Arnaud Casteigts
email: acasteig@labri.fr

Yves Métivier
email: metivier@labri.fr

John Michael Robson
email: robson@labri.fr

Akka Zemmari
email: zemmari@labri.fr

Counting in one-hop beeping networks

Keywords: Beeping model, Size computation, Counting problem, Las Vegas algorithms

Introduction

Distributed algorithms are concerned with assumptions relating to various aspects like the structure of the network (e.g. trees, rings, planar graphs, complete graphs) or knowledge available to the nodes (e.g. a bound on the network size, unique identifiers, or port numbering). Another important aspect is the size of messages, which may range from unbounded (the LOCAL model) to logarithmic size (CON GEST model), to constant size (e.g. simple bits) [START_REF] Peleg | Distributed computing -A Locality-sensitive approach[END_REF].

A natural approach in distributed computing is to reduce the assumptions as much as possible, in order to make positive results more general. Hence, when a problem is solved in some strong model, one naturally strives to solve it in a weaker model. In a recent series of works [START_REF] Cornejo | Deploying wireless networks with beeps[END_REF][START_REF] Schneider | What is the use of collision detection (in wireless networks)?[END_REF][START_REF] Afek | Beeping a maximal independent set[END_REF][START_REF] Huang | Conflict resolution and membership problem in beeping channels[END_REF][START_REF] Scott | Feedback from nature: an optimal distributed algorithm for maximal independent set selection[END_REF][START_REF] Gilbert | The computational power of beeps[END_REF], the community has started to explore new models of communications that are even weaker than constant size messages in anonymous networks, namely beeping models.

In these models, the only communication capabilities offered to the nodes are to beep or to listen for the beeps of others. Several variants exist. In [START_REF] Cornejo | Deploying wireless networks with beeps[END_REF], a node that beeps is unable to detect whether other nodes have beeped at the same time. When listening, it can distinguish between silence or the presence of at least one beep, but it cannot distinguish between one and several beeps. In Section 6 of [START_REF] Afek | Beeping a maximal independent set[END_REF], a stronger variant is considered where beeping nodes can detect whether other nodes are beeping simultaneously (sender side collision detection). In [START_REF] Schneider | What is the use of collision detection (in wireless networks)?[END_REF] and Section 4 of [START_REF] Afek | Beeping a maximal independent set[END_REF], yet another variant is considered where the nodes can tell the difference between silence, one beep, and several beeps. The ability to detect internal collision is denoted by B cd (B otherwise) and that of detecting peripheral collisions is denoted by L cd (L otherwise). The various models in literature can be reformulated in these terms. The basic model introduced by Cornejo and Kuhn in [START_REF] Cornejo | Deploying wireless networks with beeps[END_REF] is BL; the model considered by Afek et al. in [START_REF] Afek | Beeping a maximal independent set[END_REF] (Section 6) and Scott et al. in [START_REF] Scott | Feedback from nature: an optimal distributed algorithm for maximal independent set selection[END_REF] is B cd L; and the model considered in [START_REF] Schneider | What is the use of collision detection (in wireless networks)?[END_REF] and in Section 4 of [START_REF] Afek | Beeping a maximal independent set[END_REF] is BL cd . To the best of our knowledge, B cd L cd has only been considered in [START_REF] Casteigts | Design patterns in beeping algorithms: Examples, emulation, and analysis[END_REF].

Studying weak models of computation is interesting in its own right. In addition, beeping models turn out to be relevant to model real-world applications or phenomena. For instance, they reflect the features of a network at the lowest level (physical layer), where a node can probe or emit signals, with or without collision detection. At a higher level of abstraction, beeping models also reflect some communication patterns in biology, such as lateral inhibition among neighboring cells [START_REF] Collier | Pattern formation by lateral inhibition with feedback: a mathematical model of delta-notch intercellular signalling[END_REF].

Contributions. In this paper, we consider the counting problem in which nodes must determine the size of the network. We focus on the case that the communication graph is complete (one-hop networks), implying that each node can hear and be heard by all the others. As it turns out, even this version of the problem cannot be solved deterministically, due to the inherent lack of symmetry-breaking mechanisms in the beeping model. We thus consider randomised algorithms and start by providing a Las Vegas (LV) algorithm -correct result but uncertain time, though finite with probability 1 -for solving the counting problem in B cd L. The expected running time of this algorithm is linear in the number of nodes (with high probability). On the negative side, we show that n is a lower bound, which makes the algorithm optimal up to a constant factor (experimentally estimated to less than 10). Unfortunately, we also observe that no LV algorithm exists in the weaker BL model, leading us to consider a Monte Carlo (MC) variant in BL where the result is correct only with some threshold probability. This algorithm relies on a technique developed in [START_REF] Casteigts | Design patterns in beeping algorithms: Examples, emulation, and analysis[END_REF], which enables the emulation of B cd beeps with B beeps, at the cost of a logarithmic slowdown. We also discuss how to adapt the algorithm in the stronger B cd L cd model, this time with a (constant factor) gain in time complexity.

Related Work.

As explained by Chlebus [START_REF] Chlebus | Randomized communication in radio networks[END_REF], detecting a collision in a radio network is to be able to distinguish between 0 messages and at least 2 messages while detecting a collision in the beeping model is to be able to distinguish between 1 message and at least 2 messages. Thus results on the counting problem in the context of radio networks cannot be applied directly in the context of beeping models. Another problem which has been well-studied, in this context, is the k-Selection problem (also known as all-broadcast); as explained by Anta and Mosteiro [START_REF] Anta | Contention resolution in multiple-access channels: k -selection in radio networks[END_REF] (see also [START_REF] Kowalski | On selection problem in radio networks[END_REF][START_REF] Bienkowski | Randomized mutual exclusion on a multiple access channel[END_REF]): it is solved "when an unknown size-k subset of n network nodes have been able to access a unique shared channel of communication, each of them at least once". Finally, selection problems, in general, differ from the counting problem studied in this paper 1. by the fact that the collision detection does not have the same meaning in the context of radio networks and in the context of the beeping models, and 2. by the fact that in our case we look for the exact number of nodes and the k-selection problem asks that nodes access the unique shared channel at least once.

Afek et al. [START_REF] Afek | Beeping a maximal independent set[END_REF], from considerations concerning the development of certain cells, studied the Maximal Independent Set (MIS) problem in the discrete beeping model BL as presented in [START_REF] Cornejo | Deploying wireless networks with beeps[END_REF]. They consider, in particular, the wake-on-beep model (sleeping nodes wake up upon receiving a beep) and sender-side collision detection B cd L: they give a O(log 2 n) rounds MIS algorithm. After this work, Scott et al. [START_REF] Scott | Feedback from nature: an optimal distributed algorithm for maximal independent set selection[END_REF] present in the model B cd L a randomised algorithm with feedback mechanism whose expected time to compute a MIS is O(log n).

More generally, Navlakha and Bar-Joseph present in [START_REF] Navlakha | Distributed information processing in biological and computational systems[END_REF] a general survey on similarities and differences between distributed computations in biological and computational systems and, in this framework, the importance of the beeping model.

In [START_REF] Cornejo | Deploying wireless networks with beeps[END_REF], Cornejo and Kuhn study the interval colouring problem: an interval colouring assigns to each node an interval (contiguous fraction) of resources such that neighbouring nodes do not share resources (it is a variant of graph colouring). They assume that each node knows its degree and an upper bound of the maximum degree ∆ of the graph. They present in the beeping model BL a probabilistic algorithm which never stops and stabilises with a correct O(∆)-interval coloring in O(log n) periods with high probability, where: n is the size of the graph, ∆ its maximum degree and a period is

Q time slots with Q ≥ ∆, thus it stabilises in O(Q log n) slots.
Emek and Wattenhofer introduce in [START_REF] Emek | Stone age distributed computing[END_REF] a model for distributed computations which resembles the beeping model: networked finite state machines (nFSM for short). This model enables the sending of the same message to all neighbours of a node; however it is asynchronous, the states of nodes belong to a finite set, and the set of messages is also finite. In the nFSM model they give a 2-MIS algorithm for graphs of size n using a set of messages of size 3 with a time complexity equal to O(log n 2 ).

Another similar model was considered in [START_REF] Kowalski | Time of deterministic broadcasting in radio networks with local knowledge[END_REF]. In this model, in every step, each node acts either as a transmitter or as a receiver. When a node is a transmitter, its message reaches all its neigbours. When it acts as a receiver, it receives a message if, and only if, exactly one of its neighbours transmits. The authors devise algorithms to broadcast efficiently in this model.

In [START_REF] Marco | Asynchronous shared channel[END_REF], De Marco and Stachowiak consider a pretty close model: a number of stations is able to communicate by transmitting and listening to a shared channel, and a message is successfully delivered to all stations if, and only if, its source station is the only transmitter at a time. They discuss the impact of asynchrony in this model. They also consider and discuss how important the knowledge of the number of stations is, with a focus on the problem of contention resolution.

