Xuan Khanh Do

Stephane Louise
email: stephane.louise@cea.fr

Albert Cohen
email: albert.cohen@inria.fr

Transaction Parameterized Dataflow: A Model for Context-Dependent Streaming Applications

Static dataflow programming models are well suited to the development of embedded many-core systems. However, complex signal and media processing applications often display dynamic behavior that do not fit the classical static restrictions. We propose Transaction Parameterized Dataflow (TPDF), a new model of computation combining integer parameters-to express dynamic rates-and a new type of control actor-to allow topology changes and time constraints enforcement. We present static analyses for liveness and bounded memory usage. We also introduce a static scheduling heuristic to map TPDF to massively parallel embedded platforms. We validate the model and associated methods using a cognitive radio application, demonstrating significant buffer size and performance improvements compared to state of the art models including Cyclo-Static Dataflow (CSDF).

I. INTRODUCTION

The broader availability of low-power many-core platforms-such as the MPPA-256 chip from Kalray (256 cores) [START_REF] De Dinechin | A distributed run-time environment for the Kalray MPPA-256 integrated manycore processor[END_REF] or Epiphany from Adapteva (64 cores)-opens new opportunities for system designers. The complexity of these platforms also pushes for practical solutions accessible to domain experts, facilitating efficient mapping, performance tuning and analysis of applications.

Programming languages based on dataflow models of computation have emerged as a comprehensive solution towards the automation of embedded system design. Dataflow application are modeled as a directed graph where nodes represents actors (iterated execution of tasks) and edges represent communication channels. Among these, decidable dataflow models in the SDF [START_REF] Lee | Synchronous data flow[END_REF] or CSDF [START_REF] Bilsen | Cyclo-static data flow[END_REF] family are useful for their predictability, formal abstraction, and amenability to powerful optimization techniques. However, for signal processing applications, it is not always possible to represent all of the functionality in terms of purely decidable dataflow representations; typical challenges include variable data rate processing, multi-standard or multi-mode signal processing operation, and data-dependent forms of adaptive signal processing behavior. For this reason, numerous dynamic dataflow modeling techniques-whose behavior is characterized by dynamic variations in resource requirements-have been proposed. In many of these, in exchange for the increased modeling flexibility (high expressive power) provided by the underlying techniques, one must give up guarantees on compile-time buffer underflow (deadlock) and overflow validation (boundedness).

In this paper, we introduce a new dynamic Model of Computation (MoC), called Transaction Parameterized Dataflow (TPDF), allowing variable production and consumption rates and dynamic changes of the graph topology. TPDF is designed to be statically analyzable regarding the essential deadlock and boundedness properties, while avoiding the aforementioned restrictions of decidable dataflow models.

The remainder of this paper is organised as follows. Section II-A recalls some background on Cyclo-Static Dataflow (CSDF) needed to introduce our parametric and dynamic extension in Section II-B. Section III presents the static analyses for liveness and boundedness and a scheduling heuristic for this model, which is illustrated in Section IV-B by a case study. Finally, we give an overview of the related models in Section V and summarize our contributions in Section VI.

II. MODEL OF COMPUTATION

Let us first recall the principles of CSDF [START_REF] Bilsen | Cyclo-static data flow[END_REF], one of the reference dataflow MoC for applications in the signal processing domain. Then, we introduce our model as a parameterized extension of CSDF with transaction processes.

A. Basic Model: CSDF

In this work, we choose Cyclo-Static Dataflow (CSDF) [START_REF] Bilsen | Cyclo-static data flow[END_REF] as the base model for TPDF because it is deterministic and allows for checking conditions such as deadlocks and bounded memory execution at compile/design time, which is usually not possible for Dynamic Dataflow (DDF). In CSDF, a program is defined as a directed graph G " xA, Ey, where A is a set of actors, E Ď A ˆA is a set of directed communication channels. Actors represent functions that transform the input data streams into output data streams. An atomic piece of data carried by a channel is called a token. Each channel has an initial status, characterized by its initial tokens.

Each actor a j P A has a cyclic execution sequence of length τ j , rf j p0q, ¨¨¨, f j pτ j ´1qs which can be understood as follows:

The n-th time that actor a j is fired, it executes the code of function f j pn mod τ j q and produces (consumes) x u j pn mod τ j q (or y u j pn mod τ j q) tokens on its output (input) channel e u . The firing rule of a cyclo-static actor a j is evaluated as true for its n-th firing if and only if all input channels contain at least y u j pn mod τ j q tokens. The total number of tokens produced (consumed) by actor a j on channel e u during the first n invocations, denoted by X u j pnq " ř n´1 l"0 x u j plq (or Y u j pnq " ř n´1 l"0 y u j plq). One of the most important properties of the CSDF model is the ability to derive at compile-time a schedule for the actors. Definition 1. Given a connected CSDF graph G, a valid static schedule for G is a schedule that can be repeated infinitely while the buffer size remains bounded. A vector

e 1 [1,0,1] [1,1,2] 1 [ ] [2] [1,1] [0,2] a 1 a 2 a 3 e 2 e 3
Fig. 1. Figure 1 shows a CSDF graph consisting of four actors and four communication channels. Edge e 2 has two initial tokens.

Ý Ñ q " rq 1 , q 2 , ..., q n s T is a repetition vector of G if each q j represents the number of invocations of an actor a j in a valid static schedule for G. A CSDF graph is called consistent if and only if it has a non-trivial repetition vector [START_REF] Bilsen | Cyclo-static data flow[END_REF]. Theorem 1. In a CSDF graph, a repetition vector Ý Ñ q " rq 1 , q 2 , ..., q n s T is given by [START_REF] Bilsen | Cyclo-static data flow[END_REF]:

Ý Ñ q " P ¨Ý Ñ r , with P " P jk " # τ j , if j " k 0 , otherwise (1)
where Ý Ñ r " rr 1 , r 2 , ..., r n s T is a solution of

Γ ¨Ý Ñ r " 0 (2
) and where the topology matrix Γ is defined by

Γ uj " $ ' & ' % X u j pτ j q
, if task a j produces on edge e u ´Y u j pτ j q , if task a j consumes from edge e u 0 , otherwise

In Figure 1, the solutions are Ý Ñ q " r3, 2, 2s T . It can only start by firing a 3 twice; then, a 1 fired three times, and finally a 2 twice. Since each actor has been fired the exact number of times required by its solution, a schedule can be found. We represent it as the string pa 3 q 2 pa 1 q 3 pa 2 q 2 where the superscripts denote repetition count.

