Robert Trypuz
email: trypuz@loa-cnr.it

Emiliano Lorini
email: emiliano.lorini@istc.cnr.it

Laure Vieu
email: vieu@irit.fr

Solving Bratman's video game puzzle in two formalisms

Keywords: action, intention, rationality 1

The aim of this paper is to propose two formal solutions to a wellknown problem in the recent philosophical literature called the Video Game puzzle. The Video Game puzzle was introduced by Michael Bratman in the 80's and then became a challenge for any theory of intention and action. A few approaches to this puzzle have been discussed in philosophy, but to the best of our knowledge, no solution has been spelled out in a logical formalism.

The first solution proposed in this paper is based on a rich firstorder theory of time, actions and intentions in which individual actions are reified. The second one is based on a multi-modal logic of intention and action in which the concept of attempt is formalized by means of a modal operator for attempt.

Introduction

In [START_REF] Bratman | Two faces of intention[END_REF][START_REF] Bratman | Intention, Plans, and Practical Reason[END_REF], Bratman introduced the Video Game (VG) puzzle which then became a challenge for any theory of intention and action.

The VG scenario is composed of two similar video games. In each of them the player's task is to guide a missile into a certain target. It is assumed that the player is skilled in playing these games and is ambidextrous, so he can play one game with each hand. The player knows that the two games are so linked that it is impossible to hit both targets; if both targets are about to be hit simultaneously the machines shut down. He also knows that there is a reward for hitting either target. Taking into account that it is difficult to hit either target, the player decides to try to guide missile 1 towards target 1 and simultaneously to try to guide missile 2 towards target 2, seeing the risk of shutting down the machines as outweighed by the increase in his chances of hitting a target. Eventually, the player hits target 1 and fails to hit target 2 [START_REF] Bratman | Two faces of intention[END_REF].

Because the player's behavior, i.e., his guiding two missiles towards two targets, is assumed to be rational, any theory of action and intention should describe the intention(s) under which these actions are performed. And here comes the challenge, because the most intuitive and widely accepted thesis linking actions and intentions, called the Simple View, seems to be falsified by the VG scenario, given the strong consistency hypothesis, i.e., that for a rational agent his intentions must be consistent with his beliefs. The Simple View states that if A is an intentional (rational) action of an agent a, then a intends to do A. According to this view, if I hit target 1 intentionally, then I intend to hit target 1. But as Bratman argued: "Given the symmetry of the case I must also intend to hit target 2. But given my knowledge that I cannot hit both targets, these two intentions fail to be strongly consistent" [START_REF] Bratman | Two faces of intention[END_REF]. This reasoning led Bratman to conclusion that "Since my relevant intentions in favour of hitting target 1 are the same as those in favour of hitting target 2, I have neither intention. So the Simple View is false" [START_REF] Bratman | Two faces of intention[END_REF].

The VG puzzle then takes the form of a question: with what intention(s) the successful action of "hitting target 1" and the unsuccessful one of "hitting target 2" have been done?

The philosophical literature describes different approaches to this question. Here we examine how two different logical formalisms are able to answer and solve the puzzle. The first answer is based on a rich first-order theory of time, actions and intentions in which individual actions are reified [START_REF] Troquard | Towards an ontology of agency and action: From STIT to OntoSTIT+[END_REF].

The second one is based on a multi-modal logic of intention and action in which types of attempts are modal operators [START_REF] Lorini | Introducing "attempt" in a modal logic of intentional action[END_REF][START_REF] Lorini | Variations on intentional themes: From the generation of an intention to the execution of an intentional action[END_REF]. The assumptions behind these two theories are quite different, but they agree in considering that actions are non-deterministic, an essential feature for modelling the VG scenario. They also agree in accepting the strong consistency hypothesis, and describe the intentions underlying the player's actions, thus solving the VG puzzle. In the remainder, we successively present the two formal frameworks and how they model the VG scenario. We conclude by briefly comparing the solutions and situating them in the relevant philosophical literature.

2 OntoSTIT+ meets the VG puzzle

Introduction to OntoSTIT+

We briefly describe here OntoSTIT+, a sorted first-order theory whose language and axiomatics is fully developed in [START_REF] Troquard | Towards an ontology of agency and action: From STIT to OntoSTIT+[END_REF]. OntoSTIT+'s domain contains agents, moments, histories, intervals, action tokens, action courses and arbitrary non-temporal entities (including agents). The language includes a set of primitive predicates ∆ + establishing relations between individuals of the first six sorts, a set of primitive predicates, Π + over individuals of the last sort, intended to describe the states of affairs that hold at a moment m and a history h (in short, at an index m/h), a set of predicates Θ of basic action types linking action tokens to their participants (of the last sort), and two sets of predicates ΩΘ and ΓΘ describing respectively the expected outcomes and the preconditions associated to an action type. Bold, lowercase letters stand for constants.

As OntoSTIT+ is the extension of a first-order equivalent of Chellas's "seeing to it that" logic of agency [START_REF] Chellas | The logical form of imperatives[END_REF][START_REF] Belnap | Facing the future: agents and choices in our indeterminist world[END_REF], it is grounded in a branching time structure made of moments and histories (maximal chains of moments), which grasps the indeterminacy of the future. Moments are ordered by means of the precedence relation "P re" which is a strict partial order. P re(m, m ′ ) stands for "a moment m precedes a moment m ′ ". P reEq(m, m ′ ) P re(m, m ′ ) ∨ m = m ′ . For any moment m, there is some history-a possible evolution of the world-h such that m is in h (In(m, h)) and vice versa. Intervals are bounded stretches of histories, so they are linearly ordered and convex. Any interval has a beginning and an end, which are unique. By InI(m, i) we describe that a moment m is in the interval i.

Actions are considered as having a duration and as being non-deterministic. This means that action tokens may unfold into different action courses on histories that branch during their execution. Obviously, all courses of a same action token start at the same moment, but they may have different durations. CO(c, t) stands for "an action course c is a course of an action token t". Each action course runs through a particular interval i (RT (c, i)) and lies on some history h (LOn(c, h)). The agent of each action token exists and is unique. AgO(a, t) stands for "a is agent of the action token t". We assume that one and only one basic action type A i from Θ applies to each action token. An action course is successful if and only if the expected-outcomes predicate (OA i ∈ ΩΘ) associated with the basic action type of its action token holds at the end. So, the same action token might have successful courses on certain histories and unsuccessful courses on others.

Extension to mental attitudes

We extend OntoSTIT+ with modal operators, here limited to Bel and Int for agents' beliefs and outcome intentions. Actually, we introduce three kinds of intention. They result from marrying a logical or AI distinction between outcome intention that (to be) and intention to do [START_REF] Cohen | Intention is choice with commitment[END_REF][START_REF] Woolridge | Reasoning about Rational Agents[END_REF][START_REF] Herzig | C&L Intention Revised[END_REF][START_REF] Grosz | Collaborative plans for complex group action[END_REF] and a philosophical distinction between prior (future-directed) intention to do and intention-in-action (present-directed) to do [START_REF] Searle | Intentionality: An Essay in the Philosophy of Mind[END_REF][START_REF] Bratman | Two faces of intention[END_REF][START_REF] Bratman | Intention, Plans, and Practical Reason[END_REF][START_REF] Searle | Rationality in Action[END_REF]. The first two are based on first-order predicates, while the third uses the modal operator Int.

Intention-in-action (to do) is expressed by IntDo m/h a (t), which stands for "agent a intends at m/h to do the action token t" and it is defined in the following way 1 :

• IntDo m/h a (t) ∃c, i(CO(c, t)∧LOn(c, h)∧AgO(a, t)∧RT (c, i)∧InI(m, i))
By definition, this intention is contemporaneous with all courses of t.

Prior intention (to do) is expressed by P IntDo-A i m/h a ( -→ x ), which stands for "agent a at m/h believes that he is going to do some action of type A i with respect to patient(s) -→ x " and is defined 2 in the following way:

• P IntDo-A i m/h a ( -→ x ) Bel m/h a ∃m ′ , t(P re(m, m ′ )∧A i (t, a, -→ x )∧IntDo m ′ /h a (t))
The last type of intention, outcome intention (that), has the form Int m/h a ϕ(m ′ , h ′ ), which stands for "agent a intents at m/h that ϕ(m ′ , h ′ )". Formulas of type ϕ(m ′ , h ′ ) are Boolean combinations of atoms built with predicates of Π + . This intention is axiomatically constrained so that ϕ is in the power of agent a, and m ′ is in the future of m on history h ′ . This intention persists during the execution of the action the agent undertakes to obtain ϕ (but the last moment), until a believes that ϕ obtains or is impossible, or a simply stops desiring ϕ. Indeed, if an agent intends some state of affair ϕ, he does not believe that ϕ is impossible, he believes that ϕ is not the case now and he desires ϕ. The axiom ensuring that an agent's intention that ϕ entails that he does not believe that ϕ is impossible captures the strong consistency principle:

(SC O ) Int m/h a ϕ(m ′ , h ′ ) → ¬Bel m/h a (∀m ′′ (P re(m, m ′′ ) → ¬ϕ(m ′′ , h ′ ))
We assume that an action of a given type is not always done for the same reason. So, in order to relate action tokens with their motivating outcome intention a series of "Intention-Outcome" (IO) operators is finally introduced. IO-A i m/h a,t ϕ(m ′ , h ′ ) implies that at m/h, a course of the token t of the action type A i is going on together with the corresponding intention in action, a intends ϕ, and the expected outcome of t (i.e., OA i ) implies ϕ:

• IO-A i m/h a,t ϕ(m ′ , h ′ ) → (IntDo m/h a (t) ∧ A i (t, a, -→ x ) ∧ Int m/h a ϕ(m ′ , h ′ ) ∧ (OA i (m ′ , h ′ , a, - → x ) → ϕ(m ′ , h ′ )))
As just explained, we assume that the action course of the token t stops at the index in which the outcome intention that ϕ is dropped and the corresponding IO-A i ϕ stops being true.

