Ghosh

Katrin Kristjansdottir

Lars Hvam

Élise Vareilles

Measuring the Complexity of Product Configuration Systems

The complexity of product configuration systems is an important indicator of both development and maintenance effort of the systems. Existing literature proposes a couple of effort estimation approaches for configurator projects. However, these approaches do not address the issues of comprehensibility and modifiability of a configuration model. Therefore, this article proposes a metric to measure the total cognitive complexity of the configuration model corresponding to a product configuration system, expressed in the form of an UML class diagram. This metric takes into account the number and the type of attributes, constraints and the relationships between classes in an UML class diagram. The proposed metric can be used to compare two configuration models, in terms of their cognitive complexity. Moreover, a relation between development time for a PCS project and the total cognitive complexity of the corresponding configuration model is established using linear regression. To validate the proposed approach a case study is conducted where the cognitive complexity is calculated for two configuration models.

Introduction

Information technology tools, such as product configuration systems (PCSs), are widely used to handle the increased amount of information shared amongst customers, sales and production departments at companies, arising out of an increase in the demand of product customization [START_REF] Forza | Managing for variety in the order acquisition and fulfilment process: The contribution of product configuration systems[END_REF]. PCSs are knowledge-based IT systems which fulfil a configuration task. A configuration task is a special type of design activity [START_REF] Mittal | Towards a generic model of configuration tasks[END_REF] facilitated by a number of components, their corresponding properties and ports, and constraints which restrict the number of feasible combinations associated with the components [START_REF] Felfernig | UML as domain specific language for the construction of knowledge-based configuration systems[END_REF]. PCSs contain detailed information about the companies' offerings. The information included in the configuration models depend on the type of the configuration system and usually include different components, attributes and rules of how the different components can be combined. Generally, the PCSs are not standalone IT systems. These systems are linked to existing IT systems within the companies (e.g., ERP, CAD, PLM, PDM, and calculation systems) either through integrations and/or interfaces. Coupled with the inherent complexity of the product knowledge modelled into the system, the integrations to other IT systems will render these configuration systems to be highly complex.

Practitioners in the industry are interested in metrics for comparing different PCS [START_REF] Kristjansdottir | Complexity of Configurators Relative to Integrations and Field of Application[END_REF] and predicting the resource consumption required for developing, maintaining and extending the systems [START_REF] Aldanondo | Deployment of Configurator in Industry: Towards a Load Estimation[END_REF], [START_REF] Felfernig | Effort Estimation for Knowledge-based Configuration Systems[END_REF]. The approach proposed in [START_REF] Aldanondo | Deployment of Configurator in Industry: Towards a Load Estimation[END_REF] defines a load 1 Engineering Management Department, Technical University of Denmark, email: amgho@dtu.dk, katkr@dtu.dk, lahv@dtu.dk 2 Toulouse University, email: elise.vareilles@mines-albi.fr estimation function that takes into account the impact of the industry and the organization on the project and the size and complexity of the product under consideration. The activities associated with the PCS development project include modelling the product structure and programming this model into a configuration software. However, this approach does not explicitly take into the consideration the complexity of the configuration model, while estimating the load required. Another approach to estimating the costs associated with PCS projects is to calculate the functional size of the UML class diagram of the configuration knowledge base using the IFPUG Function Point Analysis (FPA) technique [START_REF] Felfernig | Effort Estimation for Knowledge-based Configuration Systems[END_REF]. This approach, however, is subjective in nature with regards to the definition of internal and external logical files (ILFs and ELFs). Moreover, the function point approach does not clarify the definition of one unit of function point [START_REF] Wang | Cognitive Complexity of Software and its Measurement[END_REF]. The parametric complexity approach proposed in [START_REF] Kristjansdottir | Complexity of Configurators Relative to Integrations and Field of Application[END_REF] involves calculating a metric on the basis of the number of business rules and the number of attributes, across two categories: field of engineering (sales, engineering and/or both) and the integration to other IT systems. However, the parametric complexity approach fails to take into account the complexity associated with the manner in which the configuration problem has been modelled into a PCS. A method to analyse the complexity of PCS is, therefore, needed.

This paper proposes a complexity metric that captures the different aspects associated with the PCS by focusing on the cognitive complexity of the configuration model. The metric can be used to effectively compare different PCS both developed on the same configuration software platforms or on different platforms. Also, the metric can be used to identify the impact of the complexity on the resource consumption for the development and maintenance activities associated with the PCS. Given that resources required for these activities are valuable and have limited availability, it is imperative that practitioners in the field have some metrics for predicting the extent of resource consumption required.

The proposed complexity metrics build on the approaches proposed in [START_REF] Felfernig | Effort Estimation for Knowledge-based Configuration Systems[END_REF] and [START_REF] Kristjansdottir | Complexity of Configurators Relative to Integrations and Field of Application[END_REF] by ascertaining the cognitive complexity of the UML class diagram associated with a given configuration problem. The proposed metric takes into account the effort required to understand and modify the way in which the PCS has been modelled, in terms of generalizations and aggregation structures, and the number and the type of business rules and attributes present in the configuration model.

The remainder of the paper is structured as follows. In Section 2 the concept of cognitive complexity known of software systems is introduced. The research methodology employed to carry out the analysis is explained in Section 3. Section 4 provides an overview of the mapping of the cognitive complexity metric of software systems to configuration models. Section 5 then presents the findings from applying the method in a case company. Finally, Section 6 discusses the results and provide guidance for further studies.

Theoretical Background

This section presents the theoretical background for the proposed complexity metric for configuration models. It provides an overview of the existing literature on the topic of cognitive complexity of software systems.

Cognitive complexity is a measure of the functional complexity associated with designing and understanding a software system, based on the basic control structures (BCSs) existing in the system [START_REF] Shao | A new measure of software complexity based on cognitive weights[END_REF]. BCSs are considered to the building blocks of any software system. They are a collection of fundamental flow control mechanisms which are necessary for constructing the logical architecture of a software system [START_REF] Wang | Cognitive Complexity of Software and its Measurement[END_REF]. Initially, Hoare et al. [START_REF] Hoare | Laws of programming[END_REF] identified three types of primitive commands (SKIP, ABORT and Assignment) and five types of more complex commands (sequential composition, non-determinism, conditional, iteration and recursion) in programming languages. Later, two further BCSs (function call, interrupt) were identified in system modelling by Wang [START_REF] Wang | The Real-Time Process Algebra (RTPA)[END_REF]. Considering the sequential BCS as being representative of a unit BCS, a different cognitive weight is assigned to each BCS. The cognitive weight of a BCS is considered to be proportional to the effort required by a user in understanding the functionality and the semantics of the BCS, relative to the sequential BCS.

Table 1 summarizes the BCSs and the corresponding cognitive weights: Existing literature proposes several approaches for calculating the cognitive complexity of programs written in object-oriented programming languages, based on the cognitive weights of the BCSs. Object-oriented programs comprise a number of classes, each of which consist of a number of attributes and methods, and are linked to other classes through aggregation, generalization or association structures. The overall complexity of object-oriented programs is obtained by calculating the cognitive complexity of the constituent classes based on the relationships between the classes. The class complexity (CC) is calculated by taking into consideration the cognitive complexity of the individual methods, which in turn are made up of the blocks of BCSs, and the constituent attributes [START_REF] Misra | A Suite of Cognitive Complexity Metrics[END_REF]. Therefore, the cognitive complexity of a method comprising q linear blocks of m layers of nesting BCSs with n linear BCSs in each layer, is calculated using the following equation ( 1):

(1) Where, MC: total cognitive weight of the method 𝑤𝑤𝑐𝑐(𝑗𝑗, 𝑘𝑘, 𝑖𝑖): cognitive weights of individual BCSs Moreover, the attributes of a class are assigned cognitive weights according to a categorization of the cognitive phenomena associated with their datatypes [START_REF] Arockiam | Attribute Weighted Class Complexity : A New Metric for Measuring Cognitive Complexity of OO Systems[END_REF]. The cognitive weights for the attribute categories are summarized in Table 2. The attribute complexity (AC) of a class is calculated by multiplying the number of attributes belonging to a particular datatype category and its corresponding cognitive weight. Therefore, for a class containing 'm' number of methods, with the i-th method having a complexity of MCi, and having an attribute complexity, AC, equation ( 2) shows the cognitive complexity of the class (CC).

(

) 2
The reusability of software code in object-oriented programming languages is facilitated through the concept of inheritance. However, the use of several levels of inheritance often has an adverse impact on the maintainability and comprehensibility of software systems [START_REF] Mishra | Object-oriented inheritance metrics in the context of cognitive complexity[END_REF], [START_REF] Harrison | Experimental assessment of the effect of inheritance on the maintainability of object-oriented systems[END_REF]. Therefore, a number of cognitive complexity metrics have been proposed to penalise the use of inheritance structures in OOPs [START_REF] Mishra | Object-oriented inheritance metrics in the context of cognitive complexity[END_REF], [START_REF] Misra | A Suite of Cognitive Complexity Metrics[END_REF].

At the class level, the cognitive complexity of a class, CCi, takes into account the number and complexity of the inherited classes, as shown in the following equation ( 3 Another approach to account for the presence of inheritance structures involves changing the way in which the total cognitive complexity of the program is calculated, depending on the level of inheritance of individual classes [START_REF] Misra | A Suite of Cognitive Complexity Metrics[END_REF]. In this case, if the classes are on the same level of inheritance, their cognitive complexity values are added together. However, if the classes are children of parent classes, then their values are multiplied. This is shown in the following equation ( 4 The cognitive complexity approach has been applied to empirically calculate the complexity of UML class diagrams. The cognitive complexity of UML class diagrams has been shown to be correlated to the generalization and association structures, with an increase in the number of classes and attributes leading to an increase in the cognitive complexity and also the time required to understand and modify the class diagrams [START_REF] Manso | Empirical Validation of Measures for UML Class Diagrams: A Meta-Analysis Study[END_REF]. This implies that, given the UML class diagram of a configuration model and, consequently, the cognitive complexity of the configuration model, the required man-hours for developing and maintaining the PCS can be estimated. In turn, this will make it possible for better resource planning for PCS projects, allowing more accurate business cases to be developed, prior to the initiation of projects.

Methodology

The authors have adopted the case study research method to calculate the complexity of a configuration model and, subsequently, propose a relation, which expresses the development time in terms of the proposed complexity metric. The case company is a world leader in catalysts and surface science. It offers a variety of catalysts and a complete range of proprietary equipment, spare parts, and consumables. The company first launched a PCS in 2013 and has since then been building up the configuration area at the company. Currently the company uses five PCSs in the company, while two configurators are under development. The PCSs used by the company support the sales process of both catalysts and equipment at the company and where the first PCS supporting the engineering process, or the detail design of an equipment is being tested. The complexity of the PCSs used at the company has quite variations but the lack of method for analysing the complexity makes it difficult both to predict maintenance effort for the different PCS in utilization at the company and development effort required for new PCS. Thus, the company's challenges were aligned with the research focus of the article.