B. Transaction Parameterized Dataflow Model

We extend CSDF by allowing rates to be parametric and a new type of control actor, channel and port. For a compact formal notations, we assume in that paper that kernels, which play the same role as computation units (actors) as in CSDF, have at most one control port. Kernels without control ports are considered to always operate in a dataflow way, i.e., a kernel starts its firings only when there is enough data tokens on all of its data input ports. Definition 2. A TPDF graph G is defined by a tuple (K, G, E, P , R k , R g , α, φ ˚) where:

' K is a non-empty finite set of kernels and G is a finite set of control actors such that K X G " ∅. For each kernel k P K, M k denotes the set of modes indicated by the control node connected to its unique control port c. The following modes are available within a TPDF graph:

-Select one of the data inputs (outputs) -Select more than one data input (output) -Select available data input with the highest priority -Wait until all data inputs are available In this context, the effect of control tokens can be also described as selecting data input and output ports besides choosing modes. Indeed, at a given time, the input and output ports of an edge may be in a different state. However, it does not affect the firings of kernels or control actors, only the data tokens that are chosen or rejected.

' E P O ˆpI Y Cq is a set of directed channels, where I, C, O is the union of all input, control and output port sets respectively. E c " EzpO ˆIq is the set of all control channels. A control channel can start only from a control actor and is connected to a control port. ' P is a set of integer parameters.

' R k : M k ˆpI k Y C k Y O k q ˆN ÝÑ
N assigns the rate to the ports of the n-th firing of k for each mode. The rate R k pm, c, nq " t0, 1u for all modes m P M k and for all firings of k. ' R g : pI g Y C g Y O g q ˆN ÝÑ N assigns the rate to each port of the n-th firing of a control actor g. ' α : pI Y C Y Oq ÝÑ N returns for each port its priority. ' φ ˚: E ÝÑ N is the initial channel status. In this paper, we assume that a kernel k P K waits until its control port becomes available to be fired by reading one token from this port. This token defines in which mode m P M k in which k will operate. One of the most important property of TPDF, which is different from SDF and CSDF, it is that a kernel or a control actor does not have to wait until sufficient tokens are available at every data input port. This new property allows the capacity of reconfiguration of graphs depending on context and time.

The n-th firing of a control actor g P G starts by waiting until R g pi, nq and R g pc, nq tokens are available at every input i P I g and c P C g , where R g pc, nq " t0, 1u. After performing its actions, the n-th firing of g ends by removing the R g pi, nq and R g pc, nq tokens from its input data and control ports and writing R g po, nq tokens to each output control port o P O g .

1 [ ] 1 [ ] 1 [ ] 1 [ ] [2] [2] [1,1] [1,1] [0,2] [2] [2] [1]
Fig. 2. A simple TPDF graph with integer parameter p and control actor C Example 1. Figure 2 a simple TPDF graph where actors have constant or parametric rates (e.g., p for the output rate of A). The repetition vector is r2, 2p, p, p, 2p, 2ps. C is a control actor and e 5 is a control channel. A sample execution of the graph is the following: A fires and produces p tokens on e 1 . Then B fires and produces one token on edge e 2 , e 3 , e 4 . Only E can fire because there are enough tokens on its input edge and produce one token on edge e 7 . B (and A if necessary) will fire a second time and produce another token on edge e 2 , e 3 , e 4 . Then C, D and E will fire and produce 2, 2 and 1 token, respectively, on edge e 5 , e 6 , e 7 . Finally, F fires two times, each time it consumes one token from its control port. This token determines in which mode F will be fired. In this case, F can choose two tokens from e 6 or one from e 7 and remove remaining tokens. This continues until each actor has fired a number of times equal to its repetition count.

In TPDF, we define 2 data distribution kernels Selectduplicate, Transaction Box [START_REF] Louise | A model of computation for real-time applications on embedded manycores[END_REF] and a new type of control clock in a dataflow way. a) Select-duplicate: kernels with one entry and n outputs (n is a maximum number for automatic sizing). At a given time any combination of the n outputs can be enabled. Each time a data token is read on the input line, it is copied on this combination of the n output channels.

b) Transaction: symmetric processes with n inputs and one output. Its role is to atomically select a predefined number of tokens from one or several of its input to its output. By using special modes predefined by TPDF and combining with a control actor, the Transaction process implements important actions not available in usual dataflow MoC: Speculation, Redundancy with vote, Highest priority at a given deadline, Selection of an active data-path among several [START_REF] Louise | A model of computation for real-time applications on embedded manycores[END_REF].

c) Clock: can be considered as a watchdog timer with control tokens sent each time there is a timing out.

III. STATIC ANALYSES This section presents the three static analyses needed to ensure consistency, boundedness and liveness of TPDF graphs. In Section III-A, we check rate consistency by adapting the analysis of CSDF to TPDF. Conditions for rate consistency and solutions of balanced equations are computed in terms of symbolic expressions. In Section III-B, we check that, along with rate consistency, the TPDF MoC with control actor and parameter setting ensures boundedness. Section III-C completes the analysis chain by checking for liveness.

A. Rate consistency

As in SDF and CSDF, we check the rate consistency of a TPDF graph by generating the associated system of balance equations expressed in matrix-form as in Equation (2) and this system must be shown to have a non null solution for all possible values of parameters, all possible reconfigurations of the graph and all modes of the kernels.

The matrix is generated by considering the parametric rates and by ignoring all possible configurations of the graph. If the system is rate consistent when all edges are present, then it is also consistent when one or more several edges are removed. Indeed, when removing edges (i.e., tokens produced in this edge are not used and will be rejected), the resulting system of balance equations will be a subset of the system of equations of the fully connected graph. Checking rate consistency of all edges maybe considered too strict because it does not take into account the fact that some input edges may not be active in the same mode. However, it simplifies the understanding and implementation since the graph has a unique iteration vector.

The minimal solutions for all actors when solving the system of equations ( 2) are found by eliminating all the coefficients or parametric factors common to all solutions. Then, we arbitrarily set one of the solutions to 1 and recursively find other solutions. Finally, we normalize the solutions to integers. If the system of equations ( 2) has a non-trivial solution, the TPDF graph also satisfies the necessary and sufficient conditions for the existence of parametric solutions, introduced for parametric models such as SPDF [START_REF] Fradet | SPDF: A schedulable parametric data-flow MoC[END_REF] and BPDF [START_REF] Bebelis | BPDF: A statically analyzable dataflow model with integer and boolean parameters[END_REF]. Example 2. For the graph of Figure 2, by setting r A " 1, we consecutively get:

r B " p, r C " p{2, r D " p{2, r E " p, r F " p{2 (4)
To normalize the fractional solutions we multiply by 2. Finally, we get the vector Ý Ñ r and also the repetition vector Ý Ñ q by multiplying with the matrix P : Ý Ñ r " r2, 2p, p, p, 2p, ps , Ý Ñ q " r2, 2p, p, p, 2p, 2ps (5) and a possible valid static schedule for this graph is

A 2 B 2p C p D p E 2p F 2p = A 2 pB 2 CDE 2 F 2 q p .

