Oana Andrei
email: oana.andrei@loria.fr

Hélène Kirchner
email: helene.kirchner@inria.fr

A Higher-Order Graph Calculus for Autonomic Computing

In this paper, we present a high-level formalism based on port graph rewriting, strategic rewriting, and rewriting calculus. We argue that this formalism is suitable for modeling autonomic systems and briefly illustrate its expressivity for modeling properties of such systems.

Introduction

Autonomic computing [START_REF] Kephart | The Vision of Autonomic Computing[END_REF] refers to self-manageable systems initially provided with some high-level instructions from administrators. This is a concept introduced in 2001 with an intended biological connotation. The four most important aspects of self-management as presented in [START_REF] Kephart | The Vision of Autonomic Computing[END_REF] are self-configuration, self-optimization, self-healing, and self-protection.

This idea of biologically inspired formalisms gained much interest with the recent development of large scale distributed systems such as service infrastructures and grids. For such systems, there is a crucial need for theories and formal frameworks to model computations, to define languages for programming and to establish foundations for verifying important properties of these systems. Several approaches contributed to this ambitious goal. Without exhaustivity, let us mention in particular the brane calculus [START_REF] Cardelli | Brane Calculi[END_REF][START_REF] Danos | Projective Brane Calculus[END_REF], membrane computing and P-systems [START_REF] Paun | Membrane Computing. An Introduction[END_REF], and the bigraphical reactive systems [START_REF] Milner | Pure bigraphs: Structure and dynamics[END_REF], but also several calculi inspired from biology such as [START_REF] Regev | BioAmbients: an abstraction for biological compartments[END_REF][START_REF] Chabrier-Rivier | The Biochemical Abstract Machine BIOCHAM[END_REF][START_REF] Laneve | A simple calculus for proteins and cells[END_REF].

Another connected approach is provided by chemical programming, which uses the chemical reaction metaphor to express the coordination of computations. This metaphor describes computation in terms of a chemical solution in which molecules (representing data) interact freely according to reaction rules. Chemical solutions are represented by multisets (a set data structure that allows several occurrences of the same element). Computation proceeds by rewritings, which consume and produce new elements according to conditions and transformation rules. The Gamma formalism was first proposed in [START_REF] Banatre | A new computational model and its discipline of programming[END_REF] and later extended to the γ-calculus and HOCL (Higher-Order Chemical Language) in [5,[START_REF] Banâtre | Programming Self-Organizing Systems with the Higher-Order Chemical Language[END_REF] for modeling self-organizing and autonomic systems or grids in particular. MGS is another formalism based on the chemical model. It was designed to represent and manipulate local transformations of entities structured by abstract topologies [START_REF] Giavitto | MGS: a Rule-Based Programming Language for Complex Objects and Collections[END_REF].

Beyond the chemical programming idea, another approach presented in [START_REF] Chakravarti | Application-Specific Scheduling for the Organic Grid[END_REF], called the Organic Grid, is similarly a radical departure from current approaches and is inspired by the self-organization property of complex biological systems.

Our previous work on biochemical applications led us to consider the structure of port graph [START_REF] Andrei | A Rewriting Calculus for Multigraphs with Ports[END_REF] (or multigraph with ports) to model interactions between molecules, in particular proteins [START_REF] Andrei | Graph Rewriting and Strategies for Modeling Biochemical Networks[END_REF]. The behavior of a protein is given by its functional domains which determine which other proteins it can bind to or interact with; these domains are usually abstracted as sites that can be bound or free, visible or hidden. Hence a protein is characterized by the collection of interaction sites on its surface and proteins can bind to each other forming molecular complexes. Based on such structures, we considered graphs with multiple edges and loops, with nodes having explicit connection points, called ports, and edges attaching, more specifically, to ports of nodes; we called them port graphs. Port graphs provide a modeling formalism for molecular complexes by restricting the connectivity of a port (called site in the biological model) to at most one other port. In [START_REF] Andrei | Graph Rewriting and Strategies for Modeling Biochemical Networks[END_REF], port graph rewriting and rewrite strategies are used to model molecular complexes and their interaction on a fragment of the epidermal growth factor receptor (EGFR) signaling pathway.

We extend the chemical model with high-level features by considering a graph structure for the molecules and permitting control on computations to combine rule applications. The result is a higher-order port graph rewriting calculus. By lifting port graph rewriting to a calculus, we are able to express rules and strategies as port graphs and so to rewrite them as well. The calculus also permits the design of rules that create new rules, providing a way of modeling emergence in a system. We borrow various concepts from graph theory, in particular from graph transformations [START_REF] Corradini | Algebraic Approaches to Graph Transformation -Part I: Basic Concepts and Double Pushout Approach[END_REF], and we use different representations for graphs already intensively formalized.

In this paper, we propose port graphs as a formal model for distributed resources and grid infrastructures. Each resource is modeled by a node with ports. We model the lack of global information, the autonomous and distributed behavior of components by a multiset of port graphs and rewrite rules which are applied locally, concurrently, and non-deterministically. Hence the computations take place wherever it is possible and in parallel as soon as they do not interfere. This approach also provides a formal framework to reason about computations and to verify desirable properties.

The paper is structured as follows. Section 2 introduces the rewriting relation for port graphs and presents some rewrite strategies used in this paper. Having all ingredients in hand, in Sect. 3 we give the main ideas of a high-level calculus for port graphs, and in Sect. 4, we argue that this calculus is a suitable formalism for modeling autonomic systems. In Sect. 5 we give some suggestions on expressing properties of a modeled system as strategies.

Port Graph Rewriting

In order to illustrate our approach and the proposed concepts, we develop the example of a mail delivery system borrowed from [START_REF] Banâtre | Chemical Specification of Autonomic Systems[END_REF]. It consists of a network of several mail servers each with its own address domain; the clients send messages for other clients first to their server domain, which in turn forwards them to the network and recovers the messages sent to its clients. Servers are distributed resources with connections between them, created when sending and receiving the messages. In Fig. 1, we illustrate an initial configuration of the mail delivery system. The network is a node with several ports, each port being connected to at most one server. We represent graphically a node as a box with the unique identifier and the name placed outside the box. The ports are represented as small points on the surface of the box. A server node has a handler port for connecting to the network, and several ports for the clients. A client node has a handler port for connecting to a server. All client and server nodes have two ports for the incoming and outgoing messages respectively. The network node has one port for the messages. Messages are nodes with only one port and their names have the form (rec @ domain # m) where rec is the identifier of the recipient client, domain is the identifier of the server domain, and m the body of the message. If redundant, the domain and/or the client identifiers are removed: this is the case as soon as the message is arrived in the server domain or at the client. In the system described in Fig. 1, the server identified by 5 is disconnected from the network node, meaning that it is crashed.

Formally, given a finite set of node names and a finite set of port names, a psignature is a function associating to each node name a set of port names.

A port graph rewrite rule L ⇒ R is a port graph consisting of two port graphs L and R over the same p-signature and one special node ⇒, called arrow node connecting them. L and R are called, as usual, the leftand right-hand side respectively. We assume here that all node identifiers are variables. The arrow node has the following characteristics:

1. for each port p in L, to which corresponds a non-empty set of ports {p 1 , . . . , p n } in R, the arrow node has a unique port r and the incident edges (p, r) and (r, p i ), for all i = 1, . . . , n; 2. all ports from L that are deleted in R are connected to a black hole port, named bh.

The arrow node together with its adjacent edges embed the correspondence between elements of L and elements of R.

We illustrate some port graph rewrite rules in Fig. 2. We represent graphically the edges incident to the arrow node only if the correspondence is ambiguous. In consequence, port graphs represent a unifying structure for representing port graph rewrite rules as well.

A port graph rewrite system R is a finite set of port graph rewrite rules.

h out j@k#m in c k:Server i:Client h out j@#m in c k:Server i:Client h out j@l#m out c k:Server i:Client h out j@l#m out if k<>l c k:Server i:Client h in i@#m in c k:Server i:Client h in m in out k:Server j@l#m h i:Network s out k:Server j@l#m h i:Network s i/o i/o in k:Server j@k#m h i:Network s i/o in k:Server j@#m h i:Network s i/o r1 r2 r3 r4 r5
Fig. 3. Basic rules for the mail delivery system Coming back to our example, the evolution of the mail delivery distributed system is modeled via port graph transformations, themselves expressed by port graph rewrite rules and the generated rewriting relation. We illustrate in Fig. 3 some basic rules for the mail system. A mail sent by a client goes to its server: if the mail is sent to a client in the same server domain then it goes to the input port by r1, otherwise to the outgoing port by r2. By rule r3 a server forwards a mail to a client if he is the recipient. Rule r4 specifies that a server forwards a mail to the network if its recipient is not in the domain, while rule r5 specifies that the network forwards a mail to the appropriate server as specified in the mail.

Let us now formalize the graph transformations induced by port graph rewrite rules. Let L ⇒ R be a port graph rewrite rule and G a port graph such that there is an injective graph morphism g from L to G; hence g(L) is a subgraph of G. Replacing g(L) by g(R) and connecting it appropriately in the context, we obtain a port graph G which represents a result of one-step rewriting of G using the rule L ⇒ R, written G → L⇒R G . There can be different such injective morphisms g from L to G leading to different results. They are built as solutions of a matching problem from L to a subgraph of G. If there is no such injective morphism, we say that G is irreducible with respect to L ⇒ R. Given a port graph rewrite system R, a port graph G rewrites to a port graph G , denoted by G → R G , if there exists a port graph rewrite rule r in R such that G → r G . The formal definition of port graph rewriting is given in [START_REF] Andrei | A Rewriting Calculus for Multigraphs with Ports[END_REF].