In this study, the authors have analysed the configuration models pertaining to two PCSs. For each PCS, the following dataset was extracted from the configuration platform and used in the analysis: These parameters are utilized to calculate the cognitive complexity metric for each configuration model. Moreover, the information regarding the development time and maintenance time for both the PCSs were also collected, in order to establish a relation between the cognitive complexity metric and the development time and maintenance time. However, the time registrations for these PCSs are not accurately maintained by the company, thereby requiring an assessment of the reliability of the data. After an initial analysis of the data, coupled with discussions with the members of the configuration team at the case company, the authors decided to analyse the two PCSs for which the time registrations were accurate and reliable. The relation between the development time for the PCSs, the cognitive complexity metrics and the unknown time constants were framed in the form of an objective function. The objective functions were solved to obtain the values for the time constants, by means of linear regression.

•

Proposed Cognitive Complexity Metric for Configuration Models

As addressed earlier, existing literature proposes a number of approaches for measuring the cognitive complexity of OOPs. However, the application of this concept to UML class diagrams of product configuration models presents an important deviation from those pertaining to OOPs. As PCSs are knowledge-based systems, the complexity of business rules (BRs) have a vital impact on the development and maintenance efforts of these systems [START_REF] Felfernig | Effort Estimation for Knowledge-based Configuration Systems[END_REF]. In order to account for the impact of the BRs, the authors have assumed that each BR corresponds to a single method with a single block of layered BCS. Each constituent BCS of a BR has been assigned a cognitive weight, based on the classification proposed by Wang [START_REF] Wang | Cognitive Complexity of Software and its Measurement[END_REF]. Table 3 summarises the cognitive weights for BCSs for each BR. Thus, the cognitive complexity of a BR (BRC), consisting of m layers of nesting BCSs with nj linear BCSs in each layer, can be calculated using the following equation ( 5):

(5) Where, 𝑤𝑤𝑐𝑐(𝑗𝑗, 𝑖𝑖): cognitive weight of the i-th BCS in the j-th layer of a nesting BCS pertaining to a BR. nj: number of BCS in the j-th layer of a nesting BCS pertaining to a BR Another feature of UML class diagrams specific to configuration models is the cardinality of the classes representing the aggregation structure. This particular feature is accounted for by the presence of the iteration BCS. A nested BR containing an iteration BCS would only be invoked in cases wherein more than a single instance of a particular class is required to be created.

As mentioned earlier, the cognitive complexity of a class also comprises the cognitive complexity of the attributes. Table 4 shows the possible attribute domains present in the configuration platform used at the case company categorised according to the datatype categories mentioned in Table 2. Therefore, given a configuration model, the cognitive complexity of a constituent class (CCi), comprising 'm' methods, 'n' attributes and 'p' business rules, is calculated by adding the cognitive complexities of the methods (MCj), attributes (AC) and the business rules (BRCk), as shown in equation ( 6): [START_REF] Aldanondo | Deployment of Configurator in Industry: Towards a Load Estimation[END_REF] However, as the source codes of the configuration platforms (such as Tacton, Configit, SAP Configurator and so on) are generally confidential in nature and not available publicly, the authors decided to consider only the attribute complexity and the complexity of the business rules. Therefore, the final form of the cognitive complexity metric for a class used in the analysis is shown in equation ( 7). In case of the class Frame in Figure 1, the calculation for the attribute complexity is shown below in Table 5. For calculating the BRC for the class Frame, the nature of the BRs are established and the component BCSs are assigned their cognitive weights based on the categorization of BCSs. BR_1 comprises of a single layer of nesting BCS (if statement) consisting of a single assignment BCS within it. Therefore, the BRCBR_1 is calculated using equation ( 5 BR_2, on the other hand, is categorized as a standard function in the PCS software which has been used to model the configuration problem. Therefore, the business rule complexity of BR_2, BRCBR_2, is assigned the cognitive weight of 1. Therefore, the cognitive complexity of the class Frame, CCFrame, is calculated as shown below, according to the equation [START_REF] Felfernig | Effort Estimation for Knowledge-based Configuration Systems[END_REF].

CCFrame = ACFrame + (BRCBR_1 + BRCBR_2) = 3+(2+1) = 6
Table 6 summarizes the results for the remainder of the classes shown in Figure 1. Depending on the inheritance structure, the total complexity of the configuration model (TC) can be calculated by a combination of the cognitive complexities of the constituent classes, as shown in equation ( 8). Therefore, the total complexity of the configuration model shown in Figure 1 is given by: TC = 6+3+5 = 14. Given the value of the total cognitive complexity metric, TC, for a particular configuration model, the authors propose a relation, as shown by equation ( 9), to estimate the development time (XTime) and the maintenance time for the model in man-hours.

𝑋𝑋𝑇𝑇𝑖𝑖𝑇𝑇e = 𝑎𝑎 + 𝑏𝑏. 𝑇𝑇C (9)
Where, 𝑎𝑎: development time constant (in man-hours) 𝑏𝑏: development time constant (in man-hours) associated with a configuration model having a cognitive complexity of 1.

Taking into consideration the development times and the cognitive complexities of the two configuration models for which the time registration is available and accurate, the values of the time constants, a and b, are calculated, using linear regression.

However, as the value of TC is often not readily available before a configuration model has been fully developed, an estimated development time, 𝑋𝑋𝑋𝑋𝑇𝑇, can be calculated for a particular configuration model if the number of constraints and the number of attributes, as shown in equation [START_REF] Hoare | Laws of programming[END_REF], or the number of classes, as shown in equation [START_REF] Wang | The Real-Time Process Algebra (RTPA)[END_REF], are known.

𝑋𝑋𝑋𝑋𝑇𝑇 = 𝑎𝑎 + 𝑏𝑏. ({#𝑎𝑎ttribute. AC𝑎𝑎v + #BR. BRC𝑎𝑎v}) (10)
𝑋𝑋𝑋𝑋𝑇𝑇 = 𝑎𝑎 + 𝑏𝑏. (#class. CC𝑎𝑎vg) (11)
The following section presents the results obtained from the application of the proposed metrics on two configuration models at the case company.

Results from the Case Study

As explained earlier, the authors have only considered two PCSs, for which reliable and accurate time registration data was available, for their analysis. To calculate the cognitive complexity metric of the corresponding configuration models, the following data was extracted from the configuration platform used at the case company: Based on this data, the total complexity, TC, of the two PCSs were calculated. The results, along with the input data are summarised in Table 7. Table 5 shows considerable differences in both the parametric and the total cognitive complexities (TC) of the analysed PCSs. This result is aligned with the initial scoping of the research of selecting PCSs representing both high complexity values and low complexity values. Moreover, three additional metrics were also defined for each model, as shown in Table 8. These metrics include the average values of the attribute complexity (ACavg), business rule complexity (BRCavg) and the class complexity (CCavg). The values for ACavg and BRavg for each of the models do not take into consideration the class structure for the configuration models.

•
Based on these three metrics, the estimated average attribute complexity, average business rule complexity and average class complexity values for a configuration model developed at the case company are 1.97, 5.48 and 89.65 respectively. However, the results also show that there is a great variation of the complexity metrics calculated for the two systems, thus, the average complexity might not be provide us with the best possible estimates for the complexity of configuration models at the case company. Moving forward, more PCSs at the case company will have to be analysed to obtain results that are more indicative of the average PCS complexity at the company. For the calculation of the time constants, a and b, pertaining to the relation between the cognitive complexity of the two configuration models and the development time for the corresponding PCSs, as expressed in Equation ( 9), the development times (in man-hours) are noted in Table 9. Therefore, given the value of the total cognitive complexity of a configuration model, TC, the estimated development time of a PCS at the case company can be calculated as:

𝑋𝑋𝑇𝑇𝑖𝑖𝑇𝑇e = 8.065 + 0.227𝑇𝑇C (12)
The ACavg, BRCavg and CCavg are obtained from the data for the PCSs that have been analysed in this paper. Therefore, the final form of the equations [START_REF] Hoare | Laws of programming[END_REF] and [START_REF] Wang | The Real-Time Process Algebra (RTPA)[END_REF] to estimate the development time of PCSs in man-hours at the case company, given the expected number of attributes and business rules or the expected number of classes, are presented in equations ( 13) and ( 14

Therefore, the following parameters of the configuration model are the pre-requisites for calculating an estimated development time for the PCS:

•

The estimated number of classes, or •

The estimated number of business rules and attributes.

Moreover, based on the hours used for development the required hours for maintenance can be calculated. Based on interviews in the company it is estimated that 30% of the total development hours are required on a yearly base for the maintenance activities.

Discussions and Conclusions

This paper proposes a metric for evaluating the complexity of a PCS, by taking into the consideration the UML class diagram of the corresponding configuration model. The proposed cognitive complexity metric takes into the account the effort required to understand and modify the way in which the configuration problem has been modelled. Furthermore, the authors also investigate the relation between the effort in man-hours required for the development of a new PCS and the proposed complexity metric. The results obtained in the present article aim to contribute to the field of PCS complexity and the impact of PCS complexity on the effort estimation associated with the development and maintenance of PCS projects.

The proposed metric for calculating the cognitive complexity of a configuration model builds on research in the fields of the cognitive complexity of object-oriented software systems [START_REF] Wang | Cognitive Complexity of Software and its Measurement[END_REF], [START_REF] Shao | A new measure of software complexity based on cognitive weights[END_REF], [START_REF] Misra | A Suite of Cognitive Complexity Metrics[END_REF], [START_REF] Arockiam | Attribute Weighted Class Complexity : A New Metric for Measuring Cognitive Complexity of OO Systems[END_REF], complexity of PCS [START_REF] Kristjansdottir | Complexity of Configurators Relative to Integrations and Field of Application[END_REF]- [START_REF] Felfernig | Effort Estimation for Knowledge-based Configuration Systems[END_REF] and the cognitive complexity of UML diagrams [START_REF] Manso | Empirical Validation of Measures for UML Class Diagrams: A Meta-Analysis Study[END_REF]. The presence of business rules and a lack of material on the source codes of commercial configuration platforms render the direct application of existing cognitive complexity metrics to configuration models unviable.

By having a more standardized way of analysing the complexity of a configuration model should enable both more accurate resource estimations and allow for a comparison of different configuration models. The authors adopted a structured approach to analyze the cognitive complexity of a configuration model and relating it to the development and maintenance efforts. First, an UML class diagram is analysed, which should give information regarding total complexity of a configuration model (based on number of classes, the number and type of attributes, number and type of business rules). Second, the average values of the attribute complexity (ACavg), business rule complexity (BRCavg) and the class complexity (CCavg) are calculated. Third, linear regression is used to analyse man-hours for already developed systems to predict the future workload for new PCS.

The proposed method is validated in a case company where two different PCS were selected. The two PCS represent both PCSs with high and low parametric complexity. The proposed metric for analysing the cognitive complexity of the PCS confirmed the variation in the complexity. Further, by analysing the man-hours used for developing the systems, a function of total complexity and man-hours is used to predict the workload for a new PCS. The testing of the proposed method confirmed its usability. Further, testing is planned with in the case company where all the PCSs will be analysed in more detail, in order to verify the accuracy of the estimated development effort in man-hours when starting new PCS projects.