Concerning the counting problem, in the context of the classical message passing model, counting Monte Carlo algorithms for anonymous rings are presented in [START_REF] Itai | Symmetry breaking in distributed networks[END_REF][START_REF] Métivier | Analysis of fully distributed splitting and naming probabilistic procedures and applications[END_REF]. The time complexity is O(n). It is also investigated in dynamic networks [START_REF] Kuhn | Distributed computation in dynamic networks[END_REF][START_REF] Di Luna | Counting in anonymous dynamic networks: An experimental perspective[END_REF][START_REF] Michail | Naming and counting in anonymous unknown dynamic networks[END_REF]. In [START_REF] Kuhn | Distributed computation in dynamic networks[END_REF] nodes have unique identifiers, the size of messages is O(log n). Nodes know the size of the graph in O(n 2 ) rounds. Networks are dynamic and anonymous in [START_REF] Di Luna | Counting in anonymous dynamic networks: An experimental perspective[END_REF]; there is a leader in the network and the termination of the counting algorithm is detected by a heuristic. In [START_REF] Michail | Naming and counting in anonymous unknown dynamic networks[END_REF] communication is asynchronous message passing, nodes have no identifiers and there exists a leader; counting algorithm which is presented produces a correct stabilizing solution that do not guarantee termination.

Summary. The paper is organised as follows. In Section 2 we provide definitions and basic observations regarding the beeping model. Section 3 presents our main results on the counting problem, including the lower bound, our optimal algorithm, and its time complexity analysis. Finally, Section 4 discusses the adaptations of our algorithm in other variants of the beeping model, including its emulation as a Monte Carlo algorithm in the weakest BL variant.

Network Model and Definitions

We consider a wireless network model and we follow definitions given in [START_REF] Afek | Beeping a maximal independent set[END_REF] and [START_REF] Cornejo | Deploying wireless networks with beeps[END_REF]. The network is anonymous: unique identifiers are not available to distinguish the processes. Communications are synchronous and encoded by a graph G = (V, E) where the nodes V represent processes and the edges E represent pairs of processes that can hear each other. Since we focus here on one-hop networks, G is a complete graph. Time is divided into discrete synchronised time intervals called slots (following the usual terminology in wireless networks). All processes wake up and start computation at the same slot. In each slot, all processors act in parallel and either beep or listen. In addition, processors can perform an unrestricted amount of local computation in-between two slots (in effect, our algorithms require little computation).

In this paper, we consider several variants of beeping models:

• if a process beeps, there are two cases:

1. it cannot know whether another process beeps simultaneously, this case is denoted by B;

2. it can distinguish whether it beeped alone or if at least one neighbour beeped concurrently, it is an internal collision; this case is called sender side collision detection, and it is denoted in this paper B cd ;

• if a process listens, there are also two cases:

1. it can distinguish between silence or the presence of at least one beep, this model is denoted L;

2. it can distinguish between silence or the presence of one beep or the presence of at least two beeps; in this case it is a peripheral collision, this model is denoted L cd in this paper.

Finally, a beeping model is defined by choosing between B or B cd and between L and L cd .

Remark 1. In general, nodes are active or passive. When they are active they beep or listen; in the description of algorithms we say explicitely when a node beeps meaning that a non beeping active node listens.

The time complexity, also called slot complexity, is the maximum number of slots needed until every node has completed its computation. Our algorithms are typically structured into phases, each of which corresponds to a small (constant or logarithmic) number of slots. In the algorithm, we specify which one is the current slot by means of a switch instruction with as many case statements as there are slots in the phase. Phases repeat until some condition holds for termination.

Remark 2. An algorithm given in a beeping model induces an algorithm in the (synchronous) message passing model. Thus, given a problem, any lower bound on the round complexity in the message passing model also holds for slot complexity in the beeping model.

In this paper, results on graphs having n nodes are expressed with high probability (w.h.p. for short), meaning with probability 1 -o(n -1 ). We write log n for the binary logarithm of n.

Distributed Randomised Algorithm. A randomised (or probabilistic) algorithm is an algorithm which makes choices based on given probability distributions. A distributed randomised algorithm is a collection of local randomised algorithms (in our case, all identical).

A Las Vegas algorithm is a randomised algorithm which terminates with probability one, and always produces a correct result. A Monte Carlo algorithm is a randomised algorithm which terminates deterministically, but whose result may be incorrect with a certain probability. Intuitively, Las Vegas algorithms have uncertain execution time but certain result, while Monte Carlo does the reverse. Classical considerations on symmetry breaking in anonymous beeping networks (see for instance Lemma 4.1 in [START_REF] Afek | Beeping a maximal independent set[END_REF]), imply that: Remark 3. There is no Las Vegas (and a fortiori no deterministic) algorithm in BL nor in BL cd which allows a node to distinguish between an execution where it is isolated and one where it has exactly one neighbour.

From this remark we deduce that there is no Las Vegas counting algorithm in BL, which advocates the use of stronger models. In what follows, we consider the B cd L model, where a beeping node can detect simultaneous beeps by others. We give a Las Vegas algorithm in this model, which is then turned into a Monte Carlo algorithm in BL using emulation techniques.

The counting problem. We say that an algorithm solves the counting problem if and only if by the end of its execution, every node knows the size of the network.

One-Hop Network Size Computation in B cd L

In the B cd L model, a node that beeps can detect simultaneous beeps by others, while a node that listens cannot distinguish between one and several beeps. Hence, only beeping nodes can detect collisions, which proves sufficient to solve the counting problem. In this section, we first prove that at least n slots are required to learn the number of nodes n; then we present a Las Vegas algorithm which takes O(n) slots to terminate (w.h.p.). Simulation results refine this complexity to less than 10n slots (i.e. less than 3.32 phases of 3 slots each).

A Lower Bound

The following lemma establishes that n slots are required for computing n in a complete graph.

Lemma 1. Any Las Vegas beeping algorithm that counts the number of nodes in a complete graph K n needs n slots.

Proof (By contradiction).

Let A be such an algorithm and let E A be an execution of A that terminates in less than n slots in the complete graph K n . Then it holds that at least one node, say v, never beeped alone. Let E A be another execution of A, but this time in the complete graph K n+1 composed of the same nodes as before, plus v . Let all the nodes behave as they did over E A and let v act exactly like v. Since v never beeped alone in E A , it does the same in E A and so does v as well, making both executions indistinguishable (two beeps are indistinguishable from three). Hence, the nodes in E A terminate as in E A , having counted n instead of n + 1, which is a contradiction. Remark 4. The bound holds even when collision detection is also available for listening nodes (thus, in B cd L cd and a fortiori in BL cd ), due to the same argument that two beeps are indistinguishable from three on the listener side.

An Algorithm for Computing One-Hop Network Size in B cd L

We now propose a beeping algorithm that solves the counting problem in one-hop networks in B cd L. Then we characterise its slot complexity both analytically and experimentally.

Informal description:

The basic idea is to have nodes beep alone as often as possible, so that they can detect it and become counted. This is achieved by means of three slots: In slot 1, the non-counted nodes beep with some probability. If they beeped alone, they re-beep in slot 2 to inform the other nodes and they can be counted. In slot 3, all non-counted nodes beep. If no one beeped in the third slot, then it means that every node is counted and the algorithm can terminate globally. The key ingredient is to use an adaptive probability 1/k to increase the chances to beep alone in the first slot, which is done by increasing the probability (decreasing k) whenever no one beeped, and decrease it (increasing k) whenever a collision is detected. As shown in the analysis section further below, this technique leads to a linear running time in the number of nodes.

The details are given on Algorithm 1. It describes the phase that repeats until termination is detected. Each case statement corresponds to a slot, and an extra case statement groups together various computation to be performed at the end of the phase: updating the count variable (line 19), detecting termination (line 21), adjusting the probability (lines 22 to 27).

Algorithm 1: Computing the size of a one-hop network in B cd L. For the sake of analysis, it is easier to think in terms of phases rather than slots. The algorithm progresses every time a node beeps alone in the first slot of a phase. The probability that this happens in a phase depends upon the value of k and the number of nodes n still contending in this phase. Intuitively, if k is too large, then it is likely that no node will beep in the first slot, while if k is too small, they will likely be several to do so. In fact, the probability of success is maximum when k = n , which is what the algorithm attempts to maintain. The following fact is important: Fact 3.1. Uncounted nodes all have the same k.

In the analysis below, we distinguish between the case that k is within "good bounds" and the case that it is not. We call a bad phase one in which k drifts out of these bounds or keeps drifting away (if it is already out). More formally, let I = [n , 3n ]. A phase φ is a bad phase if:

(i) at the start of φ, k ≤ n or k ≥ 3n , and

(ii) the phase moves k farther away from I (or k remains unchanged at 2). This shows that if T = 55n then, w.h.p., the number of bad phases is upper bounded by 23n. Thus, using Fact 3.2, we obtain that, w.h.p., the number of phases inside interval I is at least 5n. Since each phase inside I counts a node with probability at least 1/5, we can use the same arguments to prove that, w.h.p., the number of nodes counted during T = 55n phases is at least n. Which ends the proof.

From Lemma 1: Corollary 5. Algorithm 1 is optimal up to a constant factor.

Experimental Results:

The algorithm was implemented and run on complete graphs with size n ranging over all powers of 2 from 8 to 512 (inclusive). For each value of n, we performed 10000 runs and measured the number of phases before the algorithm terminates. 1 A linear regression with Gnuplot gives us an average number of phases of 3.3197n (with very small regression error of ±0.03074%). Since there are 3 slots per phases, the expected slot complexity in practice is less than 10n.

Adaptation of the algorithm in other beeping models

This section explores the possible adaptations of Algorithm 1 in other variants of the beeping model, namely in B cd L cd (the strongest), in BL (the weakest), and in BL cd . We show that the extra power available in B cd L cd allows us to reduce the slot complexity by a constant factor. Adaptation to BL comes at the price of sacrifying certainty (the adaptation is a Monte Carlo algorithm), it consists in emulating B cd beeps using techniques from [START_REF] Casteigts | Design patterns in beeping algorithms: Examples, emulation, and analysis[END_REF]. Finally, we briefly discuss the case of BL cd , in which naive adaptations do not seem to work.