Modelling the VG scenario

We assume that Hit ∈ Π + , and that the propositions Hit(m, h, mis1, tar1) and Hit(m, h, mis2, tar2) mean "at index m/h target 1 (resp. 2) has just been hit by missile 1 (2)". Among the actions types which the player p is able (skilled) to perform, is the action type hitting a target with a missile, or, in other words, guiding a missile into a target. We denote it for clarity and concision "Guide". We specify that the expected outcomes of this type of action, described by the predicate "OGuide", imply that the missile directed by the player hits the target. Then we specify the rules of the game, which say that it is impossible to hit both targets, i.e., if one target is hit the other cannot be hit either simultaneously or later:

3 (VG1) OGuide(m, h, p, mis1, tar1) → Hit(m, h, mis1, tar1) (VG2) OGuide(m, h, p, mis2, tar2) → Hit(m, h, mis2, tar2). (VG3) Hit(m, h, mis1, tar1) → ∀m ′ , h ′ ((P reEq(m, m ′ ) ∧ In(m ′ , h ′ )) → ¬Hit(m ′ , h ′ , mis2, tar2)) (VG4) Hit(m, h, mis2, tar2) → ∀m ′ , h ′ ((P reEq(m, m ′ ) ∧ In(m ′ , h ′ )) → ¬Hit(m ′ , h ′ , mis1, tar1))
Obviously (VG3) and (VG4) are in the player's beliefs, because he knows the rules of the game. The player knows that "there is a reward for hitting either target", so he starts desiring having hit either target and forms the intention at index m/h that either target is hit some time later:

(VG5) ∃m ′ , h ′ Int m/h p (Hit(m ′ , h ′ , mis1, tar1) ∨ Hit(m ′ , h ′ , mis2, tar2))
Clearly, this intention and the fact that the player believes (VG3) and (VG4) are not in contradiction with the strong consistency principle (SC O ). Now how the player deals with this disjunctive intention to decide on which actions to do is a question of strategy. In this framework, we assume the player starts searching for the actions that may lead to achieving the content of its outcome intention (VG5). From (VG1) and (VG2) he infers that the needed basic action type is "Guide" and that he can instantiate this action type with two sets of patients, mis1, tar1 and mis2, tar2, since we have as theorems:

• OGuide(m, h, p, mis1, tar1) → (Hit(m, h, mis1, tar1) ∨ Hit(m, h, mis2, tar2))

• OGuide(m, h, p, mis2, tar2) → (Hit(m, h, mis1, tar1) ∨ Hit(m, h, mis2, tar2))

In Bratman's scenario, the player decides to do the two actions simultaneously. Thus two prior intentions to do, namely, the prior intention to do Guide on mis1, tar1 and the prior intention to do Guide on mis2, tar2 are generated:

• P IntDo-Guide m/h p (mis1, tar1) and P IntDo-Guide m/h p (mis2, tar2).
At a later index m * /h * the player decides to start the two action tokens t and t ′ of basic action type Guide on p, mis1, tar1 and p, mis2, tar2 respectively. At this index the prior intentions turn into the intentions-in-action to do t and t ′ and it is required that the player p does not believe that the preconditions of Guide (P Guide) applied to both sets of patients do not hold at m * /h * . The motivating outcome-intention is linked to these actions by the operator IO-Guide. We therefore have:

(VG6) ∃t(Guide(t, p, mis1, tar1) ∧ IntDo m * /h * p (t) ∧ ∃m, h IO-Guide m * /h * p,t (Hit(m, h, mis1, tar1) ∨ Hit(m, h, mis2, tar2))) (VG7) ∃t ′ (Guide(t ′ , p, mis2, tar2) ∧ IntDo m * /h * p (t ′ ) ∧ ∃m, h IO-Guide m * /h * p,t ′ (Hit(m, h, mis1, tar1) ∨ Hit(m, h, mis2, tar2)))
As one can see, for starting both action tokens the player must have only the disjunctive outcome intention (VG5), which activates two intentional actions and give rise to two intentions-in-action. While (VG5) and the two IO-Guide formulas persist, the two action tokens are executed. When target 1 is hit, the courses of both t and t ′ end, only that of t being successful.

In OntoSTIT+ all actions are intentional and any particular action token is always done with the corresponding intention-in-action (to do). In this sense this theory assumes the Simple View. In the VG scenario, we have in addition the outcome intention that either target is hit, and this is the motivating intention associated to both actions. As advocated in the philosophical literature about unintentional side effects, in this theory it is possible for an agent to intend that ϕ and believes that ϕ → ψ, without intending that ψ. But even if we were to allow for this inference and assume that (VG1) and (VG2) hold, we would not have ∃m

′ , h ′ Int m/h p Hit(m ′ , h ′ , mis1, tar1) ∧ ∃m ′ , h ′ Int m/h p
Hit(m ′ , h ′ , mis2, tar2), because atoms formed on the predicate OGuide cannot be arguments of the Int operator since OGuide ∈ Π + . OntoSTIT+ dissociates the (prior of present-directed) intention to do an action and the intention that its expected outcomes hold. Nevertheless, it requires that some motivating outcome intention be present. This may of course be the same intention that the standard effects of the expected outcomes hold but not necessarily.

3 LIA meets the VG puzzle

Introduction to LIA

In LIA the standard operators of dynamic logic of the form [α] (where α is an element of a set of action names ACT -which corresponds to action types in OntoSTIT+) are substituded by modal operators for attempt of the form [[α]]. The main difference between LIA and standard dynamic logic is that the dynamic primitives are not atomic actions, but atomic attempts. In standard dynamic logic formula [α] ϕ is read "ϕ holds after the occurrence of action α", whereas in LIA formula [[α]] ϕ is read "ϕ holds after the agent's attempt to do α". Hence, formula [[α]] ⊥ has to be read "the agent does not try to do α". The dual of [[α]] is α and formula α ϕ is read "the agent tries to do α and ϕ holds after the agent's attempt". Hence, formula α ⊤ has to be read "the agent tries to do α".

The notion of attempt formalized in LIA corresponds to the notion of volition proposed in the philosophical literature [START_REF] Davis | Theory of Action[END_REF][START_REF] Ginet | On Action[END_REF][START_REF] Hornsby | Actions[END_REF][START_REF] Shaughnessy | Trying (as the mental "pineal gland")[END_REF]. Furthemore, an action name α in ACT is supposed to denote a so-called basic action [START_REF] Danto | Basic actions[END_REF][START_REF] Goldman | A Theory of Human Action[END_REF][START_REF] Searle | Intentionality: An Essay in the Philosophy of Mind[END_REF], that is, a particular kind of bodily movement under the voluntary control of the agent that the agent can intend to perform without thinking how to perform it. For example, α might denote a simple motor pattern such as "raising an arm", "moving a leg", but also a complex motor pattern specialized for the accomplishment of a specific task and the achievement of a specific result such as "grasping an object", "tying one's shoes", "closing a window", etc.

In LIA trying (or attempting) to do a basic action α is conceived as a mental event which is caused by a proximal intention to do α and which consists in an agent exerting voluntary control over the initiation and the execution of the bodily movement α, that is, an attempt is the mental counterpart of the intentional performance of a bodily movement. In LIA there are not only operators for attempt of the form [[α]] but also the two operators Bel and Goal for modelling mental attitudes of agents. The original LIA also includes the operators X ("next"), G ("always") and UNTIL of linear temporal logic. In this paper we abstract from time and we only present the fragment of the logic in which we can reason about mental attitudes and attempts. The operator Bel is a standard KD45 doxastic operator expressing what an agent currently believes (Belϕ is read "the agent believes that ϕ"). The operator Goal is a KD operator and refers to chosen goals of the agent, i.e., goals that the agent decides to pursue (Goalϕ is read "the agent has the chosen goal that ϕ"). For the sake of simplicity, we suppose that Goalϕ corresponds to the particular form of intention called "outcome intention that" described above. That is, Goalϕ can also be read "the agent intends that ϕ holds". 4 Every operator [[α]] is supposed to satisfy the axioms and rules of inference of the basic normal modal logic K. We here focus on some additional principles:

(Alt Att ) α ϕ → [[β]] ϕ (SC L ) Belϕ → ¬Goal¬ϕ (PosIntr Goal ) Goalϕ → BelGoalϕ (NegIntr Goal ) ¬Goalϕ → Bel¬Goalϕ (IA) α ⊤ ↔ Goal α ⊤
Axioms PosIntr Goal and NegIntr Goal are principles of positive and negative introspection for chosen goals. Axiom SC L is the strong consistency axiom relating beliefs with chosen goals. According to Axiom Alt Att , all attempts correspond to transitions to the same world, that is, all attempts occur in parallel. Thus, if the agent tries to do two different actions α and β at the same time, all effects of the attempt to do α and all effects of the attempt to do β are effects of the joint occurrence of the two attempts. This explains why formula α ⊤ can be read "the agent tries to do α" instead of "it is possible that the agent tries to do α". Axiom IA-for "Intentional Attempt"-establishes that the agent tries to do α if and only if he intends to try to do α. The direction "←" of IA says that if an agent intends to try to do α he goes through the mental effort of doing α (which consists in trying to do α). This direction of the axiom highlights the causal relation between present-directed intention and attempt. According to the direction "→" of IA attempts are by definition intentional. Indeed, an agent cannot really try to do some action α without having (at least) the intention to try to do α (compare IA with the definition of IntDo m/h a (t) in Section 2). In order to model the relationship between (basic) action occurrences and attempts, further formal constructs have to be introduced in the logic. Given a set ∆ = { α ⊥|α ∈ ACT } of all simple attempt formulas of the form α ⊤, a set of objective formulas OBJ is defined. OBJ is the smallest superset of the set Π of propositional atoms and the set ∆ of simple attempt formulas such that: if ϕ, ψ ∈ OBJ then ¬ϕ, ϕ ∨ ψ ∈ OBJ. From this, a function P re is introduced which assigns an objective formula in OBJ to each basic action, that is: P re : ACT -→ OBJ. P re(α) is supposed to denote the execution precondition of action α. The notion of execution precondition is fundamental for defining the notion of (basic) action occurrence. Formula α ϕ, which has to be read "the agent does α in a successful way and ϕ is true after α's occurrence", is defined starting from the primitive notions of attempt and execution precondition. That is, for any α, we have:

• α ϕ = def α ϕ ∧ P re(α).
This means that in LIA the successful execution of a basic action α is an attempt to do α when the execution precondition of α holds:

• α ⊤ = def α ⊤ ∧ P re(α).
Formula α ⊤ has to be read "the agent does α in a successful way". For example, raiseArm ⊤ has to be read "the agent raises his arm in a successful way". [α] ϕ is given as an abbreviation of ¬ α ¬ϕ for any α ∈ ACT . Thus, [α] ϕ has to be read "after the agent performs α in a successful way, it is the case that ϕ" ([α] ⊥ has to be read "the agent does not perform α in a successful way"). The equivalence between α ⊤ and α ⊤ ∧ P re(α) should be conceived as a non-standard way to express execution laws. In fact, execution laws have been traditionally expressed by taking actions as primitive elements, without decomposing them into more elementary constituents (viz. attempts). For instance, in Situation Calculus [START_REF] Reiter | Knowledge in action: logical foundations for specifying and implementing dynamical systems[END_REF] it is supposed that an action α is executable if and only if its execution precondition P oss(α) is true. Thus, in Situation Calculus the concept of attempt only appears implicitly in the concept of execution precondition and there is no clear distinction between the former and the latter. On the contrary, in LIA attempt and execution precondition are clearly distinguished in the formal specification of execution laws.

The distinction between trying to do α and doing α in a successful way is fundamental for distinguishing two subspecies of intention to do something: the intention to do something in a successful way and the intention to try to do something. The agent's intention to do α in a successful way is defined in LIA as the agent's chosen goal to do α in a successful way. Formally:

• IntDo(α) = def Goal α ⊤.
The agent's intention to try to do α is defined as the agent's chosen goal to try to do α. Formally:

• IntT ry(α) = def Goal α ⊤.
Thus, if an agent intends to do α in a successful way, he also intends to try to do α, i.e., IntDo(α) → IntT ry(α) is a theorem of the present logic. Moreover, an agent may intend to try to do α without intending to do α in a successful way, i.e., IntT ry(α) ∧ ¬IntDo(α) might be true. The plausibility of such a consequence has been defended by several philosophers [START_REF] Bratman | Two faces of intention[END_REF][START_REF] Bratman | Intention, Plans, and Practical Reason[END_REF][START_REF] Mele | She intends to try[END_REF][START_REF] Mele | Springs of Action: Understanding Intentional Behavior[END_REF]. In fact, we can imagine plenty of scenarios where an agent intends to try to do something without intending to accomplish it. For example, suppose that i promises to pay j a certain amount of euros if j tries to raise an arm within five seconds. Agent i assures agent j that he need not actually raise an arm in a successful way for getting the amount of euros. It is plausible to say that j intends to try to raise an arm even if he does not intend to succeed in raising an arm. In fact, j does not care whether his trying is going to succeed or to fail. 5 The following abbreviations are given in order to express that the agent intends to do α and β in parallel and the agent intends to try to do α and β in parallel:

• IntDo(α ∧ β) = def Goal( α ⊤ ∧ β ⊤); • IntT ry(α ∧ β) = def Goal( α ⊤ ∧ β ⊤).