The port graph rewrite system R generates an abstract reduction system, whose nodes are graphs and whose oriented edges are rewriting steps. Then a derivation in R is a path in the underlying graph of the associated abstract reduction system. The notions of strategy and strategic rewriting were introduced in the rewriting community in order to control rule applications, i.e. to select relevant derivations. Strategies are formalized as a subset of derivations in [START_REF] Kirchner | Strategic computations and deductions[END_REF]. A strategy can be described by a strategy language. Various approaches have been followed, yielding different strategy languages such as ELAN [START_REF] Borovanský | Rewriting with strategies in ELAN: a functional semantics[END_REF], Stratego [START_REF] Visser | Stratego: A Language for Program Transformation based on Rewriting Strategies[END_REF], TOM [START_REF] Balland | Tom: Piggybacking rewriting on Java[END_REF] or Maude [START_REF] Martí-Oliet | A Rewriting Semantics for Maude Strategies[END_REF]. All these languages share the concern to provide abstract ways to express control of rule applications. Following [START_REF] Kirchner | Strategic computations and deductions[END_REF], we can distinguish two classes of constructs in the strategy language: the first class allows construction of derivations from the basic elements, namely the rewrite rules, identity (Id ) and failure (Fail ). The second class corresponds to constructs that express the control, like sequence (Sequence or ; ) or left-biased choice (First). Moreover, the capability of expressing recursion in the language brings even more expressive power. The strategies can be composed to build other useful strategies. One composed strategy, for instance, is Try which applies a strategy if it can, and the identity strategy otherwise. Similarly, the Repeat combinator is used in combination with a fixpoint operator to iterate the application of a strategy. We will give later a formal description of strategies in our port graph rewriting calculus.

The Port Graph Rewriting Calculus

In this section, we define a rewriting calculus for port graphs, the ρ pg -calculus, whose first-class citizens are object port graphs, port graph rewrite rules and rule application. This is an instance of an Abstract Biochemical Calculus, the ρ Σ -calculus, modeling interactions between abstract molecules over a structure described by the objects of a category Σ and presented in [START_REF] Andrei | A Graph Rewriting Calculus: Applications to Biology and Autonomous Systems[END_REF]. Here, we consider the port graph structure and the port graph rewriting relation defined in Section 2 for the abstract molecules and their interactions respectively.

The ρ pg -calculus generalizes the ρ-calculus [START_REF] Cirstea | The rewriting calculus -Part I and II[END_REF] and the ρ g -calculus [START_REF] Bertolissi | A Rewriting Calculus for Cyclic Higherorder Term Graphs[END_REF], since port graphs generalize the tree-like structure of terms and the graph-like structure of termgraphs respectively. It inherits from the ρ-calculus the fact that it also generalizes the λ-calculus through a more powerful abstraction power that considers for matching not only a variable, like in the λ-calculus, but a port graph with variables.

The ρ pg -calculus provides a formal model for systems whose states correspond to a multiset of object port graphs and whose transitions are reductions obtained by applying port graph rewrite rules. Due to the intrinsic concurrent (or parallel) nature of rewriting on disjoint redexes, we model a kind of Brownian motion, a basic principle in the chemical paradigm consisting in "the free distribution and unspecified reaction order among molecules" [START_REF] Banâtre | Chemical Specification of Autonomic Systems[END_REF], if we consider port graphs as molecules.

Syntax

Let O be the set of object port graphs modeling systems states. We denote by A the set of abstractions, which are port graph rewrite rules consisting of two port graphs for the left-and right-hand side, and the arrow node embedding the correspondence between the two sides. Graphically, the abstractions are first defined as follows:

A 0 ::= ⇒ ... ( (
O ... 6 6 F F O | ⇒ ... ' ' ' ' O ⇒ O ... 4 4 B B O ⇒ O
We construct in an iterative way the set of port graph molecules. In a first step, let us consider the set G 0 of port graph molecules which are either an object port graph in O, an abstraction in A 0 , a juxtaposition of molecules from G 0 , or the empty port graph ε:

G 0 ::= O | A 0 | G 0 G 0 | ε
The juxtaposition " " is associative, commutative with ε the neutral element.

In a second step, the set of abstractions A 0 is extended with port graph rewrite rules that transform an object from O into a port graph molecule from G 0 :

A ::= A 0 | ⇒ ... ( (
( ( O ... 6 6 G G G 0
Then the set of port graph molecules G includes G 0 and A, as well as a set of variables X :

G ::= X | G 0 | A | G G
Finally, molecules are encapsulated into worlds. A world represents a state of the modeled system that contains all molecules present in the environment at a current step together with the connections between them. A world is again represented as a port graph with a node [ ] connected to all object port graphs and all abstractions in the environment. This node corresponds to a permutative variadic operator.

Reduction Semantics

In a world, an abstraction A and a port graph molecule G can interact non-deterministically. This interaction is modeled thanks to the Heating rule given in Fig. 4. This rule introduces an application node @ which connects the abstraction A and the port graph molecule G in the context of other molecules C in the world.

A successful application of an abstraction A on a port graph molecule G yields a port graph G according to a port graph rewriting step G → A G with a port graph rewrite rule A of the form L ⇒ R. The successful application of an abstraction to a port graph molecule may produce different molecules, according to different matching solutions. So we get in general a multiset of results if the application succeeds (see Rule Application in Fig. 4), while a matching failure returns the initial abstraction and the port graph molecule unchanged (see Rule ApplicationFail in Fig. 4).

After the application of the abstraction on the port graph molecule has taken place, a cooling rule, the counterpart of the heating rule, is in charge of rebuilding the state of the different produced systems. This is Rule Cooling in Fig. 4.

(Heating) [C A G] -→ [C A@G] (Application) A@G -→ {[G1] . . . [Gn]} if G →A Gi, 1 ≤ i ≤ n (ApplicationFail) A@G -→ A G if G is A-irreducible (Cooling) [C {[G1] . . . [Gn]}] -→ {[C G1] . . . [C Gn]}

Fig. 4. Semantic rules with explicit application

The full calculus is developed in [START_REF] Andrei | A Graph Rewriting Calculus: Applications to Biology and Autonomous Systems[END_REF]. All steps computing the application of an abstraction to a port graph molecule, including the matching and the replacement operations, are expressible using port graphs by considering more auxiliary nodes and extending the reduction relation with appropriate graph reduction rules. This illustrates well the expressivity of the port graph structure and transformation. Matching and replacement mechanisms are internalized in the calculus as port graph transformations, but since the rules are quite technical, we do not include them here. They can be found in [START_REF] Andrei | A Graph Rewriting Calculus: Applications to Biology and Autonomous Systems[END_REF].

Explicit Failure Handling

In the previous reduction rules for the semantics in Fig. 4, failure is implicit and the failure information is not exploited. In order to do that, we introduce the failure node stk in the ApplicationFail rule: In addition, when handling explicitly failure in this way, other rules are needed to clean up the worlds, such as :

(ApplicationFail') A@G -→ stk if G is A-irreducible
[G] [stk] -→ [G] [stk] [stk] -→ [stk]

Strategies as Abstractions

Instead of having this highly non-deterministic and non-terminating behavior of port graph rewrite rule application, one may want to introduce some control to compose or choose the rules to apply, possibly exploiting failure information. This is possible by defining strategies as extended abstractions.

In this section, we define strategies as objects of the calculus, using the basic constructs, as one can do in the λ-calculus or the γ-calculus. For such definitions, we use an approach similar to the one used in [START_REF] Cirstea | Rewrite strategies in the rewriting calculus[END_REF] where rewrite strategies are encoded by rewrite rules. Let us consider, for the rewrite strategies given in Sect. 2, the following objects: id, fail, seq, first and try.

Let S, S 1 , S 2 denote strategies. We encode the strategies Id, F ail, ; , F irst and T ry as the following aliases for extended abstractions respectively:

id X ⇒ X fail X ⇒ stk seq(S 1 , S 2 ) X ⇒ S 2 @(S 1 @X) first(S 1 , S 2 ) X ⇒ (S 1 @X) (stk ⇒ (S 2 @X))@(S 1 @X)
try(S) first(S, id)

Other useful strategies are provided for negation and test:

not(S) X ⇒ first(stk ⇒ X, X ⇒ stk)@(S@X) ifThenElse(S 1 , S 2 , S 3 ) X ⇒ first(stk ⇒ S 3 @X, X ⇒ S 2 @X)@(S 1 @X)
The composed strategy Repeat is defined with a recursion operator µ as follows: repeat(S) µX.try(seq(S, X))

We can encode the µ abstraction using the fixed-point combinator of the λ-calculus as already done for encoding iterators in the ρ-calculus(See [START_REF] Cirstea | The rewriting calculus -Part I and II[END_REF]).

Based on these strategy definitions, we can reformulate the heating rule using a failure catching mechanism: if S@G reduces to failure, i.e., to the stk node, then the abstraction stk ⇒ S G restores the initial port graphs.

(Heating') [C S G] -→ [C first(S, stk ⇒ S G)@G]

Persistent Strategies

At this level of definition of the calculus, strategies are consumed by a non-failing interaction with a port graph molecule. One advantage is that, since we work with multisets, a strategy can be given a multiplicity, and each interaction between the strategy and a port graph molecule consumes one occurrence of the strategy. This permits controlling the maximum number of times an interaction can take place.

Sometimes it may be suitable to have persistence of strategies. In this case, the strategies should not be consumed by the reduction. For that purpose, we define the persistent strategy combinator that applies a strategy given as argument and, if successful, replicates itself:

S! µX.seq(S, first(stk ⇒ stk, Y ⇒ Y X)) Indeed if S@G -→ {[G 1 ] . . . [G n ]}, then S!@G -→ {[S! G 1 ] . . . [S! G n ]}.
4 Expressivity of the ρ pg -calculus: Modeling Autonomic Systems

In autonomic computing, systems and their components reconfigure themselves automatically according to directives (rewrite rules and strategies) given initially by administrators. Based on these primary directives and their acquired knowledge along the execution, the systems and their components seek new ways of optimizing their performance and efficiency via new rewrite rules and strategies that they deduce and include in their own behavior. Since there is no ideal system, functioning problems and malicious attacks or failure cascades may occur, and the systems must be prepared to face them and solve them. Let us consider here and illustrate on the mail delivery system example, three aspects that an autonomic system must handle, namely self-configuration, self-healing, and self-protection.