Adaptation of the algorithm in B cd L cd

In the B cd L cd variant, both beeping and listening nodes can detect if several beeps occur simultaneously. In our algorithm, the purpose of the second slot is for a node to inform others that it was the only one to beep. This step is no longer necessary since listening nodes can detect it from the first slot. As a result, the phases of the algorithm can be simplified from 3 to 2 slots and the expected running time of the algorithm decreases by one third. (According to our experimentations, this would thus decrease the expected number of slots from less than 10n to less than 6.67n.)

Adaptation of the algorithm in BL

As discussed in Section 2, no algorithm can solve the counting problem with guaranteed result in BL, whether it be deterministic or Las Vegas. However, we can adapt it into a Monte Carlo algorithm (uncertain result) using emulation techniques from [START_REF] Casteigts | Design patterns in beeping algorithms: Examples, emulation, and analysis[END_REF] and [START_REF] Afek | Beeping a maximal independent set[END_REF]. We describe this adaptation here and analyse the resulting uncertainty. We show that this uncertainty can be bounded by any constant threshold if the nodes know an upper bound on the size of the network. Otherwise, we must settle for a certainty bound that depends on the size of the network (which is unknown).

The adaptation consists in replacing the beep instruction in Line 9 of Algorithm 1 by a call to the procedure EmulateB cd inBL. The other beep instructions in Algorithm 1 need not be replaced. Procedure EmulateB cd inBL emulates a B cd beep (beep with collision detection) by means of several basic B beeps. It is itself organised into phases of two slots. In each of these phases, the node beeps in one of the two slots, chosen uniformly at random, and it listens in the other. The intuitive idea is that if several nodes are to execute this procedure simultaneously, then they will eventually beep in different slots and thus detect it. Unfortunately, as long as the number of phases is finite, there is a non-zero probability that Now, if the nodes know a polynomial upper bound N = O(n Θ (1) ) on the size of the network, then the other two results from Lemma 6 can be used effectively by the algorithm as follows.

Propostion 8. For any graph G of size n and any 0 < ε < 1:

• if r = log N ε
, the running time of the main algorithm is O n log( n ε ) , and the result is correct with probability at least 1 -ε.

• if r = 2 log(N ) , the running time of the main algorithm is O (n log n), and the result is correct with probability 1 -o 1 n .

The latter is particularly relevant, as it implies that the correct result can be obtained with high probability. Furthermore, assuming that an upper bound is known is reasonable in practical scenarios. For instance, when a sensor network is deployed, one might want to learn afterhand how many sensors (among the initial amount) successfully started to operate. Similarly, when sensors use sleeping patterns (some are active, others sleep to save energy), this makes it possible to learn the number of active ones.

Adaptation of the algorithm in BL cd

Now that we have seen how to adapt the algorithm in the strongest (B cd L cd ) and the weakest (BL) beeping models, we turn our attention to the symmetrical BL cd model. In this variant, only listening nodes can detect simultaneous beeps. Algorithm 1 can be adapted into this model. The basic idea is that instead of having a node inform the others when it detects that it beeped alone, we could do the reverse and have listeners inform the beeping node when it beeped alone. Hence, the first and last slot of each phase remain as in Algorithm 1. The second slot is split into two slots. In the first of these (new slot 2), any node that was listening in slot 1 beeps. This is to detect pathetic cases where all the nodes beep at the same time. In the second of these slots (new slot 3), the listening node(s) beep if they detected a collision in slot 1. Based on this beep, if a node beeped in slot 1, it detects that it was alone (other nodes also know it, since they were all listening in slot 1). The only exception, which new slot 2 can't avoid, is the special case that n = 1 from the start. In this case, the node cannot decide whether it is alone to beep (and thus must count itself) or several nodes are beeping. This problem does not exist if n ≥ 2, even when a single node remains to be counted in the end (since counted nodes keep on listening and participating until termination).

As for the slot complexity, the number of phases still depends solely on the drawings of slot 1 and thus remains unchanged. The fact that every phase is now composed of 4 slots makes the running time increase by one third. (According to our experimentations, this would thus increase the expected number of slots from less than 10n to less than 13.34n.)

Concluding remarks

In this paper, we presented an algorithm for counting the number of processes in one-hop beeping networks. Due to natural liminations of the beeping model, we observed that no algorithm can solve the problem with guaranteed result unless some form of collision detection is available (either for beeping nodes or for listening nodes). We presented an algorithm in the case that beeping nodes can detect collision (B cd L), and prove that it runs in linear time in the number of nodes. We proved that this is optimal up to a constant factor and estimated the expected value of this factor experimentally. Interestingly, the algorithm can be adapted in B cd L cd with a small gain in slot complexity (1/3 less slots) and in BL cd with a small overhead (4/3 more slots). Its adaptation in BL is not as direct, but we proved that the algorithm can be emulated in this variant by a Monte Carlo algorithm which runs in a larger, though reasonable amount of time (log n more slots). Whether this is optimal for BL is an open question. Another open question is whether, and to which extent, the number of nodes in the network could be efficiently approximated by a randomised algorithm.

1

  Boolean counted ← f alse 2 Boolean terminated ← f alse 3 Integer k ← 2 4 Integer size ← 1

	5 repeat
	6	switch slot do
	7	case 1 do
	8	if counted = f alse then
	9	beep with probability 1 k ;	// contends
	10	case 2 do
	11	if I am the only one that beeped in slot 1 then
	12	beep ;	// wins the contest
	13	counted ← true
	14	case 3 do
	16	beep ;	// will contend in the next phase
	17	end of phase:

15 if counted = f alse then 18 if a neighbor beeped in slot 2 then 19 size ← size + 1 20 if no one beeped in slot 3 then 21 terminate ← true 22 if no one beeped in slot 1 then 23 if (k > 2) then 24 k ← k -1 25 else 26 if there was a collision in slot 1 then 27 k ← k + 1 28 until terminated = true; 3.2.2. Analysis of the Algorithm:

Source code available upon request.

We prove the following lemma: Lemma 2. The probability of a phase to be a bad one is upper bounded by 0.4.

Proof. Let φ be a phase. Assume that k verifies the conditions in (i), i.e., k ≤ n or k ≥ 3n . To prove the lemma, we study both cases separately.

• k ≤ n , then k will decrease iff no node beeps. This happens with probability p = 1 -1 k n , which is maximum when k = n and always less than e -1 , which is less that 0.4.

• k ≥ 3n , then k will increase iff at least two nodes beep. This is a particular case of (thus is less likely than) having at least one node beep, which happens with probability p = 1 -1 -1 k n . This formula is maximum when k = 3n and it is always less than 1 3 , which is less than 0.4.

We also have the following lemma:

Lemma 3. Let φ be a phase. If k ∈ I at the start of φ, then with probability at least 1/5, a node will be counted.

Proof. The probability that exactly one node beeps (and thus is counted) in phase φ is given by

Indeed, let v be a vertex that is not yet counted. The probability for v to beep is 1 k , and the probability that all the other n -1 nodes do not beep is given by (1 -1 k ) n -1 . The probability p is a decreasing function of k for k > n and thus it is lower bounded when taking k = 3n .

Using the lower bound (1 -x) n ≥ 1 -nx, we obtain:

We now give the main result of this section:

Let G be a one-hop network of size n. The execution of Algorithm 1 in G ends in at most 55n phases (165n slots), with high probability.

Proof. We denote by T a number of phases, and by T I the number of phases where k is in the interval I, and by B T the number of bad phases (both within the first T phases). We have the following fact:

, where 4n is an upper bound on the number of "external" phases, that is, n -2 initial phases from k = 2 to k = n and 3n -3 phases where k decreases from 3n to 3. The factor 2 for B T corresponds to the fact that bad phases have symmetrical "good phases" where k comes closer to the good interval (and their number is at most B T ).

Note that B T is dominated by a binomial random variable BIN (T, 0.4) with parameters T and 0.4. On the other hand, we have the following formulation of the Chernoff bound (see [START_REF]Probabilistic methods for algorithmic discrete mathematics[END_REF]):

If BIN (n, p) is a binomial random variable with parameters n and p then

for any 0 < a < np.

Then, taking T = 55n, we obtain:

these nodes always beep simultaneously in the procedure, which is why the resulting algorithm is Monte Carlo.

The detail of the procedure is given in Algorithm 2. For technical reasons, we have the nodes generate their random bits (called signature) beforehand and use the same every time the emulation procedure is called. Besides using less random bits, this improves the probability of success by avoiding the extra union bound due to repeating a successful emulation several times. Let r be the number of round in each emulation (its value is discussed later on), we denote by s the signature of a node, that is, the word formed by r bits generated uniformly at random. We say that the procedure is correct if it detects when several nodes execute it simultaneously. The probability that it fails is maximum when two nodes only execute it, which corresponds to 1/2 r . Hence, the probability that the procedure is not correct is upper bounded by 1/2 r . The results in Lemma 6 are obtained by replacing r with different values. Lemma 6. For any ε > 0 and for any n > 0:

. if r = log 1 ε , then, for any node v, the procedure is correct on v with probability at least 1 -ε, 3. if r = 2 log(n) , then, the procedure is correct w.h.p.

Since n is not known a priori, only the second result can be used effectively by the algorithm. From Lemma 6 we obtain: Theorem 7. For any graph G of size n and any 0 < ε < 1: If r = log 1 ε , each node v computes the size of the network in O n log( 1 ε ) slots, and the result is correct with probability at least 1 -ε.