Modelling the VG scenario

We suppose that the action of hitting target 1 and the action of hitting target 2 are basic actions of the video game player. Under this assumption, formulas of type hitT 1 ⊤ and hitT 2 ⊤, which respectively express the facts that "the player tries to hit target 1" and that "the player tries to hit target 2", sound acceptable.

The rules of the game say that it is impossible to hit the two targets in the same time, that is, it is impossible that the player successfully hits target 1 and successfully hits target 2. The definition of successful action being based on the preconditions, this means that the execution precondition of the action of hitting target 1 and the execution precondition of the action of hitting target 2 must be inconsistent. In fact, the player can hit target 1 when he tries to do this, only if missile 1 is correctly oriented towards target 1 and either the player does not try to hit target 2 or missile 2 is not correctly oriented towards target 2. Formally:

• P re(hitT 1) = M1T owardsT 1 ∧ ([[hitT 2]] ⊥ ∨ ¬M2T owardsT 2).
In a similar way, the player can hit target 2 when he tries to do this only if, missile 2 is correctly oriented towards target 2 and either the player does not try to hit target 1 or missile 1 is not correctly oriented towards target 1. Assuming that the player tries to hit both targets, it follows that • P re(hitT 1) → ¬P re(hitT 2).

Since P re(hitT 1) and P re(hitT 2) are inconsistent, the player must believe that he cannot successfully hit both target 1 and target 2. In fact, the following formula can be inferred by definitions of α and [α] and standard modal principles:

(A) Bel¬( hitT 1 ⊤ ∧ hitT 2 ⊤)
According to Axiom SC L , a rational agent cannot intend that ϕ if he believes that ¬ϕ. Therefore, from (A) we can infer ¬IntDo(hitT 1 ∧ hitT 2). This means that in the VG scenario, if the player is rational, he cannot intend to hit target 1 and to hit target 2 at the same time. Now the point is: how can we model the player's decision to play the two video games simultaneously? The nice aspect of LIA is that it makes the notion of attempt available and allows us to model the player's intention to try to hit both targets. In our view, this is exactly the player's intention in the VG example when he decides to have a go at both games at once. Formally:

(B) IntT ry(hitT 1 ∧ hitT 2) that is, Goal( hitT 1 ⊤ ∧ hitT 2 ⊤)
Obviously, (B) and (A) are not inconsistent. Thus, the player intends to hit both targets even if he believes that he cannot hit both targets in a successful way. Moreover, IntT ry(hitT 1 ∧ hitT 2) implies hitT 1 ⊤ ∧ hitT 2 ⊤ (by Axiom IA). This explains how the player's intention to try to hit both targets brings it about that the player mobilizes his energy and tries to hit both targets.

Discussion

Relation with the philosophical literature

We start the discussion by comparing the two presented solutions of the VG puzzle with the ones already existing in the philosophical literature. Two main approaches towards the VG puzzle have been discussed. The first one is based on intention to try (e.g., Mele [START_REF] Mele | Intending and Trying: Tuomela vs. Bratman at the Video Arcade[END_REF]) and the second one considers the disjunctive intention to hit target 1 or to hit target 2 (e.g., Tuomela [START_REF] Tuomela | The Importance of Us[END_REF]).

The LIA solution is clearly based on the one proposed by Mele who claims that the player "tries to hit target 1 (with a video missile fired with his right hand) while also trying to hit target 2 (with a video missile fired with his left hand) and he intends to try to hit target 1 while also intending to try to hit target 2" [18, p. 131]. Mele stressed that possessing intention to try to hit target 1 and intention to try to hit target 2 escapes the principle of strong consistency, since "successfully executing an intention to try to A entails trying to A. It does not entail A-ing" [18, p. 133].

On the other hand, the solution of the VG puzzle in OntoSTIT+ appears to be related to the answer given by Tuomela who says that the player acts under "intention by his shooting behavior to hit 1 or hit 2" [26, p. 65]. Similarly to Tuomela's solution, in OntoSTIT+, the player acts under the disjunctive intention, but OntoSTIT+ refers to intention that, whereas Tuomela considers the intention to do. In OntoSTIT+, both intentions to do are actually present.

Comparison of two frameworks

The two frameworks largely differ in expressivity. While the first uses a rich temporal structure, and a rich notion of action with duration, with action types and two sorts of action individuals, the second doesn't even require time to solve the puzzle, and uses only operators based on names for actions and attempts, i.e., action types. They both model several kinds of intentions, but the first focuses on the ontological differences between (prior) intentionto-do, intention-that and intention-in-action, while for the second, intentionthat, intention-to-do and intention-to-try are all based on a single intention operator, the difference lying in the use of action or attempt operators.

In the light of this as well as in the light of how they are related to the literature, it would seem that the two solutions are of a different essence.

The puzzle is solved in OntoSTIT+ by exploiting the independence between intention-to-do an action and intention-that its outcomes be true, with the same disjunctive intention-that motivating to two different intentions-to-do. On the other hand, the puzzle is solved in LIA by distinguishing between attempts and intention-to-try and actions and intention-to-do, the player intending to try both actions but not intending to do both actions.

However, it appears that since actions in OntoSTIT+ are non-deterministic, they actually correspond to attempts in LIA. And successful actions are defined in terms of "action/attempt" in both frameworks. 6 So, intentionsto-do in OntoSTIT+ correspond to intentions-to-try in LIA. The fact that in OntoSTIT+ there is no inference from intention to do an action to intention that all the action's outcomes be true ends up being very similar to the fact that in LIA, intention-to-try doesn't imply intention to do successfully. Thus OntoSTIT+ is also related to Mele's solution, which shows that the two existing approaches towards the VG puzzle are not incompatible.

Notes

1 This fact restricts also the concept of action to those actions which do no go beyond bodily movement such as running a marathon or signing a document. In order to allow for actions which do go beyond bodily movement, we need replace this definition by the following axiom:

• IntDo m/h a (t) → ∃c, i(CO(c, t) ∧ LOn(c, h) ∧ AgO(a, t) ∧ RT (c, i) ∧ InI(m, i))

and accept the predicate "IntDo" as primitive.

substantive intention. Differently from McCann's conception of trying, in LIA trying has a precise denotation. Therefore, we do not see any problem in having it as a possible content of intention. 6 The success of an action/attempt is not based on the same grounds, because of a different assumption regarding the duration of actions. In LIA (with time), attempts are one-step, so the success of an attempt depends only on its preconditions being satisfied as explained above. In OntoSTIT+, actions have any duration, so the success of an action lies in preconditions as well as other factors (for instance, the agent may change its mind and abort the action during its execution).

This is a definition schema.

Because we are in branching time, we need to quantify over future moments and all alternative histories.

We are aware that this assumption is over-simplistic in two senses. First, an intentionthat is not reducible to a chosen goal. As in OntoSTIT+, and as argued in[START_REF] Baier | Act and intent[END_REF][START_REF] Searle | Intentionality: An Essay in the Philosophy of Mind[END_REF][START_REF] Lorini | Delegation and mental states[END_REF], an agent intends that ϕ if and only if he wants ϕ to be true and believes that ϕ is under his control. So, an intention-that is a complex mental attitude which involves both a goal and a particular kind of belief. Second, as taken into account in OntoSTIT+, an intention-that is by definition a future-directed mental state. That is, when an agent intends that ϕ then he wants ϕ to be true at some point in the future. Here we abstract from time and we simply do not consider this temporal aspect of intention-that.

[START_REF] Chellas | The logical form of imperatives[END_REF] Nevertheless, it has to be noted that other authors have opposed to the idea that an agent can intend to try to do something without intending to do it in a successful way. For instance, McCann has committed himself to the view that "intending to try to do α" entails "intending to do α in a successful way"[START_REF] Mccann | Rationality and the range of intention[END_REF]. For McCann, in fact, trying is a vague concept and intending to try is totally vacuous unless it is supplemented by a more


Yu-Ting Qi

Hong Jiang

Wen-Tao Wu

Fu-Li Zhang

Si-Yu Tian

Wen-Ting Fan

Yan-Ling Liu

Christian Amatore

Wei-Hua Huang

Homeostasis Inside Single Activated Phagolysosomes: Quantitative and Selective Measurements of sub-Millisecond Dynamics of ROS/RNS Production with a Nanoelectrochemical Sensor

Keywords: phagolysosomes, homeostatic regulation, ROS/RNS differentiation, Pt NPs decorated nanowire electrode, nano bioanalytical electrochemistry

Reactive oxygen and nitrogen species (ROS/RNS) are generated by macrophages inside their phagolysosomes. This production is essential for phagocytosis of damaged cells and pathogens, i.e., protecting our organism and maintaining immune homeostasis. The ability to quantitatively and individually monitor the four primary ROS/RNS (ONOO -, H2O2, NO, and NO2 -) with sub-millisecond resolution is clearly warranted to elucidate the still unclear mechanisms of their rapid generation and to track their concentrations variations over time inside phagolysosomes, in particular, to document the origin of ROS/RNS homeostasis during phagocytosis. A novel nanowire electrode (NWE) has been specifically developed for this purpose. It consisted of wrapping a SiC NW with a mat of 3 nm platinum nanoparticles (Pt NPs) whose high electrocatalytic performances allow the characterization and individual measurements of each of the four primary ROS/RNS. This allowed for the first time a quantitative, selective and statistically robust determination of the individual amounts of ROS/RNS present in single dormant phagolysosomes. Additionally, the sub-millisecond resolution of the nanosensor allowed confirmation and measurement of the rapid ability of phagolysosomes to differentially mobilize their enzyme pools of NADPH oxidases (NOX) and inducible nitric oxide synthases (iNOS) to finely regulate their homeostasis. This reveals an essential key to immune responses and immunotherapies and rationalizes its biomolecular origin.