B. Boundedness

Without dynamic topology changes, rate consistency is sufficient to ensure that a graph returns to its initial state after each iteration and boundedness is guaranteed. However, in TPDF, a graph can change its topology within a valid static schedule by using the control actor. Yet, not all static schedules are safe and their boundedness must be checked. The criterion ensuring that reconfiguration by using control actor and several modes for one kernel are safe relies on the notion of control area. Intuitively, the criterion states that each control actor will be fired once per local iteration of the area it reconfigures. Definition 3. (Control area): The area of a control actor g P G, noted Areapgq, is defined as:

Areapgq " precpgq Y succpgq Y inflpgq (6) where succpgq " ta i P pK Y Gq : De u " pg, a i q P Eu precpgq " ta i P pK Y Gq : De u " pa i , gq P Eu (7)

and inflpgq " psuccpprecpgqq X precpsuccpgqqqztgu is the list of actors between precpgq and succpgq, influenced by g.

The control area of g is the set containing its sources, kernels or controls that receive its control tokens and all other influenced actors between these actors. Definition 4. (Local Solution) The local solution of an actor (kernel or control actor) a i in a subset of actors Z " ta 1 , . . . , a n u, written q L ai , is defined as: q L ai "

q ai q G pZq (8)
where q G pZq " gcdpq ai {τ i q @a i P Z (gcd denotes the greatest common divisor). Local solutions can be considered as a repetition vector for a subset of actors.

Definition 5. (Rate Safety): A TPDF graph is rate safe if and only if, for each control actor g P G and each actor a P Areapgq, the consumption and production rates of these actors ensure that, during a local iteration of its area, a control actor will be fired only one time. This condition is guaranteed, if and only if, for each control actor g P G and for each actor a i P precpgq Y succpgq, connected with g by the channel e u : # X u g p1q " Y u i pq L ai q if g is the production actor Y u g p1q " X u i pq L ai q if g is the consumption actor

Rate safety ensures that, during a local iteration of an area of a given control actor, the total number of tokens consumed (produced) on any edge connected with the control actor is sufficient for this actor to fire exactly one time. It is ensured by a simple syntactic check on TPDF graphs. Example 3. In Figure 2, AreapCq " tB, D, E, F u and possible static schedules for this graph are A 2 B 2p C p D p E 2p F 2p and A 2 pB 2 CDE 2 F 2 q p , where B 2 CDE 2 F 2 is a local solution for the AreapCq. C will be fired only one time for each iteration of this local area. Theorem 2. (Boundedness) A rate consistent, safe and live TPDF graph returns to its initial state at the end of its iteration. Hence it can be scheduled in bounded memory.

Proof. There are several modes defined by a control actor as defined in Section II-B. In fact, the Rate safety ensures that, during a local iteration of a control area, its influenced kernels receive synchronous control tokens, calculated by only one firing of the control actor and define in which mode this kernel will fire. For the modes that choose between the data inputs (e.g., Transaction), the dependence with kernels which produce these input tokens is not broken here because unchosen data input are considered only as not to be used. For the modes which choose between data outputs (e.g., Select-duplicate), we assume that there is a virtual control actor and a virtual kernel which chooses between data inputs, as in Figure 3. A

[1] [1] [1] [2] e 1 A [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1]
⬌ Fig. 3. B is a Select-duplicate to choose between D and E. This graph is equivalent with the second graph by adding two virtual actors: C and F , which consume data outputs from C, D and E. When B must choose between its data outputs, it sends a signal token to C, this control actor will send a control token to F , which choose only the data-paths chosen by B. In this case, boundedness of the graph is guaranteed.

Rate consistency and safety were crucial to ensure that the graph returns to its initial state after an iteration. However, we assumed that actors can be fired in the right order to respect dataflow constraints. This holds only when the graph is live and the next section shows how it is checked.

C. Liveness

In SDF and CSDF, checking liveness is performed by finding a schedule for a basic iteration. For TPDF, the situation is more complex for two reasons:

' First, control tokens change the topology of the graph by the selection or removal of data tokens within the iteration. However, this selection does not introduce new constraints among firings of control and kernel actors. Then, the topology change of the graph is not a reason which may introduce deadlocks. ' Second, actors may have to be fired a parametric number of times during an iteration. Finding a schedule may, in general, involve some inductive reasoning. We resolve this problem by using the following analysis. A (C)SDF and TPDF graph deadlocks only if it contains at least one cycle. To deal with such problems, we use the standard clustering described in [START_REF] Battacharyya | Software Synthesis from Dataflow Graphs[END_REF]. Given a connected, consistent TPDF graph G, a subset Z Ď pK Y Gq, clustering Z involves replacing Z by a single actor Ω. The new actor Ω is connected to the same external ports as Z was, but the port rate and execution sequence must be adjusted. The rate sequence of each port of an actor a i P Z connected to the rest of the graph is replaced by r " Y u i pq L ai q if e u connected to an input port of a i or r " X u i pq L ai q if e u connected to an output port of a i . It follows that a firing of Z corresponds to q L ai firings of its actors. Here, by clustering only cycles, we resolve the problem of liveness by checking the local solution of the clustered cycles. For the example in Figure 4(a), by clustering the cycle Z " pB, Cq into a new actor Ω to get the new graph in Figure 4(c). By resolving the balance equation ( 2), we find the schedule A 2 Ω p which corresponds to A 2 pB 2 C 2 q p for the original graph (with q G pZq " p, q L B " 2 and q L C " 2), which is therefore correctly found to be live.

A B [1,1] [p,p] C [0,2] [1] [1] [1,1] 2 (a) A B [1,1] [p,p] C [2,0] [1] [1] [1,1] 1 (b) A Ω [2] [p,p] (c)
A final refinement is needed to take into account the case in Figure 4(b). For instance, the previous refined algorithm would fail to find a schedule for the cycle with only one initial token. However, it is clearly live with the schedule A 2 pBCq 2p or A 2 pBCCBq p . In this case, we construct a Late schedule [START_REF] Do | Managing the latency of datadependent tasks in embedded streaming applications[END_REF], which introduces the execution order between actors in CSDF and TPDF graphs. For instance, the cycle in Figure 4(b) has a local Late schedule pBCCBq by applying the Algorithm presented in [START_REF] Do | Managing the latency of datadependent tasks in embedded streaming applications[END_REF] for q L C firings of C. Then, the original graph is live with the global schedule A 2 Z p or A 2 pBCCBq p .

D. Scheduling

In Section III-C, we described a way to find a sequential schedule for TPDF applications. However, our objective is to use TPDF to implement streaming applications on many-core platforms with highly parallel schedules such as the MPPA-256 [START_REF] De Dinechin | A distributed run-time environment for the Kalray MPPA-256 integrated manycore processor[END_REF] clustered architecture, from Kalray, comprising 256 cores. The native dataflow programming model developed in ΣC (Sigma-C) for MPPA-256 uses the notion of canonical period [START_REF] Aubry | Extended cyclostatic dataflow program compilation and execution for an integrated manycore processor[END_REF], which represents the partial order corresponding to the execution of one iteration of the application in the form of a graph whose vertices are, for each task a i , the q i first occurrences of this task and channels are dependencies between these occurrences.

For TPDF graphs, we reuse this notion of canonical period with several changes in the scheduling techniques:

' The control actor is scheduled for execution with the highest priority (i.e., if there are several kernels and a control actor available concurrently, the control actor is ensured to have a processing unit available before the others). Message passing time must be accounted for within the scheduling so that the system acts as if it was instantaneous.

