Michel Lemaître
email: michel.lemaitre@onera.fr

Gérard Verfaillie
email: gerard.verfaillie@onera.fr

Hélène Fargier
email: fargier@irit.fr

Jérôme Lang
email: lang@irit.fr

Nicolas Bataille
email: nicolas.bataille@cnes.fr

Jean-Michel Lachiver
email: jean-michel.lachiver@cnes.fr

Sharing the use of Earth observation satellites

Because they are more and more costly, space projects are more and more frequently funded by several entities, which share the use of the space system. This sharing must, on the one hand, satisfy as best as possible each entity and, on the other hand, meet as best as possible predefined sharing rules. In this paper we report studies which have been carried out in the specific context of shared Earth observation satellites. We describe informally the sharing requirements and the sharing principles we adopt. Then, we describe a sharing protocol, based on these principles and on three levels of utility.

Background about agile optical Earth observation satellites

Earth observation satellites are placed on low altitude, circular, quasi polar, heliosynchronous, and phased orbits. They are equipped with optical, radar, or infra-red observation instruments. Degrees of freedom for image acquisition can be provided in various ways. In the special case we consider (that of agile optical Earth observation satellites), they are provided by the satellite attitude control system which is able to move the whole satellite along the roll, pitch, and yaw axes. That allows the instrument to acquire any strip of a fixed width, but of any direction and any length, at the Earth surface on each side of the track of the satellite on this surface (within some limits; see Figure 1). Acquired images are either immediately downloaded, or recorded on board and downloaded when the satellite is within the visibility window of a ground station. Image acquisitions are thus time, energy, and memory consuming. Transitions between image acquisitions are time and energy consuming too. Observation requests may be submitted at any time by users to a mission control center. With each request are associated five main parameters: (i) a geographical area, which can be either a target (a small circular area, which can be acquired in one pass) or a polygon (a large polygonal area, which must be split into parallel strips and acquired in several passes, possibly from several satellite revolutions), (ii) a validity period, outside of which its acquisition has no utility, (iii) a set of acquisition angular constraints (minimum and maximum roll and pitch acquisition angles), (iv) a type, which can be either mono or stereo, and (v) either a weight or a priority, which expresses its importance from the user's point of view.

Mission management reasons on a specified horizon, which may be either one day or a satellite revolution around the Earth (in fact only the illuminated half-revolution from which image acquisition is possible with an optical instrument). From the set of strips that can be acquired on that horizon, it selects a subset the associated gain of which is as highest as possible and then orders them along time. In other words, it builds a sequence of strip acquisitions which is feasible and of as highest as possible utility (see Figure 2 a target a polygon Figure 2: Example of a sequence of strip acquisitions.

for an example of a sequence of strip acquisitions).

Although many mission management modes are possible (see for example [START_REF] Verfaillie | Designing and Evaluating an On-line On-board Autonomous Earth Observation Satellite Scheduling System[END_REF]), this selection and scheduling task is usually performed off-line before execution (either the day i for the day i + 1, or during the non-illuminated half-revolution for the following illuminated half-revolution). It is also performed on the ground in a mission control center, and semi-automatically under the supervision of human operators.

For more details, see either [START_REF] Verfaillie | Selecting and Scheduling Observations for Agile Satellites: Some Lessons from the Constraint Reasoning Community Point of View[END_REF]) or [START_REF] Lemaître | Selecting and Scheduling Observations of Agile Satellites[END_REF].

Sharing requirements

In the previous section, we made the assumption that there was only one user of the satellite, in fact only one entity (the mission control center) which is assumed to act fairly on behalf of a set of end users. Such an assumption is at the basis of many studies which have been performed about the selection and scheduling of Earth observation activities (see [START_REF] Bensana | Exact and Approximate Methods for the Daily Management of an Earth Observation Satellite[END_REF], [START_REF] Bensana | Earth Observation Satellite Management[END_REF], [START_REF] Gabrel | A New Single Model and Derived Algorithms for the Satellite Shot Planning Problem Using Graph Theory Concepts[END_REF], [START_REF] Vasquez | A Logic-constrained Knapsack Formulation and a Tabu Algorithm for the Daily Photograph Scheduling of an Earth Observation Satellite[END_REF], [START_REF] Vasquez | Upper Bounds for the SPOT5 Daily Photograph Scheduling Problem[END_REF], [START_REF] Bornschlegl | On-Board Software and Operation for Proba Small Satellite Autonomy[END_REF], [START_REF] Pemberton | Towards scheduling over-constrained remote-sensing satellites[END_REF], [START_REF] Frank | Planning and Scheduling for Fleets of Earth Observing Satellites[END_REF], [START_REF] Dungan | Advances in Planning and Scheduling of Remote Sensing Instruments for Fleets of Earth Orbiting Satellites[END_REF], [START_REF] Hall | Maximizing the Value of a Space Mission[END_REF], and [START_REF] Wolfe | Three Scheduling Algorithms applied to the Earth Observing Systems Domain[END_REF]).