INTRODUCTION

Macrophages play a significant role in immune protection by eliminating pathogens, cellular debris, necrotic and damaged cells. When encountering pathogens, macrophages activate and stretch pseudopodia to grab and internalize pathogens into their cytoplasm by encapsulating them inside vacuoles called phagosomes. These then combine with lysosomes, another type of vacuole equipped with active enzymes bound to their membranes, to generate phagolysosomes. [START_REF] Vieira | Phagosome maturation: aging gracefully[END_REF][2][3][4][5][6] To efficiently digest their endocytic contents while avoiding cellular self-damage, these enzyme pools include NADPH oxidases (NOX) and inducible nitric oxide synthases (iNOS) that are supposed to be activated to produce fluxes of superoxide ions (O2 •-) and nitric oxide (NO). These two parent species undergo follow-on reactions that give rise to a cocktail of four primary reactive oxygen (ROS) and nitrogen (RNS) species (e.g., ONOO -, H2O2, and NO2 -) that shred pathogens down to molecular levels. [7][8][9][10] Studies published over the past decades have provided significant understanding of the generation, regulation, and roles of ROS/RNS in resistance to infection, based on the analysis of endpoints or long-term consequences (from minute to week). 11,12 This suggested, although it could only be established recently by two different strategies, 13,14 that once intra-phagolysosome ROS/RNS are depleted, NOX and iNOS rapidly (within milliseconds ) replenish O2 •-and NO to maintain the high phagolysosome performance. However, the kinetic regulation of the enzymes' activities and the precise nature of the mechanisms that maintain ROS/RNS content in phagolysosomes at levels high enough to digest unwanted biological material without endangering macrophages still remain undetermined. 9,10,[12][13][14] We wish to show here that a new, specifically designed class of platinized SiC nanowire electrodes (SiC@Pt NWEs) provides substantial answers to these important questions related to ROS/RNS-based immunoprotection by enabling statistically significant dynamic measurements of four Scheme 1. Schematic diagrams describing the fabrication of SiC@Pt NWEs for quantitative differentiation of ROS/RNS in individual phagolysosomes. A) Two-step electroless plating of SiC@Pt NWs. B) Mounting a SiC@Pt NW at the tip of a nanopipette for intracellular differential measurement of four primary ROS/RNS (ONOO -, H2O2, NO, NO2 -) at four different electrochemical potentials.

primary ROS/RNS (ONOO -, H2O2, NO, NO2 -) production at the single phagolysosome level inside living activated macrophages.

RESULTS AND DISCUSSION

Principle of the Present Experimental Strategy. Cylindrical nanoelectrodes of nanometer diameter allow to penetrate through the membranes of living cells and organelles while keeping their integrity and their functionalities to carry out sensitive electroanalytical measurements in their interior with selectivity and spatio-temporal resolution to characterize and quantify the internal dynamics of molecular species at the single cell level or organelle level. [10][11][12][13][14][15][START_REF] Ying | Advanced electroanalytical chemistry at nanoelectrodes[END_REF][START_REF] Zhang | Real-time intracellular measurements of ROS and RNS in living cells with single core-shell nanowire electrodes[END_REF][START_REF] Zhang | New frontiers and challenges for single-cell electrochemical analysis[END_REF][START_REF] Lu | Electrochemical sensing at a confined space[END_REF][START_REF] Pan | Enzymatic electrochemical biosensors for in situ neurochemical measurement[END_REF][START_REF] Zhang | Nanoelectrochemical analysis inside a single living cell[END_REF] This is possible because the high aspect ratio of these electrodes allows them to impose a strong localized pressure against the cell membrane so that a tight nanopore opens [START_REF] Taupin | Osmotic pressure induced pores in phospholipid vesicles[END_REF] through which the nanoelectrode can slip while the membrane immediately seals back around it. This makes it possible to maintain unchanged the mechanisms ensuring intracellular metabolism during the progression of the electrode inside the cellular cytoplasm.

Ensuring and maintaining the nanosensors' ability to detect and differentiate oxidation waves of the four primary ROS/RNS (ONOO -, H2O2, NO, NO2 -) while preventing any degradation of their responses require the nanosensor to be coated with platinum black (Pt-black). 10,[START_REF] Pan | Enzymatic electrochemical biosensors for in situ neurochemical measurement[END_REF][START_REF] Amatore | Real-time amperometric analysis of reactive oxygen and nitrogen species released by single immunostimulated macrophages[END_REF][START_REF] Amatore | Characterization of the electrochemical oxidation of peroxynitrite: relevance to oxidative stress bursts measured at the single cell level[END_REF][START_REF] Amatore | Monitoring in real time with a microelectrode the release of reactive oxygen and nitrogen species by a single macrophage stimulated by its membrane mechanical depolarization[END_REF][START_REF] Li | Electrochemical Detection of nitric oxide and peroxynitrite anion in microchannels at highly sensitive platinum-black coated electrodes. application to Ros and Rns mixtures prior to biological investigations[END_REF][START_REF] Pan | Resistive-pulse sensing inside single living cells[END_REF] For example, nanopipette-based electrodes fitted with embedded Pt-black deposits encased at their tips and functioning as scanning electrochemical microscopy (SECM) probes could be inserted into single phagolysosomes to individually monitor and quantify during tens of minutes the four primary ROS/RNS with quadruple potential chronoam-perometric sequences. This pioneered direct measurements of long-term dynamic changes in ROS/RNS inside large, intact phagolysosomes as they underwent a homeostatic activity. 13 However, to avoid corrupting the faradic information with residual charging currents due to large areas of platinum black, the method had to have a time resolution of a few seconds at best. Moreover, the difficulty of its SECM operation did not allow monitoring a sufficient number of events during a reasonable time duration to draw statistically significant conclusions. 12,13 For this reason, we developed in parallel another strategy based on platinized carbon deposited SiC nanowire electrodes to analyze ROS/RNS effluxes released by individual phagolysosomes with a temporal resolution down to milliseconds in order to study the processes of establishment of homeostasis at short times. 14,[START_REF] Zhang | Real-time intracellular measurements of ROS and RNS in living cells with single core-shell nanowire electrodes[END_REF] However, the quasi-crystalline Pt coatings of these nanoelectrodes did not provide sufficient electrochemical resolution to differentiate the four primary ROS/RNS, so only their overall quantity and dynamics could be determined. 12 Thus, a new strategy capable of measuring ROS/RNS inside single living cells and their intracellular organelles with sufficient spatial, kinetic and chemical resolution is clearly needed in order to better monitor and reveal the physiological homeostatic processes taking place inside the phagolysosomes of macrophages while gathering a sufficient collection of data to offer important statistical information. Based on the two previous attempts described above, it was concluded that the key issue to achieve this objective resided in a perfect design of the nanostructure of the Pt deposit to ensure the sought electrocatalytic properties. This problem was solved by constructing a high-density coating of contiguous ultrasmall Pt nanoparticles (Pt NPs) using their spontaneous electrostatic grafting onto the previously modified surface of bare SiC nanowires (SiC NW) by positive 3-aminoprooyltriethoxysilane (APTES) monolayer (Scheme 1A). Due to the excellent electrical conductivity of the dense coating of nanoscale Pt NPs bonded by electrostatic interactions on the surface of APTES-modified SiC and their high electrocatalytic properties, the SiC@Pt nanowire electrodes (NWEs) made it possible to discriminate and monitor individually the four primary ROS/RNS (ONOO -, H2O2, NO, NO2 -) and measure their dynamic fluxes with sub-millisecond temporal resolution when combined with the IVIEC (intracellular vesicle impact electrochemical cytometry) technique introduced by Ewing et al [START_REF] Li | Quantitative measurement of transmitters in individual vesicles in the cytoplasm of single cells with nanotip electrodes[END_REF][START_REF] Lovric | On the mechanism of electrochemical vesicle cytometry: chromaffin cell vesicles and liposomes[END_REF][START_REF] Phan | Measuring synaptic vesicles using cellular electrochemistry and nanoscale molecular imaging[END_REF] (Scheme 1B).

SiC@Pt NWEs could then be appropriately inserted into single macrophages and monitored therein for the dynamic concentrations of each of the four primary ROS/RNS released by a series of phagolysosomes with the required sensitivity, precision and selectivity with a sub-millisecond temporal resolution. As will be developed in what follows, these measurements highlighted that when the concentrations of ROS/RNS inside a phagolysosome decrease below a threshold value due to their electrooxidation at the SiC@Pt NWE tip, mimicking what happens when they react with biological moieties, iNOS and NOX are immediately activated to compensate for ROS/RNS losses. This is quite consistent with the homeostatic behavior observed before. [12][13][14] However and unexpectedly, iNOS and NOX responses were found to be extremely different on submillisecond timescales. iNOS greatly increased their activity to release large amounts of NO, while NOX could only generate relatively weaker fluxes of O2 •-at the beginning. [START_REF] Decoursey | Regulation and termination of nadph oxidase activity[END_REF][START_REF] Winterbourn | Reactive oxygen species and neutrophil function[END_REF] On larger timescales, O2 •-began to be continuously generated by the NO-regulated NOX pool, [START_REF] Wink | Nitric oxide and redox mechanisms in the immune response[END_REF] eventually producing a dynamic ROS/RNS homeostatic response essentially composed of ONOO -and NO excess, whose composition differs radically from those inside resting phagolysosomes, thereby providing unsuspected new insights into the key mechanisms supporting phagocytosis.

Fabrication and Characterization of Single SiC@Pt NWEs. As summarized in the previous section, Pt NPs were successfully grafted on SiC NWs surfaces by a simple chemical reduction method (Scheme 1) after the SiC NWs surfaces were modified with 3-aminoprooyltriethoxysilane (APTES) to make the surface uniformly positively charged for promoting the absorption of the negatively charged chloroplatinic anion (PtCl6 2-) (Figure S1). [START_REF] Williams | Immobilization of streptavidin on 4h-SiC for biosensor development[END_REF][START_REF] Zhang | Selfassembly of graphene-encapsulated Cu composites for nonenzymatic glucose sensing[END_REF] PtCl6 2-was then reduced by formic acid (HCOOH) to form Pt nanonuclei (Pt NNs) with the size and morphology suitable for optimal electrocatalytic performance. [START_REF] Sun | Synthesis and Characterization of platinum nanowire-carbon nanotube heterostructures[END_REF][START_REF] Sun | Template-and surfactant-free room temperature synthesis of self-assembled 3D Pt nanoflowers from single-crystal nanowires[END_REF][START_REF] Meng | Morphology controllable growth of pt nanoparticles/nanowires on carbon powders and its application as novel electro-catalyst for methanol oxidation[END_REF][START_REF] Meng | Factors influencing the growth of Pt nanowires via chemical selfassembly and their fuel cell performance[END_REF][START_REF] Fan | Stretchable electrode based on Au@Pt nanotube networks for real-time monitoring of ROS signaling in endothelial mechanotransduction[END_REF] Once the Pt nucleation started, a large number of Pt NNs spontane-ously formed onto the surface of SiC NWs (Figure S2). However, pursuing the reaction beyond this stage triggered an autocatalytic reduction of PtCl6 2-onto the Pt NNs surface, yielding too large Pt aggregates (Figure S3). [START_REF] Chen | Single-crystal nanowires of platinum can be synthesized by controlling the reaction rate of a polyol process[END_REF][START_REF] Lee | Growing Pt nanowires as a densely packed array on metal gauze[END_REF] Such large Pt aggregates presented a too low detection sensitivity and most of all exhibited a poor chemical resolution among the four primary ROS/RNS as occurred in our previous works. [START_REF] Zhang | Real-time intracellular measurements of ROS and RNS in living cells with single core-shell nanowire electrodes[END_REF][START_REF] Hall | Electrochemical oxidation of hydrogen peroxide at platinum electrodes. Part 1. an adsorption-controlled mechanism[END_REF] To avoid forming such large aggregates, the Pt NNs-modified SiC NWs were ultrasonically re-dispersed in the reaction solution to re-uniformize the Pt nucleation in order to ultimately coat the SiC nanowire surface with a high density of ultrasmall Pt NPs (ca. 3nm in diameter) forming a Pt layer about 50 nm thick (Figure 1A and Figure S4). High-resolution TEM indicated that the resulting Pt NPs had a mean diameter of ca. 3 nm and a lattice spacing of 0.225 nm corresponding to (111) planes (Figure 1B). [START_REF] Meng | Morphology controllable growth of pt nanoparticles/nanowires on carbon powders and its application as novel electro-catalyst for methanol oxidation[END_REF][START_REF] Meng | Factors influencing the growth of Pt nanowires via chemical selfassembly and their fuel cell performance[END_REF] SEM-EDX mapping and XPS confirmed the successful and reproducible fabrication of batches of SiC@Pt NWs (Figure S5 and Figure S6).