' The kernel which receives the control token is fired immediately after receiving the control token. If this kernel has to wait until its input data tokens are available, it passes into a sleeping queue and wakes up when there is enough tokens in its inputs ports, as requested by the control token. If this kernel is fired in a mode where several of its input ports are rejected, the scheduler uses the Actor Dependence Function [START_REF] Do | Managing the latency of datadependent tasks in embedded streaming applications[END_REF] which defines the dependency between actors' executions to stop unnecessary firings.

A1 A2 B1 B2 C1 D1 E1 E2 F1 F2
Fig. 5. Canonical period of the example graph in Figure 2 for p " 1. Number next to the name of each actor is its ordinal number of execution. C1 is mapped onto a separate processing element. F1 and F2 are fired immediately after receiving the control tokens. Depending on this control token, it decides to wait until its input data available or not.

IV. CASE STUDIES A. Case-study on Edge Detection

Edge detection is one of the most significant tasks in image processing systems with various proposed algorithms: Quick Mask, Sobel, Prewitt, Kirsch, Canny. Gradient based edge detectors like Prewitt and Sobel are relatively simple and easy to implement, but are very sensitive to noise. The Canny algorithm is an optimal solution to problem of edge detection which gives better detection specially in presence of noise, but it is time consuming and require a lot of parameter setting. As can be seen in Figure 6, the execution time of Quick Mask is the shorter and Canny is the longest (tested on a standard Intel Core i3@2.53GHz for a 1024 ˆ1024 image).

In an ideal world, a programmer would use the best algorithm and be done with it, but possible real-time constraints can mitigate this idyllic view. When dealing with timing constraint, an average quality result at the right time is far better than an excellent result, later. The Canny filter may be the best algorithm for edge detections, but the execution time depends on the input image. In contrast, Quick Mask or Sobel have image-independent execution time (i.e., depending only on the size of the input image, not on its contents). So we can use a control actor of type clock to implement this time constraint, as can be seen in Figure 6. The IRead actor reads images from source and duplicates this image to be tested by different Edge Detection methods: Quick Mask, Sobel, Prewitt, Canny,. . . and its output is connected directly to the Transaction kernel. This box will select the best results in accordance with the deadline, implemented by using a control token received from the control actor every 500ms. This kind of time-dependent decision is not available in usual CSDF. By contrast, our model fits well the case by using control actors.

B. Case-Study on Cognitive Radio

We have applied the TPDF approach to an OFDM demodulator from the domain of cognitive radio, which is one of the fundamental subsystems of LTE and WiMAX wireless communication systems. Figure 7 illustrates a runtimereconfigurable OFDM demodulator that is modeled as a TPDF graph. Here, actor SRC represents a data source that generates random values to simulate a sampler. In a wideband OFDM system, information is encoded on a large number of carrier frequencies, forming an OFDM symbol stream. In baseband processing, a symbol stream can be viewed in terms of consecutive vectors of length N . The symbol is usually padded with a cyclic prefix (CP) of length L to reduce inter-symbol inference (ISI) [START_REF] Van De Beek | Lowcomplex frame synchronization in OFDM systems[END_REF]. In Figure 7, the CP is removed by actor RCP. Then, actor FFT performs a fast Fourier transform (FFT) to convert the symbol stream to the frequency domain. This kernel is connected to a M-ary QAM demodulation, with a configurable QPSK configuration (M " 2 or M " 4). Finally, the output bits are collected by the data sink SNK.

[βN]

[βN]

SRC [β(N+L)] [β(N+L)] [βMN] [βMN] RCP FFT DUP QPSK QAM CON TRAN SNK [βN] [βN] [2βN] [2βN] [βN] [βN] [4βN] [4βN] [βN] [βN]
Fig. 7. TPDF model of a OFDM demodulator with a configurable QPSK (M " 2) or QAM (M " 4) configuration. Omitted rates equal to 1.

In summary, there are four principal parameters: β, M , N and L, where L depends on the cyclic prefix, N is the OFDM symbol length (N " 512 or N " 1024) and β, which varies between 1 and 100, is the number of OFDM symbols to be processed in a single activation of the actor. For example, if M " 4 and β " 10, this means that the system is operating in a mode that uses QAM as the demapping scheme, and executes actors in blocks of 10 firings each. A possible scheduling for this application: SRC rCON RCP FFT DUP QPSK QAMs TRAN SNK. When SRC fired, it send a data token to the control node, which decides to choose between QPSK or QAM, depending on the value of M . The square bracket is used to inform the compiler the region influenced by the control token, starting from the firing of the control node and terminating with the firing of all nodes which receive this control token. Figure 8 presents the minimum buffer size required by the application, depending on the vectorization degree β and the symbol length N (L " 1 and M is chosen by the control node). We find out that the buffer size increases proportionally to the vectorization degree and we have an improvement of 29% in comparison with the implementation by using CSDF. This result can be explained by the fact that the dynamic topology obtained using TPDF is more flexible than the static topology of CSDF, allowing to remove unused edges and decrease the minimum buffer size required by one iteration of the TPDF graph. In a similar way, several StreamIt benchmarks (e.g., FM Radio [START_REF] Thies | An empirical characterization of stream programs and its implications for language and compiler design[END_REF]) must perform redundant calculations that are not needed with models allowing dynamic topology changes such as TPDF. V. RELATED WORK Several parametric dataflow models have been proposed, for instance PSDF [START_REF] Bhattacharya | Parameterized dataflow modeling for DSP systems[END_REF], VRDF [START_REF] Wiggers | Buffer capacity computation for throughput constrained streaming applications with data-dependent inter-task communication[END_REF], SPDF [START_REF] Fradet | SPDF: A schedulable parametric data-flow MoC[END_REF]. In contrast to CSDF, these models allow a dynamic variation of the production and consumption rates of actors to change at runtime according to the manipulated data. However, none of these models provide any of the static guarantees that TPDF does (rate consistency, boundedness and liveness) or propose parametric rates without dynamic topology changes. Another related model is the Scenario-Aware Data-Flow (SADF) MoC [START_REF] Theelen | A scenario-aware data flow model for combined long-run average and worst-case performance analysis[END_REF], which exploits also the mode-based approach where the dynamic behavior of an application is viewed as a collection of different scenarios; yet, our model is more generic as it provides a unified view of manycore systems, which is entirely composable. Our approach is somewhat similar to Boolean Parametric Dataflow (BPDF) [START_REF] Bebelis | BPDF: A statically analyzable dataflow model with integer and boolean parameters[END_REF] which allows not only dynamic variations of rates but also dynamic changes of the graph topology. Each BFDF edge can be annotated with a boolean parameter which changes the topology of the graph. When a boolean parameter is false, the edge annotated by this parameter is considered absent. Still, this is not enough because this model lacks the ability to impose real-time constraints, a feature also required to program modern safety critical applications which will be both highly parallel and time constrained. Our model already solves this problem by using control actors of type clock. Moreover, all SPDF and BPDF case studies (e.g., the VC-1 Video Decoder), presented in [START_REF] Fradet | SPDF: A schedulable parametric data-flow MoC[END_REF], [START_REF] Bebelis | BPDF: A statically analyzable dataflow model with integer and boolean parameters[END_REF] and [START_REF] Bebelis | A framework to schedule parametric dataflow applications on many-core platforms[END_REF], can be replicated using our approach without introducing parameter communication and synchronization between firings of modifiers and users, which would have complicated scheduling significantly because of the additional actors, edges and ports. We also improved the quality of the AVC Encoder, a much more complex application, by using a quality threshold for the motion vector detection, implemented with a Transaction kernel, to choose dynamically the highest quality video available within real-time constraints.