Lehmann

Paquet

Quillard- Muraine

Laplanche Jl

Bouaziz-Amar

Peoc'

Katell Peoc'
email: katell.peoch@aphp.fr

Diagnosis associated with Tau higher than 1200 pg/ mL: insights from the clinical and laboratory practice

Keywords: Alzheimer disease, Creutzfeldt-Jakob disease, Cerebrospinal fluid, Tau protein, 14-3-3 protein, dementia

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Most neurodegenerative diseases are associated with the accumulation of abnormal forms of proteins in the brain, leading to neuronal death, and frequently associated with a pathological variation of biomarkers in the cerebrospinal fluid (CSF). These biomarkers have been included in the state-of-the-art differential diagnosis of dementia.

Protein Tau is a soluble protein, which favors the stability of microtubules in the axon and regulates the neuronal cytoskeleton's dynamic [START_REF] Trinczek | Domains of tau protein, differential phosphorylation, and dynamic instability of microtubules[END_REF]. Under pathological conditions, the protein Tau undergoes post-transcriptional phosphorylation processes and aggregates into filamentous brain inclusions, known as neuronal fibrillary tangles [START_REF] Duyckaerts | Alzheimer disease models and human neuropathology: similarities and differences[END_REF]. The presence of protein Tau in the CSF has been related to the passive release of the protein by altered neurons [START_REF] Pooler | Amyloid accelerates tau propagation and toxicity in a model of early Alzheimer's disease[END_REF], or secretion by neurons [START_REF] Saman | Exosome-associated Tau Is Secreted in Tauopathy Models and Is Selectively Phosphorylated in Cerebrospinal Fluid in Early Alzheimer Disease[END_REF].

In clinical practice, a drastic Tau elevation is challenging to interpret for both the clinical biologists and physicians. Moreover, the medico-economic utility of performing dilution for precise quantification of Tau in this setting is not explicitly stated. However, clinical biologists are mandated to provide counseling regarding the interpretation of biological results according to the International Organization for Standardization (ISO) 15189.

In a multicentric European study including 3,034 patients with various rapidly progressive neurodegenerative diseases, the median CSF protein Tau concentration was 224 pg/mL in all neurodegenerative diseases (Min-Max: 0-38,400) except Creuzfeldt-Jakob disease (CJD), and very high Tau concentrations were a rare pattern observed in only a few percent of the patients (7.6% of patients with Tau>1300 pg/mL and Alzheimer disease -AD-) [START_REF] Stoeck | Cerebrospinal fluid biomarker supported diagnosis of Creutzfeldt-Jakob disease and rapid dementias: a longitudinal multicentre study over 10 years[END_REF].

We, therefore, aimed to investigate within a retrospective descriptive multicentric study which diagnosis very high CSF Tau concentrations tended to be associated with, and which patterns of biomarkers could provide a practical help to differentiate them.

MATERIALS AND METHODS

Subjects

Patients enrolled in this retrospective study were all coming for exploration in a specialized center of the French ePLM network and had a lumbar puncture (LP) in this setting. The ePLM network [START_REF] Gabelle | Impact of the 2008-2012 French Alzheimer Plan on the use of cerebrospinal fluid biomarkers in research memory center: the PLM Study[END_REF] includes seven French memory research centers, specialized in the diagnosis, treatment, and follow-up of patients with dementia with suspected dementia and neurodegenerative diseases, using the same diagnostic procedure and criteria. Eligibility criteria's were age over 18 years and cognitive of behavioral disorders.

Patients' familial history of dementia, psychiatric disorders, and neurological diseases were systematically recorded at the initial outpatient consultation. When appropriate, LP and CSF analysis were performed in the routine clinical testing on patients with cognitive or behavioral deficits, in keeping with the local French regulations applying to Memory clinics. For each patient, the diagnosis was made according to validated clinical diagnostic criteria [START_REF] Mckhann | The diagnosis of dementia due to Alzheimer's disease: Recommendations from the National Institute on Aging-Alzheimer's Association workgroups on diagnostic guidelines for Alzheimer's disease[END_REF][8] [START_REF] Jellinger | Neuropathological evaluation of mixed dementia[END_REF][10] [START_REF]Diagnosis and Therapy of Human Transmissible Spongiform Encephalopathies: Report of a WHO Consultation[END_REF] and considering CSF biomarkers results. All the patients showing a CSF Tau level above 1200 pg/mL were retrospectively selected.

CSF samples

CSF, obtained by LP using a 25-gauge needle and standardized procedures [START_REF] Duits | Performance and complications of lumbar puncture in memory clinics: Results of the multicenter lumbar puncture feasibility study[END_REF][13] [START_REF] Engelborghs | Consensus guidelines for lumbar puncture in patients with neurological diseases[END_REF], was collected in polypropylene tubes [START_REF] Lehmann | Impact of harmonization of collection tubes on Alzheimer's disease diagnosis[END_REF]. CSF samples were transferred to laboratories within 4h, centrifuged at 1,000g for 10 min at 4°C, aliquoted into 0.5 mL polypropylene tubes, and stored at -80°C for further analysis within two months. The intra-assay variability observed in replicates was less than 10%, or the assay result was excluded and the sample re-assayed. All the laboratories in this study participated in an external quality control assessment organized by the Alzheimer's association's external quality controls program. Internal quality controls were included in each series, and followed with time, to identify a shift of the results. When drastic changes or shifts were observed on controls, a new batch was verified and used. The 14-3-3 protein detection in the CSF was carried out when CJD was thought to be a possible diagnosis, as recommended in routine clinical practice. A semi-quantitative interpretation was performed by western blot [START_REF] Brandel | 14-3-3 protein cerebrospinal fluid detection in human growth hormone-treated Creutzfeldt-Jakob disease patients[END_REF]. Results were classified as negative, positive or trace. For further statistical analysis, traces were classified as negative. The ePLM laboratories performing this detection (Montpellier and Paris) participated in national and international external quality assessment schemes.

CSF Biomarkers

CSF

Statistical analysis

Descriptive analysis, statistical tests and graphs were performed using the GraphPad Prism 7 (GraphPad, CA, USA), Past (3.2) and Excel software (Microsoft). Kruskal-Wallis tests were realized to compare biomarkers between all groups, and the results were considered significant for p < 0.05. Comparison of data between groups was performed by the Mann-Whitney U test for quantitative variables. Tree diagram was conceived in Smartdraw (https://www.smartdraw.com/).

RESULTS

Population description

We included 1,743 patients from January 1, 2008, to December 31, 2013. A CSF protein Tau concentration above 1200 pg/mL with a confirmed final diagnosis after one to six years were obtained for 4.5 to 10% of the patients according to the center, leading to a final population of 205 patients.

The patients were mostly female (sex ratio: 0.72). Patients' mean age was 68 years (range: 23-91 years). Final diagnoses are presented in Table 1. One hundred and five patients were diagnosed as suffering from AD (51.2%). Eight presented a combination of AD and vascular dementia. The second most frequent diagnosis in our cohort was CJD (37 patients; 18%). All CJD patients were either certain or probable sporadic cases, according to WHO criteria [START_REF]Diagnosis and Therapy of Human Transmissible Spongiform Encephalopathies: Report of a WHO Consultation[END_REF].

The prion protein gene PRNP 129 genotype was available in 14 patients (nine patients Met/Met, four Val/Val, and one Met/Val).

Sixty-three patients (30.7 %) exhibited another neurological disease, including frontotemporal dementia, paraneoplastic and CNS tumor, toxic or metabolic dementia, amyloid angiopathy, Lewy body dementia, or infectious diseases. Nine patients were suffering from other neurodegenerative conditions with dementia (two patients with MCI and dementia, one patient with a thalamic hematoma, one patient with a Gayet-Wernicke encephalopathy and acute seizure, one patient with narcolepsy, one patient with normal pressure hydrocephaly, one patient with acute seizures, one patient with multiple system atrophy, and one patient with both alcohol chronic intoxication and possible frontotemporal dementia). The autopsy results obtained for six patients (five CJD and one AD) were by the antemortem "confirmed final diagnosis."

Patients were then divided into three groups AD, CJD, and non-AD non-CJD for further analysis. The time elapsed between the onset of the first symptoms and the LP was available for 82 patients (36 AD, 11 CJD, and 35 non-AD non-CJD patients). It was significantly different between groups (Figure 1). The lower median was obtained for CJD patients (3 months; range: 1 to 18 months) compared to non-AD non-CJD patients (median: 2 years; range: 1 month to 18 years), and AD patients (median: 3 years; range: 1 month to 10 years).

pTau and Aβ1-42/ pTau ratio are useful to discriminate between the three groups of patients

Table 2 summarized the results obtained for biomarkers in the three groups of patients. We used Aβ1-42/pTau ratio to integrate both beta-amyloid and Tau pathways in a single index.

Similarly to patients with a moderate increase in protein Tau, AD patients mostly presented decreased Aβ1-42 concentrations and increased pTau concentrations. Using the following thresholds (550 pg/mL and 60 pg/mL for Aβ1-42 and pTau respectively), 25 AD patients were above the threshold for Aβ1-42, and 31 below the threshold for pTau. Using both pTau and Aβ 1-42, 69 patients would have been successfully classified on a total of 105. The Aβ1-42/pTau ratio ranged from 0.556 to 22.39 with a median at 2.98. The Aβ1-42/pTau ratio threshold for AD would be less than 8.3.