The self-configuration is simply described by the concurrent application of the five rules given in Fig. 3 using the reduction semantics introduced in Sect. 3. An interesting problem may concern the operations of splitting and merging servers (their domains). Then biologically inspired port graph rules from Fig. 2 (a) and (c) could be applied as well for servers.

An autonomic system detects when a server crashes and the connection of the crashed server to the network is cut. It is expected to repair the problem of the clients connected to the crashed server and the problem of the mails that were about to be sent from that particular server. This self-healing behavior can be described by rules that detect the problems and by rules that repair them by modifying the configuration or introducing new rules in the system. The same method can be used as well for selfoptimization. For finding the problem in the system, the calculus is powerful enough to find the right pattern and apply the appropriate rule.

We show in the following a concrete example for self-protection behavior of the mail system. Let us consider the rules in Fig. 7. When a spam arrives at a server node, the filtering rule r6 deletes it, assuming that the server has a procedure for deciding when a mail is a spam. The rules r7 and r8 are analogous to r6 but for a client node and a network node respectively, assuming as well that both entities have their own spam detection procedure. In order to limit spam sending, the rule r8 should have a higher priority than r5 in Fig. 1, and the rule r6 a higher priority than r3. Then we replace r3 and r6 by seq(try(r6), r3), and r5 and r7 by seq(try(r8), r5).

When a client receives a mail and, based on a spam decision procedure, concludes that the mail is a spam, it deletes the mail and provides the server with a new rule specifying that from now on the server node should delete all mails of this kind. This behavior is specified by the rule r9.

A bigger development of this mail delivery system example with further rules can be found in [START_REF] Andrei | A Graph Rewriting Calculus: Applications to Biology and Autonomous Systems[END_REF].

Embedding Runtime Verification

We have shown in Sect. 4 how a particular autonomic system can be modeled using the ρ pg -calculus. The model should also ensure formally that the intended self-managing specification of the system helps indeed preserving the properties of the system. Some properties can be verified by checking the presence of particular port graphs. Such properties can be easily encoded as object port graphs, abstractions, or strategies, hence as entities of the calculus. Consequently, the properties can be placed at the same level as the specification of the modeled system and they can be tested at any time.

An invariant of the system can be expressed as a port graph rewrite rule with identical sides, G ⇒ G, testing the presence of a port graph G. The failure of the invariant is handled by a failure port graph Failure that does not allow the execution to continue. The strategy verifying such an invariant is then:

first(G ⇒ G, X ⇒ Failure)! Such strategy is useful for instance to ensure, in our running example, the persistence of a given critical server of the network, or may be used also to check that there is always a minimal number of servers available in the network. From another perspective, we express the unwanted occurrence of a concrete port graph G in the system using the strategy:

(G ⇒ Failure)!

In practice, such strategies are employed in model checking applications to test unwanted situations. In both cases above, instead of yielding the failure Failure signaling that a property of the system is not satisfied, the problem can be "repaired" by associating to each property the necessary rules or strategies to be inserted in the system in case of failure. Such ideas need to be further explored since they open a wide field of possibilities for combining runtime verification and self-healing in ρ pg -calculus.

Conclusion

In this paper our main objective was to propose a formalism, the port graph calculus, for modeling autonomic systems.

From the computational point of view, we have shown that this calculus allows us to model concurrent interactions between port graph rewrite rules and object port graphs, as well as interactions between rewrite rules or interactions creating new rewrite rules. Thanks to strategies, some interactions may be designed with more control. The suitable balance between controlled and uncontrolled interactions is an interesting question to address for a given application. Here again, biological systems may provide us with valuable intuitions.

From the verification point of view, we can take advantage of the classical techniques used in rewriting for checking properties of autonomic systems. However, rules may also interfere giving rise to some conflicts. Detecting them can be done through confluence check and computation of critical pairs. Also some processes may be required to terminate when they are involved in computations. On the contrary, for known non-terminating processes, detecting periodicity of the processes may be of interest. Therefore, further work needs to address the verification of such properties for port graph rewriting. We have also outlined in this paper some ideas for runtime verification of properties in such systems, that need further exploration.

Fig. 1 .

 1 Fig. 1. A mail system configuration

Fig. 2 .

 2 Fig. 2. Some port graph rewrite rules: (a) splitting node i in two; (b) deleting node i; (c) merging nodes i and j.

Fig. 5 .

 5 Fig. 5. Semantic rule for explicit failure

Fig. 6 .

 6 Fig. 6. Semantic rule for failure catching

Fig. 7 .

 7 Fig. 7. Rules for self-protection in the mail delivery system


Thomas Boudou

Tomas Andersen

Martial Balland

On the spatiotemporal regulation of cell tensional state

Since the emergence of mechanobiology, mechanical signals have been shown to influence almost every process in biology. Cells transduce mechanical signals into biochemical signaling pathways, adjust their behavior and/or phenotype before transmitting these signals to neighboring cells. Mechanical signals thus appear as information, which can be "written" by cells in the surrounding extracellular matrix, "transmitted" through it and "read" by other cells. This brief review summarizes our current understanding of the mechanisms regulating the tensional state of cells and tissues subjected to mechanical perturbations, before examining existing or potential experimental approaches to study these mechanisms.

Introduction

Since the emergence of mechanobiology, mechanical signals have been shown to influence almost every processes in biology. Macroscopic signals such as physical exercise, breathing or heart pumping have thus been suspected to regulate tissue development more than a century ago [START_REF] Thompson | On growth and form[END_REF], while the impact of microscopic mechanical signals, such as cell-generated forces or blood flow, on cell adhesion or differentiation are only evidenced since the 1980's [START_REF] Eyckmans | A hitchhiker's guide to mechanobiology[END_REF]. Step by step, and in close correlation with the advent of technologies to measure and manipulate mechanical signals in vitro and in vivo, scientists have indeed progressively unraveled some of the mysteries surrounding how cells generate, perceive, transmit and regulate mechanical signals [START_REF] Humphrey | Mechanotransduction and extracellular matrix homeostasis[END_REF]. Extensive work and excellent review articles have been dedicated to the mechanisms of generation, perception and transmission of mechanical signals in biology [START_REF] Eyckmans | A hitchhiker's guide to mechanobiology[END_REF][START_REF] Heisenberg | Forces in Tissue Morphogenesis and Patterning[END_REF]. Here this brief review focuses on this dynamic regulation of mechanical signals in cells and tissues submitted to mechanical perturbations.

In the cytoplasm, the highly dynamic cytoskeleton is the key player in generating and regulating mechanical signals, through its scaffolding architecture composed of actin, intermediate filaments and microtubules. Briefly, the perpetual polymerization/depolymerization of those constituents, as well as the myosin II-induced movement of actin filaments, are responsible for the production of active forces. These forces are directly applied either on the nucleus, through the linker of the nucleoskeleton and cytoskeleton (LINC) complex [START_REF] Aureille | Mechanotransduction via the nuclear envelope: a distant reflection of the cell surface[END_REF], on the membrane and the focal adhesions, through integrin receptors which transmit them across the cell membrane and deform the ECM [START_REF] Humphrey | Mechanotransduction and extracellular matrix homeostasis[END_REF], or to adherens junctions, where cadherin receptors convey these forces to the neighboring cells [START_REF] Yap | Mechanosensing and Mechanotransduction at Cell-Cell Junctions[END_REF]. Further along the line, these mechanical signals, propagated through direct cell-cell contact or via the deformation of the ECM mesh, follow the opposite direction, transit through focal adhesions or adherens junctions and deform nearly every intracellular organelle thanks to the connected architecture of the cytoskeleton.

As a result, cells amplify, propagate and transduce this back-and-forth mechanical signaling into intracellular, biochemical signaling pathways and adjust their behavior and/or phenotype, a process called mechanotransduction [START_REF] Chen | Mechanotransduction -a field pulling together?[END_REF]. A bidirectional coupling can then be identified between the external physical cues and the corresponding cellular response. Overall, mechanical signals thus appear as information, which can be "written" by cells in the surrounding ECM, "transmitted" through it and "read" by other cells. And as any system processing information, the stability and reproducibility of this information is crucial to the system's stability. The mechanotransduction process is thus equipped with numerous positive and negative feedback loops that generate a highly complex and dynamic mechanical regulation of this information (Fig. 1). Here we summarize our current understanding of the mechanisms regulating the tensional state of cells and tissues subjected to mechanical perturbations, before examining existing or potential experimental approaches to study these mechanisms. We finally examine future directions in this blooming field.

Regulation of cellular forces in mechanobiology

In order to exert their functions, cells and tissues need to maintain their mechanical integrity by sustaining optimal tensional values and mechanical equilibrium. A collapse of this integrity or abnormal transduction of mechanical information can indeed lead to defective morphogenesis [START_REF] Barnes | Tissue mechanics regulate brain development, homeostasis and disease[END_REF][START_REF] Farge | Mechanotransduction in Development[END_REF] or pathophysiological dysfunctions such as fibrosis, atherosclerosis or cancer [START_REF] Dufort | Balancing forces: architectural control of mechanotransduction[END_REF][START_REF] Jaalouk | Mechanotransduction gone awry[END_REF]. This state of equilibrium has been linked to the ability of cells and tissues to maintain mechanical tension at a preferred set-point value when faced with external mechanical stimuli, and thus maintain proper physiological functions.