VI. CONCLUSION We presented TPDF, a novel parametric dataflow model of computtion for embedded streaming applications. TPDF extends CSDF with parametric rates and a new type of control actor, channel and port, which expresses dynamic changes of the graph topology and time-triggered semantics. We described static analyses to guarantee the boundedness and liveness when executing a TPDF application, and validated these on realistic applications.

Fig. 4 .

 4 Fig. 4. (a), (b): Live TPDF graphs; (c): New graph obtained by clustering the cycle Z " pB, Cq into a single new actor Ω

Fig. 8 .

 8 Fig.8. Minimum buffer size increased proportionally to β, given by Buf f " 3 `β ˆp12 ˆN `Lq for TPDF and Buf f " β ˆp17 ˆN `Lq for CSDF.

  Fig.[START_REF] Bebelis | BPDF: A statically analyzable dataflow model with integer and boolean parameters[END_REF]. TPDF graph of the Edge Detection application. Omitted rates equal to the image size p ˆq. Execution time of different methods are measured for a 1024 ˆ1024 image. At the deadline, the best result will be chosen, according to the order: Canny ą Prewitt ą Sobel ą Quick Mask.

			IRead
			IDuplicate	[1]
					[1]
	QMask	Sobel	Prewitt	Canny	500ms	Parallel Methods
				[1]
			Trans	[1]	Quick Mask Sobel	Prewitt	Canny
				Time(ms)	200	473	522	1040
			IWrite


Gérard Jaouen
email: jaouen@ext.jussieu.fr

Siden Top

Anne Vessières

Pascal Pigeon

Guy Leclercq

Ionna Laios

First anti-oestrogen in the cyclopentadienyl rhenium tricarbonyl series. Synthesis and study of antiproliferative effects

A route to the organometallic complex 8 is described, along with a study of its antiproliferative effects on breast cancer cell lines; in the examples studied, 8 behaves in a very similar manner to tamoxifen, suggesting new possibilities for applications in organometallic chemistry.

Tamoxifen 1 and its active metabolite, 4-hydroxytamoxifen 2 (Scheme 1) have been the subject of numerous studies owing to their efficacy in breast cancer treatment. 1,2 Currently however, substitutes are being sought in order to obviate the effects of resistance build up, as well as to improve the therapeutic effectiveness of the current treatments. 3,4 Our study is an attempt to potentiate the effects of these medications by introducing an organometallic-type modification to the base skeleton. Some organometallic complexes have in fact proven to be of interest either as antitumour agents, as in the case of the metallocenes of Fe and Ti, 5,6 or as radiopharmaceuticals, for example certain isotopes of Tc and Re. 7,8 If the organometallic moiety could be incorporated into this molecule while still preserving its character as an antioestrogen vector, this would provide a route to new products of added interest in a variety of applications. The question of preservation of antagonist activity is not an idle concern; we have shown that merely substituting the phenyl in the β position in 2 with a ferrocenyl group in 3 resulted in a significant drop in anti-oestrogenic effects in vitro on breast cancer cell lines, as well as in vivo, in nude mice. 9,10 Here we show that by attaching to the diphenylethylene skeleton a moiety of Re(I), in the form of cyclopentadienyl Re(CO)3, small in size and difficult to oxidize, we obtain an anti-oestrogenic organometallic complex comparable to hydroxytamoxifen 2 but with the added advantage, owing to the presence of the metal Re, of allowing access to a new type of radiopharmaceutical compounds of 99m Tc, 186 Re or 188 Re.

Compound 8 is prepared as shown in Scheme 2 starting from dihydroxybenzophenone 4 and the (η 5 -C5H4COEt)Re(CO)3 complex 6, itself prepared by a Friedel-Crafts reaction between cyclopentadienyl rhenium tricarbonyl and propionyl chloride. The aromatic ketone 4 is first reacted with KH, to give the potassium salt, which reacts with dibromobutane. The monobrominated compound 5 is obtained in 35% yield. A McMurry cross-coupling reaction 11,12 between 5 and the organometallic compound 6 in the presence of TiCl4 and Zn in THF under reflux gives 7 in 62% yield, and the latter when heated with dimethylamine in an autoclave produces 8 (Z + E) in a yield of 64%. † Separation of the isomers 8Z and 8E was done by reverse phase preparative HPLC. Identification of the isomers was ascertained by NMR on the E isomer (effect between the protons CH3-CH2 and C6H4-O(CH2)4N(CH3)2, as well as between η 5 -C5H4-Re(CO)3 and C6H4-OH). In contrast to what is observed in the ferrocene series, no rapid interconversion was noticed between 8Z and 8E, then showing a similarity of the rhenium derivatives with tamoxifen.

The relative binding affinity values (RBA) of 8 were measured for the mixture (Z + E) and for the individual isomers Z and E on the two oestrogen receptor subtypes ERα and ERβ using a competitive radiometric binding assay, with tritium-labeled oestradiol as tracer and protamine sulfate precipitation of the bound fraction of the tracer. 13 ERα was prepared from sheep uterus and ERβ, expressed in baculovirus, was obtained commercially from PanVera.

The RBA values (mean of 2 or 3 experiments) found at 0 °C for 8 on ERα are 8% for the mixture 8 (Z + E), 7.4% for 8Z and 5.2% for 8E, thus showing only a slight difference between the two isomers. In contrast, the RBA value obtained for ERβ is higher with 8Z (17.8%) than for the mixture 8 (Z + E) (6%) or the E isomer 8E (5.6%). However it is important to notice that ERβ is a purified receptor devoid of the effectors naturally present in the receptor alpha preparation obtained from sheep. Nevertheless the affinity for both ERα and ERβ are still satisfactory even if these RBA values are lower than the values found for 2 (Z + E) on ERα (38.5%) and ERβ (20%). This decrease probably reflects the greater steric crowding of (η 5 -C5H4)Re(CO)3 in 8 relative to the phenyl group in 2.