There are a few limitations to the research presented in this article. The proposed cognitive complexity metric primarily addresses only those configuration models which can be presented in form of an UML diagram. Further research will have to conducted in order to investigate the viability of applying cognitive complexity concepts to declaratively modeled products. Moreover, in case of declarative BRs, the authors have used their discretion to assign cognitive weights to such BRs. In certain cases, the procedural equivalent of the declarative BR is assigned the corresponding cognitive weight, whilst in others, the authors have considered the declarative BR to be either a standard function of the PCS or a user defined function.

This study focuses on the complexity of the configuration model. This means that the complexity resulting from integrations to other IT systems are not considered. Also, complexity for generating user interfaces and output documents are not taken into the account in the present study. Future work will, therefore, focus on including these parameters to better capture the overall complexity associated with a PCS and not only the complexity of the configuration model.

  of the i-th class due to inheritance : cognitive complexity of an inherited class of class i 𝑘𝑘: the number of inherited classes of class i 𝑙𝑙: the number of constituent methods in class i : the cognitive complexity of the j-th method of class i

  : cognitive complexity of the program WCC𝑗𝑗𝑘𝑘: cognitive complexity of k-th class at level j of inheritance.

  Model properties and statistics o Number of business rules o Number of attributes o Number of classes • Documentation of the configuration model o Class structure o The attributes and their domains for each class o The business rules for each class

( 7 )

 7 As an example to illustrate the various calculations, an excerpt of an UML class diagram, depicting the configuration model pertaining to a bicycle, is presented in Figure 1. The model comprises three classes (class Frame, class Suspension and class Fork). The model comprises two aggregation relationships (wherein class Suspension and class Fork are "parts of" the class Frame) but no inheritance structures. The corresponding cardinalities, attributes and business rules are also shown in the figure.

Figure 1 :

 1 Figure 1: Descriptive example of bicycle

  ) as shown below: BRCBR_1 = (Cognitive weight of if statement) * (Cognitive weight of assignment statement) BRCBR_1 = 2*1 = 2

  cognitive complexity of the k-th class at the j-th level of inheritance.

  The UML class diagrams • The attributes and their datatypes for each class • The business rules associated with each class • Statistics pertaining to the overall configuration model: o Number of classes in the UML class diagram o Total number of attributes in the UML class diagram o Total number of constraints in the UML class diagram

  ) respectively: 𝑋𝑋𝑋𝑋𝑇𝑇 = 8.065 + 0.227({#attribute × (1.97) + #BR × (5.48)}) (13) 𝑋𝑋𝑋𝑋𝑇𝑇 = 8.065 + 0.227({#𝑐𝑐lass × (89.65)})

Table 1 :

 1 Cognitive weights of basic control structures (Adapted fromWang, 2006 [9]

Category of BCS BCS Cognitive Weight

	Sequential	Sequence (SEQ)	1
	Branch	If-Then-	2
		Else (I-T-E)
		Case	3
	Iteration	For-do	3
		Repeat-until	3
		While-do	3
	Embedded	Function Call (FC)	2
		Recursion (REC)	3
	Concurrency	Parallel (PAR)	4
		Interrupt (INT)	4

Table 2 :

 2 Cognitive weights assigned to attributes (Adapted from Arockiam and Aloysius[START_REF] Arockiam | Attribute Weighted Class Complexity : A New Metric for Measuring Cognitive Complexity of OO Systems[END_REF])

	Attribute	Associated Cognitive	Cognitive Weight
	Datatype	Phenomena
	Primary	Sub-concious cognitive	1
		function
	Derived	Meta cognitive function	2
	User-defined	Higher cognitive function	3

Table 3 :

 3 Cognitive weight of BCS for BR

	Category of BCS	BCS	Cognitive Weight
	Assignment	Assignment (ASS)	1
	Branch	If-Then-Else (I-TE)	2
		or implication
	Iteration	Iteration	3
	Embedded	User Function Call	2
		(UFC)
		Standard Function	1
		Call (SFC)

Table 4 :

 4 Cognitive Weights of Attribute Datatypes

	Datatype Category Attribute Domain	Cognitive Weight
	Primary	Integer, Float,	1
		Boolean
	Derived	Named Domain	2
	User-defined	Function, Class	3

Table 5 :

 5 Descriptive example of bicycle: Calculation of attribute complexity

	Attribute	Domain	Datatype	Cognitive	Attribute
	Name		category	Weight	Complexity
					(AC)
	Size	Integer	Primary	1
	Material	Named	Derived	2	1+2 = 3
		Domain

Table 6 :

 6 Descriptive example of bicycle: Calculation of class complexity

	Class Name	BRC	AC	CC
	Frame	3	3	6
	Suspension	0	3	3
	Fork	1	4	5

Table 7 :

 7 Complexity calculations and statistics for the two PCSs analysed

	Model #Classes #Attributes #Rules	Parametric complexity	Cognitive complexity
	PCS_1 82	1462	940	2402	9731
	PCS_2 27	334	262	596	1637

Table 8 :

 8 Additional metrics representing the complexity of the PCS

	Model	ACavg BRavg	CCavg
	PCS_1	2.24	6.87	118.67
	PCS_2	1.71	4.08	60.63
	Overall average for any PCS	1.97	5.48	89.65

Table 9 :

 9 Development time in man-hours for the analysed PCS in the case company

	Model	Development Time (in man-hours)
	PCS_1	2219
	PCS_2	380


Professor Mir Wais Hosseini

Lionel Tarrago
email: lioneltarrago@msn.com

Camille Modolo

Mehdi Yemloul

Viviane Robert

Pierre Rousselot-Pailley

Thierry Tron
email: thierry.tron@univ-amu.fr

Controlling the polymerization of coniferyl alcohol with cyclodextrins

The mono-electronic oxidation of coniferyl alcohol leads to phenoxy radicals and ultimately to the synthesis of dimeric lignans. Coniferyl alcohol and lignans are all potential guests for cyclodextrins (CDs) to form noncovalent host-guest inclusion complexes. Here, the influence of CDs with different cavity volumes (i.e. α, β or γCD) on the laccase-driven oxidation of coniferyl alcohol is studied. We are clearly showing that βCD interacts with the lignan products and selectively prevent their further oxidation by the enzyme. Moreover, amongst the three lignans generated the system made of a laccase and βCD allows a selective enrichment of pinoresinol, a behaviour somehow mimicking that of plant dirigent proteins.

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! Introduction

Natural molecules such as sugars and amino acids are produced in cell as pure enantiomers by dedicated enzymes. One peculiar situation is however found in the synthesis of some plant metabolites (scheme 1) deriving from the monoelectronic oxidation of the lignol coniferyl alcohol (as the result from the activity of oxidases such as laccases) which leads initially to phenoxy radicals. 1 In vitro a bimolecular radical coupling results in the transient accumulation of a mixture of (±)-dehydrodiconiferyl alcohols ( 2), (±)-pinoresinols (3), and (±)-guaiacylglycerol 8-O-4-coniferyl alcohol ethers (4) prior a further polymerization. In plants however either the (+)-or (-)enantiomer of pinoresinol is preferentially formed. 2 Regio-and enantioselectivity are provided by dirigent proteins (DP) such as FiDIR1 and AtDIR6, which have been shown to be respectively responsible for the formation of (+)-pinoresinol in Forsythia intermedia 2a and of (-)-pinoresinol in Arabidopsis thaliana 2b . These proteins, which might not possess a catalytic center per se, are proposed to act as a scaffold interacting with radicals of coniferyl alcohol to direct the bimolecular coupling through a yet undetermined host/guest mechanism. In a bioconversion, the combined use of these proteins and a laccase or a chemical oxidant such as ammonium persulfate allows the enantioselective enrichment of pinoresinol. [START_REF] Scott | [END_REF] Produced from the enzymatic degradation of starch the naturally occurring cyclic oligosaccharides cyclodextrins (CDs) share with DPs the ability to host guest molecules. Most commons CDs are made of 6 (αCD), 7 (βCD) or 8 (γCD) α-Dglucopyranoside units linked by α-1,4 bonds. [START_REF] Hinsberg | Kinetiscope™, a stochastic simulator v1[END_REF] They have the form of truncated cones in which the hydroxyl groups are exposed to the solvent, making the exterior of the cone hydrophilic whereas the interior, considerably less hydrophilic than the aqueous environment, is able to host hydrophobic molecules. While the height of the torus remains constant (0.79 nm), the cavity diameter varies from 0.47-0.53 nm for the αCD, 0.6-0.65 nm for the βCD and 0.75-0.83 nm for the γCD. The internal cavity volume of α, β and γCD directly influences the size of the guest a CD molecule can accommodate. [START_REF] Hinsberg | Kinetiscope™, a stochastic simulator v1[END_REF] Because of these properties, CDs are used to enhance the solubility and bioavailability of numerous Notably, in enantioselective synthesis, CDs or their derivatized forms have been shown to increase the enantiopure production of β-amino alcohols 5 and to facilitate the enantioselective N-acylation of primary amines 6 . CDs have been also shown to significantly improve enantiomeric excess in enzyme-catalysed reactions, such as the peroxidase catalysed synthesis of binaphthyl derivatives from naphtols and the esterase catalysed synthesis of the S-enantiomer of the anti-inflammatory drug naproxen.

7

In this work, we studied the influence of CDs with different cavity volumes on the laccase-driven oxidation of coniferyl alcohol in bimolecular systems in which the substrate is mixed with an excess of CDs. We are clearly showing that while the dimerization of coniferyl alcohol is unaffected by the presence of CDs, the βCD cavity is stabilizing the lignan products and prevent their further oxidation by the enzyme. Moreover, amongst the three lignans generated the combination of laccase with βCD allows a selective enrichment of pinoresinol, a behaviour somehow reminiscent of lignan synthesis in the presence of plant dirigent proteins.

Results and Discussion

In 1)). In our experimental conditions lignans 2 and 3 account for more than 80% of the dimers formed (Fig. 1, graphs ( 2) and ( 3)).

‡ The neosynthesized lignans containing phenolic moieties (i.e. a 2metoxyphenol), their concentration is rapidly high enough to compete with 1 as substrates for the LAC3 enzyme. Thus, after reaching a maximum (equilibrium between formation and disappearance) the concentration of lignans was significantly decreasing with initial velocities of ca. 0.16 x 10 -3 mol.L -1 .h -1 (2) and ca. 0.10 x 10 -3 mol.L -1 .h -1 (3) ((Fig. 1, graphs ( 2) and ( 3)). As the reaction proceeds through mono-electronic oxidations, these observations are consistent with a further oxidation of the dimeric lignans produced from coniferyl alcohol oxidation into polymers.