But more and more space projects are funded by several entities, from the same country or from several countries, for example by several space agencies or by civil and military organizations. When funding the space system, these entities want to have the guarantee that they will be able to use it proportionally to their financial investment.

The problem is no more to maximize only the utility of one entity. It is to maximize the utility of each entity involved in the project and to meet as best as possible sharing rules on which all the entities came to an agreement before using the system.

In the problem we consider (the sharing of an agile optical Earth observation satellite between several entities), the mission management is decomposed into three phases which are activated in sequence: management of the high priority requests, management of the medium priority requests, and management of the remaining ones.

In the first phase we only consider in this paper, the request emitted by an entity is assumed to be a list of unit requests1 (i.e. the associated geographical area of which is a square of a specified dimension) which is ordered according to a decreasing priority. This order is interpreted as follows: the associated entity prefers the satisfaction of a unit request of a given priority to the satisfaction of any number of requests of lower priority. For example, if the ordered list of an entity is (r 1 , r 2 , r 3 ), this entity prefers that request r 1 be satisfied rather than requests r 2 and r 3 together. Moreover, the number of satisfied unit requests is for each entity limited to a specified number, which depends on its investment in the project and which we refer to as its rights.

Sharing principles

In this section and in the following, we call selection a subset of the candidate unit requests, which can be scheduled taking into account satellite acquisition constraints.

Arbitration versus negotiation

Sharing procedures (or protocols) can be divided into two main classes:

• the decentralized game or negotiation procedures, where all the entities together agree with game or negotiation rules, and then act for their own interest by respecting the common rules (see for example [START_REF] Rosenschein | Rules of Encounter : Designing Conventions for Automated Negotiation among Computers[END_REF][START_REF] Brams | Fair Division: from cakecutting to dispute resolution[END_REF]);

• the centralized arbitration procedures, where one central entity, which is assumed to be fair and to act according to principles that have been accepted by all the entities, decides about the sharing (see [START_REF] Moulin | Axioms of Cooperative Decision Making[END_REF][START_REF] Young | Equity in Theory and Practice[END_REF])).

We chose to explore centralized arbitration procedures for four reasons: (i) the entities may want to maintain confidentiality about their own requests and we guess this confidentiality can be guaranteed by a centralized arbitration procedure (the arbitration agent says nothing to an entity about the requests of the others) better than by a decentralized negotiation procedure, which imposes to exchange information; (ii) the number of unit requests which must be dealt with may be high (dozens and possibly hundreds of requests) and a negotiation seems to be in that case very difficult to manage; (iii) the time which is available for the mission management task may be very short and we guess that a decentralized negotiation procedure would be too time consuming; and (iv) if the optimization criteria can be clearly defined and if the associated optimization algorithms are efficient enough, a centralized arbitration procedure is at least as efficient as and often more efficient than a decentralized negotiation procedure.

Three utility levels

A centralized arbitration procedure shall reason about three levels of utility: • the utility of a selection for an entity and a priority level;

min(u1,u2) = k' u1+u2=k u2(x) u1(x)
this utility depends basically on the selection or not of the request this entity has submitted at this priority level;

• the utility of a selection for an entity; this utility results from an aggregation (to be defined) of the utilities of this selection for this entity and all priority levels, i.e basically on the selection or not of the requests this entity has submitted;

• finally, the social utility of a selection; this utility results from an aggregation (to be defined) of the utilities of this selection for all the entities.

Efficiency versus equity

The problems we have to deal with are in fact usual multicriteria optimization problems: How to build and how to compare aggregated utilities? How to compare the utilities of a selection for two entities? How to compare the social utilities of two selections?