The ensuing nanoelectrochemical sensors were assembled by inserting individual SiC@Pt NWs into a pulled glass micropipette filled with liquid metal and wax while leaving a length of ca. 10 µm protruding out of the sealed micropipette (Figure 1C). [START_REF] Zhang | Real-time intracellular measurements of ROS and RNS in living cells with single core-shell nanowire electrodes[END_REF][START_REF] Wu | Large-scale synthesis of functionalized nanowires to construct nanoelectrodes for intracellular sensing[END_REF] To ensure that no extracellular signals could be detected after inserting sealed SiC@Pt NWEs inside cells, their whole surfaces were first entirely insulated with a thin SU8-2002 photoresist layer. Dipping the tip of these mounted SiC@Pt NWEs in acetone dissolved the photoresist and exposed a ca. 300 nm diameter Ptmodified electroactive tip with a length of ca. 2-3 µm (Figure 1C, Scheme 1B, Figure S7, and Figure S8). The consistency of the fabrication procedure was assessed by recording steady-state cyclic voltammograms (CVs) for the reduction of 1 mM Ru(NH3)6 3+ (i) after mounting them, (ii) after their complete insulation, and (iii) after exposing their tip (Figure 1D). The excellent stability of the insulation and of the electroactive Pt tip was confirmed by monitoring the resilience of CV Ru(III) reduction currents for hundreds of CV cycles (compare Figure 1E). The reproducibility of the sizes and electrocatalytic performance of the final SiC@Pt NWEs was excellent, even though the SiC@Pt NWs were fabricated in large batch batches. For example, compare the excellent reproducibility (standard deviation of 3.2%) of H2O2 oxidation CV currents obtained with eight SiC@Pt NWEs mounted with eight randomly selected SiC@Pt NWs in Figure S9.

Electrocatalytic Performance of SiC@Pt NWEs vs. the Four Primary ROS/RNS. The voltammetric oxidations of each of the four key ROS/RNS (ONOO -, H2O2, NO, NO2 -) were recorded independently at these SiC@Pt NWEs (Figure S10) to provide a reference set of normalized oxidation voltammograms at physiological pH 7.4 (Figure 1F) except for ONOO -whose calibration solutions needed to be prepared at pH 10.0 due to its life time of a few seconds at most except under alkaline conditions. [START_REF] Amatore | Characterization of the electrochemical oxidation of peroxynitrite: relevance to oxidative stress bursts measured at the single cell level[END_REF] As observed, the oxidation currents of ONOO -and H2O2, on the one hand, and of H2O2 and NO, on the other hand, overlapped slightly (<5% for normalized currents) while that of NO2 -was well separated from the others. Note that the electrocatalytic properties of Pt NPs formed on the SiC@Pt NWEs in this work differed from those of the Pt-black tips used in previous works by some of us. [11][12][13][START_REF] Amatore | Real-time amperometric analysis of reactive oxygen and nitrogen species released by single immunostimulated macrophages[END_REF][START_REF] Amatore | Characterization of the electrochemical oxidation of peroxynitrite: relevance to oxidative stress bursts measured at the single cell level[END_REF][START_REF] Amatore | Monitoring in real time with a microelectrode the release of reactive oxygen and nitrogen species by a single macrophage stimulated by its membrane mechanical depolarization[END_REF][START_REF] Li | Electrochemical Detection of nitric oxide and peroxynitrite anion in microchannels at highly sensitive platinum-black coated electrodes. application to Ros and Rns mixtures prior to biological investigations[END_REF] Accordingly, the oxidation potentials order determined for ONOO -and H2O2 resulted inverted but this was irrelevant to the performance and application of the current nanosensors. Optimal detection potentials (+100, 500, 600, 800 mV vs. Ag/AgCl) shown by the vertical dashed lines in Figure 1F should have been selected in order to differentiate each primary ROS/RNS while minimizing interference from other ROS/RNS. [11][12][13][START_REF] Amatore | Real-time amperometric analysis of reactive oxygen and nitrogen species released by single immunostimulated macrophages[END_REF][START_REF] Amatore | Characterization of the electrochemical oxidation of peroxynitrite: relevance to oxidative stress bursts measured at the single cell level[END_REF][START_REF] Amatore | Monitoring in real time with a microelectrode the release of reactive oxygen and nitrogen species by a single macrophage stimulated by its membrane mechanical depolarization[END_REF][START_REF] Li | Electrochemical Detection of nitric oxide and peroxynitrite anion in microchannels at highly sensitive platinum-black coated electrodes. application to Ros and Rns mixtures prior to biological investigations[END_REF] However, successfully applying the IVIEC method to phagolysosomes required that NWEs potential was set at 500 mV at least. [START_REF] Li | Quantitative measurement of transmitters in individual vesicles in the cytoplasm of single cells with nanotip electrodes[END_REF][START_REF] Lovric | On the mechanism of electrochemical vesicle cytometry: chromaffin cell vesicles and liposomes[END_REF][START_REF] Phan | Measuring synaptic vesicles using cellular electrochemistry and nanoscale molecular imaging[END_REF] Below this value, most of the phagolysosomes hitting the nanosensor tip did not release their content. Accordingly, all the oxidation of all four primary ROS/RNS species could be amperometrically recorded, but those of ONOO -and H2O2 could not be monitored individually since their oxidations occurred simultaneously at 500 mV (see below for their individual resolution).

Charges of amperometric spikes recorded during ROS/RNS releasing events (see later) reflect more adequately the fluxes of ROS/RNS released by application of Faraday law. [START_REF] Amatore | Monitoring in real time with a microelectrode the release of reactive oxygen and nitrogen species by a single macrophage stimulated by its membrane mechanical depolarization[END_REF][START_REF] Li | Electrochemical Detection of nitric oxide and peroxynitrite anion in microchannels at highly sensitive platinum-black coated electrodes. application to Ros and Rns mixtures prior to biological investigations[END_REF] Charges are additive for all species oxidizable at each of the above potentials, resulting in the following system of linear equations:

Q 800 mV =Q ONOO -+Q H 2 O 2 +Q NO +Q NO 2 - (1)
Q 600 mV =Q ONOO -+Q H 2 O 2 +Q NO (2) Q 500 mV =Q ONOO -+0.95Q H 2 O 2 ( 3
)
where Qspecies is the charge featuring the complete oxidation of the released species, while Qpotential is the total charge measured at one given potential. [START_REF] Amatore | Monitoring in real time with a microelectrode the release of reactive oxygen and nitrogen species by a single macrophage stimulated by its membrane mechanical depolarization[END_REF][START_REF] Li | Electrochemical Detection of nitric oxide and peroxynitrite anion in microchannels at highly sensitive platinum-black coated electrodes. application to Ros and Rns mixtures prior to biological investigations[END_REF] The charge values corresponding to the complete oxidation of each ROS/RNS released quantities could thus be simply deduced through solving the above linear system of equations.

IVIEC measurements are performed by fast amperometry, so we controlled that the recorded currents were not altered over the time scales considered by investigating the relationship between the voltammetric peak currents (ip) and scan rate (v) monitored for H2O2, NO and NO2 -at the present SiC@Pt NWEs. This showed that the oxidations of these species are diffusion-controlled (ip values being proportional to v 1/2 ), and similar CV shapes were recorded over the range of scan rates (Figure S11). These two results demonstrated that the selectivity represented by equations (1-3) remained valid whatever the time spans of the recorded spikes.

Quantitative Differentiation of ROS/RNS in Individual Phagolysosome. RAW 264.7 murine macrophages were pretreated during 24 h with interferon-γ (IFN-γ) and lipopolysaccharide (LPS) to mimic an in vivo inflammatory situation. [START_REF] Schroder | Interferongamma: an overview of signals, mechanisms and functions[END_REF][START_REF] Billiau | Interferon-gamma: a historical perspective[END_REF][START_REF] Bryant | The molecular basis of the host response to lipopolysaccharide[END_REF][START_REF] Orecchioni | Macrophage polarization: different gene signatures in M1(LPS+) vs. classically and M2(LPS-) vs. alternatively activated macrophages[END_REF] Bight-field microscopy images confirmed the successful transformation of macrophages from their resting type (M0) into their activated one (M1) as evidenced by significantly larger size and drastic shape changes (Figure 2Aa-b). [START_REF] Van Den Bossche | Macrophage immunometabolism: where are we (going)?[END_REF][START_REF] Murray | Macrophage polarization[END_REF] SiC@Pt NWEs could be easily moved across the membrane of M0 or M1 RAW 264.7 macrophages resting in PBS containing the inert Ru(NH3)6 3+ cation whose charge prevented its penetration inside the cell cytoplasm. The progressive disappearance of the Ru(III) reduction current (Figure 2Ac-d and Figure 2B) was then directly reporting on the gradual penetration of SiC@Pt NWEs through the cell membrane. When it was pulled out of the cell, the Ru(NH3)6 3+ reduction current was almost restored to its value initially measured outside the cell (ca. 90% in Figure 2B) demonstrating that the SiC@Pt NWE sensing tip was not significantly altered during its penetration and its performance inside macrophages. Importantly, NEWpenetrated M1 cells maintained their high viability during and after SiC@Pt NWEs insertion as checked by fluorescent staining with Calcein-AM and propidium iodide (PI) (Figure 2C). Importantly, no current spikes could be observed upon using NWEs fabricated by depositing a carbon layer and no Pt NPs to monitor M1 cell types (Figure S12). This excluded any possible interference from other electroactive substances. In M1 cell types, many ROS/RNS-loaded phagolysosomes hit sequentially the electroactive tip during each single insertion experiment so that an amperometric trace consisting in a sequence of spikes (Figure 3Aa-c) was generated at each of the three potentials identified above (+500, 600, 800 mV vs. Ag/AgCl) featuring a succession of successful IVIEC events during which all phagolysosomes hitting the nanosensor tip opened and released their content. [START_REF] Li | Quantitative measurement of transmitters in individual vesicles in the cytoplasm of single cells with nanotip electrodes[END_REF][START_REF] Lovric | On the mechanism of electrochemical vesicle cytometry: chromaffin cell vesicles and liposomes[END_REF][START_REF] Phan | Measuring synaptic vesicles using cellular electrochemistry and nanoscale molecular imaging[END_REF] In order to distinguish H2O2 and ONOO -, M1 type RAW 264.7 cells were preincubated with a specific scavenger of H2O2 (catalase-polyethylene glycol, CAT) [START_REF] Wen | Multicolor fluorescence based on fret regulated by functional peptides to screen high metastatic potential cancer cells[END_REF] or of ONOO -(5, 10, 15, 20-tetrakis (4-sulfonatophenyl) porphyrinato iron (III) chloride, FeTPPS) [START_REF] Zhang | 5,10,15,20-Tetrakis(4-sulfonatophenyl)porphyrinato iron(III) chloride (FeTPPS), a peroxynitrite decomposition catalyst, catalyzes protein tyrosine nitration in the presence of hydrogen peroxide and nitrite[END_REF][START_REF] Mander | Activation of microglial NADPH oxidase is synergistic with glial iNOS expression in inducing neuronal death: a dual-key mechanism of inflammatory neurodegeneration[END_REF][START_REF] Ali | Peroxynitrite mediates retinal neurodegeneration by inhibiting nerve growth factor survival signaling in experimental and human diabetes[END_REF] . The products (H2O, O2, NO2 -, NO3 -) of these two scavengers could not be detected at the potential +500 mV, thus could not cause interference in the measurements. No current spikes were observed at +500 mV when the cells were preincubated with both scavengers (CAT and FeTPPS), illustrating the effectiveness of each scavenger (Figure S13A). After the cells were treated with FeTPPS to scavenge ONOO -, the resulting spikes were too small to obtain reliable statistics since their maximum currents were less than only 1-2 pA while the current noise had generally a ca. 5 pA peak-to-peak amplitude (Figure S13B). On the contrary, when the cells were incubated with CAT to scavenge H2O2 (the inhibition effect was also confirmed by fluorescent staining by DCFH-DA, Figure S14), a series of amperometric spikes displaying substantial current were recorded at +500 mV (Figure 3Ad). Altogether, these inhibitors-based experiments demonstrated that H2O2, if any, was present at extremely low concentrations in the phagolysosomes, so that ONOO -could be detected alone at +500 mV. The two other ROS/RNS were detected at +600 mV (NO + ONOO -) and +800 mV (NO2 -+ NO + ONOO -) (Figure 1F), and their individual oxidation charges were deduced by application of the set of linear equations (1-3) (Figure 3Aa-b).