Evolution of the oxidation products was differentially influenced by the presence of α, β or γCD in the reaction mixture (Fig. 1). Addition of αCD to the reaction mixture had influence neither on the oxidation of 1 nor on that of the neosynthesized lignans. To the contrary, the presence of CDs with a larger cavity volume had a marked effect on the disappearance of the reaction products maintaining the concentration of the lignans 2 and 3 fairly stable around 80 to 85% of the maximum values for several hours without apparently affecting the oxidation rate of 1 (Fig. 1). Thus, addition of βCD to the reaction mixture is stabilizing lignans, probably forming a β-CD:lignan complex that is significantly slowing down lignans oxidation by the enzyme (vide infra). In the presence of γCD, the stabilization effect is clearly less pronounced as apparent initial rates of lignans oxidation were three times faster in the presence of γCD than in the presence of βCD (ca. 0.09 x 10 -3 mol.L -1 .h -1 vs. 0.03 x 10 -3 mol.L -1 .h -1 and 0.06 x 10 -3 mol.L -1 .h -1 vs. 0.02 x 10 -3 mol.L -1 .h -1 for 2 and 3 respectively). Overall, in these experiments β and γCDs have apparently no significant effect on the rate of oxidation of 1

Please do not adjust margins Please do not adjust margins whereas they have a marked effect on the stabilization of lignans. -3 M) of either βCD (black squares) or γCD (black triangles). Oxidations were monitored by RP-HPLC. Fits (dashed lines) were obtained using a single decay (exponential) model.

Both the apparent complexity of the kinetics due to an oxidation of the products concomitant to their generation and the absence of exploitable data on the fate of lignan 4 lead us to further study the oxidation of pure lignans (see Supplementary Information for details about the origin of lignans). In the absence of CD, 3 is oxidized by laccase at a significantly faster rate than 2 and 4 (i.e. 1.3 x 10 -3 mol.L -1 .h -1 vs 0.7 x 10 -3 mol.L -1 .h -1 and 0.6 x 10 -3 mol.L -1 .h -1 respectively) the kinetics of oxidation of which were otherwise similar (Fig. 2). On the other hand, lignans oxidation rates are globally slower than the rate of oxidation of 1 (compare graph (1) from Fig. 1 and data (black circle) from Fig. 2). Amongst different factors, this might be mainly linked to differences in redox potentials between lignans and 1 (for example E° 1 -/1 • = 0.48 V vs SHE) 9 . Cleared of the step corresponding to the dimerization of 1, the effects of CDs on laccase-mediated oxidation of 2, 3 or 4 are simpler to analyse. Regardless of their specific oxidation rates, the oxidation of each lignan was similarly slowed down in the presence of β (0.04 h -1 for all lignans) or γCD (0.08 to 0.1 h -1 ) suggesting a similar mode of interaction of the three different lignans with each of the CDs. As observed previously for the oxidation products of 1 (Fig. 1), γCD was less effective than βCD in protecting lignans from oxidation.

The ability of a CD to form an inclusion complex with a guest molecule is function both of a steric factor (the relative size of the CD cavity to the size of the guest) and of a thermodynamic factor (a driving force bringing the guest into the cavity).

10

Altogether, the differential effects induced by α, βCD or γCD on coniferyl alcohol and lignans oxidation match well both the physico-chemical properties of guests and CDs structural differences (i.e. cavity volume and rigidity). Lignans 2 to 4 contain each at least one aromatic 2-metoxyphenol moiety inherited from their precursor the coniferyl alcohol molecule (1) (see scheme 1). The molecular volume of 2-metoxyphenol is estimated to be roughly 180 Å [START_REF] Hinsberg | Kinetiscope™, a stochastic simulator v1[END_REF] . Although an α-CD:coniferyl alcohol inclusion complex has been postulated from 1D 1 H NMR experiments 11 it seems that the internal cavity of αCD (174 Å 3 ) might be eventually too small to stably accommodate neither the substrate nor the lignans. On the other hand, γ (427 Å 3 ) and β (262 Å 3 ) CDs are both likely capable to accommodate molecules of the volume of guaiacol and larger.

As γCD is both larger and more flexible than βCD, γCD:lignan complexes are potentially less stable than βCD:lignan complexes and that can account for observed kinetic differences. The absence of any "CD effect" on the oxidation kinetics of coniferyl alcohol (1) suggests that CDs may have a significantly less affinity for 1 than for lignans. Excepting αCD the cavity of which is probably too small (vide supra), γ and βCD cavities could be too large to stabilize 1. Beyond the internal CD cavity volume, a simple examination of theoretical values describing the hydrophobic character and the water solubility of the ligand molecules point 1 as the least favourable ligand for forming an inclusion complex with CDs amongst the molecules we tested (3>2>4>1).

12 CD:guest complexes were studied by Please do not adjust margins Please do not adjust margins

In addition, plotting the extend of the shifts as function of the evolution of the molar ratio between the CD (β or γCD) and the guest suggested a 1:1 stoichiometry for all the CD:guest complexes studied (see Fig. SI3). Next, we used Rotating frame nuclear Overhauser Effect SpectroscopY (2D-ROESY) experiments to further characterize 1, 2, 3 and 4: βCD inclusion complexes. Highlighting intra and inter-molecular spatial proximity (below 6Å) the Nuclear Overhauser Effect is widely used for the characterization of host-guest intermolecular interactions. [START_REF] Schneider | [END_REF] Globally, disregarding relaxation and molecular motions, in the phase sensitive 2D-ROESY experiments [START_REF] Schneider | [END_REF] the integrated intensity of the cross-peaks is directly correlated with the inter-nuclear distance of the two observed protons. Beyond the observation of 1 H chemical shift displacements of host and/or guest molecules as often found in descriptions of ligand:CD complexes, this approach allows a more accurate description of inclusion complexes classifying interatomic distances from each βCD proton. For each complex, we studied the cross peaks involving H'3 and H'5 protons from the inside of the CDs cavity and the H'6 proton located out at the narrow rim (crown). 2D-ROESY spectra in which the intermolecular cross-peaks are highlighted are presented in supplementary information (Fig. SI4 andSI5). These NMR data are consistent with a potential insertion of lignans 2, 3 or 4 into the βCD cavity and their stabilization at the narrow rim. A scheme of a potential inclusion complex reflecting correlations observed between protons H2, H5, H6 of 3 and protons H'3, H'5, H'6 of βCD is proposed in Figure 3. However, as CD may also form non-inclusion complexes with guest molecules, 3 a stabilization of lignans at the narrow rim but outside the cavity cannot be formally ruled out. Whatever their structure (i.e. inclusion or non-inclusion), βCD:guest complexes stabilize lignans thereby offering them a protection against oxidation.

Considering the above results, only βCD was further investigated. Proportions of lignans 2, 3 and 4 derived from the oxidation of 1 were found insensitive to a variation of the β-CD concentration (0-13 10 -3 M range). Whereas in several cases of catalysed reactions the presence of βCD has been shown to influence the selectivity 5-7, 15-19 , there is here no selectivity in the oxidation of 1 (as assessed by separation of the lignan products on a chiral column) simply because 1 is not (or too weakly) interacting with the CD. Besides, amounts of lignans remaining non-oxidized in the reaction mixture were found to follow a saturation profile as the concentration of βCD increased (Fig. 4). -1 ) at 30°C in the presence of variable concentrations (0-13 x 10 -6 M) of βCD for 6 hours. C = lignan concentration in the absence of βCD; C β = lignan concentration in the presence of βCD. Fits (dotted lines) were obtained using a one-phase association (exponential) model.

Comparatively, the amplitude of the variation in dimer concentrations in the presence of βCD versus in the absence of βCD is higher for dimer 3 than for dimer 2 (note that the concentration of 4 was too low be properly analysed). Since oxidation rates of lignans 2 and 3 obtained in the presence of βCD are quite similar (see Fig. 2), this behaviour is totally attributable to differences in oxidation rates of the lignans by the enzyme alone. On the other hand, the protective effect of βCD on lignan oxidation decreased as the initial concentration of 1 increased (Fig. SI6). This is both related to the rate of lignan synthesis and to the formation of lignan:CD complexes that is limited by the concentration of βCD (12-13 x 10 -3 M). With a LAC3 apparent Michaelis constant (K Mapp ) value estimated around 10 x 10 -3 M for 1, the rate of lignans formation is likely not maximal at low concentrations of 1 (e. g. -3 M). All lignans produced are probably forming a complex with βCD molecules which protects them from a further oxidation by LAC3. As the concentration of 1 increases, lignans accumulate and there is a competition between lignans:βCD complexes formation and oxidation of lignans by LAC3.

Entry

CDs are known to interact with the surface of macromolecules, a property often used to stabilize these objects. 20 Beyond a sequestration of the substrate 21 that is apparently here not influencing the fate of 1 (vide supra), a direct laccase:CD interaction was challenged. Whether or not βCD interferes with the oxidation of 1 by LAC3 (pseudo competition) was tested recording enzyme kinetics in the presence of increasing concentrations of βCD. βCD had no influence on initial rates of consumption of 1.

Neither it has an influence on initial rates of production of dimers as dimerization occurs through a radicalradical coupling independent of the presence of the enzyme. Therefore, in the oxidation of 1, βCD is not a modulator of the laccase activity neither through the formation of a complex with 1 or through a direct CD:enzyme interaction. This leaves that the observed stabilisation of the dimers is entirely due to their interaction with the βCD.

Experimental

All chemicals were purchased from Sigma-Aldrich and used as received except for βCD which was recrystallized twice in 60 % ethanol. The laccase LAC3 (from Trametes sp C30) 8a was produced in Aspergillus niger and purified as previously described 8b . Oxidation of coniferyl alcohol was performed with laccase at 30°C in Britton-Robinson buffer adjusted at pH 5.0 and oxidation products were separated by reverse phase HPLC. All NMR experiments were performed at 298K in D 2 O on a Bruker Avance III 600MHz spectrometer, equipped with a 5mm triple resonance high resolution probe. All NMR datasets were processed in TOPSPIN 3.2 version (Bruker BioSpin, Germany).

Conclusions

The use of cyclodextrins in the laccase catalysed oxidation of coniferyl alcohol allows a control of the polymerisation by a stabilisation of the dimers resulting from radical coupling.

Stabilisation goes through complexes depending on the size of the CD cavity and is maximum for βCD. Whereas a CD:coniferyl alcohol inclusion complex is not forming in the catalytic conditions used, all three dimeric lignans are protected from further oxidation by the enzyme through a complexation by CDs. As the oxidation rate of the unprotected (±) pinoresinol is faster than that of the other lignans, the formation of a complex with βCD induces an apparent bias in the relative proportions of dimers. So, amongst the three lignans generated the laccase-βCD system allows a selective enrichment of pinoresinol, a behaviour somehow resembling that of plant dirigent proteins. 2 Overall, results obtained from this study point a selective interaction of CDs with lignans and open the possibility to use CDs to control the polymerization process of lignans or related phenolic molecules for the synthesis of molecules of interest.

Notes and references ‡ In the conditions chosen for a maximum separation of 2 and 3, peaks of 1 (decreasing) and 4 (increasing) were coincidental, both preventing a precise follow up of the kinetics of the appearance of the minor product 4 and introducing a bias in the evaluation of the concentration of 1. Although the effect is minor for the interpretation of the kinetics for 2 and 3 this has to be stated here.

Supplementary Information

Enzymes and chemicals

The laccase LAC3 (from Trametes sp C30) was produced in Aspergillus niger and purified as described previously. 1 Protein concentration was estimated by UV-visible spectroscopy using an ε 600 nm = 5 x 10 3 M -1 •cm -1 for the T1 copper. Laccase activity of the purified protein solution was assayed using 2,2'-azino-bis(3-ethylbenzthiazoline-6-sulphonic acid) (ABTS). One unit (U) of laccase oxidizes one micromole of ABTS per minute.