In CJD patients, 28 patients were above 550 pg/mL for Aβ1-42 and 24 below 60 pg/mL for pTau. A classification based on these biomarkers would have led to the correct classification of 19 patients. An ambiguous pattern with high pTau and normal Aβ1-42 concentration was observed in 11 patients. The Aβ1-42/pTau ratio was high (median: 14.85; range 2.96-41).

Finally, in non-AD non-CJD patients, the profile generally showed low or subnormal Aβ1-42 concentrations and slightly increased pTau concentrations. Among those 63 patients, 31 were above 550 pg/mL for Aβ1-42 and 28 below 60 pg/mL for pTau. A classification based on these biomarkers would have led to an incorrect classification of 18 patients as AD patients.

The protein 14-3-3 to discriminate between AD and CJD patients

We then analyzed the 14-3-3 detection to evaluate whether this analysis would help for the differential diagnosis. Among the 36 CJD patients with 14-3-3 detection, a positive result would have led to the appropriate classification of 29 patients, 27 when traces was considered as negative.

DISCUSSION

The diagnosis of neurodegenerative diseases is challenging in clinical practice, particularly at the onset of the disease, or when dealing with atypical clinical pictures. CSF biomarkers provide useful tools in clinical practice.

Our results confirmed that few patients displayed protein Tau concentration >1200 pg/mL in the CSF (nearly 10% in patients with a final diagnosis).

Very high Tau protein concentrations were first associated with CJD [START_REF] Otto | Tau protein and 14-3-3 protein in the differential diagnosis of Creutzfeldt-Jakob disease[END_REF] [START_REF] Schoonenboom | Cerebrospinal fluid markers for differential dementia diagnosis in a large memory clinic cohort[END_REF]. They have also been described in patients with acute stroke [START_REF] Hesse | Transient increase in total tau but not phospho-tau in human cerebrospinal fluid after acute stroke[END_REF], traumatic brain injury [START_REF] Ost | Initial CSF total tau correlates with 1-year outcome in patients with traumatic brain injury[END_REF], herpetic encephalitis [START_REF] Zanusso | Cerebrospinal Fluid Markers in Sporadic Creutzfeldt-Jakob Disease[END_REF] and some AD patients [START_REF] Grangeon | collaborators of the ePLM.fr group, Differential Diagnosis of Dementia with High Levels of Cerebrospinal Fluid Tau Protein[END_REF].

In our cohort, most of the patients with Tau>1200 pg/mL were suffering from AD. According to this result, Van der Vlies et al. described that nearly 10% of AD patients presented very high protein Tau concentrations (mean 1,720 pg/mL) [START_REF] Van Der Vlies | CSF biomarkers in relationship to cognitive profiles in Alzheimer disease[END_REF], associated with worse performances in memory tests. A protein Tau concentration >900 pg/mL in AD has been associated with earlier nursing home placement [START_REF] Degerman Gunnarsson | High tau levels in cerebrospinal fluid predict nursing home placement and rapid progression in Alzheimer's disease[END_REF]. The pathological process leading to the release of a large amount of protein Tau in the CSF in a few AD patients remains to be elucidated. It could be related to the duration of evolution. In our cohort, the recorded times elapsed since the first symptoms obtained for 36 AD patients were heterogeneous, ranging from 2 to 10 years, whereas it ranges from 1.5 to 18 months for CJD (n=11 patients) and 1.5 months and 18 years for non-AD-non-CJD patients (n=35 patients). Most extensive studies should be undertaken to unravel any association between very Tau levels and the duration of the disease in AD.

CJD was the second most frequent diagnosis in our study, although its estimated annual prevalence is around 1.5 per million inhabitants in Europe [START_REF] Brandel | The French surveillance network of Creutzfeldt-Jakob disease. Epidemiological data in France and worldwide[END_REF], but according to with the fact that the disease is associated with high Tau concentrations, mainly unphosphorylated Tau [START_REF] Ermann | CSF nonphosphorylated Tau as a biomarker for the discrimination of AD from CJD[END_REF]. pTau concentrations were generally low, whereas Aβ1-42 concentrations were generally high in those patients, differentiating them from AD patients. Indeed, in our cohort, no CJD patient exhibited pTau higher than 101 pg/mL. In most cases, our patients beneficiated of a protein 14-3-3 detection, that was positive in 73%, and ambiguous in 19%. The detection of the 14-3-3 protein in the CSF is currently used in the pre-mortem diagnosis of sporadic Creutzfeldt Jakob disease (CJD) [START_REF] Peoc'h | Diagnostic value of CSF 14-3-3 detection in sporadic CJD diagnosis according to the age of the patient[END_REF]. The detection of the pathologic prion protein by real-time in vitro protein amplification is however quite promising in this setting [START_REF] Hermann | Validation and utilization of amended diagnostic criteria in Creutzfeldt-Jakob Disease surveillance[END_REF] [START_REF] Bizzi | Amended diagnostic protocol increases the early diagnosis of sporadic Creutzfeldt-Jakob disease[END_REF].

Finally, the third group of patients displayed neurodegenerative dementia (frontotemporal dementia, Lewy body dementia), but also toxic, metabolic, neoplastic, infectious, and vascular neurological diseases. This subgroup could be underestimated since we retained for our study only patients with an ante-mortem final diagnosis after one to six years after LP. This group was highly heterogeneous in term of etiology, duration and biomarkers' patterns.

Our secondary objective was to determine which biomarkers were the most relevant to differentiate these groups biologically.

First, there was a significant overlap of biomarkers in the three patients groups, underlying the difficulty of differential diagnosis. As could be expected, CJD and AD patients were the most straightforward groups to differentiate, both using biomarkers and the duration of the disease.

A very high Tau concentration with a low Aβ1-42 and a high pTau first evoke AD, particularly after several months of evolution.

However, low Aβ1-42 was not a significant reason to rule out the diagnosis of CJD, since eight patients finally diagnosed as CJD presented Aβ1-42 lower than 550 pg/mL. In this setting, the diagnostic of CJD could be documented by 14-3-3 detection.

We finally evidenced that a ratio Aβ1-42/pTau comprised between 4.5 (Upper 95 percentile of CI of mean for AD group) and 12.6 (Lower 95 percentile of CI of mean for CJD group) was suggestive of non-AD non-CJD diagnosis in patients with protein Tau concentration >1200 pg/mL. Typical patterns of biomarkers in the three groups are presented in Table 3. A tree diagram is proposed in Figure 4.

The main limitation of our study is its retrospective setting, which is a limitation for evaluating a personalized approach in the diagnosis. Moreover, biomarkers were used in the diagnosis which may generate a bias.

In conclusion, this study gave some avenues for interpreting biomarkers for patients with Tau>1200 pg/mL. Using Aβ1-42/1-40 ratio, instead of CSF Aβ1-42 alone, is also known to reduce the number of discordant cases. Moreover, a combination of biological fluids and imaging biomarkers such as PET, is probably the best way to capture all the aspects of the Tau pathology, as previously published [START_REF] Hall | In vivo tau PET imaging in dementia: Pathophysiology, radiotracer quantification, and a systematic review of clinical findings[END_REF].

  Amyloid β1-42 (Aβ1-42), Tau, and Human tau phosphorylated at Thr181 (pTau) were quantified by standard commercially available INNOTEST® sandwich ELISA assays (INNOTEST_ hTAU Ag, INNOTEST_β-AMYLOID(1-42); INNOTEST_ PHOSPHO-TAU(181P), Fujirebio, Courtaboeuf, France) according to the manufacturer's instructions.

Figures 2 and 3

 3 Figures 2 and 3 presented individual data. The patient's data presented a high degree of overlap. Median pTau, Aβ1-42 concentrations, and Aβ1-42/pTau ratio differed significantly between the three groups of patients (p<0.0001; Fig 3). CJD patients presented the lowest pTau values, with no patients with pTau higher than 101 pg/mL.

Figure 1 :

 1 Figure 1: Comparison of the duration between the first recorded symptoms and LP in

Figure 2 :

 2 Figure 2: XY plot of the studied population All patients' results were plotted according to their respective values of pTau and Aβ1-42 in

Figure 3 :

 3 Figure 3: Scatter dot plot (Median with IQ range) of CSF biomarkers in patients divided

Figure 4 :

 4 Figure 4 : Tree diagram for diagnosis of patients with Tau higher than 1200 pg/mL *For AD diagnosis, low Αβ1-42 and high pTau refer to values above 550 pg/mL for Aβ1-42 and below 60 pg/mL for pTau.

TABLE LEGENDS Table 1 : Diagnosis spectrum of Tau>1200 pg/mL in CSF from patients with final diagnosisTable 2 : Concentrations of CSF biomarkers in the different groups of patients. IQ : interquartileTable 3 : Typical Biomarkers' patterns compared to threshold in the tree groups of patients with Tau higher than 1200 pg/mL

 LEGENDS123

Table 1

 1 DiagnosisNumber of patients (%)

	Alzheimer Disease	105 (51.2)
	Isolated	97 (47.3)
	Mixed/combined	8 (3.9)
	Sporadic Creuztfeldt Jakob Disease	37 (18)
	Other	63 (30.7)
	Paraneoplastic/CNS Tumour	8 (3.9)
	Frontotemporal dementia	7 (3.4)
	Vascular	5 (2.4)
	Toxic and metabolic dementia	4 (2)
	Amyloid angiopathy	3 (1.5)
	Lewy body dementia	3 (1.5)
	Infectious	2 (1)
	Other dementia or neurological diseases	9 (4.4)
	Total	205 (100)

ACKNOWLEDGMENTS

The authors thank all the patients for their participation, the physicians and staff working at the Neurology day care hospital units where explorations were performed, and the laboratory staff for their excellent technical assistance. The authors also want to thank the French Network for prion diseases surveillance for providing diagnosis.