Statistical analyses revealed that charges Q, i.e., the i-t spikes areas, obeyed log-normal distributions (Figure 3B) with maxima and half-widths values exhibiting significant differences depending on the applied potential: log 10 Q 800 mV =-13.7±0.28 , log 10 Q 600 mV =-13.9±0.15 , log 10 Q 500 mV =-14.2±0. 20 , and log 10 Q 500 mV+CAT =-14.4±0.16 (Figure 3C). The average quantities of each primary ROS/RNS, nROS/RNS, in zeptomoles per phagolysosome could then be calculated according to equations (1-3) and Faraday's law, Q=nzF where F = 96 500C is the Faraday constant and z is the electron stoichiometry of the species electrochemical oxi-

dation ( z H 2 O 2 =z NO 2 -=2, z ONOO -=z NO =1 ). 11 n H 2 O 2 =10 zmol , n ONOO -=45 zmol, n NO 2 -=45
zmol, and n NO =80 zmol were thus obtained (Figure 3D).

Importantly, almost no spikes could be recorded (Figure S15) after adding specific inhibitors of NOX (apocynin) and iNOS (NG-monomethyl-L-arginine monoacetate salt or 1400W dihydrochloride) to the IFN-γ/LPS culture medium of RAW 264.7. This confirmed the crucial roles of iNOS and NOX membrane-bound phagolysosomes enzymes in the production of O2 •-and NO that acted as precursors of all released ROS/RNS. 11 Their initial quantities of these two parent species produced in an average phagolysosome could be evaluated according to the stoichiometries in Figure S16, 11 as summarized in Figure 3D: n O 2 •- parent =110 zmol and n NO parent =170 zmol.

The initial production of the parent superoxide ions is ca. only half of the parent NO in agreement with a previous report by some of us. 13 In addition, it is noted that the radical-radical coupling between NO and O2 •-occurs at the diffusion limit, i.e., kcoupling = (4-16) × 10 9 M -1 s -1 , while the disproportionation of O2 •-is slower even in the presence of SOD, i.e., kdisp = (1-2) × 10 9 M -1 s -1 , and is certainly much less rapid in the absence of SOD as expected inside phagolysosomes. 11,[START_REF] Szabó | Peroxynitrite: biochemistry, pathophysiology and development of therapeutics[END_REF][START_REF] Ferrer-Sueta | Biochemistry of peroxynitrite and protein tyrosine nitration[END_REF] Hence, most of the superoxide ions have to end up under the form of peroxynitrite and then of nitrite ion its follow up product (Figure 3D), leaving out about 50% of unreacted NO vs. its initial production. The presence of this important residual excess of NO in activated M1 cells was also confirmed by the high fluorescent intensity observed upon staining the cells with the NO probe DAF-FM DA (Figure S17), while staining with DCFH-DA (ROS probe) gave rise to a much lower fluorescent intensity (Figure S18).

Data Analysis of Spikes with Shoulders.

In a previous work by some of us in which all primary ROS/RNS were detected at +850 mV, 14 it was noticed that a majority 0f spikes displayed "shoulder" (see inset in Figure 4B), i.e., currents falloff tails that significantly deviated from the normal exponential expected behavior. This evidenced the existence of a fast ROS/RNS homeostasis, indicating that the activities of NOX and iNOS enzymes were either reactivated or boosted to swiftly produce fresh ROS/RNS within milliseconds in order to maintain a highly scavenging activity inside phagolysosomes even though their initial ROS/RNS load was removed by its oxidation at the nanoelectrode tip surface. In full agreement with this previous work, a large variety of spikes monitored in this work displayed similar "shoulders". Interestingly, the percentage of spikes displaying such a typical feature was lower at lower potentials: from 75% of the events at +800 mV, to only 65% at +600 mV and less than 10% at +500 mV (with or without pretreatment with CAT) (Figure 4A). Such a low percentage at +500 mV indicated that H2O2 and ONOO -did not significantly contribute (i.e., less than 10%) to this homeostatic issue. A similar conclusion is drawn about NO2 -since its maximum fraction is again around 10% at most (viz. equal to the difference between 75% and 65%). This implies that NO is the main species produced during these homeostatic events, thus suggesting that only iNOS are efficiently triggered during homeostatic processes at short times.

In order to further investigate this issue, the spikes exhibiting shoulders were analyzed based on a previously established kinetic model (see Equation (1) in reference ( 14)) that allows separating the contributions of diffusional release of (i) the initial quantity, Q0 (green area in the inset in Figure 4B) of ROS/RNS stored inside a phagolysosome before it undergoes an IVIEC event, [START_REF] Li | Quantitative measurement of transmitters in individual vesicles in the cytoplasm of single cells with nanotip electrodes[END_REF][START_REF] Lovric | On the mechanism of electrochemical vesicle cytometry: chromaffin cell vesicles and liposomes[END_REF][START_REF] Phan | Measuring synaptic vesicles using cellular electrochemistry and nanoscale molecular imaging[END_REF] from (ii) that, Qprod (orange area in the inset in Figure 4B), produced after the fast consumption of the initial content is drastically decreased during IVIEC events triggered a homeostatic production of fresh ROS/RNS. Briefly, the method amounts to deconvolute mathematically the current time variations, i0(t), featuring the release flux due to the stored material based on the behavior of the spike current, i(t), before the inflexion point located on its descending trend. [START_REF] Oleinick | Full Fusion' is not ineluctable during vesicular exocytosis of neurotransmitters by endocrine cells[END_REF] Extrapolating mathematically the current-time function i0(t) beyond this point and subtracting it from the total current provides the current iprod(t) featuring the release of the freshly produced ROS/RNS through quick homeostasis. 14 Q0 and Qprod are then readily obtained by independent time integrations of i0(t) and iprod(t) respectively.

Statistical analyses revealed that both Q0 (Figure 4C) and Qprod (Figure 4F) obeyed log-normal distributions. The statistical results of Q0 values measured at different potentials were significantly different: log 10 Q 0, 800 mV =-13.8±0.23, log 10 Q 0, 600 mV =-14.1±0.20 , log 10 Q 0, 500 mV =-14.3±0.12 , and log 10 Q 0, 500 mV+CAT =-14.5±0.16 (Figure 4D). This corresponds to the cocktail of ROS/RNS shown in Figure 4E, i.e., n H 2 O 2 0 =5 zmol , n ONOO - 0 =35 zmol , n NO 0 =40 zmol , and n NO 2 - 0 =45 zmol which stem from the initial synthesis of n O 2 •- parent,0 =90 zmol and n NO parent,0 =120 zmol. Note that these values are less than those derived from the global analysis of all spikes, i.e., including both the main spikes (Q0) and the shoulders (Qprod) when they exist. These results establish that H2O2 only accounts for 5% of the initial content of phagolysosomes before they undergo an IVIEC occurrence, in conformity with the function of phagolysosomes of eliminating pathogens, impaired cells and organic debris. [START_REF] Schroder | Interferongamma: an overview of signals, mechanisms and functions[END_REF] This is in full agreement with the fact that the protonated form ONOOH (pKa = 6.8) of peroxynitrite acts as an extremely efficient molecular scissor by spontaneously generating OH radicals in lipidic environments, [START_REF] Denicola | Nitric oxide diffusion in membranes determined by fluorescence quenching[END_REF][START_REF] Denicola | Diffusion of peroxynitrite across erythrocyte membranes[END_REF][START_REF] Möller | Chapter 2 the interaction of reactive oxygen and nitrogen species with membranes[END_REF][START_REF] Giacovazzi | Copper-amyloid-β complex may catalyze peroxynitrite production in brain: evidence from molecular modeling[END_REF] while H2O2 requires the presence of free transition metal ions to do the same. Contrastingly, Qprod values recorded at +800 mV ( log 10 Q prod, 800 mV =-14.2±0.23 ) and +600 mV ( log 10 Q prod, 600 mV =-14.2±0.13 ) presented no significant difference confirming that the homeostatic events giving rise to the spikes' shoulders generated mostly NO as already remarked above. Accordingly, released quantities monitored at +500 mV (log 10 Q prod, 500 mV =-14.9±0.12) or +500 mV after pretreatment with CAT (log 10 Q prod, 500 mV+CAT =-15.0±0.17) were identical and comparatively smaller, evidencing a small production of peroxynitrite ions and almost none of hydrogen peroxide during the homeostatic response at short times (Figure 4G). The average values of the corresponding quantities of ROS/RNS (Figure 4H) were indeed: n H 2 O 2 prod =1 zmol , n ONOO - prod =10 zmol , n NO prod =45 zmol , and n NO 2 - prod =1 zmol . These quantities allowed to evaluate those of the O2 •-and NO precursors generated to produce the homeostatic response: n O 2 •- parent,prod =15 zmol and n NO parent,prod =60 zmol . This confirmed that iNOS are responsible of ca. 80% of the homeostatic response, essentially yielding NO, while NOX that usually form O2 •-corresponded to ca. only one fifth of it. These figures compare drastically with the almost equivalent productions of O2 •-and NO that were responsible for the amount of ROS/RNS stored in phagolysosomes of activated M1 RAW 264.7 macrophages.