Alpha-cyclodextrin (αCD), beta-cyclodextrin (βCD) and gamma-cyclodextrin (γCD) were obtained from Aldrich or TCI Europe. Beta-cyclodextrin (βCD) was recrystallized twice in 60 % ethanol. Dehydrodiconiferyl alcohols ( 2) and (±)-pinoresinols (3) were obtained from the bioconversion of coniferyl alcohol (1) (purchased from Sigma France) catalysed by the enzyme LAC3, purified by preparative chromatography (silica) and characterized by 1 H NMR and mass spectrometry. All other chemicals were purchased from Sigma France.

Synthesis of (±)-guaiacylglycerol 8-O-4-coniferyl alcohol ethers (4)

4 was obtained by oxidation of 1 in the presence of silver oxide (Ag 2 O) following a protocol described Kishimoto et al., 2015. 2 The product of interest was purified by preparative chromatography (silica) and characterized by 1 H NMR and mass spectrometry.

Coniferyl alcohol oxidation in the presence of CD

Oxidation of coniferyl alcohol was performed at 30°C in Britton-Robinson buffer adjusted at pH 5.0 and oxidation products were detected by reverse phase HPLC. A typical reaction mixture (1 mL) contained LAC3 (5 U/L) and coniferyl alcohol (2.5 10 -3 M) in the absence or presence of CD (up to 12 10 -3 M). The reaction proceeded for 8-hours and was initiated by the addition of the enzyme. For each time-point, the reaction was stopped by mixing 100-µL aliquot to 100 µL acetonitrile containing 2.85 mM benzophenone. 30 µL was injected on C18 column (EC150/4 Nucleosil® 100-5-18 Macherey-Nagel™) and analyzed by HPLC (Waters™ Alliance® 2690/2690D Separations Module) with the following gradient: solvent A water containing 3% acetic acid, solvent B acetonitrile; t=0min 90%A 10%B, t=5min 90%A 10%B, t=25 min 50% A 50% B, t= 27 min 50% A 50% B, t=28 min 90%A 10% B, t=30 min 90%A 10%B. Coniferyl alcohol, dehydrodiconiferyl alcohol, pinoresinol and benzophenone were eluted at 4.0 min, 6.6 min, 8.2 min and 16.6 min, respectively. Quantity was normalized using benzophenone as internal reference.

Apparent K M and k cat values were obtained from the initial rate (v), enzyme concentration (E) and substrate concentration (S) according to the equation v = k cat E S/(K M + S). Inhibition kinetics data were obtained using appropriate equations. All data were determined using non-linear regression fitting using Prism software, Graphpad, San Diego, (CA). Because laccase catalysis involves two substrates and the [O 2 ] was invariant and assumed to be saturating in this study, the measured K M for the various substrates used should be considered apparent. Because of the assumption that 100% of the laccase participated in the catalysis as active enzyme, the measured k cat should also be considered apparent.

Fitting kinetics

The oxidation of coniferyl alcohol (1) by the enzyme laccase is a mono-electronic process leading to the transient formation of a radical species (1 • ) (eq. 1). Radical molecules recombine to give dimers 2, 3 and 4 according to eq. 2. Dimers are themselves subsequently oxidized by the enzyme (eq. 2, 4, 5) in a reaction similar to the oxidation of 1.

Kinetic data presented in Figure 1 from the main article were simulated using the stochastic kinetics simulator Kinetiscope (freeware) [START_REF] Hinsberg | Kinetiscope™, a stochastic simulator v1[END_REF] . In the simulation, we introduced:

• the initial concentration of coniferyl alcohol [1] = 2.5 10 -3 M • rate constants from (eq. 1, 3, 4, 5) initially derived from experimental data presented in Fig. 1 and Fig. 2 from the main article:

k 1 = 3.3 h -1 ; k 2 = 0.3 h -1 ; k 3 = 0.5 h -1 ; k 4 = 0.25 h -1
• a bi-molecular constant k dim from (eq. 2) arbitrary set to a value of >> k 1 , k 2 , k 3, k 4 (i.e.10 6 M -1 .

h -1 ). With this approximation we recognize the recombination of radicals as a process considerably faster than oxidation steps and we do not distinguish the formation of each dimer 2, 3 and 4 (eq. 2).

The model obtained (Fig. SI1) is compatible with experimental data (Fig. 1 main text).

= 3.3 h -1 ; k 2 = 0.3 h -1 ; k 3 = 0.5 h -1 ; k 4 = 0.25 h -1 . 1 1 • n1 • m2 + k3 + l4 2 2 • 3 3 • 4 4 • (eq. 1)
(eq. 2)

(eq. 3)

(eq. 4)

(eq. 5)

-H + -e - -H + -e - -H + -e - -H + -e - k 1 k 2 k 3 k 4 k dim 3
Eventually, kinetics of the two successive oxidations leading to the formation and to the disappearance of each dimer (see Fig. 1 panels 2 and 3 main text) can be fitted using the simple model: treated as a succession of order 1 kinetics in which the dimerization step is not influencing the rate (i.e.

k dim >> k 1 , k 2 ). Y=((a * k 1 )/( k 2 -k 1 )) * (exp(-k 1 * X)-exp(-k 2 *X))
with k 1 = rate constant for the oxidation of the alcohol and k 2 = rate constant for the oxidation of the dimer.

Determination of the apparent association constant and complex structure by NMR

All experiments were performed at 298K in D 2 O on a Bruker Advance III 600MHz spectrometer, equipped with a 5mm triple resonance high resolution probe. All NMR datasets were processed in TOPSPIN 3.2 version (Bruker BioSpin, Germany). Proton NMR spectra were acquired with a spectral width of 6000 Hz and relaxation delay of 2s during which a water pre-saturation was applied. The stoichiometry for all the CD:guest complexes was studied plotting the extend of the shifts as function of the evolution of the molar ratio between the CD (β or γCD) and the ligand (Job Plots). Plots for βCD complexes are given in Figure SI3. For complex structure analysis, 2D phase-sensitive ROESY were acquired by pulse field gradientselected methods, with 32 scans and 2048-time domain in F2, and 384 experiments in F1 by using the TPPI method and a mixing time (spin-lock) of 200 ms at a field of 6 kHz. CD/pinoresinol complex deduced from the observed strong, medium, and low ROESY correlations effects between protons H 2 , H 5 , H 6 of (±)-pinoresinol and protons H' 3 , H' 5 , H' 6 ofCD is presented in the main text (Fig. 3). The proposed model is consolidated by strong interactions between protons H 8 and H 9 of (±)-pinoresinol with protons H' 5 of CD (red double arrows).

Ka

It should be pointed out that only unambiguous correlations were considered. Those with overlapping patterns potentially involving intramolecular interactions were discarded as for example in the coniferyl alcohol 2D-ROESY map (see red rectangle in panel B of H 15 of dehydro di-coniferyl alcohol (red double arrow). The orientation of dehydro di-coniferyl alcohol inside the CD cavity is based on the interaction of H' 6 and H' 3 with H 16 and H 9 , respectively (green double arrows). However, this deep inclusion concerns only one of the two stereoisomers since the other H 15 presents lower cross peaks. Therefore, only the complex with the deepest inclusion is illustrated in Figure SI5.

Evolution of lignans production as function of the initial coniferyl alcohol concentration

Oxidation of coniferyl alcohol was performed and analysed as described earlier in the text (see paragraph 2). A typical reaction mixture (1 mL) contained LAC3 (5 U/L) coniferyl alcohol (2.5, 5 or 10 10 -3 M) in the presence (or absence) of 12 10 -3 M of βCD.

Introduction

Natural molecules such as sugars and amino acids are produced in cell as pure enantiomers by dedicated enzymes. One peculiar situation is however found in the synthesis of some plant metabolites (scheme 1) deriving from the monoelectronic oxidation of the lignol coniferyl alcohol (as the result from the activity of oxidases such as laccases) which leads initially to phenoxy radicals. 1 In vitro a bimolecular radical coupling results in the transient accumulation of a mixture of (±)-dehydrodiconiferyl alcohols (neo-lignan 2), (±)-pinoresinols (lignan 3), and (±)-guaiacylglycerol 8-O-4'-coniferyl alcohol ethers (neo-lignan 4) prior a further polymerization. In plants however either the (+)-or (-)-enantiomer of pinoresinol is preferentially formed. 2 Regio-and enantioselectivity are provided by dirigent proteins (DP) such as FiDIR1 and AtDIR6, which have been shown to be respectively responsible for the formation of (+)-pinoresinol in Forsythia intermedia 2a and of (-)-pinoresinol in Arabidopsis thaliana 2b . These proteins, which might not possess a catalytic center per se, are proposed to act as a scaffold interacting with radicals of coniferyl alcohol to direct the bimolecular coupling through a yet undetermined host/guest mechanism. In a bioconversion, the combined use of these proteins and a laccase or a chemical oxidant such as ammonium persulfate allows the enantioselective enrichment of pinoresinol. [START_REF] Scott | [END_REF] Produced from the enzymatic degradation of starch the naturally occurring cyclic oligosaccharides cyclodextrins (CDs) share with DPs the ability to host guest molecules. Most commons CDs are made of 6 (αCD), 7 (βCD) or 8 (γCD) α-Dglucopyranoside units linked by α-1,4 bonds. [START_REF] Hinsberg | Kinetiscope™, a stochastic simulator v1[END_REF] They have the form of truncated cones in which the hydroxyl groups are exposed to the solvent, making the exterior of the cone hydrophilic whereas the interior, considerably less hydrophilic than the aqueous environment, is able to host hydrophobic molecules. While the height of the torus remains constant (0.79 nm), the cavity diameter varies from 0.47-0.53 nm for the αCD, 0.6-0.65 nm for the βCD and 0.75-0.83 nm for the γCD. The internal cavity volume of α, β and γCD directly influences the size of the guest a CD molecule can accommodate. [START_REF] Hinsberg | Kinetiscope™, a stochastic simulator v1[END_REF] Because of these properties, CDs are used to Notably, in enantioselective synthesis, CDs or their derivatized forms have been shown to increase the enantiopure production of β-amino alcohols 5 and to facilitate the enantioselective N-acylation of primary amines 6 . CDs have been also shown to significantly improve enantiomeric excess in enzyme-catalysed reactions, such as the peroxidase catalysed synthesis of binaphthyl derivatives from naphtols and the esterase catalysed synthesis of the S-enantiomer of the anti-inflammatory drug naproxen. 7 In this work, we studied the influence of CDs with different cavity volumes on the laccase-driven oxidation of coniferyl alcohol in bimolecular systems in which the substrate is mixed with an excess of CDs. We are clearly showing that while the dimerization of coniferyl alcohol is unaffected by the presence of CDs, the βCD cavity is stabilizing the lignan ( 3) and neolignans (2, 4) products and prevent their further oxidation by the enzyme. Moreover, amongst the three dimeric products generated the combination of laccase with βCD allows a selective enrichment of pinoresinol, a behaviour somehow reminiscent of lignan synthesis in the presence of plant dirigent proteins.

Results and Discussion

In 1)). In our experimental conditions 2 and 3 accounted for more than 80% of the dimers formed (Fig. 1, graphs ( 2) and ( 3)).