Conflict of interest statement

The authors have no conflict of interest to declare.

Abbreviations


David Romano
email: david.romano@univ-amu.fr

Klotz communication 2019 : New insights into the pathophysiology and treatment of Neuroendocrine Tumors Relevance of neuroendocrine tumours models assessed by kinomic profiling Pertinence des modèles de tumeurs neuroendocrines évalués sur le profil des kinases

Keywords: neuroendocrine tumours cell lines, signalling pathways, kinases, proteomics

Although there is evidence of a significant rise of neuroendocrine tumours (NETs) incidence, current treatments are largely insufficient due to somewhat poor knowledge of these tumours. Despite many efforts achieved to expose driver oncogene mutations in NETs, the genetic landscape of NETs is characterized by relatively few mutations and chromosomal aberrations per tumour compared with other tumour types. In addition, NETs display few actionable mutations providing compelling rationale for targeted therapies. Recent works aiming at characterizing currently used NETs in vitro models at the genomic level raised concerns on their reliability as bona fide tools to study NETs biology. However, the lack of actionable mutation in NETs implies that sole use of genomic is not sufficient to describe these models and establish appropriate therapeutic strategies. Several kinases and kinase-involving signalling pathways have been demonstrated as abnormally regulated in NETs. Yet, kinases have only been investigated regardless of their involvement in large intracellular signalling networks. In order to assess the validity of in vitro NETs models to study NETs biology, "next-generation" high throughput functional technologies based on "kinome-wide activity" will demonstrate the similarities between signalling pathways in NETs models and patients' samples. These approaches will significantly assist in identifying actionable alterations in NETs signalling pathways and guide patient stratification into early-phase clinical trials based on kinase inhibition targeted therapies.

Résumé

Malgré une augmentation significative de l'incidence des tumeurs neuroendocrines (TNE), les traitements actuels sont largement insatisfaisants en raison d'une connaissance insuffisante de ces tumeurs. Malgré les nombreux efforts déployés pour identifier des mutations oncogéniques dans les TNE, le profil génétique des TNE est caractérisé par relativement peu de mutations et aberrations chromosomiques en comparaison avec d'autres types de tumeurs.

En outre, les TNE possèdent peu de mutations conductrices justifiant de manière convaincante des stratégies de thérapies ciblées. Des travaux récents visant à caractériser les modèles in vitro de TNE actuellement utilisés au niveau génomique ont émis des doutes quant à leur fiabilité pour étudier la biologie des TNE. Cependant, l'absence de mutation conductrice dans les TNE signifie que la génomique à elle seule ne permet pas de caractériser les modèles d'étude de TNE ni d'établir des stratégies thérapeutiques appropriées. Plusieurs kinases et voies de signalisation ont été démontrées comme anormalement régulées dans les TNE. Cependant, ces travaux n'ont pas pris en compte l'implication de ces kinases dans de grands réseaux de signalisation intracellulaire. Afin d'évaluer la validité des modèles de TNE in vitro pour étudier la biologie des TNE, des technologies fonctionnelles à haut débit dites «de nouvelle génération», basées sur l'activité du « kinome », permettront de révéler les similitudes entre les voies de signalisation des modèles de TNE et les échantillons de patients.

Ces approches aideront de manière significative à identifier des perturbations dans les voies de signalisation dans les TNE et guideront la stratification des patients pour développer des essais cliniques basés sur une pharmacologie ciblée des kinases.

Mots clés: lignées cellulaires de tumeurs neuroendocrine, voies de signalisation, kinases, protéomique

Introduction

High throughput genomics technologies, such as next-generation sequencing (NGS), allowed the identification of actionable mutations in tumours, to which targeted therapies can be developed with the potential to improve therapeutic index aiming at targeting the tumour versus normal tissues in contrast to conventional cytotoxic agents. Increasingly, NGS of patient tumour samples guides patient stratification into clinical trials, such that only the patients bearing specific molecular alterations will receive the corresponding targeted therapy.

In parallel, extensive use of well-characterized in vitro preclinical models (e.g. cell lines) improved significantly our knowledge of tumour biology. Despite initial success and clinical deployment of this concept, several limitations have emerged [START_REF] Tannock | Limits to Personalized Cancer Medicine[END_REF][START_REF] Friedman | Precision medicine for cancer with nextgeneration functional diagnostics[END_REF], such as the lack of driver mutations in a majority of tumours that are sequenced in the clinic and the differences between in vitro models and original tumours. These obstacles are particularly accurate in rare tumours or tumours with few, if any, actionable mutations, like neuroendocrine tumours, representing a significant unmet challenge in precision oncology. This highlights the need to bring forward cost-effective complementary approaches that will assist in identifying activated pathways that can be targeted therapeutically [START_REF] Friedman | Precision medicine for cancer with nextgeneration functional diagnostics[END_REF].

Genomic pitfalls and caveats of in vitro neuroendocrine tumours models

Neuroendocrine tumours (NETs) are neoplasms originating in hormone producing cells of the endocrine system. NETs can exhibit functional and non-functional symptoms and represent a heterogeneous group of neoplasm. Based on pathological analysis, NETs are generally classified into well-differentiated low-to-intermediate grade (grade 1 and 2) versus aggressive poorly differentiated tumours (grade 3, also named neuroendocrine carcinomas or NEC).

Alike more frequent type of tumours, the understanding of NETs biology depends essentially on advances in techniques such as tumour tissue and cell culture [START_REF] Witkowski | Experimental pathology and the origins of tissue culture: Leo Loeb's contribution[END_REF]. Patient tumour-derived cell lines have been widely used to study the molecular mechanisms of tumours, their response to therapy and thus have considerably contributed to improve cancer research over recent decades. Cell lines, as disease models, present several outstanding advantages, such as their ease of manipulation and low cost, facilitating also their use for drug screening (e.g. concomitant study of multiple cell lines and multiple combinations of drugs). When a model system is used, it is essential to consider the similarities and differences between the model and reality, so that the model can be validly applied. There are also important limitations, such as the occurrence of changes/transformations in the original cell required for in vitro growth or differences from the original tumour microenvironment (deficit in vascularization and hypoxia). In addition, cell lines do not exactly reflect their tumour of origin and can differ substantially in terms of genomic alterations, protein expression and therapeutic sensitivity [START_REF] Stein | A Serial Analysis of Gene Expression (SAGE) database analysis of chemosensitivity: comparing solid tumors with cell lines and comparing solid tumors from different tissue origins[END_REF][START_REF] Sandberg | Assessment of tumor characteristic gene expression in cell lines using a tissue similarity index (TSI)[END_REF][START_REF] Ertel | Pathway-specific differences between tumor cell lines and normal and tumor tissue cells[END_REF][START_REF] Gillet | Redefining the relevance of established cancer cell lines to the study of mechanisms of clinical anti-cancer drug resistance[END_REF][START_REF] Domcke | Evaluating cell lines as tumour models by comparison of genomic profiles[END_REF]. These biological differences between in vivo/in vitro tumour cell lines and human neoplasms must be considered when experimental systems are used as models for human cancer [START_REF] Rockwell | In vivo-in vitro tumour cell lines: characteristics and limitations as models for human cancer[END_REF].

The establishment of NETs cell lines has proved to be difficult. This has been attributed, at least in part, to the low proliferation rate of NETs [START_REF] Modlin | Priorities for improving the management of gastroenteropancreatic neuroendocrine tumors[END_REF]. Despite these challenges, several cell lines of human and rodent origins have been established from small intestinal and pancreatic NETs [START_REF] Kawasaki | Gastroenteropancreatic neuroendocrine neoplasms: genes, therapies and models[END_REF]. The most commonly used human neuroendocrine cell lines origin include the pancreatic cell lines BON-1 [START_REF] Evers | Establishment and characterization of a human carcinoid in nude mice and effect of various agents on tumor growth[END_REF] and QGP-1 [START_REF] Kaku | Establishment of a carcinoembryonic antigen-producing cell line from human pancreatic carcinoma[END_REF], as well as the small intestinal cell lines GOT1 [START_REF] Kölby | A transplantable human carcinoid as model for somatostatin receptor-mediated and amine transporter-mediated radionuclide uptake[END_REF], P-STS, L-STS and H-STS [START_REF] Pfragner | Establishment and characterization of three novel cell lines -P-STS, L-STS, H-STS -derived from a human metastatic midgut carcinoid[END_REF], the neuroendocrine carcinoma cell lines NEC-DUE1, NEC-DUE2 [START_REF] Krieg | New model for gastroenteropancreatic large-cell neuroendocrine carcinoma: establishment of two clinically relevant cell lines[END_REF] and N-TAK1 [START_REF] Yamada | Establishment and characterization of a human rectal neuroendocrine cell carcinoma in vitro[END_REF] and carcinoid lung cell lines, such as H727. As it stands, authentic NETs cell lines are rare, their genomic and mutational features poorly described and comprehensive information regarding their therapeutic sensitivity is incomplete. Recently, efforts have been made to characterize pancreatic NET-derived cell lines BON-1 and QGP-1 by exome sequencing and genome-wide copy number analysis.