We studied the agonist-antagonist effect of compound 8 (Z + E) on cell lines derived from breast cancer tumours (MVLN, MDA-MB231) (Table 1). In the MVLN line recently developed by Pons 14 it has been shown that the expression of the luciferase gene is proportional to the oestrogenic effect of the product tested. It contains a high level of ERα while the MDA-MB231 line does not contain any. In these tests, the control value is set by definition at 100%. For any given product, a value above 100% indicates an oestrogenic effect, and a value below 100% an anti-oestrogenic effect. As usual oestradiol is used as the reference for oestrogens and hydroxytamoxifen 2 (Z + E) for anti-oestrogens. The results obtained with MVLN cells show that the Re complex 8 behaves as an anti-oestrogen with almost identical efficacy as 2. The observed effect with 8 is certainly hormonally based, since it is abolished by addition of oestradiol into the medium (values in square brackets in the Table ). On MDA-MB231 cells which do not possess ERα but may possess ERβ, [START_REF] Kuiper | Proc. Natl. Acad. Sci[END_REF] 8 and 2 have no effect. It thus appears that the observed antiproliferative effect is dependent on the oestradiol receptor α, as is also the case with tamoxifen. a) Cells with a high level of ERα. Results are expressed as percentage of the luciferase induction after 24 h of culture. 14 b) Cells with no ERα, but presumably with ERß. [START_REF] Kuiper | Proc. Natl. Acad. Sci[END_REF] Results are expressed as the percentage of DNA/control after 120 h of culture. 16 c) Value obtained after simultaneous addition in the medium of 10 nM of E2.

Compound

Molarity (M)

Cell

It appears that 8 may have a higher potential as an organometallic radiopharmaceutical, despite the fact that up to now the chelate route has been the one explored with tamoxifen; 17 in the latter case the ER binding rate was found to be too small to measure, which was not the case with 8. It is therefore important to find a rapid route by which to attach useful isotopes of Tc and Re to 8. To this end, we plan to use a selective photochemical decomplexation reaction that we have recently discovered, followed by rapid recomplexation in water with a new reagent reported by Alberto, 18,19 (H2O)3M + (CO)3 with M = 99m Tc, 188 Re.

Notes and references † Procedure for the preparation of 7 and 8. Titanium tetrachloride (2 ml, 18 mmol) was added dropwise to a suspension of zinc powder (2.34 g, 36 mmol) in 60 ml of THF at 0 °C. The mixture obtained was heated at reflux for 2 h and then cooled to rt. A second solution was prepared by dissolving 4-(4-bromobutoxy)-4A-hydroxybenzophenone (4.25 g, 6 mmol) and cyclopentadienyltricarbonylrhenium ethyl ketone (2.35 g, 6 mmol) in 30 ml of THF. This latter solution was added dropwise to the first one and then the resulting mixture was heated for 2 h. After cooling to rt, the mixture was stirred with water and CH2Cl2. After treatment the pure oily Z + E mixture of 7 was obtained with a yield of 62%; MS (IE, 70 eV) m/z: 708 (M + .), 624 (M -3CO) + . Halide 7 (3 mmol) and a solution of dimethylamine in MeOH (2 M, 15 ml, 30 mmol) were heated with stirring in an autoclave at 60 °C for 1 day. After cooling, the solution was concentrated under reduced pressure. After treatment the pure amines 8 (Z + E) were isolated as oil containing a mixture of Z and E isomers with a yield of 64%; MS (IE,

  70 eV) m/z: 673 (M + .). The Z and E isomers were separated on reverse phase preparative Kromasil C18 column, solvent MeOH phosphate buffer (KH2PO4, 25 mM, pH 7) 80/20, flow rate 6 mL min -1 . The retention times obtained on an analytical column of the same type (Kromasil C18, 10 µM, 250 mm) are repectively of 19.4 min for 8Z and 26.4 min for 8E in the proportion 48.5/51.5. Selected data for the two isomers: 8E: mp 153 °C, 1 H NMR δ 7.04 (d, J = 8.4 Hz, 2H, Harom), 6.93 (d, J = 8.4 Hz, 2H, Harom), 6.78 (d, J = 8.4 Hz, 2H, Harom), 6.70 (d, J = 8.4 Hz, 2H, Harom), 13 C NMR δ (all aromatic carbons) 135.5 (C), 134.6 (C), 130.6 (2 CH), 130.1 (2 CH), 129.9 (C), 115.6 (2 CH), 114.1 (2 CH). 8Z: mp 134°C, 1 H NMR δ 7.00 (d, J = 8.4 Hz, 2H, Harom), 6.99 (d, J = 8.4 Hz, 2H, Harom), 6.75 (d, J = 8.4 Hz, 2H, Harom), 6.74 (d, J = 8.4 Hz, 2H, Harom), 13 C NMR (all aromatic carbons) δ 135.9 (C), 134.8 (C), 130.5 (2 CH), 129.9 (2 CH + C), 115.3 (2 CH), 114.3 (2 CH). 1 K. Dhingra, Invest. New Drugs, 1999, 17, 285. S. Top, E. B. Kaloun and G. Jaouen, J. Am. Chem. Soc., 2000, 122, 736.

  Scheme 1

Table .

 . Antiproliferative activity of compounds 8, 2 and E2 on different cell lines.

V. C. Jordan, J. Nat. Cancer Inst., 1998, 90, 967.


Adam Daïch

Stefan Marchalin

Pascal Pigeon

Bernard Decroix

Synthesis of benzo(or furo)[5,6]azepino[2,1-a]isoindolone derivatives: π-cyclisations of N-acyliminium ions

Keywords:

azepino[2,1-a]isoindolone and derivatives were obtained easily in one-pot via N-acyliminium ions by treatment of 2-(2-methoxycarbonylbenzyl(or fur-3-yl))phthalimide with alkylmagnesium iodide followed by an acidic hydrolysis.

Because of their potential biological properties, benzazepines and derivatives annelated to an isoindole or pyrrolidine ring as in numerous natural alkaloids, have attracted considerable interest in recent years. These structures were exemplified by Chilenine 1 [1,2,3], Lennoxamine 2 [1,4] extracted from Chilean Berberidaceae, Berberis darwinii Hook and Cephalotaxine 3 [5] isolated from Taxus baccata (Chart 1 ).

Our previous studies on the synthetic utility of amidoalkylation reactions [6,7] via πcyclisations of N-acyliminium ions together with our interest in the development of synthetic approaches to diversely substituted polyheterocyclic systems, allowed us to report the first preparation of benzo(or furo)azepinoisoindolone 4 or 5 (Chart 1). These latter bear an exocyclic double bond and an angular alkyl group and were prepared in one-pot reaction using an imide-ester functionality as precursor.

If benzo(or thieno)azepinoisoindolones [8] with an exocyclic olefin are few reported in literature in contrast to those with an endocyclic one [1,2,[8][9][10], in our knowledge no report have been done on the chemistry of furoazepines fused to an isoindole ring.

Indeed, taking into account that hydroxylactams and tertiary alcohols functions (8a,b and 9a,b) generate respectively N-acyliminium ions and olefins (11) in acidic medium [11,[START_REF] Hiemstra | Comprehensive Organic Synthesis[END_REF]. The ring closure could take place through an intramolecular (α-amidoalkylation cyclisation with olefin as internal nucleophile in intermediate 11 leading to the stabilised benzylic type carbocation 13 (Chart 2). The latter could also be obtained from 12 in equilibrium with 11 in acidic conditions. Finally, the loss of the proton attached to Cα carbon gave the title compounds 4 or 5 rather than the regioisomers 14 or 15 with an endocyclic double bond.