‡ The neo-synthesized dimers 2, 3 and 4 containing phenolic moieties (i.e. a 2metoxyphenol), their concentration is rapidly high enough to compete with 1 as substrates for the LAC3 enzyme. Thus, after reaching a maximum (equilibrium between formation and disappearance) the concentration of 2, 3 and 4 was significantly decreasing with initial velocities of ca. 0.16 x 10 -3 mol.L -1 .h -1 (2) and ca. 0.10 x 10 -3 mol.L -1 .h -1 (3) ((Fig. 1, graphs ( 2) and ( 3)). As the reaction proceeds through mono-electronic oxidations, these observations are consistent with a further oxidation of the dimers 2, 3 and 4 produced from coniferyl alcohol oxidation into polymers.

Evolution of the oxidation products was differentially influenced by the presence of α, β or γCD in the reaction mixture (Fig. 1). Addition of αCD to the reaction mixture had influence neither on the oxidation of 1 nor on that of the neosynthesized dimers. To the contrary, the presence of CDs with a larger cavity volume had a marked effect on the disappearance of the reaction products maintaining the concentration of 2 and 3 fairly stable around 80 to 85% of the maximum values for several hours without apparently affecting the oxidation rate of 1 (Fig. 1). Thus, addition of βCD to the reaction mixture is stabilizing 2, 3 and 4, probably forming β-CD:dimer complexes that are significantly slowing down their further oxidation by the enzyme (vide infra). In the presence of γCD, the stabilization effect is clearly less pronounced as apparent initial rates of dimers oxidation were three times faster in the presence of γCD than in the presence of βCD (ca. 0.09 x 10 -3 mol.L -1 .h -1 vs. 0.03 x 10 -3 mol.L -1 .h -1 and 0.06 x 10 -3 mol.L -1 .h -1 vs. 0.02 x 10 -3 mol.L -1 .h -1 for 2 and 3 respectively). Overall, in these experiments β and γCDs have Please do not adjust margins Please do not adjust margins apparently no significant effect on the rate of oxidation of 1 whereas they have a marked effect on the stabilization of 2, 3 ) at 30°C in the absence (black circles) or presence of an excess (12 x 10 -3 M) of either βCD (black squares) or γCD (black triangles). Oxidations were monitored by RP-HPLC. Fits (dashed lines) were obtained using a single decay (exponential) model.

Both the apparent complexity of the kinetics due to an oxidation of the products concomitant to their generation and the absence of exploitable data on the fate of the neo-lignan 4 lead us to further study the oxidation of pure dimers 2, 3 and 4 (see Supplementary Information for details about the origin of dimers). In the absence of CD, 3 is oxidized by laccase at a significantly faster rate than 2 and 4 (i.e. 1.3 x 10 -3 mol.L -1 .h -1 vs 0.7 x 10 -3 mol.L -1 .h -1 and 0.6 x 10 -3 mol.L -1 .h -1 respectively) the kinetics of oxidation of which were otherwise similar (Fig. 2). On the other hand, oxidation rates for 2, 3 and 4 are globally slower than the rate of oxidation of 1 (compare graph (1) from Fig. 1 and data (black circle) from Fig. 2). It is to note that these differences in kinetics are similar to those previously reported for the oxidation of 1, 2, 3, 4 by a peroxidase. 9 Despite the fact that Matsushita and colleagues in the same article reported no difference in apparent oxidation potentials (E ox ) for 1, 2, 3, 4, we cannot exclude here that these kinetic differences might be still mainly linked to different E° between dimers 2, 3, 4 and 1. Indeed, these electrochemical systems are irreversible as their oxidation is coupled to a chemical reaction (dimerization) and measuring their redox potentials (E°) requires specific setting and conditions (in particular very high scan rates).

10

Cleared of the step corresponding to the dimerization of 1, the effects of CDs on laccase-mediated oxidation of 2, 3 or 4 are simpler to analyse. Regardless of their specific oxidation rates, the oxidation of each dimer 2, 3 or 4 was similarly slowed down in the presence of β (0.04 h -1 for all lignans) or γCD (0.08 to 0.1 h -1 ) suggesting a similar mode of interaction of the three different dimers with each of the CDs. As observed previously for the oxidation products of 1 (Fig. 1), γCD was less effective than βCD in protecting dimers 2, 3 and 4 from oxidation.

The ability of a CD to form an inclusion complex with a guest molecule is function both of a steric factor (the relative size of the CD cavity to the size of the guest) and of a thermodynamic factor (a driving force bringing the guest into the cavity).

11

Altogether, the differential effects induced by α, βCD or γCD on coniferyl alcohol and the neo-synthesized dimers oxidation match well both the physico-chemical properties of guests and CDs structural differences (i.e. cavity volume and rigidity). Dimers 2 to 4 contain each at least one aromatic 2metoxyphenol moiety inherited from their precursor the coniferyl alcohol molecule (1) (see scheme 1). The molecular volume of 2-metoxyphenol is estimated to be roughly 180 Å [START_REF] Hinsberg | Kinetiscope™, a stochastic simulator v1[END_REF] .

Although an α-CD:coniferyl alcohol inclusion complex has been postulated from 1D 1 H NMR experiments 12 it seems that the internal cavity of αCD (174 Å 3 ) might be eventually too small to stably accommodate neither the substrate nor the neosynthesized dimers. On the other hand, γ (427 Å 3 ) and β (262 Å 3 ) CDs are both likely capable to accommodate molecules of the volume of guaiacol and larger. As γCD is both larger and more flexible than βCD, γCD:dimer complexes are potentially less stable than βCD:dimer complexes and that can account for observed kinetic differences. The absence of any "CD effect" on the oxidation kinetics of coniferyl alcohol (1) suggests that CDs may have a significantly less affinity for 1 than for the neosynthesized dimers. Excepting αCD the cavity of which is probably too small (vide supra), γ and βCD cavities could be too large to stabilize 1. Beyond the internal CD cavity volume, a simple examination of theoretical values describing the hydrophobic character and the water solubility of the ligand molecules point 1 as the least favourable ligand for forming an inclusion complex with CDs amongst the molecules we tested (3>2>4>1). . Ka values for a potential 1:CD complex are extremely low and their significance questionable. Both the absence of substantial effect on the oxidation rate of 1 (see Fig. 1) and low Ka values strongly support that 1 is not forming stable complexes with CDs.

Table 1. Association constants (M -1 ) measured for lignans/CD complexes.

In addition, plotting the extend of the shifts as function of the evolution of the molar ratio between the CD (β or γCD) and the guest suggested a 1:1 stoichiometry for all the CD:guest complexes studied (see Fig. SI3). Next, we used Rotating frame nuclear Overhauser Effect SpectroscopY (2D-ROESY) experiments to further characterize 1, 2, 3 and 4: βCD inclusion complexes. Highlighting intra and inter-molecular spatial proximity (below 6Å) the Nuclear Overhauser Effect is widely used for the characterization of host-guest intermolecular interactions. [START_REF] Schneider | [END_REF] Globally, disregarding relaxation and molecular motions, in the phase sensitive 2D-ROESY experiments 15 the integrated intensity of the cross-peaks is directly correlated with the inter-nuclear distance of the two observed protons. Beyond the observation of 1 H chemical shift displacements of host and/or guest molecules as often found in descriptions of ligand:CD complexes, this approach allows a more accurate description of inclusion complexes classifying interatomic distances from each βCD proton. For each complex, we studied the cross peaks involving H'3 and H'5 protons from the inside of the CDs cavity and the H'6 proton located out at the narrow rim (crown). 2D-ROESY spectra in which the intermolecular cross-peaks are highlighted are presented in supplementary information (Fig. SI4 andSI5). These NMR data are consistent with a potential insertion of lignans 2, 3 or 4 into the βCD cavity and their stabilization at the narrow rim. A scheme of a potential inclusion complex reflecting correlations observed between protons H2, H5, H6 of 3 and protons H'3, H'5, H'6 of βCD is proposed in Figure 3. However, as CD may also form non-inclusion complexes with guest molecules, Considering the above results, only βCD was further investigated. Proportions of dimers 2, 3 and 4 derived from the oxidation of 1 were found insensitive to a variation of the β-CD concentration (0-13 10 -3 M range). Whereas in several cases of catalysed reactions the presence of βCD has been shown to influence the selectivity [5][6][7][16][17][18][19][20] , there is here no selectivity in the oxidation of 1 (as assessed by separation of the neosynthesized dimeric products on a chiral column) simply because 1 is not (or too weakly) interacting with the CD. Besides, amounts of 2 and 3 remaining non-oxidized in the reaction mixture were found to follow a saturation profile as the concentration of βCD increased (Fig. 4). Comparatively, the amplitude of the variation in dimer concentrations in the presence of βCD versus in the absence of βCD is higher for dimer 3 than for dimer 2 (note that the concentration of 4 was too low be properly analysed). Since oxidation rates of dimers 2 and 3 obtained in the presence of βCD are quite similar (see Fig. 2), this behaviour is totally attributable to differences in oxidation rates of the dimers by the enzyme alone. On the other hand, the protective effect of βCD on dimer oxidation decreased as the initial concentration of 1 increased (Fig. SI6). This is both related to the rate of dimer synthesis and to the formation of dimer:CD complexes that is limited by the concentration of βCD (12-13 x 10 -3 M for 1, the rate of dimer formation is likely not maximal at low concentrations of 1 (e. g. 2.5 x 10 -3 M). All the neo-synthetized dimers produced are probably forming a complex with βCD molecules which protects them from a further oxidation by LAC3. As the concentration of 1 increases, the neo-synthetized dimers 2, 3 and 4 accumulate and there is a competition between dimer:βCD complexes formation and oxidation of the neosynthetized dimers by LAC3.

CDs are known to interact with the surface of macromolecules, a property often used to stabilize these objects. 21 Beyond a sequestration of the substrate 22 that is apparently here not influencing the fate of 1 (vide supra), a direct laccase:CD interaction was challenged. Whether or not βCD interferes with the oxidation of 1 by LAC3 (pseudo competition) was tested recording enzyme kinetics in the presence of increasing concentrations of βCD. βCD had no influence on initial rates of consumption of 1.

Neither it has an influence on initial rates of production of dimers as dimerization occurs through a radicalradical coupling independent of the presence of the enzyme. Therefore, in the oxidation of 1, βCD is not a modulator of the laccase activity neither through the formation of a complex with 1 or through a direct CD:enzyme interaction. This leaves that the observed stabilisation of the dimers is entirely due to their interaction with the βCD.

Experimental

All chemicals were purchased from Sigma-Aldrich and used as received except for βCD which was recrystallized twice in 60 % ethanol. The laccase LAC3 (from Trametes sp C30) 8a was produced in Aspergillus niger and purified as previously described 8b . Oxidation of coniferyl alcohol was performed with laccase at 30°C in Britton-Robinson buffer adjusted at pH 5.0 and oxidation products were separated by reverse phase HPLC. All NMR experiments were performed at 298K in D 2 O on a Bruker Avance III 600MHz spectrometer, equipped with a 5mm triple resonance high resolution probe. All NMR datasets were processed in TOPSPIN 3.2 version (Bruker BioSpin, Germany).