These studies have raised questions regarding their relevance as models due to their deficiency in pancreatic NET-associated mutations [START_REF] Boora | Exome-level comparison of primary well-differentiated neuroendocrine tumors and their cell lines[END_REF][START_REF] Vandamme | Next generation exome sequencing of pancreatic neuroendocrine tumor cell lines BON-1 and QGP-1 reveals different lineages[END_REF]. In addition, several NET-derived cell lines were recently comprehensively characterized, including evaluation of their neuroendocrine phenotype, genomic alterations and therapeutic sensitivity profiles [START_REF] Hofving | The neuroendocrine phenotype, genomic profile and therapeutic sensitivity of GEPNET cell lines[END_REF]. This work found that neuroendocrine phenotype was preserved in only a subset of these NETs cell lines and that they harbour additional genomic alterations than those depicted for NETs. One major concern is the origin of NETs cell lines and whether they were derived from welldifferentiated neuroendocrine tumours or poorly differentiated neuroendocrine carcinomas. It is straightforwardly questionable that available NET cell lines were established from more aggressive tumours than expected and thus should be classified as NEC. The occurrence of TP53 mutations in several NET cell lines (P-STS, BON-1 and QGP-1) further strengthens this concern [START_REF] Vandamme | Next generation exome sequencing of pancreatic neuroendocrine tumor cell lines BON-1 and QGP-1 reveals different lineages[END_REF][START_REF] Hofving | The neuroendocrine phenotype, genomic profile and therapeutic sensitivity of GEPNET cell lines[END_REF]. The original publications on NETs cell lines do not contain sufficient data to determine the grade of the tumours from which cell lines were derived. As a consequence, these observations emphasises the need to be cautious when drawing conclusions from studies performed on NET cell lines.

In addition to traditionally obtained patient-derived cell lines, our group recently developed a new method for culturing primary pancreatic NETs cells using bovine extracellular matrix [START_REF] Mohamed | Antiproliferative and anti-secretory effects of everolimus on human pancreatic neuroendocrine tumors primary cultures: is there any benefit from combination with somatostatin analogs?[END_REF][START_REF] Mohamed | Pasireotide and octreotide antiproliferative effects and sst2 trafficking in human pancreatic neuroendocrine tumor cultures[END_REF]. This culturing method established on 30 pancreatic NETs allowed maintaining cells with neuroendocrine features and assessing their genomic mutations and drug responses [START_REF] Mohamed | Antiproliferative and anti-secretory effects of everolimus on human pancreatic neuroendocrine tumors primary cultures: is there any benefit from combination with somatostatin analogs?[END_REF][START_REF] Mohamed | Pasireotide and octreotide antiproliferative effects and sst2 trafficking in human pancreatic neuroendocrine tumor cultures[END_REF]. Primary cultures of pancreatic NET, as well as NEC models, have also been achieved by other laboratories [START_REF] Krieg | New model for gastroenteropancreatic large-cell neuroendocrine carcinoma: establishment of two clinically relevant cell lines[END_REF][START_REF] Falletta | mTOR inhibitors response and mTOR pathway in pancreatic neuroendocrine tumors[END_REF][START_REF] Ohmoto | Establishment of preclinical chemotherapy models for gastroenteropancreatic neuroendocrine carcinoma[END_REF][START_REF] Yachida | Establishment and characterization of a new cell line, A99, from a primary small cell carcinoma of the pancreas[END_REF] and can be considered as appropriate models to use.

The common objective of cancer researchers and clinicians is to better match patients with therapies. So far, NGS-based matching has been the most advanced technology applied to this problem. Cancers accumulate genetic alterations, but we may be approaching a running time limit regarding detection these driver oncogenes [START_REF] Lawrence | Discovery and saturation analysis of cancer genes across 21 tumour types[END_REF]. Indeed, multiple studies revealed that most malignancies lack actionable mutations or harbour mutations either in non-druggable oncogenes (e.g. RAS, MYC family proteins) or in genes of poorly characterized therapeutic value [START_REF] Chia | Phenotype-driven precision oncology as a guide for clinical decisions one patient at a time[END_REF][START_REF] Garofalo | The impact of tumor profiling approaches and genomic data strategies for cancer precision medicine[END_REF][START_REF] Commo | Impact of centralization on aCGH-based genomic profiles for precision medicine in oncology[END_REF][START_REF] Macconaill | Prospective enterprise-level molecular genotyping of a cohort of cancer patients[END_REF]. Moreover, even the best achievements demonstrate that identifying wellcharacterized mutations in an individual patient may generate transient, if any, benefit from single-agent targeted therapy. For instance, while mutation-directed therapy often achieves a remarkable initial response, this is almost inevitably followed by relapse and emergence of drug resistance [START_REF] Cree | Molecular chess? Hallmarks of anti-cancer drug resistance[END_REF][START_REF] Holohan | Cancer drug resistance: an evolving paradigm[END_REF]. Finally, widespread analysis of hundreds of cell lines and compounds shows that, with some remarkable exceptions (e.g. BRAF, HER2/ERBB2, EGFR inhibitors), mutations are poor predictor of drug sensitivity [START_REF] Goodspeed | Tumor-Derived Cell Lines as Molecular Models of Cancer Pharmacogenomics[END_REF][START_REF] Basu | An interactive resource to identify cancer genetic and lineage dependencies targeted by small molecules[END_REF].

Therapeutic management of NETs faces multiple challenges due to tumour heterogeneity and relatively poor knowledge of their biology. The therapeutic route for NETs has recently rapidly evolved and the increasing number of treatment options for patients unveiled matters such as timing, sequencing and selection of therapies as core priorities [START_REF] Uri | Current treatment strategies for patients with advanced gastroenteropancreatic neuroendocrine tumors (GEP-NETs)[END_REF]. Since traditional treatments usually induce tumour stabilization for limited length of time, there is a need to develop novel approaches to overcome treatment-related resistance in patients with advanced and progressive NETs. With this goal in mind, many efforts were recently put together in order to expose driver oncogene mutations in NETs [START_REF] Scarpa | Whole-genome landscape of pancreatic neuroendocrine tumours[END_REF][START_REF] Jiao | DAXX/ATRX, MEN1, and mTOR pathway genes are frequently altered in pancreatic neuroendocrine tumors[END_REF]. However, despite growing evidences that poorly differentiated NETs may harbour mutations commonly observed in pancreatic or colorectal adenocarcinomas [START_REF] Konukiewitz | Pancreatic neuroendocrine carcinomas reveal a closer relationship to ductal adenocarcinomas than to neuroendocrine tumors G3[END_REF][START_REF] Simbolo | Mutational and copy number asset of primary sporadic neuroendocrine tumors of the small intestine[END_REF][START_REF] Shamir | Identification of high-risk human papillomavirus and Rb/E2F pathway genomic alterations in mutually exclusive subsets of colorectal neuroendocrine carcinoma[END_REF][START_REF] Girardi | Unraveling molecular pathways of poorly differentiated neuroendocrine carcinomas of the gastroenteropancreatic system: A systematic review[END_REF][START_REF] Klempner | BRAFV600E Mutations in High-Grade Colorectal Neuroendocrine Tumors May Predict Responsiveness to BRAF-MEK Combination Therapy[END_REF], the genetic landscape of NETs is characterized by relatively few mutations and chromosomal aberrations per tumour compared with other tumour types [START_REF] Scarpa | Whole-genome landscape of pancreatic neuroendocrine tumours[END_REF]. In addition, whole-genome integrated analysis confirmed previous observations that NETs display few, if any, actionable mutations providing compelling rationale for targeted therapies [START_REF] Scarpa | Whole-genome landscape of pancreatic neuroendocrine tumours[END_REF]. As such, only a small proportion of mutations identified from whole-genome sequencing have functional data suggesting that they should be targeted with drugs [START_REF] Kawasaki | Gastroenteropancreatic neuroendocrine neoplasms: genes, therapies and models[END_REF][START_REF] Scarpa | Whole-genome landscape of pancreatic neuroendocrine tumours[END_REF]. The overwhelming complexity of the cancer genome suggests we are in the earliest phases of interpreting such results and translating that data into knowledge that is useful to clinicians. Thus, new transversal technologies are needed to hasten the era of precision medicine in cancer.

Kinome study to the rescue

In recent years, much attention has focused on identifying key cellular signal transduction pathways that are abnormally regulated in the cancer cell. Such pathways regulate cancerrelevant cellular processes, such as cell growth, cell division and cell survival. Typically, these pathways involve cascades of cytoplasmic kinases that ultimately impact on gene transcription. Recent advances in our understanding of the fundamental molecular mechanisms underlying cancer cell signalling have elucidated a crucial role for kinases in the carcinogenesis and metastases of various types of cancer [START_REF] Fleuren | The kinome 'at large' in cancer[END_REF][START_REF] Wilson | New Perspectives, Opportunities, and Challenges in Exploring the Human Protein Kinome[END_REF]. Since most protein kinases promote cell proliferation, survival and migration, when overexpressed or activated by unlicensed inputs (e.g. by constitutively active mutations or permanently activated by abnormally upstream signalling partners), they are also directly associated with tumorigenesis and/or tumour progression. Genome-wide studies of kinase mutations have revealed that genetically inherited variants of specific kinases are causally associated with cancer initiation, promotion, progression as well as recurrence [START_REF] Maurer | Raf kinases in cancer-roles and therapeutic opportunities[END_REF][START_REF] Kittler | Driver mutations in the mitogen-activated protein kinase pathway: the seeds of good and evil[END_REF][START_REF] Bardelli | Mutational analysis of the tyrosine kinome in colorectal cancers[END_REF]. Over the last decades, multiple human malignancies have been identified to be associated with modulation and dysfunction of protein and lipid kinases and deactivated phosphatases on account of chromosomal reshuffling and genetic mutations. Deregulation of kinases has also been demonstrated in many human disorders including immune, neurological and infectious diseases. However, there is probably no greater clinical niche for kinases as key targets for developing drugs than in cancer therapy. Kinome, the complete set of protein kinases encoded in its genome, has become an attractive target for the treatment of numerous types of cancer. Single and multiple kinase inhibitors, both synthetic and natural molecules, are now targeted therapeutic strategies for treatment of human malignancies. As such, there is keen interest in elucidating the specific pathways altered in a given tumour in order to identify relevant targets and help predict treatment responses.