Many definitions have been proposed to address the mentioned biological balance. Following the ideas presented by Claude Bernard back in 1865 regarding internal equilibrium, coined later as homeostasis by Walter Cannon in "The Wisdom of the Body" in 1932, Eastwood et al. introduced in 1998 the concept of tensional homeostasis as: "the control mechanism by which fibroblasts establish a tension within their extracellular collagenous matrix and maintain its level against opposing influences of external loading" [START_REF] Brown | Tensional homeostasis in dermal fibroblasts : mechanical responses to mechanical loading in three-dimensional substrates[END_REF].

In the early 1980's, and in accordance with the homeostatic principles of Cannon, Bornstein and Bissel discussed the concept of dynamic reciprocity, a more refined term that introduced the idea of dynamic feedback loops between cells and extracellular matrix: "the influence of extracellular matrix on the cell, both during the developmental process and in established tissues, appears to evolve continually" [START_REF] Bissell | How does the extracellular matrix direct gene expression?[END_REF][START_REF] Bornstein | Synthesis and Secretion of Structural Macromolecules by Endothelial Cells in Culture[END_REF].

Since then, the ability of cells to maintain a constant level of tension has been challenged by inducing different perturbations in their environment. It is beyond the scope of this review to give a universal definition to the internal tensional balance observed in cells and tissues. The debate this work aims at is how cells adapt their force production to perturbations which occur at different time and space scales, ranging from milliseconds to hours and from the subcellular to the tissue level, and how to experimentally address this phenomenon. Most of the current approaches to perturb and analyze the dynamic regulation of the cell's behavior are based on either (i) biological perturbations (e.g. pharmacology, genetics, inducible promoters) or (ii) physical perturbations (e.g. fluid flow, AFM-indentation, geometrical and adhesive constraints). While these techniques helped furthering our understanding of the mechanisms behind the ability of cells to mechanically adapt their behavior to their environment, these biological and physical stimulations are strongly limited by their spatial and temporal resolutions. For example, most drugs can only be applied to the whole cell or tissue at once and takes minutes to induce a noticeable relaxation of cell forces. If one looks for periodical stimulations, the drug needs to be sequentially added and washed, with a temporal resolution no faster than several minutes. As a consequence, most investigations aim at probing more of a steady state of the cell or tissue than dynamical processes, while this dynamic regulation of the cell tensional state has been shown to be key in major cellular processes, such as migration or division. As an example, Théry et al. demonstrated that despite strong heterogeneities in shape and size, normal and transformed MCF10A epithelial cells exhibited a robust tendency relating cell mechanical and motile properties, with a negative correlation between contractile forces and cell speed [START_REF] Leal-Egaña | The sizespeed-force relationship governs migratory cell response to tumorigenic factors[END_REF]. On the dynamics of cell division, Trepat and colleagues recently established that the entire cell cycle was regulated by temporal mechanical patterns and showed that tension and mechanical energy could be better predictors of the duration of the G1 phase [START_REF] Uroz | Regulation of cell cycle progression by cell-cell and cell-matrix forces[END_REF]. Both mentioned results highlight the potential of biomechanical cues in the dynamic regulation of cell processes.

Several recent studies have investigated the dynamic regulation of the cell tensional state. Stamenović and colleagues demonstrated that isolated human endothelial cells exhibited unstable and erratic traction fields [START_REF] Krishnan | Fluidization, resolidification, and reorientation of the endothelial cell in response to slow tidal stretches[END_REF]. By applying dynamic mechanical stimulation through the deformation of an elastic substrate to which cells are attached, they also observed that this traction field reoriented transversely to the axis of a periodical stretch, but that tractions remained highly unstable long after their reorientation, suggesting the absence of tensional homeostasis in isolated endothelial cells, as defined by Eastwood et al. [START_REF] Brown | Tensional homeostasis in dermal fibroblasts : mechanical responses to mechanical loading in three-dimensional substrates[END_REF]. Lately, they evidenced that the ability of isolated cells to maintain this tensional homeostasis was dependent upon cell type and that the dynamic fluctuations of the traction field decreased with cell density, suggesting that tensional homeostasis may require multicellularity for specific cell types [START_REF] Canović | Tensional homeostasis in endothelial cells is a multicellular phenomenon[END_REF][START_REF] Zollinger | Dependence of Tensional Homeostasis on Cell Type and on Cell-Cell Interactions[END_REF]. Several authors probed the dynamic regulation of the tensional state of multicellular assemblies. The total elastic strain energy generated by epithelial cell colonies was thus shown to increase linearly with the size of the colony [START_REF] Mertz | Cadherin-based intercellular adhesions organize epithelial cellmatrix traction forces[END_REF][START_REF] Mertz | Scaling of Traction Forces with the Size of Cohesive Cell Colonies[END_REF],

similarly to the active tension of an expanding epithelial monolayer [START_REF] Vincent | Active Tensile Modulus of an Epithelial Monolayer[END_REF]. During wound healing, Murrell et al. measured the linear decrease of elastic strain energy with the perimeter of the wound [START_REF] Elosegui-Artola | Force Triggers YAP Nuclear Entry by Regulating Transport across Nuclear Pores[END_REF]. Overall, these results demonstrate the conservation of the average energy density at a constant level.

In parallel, Fletcher et al. used a feedback-controlled atomic force microscope to evidence that single NIH 3T3 fibroblasts do not exhibit tensional homeostasis in the strictest sense, i.e. they do not maintain a single, inherent tensional state [START_REF] Brown | Tensional homeostasis in dermal fibroblasts : mechanical responses to mechanical loading in three-dimensional substrates[END_REF], but instead generated different levels of forces in response to mechanical displacement in a strain-rate-dependent manner [START_REF] Webster | An AFM-based stiffness clamp for dynamic control of rigidity[END_REF]. Fletcher proposed the concept of tensional buffering, i.e. rather than maintain a constant mechanical state, cells may transition between different tensional states depending on how they are perturbed, permitting distinct responses to slow deformations during morphogenesis and rapid deformations associated with injury.

On the other hand, Weng et al. demonstrated the stability, over time and upon mechanical perturbation, of cytoskeletal tension and focal adhesion size in single rat embryo fibroblasts, human mesenchymal stem cells and human skin fibroblasts [START_REF] Weng | Mechanosensitive subcellular rheostasis drives emergent single-cell mechanical homeostasis[END_REF]. They showed this single-cell mechanical homeostasis to be an emergent phenomenon collectively driven by the graduated dynamics of cytoskeletal tension and focal adhesions, the latter a more sensitive gating mechanism for the maintenance or exit of single-cell homeostasis.

Overall, these studies evidenced the existence of a system-dependent regulatory process actively promoting the equilibrium of tension and the conservation of a mechanical function. This mechanism relies on feedback loops fed by information coming from various probes with intrinsic spatial and temporal scales (Fig. 1). The system will try to adapt to an external perturbation, depending on its amplitude, speed and frequency, which is key to the preservation of healthy and functional cells and tissues. A large body of work thus remains to be done exploring the spatiotemporal range of perturbation within which biological systems can resist and/or adapt to the perturbation. To this end, novel tools will be necessary to mechanically stimulate biological systems, with an independent spatial and temporal control.

How to study the regulation of cell tensional state in mechanobiology?

Three key elements are required for designing the dream experiment to study the regulation of cell tensional state in mechanobiology: (i) a time-and space-resolved quantification of the mechanical and biological responses of the system; (ii) a method for dynamically perturbing the system of interest (cell or tissue), with spatial and temporal control; and (iii) a high enough throughput screening in order to improve the experiment's statistics and highlight small intercellular variabilities.

Although no experiment can currently fulfill all these requirements, several recent studies presented promising technologies. The spatiotemporal quantification of the mechanical response of cells or tissues is indeed already well established, mostly by measuring the deformation of a soft environment by cell forces.

Since the late 1990's, several approaches have been developed and advanced for quantifying cell forces on 2D substrates [START_REF] Dembo | Stresses at the Cell-to-Substrate Interface during Locomotion of Fibroblasts[END_REF][START_REF] Butler | Traction fields, moments, and strain energy that cells exert on their surroundings[END_REF][START_REF] Tan | Cells lying on a bed of microneedles: An approach to isolate mechanical force[END_REF] or in 3D matrices [START_REF] Legant | Measurement of mechanical tractions exerted by cells in three-dimensional matrices[END_REF][START_REF] Gjorevski | Mapping of mechanical strains and stresses around quiescent engineered three-dimensional epithelial tissues[END_REF][START_REF] Legant | Microfabricated tissue gauges to measure and manipulate forces from 3D microtissues[END_REF], and few techniques emerged to assess intercellular forces [START_REF] Liu | Mechanical tugging force regulates the size of cell-cell junctions[END_REF][START_REF] Borghi | E-cadherin is under constitutive actomyosin-generated tension that is increased at cell-cell contacts upon externally applied stretch[END_REF][START_REF] Tseng | Spatial organization of the extracellular matrix regulates cell-cell junction positioning[END_REF][START_REF] Tambe | Collective cell guidance by cooperative intercellular forces[END_REF][START_REF] Maruthamuthu | Cell-ECM traction force modulates endogenous tension at cell-cell contacts[END_REF][START_REF] Campàs | Quantifying cell-generated mechanical forces within living embryonic tissues[END_REF][START_REF] Dolega | Cell-like pressure sensors reveal increase of mechanical stress towards the core of multicellular spheroids under compression[END_REF]. However, most of these approaches require manual steps that limit the throughput to a 10-50 cells or tissues in a typical experiment, with the exception of a very recent work by Di Carlo and colleagues who used micropatterns of fluorescently labeled-ECM proteins, integrated in a multi-well plate format, to obtain highly parallelized time-course studies of single cell forces [START_REF] Pushkarsky | Elastomeric sensor surfaces for high-Throughput single-cell force cytometry[END_REF]. At the tissue scale, Asmani et al.

extended the work developed by Legant et al. [START_REF] Legant | Microfabricated tissue gauges to measure and manipulate forces from 3D microtissues[END_REF] by creating microtissue arrays in a multi-well plate format, thus enabling multi-parameter, phenotypic analysis of drug candidates with a throughput higher than conventional assays [START_REF] Asmani | Fibrotic microtissue array to predict anti-fibrosis drug efficacy[END_REF].