The first principle with which everyone agrees in multicriteria decision making is that of efficiency (or Pareto optimality; see for example [START_REF] Keeney | Decisions with Multiple Objectives: Preferences and Value Tradeoffs[END_REF][START_REF] Ehrgott | Multicriteria Optimization[END_REF]): (i) a solution s dominates another solution s if and only if s is strictly better than s according to at least one of its components and not worse than s according to the other components (in Figure 3, solution e is dominated by solution d, which is itself dominated by solution c); (ii) a solution is said efficient (or Pareto optimal) if and only if it is dominated by no other solution (in Figure 3, solutions a, b, c, f , g, and h are all efficient).

We are obviously looking for efficient solutions. The problem is that not all the efficient solutions are fair. Some of them can even be very unfair (see for example Figure 3 where solutions a and h are efficient, but very unfair).

Utilitarism versus Egalitarism

Methods for aggregating individual comparable utilities can be divided into two main families: (i) the utilitarist ones where the aggregation operator is the sum and (ii) the egalitarist ones where it is the min. In the first case, one wants to maximize the sum of the individual utilities. In the second case, one wants to maximize the minimum on all the individual utilities. On the example of Figure 3, solution b would be chosen in the first case; either solution c or solution d in the second case.

All the optimal solutions according to the sum aggregation operator are efficient, but some of them (possibly all of them) may be very unfair (see for example solution b in Figure 3). Some mechanisms can however counterbalance this phenomenon:

• it is possible to select, among the optimal solutions according to the utilitarist criterion, those that are the fairest ones;

• it is also possible to take advantage of the repetitive nature of the sharing process (performed either each day or for each satellite revolution) and, either to rely on the law of large numbers to obtain fairness, or to compensate any unfair sharing by changes in the data of the following ones (in order to favour entities that have been at a disadvantage during the previous sharings).

On the other hand, the min aggregation operator directly favours fairness by maximizing the utility of the less favoured entity. But it can select non efficient solutions, like solution d in the example of Figure 3.

Fortunately, it can be refined using the leximin operator, which orders according to an increasing utility each of the utility vectors to be compared and then compares the ordered vectors using a lexicographic order (the order that is used in a dictionary).

For example, if we have two utility vectors u = (4, 1, 2) and v = (1, 3, 1), they are first ordered according to an increasing utility of their components, resulting in the vectors u * = (1, 2, 4) and v * = (1, 1, 3). The lexicographic comparison between u * and v * shows that u must be preferred to v (equality according to the first least favoured component, advantage for u * according to the second component). On the example of Figure 3, solution c would be selected using this operator.

The main advantage of the leximin operator is that all the optimal solutions according to this operator are both optimal according to the min operator and efficient. This is why we chose this approach (an egalitarist approach with a leximin operator) for dealing with the sharing of an agile optical Earth observation satellite.

Note that we already explored an utilitarist approach in [START_REF] Lemaître | Exploiting a Common Property Resource under a Fairness Constraint: a Case Study[END_REF] and that there exist families of operators, such as the generalized mean operators (see [START_REF] Moulin | Axioms of Cooperative Decision Making[END_REF], chapter 2) or the more recent ordered weighted averaging operators (see [START_REF] Yager | On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decision Making[END_REF])), which offer a continuum between utilitarism and egalitarism and could be profitably explored too.

A sharing protocol

The sharing protocol we designed can be described using the three levels of utility, introduced in section 1. Let n be the number of entities. Let m be the maximum number of requests each entity can submit. For each entity i, let m i be the number of requests that entity i has submitted (m i ≤ m). We assume that these requests are numbered from 1 to m i according to a decreasing priority. For each entity i too, let d i be its rights (i.e the maximum number of its requests that can be selected). Let x be any selection.

Utility of a selection for an entity and a priority level

Basically, the utility of a selection x for an entity i and a priority level p (noted u ip (x)) is equal to 1 if the request that entity i has submitted at priority level p has been selected in x (noted s ip (x) = 1) and 0 if not. But to take into account the fact that the rights are not the same for all the entities and that these entities can submit as many requests as they want within the limit of m, u ip (x) is refined as follows: it is equal to 1 if and only if one of the following three conditions holds: (i) a request has been submitted by entity i at priority level p (p ≤ m i ) and it has been selected (s ip (x) = 1); (ii) the rights of entity i have been exhausted at priority level p (∑ p <p s ip (x) = d i ); (iii) no request has been submitted by entity i at priority level p (p > m i ).

Utility of a selection for an entity

The utility of a selection x for an entity i (noted u i (x)) is simply the vector of size m of the utilities of selection x for entity i and all the priority levels.