As depicted in chart 3, imide-esters 7a and 7b [START_REF] Pigeon | [END_REF] (obtained by classical condensation of phthalimide with the known methyl 3-bromomethylfurane-2-carboxylate 6a [14] and methyl o-bromomethylbenzoate 6b [15]) were reacted with more than 5 equivalents of freshly prepared methylmagnesium iodide at 0-5°C for 3 hours. This yielded after water hydrolysis the hydroxylactam-alcohols 8a and 8b in good yields (71 and 78% respectively). Moreover, an acidic hydrolysis gave directly the cyclised products as 4a and 4b in 79 and 83% yields.

The rate of the Grignard reaction decreased at lower temperature (< 0°C) whatever the nature of solvent used (tetrahydrofuran, diethyl ether or dichloromethane) but when the temperature rised to room temperature, dehydration reactions of hydroxylactam and alcohol functions took place giving a complexe mixture of unseparable products. Nevertheless, heating pure 8a or 8b under azeotropic conditions in dry toluene with a catalytic amount of PTSA furnished after flash chromatography purification on silica gel the same tetracyclic azepine 4a or 4b (55 and 70% respectively) (Chart 3).

Under similar conditions as above, with ethylmagnesium iodide as the Grignard reagent, the imide-ester 7a led to ω-ethyl-ω-carbinol lactam 9a (73% yield) which cyclised under azeotropic conditions into tetracyclic azepine 5a (62% yield). The same product was obtained from 7a under one-pot cyclisation conditions (78% yield). From 7b, the formation of diol 9b was never observed whatever the quantity of ethylmagnesium iodide (> 5 equivalents) but under the one-pot cyclisation conditions, 7b led only to the dehydration product 10 in 82% yield.

The typical reaction leading in one-pot to the title products (78 to 83% yield), was performed by addition of more than 5 equivalents of alkylmagnesium iodide to imide-ester 7

under stirring in dry dichloromethane followed by hydrolysis for 30 minutes with 6M ammonium chloride solution and then with a diluted hydrochloric or sulfuric acid solution for an additional 1 hour. After a classical work up, the structures of the isolated intermediates 8-10 and final products 4a,b and 5a were well established by their ir, 1 H and 13 C nmr spectra (200 MHz), mass spectra as well as by their microanalyses (Chart 4).

The methylidene hydrogens in 4a appear as a doublet with the characteristic coupling constant of J=2.3 Hz, the C7 protons appear as a singlet while the C3 protons appear as two multiplets (the protons are non equivalents and are coupled with the angular methyl group as indicated by both decoupling and 2D symmetric COSY experiments) with coupling constants of J=l.4 and J=0.8 Hz. Likewise, the 13 C nmr spectra of 4a reveals the presence of the exomethylene carbon in aromatic region at δ=113.7 ppm which inverts in the corresponding DEPT program spectrum (similar observations can be made in the 1 H and 13 C nmr spectra of compound 4b). For 5a, the 1 H nmr spectrum shows a non separable 78/22 mixture of Z and E isomers. The assignments of Z or E configuration is based on the nmr data of related compounds [15][16][17][18](Chart 5).

In summary, a straightforward and efficient synthesis of functionalised furoazepinoisoindolones 4a,5a and benzoazepinoisoindolone 4b bearing an angular alkyl group were described from imide-esters 7a,b in one-pot reactions with alkylmagnesium iodide. Further studies of the addition of various organometallic reagents are in progress and the results will be published soon.


Tetrahedron Letters (1997), 38 (6) Over the last ten years many synthetic efforts have been directed toward synthesis of [2] or [3] benzazepines annelated to various rings (isoindole, pyrrolidine, benzene...) because a number of natural products as Chilenine l , Lennoxamine 2 , Cephalotaxine 3 contains this moiety and present potential biological activities. Any number derivatives of dibenz[c,e ; b,e ; b,f]azepines are known and present hypolipidermic activity 4 , central nervous system activity 5 , antiarrhythmic activity 6 respectively. With our interest in the synthesis of diversely substituted polycyclic systems [7][8][9][10] we wish to report herein an interesting approach to dibenzazepine or thienobenzazepine annelated to an isoindole moiety as 4a or 4b.

We have shown 11 From these results we suggested to use the hydroxylactam 3a for the synthesis of the dibenzazepine derivative 4a. N-acyliminium ion precursor 3a was prepared from phthalimide derivative 1a. A palladium (0) catalyzed cross coupling of bromo derivative la with phenylboronic acid provided the biphenyl compound 2a in good yield (76%). Reduction of imide 2a by sodium borohydride in the presence of acid 13 , afforded the hydroxylactam 3a (82%). This latter was then subjected to trifluoroacetic acid at room temperature and according to the Baldwin's rules 14 led to the expected formation of a 7-membered ring, the new dibenz[c,e]azepine 4a annelated to an isoindole moiety in a yield of 95%. The structure of 4a was supported by NMR ( 1 H, 13 C) spectroscopic analyses [START_REF] Bax | The HETCOR spectrum of 4a was acquired using the standard Bruker microprogram XHCORR.AU[END_REF] . A study of the long range heteronuclear shift correlation (HETCOR) spectrum of 4a further substantiated our conclusions. The spectrum showed seven different signals for the benzenic correlation. Such correlations would not be expected from the isomeric structure 5a.

This promoted result allied to the fact that a N-acyliminium ion cyclization gave a 5 or 6-membered ring from the α position of thiophene and only a 6-membered ring from the β position of the thiophene 16 we tested the hydroxylactam 3b. In similar conditions (CF3COOH, room temperature), cyclization of 3b gave a 7-membered ring (4b) as in the above benzene series rather than a 5-membered one (5b).

The structure of the thienobenzazepine 4b was supported by NMR ( 1 H, 13 C) spectroscopic analyses 17 . The two protons of the thiophene ring appear as doublets (AB system) with chemical shifts of 7.

  , 1041-1042. DOI : 10.1016/S0040-4039(96)02497-5 Synthesis of Dibenz[c,e]azepine and Benzo[e]thieno[c]azepine via N-Acyliminium ion Cyclization Pascal Pigeon and Bernard Decroix* Laboratoire de Chimie, Faculté des Sciences et des Techniques de l'Université du Havre, 30, rue Gabriel-Péri, 76600 Le Havre, France New address: Université du Havre, URCOM, 25 rue Philippe Lebon, BP 1123, 76063 Le Havre cedex, France Abstract: Dibenz[c,e]azepine 4a and benzo[e]thieno[c]azepine 4b have been synthesized utilizing the acid-catalyzed cyclization of hydroxylactams 3a,b as key step.

  that 3-phenyl-2-(2'-bromothien-3'-ylmethyl)phthalimide subjected to the usual radical cyclization conditions (AIBN, Bu3SnH, toluene) or intramolecular Heck reaction did not give the expected[2]benzazepine 4b. On the other hand it was reported12 that cyclodehydration of N-(o-biphenyl)hydroxyphthalimidine under refluxing of trifluoroacetic acid occurred leading to a new isoindolophenanthridine.