Several solutions are thus advanced enough to allow for high throughput quantification of the tensional state of cells and tissues, whereas only very few techniques exist for perturbing them with a spatiotemporal control and a high enough throughput. As presented before, stretchable substrates are of major interest for studying the impact of dynamic perturbations, but do not allow for a spatial control of local perturbations [START_REF] Krishnan | Fluidization, resolidification, and reorientation of the endothelial cell in response to slow tidal stretches[END_REF][START_REF] Weng | Mechanosensitive subcellular rheostasis drives emergent single-cell mechanical homeostasis[END_REF]. Of note, using soft lithography, Michielin et al. recently engineered a microfluidic-based cellstretching device which was used to analyze the impact of local, dynamic mechanical perturbations on cytoskeletal remodeling and membrane permeability of healthy and diseased human skeletal muscle cells [START_REF] Michielin | Microfluidic-assisted cyclic mechanical stimulation affects cellular membrane integrity in a human muscular dystrophy in vitro model[END_REF]. By combining this approach with microcontact printing, Xue and colleagues were later able to demonstrate the impact of ectopic mechanical stimulation on the embryonic patterning of neuroectoderm [START_REF] Xue | Mechanics-guided embryonic patterning of neuroectoderm tissue from human pluripotent stem cells[END_REF]. Although these locally stretchable substrates allow for dynamically perturbing parts of a tissue, they do not enable cell-scale perturbations and are not compatible with a spatial and temporal quantification of the tissue's tensional state yet.

Alternatively, synthetic materials that are capable of responding to external or internal stimuli represent a very exciting emergent area of scientific interest [START_REF] Uto | Dynamically tunable cell culture platforms for tissue engineering and mechanobiology[END_REF]. While the spatial and temporal resolution of some external stimuli such as heat, electrical or magnetic fields may be insufficient for mechanobiology studies, light sensitive materials could be powerful tools for analyzing the dynamic response of cells to well-defined perturbations. The Garcia's team thus developed a general strategy to temporally and spatially control the presentation of cell-adhesive peptides via light exposure [START_REF] Lee | Light-triggered in vivo activation of adhesive peptides regulates cell adhesion, inflammation and vascularization of biomaterials[END_REF], while Shou et al. engineered surfaces where topography changes upon light exposure [START_REF] Shou | Near-infrared-irradiation-induced remote activation of surface shape-memory to direct cell orientations[END_REF]. Although not reversible yet, this kind of approach seems promising for studying resilience in mechanobiology, owing to the high degree of spatiotemporal control afforded by light.

Based on the similar idea that light is an excellent candidate for perturbing biological systems, optogenetics has recently emerged as a very potent approach for spatiotemporally controlling the tensional state of cells. By combining optogenetic control of RhoA, live-cell imaging and traction force microscopy, Oakes et al. have demonstrated that local activation of RhoA stimulated local recruitment of actin and myosin, and increased cell forces. This perturbation in the cell's tensional state rapidly propagates across the cell via stress fibers and drives increased actin flow [START_REF] Oakes | Optogenetic control of RhoA reveals zyxin-mediated elasticity of stress fibres[END_REF]. Similarly, Trepat and colleagues engineered an elegant optogenetic system for activating RhoA either at the plasma membrane or at the mitochondrial membrane [START_REF] Valon | Optogenetic control of cellular forces and mechanotransduction[END_REF]. They showed that the optogenetic activation of RhoA at the plasma membrane caused a rapid, local and reversible increase in cellular traction, intercellular tension and tissue compaction. By contrast, the translocation of RhoA at the mitochondria membrane induced opposite results. Using this tool, they were able to quantify the almost immediate impact of contractility variation on the nuclear localization of the transcriptional regulator YAP. In addition, this optogenetic approach allows to locally modify cellular tension, thus opening the way to modify the forces generated by a cell or a group of cells while quantifying the effect of these cell-generated forces on neighboring cells. Trepat et al. thus demonstrated that the forces exerted on cells by other cells induced tissue deformation [START_REF] Valon | Optogenetic control of cellular forces and mechanotransduction[END_REF] and regulated the duration of mitosis [START_REF] Uroz | Regulation of cell cycle progression by cell-cell and cell-matrix forces[END_REF]. In this case, the light-induced mechanical response of a cell is also the mechanical stimulus that perturb the neighboring cells. Herein, using a cell as a biological actuator thanks to optogenetics allows for mimicking physiological mechanical stimuli.

Altogether, these recent results combining spatiotemporal control and measurement of cellular contractility pave the way to the study of subcellular, cellular and multicellular processes with micrometer resolution and seconds timescale, opening an exciting avenue for the study of the regulation of cell tensional state in mechanobiology.

Future directions.

While the mechanobiological studies described in this review have provided important information on the spatiotemporal regulation of cell tensional state, several key questions remain unanswered. For instance, the intra-and intercellular stability of the cell contractility remain under debate. As stated above, a precise determination of the spatiotemporal range of perturbation within which this regulation is achieved will be crucial to clarify this question. Similarly, while organs maintain optimal tensional values and mechanical equilibrium [START_REF] Porazinski | YAP is essential for tissue tension to ensure vertebrate 3D body shape[END_REF], it is still unclear how this maintenance capacity emerges from the assembly of single cells exhibiting very dynamic, at times erratic, mechanical behavior. This multicellular stability may thus require a higher level of organization than that of a single cell, suggesting that future studies should consider cross-signaling, positive and negative feedback mechanisms within the cell, between neighboring cells as well as between cells and the ECM.

The ECM appears indeed to be a largely neglected player in this spatiotemporal regulation of cell contractility, as most studies are done on plastic or synthetic gels. The ECM is key to architecture in the tissue across multiple length scales, ranging from the organization of ligands and growth factors at the nanoscale to the cell shape and connectivity at the microscale and larger [START_REF] Baker | Deconstructing the third dimension: how 3D culture microenvironments alter cellular cues[END_REF]. As the composition and architecture of the ECM can be modified or stabilized by the cells, thus perpetuating either a physio-or a pathological behavior, it is highly probable that the ECM is key to the dynamic regulation of cell tensional state. As such, the engineering of dynamically and locally tunable fibrillary synthetic and natural matrices will be required to bring to light the hidden feedback mechanisms regulating cell/ECM tensional state [START_REF] Baker | Cellmediated fibre recruitment drives extracellular matrix mechanosensing in engineered fibrillar microenvironments[END_REF].

Overall, there is thus a strong need for experimental techniques to spatiotemporally control forceresponsive molecules in cells. The ability to reversibly activate individual focal adhesions or molecular motors, for instance, similarly to a geneticist modifying individual genes, would be crucial to defining the relevant timescales and amplitudes of perturbations in mechanobiology, ensure robust parameter estimation and identify mechanical dose response curves. In a similar way to genomics or proteomics, such comprehensive quantification of the spatial and temporal regulation of cell mechanics would allow the emergence of mechanomics, i.e. a spatiotemporal mapping of how forces are generated, transmitted, transduced and regulated in cells and tissues, dysregulation of which has been associated with pathophysiological conditions in developmental disorders and diseases [START_REF] Broders-Bondon | Mechanotransduction in tumor progression: The dark side of the force[END_REF][START_REF] Vermeulen | Stem cell dynamics in homeostasis and cancer of the intestine[END_REF].

Figure 1 :

 1 Figure 1: Spatiotemporal regulation of a cell's tensional state through positive and negative feedback loops fed by information coming from various probes, depending on the amplitude, speed and frequency of the perturbations.

Aknowledgments

. T.B. and M.B. acknowledge financial support from the CNRS "Mission pour l'Interdisciplinarité" and the Center of Excellence of Multifunctional Architectured Materials "CEMAM" (n° AN-10-LABX-44-01). M.B. acknowledges financial support from the ANR MechanoSwitch project, grant ANR-17-CE30-0032-01 of the French Agence Nationale de la Recherche.