Conclusions

The use of cyclodextrins in the laccase catalysed oxidation of coniferyl alcohol allows a control of the polymerisation by a stabilisation of the dimers resulting from radical coupling.

Stabilisation goes through complexes depending on the size of the CD cavity and is maximum for βCD. Whereas a CD:coniferyl alcohol inclusion complex is not forming in the catalytic conditions used, all three dimeric product (one lignan and two neo-lignans) are protected from further oxidation by the enzyme through a complexation by CDs. As the oxidation rate of the unprotected (±) pinoresinol is faster than that of the other dimeric products, the formation of a complex with βCD induces an apparent bias in the relative proportions of dimers. So, amongst the three dimeric products generated the laccase-βCD system allows a selective enrichment of pinoresinol, a behaviour somehow resembling that of plant dirigent proteins. 2 Overall, results obtained from this study point a selective interaction of CDs with lignan and neo-lignan molecules and open the possibility to use CDs to control the polymerization process of lignans or related phenolic molecules for the synthesis of molecules of interest.

substrates and the [O 2 ] was invariant and assumed to be saturating in this study, the measured K M for the various substrates used should be considered apparent. Because of the assumption that 100% of the laccase participated in the catalysis as active enzyme, the measured k cat should also be considered apparent.

Fitting kinetics

The oxidation of coniferyl alcohol (1) by the enzyme laccase is a mono-electronic process leading to the transient formation of a radical species (1 • ) (eq. 1). Radical molecules recombine to give dimers 2, 3 and 4 according to eq. 2. Dimers are themselves subsequently oxidized by the enzyme (eq. 2, 4, 5) in a reaction similar to the oxidation of 1.

Kinetic presented in Figure 1 from the main article were simulated using the stochastic kinetics simulator Kinetiscope (freeware) [START_REF] Hinsberg | Kinetiscope™, a stochastic simulator v1[END_REF] . In the simulation, we introduced:

• the initial concentration of coniferyl alcohol [1] = 2.5 10 -3 M • rate constants from (eq. 1, 3, 4, 5) initially derived from experimental data presented in Fig. 1 and Fig. 2 from the main article: k 1 = 3.3 h -1 ; k 2 = 0.3 h -1 ; k 3 = 0.5 h -1 ; k 4 = 0.25 h -1 • a bi-molecular constant k dim from (eq. 2) arbitrary set to a value of >> k 1 , k 2 , k 3, k 4 (i.e.10 6 M -1 .

h -1 ). With this approximation we recognize the recombination of radicals as a process considerably faster than oxidation steps and we do not distinguish the formation of each dimer 2, 3 and 4 (eq. 2).

The model obtained (Fig. SI1) is compatible with experimental data (Fig. 1 main text). (eq. 2)

(eq. 3)

(eq. 4)

(eq. 5)

-H + -e - -H + -e - -H + -e - -H + -e - For complex structure analysis, 2D phase-sensitive ROESY were acquired by pulse field gradientselected methods, with 32 scans and 2048-time domain in F2, and 384 experiments in F1 by using the TPPI method and a mixing time (spin-lock) of 200 ms at a field of 6 kHz. CD/pinoresinol complex deduced from the observed strong, medium, and low ROESY correlations effects between protons H 2 , H 5 , H 6 of (±)-pinoresinol and protons H' 3 , H' 5 , H' 6 ofCD is presented in the main text (Fig. 3). The proposed model is consolidated by strong interactions between protons H 8 and H 9 of (±)-pinoresinol with protons H' 5 of CD (red double arrows). H 15 of dehydro di-coniferyl alcohol (red double arrow). The orientation of dehydro di-coniferyl alcohol inside the βCD cavity is based on the interaction of H' 6 and H' 3 with H 16 and H 9 , respectively (green double arrows). However, this deep inclusion concerns only one of the two stereoisomers since the other H 15 presents lower cross peaks. Therefore, only the complex with the deepest inclusion is illustrated in Figure SI5.

Evolution of dimers production as function of the initial coniferyl alcohol concentration

Oxidation of coniferyl alcohol was performed and analysed as described earlier in the text (see paragraph 2). A typical reaction mixture (1 mL) contained LAC3 (5 U/L) coniferyl alcohol (2.5, 5 or 10

2 |

 2 J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins hydrophobic compounds such as drugs.3d, e Moreover, CDs can selectively bind chiral molecules and are used to produce commercial HPLC columns for enantiomers separation.

4

 4

vitro oxidation of coniferyl alcohol 1 ( 4

 14 as initial products accumulating during the rapid phase of substrate consumption (see scheme 1). Influence of the CD cavity volume on the oxidation of 1 by LAC3 was evaluated in the presence of an excess (12 x 10 -3 M) of either α, β or γCD. Both the consumption of 1 and the production of the dimeric lignans were followed as function of time by Reverse-Phase High Performance Liquid Chromatography (RP-HPLC). Analysis of the chromatograms is presented Figure 1. In the absence of CDs, the kinetic of consumption of 1 follows a decreasing exponential with a consumption of nearly 90% of the substrate during the first hour (Fig. 1, graph (

Figure 1 .

 1 Figure 1. Influence of CDs on the laccase catalysed oxidation of coniferyl alcohol. Coniferyl alcohol (1) (2.5 x 10 -3 M) was incubated with the laccase LAC3 (5 U.L -1 ) at 30°C in the absence (open square) or presence of an excess (12 x 10 -3 M) of either

Figure 2 .

 2 Influence of CDs on the laccase catalysed oxidation of lignans. Dehydroconiferyl alcohol (2), pinoresinol (3) or erythro guaiacyl glycerol (4) (2.5 x 10 -3 M) were each incubated with the laccase LAC3 (5 U.L -1 ) at 30°C in the absence (black circles) or presence of an excess (12 x 10

Figure 3 .

 3 Figure 3. Schematic view of a potential CD/)-pinoresinol inclusion complex as deduced from 2D-ROESY data. Double arrows indicate spatial dipolar interactions classified from each CD proton: close (red), intermediate (green), far (blue).

Figure 4 .

 4 Figure 4. Influence of varying the concentration of βCD on final concentrations of lignans. Lignans (2.5 x 10 -3 M) were incubated with the laccase LAC3 (5 U.L-1 ) at 30°C in the presence of variable concentrations (0-13 x 10 -6 M) of βCD for 6 hours. C = lignan concentration in the absence of βCD; C β = lignan concentration in the presence of βCD. Fits (dotted lines) were obtained using a one-phase association (exponential) model.

Figure SI1 .

 SI1 Figure SI1. Simulation of the formation of lignans from the oxidation of coniferyl alcool. Stochastic calculations performed with the freeware Kineticsope. Initial parameters: [1] = 2.5 10 -3 M, k 1 = 3.3 h -1 ; k 2 = 0.3 h -1 ; k 3 = 0.5 h -1 ; k 4 = 0.25 h -1 .

  values were extracted from Scott plots ([CD] t / obs = ([CD] t / c ) + (1/Ka c )). 4 δl = chemical shift of a proton from the ligand or from the free CD. δc = chemical shift of the same proton in the ligand:CD complex. ∆δobs = δl -δc Plots for βCD complexes are given in Figure SI2.

Figure SI2 .

 SI2 Figure SI2. Representation of the ligand: βCD interaction (Scott plots). [Ligand] = 0.5 10 -3 M, [βCD] = 2-7 10 -3 M.

Figure SI3 .

 SI3 Figure SI3. Representation of the ligand: βCD interaction (Job plots). [Ligand] = 0-8 10 -3 M, [βCD] = 8-0 10 -3 M. Chemical shifts from βCD protons H1, H2 and H5.

  Fig. SI.4).

Figure SI4 .

 SI4 Figure SI4. Fragments of ROESY spectra showing the intermolecular interactions between protons from ligands and proton from βCD. Panel A, ligand = (±)-pinoresinol; panel B, ligand = coniferyl alcohol. Interaction of dehydro di-coniferyl alcohol with -CD led to splitting of some peaks in the 2D-ROESY spectrum indicating the presence of diastereoselective complexes that exhibit different cross peaks. The model proposed in Figure SI5 is based on strong interactions between H' 3 and H' 5 of CD with the

Figure SI5 .

 SI5 Figure SI5. Fragments of ROESY spectra showing the intermolecular interactions between protons from dehydro di-coniferyl alcohol and proton from βCD. Panel A, zoom in the interactions between the proton H15 of dehydro di-coniferyl alcohol and protons H'3 and H'5 of βCD; panel B, zoom in the interactions between the proton H9 of dehydro di-coniferyl alcohol and protons H'3 of βCD (figure panel D); panel C, zoom in the interactions between the proton H16 of dehydro di-coniferyl alcohol and protons H'5 and H'6 of βCD (figure panel D); panel D, scheme of the potential interactions; double arrows indicate spatial dipolar interactions classified from each CD proton: close (red), intermediate (green).

Figure SI6 .

 SI6 Figure SI6. Effects of a variable initial concentrations of coniferyl alcohol on the formation of dimeric lignans in the presence of βCD.

2 |

 2 J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xxPlease do not adjust margins Please do not adjust margins enhance the solubility and bioavailability of numerous hydrophobic compounds such as drugs.3d, e Moreover, CDs can selectively bind chiral molecules and are used to produce commercial HPLC columns for enantiomers separation.

4

 4

vitro oxidation of coniferyl alcohol 1 ( 4

 14 as initial products accumulating during the rapid phase of substrate consumption (see scheme 1). Influence of the CD cavity volume on the oxidation of 1 by LAC3 was evaluated in the presence of an excess (12 x 10 -3 M) of either α, β or γCD. Both the consumption of 1 and the production of 2, 3 and 4 were followed as function of time by Reverse-Phase High Performance Liquid Chromatography (RP-HPLC). Analysis of the chromatograms is presented Figure 1. In the absence of CDs, the kinetic of consumption of 1 follows a decreasing exponential with a consumption of nearly 90% of the substrate during the first hour (Fig. 1, graph (

Figure 1 .

 1 Figure 1. Influence of CDs on the laccase catalysed oxidation of coniferyl alcohol. Coniferyl alcohol (1) (2.5 x 10 -3 M) was incubated with the laccase LAC3 (5 U.L -1 ) at 30°C in the absence (open square) or presence of an excess (12 x 10 -3 M) of either αCD (crosses), βCD (black circles) or γCD (black triangles). Consumption of 1 and apparition of 2 and 3 were monitored by RP-

Figure 2 .

 2 Figure 2. Influence of CDs on the laccase catalysed oxidation of the dimers 2, 3 and 4. Dehydroconiferyl alcohol (2), pinoresinol (3) or erythro guaiacyl glycerol (4) (2.5 x 10 -3 M) were each incubated with the laccase LAC3 (5 U.L -1) at 30°C in the absence (black circles) or presence of an excess (12 x 10 -3 M) of either βCD (black squares) or γCD (black triangles). Oxidations were monitored by RP-HPLC. Fits (dashed lines) were obtained using a single decay (exponential) model.