For example, lets assume three entities (n = 3), the rights of which are all equal (d 1 = d 2 = d 3 = 2) and which can submit at most three requests each (m = 3). Lets assume that entities 1 and 2 have submitted three requests and that entity 3 has submitted only two requests (m 1 = m 2 = 3, m 3 = 2). Let us assume that, in selection x, the first and the third requests from entity 1 have been selected (s 11 (x) = s 13 (x) = 1, s 12 (x) = 0), that the first two requests of entity 2 have been selected (s 21 (x) = s 22 (x) = 1, s 23 = 0), and that only the first request of entity 3 has been selected (s 31 (x) = 1, s 32 (x) = 0). The utility vector of this selection for entity 1 is u 1 (x) = (1, 0, 1) (the first and the third request have been selected, but the second one not). For entity 2 it is u 2 (x) = (1, 1, 1) (the first two requests have been selected, the third one not, but the rights of this entity have been exhausted by the first two selections). For entity 3 it is u 3 (x) = (1, 0, 1) (the first request has been selected, the second one not, but no third request has been submitted by this entity).

These vectors can be compared, using a lexicographic order. In our example, the utilities of this selection for entities 1 and 3 are equal and both worse than the one of entity 2.

Social utility of a selection

The social utility of a selection x (noted u(x)) is simply the vector of size n of the utilities of selection x for all the entities: a vector of vectors. On the example of the previous section, it is u(x) = ((1, 0, 1), (1, 1, 1), (1, 0, 1)).

To be compared using the leximin operator, these vectors must be ordered according to the order on utilities of a selection for an entity (defined in the previous section), starting from the lowest utilities (the least favoured entities first). For example, once ordered, the vector u(x) becomes u * (x) = ((1, 0, 1), (1, 0, 1), (1, 1, 1)).

Let us assume that we have to compare two candidate selections x and x the associated utility vectors of which are respectively u(x) = (( 1, 0, 1), (1, 1, 1), (1, 0, 1)) andu(x ) = ((1, 1, 0), (1, 0, 1), (1, 1, 0)). Let us observe that, with the first selection, the first and the third entities are the least favoured, whereas, with the second one, it is the second entity.

Both vectors are ordered, resulting in u * (x) = ((1, 0, 1), (1, 0, 1), (1, 1, 1)) and u * (x ) = ((1, 0, 1), (1, 1, 0), (1, 1, 0)).

By comparing u * (x) and u * (x ), using a lexicographic order, we conclude that x must be preferred to x (equality on the first least favoured entity, but advantage for x on the second least favoured entity:

(1, 0, 1) for x and (1, 1, 0) for x .

Maximizing the social utility

The objective of the mission control center can thus be defined as searching for a feasible selection the social utility of which is maximum or as high as possible.

Conclusion and Perspectives

We have defined a basic protocol which enforces a fair sharing between self-interested entities of an Earth observation satellite. Its main advantages are (i) that it is based on a clear and consistent egalitarist approach, (ii) that it guarantees the quality of each sharing, and (iii) that no compensation mechanism between successive sharings is a priori necessary.

It has been already extended to the other management phases (management of the medium and low priority requests) for which the sharing requirements are not exactly the same. It is now necessary (i) to adapt it to all the specific characteristics of the management of agile optical Earth observation satellites and besides of constellations of such satellites, (ii) to define and implement efficient constrained optimization algorithms based on the leximin aggregation operator, and (iii) to experiment them on realistic scenarii and to analyze their results in terms of sharing and efficiency.

On the other hand, it should be noted that this study and its main results can be profitably reused to deal with the problem of the sharing of any resource between self-interested entities, in or out of the space domain (space laboratory, interplanetary space probe, either space or ground telescope, telecommunication network, computing resource . . . ).

However, an important aspect of the sharing problem remains incompletely and imperfectly solved: Can these sharing protocols resist against manipulations from some entities? Can they consequently discourage entities from trying to manipulate them?

We started trying to answer these questions, by defining what a manipulation is. A manipulation can be defined as a modification by an entity of its requests (going from genuine to non genuine ones) with the aim of increasing its own utility. That may be an adding or a removal of requests, as well as a change in their respective priorities. It is then necessary to be more precise about the context in which a manipulation may occur: precise or imprecise knowledge of all the mechanisms of the selection algorithm; complete, partial, probabilistic, or null knowledge of the requests that will be submitted by the other entities. It is also necessary to define what a profitable manipulation is: absolutely certain gain, absolutely certain absence of loss, positive expected gain. It is finally necessary to establish whether the proposed protocols can be manipulated or not, according to the possible contexts and the chosen definitions. Maybe the subject of other communications . . .