Karine Rehel

Isabelle Linossier

Tiffany Le Norcy

Fabienne Fay
email: fabienne.fay@univ-ubs.fr

Claudia Zea Obando

Claire Hellio

Fabienne Faÿ

Karine Réhel

A new method for evaluation of antifouling activity of molecules against microalgal biofilms using confocal laser scanning microscopy-microfluidic flow-cells

Keywords: Microalgae, flow-cell, adhesion, biofilm, CLSM, multi-well plate, bioassay, antifouling, methodology, Cylindrotheca closterium, Porphyridium purpureum

Introduction

Biofilms consists of agglomerates of microorganisms surrounded by a self-produced extracellular matrix (ECM) composed primarily of extracellular polymeric substances (EPS). In seawater, biofilms on submerged surfaces are mainly composed of bacteria and microalgae [START_REF] Wahl | Marine epibiosis. I. Fouling and antifouling: some basic aspects[END_REF], Cooksey and Wigglesworth-Cooksey1995, Dang and Lowell 2016). These complex structures have been observed by sampling biofilms from various substrates collected in the marine environment [START_REF] Arrhenius | A novel bioassay for evaluating the efficacy of biocides to inhibit settling and early establishment of marine biofilms[END_REF][START_REF] Maso | Microfouling communities from pelagic and benthic marine plastic debris sampled across Mediterranean coastal waters[END_REF][START_REF] Faÿ | Effect of biocidal coatings on microfouling: in vitro and in situ results[END_REF][START_REF] Balqadi | Microfouling development on artificial substrates deployed in the central Red Sea[END_REF] or by using laboratory methods combining culture and imaging of biofilms [START_REF] Doiron | Dynamic approaches of mixed species biofilm formation using modern technologies[END_REF][START_REF] Reddy | Long alkyl-chain imidaolium ionic liquids: antibiofilm activity against phototrophic biofilms[END_REF][START_REF] He | Mg 2+ /Ca 2+ promotes the adhesion of marine bacteria and algae and enhances following biofilm formation in artificial seawater[END_REF], Di Peppo and Congestri, 2017). Indeed, the characterization of biofilms in terms of composition and structure has been made possible by the development of 3-D mapping techniques associated with confocal laser scanning microscopy (CLSM). This method has been extensively used in the studies of bacterial biofilm formation (Azerdo et al. 2017[START_REF] Pamp | Insight into the microbial Multicellular Lifestyle via Flow-Cell Technology and Confocal Microscopy[END_REF][START_REF] Arai | Actinomyces naeslundii GroEL-dependent initial attachment and biofilm formation in a flow cell system[END_REF][START_REF] Smaldone | Growth of Myxococcus xanthus in Continous-Flow-Cell Bioreactors as a Method for studying Development[END_REF][START_REF] Haagensen | Development of Spatial Distribution Patterns by Biofilms Cells[END_REF], cyanobacteria [START_REF] David | Starilization of single species Synechocystis biofilms by cultivation under segmented flow[END_REF] and natural communities [START_REF] Larson | Spectral fingerprinting of algal communities: a novel approach to biofilm analysis and biomonitoring[END_REF][START_REF] Proia | Nutrients and light effects on stream biofilms: a combined assessment with CLSM, structural and functional parameters[END_REF], Mueller et al. 2006[START_REF] Risse-Buhl | The role of hydrodynamics in shaping the composition and architecture of epilithic biofilms in fluvial ecosystems[END_REF]. The use of microfluidics associated with CLSM is particularly interesting to study microbial adhesion and detachment, biofilm integrity and structural parameters (biomass, thickness and cell viability), as well as biofilm susceptibility to antibiotics [START_REF] Macia | Antimicrobial susceptibility testing in biofilmgrowing bacteria[END_REF]al. 2014, Pousti et al. 2019). Direct real-time non-destructive visualization of biofilms developed on substrata informs on spatial relationships between organisms as well as with substrata. Nevertheless, the use of flowcell systems associated with CLSM to observe mono-species microalgal biofilms is so far poorly described [START_REF] Irving | Species and materials considerations in the formation and development of microalgal biofilms[END_REF]Allen 2011, Ozkan 2013a). Most of the studies concerning microalgae focus on the design of devices dedicated to biomass and lipid productions, and, treatment of wastewaters [START_REF] Berner | Microalgal biofilms for biomass production[END_REF][START_REF] Katarzyna | Non-enclosure methods for non-suspended microalgal cultivation: literature review and research needs[END_REF][START_REF] Bruno | Characterization of biofilm-forming cyanobacteria for biomass and lipid production[END_REF][START_REF] Boelee | Nitrogen and phosphorous removal from municipal wastewater effluent using microalgal biofilms[END_REF][START_REF] Gismondi | Phosphorus removal coupled to bioenergy production by three cyanobacterial isolates in a biofilm dynamic growth system[END_REF], Chaudhary et al. 2017). Hence, the first objective of this paper was to determine experimental parameters suitable to obtain in vitro microalgal biofilms in flow cell by using a system adapted from the protocol of Sternberg and co-workers [START_REF] Sternberg | Growing and analyzing biofilms in flow cells[END_REF], Tolker-Nielson and Steinberg 2011[START_REF] Pamp | Insight into the microbial Multicellular Lifestyle via Flow-Cell Technology and Confocal Microscopy[END_REF]. For this, two model microalgae strains were used: Cylindrotheca closterium (Bacillariophyceae) and Porphyridium purpureum (Porphyridiophyceae). Both strains were chosen because they are involved in colonization of marine substrates [START_REF] Jellali | Antifouling activity of novel polyisoprene-based coatings made from photocurable natural rubber derived oligomers[END_REF]) and are commonly studied in colonization assessment (Briand et al., 2012, Zargiel and[START_REF] Zargiel | Static vs dynamic settlement and adhesion of diatoms to ship hull coatings[END_REF]. They are associated with strong adhesion on surfaces and play an important role as exopolysaccharides producers within biofilms [START_REF] Staats | Isolation and characterization of extracellular polysaccharides from the epipelic diatoms Cylindrotheca closterium and Navicula salinarum[END_REF][START_REF] Zaouk | Filterability of exopolysachharides solutions from the red microalga porphyridium cruentum by tangential filtration on a polymeric membrane[END_REF]. Thus, inhibition of the adhesion of these strains is a real challenge for the maritime industries, especially because they can be as well involved in biocorrosion (Landousli et al., 2011).

In addition, in the context of antifouling coatings and ever more pressing regulatory constraints (for example, EU Biocidal Product Regulation EU 528/2012) the development of tools for assessing anti-bioadhesion molecules is essential. The second part of this study consisted of using the method previously developed to evaluate a known antifouling molecule dibromohemibastadin-1 (DBHB) [START_REF] Bayer | Antifouling Bastadin Congeners Target Mussel Phenoloxidase and Complex Copper(II) ions[END_REF][START_REF] Niemann | SAR of Sponge-Inspired Hemibastadin Congeners Inhibiting Blue Mussel PhenolOxidase[END_REF][START_REF] Ortlepp | Antifouling Activity of Bromotyrosine-derived Sponge Metabolites and Synthetic Analogues[END_REF], Le Norcy et al. 2017a) in comparison with the reference method (multi-well plates). Generally, microplates or classical microbiological techniques are used to determine minimum inhibitory concentrations (MIC) of compounds against bacteria and microalgae [START_REF] Plouguerne | Anti-microfouling activity of lipidic metabolites from the invasive brown alga sargassum muticum (yendo) fensholt[END_REF][START_REF] Iyapparaj | Antifouling and toxic properties of the bioactive metabolites from the seagrasses Syringodium isoetifolium and Cymodocea serrulata Ecotoxicological and[END_REF][START_REF] Prakash | Environmentally benign antifouling potentials of triterpene-glycosides from Streptomyces fradiae: a mangrove isolate[END_REF][START_REF] Gao | Antifouling potential of the marine microalga Dunaliella salina[END_REF][START_REF] Bressy | Efficacy testing of biocides and biocidal coatings[END_REF]. However, with these technics, only the impact of compounds on the growth or toxicity can be evaluated and only few papers have studied the impact of compounds on adhesion [START_REF] Jin | Antidiatom activity of marine bacteria associated with sponges from San Juan Island, Washington[END_REF][START_REF] Xin | Potential antifouling compounds with antidaitom adhesion activities from the sponge-associated bacteria, Bacillus pumilus[END_REF][START_REF] Abed | Quorum-sensing inhibitory compounds from extremophilic microorganisms isolated from a hypersaline cyanobacterial mat[END_REF]. In this paper, the impact of a reference compound on cell adhesion, adhesion strength and cell growth rate on surfaces was studied via the CLSM-Microfluidic Flow-cells method.

Materials and Methods

Strains

Microalgal

Growth

Before use, strain axenisation was realized by a treatment with a mixture of three antibiotics: chloramphenicol (100 µg/mL), penicillin (1000 µg/mL) and streptomycin (500 µg/mL) during 24 hours [START_REF] Druehl | Axenic culture of Laminariales in defined media[END_REF]. Both strains were grown in sterile artificial seawater (ASW, 30 g/L, Sigma Aldrich) supplemented with Guillard's F/2 medium at 2% [START_REF] Guillard | Studies of marine planktonic diatoms, I: Cyclotella nana (Hustedt) and Detonula confervacea (Cleve)[END_REF] Sigma Aldrich) at 20°C. Guillard's F/2 was added after sterilisation and culture medium was stored at 4°C before use. Erlenmeyer flasks were maintained under controlled illumination of 250 µmol.photons.m -2 .s -1 white fluorescent lamps (Philips Master TL5 HO 54W/840 1SL/20) at 20°C with a 12h:12h light:dark cycle in a Hélios 600 phytotron (Cryotec, Saint-Gély-du-Fesc, France).

This procedure favored the cellular growth [START_REF] Forjan | Microalgae: Fast-Growth sustainable Green Factories[END_REF]. Cultures of C. closterium and P.

purpureum were initially started with about 10 3 cell mL -1 . C. closterium reached the exponential phase after 3 days, whereas P. purpureum needed more time (6 days). After 15 days, both strains were in stationary phase. C. closterium showed longitudinal shape with a length of 65±10 µm, whereas P. purpureum showed a round shape (5±0.5µm) (Figure S1).

Culture in flow-cells

Microalgae were grown under hydrodynamic conditions in flow-cells. The flow-cell system was a tool originally used for the in vitro observation of bacterial biofilm (Tolker-Nielsen and [START_REF] Tolker-Nielsen | Growing and analyzing biofilms in flow chambers[END_REF] and has been adapted for microalgal biofilm observation. Microalgal biofilm was grown in a three channels flow-cell (1x4x44 mm; 1.76 mL; Biocentrum, DTU, Denmark) prepared with microscope glass coverslip (24x50 mm) (Knittel Glasser, Braunschweig, Germany) (Figure 1).

Before the experiment began, the flow-cells were sterilized by flowing a solution of sodium hypochlorite (1.5%, 150 µL/min) for 1 hour. They were then rinsed by ASW supplemented with Guillard's F/2 medium at 2% for 2 hours. All experiments were performed in a thermostatic stove at 20°C under 12:12 h light-dark cycle at 250 µmol.m -2 .s -1 . Distance between the flow cell and light source (2 fluorescent tubex, T4 TL2004A, 12W, Intertek, France) was 13.5 cm.