13 CD:

 13 guest complexes were studied by1 H NMR experiments as their formation induce shifts of host and guest representative signals. Initially, the equilibrium between the constituents of a given complex was challenged in a titration of a low concentration of ligand (i.e. . Name., 2012, 00,1-3 This journal is © The Royal Society of Chemistry 20xx

  [START_REF] Hinsberg | Kinetiscope™, a stochastic simulator v1[END_REF] a stabilization of dimers 2, 3 and 4 at the narrow rim but outside the cavity cannot be formally ruled out. Whatever their structure (i.e. inclusion or non-inclusion), βCD:guest complexes stabilize dimers 2, 3 and 4 thereby offering them a protection against oxidation.

Figure 3 .

 3 Figure 3. Schematic view of a potential βCD/(±)-pinoresinol inclusion complex as deduced from 2D-ROESY data. Double arrows indicate spatial dipolar interactions classified from each CD proton: close (red), intermediate (green), far (blue).

Figure 4 .

 4 Figure 4. Influence of varying the concentration of βCD on final concentrations of dimers 2 and 3. Dimers 2 and 3 (2.5 x 10-3 M) were incubated with the laccase LAC3 (5 U.L -1 ) at 30°C in the presence of variable concentrations (0-13 x 10 -6 M) of βCD for 6 hours. C = dimer concentration in the absence of βCD; C β = dimer concentration in the presence of βCD. Fits (dotted lines) were obtained using a one-phase association (exponential) model.

Figure SI1 .

 SI1 Figure SI1. Simulation of the formation of lignans from the oxidation of coniferyl alcool. Stochastic calculations performed with the freeware Kineticsope. Initial parameters: [1] = 2.5 10 -3 M, k 1 = 3.3 h -1 ; k 2 = 0.3 h -1 ; k 3 = 0.5 h -1 ; k 4 = 0.25 h -1 .

Figure SI3 .

 SI3 Figure SI3. Representation of the ligand: βCD interaction (Job plots). [Ligand] = 0-8 10 -3 M, [βCD] = 8-0 10 -3 M. Chemical shifts from βCD protons H1, H2 and H5.

  It should be pointed out that only unambiguous correlations were considered. Those with overlapping patterns potentially involving intramolecular interactions were discarded as for example in the coniferyl alcohol 2D-ROESY map (see red rectangle in panel B ofFig. SI.4).

Figure SI4 .

 SI4 Figure SI4. Fragments of ROESY spectra showing the intermolecular interactions between protons from ligands and proton from βCD. Panel A, ligand = (±)-pinoresinol; panel B, ligand = coniferyl alcohol. Interaction of dehydro di-coniferyl alcohol with -CD led to splitting of some peaks in the 2D-ROESY spectrum indicating the presence of diastereoselective complexes that exhibit different cross peaks. The model proposed in Figure SI5 is based on strong interactions between H' 3 and H' 5 of CD with the

Figure SI5 .

 SI5 Figure SI5. Fragments of ROESY spectra showing the intermolecular interactions between protons from dehydro di-coniferyl alcohol and proton from βCD. Panel A, zoom in the interactions between the proton H15 of dehydro di-coniferyl alcohol and protons H'3 and H'5 of βCD; panel B, zoom in the interactions between the proton H9 of dehydro di-coniferyl alcohol and protons H'3 of βCD (figure panel D); panel C, zoom in the interactions between the proton H16 of dehydro di-coniferyl alcohol and protons H'5 and H'6 of βCD (figure panel D); panel D, scheme of the potential interactions; double arrows indicate spatial dipolar interactions classified from each CD proton: close (red), intermediate (green).

10 - 3 M

 103 ) in the presence (or absence) of 12 10 -3 M of βCD.

Figure SI6 .

 SI6 Figure SI6. Effects of a variable initial concentrations of coniferyl alcohol on the formation of dimers in the presence of βCD.

Table 1 .

 1 Association

	1 H NMR experiments as

4 | J. Name.,

2012, 00, 1-3

This journal is © The Royal Society of Chemistry 20xx

  Mekmouche, S. M. Zhou, A. M. Cusano, E. Record, A. Lomascolo, V. Robert, A. J. Simaan, P. Rousselot-Pailley, S. Ullah, F. Chaspoul, T. Tron, J.Biosc. and Bioeng., 2014, 117, 25-27. Kishimoto T., Takahashi N., Hamada M., Nakajima N., J. Agri. Food Chem., 2015, 63, 2277-2283.

	3	W. Hinsberg, F. Houle. Kinetiscope™, a stochastic simulator v1.0.593.x64. © Columbia Hill Technical Consulting
		(2015)
		A	H15	B		H9
		H'5
			H'3
		H'3
		H16			OH	CH 3
		C		D	H	O
					H	H
		H'5		H' 3	O H	O	H' 3
		H'6		H' 5	H	O	C	H' 5
						H	3 H
				OH	H' 6 H' 6		H' 6	H' 6	OH
					O
					H

1

Y.

2

  Please do not adjust margins Please do not adjust margins from Scott Plots ([CD] 0 /∆δ obs = f ([CD] 0 ), see Supplementary information Fig. SI2 for details) are presented in Table 1. Reflecting a dynamic exchange in CD:guest complexes Ka values are notoriously fairly low. 11a As expected, values for γCD are lower than those calculated for βCD. Nevertheless, amongst complexes the apparent hierarchy 3:CD > 2:CD > 4:CD > 1:CD matches that deduced from theoretical physicochemical properties of ligands (vide supra)

New Journal of Chemistry

 Scott. R. L, Rec. Trav. Chem. Pays -Bas, 1956, 75, 787 -789.

Acknowledgements

This study was supported by funds from the CNRS and Aix Marseille Université and from a grant from the Agence Nationale de la Recherche (ANR-09-BLANC-0176). CM is a recipient of a fellowship from the Fondation Pierre Pottier. We thank Elise Courvoisier-Dezord from the Plateforme AVB (AMU): Analyse et Valorisation de la Biodiversité and Yolande Charmasson for help in the production of the recombinant enzymes. We also thank Frédéric Turpin and El Mustapha Belgsir (Biocydex Ltd) as well as Ariane J. Simaan for helpful discussions.

Acknowledgements

This study was supported by funds from the CNRS and Aix Marseille Université and from a grant from the Agence Nationale de la Recherche (ANR-09-BLANC-0176). CM is a recipient of a fellowship from the Fondation Pierre Pottier. We thank Elise Courvoisier-Dezord from the Plateforme AVB (AMU): Analyse et Valorisation de la Biodiversité and Yolande Charmasson for help in the production of the recombinant enzymes. We also thank Frédéric Turpin and El Mustapha Belgsir (Biocydex Ltd) as well as Ariane J. Simaan for helpful discussions.

Conflicts of interest

There are no conflicts to declare.

ARTICLE

Journal Name 6 | J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins

Please do not adjust margins

Conflicts of interest

There are no conflicts to declare.

Notes and references ‡ In the conditions chosen for a maximum separation of 2 and 3, peaks of 1 (decreasing) and 4 (increasing) were coincidental, both preventing a precise follow up of the kinetics of the appearance of the minor product 4 and introducing a bias in the evaluation of the concentration of 1. Although the effect is minor for the interpretation of the kinetics for 2 and 3 this has to be stated here. Please do not adjust margins Please do not adjust margins

ARTICLE

Supplementary Information

Enzymes and chemicals

The laccase LAC3 (from Trametes sp C30) was produced in Aspergillus niger and purified as described previously. 1 Protein concentration was estimated by UV-visible spectroscopy using an ε 600 nm = 5 x 10 3 M -1 •cm -1 for the T1 copper. Laccase activity of the purified protein solution was assayed using 2,2'-azino-bis(3-ethylbenzthiazoline-6-sulphonic acid) (ABTS). One unit (U) of laccase oxidizes one micromole of ABTS per minute.

Alpha-cyclodextrin (αCD), beta-cyclodextrin (βCD) and gamma-cyclodextrin (γCD) were obtained from Aldrich or TCI Europe. Beta-cyclodextrin (βCD) was recrystallized twice in 60 % ethanol. Dehydrodiconiferyl alcohols ( 2) and (±)-pinoresinols (3) were obtained from the bioconversion of coniferyl alcohol (1) (purchased from Sigma France) catalysed by the enzyme LAC3, purified by preparative chromatography (silica) and characterized by 1 H NMR and mass spectrometry. All other chemicals were purchased from Sigma France.

Synthesis of (±)-guaiacylglycerol 8-O-4'-coniferyl alcohol ethers (4)

4 was obtained by oxidation of 1 in the presence of silver oxide (Ag 2 O) following a protocol described Kishimoto et al., 2015. 2 The product of interest was purified by preparative chromatography (silica) and characterized by 1 H NMR and mass spectrometry.

Coniferyl alcohol oxidation in the presence of CD

Oxidation of coniferyl alcohol was performed at 30°C in Britton-Robinson buffer adjusted at pH 5.0 and oxidation products were detected by reverse phase HPLC. A typical reaction mixture (1 mL) contained LAC3 (5 U/L) and coniferyl alcohol (2.5 10 -3 M) in the absence or presence of CD (up to 12 10 -3 M). The reaction proceeded for 8-hours and was initiated by the addition of the enzyme. For each time-point, the reaction was stopped by mixing 100-µL aliquot to 100 µL acetonitrile containing 2.85 mM benzophenone. 30 µL was injected on C18 column (EC150/4 Nucleosil® 100-5-18 Macherey-Nagel™) and analyzed by HPLC (Waters™ Alliance® 2690/2690D Separations Module) with the following gradient: solvent A water containing 3% acetic acid, solvent B acetonitrile; t=0min 90%A 10%B, t=5min 90%A 10%B, t=25 min 50% A 50% B, t= 27 min 50% A 50% B, t=28 min 90%A 10% B, t=30 min 90%A 10%B. Coniferyl alcohol, dehydrodiconiferyl alcohol, pinoresinol and benzophenone were eluted at 4.0 min, 6.6 min, 8.2 min and 16.6 min, respectively. Quantity was normalized using benzophenone as internal reference.

Apparent K M and k cat values were obtained from the initial rate (v), enzyme concentration (E) and substrate concentration (S) according to the equation v = k cat E S/(K M + S). Inhibition kinetics data were obtained using appropriate equations. All data were determined using non-linear regression fitting using Prism software, Graphpad, San Diego, (CA). Because laccase catalysis involves two Eventually, kinetics of the two successive oxidations leading to the formation and to the disappearance of each dimer (see Fig. 1 panels 2 and 3 main text) can be fitted using the simple model: treated as a succession of order 1 kinetics in which the dimerization step is not influencing the rate (i.e.

with k 1 = rate constant for the oxidation of the alcohol and k 2 = rate constant for the oxidation of the dimer.

Determination of the apparent association constant and complex structure by NMR

All experiments were performed at 298K in D 2 O on a Bruker Advance III 600MHz spectrometer, equipped with a 5mm triple resonance high resolution probe. All NMR datasets were processed in TOPSPIN 3.2 version (Bruker BioSpin, Germany). Proton NMR spectra were acquired with a spectral width of 6000 Hz and relaxation delay of 2s during which a water pre-saturation was applied. The stoichiometry for all the CD:guest complexes was studied plotting the extend of the shifts as function of the evolution of the molar ratio between the CD (β or γCD) and the ligand (Job Plots). Plots for βCD complexes are given in Figure SI3.