Figure 1 :

 1 Figure 1: Acquisition of a strip.

Figure 3 :

 3 Figure3: Representation of the solutions of a problem including two utility components u 1 and u 2 . The closer a solution is to the diagonal dotted line, the fairer it is.

Although it is possible to extend the mechanisms that are presented in this paper to non unit requests (strips of any length, polygons, stereo requests), the mechanisms that allow this are out of the scope of this paper.


Niroj Shrestha

Klaus Zorn-Pauly

Pietro Mesirca

Chintan N Koyani

Gerald Wölkart

Valentina Di Biase

Eleonora Torre

Petra Lang

ME Mangoni, B Pelzmann Astrid Gorischek

Wolfgang Schreibmayer

Robert Arnold

Heinrich Maechler

Bernd Mayer

Dirk Von Lewinski

Angelo Giovanni Torrente

Matteo Elia Mangoni

Brigitte Pelzmann
email: brigitte.pelzmann@medunigraz.atsusanne.scheruebel@medunigraz.at

Susanne N Scheruebel

Di Biase

Shrestha

Lipopolysaccharide-induced sepsis impairs M2R-GIRK signaling in mouse sinoatrial node

Keywords: Carbachol, Ca 2+ transient, Heart rate variability, I KACh, Langendorff's

Sepsis has emerged as a global health burden associated with multiple organ dysfunction and 20% mortality rate in patients. Numerous clinical studies over the past two decades have correlated the disease severity and mortality in septic patients with impaired heart rate variability (HRV), as a consequence of impaired chronotropic response of sinoatrial node (SAN) pacemaker activity to vagal/parasympathetic stimulation. However, the molecular mechanism(s) downstream to parasympathetic inputs have not been investigated yet in sepsis, particularly in the SAN.

Based on electrocardiography, fluorescence Ca 2+ imaging, electrophysiology, and protein assays from organ to sub-cellular level, we report that impaired M2R-GIRK signaling in a lipopolysaccharide-induced proxy septic mouse model plays a critical role in SAN pacemaking and HRV. The parasympathetic responses to a muscarinic agonist, namely I KACh activation in SAN cells, reduction in Ca 2+ mobilization of SAN tissues, lowering of heart rate and increase in HRV, were profoundly attenuated upon lipopolysaccharide-induced sepsis. These functional alterations manifested as a direct consequence of reduced expression of key ion-channel components (GIRK1, GIRK4, and M2R) in the mouse SAN tissues and cells, which was further evident in the human right atrial appendages of septic patients and likely not mediated by the common pro-inflammatory cytokines elevated in sepsis.

Significance statement

Altered heart rate variability (HRV), arising from impaired chronotropic response of sinoatrial node (SAN) pacemaker activity to vagal input, has been proposed as an early diagnostic marker in sepsis. However, the underlying pathophysiological changes in the SAN have not been investigated yet. We discovered the downstream M2R-GIRK signaling in a lipopolysaccharideinduced proxy septic model is impaired, consequent to reduced expression of GIRK isoforms, leading to compromised chronotropic regulation of SAN pacemaking and HRV by I KACh .

Intriguingly, downregulation of GIRK channels was not directly mediated by the common proinflammatory cytokines elevated in sepsis. Our findings provide insights into parasympathetic regulation of SAN and clinical monitoring of altered HRV in sepsis, which potentially help to reduce risk of death in patients.

Introduction

Sepsis refers to a life-threatening, dysregulated host response to infection, manifesting into multiple organ dysfunction and ultimately death, unless diagnosed and treated promptly [START_REF] Singer | The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF].

Sepsis is a major health problem that accounted for 11 million deaths out of 49 million reported cases worldwide in 2017 and nearly 40% of fatal outcome were related to cardiovascular complications [START_REF] Rudd | Global, regional, and national sepsis incidence and mortality, 1990-2017: analysis for the Global Burden of Disease Study[END_REF]. The precise etiology and mechanism(s) underlying cardiac dysfunction in sepsis are complex and not entirely understood, which hinders timely diagnosis and therapeutic intervention in patients. Various mediators such as pro-inflammatory cytokines, nitric oxide, and reactive oxygen species have been linked to cardiac dysfunction [START_REF] Kakihana | Sepsis-induced myocardial dysfunction: pathophysiology and management[END_REF][START_REF] Pierrakos | Biomarkers of sepsis: time for a reappraisal[END_REF].