Adhesion of planktonic cells

250 µL of microalgal culture (10 5 cells/mL) diluted in ASW supplemented with Guillard's F/2 medium (2%) were inoculated in each channel by using a sterile 1mL syringe. The medium flow was not activated, thus allowing attachment of cells to the glass surface. Hence, the adhesion step was realized in static condition. Four incubation times were studied: 8, 24, 48 and 72 hours. The number of adhered cells per cm 2 after the incubation time was evaluated by CLSM observation (Zeiss, LSM710) equipped with helium-neon laser source and X20 air objective. The acquisition software was Zen Software (Zeiss). Cells were observed by the natural auto-fluorescence of chlorophyll (λexcitation = 633 nm, λemission = 638-720 nm). Experiments were realized with three independent cultures. The three channels of each flow cell were inoculated and three randomly observations were realized by channel. Hence, 27 randomly fields were considered during quantification.

Growth of adhered cells

Biofilm maturation was evaluated after the adhesion step (24 hours without any flow of medium to allow the microalgae adhesion). For this purpose, a flow (90 or 15 µL/min) was activated with ASW supplemented with Guillard's F/2 medium (2%) using a Watson Marlow 205U peristaltic pump (Watson Marlow, Falmouth, UK). Biofilm was observed after 24, 48, 72, 96 and 120 hours.

Images were taken every micrometer throughout the whole biofilm thickness. The Zen software (Zeiss) was used to process data of 3D image with maximal intensity projection. The average thickness of the biofilm (µm) and the biovolume (µm 3 /µm 2 ) were measured using COMSTAT software [START_REF] Heydorn | Quantification of biofilm structures by the novel computer program COMSTAT[END_REF]. Results were representative of 27 randomly fields.

Evaluation of reference compound by multi-well plate assay

Reference compound was dibromohemibastadin-1 (DBHB). It was furnished by Prof. Proksch (Institute of Pharmaceutical Biology and Biotechnology, University of Düsseldorf, Germany). It was evaluated at 0.016, 1.6, 8, 16, 32 and 80 µM in 12 replicates in 96-wells microplate (black with transparent base, Fisher-Scientific, Waltham, MA, USA). Methanol was used as a carrier solvent to add DBHB in the microplate, and was evaporated prior to the bioassay. A well without DBHB was used as control. Then, one hundred microliters microalgal cultures of 2 weeks at 10 3 cells/mL were added in each well and microplates were incubated at 20°C during 5 days under controlled illumination (250.µmol.photon.m -2 .s -1 ) with a 12:12 light-dark cycle. The fluorescence was measured (λexcitation = 633 nm, λemission = 638-720 nm) by using a TECAN microplate reader (Magellan, France) in order to quantify the total cells density in each well. Then, the microplate was emptied by flipping and washed twice with ASW. The fluorescence was again measured in order to quantify adhered microalgae. The difference between the total cells number and the adhered cells number was calculated to obtain the number of planktonic cells. MIC was defined as the lowest concentration that produced a significant reduction in growth or adhesion.

Experiments were repeated three times.

Evaluation of reference compound by flow-cell assay

Impact on adhesion from planktonic cells

The experimental procedure was the same that described above (2.3.1). The impact of compound was evaluated by adding DBHB in the flow-cell at 16 or 80 µM in the microalgae inoculum immediately prior to the inoculation in flow cell channels. After 24h of adhesion, the flow (120 µL/min) was activated during 30 minutes to remove free diatoms. The number of adhered cells was compared to the control without DBHB.

Impact on adhesion strengths

The impact of DBHB on adhesion strength of microalgae was determined after the adhesion stage.

Experiment was realized in the presence of DBHB (16 µM) during adhesion step (72h) as described above (2.5.1), then the application of a high shear stress was realized to quantify the removal percentage. The flow was activated at 330 µL/min (8.10 -3 Pa) during 30 minutes. The cells number adhered on the surface were counted again and the removal percent was determined as following:

. . .

100.

The removal percentage determined for the experiment in the presence of DBHB was compared to the control without DBHB.

Impact on growth of adhered cells

The impact of DBHB on biofilm maturation was evaluated by adding DBHB (16 µM) in the growth medium flow. After 72 hours of adhesion without DBHB, the growth medium containing DBHB was "activated" as described above (2.3.2) at 150 µL/min during 24, 48, 72, 96 or 120 hours. The biovolume and the average thickness were determined with the COMSTAT program. Experiments without DBHB in the growth medium were used as control. All experiments were realized three times.

Statistical analysis

The one-factor analysis variance (ANOVA) was used to determine the effect of studied conditions.

The level of significance was set to p <0.01. Values were means ± standard deviation (sd).

Results and discussion

3.1 Culture of microalgal biofilm in flow-cell system. However, the adhered cells number for both strains was significantly different. The number of adhered cells increased with the time: a significant (p <0.01) difference was observed between each observation. For C. closterium, the results indicated that the rate of adhesion to glass can be divided in 3 parts: 1) during the first 8 hours, the density increased with a rate of 1280 cells/cm 2 /h, 2) the rate decreased to 330 cells/cm 2 /h during the subsequent 48 hours (r 2 = 0.9998), and 3) finally in the last 24 hours the rate decreased further to 65 cells/cm 2 /h. This profile of cells multiplication on glass slide has been already shown for Chlorella vulgaris (Ozkan et al. 2013a). For P. purpureum, the rate adhesion rate showed only 2 parts: after a high adhesion rate during the first 8 hours (2145 cells/cm 2 /h), a linear rate (r 2 = 0.9989) of 555 cells/cm 2 /h was observed to the end of the experiment.

Adhesion from planktonic cells

Cells densities (2.5.10 4 and 5.1.10 4 cells/cm 2 respectively at 72h) were significantly different (p <0.01) for C. closterium and P. purpureum. This observation could be explained by the morphology of microalgae. C. closterium is elongated (65 µm) whereas P. purpureum is spherical and smaller (5µm diameter). For an equal space and for reasons of steric constraints, more P.

purpureum cells are likely to adhere than C. closterium cells. These results were consistent with the observation of [START_REF] Sekar | Laboratory studies on adhesion of microalgae to hard substrates[END_REF], who indicated variability in the microalgal adhesion levels and an increase of adhesion with exposure time.

Growth of adhered cells

Biofilm formation of C. closterium and P. purpureum was evaluated under constant flow conditions, after the step of adhesion (24h). In the case of bacteria, it has been established that two factors influenced the structure of biofilms and needed to be controlled: the flow velocity and the nutrient status. Indeed, the flow velocity determined the hydrodynamic shear and the mass transfer characteristics of a system [START_REF] Stoodley | Influence od hydrodynamics and nutrients on biofilm structure[END_REF]. Hence, microalgal biofilms were grown during application of a continuous flow (90 or 150 µL/min) in the presence of medium culture (ASW supplemented with Guillard's F/2). Microalgal biovolume was quantified during 120 hours and the growth kinetics was determined (Figure 3). The cellular density increased with time and the medium flow velocity. As for bacteria, an increase of fluid flow velocity in the flow-cells resulted in faster development of microorganisms due to higher nutrients transport (Bussher and van der Mei 2006). For both strains, the biovolume increased linearly with time after 48 hours of medium flow which indicated a cellular multiplication at a constant rate during the time of experiment. In the case of C. closterium a time lag was observed. Then, a growth rate could be determined. Results

showed a significant higher (p<0.01) growth rate at a flow velocity of 150 µL/min (0.1102 µm 3 /µm 2 /h) compared to the flow velocity at 90 µL/µmin (0.0612 µm 3 /µm 2 /h). The biomass reached after 120 hours a value significantly higher (9.1 µm 3 /µm 2 versus 5.5 µm 3 /µm 2 respectively). For P. purpureum, no time lag was observed. The cellular multiplication took place mainly in the first 48 hours, then a decrease of cellular multiplication was observed indicating the end of the maturation process: the increase in the cells number between two times was not significant (p>0.05). Moreover, the impact of flow velocity was not significant (p>0.05): similar growth rates (0.0083 µm 3 /µm 2 /h) were determined. On the other hand, the biovolume was significantly (p<0.01) higher for C. closterium: the denser biofilm was obtained for a flow velocity of 150 µL/min. This result could be explained by the size of cells and their respective growth rates (10 times greater on average for C. closterium).

The microscopic observations of biofilms developed during 48, 72, 96 and 120 hours at a flow velocity of 150 µL/min are shown in Figure 4A. The qualitative results described the spatial organization of microalgae in biofilm: cells agglomerated to each other and at the glass surface.

Results showed the capability of C. closterium and P. purpureum to form a biofilm in flow-cell experiment after 120 hours. Nevertheless, the structure of biofilm was dependent on the strain studied. In the case of C. closterium biofilms, cells formed dense aggregates, whereas in P.

purpureum biofilms cells were more scattered. Based on the biofilm image analysis, biovolumes were quantified for each strain and results are shown Figure 4B. Biofilm formation was highly repeatable between independent experiments (standard deviation lower than 1 µm 3 /µm 2 and 0.2 µm 3 /µm 2 for C. closterium and P. purpureum biovolume respectively). However, the observed biofilms indicated average thicknesses relatively low (< 40 µm) (Figure 4C) compared to those of millimeters or more observed in natural environment (Irvin et al. 2011). The biofilm observed for C. closterium was denser (9.1 µm 3 /µm 2 ) and thicker (38 µm) than for P. purpureum which indicated only 1.5 µm 3 /µm 2 and 10.2 µm for biovolume and average thickness respectively. C. closterium covered more quickly the surface, then cells adhered to each other to form a 3D structure (from 72 h). Another species of the genus Cylindrotheca (C. fusiformis) was identified as excellent candidates to form biofilms due to their strong attractiveness to glass but also cell to cell interactions (Ozkan et al. 2013b). On the contrary, P. purpureum developed longitudinally on the surface. A relatively homogeneous surface pattern interspersed with a few macro-colonies was observed after 120 hours. These differences could be explained in particular by the size of cells.