Several signalling pathways involving multiple kinases regulate NETs tumorigenesis and tumour progression (for extensive reviews, see [START_REF] Patel | Molecular challenges of neuroendocrine tumors[END_REF] and [START_REF] Prada | Targeted therapy of gastroenteropancreatic neuroendocrine tumours: preclinical strategies and future targets[END_REF]). To briefly summarize, pathways such as PI3K/Akt/mTor, Ras/MAPK and Notch have been shown as deregulated NETs. In particular, the PI3K/AKT/mTor pathway has been highlighted as a key player in the development of NETs, particularly from pancreas [START_REF] Qian | Prognostic significance of MTOR pathway component expression in neuroendocrine tumors[END_REF][START_REF] Missiaglia | Pancreatic endocrine tumors: expression profiling evidences a role for AKT-mTOR pathway[END_REF]. In this context, the mTor inhibitor Everolimus has been largely studied in NETs and approved by both Food and Drug Agency (FDA) and European Medical Agency (EMA) for patients with advanced well/moderately differentiated pancreatic NETs. However, comprehensive clinical studies relying on Everolimus did not allow observing any improvement of overall survival of NETs patients despite a significant increase in progression free survival [START_REF] Yao | Everolimus for the treatment of advanced, non-functional neuroendocrine tumours of the lung or gastrointestinal tract (RADIANT-4): a randomised, placebo-controlled, phase 3 study[END_REF][START_REF] Lee | Everolimus in the treatment of neuroendocrine tumors: efficacy, side-effects, resistance, and factors affecting its place in the treatment sequence[END_REF][START_REF] Lamberti | The Role of mTOR in Neuroendocrine Tumors: Future Cornerstone of a Winning Strategy?[END_REF][START_REF] Fazio | Everolimus in advanced, progressive, well-differentiated, non-functional neuroendocrine tumors: RADIANT-4 lung subgroup analysis[END_REF]. This relative lack of efficiency has been attributed to feedback mechanisms acting as compensation between Ras/MAPK and AKT/mTor pathways in order to maintain a prosurvival signal and cell homeostasis in the presence of these inhibitors [START_REF] Mohamed | Antiproliferative and anti-secretory effects of everolimus on human pancreatic neuroendocrine tumors primary cultures: is there any benefit from combination with somatostatin analogs?[END_REF][START_REF] Passacantilli | Combined therapy with RAD001 e BEZ235 overcomes resistance of PET immortalized cell lines to mTOR inhibition[END_REF][START_REF] Zitzmann | Compensatory activation of Akt in response to mTOR and Raf inhibitors -a rationale for dual-targeted therapy approaches in neuroendocrine tumor disease[END_REF]. Overall, studies focusing on specific candidate kinases sporadically identified abnormalities in expression and/or activation levels of isolated kinases in NETs [START_REF] Corbo | Pancreatic endocrine tumours: mutational and immunohistochemical survey of protein kinases reveals alterations in targetable kinases in cancer cell lines and rare primaries[END_REF][START_REF] Florio | Src kinase activity coordinates cell adhesion and spreading with activation of mammalian target of rapamycin in pancreatic endocrine tumour cells[END_REF][START_REF] Florio | Src family kinase activity regulates adhesion, spreading and migration of pancreatic endocrine tumour cells[END_REF][START_REF] Capurso | Gene expression profiles of progressive pancreatic endocrine tumours and their liver metastases reveal potential novel markers and therapeutic targets[END_REF][START_REF] Banck | The genomic landscape of small intestine neuroendocrine tumors[END_REF][START_REF] Kidd | EGFR/TGFα and TGFβ/CTGF Signaling in Neuroendocrine Neoplasia: Theoretical Therapeutic Targets[END_REF][START_REF] Shah | Epidermal growth factor receptor expression and activation in neuroendocrine tumours[END_REF][START_REF] Pàez-Ribes | Antiangiogenic therapy elicits malignant progression of tumors to increased local invasion and distant metastasis[END_REF] without considering their multiple interactions within signalling modules.

The human protein kinome comprises over 500 proteins controlling intracellular signalling networks. There is increasing appreciation among researchers and clinicians of the value of investigating biology and pathobiology at the level of cellular kinome activity. Kinome analysis provides valuable opportunity to gain insights into complex biology (including diseases), to identify biomarkers of critical phenotypes (for prognosis and therapeutic efficacy) and targets for therapeutic intervention through kinase inhibitors [START_REF] Fleuren | The kinome 'at large' in cancer[END_REF]. Although genomic and transcriptomic approaches have identified many driver kinases in human cancer, the map portrayed by these approaches is incomplete. This is because protein kinases are regulated at multiple levels, including protein translation, stability and post-translational modification, presenting further mechanisms for deregulation in cancer that are not revealed by interrogation of samples at the DNA and mRNA levels. Consequently DNA-or mRNAbased studies can result in false negatives by not identifying protein kinases deregulated at one or more post-transcriptional levels, and false positives -for example, mutated kinases with low protein stability or kinases that are not overexpressed upon cognate gene amplification [START_REF] Fleuren | The kinome 'at large' in cancer[END_REF][START_REF] Wilson | New Perspectives, Opportunities, and Challenges in Exploring the Human Protein Kinome[END_REF]. A further confounding issue is that protein kinases usually function as components of larger pathways and networks, in which signal output can be subject to control mechanisms that act on separate pathway or network components. As such, kinases can also be deregulated as a result of molecular perturbations of interacting and/or regulatory partners.

Consequently, pathway and network activity also needs to be taken into consideration when assessing the potential driver role of a given protein kinase. Importantly, these shortcomings can be addressed using proteomics.

Recently, considerable advances in methods to assess the activity of the kinome were achieved (for review see [START_REF] Baharani | Technological advances for interrogating the human kinome[END_REF][START_REF] Cann | Measuring Kinase Activity-A Global Challenge[END_REF][START_REF] Radu | Recent advances in methods to assess the activity of the kinome[END_REF]). These technological innovations allow a comprehensive interrogation of kinome activity in different conditions, e.g. drug response. Two general approaches have emerged to assess the activity and architecture of the kinome in cells: one based on activation state-specific antibodies and another based on mass-spectroscopic analysis of phosphorylated substrates or of kinases captured in their activated state on inhibitor-coated beads. While there are obviously conceptual linkages in these approaches, they are based on distinct experimental techniques and priorities. It is important to emphasize that kinome analysis serves to define the activities of kinases that are responsible for mediating many phosphorylation events to regulate distinct, but probably complementary, biological responses. In contrast, mass-spectrometric based phosphoproteome analysis seeks to provide information about the phosphorylation status of every kinase substrates (byidentification of phosphor-acceptor sites) within the proteome. The conceptual difference between the two approaches is perhaps best demonstrated by the consideration that complete coverage of the kinome could be achieved with around 500 data points, whereas comprehensive coverage of the phosphoproteome would require in the order of 100 000 data points.

In order to better depict NETs models, speed up acute data acquisition and thus establish a precise mapping of key signalling modules important for NETs biology, we have recently been using a novel micro-array based method to study kinome activity developed by PamGene (Hertogenbosch, The Netherlands). This highly sensitive method not only channels the study of kinomics from NETs cell lines, but also from tumour samples and then be an asset for the design of therapeutic strategies based on kinomics (unpublished data). It also provides a unique opportunity to compare kinome profiles from in vitro models and patients' samples in order to assess the relevance of preclinical models based on a functional assay despite their genetic discrepancies with NETs. This study will then fulfil the ID card of NETs in vitro models and will enable a better judgement towards their validity as good models to study NETs biology. Additional complexities arise from the ability of microenvironmental factors to influence phosphorylation-dependent signalling and from the tendency for some signalling processes to occur heterogeneously among tumour cells. However, kinomics profiling offers the prospect to select a therapeutic option not only based on proliferation rate or mutational background, as set by current standard strategies for NETs, but also on selective activated kinases identified by global kinome activity analysis.

Concluding remarks

Precision medicine is about matching the right drugs to the right patients and its application into clinical practice has considerably impacted the management of cancer over the last decade. Although this approach is technology agnostic, there is a clear inclination to make precision medicine synonymous with genomics in cancer. However, lack of detection of actionable mutations by sole use of genomic techniques is a frequent problem in the clinic. A recent cancer genomics study has shown that half of driver mutations in tumours occur outside of well-characterized cancer genes [START_REF] Martincorena | Universal Patterns of Selection in Cancer and Somatic Tissues[END_REF]. Such mutations will not be identified in tumour sequencing studies. Therefore, clinical implementation of unbiased signalling pathway analysis technologies to large patient cohorts or rare tumour cases, such as NETs, could improve (i) validation of preclinical models used for investigation, (ii) selection of patients to early-phase clinical trials for kinase-inhibition-based targeted therapies. Such need to broaden the spectrum of techniques to detect genetic and non-genetic targetable cancer vulnerabilities is currently increasingly raised in precision oncology.

Disclosure of interests

The author declares that he as no competing interest.