A number of clinical studies over the past two decades have correlated the disease severity and mortality in septic patients with altered heart rate variability (HRV), as a consequence of dampened cardiac response to vagal/parasympathetic stimulation [START_REF] Schmidt | Autonomic dysfunction predicts mortality in patients with multiple organ dysfunction syndrome of different age groups[END_REF][START_REF] Chen | Heart rate variability measures as predictors of in-hospital mortality in ED patients with sepsis[END_REF][START_REF] De Castilho | Heart rate variability as predictor of mortality in sepsis: A prospective cohort study[END_REF][START_REF] Pong | Combining Heart Rate Variability with Disease Severity Score Variables for Mortality Risk Stratification in Septic Patients Presenting at the Emergency Department[END_REF]. HRV refers to beat-to-beat variability (BBV) between successive RR intervals on an electrocardiogram (ECG). This variability predominantly arises from adaptive autonomic nervous system modulations of a specialized group of cardiac cells in sinoatrial node (SAN) that constitute the natural pacemaker of heart. Besides, a certain degree of BBV is intrinsic to the SAN cells due to fluctuations in the spontaneous pacemaking machinery [START_REF] Yaniv | Synchronization of sinoatrial node pacemaker cell clocks and its autonomic modulation impart complexity to heart beating intervals[END_REF][START_REF] Zaniboni | Beat-to-beat cycle length variability of spontaneously beating guinea pig sinoatrial cells: relative contributions of the membrane and calcium clocks[END_REF]. Previous animal studies on isolated SAN cells and tissues showed that spontaneous diastolic depolarization and action potential firing in SAN cells is generated by a functional interplay between two tightly linked intracellular clocks, namely the membrane clock and the calcium clock. The membrane clock involves periodic opening of transmembrane ion channels: hyperpolarization-activated cyclic nucleotide-gated (HCN) channels encoding the funny current (I f ), voltage-gated Ca 2+ channels (Ltype Ca v 1.3 and T-type Ca v 3.1), Ca 2+ -activated K + channels, and transient receptor potential channels [START_REF] Mesirca | Pharmacologic Approach to Sinoatrial Node Dysfunction[END_REF]. The calcium clock involves local Ca 2+ release through ryanodine receptors from the sarcoplasmic reticulum (SR), which can be either spontaneous [START_REF] Vinogradova | Rhythmic ryanodine receptor Ca2+ releases during diastolic depolarization of sinoatrial pacemaker cells do not require membrane depolarization[END_REF] or activated by Ca v 1.3 channels [START_REF] Torrente | L-type Cav1.3 channels regulate ryanodine receptor-dependent Ca2+ release during sino-atrial node pacemaker activity[END_REF][START_REF] Louradour | L-Type Cav1.3 Calcium Channels Are Required for Beta-Adrenergic Triggered Automaticity in Dormant Mouse Sinoatrial Pacemaker Cells[END_REF]. Local Ca 2+ release is coupled to diastolic depolarization via activation of the cardiac Na + /Ca 2+ exchanger (NCX1) [START_REF] Zaniboni | Beat-to-beat cycle length variability of spontaneously beating guinea pig sinoatrial cells: relative contributions of the membrane and calcium clocks[END_REF][START_REF] Bogdanov | Membrane potential fluctuations resulting from submembrane Ca2+ releases in rabbit sinoatrial nodal cells impart an exponential phase to the late diastolic depolarization that controls their chronotropic state[END_REF][START_REF] Yaniv | Stochasticity intrinsic to coupled-clock mechanisms underlies beat-to-beat variability of spontaneous action potential firing in sinoatrial node pacemaker cells[END_REF][START_REF] Torrente | Burst pacemaker activity of the sinoatrial node in sodium-calcium exchanger knockout mice[END_REF]. Sympathetic stimulation of β-adrenergic receptor on isolated SAN cells promotes action potential firing rate [START_REF] Yaniv | Real-time relationship between PKA biochemical signal network dynamics and increased action potential firing rate in heart pacemaker cells: Kinetics of PKA activation in heart pacemaker cells[END_REF][START_REF] Behar | The Autonomic Nervous System Regulates the Heart Rate through cAMP-PKA Dependent and Independent Coupled-Clock Pacemaker Cell Mechanisms[END_REF] and reduces BBV [START_REF] Yaniv | Synchronization of sinoatrial node pacemaker cell clocks and its autonomic modulation impart complexity to heart beating intervals[END_REF] via coupled G-protein alpha stimulatory subunit (Gα s )-mediated cyclic adenosine monophosphate-protein kinase A (cAMP-PKA) pathway, which is counterbalanced by the parasympathetic stimulation of muscarinic receptor subtype 2 (M2R)-inhibitory subunit Gα i leading to lower action potential firing rate and higher BBV [START_REF] Yaniv | Synchronization of sinoatrial node pacemaker cell clocks and its autonomic modulation impart complexity to heart beating intervals[END_REF][START_REF] Zaniboni | Beat-to-beat cycle length variability of spontaneously beating guinea pig sinoatrial cells: relative contributions of the membrane and calcium clocks[END_REF][START_REF] Behar | The Autonomic Nervous System Regulates the Heart Rate through cAMP-PKA Dependent and Independent Coupled-Clock Pacemaker Cell Mechanisms[END_REF][START_REF] Lyashkov | Cholinergic receptor signaling modulates spontaneous firing of sinoatrial nodal cells via integrated effects on PKA-dependent Ca(2+) cycling and I(KACh)[END_REF][START_REF] Van Borren | Effects of muscarinic receptor stimulation on Ca2+ transient, cAMP production and pacemaker frequency of rabbit sinoatrial node cells[END_REF]. Moreover, upon M2R stimulation by agonists in isolated SAN cells, the coupled G-protein beta-gamma (Gβγ) subunit directly activates acetylcholine-activated inwardly-rectifying potassium current (I KACh ). The cardiac I KACh is conducted by G protein-activated inwardly-rectifying potassium (GIRK) channels, consisting of GIRK1 and GIRK4 heteromers, which results in K + efflux and membrane hyperpolarization with consequent reduction in action potential firing rate [START_REF] Behar | The Autonomic Nervous System Regulates the Heart Rate through cAMP-PKA Dependent and Independent Coupled-Clock Pacemaker Cell Mechanisms[END_REF][START_REF] Lyashkov | Cholinergic receptor signaling modulates spontaneous firing of sinoatrial nodal cells via integrated effects on PKA-dependent Ca(2+) cycling and I(KACh)[END_REF][START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF][START_REF] Wickman | Abnormal heart rate regulation in GIRK4 knockout mice[END_REF]. I KACh plays a major role in the generation of HRV in response to vagal stimulation and in recovering basal heart rate after sympathetic activation [START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF][START_REF] Wickman | Abnormal heart rate regulation in GIRK4 knockout mice[END_REF].