  13 ppm and 7.38 ppm and a coupling constant of 5 Hz characteristic of a α,β substituted thiophene. The present investigation has thus led to a new method of synthesis of dibenzo[c,e]azepine or benzo[e]thieno[c]azepine annelated to an isoindole moiety starting from hydroxylactams.


Meral Görmen

Damian Plazuk

Pascal Pigeon

Elisabeth A Hillard

Marie-Aude Plamont

Siden Top
email: top@chimie-paristech.fr

Anne Vessières

Gérard Jaouen

Meral Gormen

Elizabeth A Hillard

Comparative toxicity of [3]ferrocenophane and ferrocene moieties on breast cancer cells

Keywords: Ferrocenophane, Breast cancer, Bioorganometallic, Cytotoxicity

scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

We have recently reported the synthesis and powerful antiproliferative effects on breast and prostate cancer cells of the diphenolic [3]ferrocenophane 1. 1 This compound is considerably more potent than its non-cyclic analog 2, 2 with respective IC50 values of 0.09 and 0.6 µM on hormone-independent MDA-MB-231 breast cancer cells. The point of attachment of the olefin was shown to be critical; when it was transposed from the 1 to the 2 position of the bridge, the cytotoxic properties declined by an order of magnitude. This could be a result of breaking the conjugation between the ferrocene group and the phenol groups, as it has been shown that conjugated molecules in this class are more toxic than their unconjugated analogs. 3 Ferrocene has been widely used in experimental medicinal chemistry, [START_REF] Metzler-Nolte | Ferrocenes Ligands Materials and Biomolecules[END_REF][5][6] including a [3]ferrocenophane created from the coordination of the 1,1'bis(diphenylphosphino)ferrocene with gold, which was active against a panel of cancer cells. 7 We have also examined the influence of changing the hydroxyl group for other functionalities, such as amines and halogens. 8 The presence of a protic substituent is crucial for activity, and toxicity can be enhanced by replacement of the hydroxy group by NH2 or NHC(O)CH3. 8 This is consistent with our proposed mechanism that quinoid compounds generated in situ are responsible for the toxicity of these compounds. 9 We here show that, in this system, the [3]ferrocenophane motif is more toxic than the ferrocene moiety, via the comparison of the ferrocene compounds 3a-c (Fig. 1) with the analogous [3]ferrocephanes 4a-c on hormone-independent breast cancer cells (MDA-MB-

231).

Compounds 3a-c have been previously prepared by our group. 8a,10 1-[(p-R-phenyl)phenyl-methylidenyl]- [3]ferrocenophane derivatives 4a-b were prepared in good yield via a

McMurry cross-coupling reaction between [3]ferrocenophan-1-one 11 and the appropriately substituted benzophenones, 8a Scheme 1. [START_REF]Compound 4a: 74% yield; 81/19 isomer ratio; 1 H NMR (300 MHz, acetone-d6): δ 2[END_REF] Compound 4c was synthesized by the acetylation of the ferrocenophane aniline 4a using acetyl chloride in THF/pyridine. 8,[START_REF]c: 75% yield; 80/20 isomer ratio; 1 H NMR (300 MHz, CDCl3): δ 2.11[END_REF] The E and Z isomers could not be separated by semi-preparative HPLC. The two isomers (E + Z) were co-crystallised in a 50:50 ratio, thus the hydroxyl groups have been modeled as disordered over the two phenyl rings, with an occupancy at each position of 50%. The ferrocenyl moiety is oriented away from the phenyl group linked to the opposite carbon atom of the olefinic bond, presumably to minimize steric interactions. Similarly, there is a slight narrowing of the bond angle between the ethyl substituent and the ferrocene group connected to the same carbon atom of the double bond; and likewise for the two phenyl groups connected to the other carbon atom of the double bond. The ethylenic skeleton is moderately distorted with torsion angles of 11.2° and 12.8°. The two phenyl moieties are tilted about 55° with respect to the olefinic plane, while a corresponding twist angle of 37° is observed for the ferrocene moiety. Our previous studies of non-cyclic tetra-substituted ferrocenyl olefins show that parasubstitution of one or more of the phenyl rings with OH, NH2, and NHC(O)CH3 yield the most toxic compounds. Thus we have tested the ferrocene and ferrocenophane derivatives with such substitution on the hormone-independent MDA-MB-231 breast cancer cell line, which does not respond to estrogenic or anti-estrogenic properties of molecules. Table 1 shows that IC50 values for the ferrocene-based compounds ranges from 1.1 to 0.65 µM. The ferrocenophane compounds are more toxic in each instance, with IC50 values ranging from 0.47 to 0.21 µM. Compounds 4c and 4a showed about a two-fold improvement, while 4b, with NH2 substitution, was significantly more potent than its non-cyclic analog.

It should also be noted that the presence of two phenol groups versus one enhances the toxicity of compounds in both the ferrocene and [3]ferrocenophane series. In the ferrocene series the IC50 decreased from 1.13 to 0.6 µM for the monophenol and diphenol; 11 for the ferrocenophanes the corresponding decrease is from 0.47 to 0.09 µM. 1 Therefore, the next logical step is to prepare compounds with two identical or mixed substituents, particularly incorporating the NH2 group. With some nuances regarding the magnitude of the antiproliferative effect observed as a function of the substituents, NH2, OH, and NHC(O)CH3, it is clear that the rigid [3]ferrocenophane permits an increase in the cytotoxic efficacy of the Fc-alkene-phenyl-R motif.

Supplementary data

Crystallographic data (excluding structure factors) for the structure in this paper have been deposited with the Cambridge Crystallographic Data Centre as supplementary publication no. 748334. Copies of the data can be obtained, free of charge, on application to CCDC, 12 Union Road, Cambridge CB2 1EZ, UK, (fax: +44(0)1223 336033 or email: deposit@ccdc.cam.ac.uk).

Figure 1 .

 1 Figure 1. Numbers following 1 and 2 are the IC50 values after 5 days of incubation with MDA-MB-231 hormone-independent breast cancer cells: (a) OH; (b) NH2; and (c) NHC(O)CH3.

Figure 2 .

 2 Figure 2. ORTEP diagram of 3a; thermal ellipsoids shown at 50% probability level. Bond distances (Å) and angles (°): Fe-C (mean) 2.065(2), C12-C19 1.371(2), C12-C13 1.507(2), C12-C7 1.505(2), C19-C24 1.490(3), C19-C3 1.533(3); C3-C19-C24 116.6(2), C13-C12-C7 113.5(2), C7-C12-C19-C24 11.2(2), C3-C19-C12-C13 12.8(2).

Acknowledgements

We thank P. Herson for X-ray structural characterization as well as the Agence Nationale de la Recherche (No. ANR-06-BLAN-0384-01, 'FerVect') financial support. M.G. acknowledges a fellowship from the Ministère des Affaires Etrangères.