Use of culture in flow-cells to evaluate antibiofilm/ anti-bioadhesion compounds

The use of bioassays to evaluate anti-biofilms compounds is essential to screen potential substances and understanding their mode of action. Among bioassays developed, the use of multiwell plates is particularly common [START_REF] Trepos | Antifouling Compounds from the sub-artic ascidian synoicum pulmonaria:synoxazolidinones A and C, Pulmonarins A and B, and synthetic analogues[END_REF], Hellio et al. 2015). However, biofilms developed in flow-cells could also be useful to evaluate the anti-microalgal biofilm activity of compounds (Table 1). Data obtained with both bioassays are listed in Table 2 and it appeared clearly that study in flow cells led deeper analysis.

In this context, a reference compound has been tested using both bioassays: multi-well plates and flow-cell system. A hemibastadin analog named dibromohemibastadin-1 was selected. It has been shown an anti-bacterial biofilm and anti-quorum sensing activities without toxic activity (Le Norcy et al. 2017a). DBHB can inhibit the settlement of cyprid larvae of Balanus improvisus and byssus formation of Mytilus edulis without toxicity on nauplii of Artemia salina [START_REF] Bayer | Antifouling Bastadin Congeners Target Mussel Phenoloxidase and Complex Copper(II) ions[END_REF][START_REF] Niemann | SAR of Sponge-Inspired Hemibastadin Congeners Inhibiting Blue Mussel PhenolOxidase[END_REF][START_REF] Ortlepp | Antifouling Activity of Bromotyrosine-derived Sponge Metabolites and Synthetic Analogues[END_REF]. Moreover, on four species tested, DBHB affected the growth of two microalgae (C. closterium and Exanthemachrysis gayraliae) with a MIC of 80 µM after 5 days (Le Norcy 1017b).

Study of DBHB by multi-well plates

DBHB activity (at concentration from 0.016 to 80 µM ) was evaluated towards microalgal adhesion and growth and MIC values were determined. MIC is defined as the lowest concentration that produces a significant reduction in growth or adhesion (Hellio et al. 2015). Strains showed different sensitivity to DBHB. DBHB exhibited an inhibitory activity against C. closterium (80 µM) in terms of both growth and adhesion whereas P. pupureum displayed a lower sensitivity towards DBHB (no inhibition up to 80µM). This result correlated well with previous studies using the same bioassay for the screening of natural antifoulants: P. purpureum was described as a resisting strain [START_REF] Moodie | Design and biological evaluation of antifouling dihydrostilbene oxime hybrids[END_REF].

Impact of DBHB on adhesion of planktonic cells by flow-cells

From results obtained using multi-well plates, the evaluation of DBHB activity against microalgal adhesion was realized by using flow-cell system. It was operated at two concentrations: 16 and 80 µM. At 16 µM, no impact on the microalgal growth was observed in multi-well plates whereas 80 µM corresponding to the MIC.

The impact of DBHB on C. closterium and P. purpureum is evaluated (Figure S3). For this purpose, DBHB (16 or 80 µM) was injected in the flow cell at the same time as microalgal cells. After 24 hours of static adhesion, a difference of adhesion was observed between both strains. DBHB did not affect the P. purpureum adhesion at the tested concentrations. Concerning, C. closterium a significant (p<0.01) decrease of adhesion was observed for a concentration of 80µM whereas for 16 µM, no significant effect (p>0.05) was observed on the number of adhered cells. All results corroborated with those mentioned above. However, it could be pointed out that for C. closterium, in the presence of 80 µM, the inhibition rates diverged: inhibition percentages of 100% and 40%

(comparatively to control) were quantified for multi-well plates and flow-cell bioassay, respectively. The adhesion of cells was influenced by several parameters. For example, the adhesion surface (polystyrene versus glass), the physiological state of cells during experiment (5 days versus 24 hours), the inoculation cellular concentration (10 3 vs 10 5 cells/mL), the washing method (pipette versus peristaltic pump) were parameters that could impact microalgal adhesion evaluation.

Impact of DBHB on adhesion strengths in flow-cells

The use of flow-cells allowed the determination of the impact of DBHB on the adhesion strengths of microalgae. For that, after 72 hours of adhesion in flow cells with DBHB, a continuous flow (330 µL/min, 8.10 -3 Pa) was applied during 30 minutes. The concentration of 16 µM was applied to be lower than the MIC (80µM). The number of adhered cells on glass slide was quantified before and after activation of flow and the removal percentage was determined. These data provided key information about adhesion strengths of cells on the glass surface which increased with time as observed in previous studies [START_REF] Schultz | A turbulent channel flow apparatus for the determination of the adhesion strength of microfouling organisms[END_REF][START_REF] Holland | Adhesion and motility of fouling diatoms on a silicone elastomer[END_REF][START_REF] Finlay | A novel biofilm channel for evaluating the adhesion of diatoms to non-biocidal coatings[END_REF][START_REF] Alles | Microfluidic detachment assay to probe the adhesion of diatoms[END_REF][START_REF] Nolte | Microfluidic accumulation assay probes attachment of biofilm forming diatom cells[END_REF]. Concerning C. closterium, a significant (p<0.01) increase of removal percent was observed after 72 hours in the presence of DBHB (from 24 ± 4% to 41 ± 2%):

the adhesion strengths were lesser. This result was particularly interesting because C. closterium is a large diatom. It has been shown that the magnitude of interactions (as electrostatic, van de Waals and acid base) increased with increasing cell size. Moreover, the drag forces acting on cells augmented with increasing cell size in systems involving medium flow (Ozkan et al. 2013b). For P. purpureum, no significant difference was observed between the standard and the experiment containing DBHB. DBHB did not act in the same way against C. closterium than P. purpureum.

The adhesion of microalgae was strongly linked to the physico-chemical attraction between microalgal cells containing bound extracellular polymeric substances and the substratum [START_REF] Klein | Marine diatom Navicula jeffreyi from biochemical composition and physicochemical surface properties to understanding the first step of benthic biofilm formation[END_REF], Ozkan et al. 2013a). Hypothetically, DBHB could affect these parameters disturbing not only the number of adhered cells but also their adhesion strengths. Hence, flow cell bioassay could inform not only on the ability of bioactive compounds to inhibit the adhesion but also on mechanisms of action of bioactive compounds.

Impact of DBHB on growth of adhered cells in flow cell

To evaluate the impact of DBHB on the growth of adhered cells, the compound in solution (at 16 µM) was added in the growth medium. After application of a continuous flow, the biovolume developed on glass slide was quantified. Two different behaviors were observed depending on the strains.

For C. closterium, no cell was observed after 24 hours. Cells previously adhered in flow cell system were probably detached from glass surface in the presence of DBHB and the application of flow.

Results confirmed those mentioned above: DBHB decreased C. closterium adhesion strengths.

For P. purpureum no effect of DBHB was observed. Whatever the incubation time tested, the biovolume developed in the presence of 16 µM DBHB was not significantly different (p>0.05) from control (Figure S4). This result was in accordance with results obtained in multi-well plates:

DBHB did not affect P. purpureum growth.

Conclusion

The results of our experiments have shown the ability of microalgae to form biofilms in flow-cells.

P. purpureum cells adhered in higher number on glass surfaces than C. closterium cells.

Nevertheless, C. closterium formed thicker biofilms. The results corroborated those obtained with the reference method (multiwell plate). However, flow-cell system was able to discriminate the adhesion of planktonic cells and the growth of adhered cells contrary to multi-well plate assay.

Additional data could also be obtained as the impact of compounds on adhesion strengths and the morphology of biofilms. The flow-cell system appeared to be a complementary method to multiwell plate assay, which remains a first essential step for the screening of potential antibiofilm compounds. This method is more informative but it is nonetheless more difficult to implement, requires more compound and especially requires a confocal laser scanning microscope to provide biofilms structural observations and digital data as biovolume. The method can be applied in the research of antibiofilm/antifouling compounds (natural substances, commercial organic biocides) used in antifouling paint as well as in other domains impacted by biofilms development (water treatment, fish farming, industrial processes…). Biochemical process and mechanisms could be evaluated in further works to improve the current knowledge.

  strains were obtained from Algobank (Biological Resource Center of the University of Caen Normandie, France): Cylindrotheca closterium (AC-170) (Bacillariophyceae, (Ehrenberg) Reimann & Lewin) and Porphyridium purpureum (AC-122) (Porphyridiophyceae (Bory) Drew & Ross).

Figures 2 and

 2 Figures 2 and S2 show the adhesion kinetics of C. closterium and P. purpureum in flow-cells over 72 hours. The count represents the number of cells irreversibly adhered. Single cells were observed on the totality of the cover glass, which indicated that initial attachment of cells was homogeneous.

Figure 2 :Figure 3 :

 23 Figure 2: Adhesion kinetics on flow cell during 72h for C. closterium and P. purpureum. ANOVA *p <0.01, compared to the precedent time #p <0.01; compared between microalgae. The errors bars represent standard deviations calculated from three independent experiments.

Acknowledgements: The authors acknowledge the financial support for the PhD of T. Le Norcy: Région Bretagne (ARED LACTOPAI) and the Université de Bretagne occidentale. Authors are gratefully acknowledged to Prof Peter Proksch (Institute of Pharmaceutical Biology and Biotechnology, University of Düsseldorf, Germany) for allowing the study on DBHB by the synthesis of the molecule. Declaration of interest: none