Figure 5A-C summarizes these findings and compares the average proportions of each of the four primary ROS/RNS (H2O2, ONOO -, NO and NO2 -) as well as those of their corresponding precursors, O2 -and NO, that were detected globally (Figure 5A), i.e., without distinguishing between those that were initially stored inside the phagolysosomes (Figure 5B), or produced during the homeostatic response to an IVIEC episode (Figure 5C). Interestingly, in contradiction with the general belief that digestion of unwanted biological material in phagolysosomes of activated macrophages was mostly ensured by Fenton reactions involving a specific production of H2O2, it is observed that hydrogen peroxide is the ROS/RNS with the lowest proportion, either in stored contents (<5%) or in those produced during homeostatic episodes (<1%). Considering that NO2 -is a decay end-product of peroxynitrite ions, it is also observed that the global production of ONOO -, [START_REF] Szabó | Peroxynitrite: biochemistry, pathophysiology and development of therapeutics[END_REF][START_REF] Ferrer-Sueta | Biochemistry of peroxynitrite and protein tyrosine nitration[END_REF] as represented by the sum of ONOO -and NO2 -quantities, is the essential species stored within phagolysosomes (ca. 60%, Figure 5B). This proportion drops in the homoeostatic response (ca. 20%, Figure 5C) mostly because NO is then the major parent precursor (ca. 80%) vs. O2 •-(ca. 20%) (Figure 5C). This may be due to the short time duration elapsed between the production and the detection of NO (milliseconds at most), so in contrast with the longer time durations experienced during the storage phases, it may not have time to diffuse away. Indeed, NO may easily diffuse across bilipidic membranes such as those of phagolysosomes. [START_REF] Denicola | Nitric oxide diffusion in membranes determined by fluorescence quenching[END_REF][START_REF] Möller | Chapter 2 the interaction of reactive oxygen and nitrogen species with membranes[END_REF] Note that the importance of the time duration in our experiments is also evidenced by the extremely small ratio of NO2 -vs. ONOO -in the released homeostatic pulses (ca. 15% at most of initial ONOO -could decay into NO2 -, Figure 5C) compared to the larger ratio for stored material (ca. 50% of initial ONOO - had decayed into NO2 -, Figure 5B). Such interpretation is perfectly coherent with the sequential cartoons shown in Figure 5D.

NOX and iNOS Enzymes Activities during Storage vs.

Homeostatic Responses. The above results evidenced that the relative proportions of each primary ROS/RNS significantly differed depending on whether their stored contents (i.e., oxidized in the main IVIEC current spike component) or their homeostatic responses (i.e., the spike shoulders) were considered. To our knowledge, this is a previously unsuspected information of considerable importance for understanding the behavior of the most fundamental players in our immune system. Indeed, up to know it was implicitly thought that the two stages involved in the same way of phagolysosomes' NOX and iNOS pools. At present, we cannot offer a definitive answer as to why this is happening, but do offer a hypothetical rationalization for this startling finding nonetheless.

It must first be remembered that the activity of NOX enzymes in phagocytes is necessarily transient because the assembled NOX can retain their active structure for at most a few minutes before disassembling. [START_REF] Decoursey | Regulation and termination of nadph oxidase activity[END_REF][START_REF] Winterbourn | Reactive oxygen species and neutrophil function[END_REF] Therefore, the actual production of O2 •-is time-dependent, being finely controlled by the dynamic balance between the assembly and disassembly processes of transmembrane NOX. Conversely, iNOS enzymes can generate large amounts of NO by acting over prolonged periods (several hours to several days) after being assembled in response to pathogenic stimulation. [START_REF] Winterbourn | Reactive oxygen species and neutrophil function[END_REF] Yet, importantly, NO in turn regulates the activity of NOX enzymes through concentration changes to minimize collateral damage from ROS species. [START_REF] Winterbourn | Reactive oxygen species and neutrophil function[END_REF] Based on these two known facts, a new perspective can be offered on the process of rapid ROS/RNS production in relation to short-term homeostatic responses (Figure 5D).

Once the ROS/RNS are significantly consumed by reacting with biological materials captured inside a phagolysosome (a situation mimicked in our work by the oxidation of ROS/RNS on the surface of the SiC@Pt during IVIEC events), the still reactive iNOS enzymes may perform to renew intravesicular NO content. In contrast, partially assembled NOX enzymes may produce only small amounts of O2 •-which immediately reacts in less than a millisecond with local excess NO to form ONOO -and not produce any amounts of H2O2. This transient behavior corresponds to the "shoulder currents" monitored by SiC@Pt NWEs through oxidation of the limited cocktail described in Fig- ure 5C. On the other hand, when phagolysosomes have matured over long periods, continuous production of O2 •- by NO-regulated NOX activity may result in higher yields of H2O2 and ONOO -. Simultaneously, the intra-phagolysosome concentration of NO can also decrease significantly due to its easy diffusion across the membrane of the phagolysosome, 10,[START_REF] Möller | Chapter 2 the interaction of reactive oxygen and nitrogen species with membranes[END_REF] while over long storage times, ONOO -can significantly decompose to NO2 -, its stable end product (Figure 5B). [START_REF] Szabó | Peroxynitrite: biochemistry, pathophysiology and development of therapeutics[END_REF][START_REF] Ferrer-Sueta | Biochemistry of peroxynitrite and protein tyrosine nitration[END_REF] The steady state amounts of ROS/RNS resulting from these dynamics inside phagolysosomes (compare the kinetics in Figure 5D, right-hand side cartoon) give rise to the normal IVIEC component of current spikes.

CONCLUSIONS

A new and robust electrode fabricated by coating SiC nanowires with Pt nanoparticles has been specially designed to present high electrocatalytic activity and selectivity to study the sub-millisecond dynamics of the four primary reactive oxygen and nitrogen species (i.e., ONOO -, H2O2, NO, and NO2 -) produced within activated living macrophages. The fluxes of these reactive species could then be individually monitored during rapid homeostatic processes occurring in single activated phagolysosomes of murine RAW 264.7 macrophages.

The corresponding results established unambiguously that phagolysosomes mainly produce ONOO -, NO and NO2 - in approximately equal yields during continuous inflammatory situations. In comparison, only small amounts of H2O2 are produced contrary to general medical and biological beliefs. However, when a phagolysosome has to compensate for a sudden decrease in its internal ROS/RNS content, a complex homeostatic mechanism is triggered in an attempt to compensate for the ROS/RNS losses. Intense ROS/RNS bursts are then generated over a sub-millisecond time range, but with a radically different composition, mainly involving ONOO -and large excesses of NO.

These contrasting results revealed for the first time a drastic change in the relative activities of NOX (which mainly generate superoxide ions) and iNOS (which mainly generate nitric oxide) enzymatic pools when a phagolysosome switches from a continuous inflammatory state to a homeostatic one. Although unexpected, this drastic change in the relative activities of the enzymes appears to be the optimal solution for suddenly increasing pathogen clearance rates without overproducing destructive ROS/RNS that would endanger the phagolysosome and the macrophage itself.

Future developments of the electrochemical strategy presented in this work will undoubtedly provide a deep quantitative understanding of the complex mechanisms that allow phagocytosis. Due to the crucial importance of macrophages as a versatile first line of defense against diseases, bacteria, viruses, mutated cells, etc., we believe that the search for such detailed quantitative knowledge is fully justified.

ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge at http://pubs.acs.org.

Experimental details and supplement data including characterization analysis, electrochemical measurements and cell experiments (PDF) corresponding also to 1O2 •-and 1NO per NO2 -). 14,15 The residual NO excess is detected directly by diffusion to the nanoelectrode tip.

Figure 1 .

 1 Figure1. A) SEM images of SiC@Pt NWs; inset: enlarged SEM image showing details of the SiC@Pt NWs. B) TEM image of the edge of a SiC@Pt NW; inset: HRTEM of Pt NPs located in the red rectangle in main view. C) SEM of a SiC@Pt NWE; inset: a magnified SEM image of its exposed part (ca. 160 nm radius) at the tip of the insulated section. D) CVs of 1 mM Ru(NH3)6 3+ /1 M KCl at an untreated, insulated and tip-exposed SiC@Pt NWE confirming the decrease of the Ru(III) reduction current by 98% and 60%, respectively (n = 5) as expected based on its SEM geometry in C. E) Repetitive CVs (100 cycles) of 1 mM Ru(NH3)6 3+ /1 M KCl of an exposed SiC@Pt NWE. F) Voltammetric oxidation of ONOO -(blue curve, 1 mM, pH=10.0), H2O2 (orange curve, 1 mM, pH=7.4), NO (green curve, 1 mM, pH=7.4) and NO2 -(purple curve, 1 mM, pH=7.4) in PBS solution; currents were normalized to their maximum value to help comparison. Vertical dashed lines indicate the optimal detection potentials for each ROS/RNS species (see text).

Figure 2 .

 2 Figure 2. A) Bright-field images of (a) M0 and (b) M1 (stimulated with IFN-γ/LPS for 24 h) RAW 264.7; view of a SiC@Pt NWE (c) before and (d) after complete insertion into a M1 type macrophage. B) CVs recorded at different penetration depths of one SiC@Pt NWE within a M1 type RAW 264.7 placed in a 1 mM Ru(NH3)6 3+ PBS bath: (ⅰ) before insertion, (ii) after ca. 50% insertion of the electroactive tip, (iii) after its complete insertion, and (iv) after its withdrawal out of the cell. C) Bright-field (BF) and fluorescent microscopy images of M1 type RAW 264.7 cells inserted by SiC@Pt NWEs (indicated by arrows) after staining with Calcein-AM and propidium iodide (PI) as indicated (the "merge" view is composed by the merging of bright-field, Calcein-AM and PI fluorescent images).

Figure 3 .

 3 Figure 3. A) Representative amperometric traces recorded after insertion of SiC@Pt NWEs into IFN-γ/LPS stimulated RAW 264.7 macrophages at (a) +800 mV, (b) +600 mV, (c) +500 mV and (d) +500 mV+CAT (see text). Typical events marked with an asterisk in each trace are shown at large resolution (the red asterisks indicated spikes with shoulders, while black ones indicated normal IVIEC spikes). B) Normalized log-normal histograms (log10Q) describing the frequency distributions of the charge values detected at different potentials (purple, +800 mV, n=416 events from 20 cells; green, +600 mV, n=425 events from 17 cells; orange, +500 mV, n=403 events from 15 cells; blue, +500 mV+CAT, n=418 events from 20 cells). C) Statistical analyses of the log10Q at different potentials (means ± SEM; one-way ANOVA, **p ≤ 0.01,*p ≤ 0.05). D) Scheme of the chemical relationships between four primary ROS/RNS and their precursors O2 •-and NO. The average amounts of substance (n) of each species are indicated in parentheses.

Figure 4 .

 4 Figure 4. A) Proportions of normal peaks and peaks with distinctive shoulders recorded as a function of the detection potentials.B) Principle of quantitative monitoring of initial and freshly produced ROS/RNS released by individual phagolysosomes with a single SiC@Pt NWE during one IVIEC event. C,F) Normalized histograms describing the frequency of log-normal distributions of the initial charges Q0 (C) and freshly produced charges Qprod (F) of detected ROS/RNS at different potentials (purple, +800 mV, n=316 events from 20 cells; green, +600 mV, n=279 events from 17 cells; orange, +500 mV, n=43 events from 7 cells; blue, +500 mV+CAT, n=35 events from 10 cells). D,G) Statistical analyses of the logarithm of initial charges Q0 (D) and freshly produced charges Qprod (G) of ROS/RNS detected at different potentials (means ± SEM; one-way ANOVA, ***p ≤ 0.001, **p ≤ 0.01, *p ≤ 0.05, n.s.: not significant). E,H) Recapitulative schemes of the chemical relationships between the four primary detected ROS/RNS and their precursors O2 •-and NO observed in M1 RAW 264.7 macrophages based on the initial phagolysosome contents (E) or on the freshly produced ones (H); the quantities, n, of each species are shown in parentheses.

Figure 5 .

 5 Figure 5. Relative proportions of the four primary ROS/RNS (H2O2, ONOO -, NO and NO2 -) and of their two precursors (O2 •-and NO) within (A) global content (stored + homeostatic), (B) stored quantities (normal "IVIEC components" of current spikes), and (C) freshly produced during the homeostatic phase ("shoulder components"). D) Graphical summary of possible mechanisms coherent with the detected ROS/RNS quantities (relative diameters of color patches associated to the four primary ROS/RNS represent their relative detected quantities; thicknesses of arrows represent the relative kinetic magnitudes of the reactions occurring within phagolysosomes).

Figure S7 .

 S7 Figure S7. Schematic principle of insulating a mounted SiC@Pt NWE (step 1) and exposing its tip (step 2).

Figure S8 .

 S8 Figure S8. SEM images of a mounted SiC@Pt NWE (A) before its insulation and (B) after partial insulation of the exposed part with SU8-2002.

Figure S9 .

 S9 Figure S9. H2O2 anodic CVs recorded at 8 different SiC@Pt NWEs (H2O2, 1 mM in PBS). Baselines recorded in the absence of H2O2 are shown in black.

Figure S10 .

 S10 Figure S10. Anodic CVs of (A) ONOO -(pH=10.0, 1 mM), 12,13 (B) H2O2 (pH=7.4, 1 mM), (C) NO (pH=7.4, 1 mM)) and (D) NO2 -(pH=7.4, 1 mM) in PBS, scan rate 0.1 V/s.

Figure S11 .

 S11 Figure S11. Voltammetric oxidation of (A) H2O2, (C) NO and (E) NO2 -at different scan rate (V/s). Linear correlation of log peak current (lg ip) vs. log scan rate (lg v) of (B) H2O2, (D) NO and (F) NO2 -.

Figure S12 .

 S12 Figure S12. Representative amperometric trace recorded at carbon layer modified SiC nanowire electrode (SiC@C NWE) at +850 mV inside IFN-γ/LPS stimulated RAW 264.7 macrophages.

Figure S13 .

 S13 Figure S13. Representative amperometric traces recorded at +500 mV inside IFN-γ/LPS stimulated RAW 264.7 macrophages pre-incubated with (A) FeTPPS+CAT or (B) FeTPPS during for 30 min.

Figure S14 .

 S14 Figure S14. Bright-field and fluorescent images of IFN-γ/LPS stimulated RAW 264.7 macrophages with (right) and without (left) incubation with 1000 U/mL CAT for 30 min before staining with DCFH-DA.

Figure S15 .

 S15 Figure S15. Representative amperometric traces recorded at +800 mV inside IFN-γ/LPS stimulated RAW 264.7 macrophages pre-incubated with (A) L-NMMA+apocynin or (B) 1400W+apocynin.

Figure S16 .

 S16 Figure S16. Follow-up reactions of O2 •-and NO yielding the four primary ROS/RNS. More precisely, O2 •-and NO, the precursors of all ROS/RNS, are generated by NOX and iNOS, respectively. O2 •- disproportionates into H2O2 (stoichiometry: 2O2 •-per H2O2) either spontaneously or through catalysis by superoxide dismutase; O2 •-also combines efficiently with NO to form ONOO -(stoichiometry: 1O2 •- and 1NO per ONOO -) which is a transient species that rapidly evolves into its end-product NO2 -(viz.

Figure S17 .

 S17 Figure S17. Bright-field and fluorescent images of M0 (left) or M1 (right) RAW 264.7 macrophages after staining with DAF-FM DA.

Figure S18 .

 S18 Figure S18. Bright-field and fluorescent images of M0 (left) or M1 (right) RAW 264.7 macrophages after staining with DCFH-DA.

ACKNOWLEDGMENT

We gratefully acknowledge financial support from the National Natural Science Foundation of China (Grants 21725504, 22090050, 22090051, and 21721005), the University of Xiamen and the State Key Laboratory of Physical Chemistry of Solid Surfaces (PCOSS, University of Xiamen, China) through a Distinguished Scientist Chair awarded to C.A. In France, it was supported in part by PSL University, École Normale Supérieure, CNRS, and Sorbonne University (UMR 8640). Both teams gratefully acknowledge the CNRS Sino-French support (LIA "Nano-BioCatEchem").

AUTHOR INFORMATION Corresponding Author

Wei-Hua Huang-College of Chemistry and Molecular Sciences, Wuhan University, Wuhan 430072, P. R. China; E-mail: whhuang@whu.edu.cn Christian Amatore-State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China, and PASTEUR, Départment de Chimie, École Normale Supérieure, PSL Research University, Sorbonne University, UPMC Univ. Paris 06, CNRS 24 rue Lhomond, Paris 75005, France; E-mail: christian.amatore@ens.psl.eu

Authors Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interest.

Supporting Information

Homeostasis Inside Single Activated Phagolysosomes: Quantitative and Selective Measurements of sub-Millisecond Dynamics of ROS/RNS Production with a Nanoelectrochemical Sensor

Yu-Ting Qi, † Hong Jiang, † Wen-Tao Wu, † Fu-Li Zhang, † Si-Yu Tian, † Wen-Ting Fan, † Yan-Ling Liu, † Christian Amatore,* , ‡, § and Wei-Hua Huang* Scanning electron microscopy (SEM) images were obtained with field-emission scanning electron microscopes (Zeiss Sigma and Zeiss Merlin Compact). Energy-dispersive X-ray spectroscopy (EDX) images were obtained with an EDX spectrometer (X-MaxN). Transmission electron microscopy (TEM) images were taken with a transmission electron microscope (JEM-2100). X-ray photoelectron spectroscopy (XPS) measurements were implemented on a photoelectron spectrometer (ESCALAB250Xi, Thermo Fisher Scientific). The C 1s peak (284.6 eV) was chosen as a reference to calibrate binding energies and Al Kα X-ray radiation was used as the X-ray source. Bright-field and fluorescent images were taken by an inverted fluorescent microscope (AxioObserver Z1 and Axiovert 200M, Zeiss). A microforge (World Precision Instruments, ×40 objective) was used to fabricate NWEs. Electrochemical measurements were conducted with a CHI 660e electrochemical workstation (CHI Instruments) in a two-electrode configuration with a homemade Ag/AgCl electrode of large size to perform simultaneously as a reference and a counter electrode. Amperometric recordings were achieved with a patch clamp amplifier (EPC-10, HEKA Electronics) coupled with a micromanipulator (TransferMan 4r, Eppendorf).

Modification of SiC NWs with APTES

SiC NWs (1 mg) were dispersed into ethanol (25 mL) via ultrasonication, before adding APTES (1 mL) in the suspension. Next, the mixture was ultrasonically treated, magnetically stirred, and maintained at 85 °C for 24 h. The resulting suspension was then washed 3 times with ethanol and ultrapure water respectively.

Synthesis of SiC@Pt NWs

We followed previously described guidelines reported in the literature, [START_REF] Vieira | Phagosome maturation: aging gracefully[END_REF][2][3][4][5] after slightly modifying some steps as indicated below:

During the Pt-seeding reaction, SiC@APTES NWs were firstly dispersed into ultrapure water (15 mL) via ultrasonication, followed by 0.5 mM H2PtCl6•6H2O and 0.3 M HCOOH addition into it. Next, the mixture was ultrasonically treated and kept steadily at 50 °C for 4 h until the solution turned black.

Due to gravity, nanowires agglomerated at the bottom of reaction vessels. Finally, nanowires were collected and redispersed into ultrapure water again via ultrasonication.

During the second step, 0.5 mM H2PtCl6•6H2O and 0.3 M HCOOH were added into the 15 mL dispersion of the freshly modified nanowires in ultrapure water, and the reaction temperature was adjusted to 25°C until the solution turned black completely (ca. for 2 h). SiC@Pt NWs were then collected at the bottom of the reaction vessel and washed 3 times with ultrapure water.

Fabrication of SiC@Pt NWEs

Mechanical procedures of NWEs fabrication were the same as in our previous works. 6,7 Prepared SiC@Pt NWs dispersed in 20 mL ultrapure water were added dropwise to the center of a glass sheet and gently heated to evaporate water. Then the glass sheet was cut into two parts to allow for a partial protrusion of NWs over glass slide edges. Next, using microforges manipulators, SiC@Pt NW was carefully inserted into a prepared glass micropipette holder filled with liquid metal and wax to fabricate a SiC@Pt NWE with the protruding length of SiC@Pt NW about 10 μm.

Subsequently, the SiC@Pt NWE was inserted into a glass capillary equipped with SU8-2002 for several seconds and quickly pulled out (Figure S7 step 1). This ensured that the protruding shaft of the SiC@Pt NWE was evenly coated with an insulating layer of SU8-2002.

Finally, a length of 2-3 μm at the tip of the insulated SiC@Pt NWE nanoelectrode was carefully inserted into a glass capillary filled with acetone for about 10 seconds to allow for a total SU8-2002 dissolution (Figure S7 step 2). The partially insulated nanoelectrodes were then stored at room temperature overnight to allow SU8-2002 to dry out completely.

Cell Experiment

Cells culture

RAW 264.7 cells were cultured in DMEM medium supplemented with 10% fetal bovine serum, 1% horse serum, and 1% penicillin-streptomyci at 37 °C under 5% CO2 atmosphere. Before performing any experiment, the RAW 264.7 cells were seeded on small cell culture dishes (diameter 35 mm) in which 1 µg/mL LPS and 100 units/mL IFN-γ were simultaneously added. After incubation for 24 hours under cell culture conditions, the majority of M0 type macrophages were activated and transformed in M1 type.

Incubations of RAW 264.7 cells with ROS/RNS scavenger or enzyme inhibitor

IFN-γ/LPS stimulated RAW 264.7 were treated with 1000 U/mL CAT or 10 μM/L FeTPPS for 30 min before electrochemical detections. 500 µM/L apocynin, 1 mM/L L-NMMA or 10 µM/L 1400W were added with IFN-γ/LPS together to the cell medium for 24 h. Then the electrochemical detection was performed as soon as possible.

Fluorescence imaging of ROS

Amperometric Data Acquisition and Analysis

All cell-free electrochemical experiments were performed using CHI 660e inside a well-grounded Faraday cage. Besides, all amperometric measurement involving living cells were performed inside a well-grounded Faraday cage under an inverted microscope control equipped with a 40× objective lens.

Single SiC@Pt NWEs were inserted across cell membranes with a micromanipulator (TransferMan 4r, Eppendorf) under the microscope. The amperometric traces were recorded with a 2-electrode electrochemical system using a patch-clamp amplifier (EPC-10, HEKA Electronics, Germany) at different potentials vs. the Ag/AgCl electrode. Amperometric traces were sampled at 50 kHz and Bessel-filtered at 2.9 kHz. The peak-to-peak noise value of platinized SiC@Pt NWEs before and after insertion was less than 5 pA (compare Figures S11 andS13).

Raw amperometric data were gathered with the "Pulse" software and analyzed by the "Igor Pro" software (Igor Pro, Wave Metrics) kindly provided by Dr. E. V. Mosharov from Columbia University.

The initial (Q0) and produced (Qprod) ROS/RNS contents of each recorded amperometric spike were obtained after separating mathematically the shoulder components from the normal IVIEC components using a homemade program implemented in Mathlab as previously described. 8,9 Supporting Figures