Various animal models of sepsis point out the impact of the parasympathetic nervous system on cardiac dysfunction. In a lipopolysaccharide (LPS)-induced endotoxemic rat model, the observed narrowed BBV of the isolated SAN-atria region was linked to blunted or uncoupled cardiac response to cholinergic stimulation [START_REF] Gholami | Endotoxemia is associated with partial uncoupling of cardiac pacemaker from cholinergic neural control in rats[END_REF]. Other studies reported that electrical stimulation of the vagus nerve attenuated the myocardial inflammation and hemodynamic impairment in LPSinduced endotoxemia in vagotomized rats [START_REF] Borovikova | Vagus nerve stimulation attenuates the systemic inflammatory response to endotoxin[END_REF][START_REF] Schulte | Loss of vagal tone aggravates systemic inflammation and cardiac impairment in endotoxemic rats[END_REF]. Another rat model of sepsis obtained by cecal ligation and puncture demonstrated altered biphasic redistribution and phosphorylation of M2R receptor in the isolated heart [START_REF] Dong | Biphasic redistribution of muscarinic receptor and the altered receptor phosphorylation and gene transcription are underlying mechanisms in the rat heart during sepsis[END_REF]. However, the molecular mechanism(s) downstream to vagal/parasympathetic stimulation particularly in the SAN tissue have not been explored in detail in sepsis. Given the fact that GIRK1/4 channels are mainly expressed in SAN and atrial tissues, and are involved in determination of HRV [START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF][START_REF] Wickman | Abnormal heart rate regulation in GIRK4 knockout mice[END_REF], we hypothesized that impaired vagal activity during sepsis might be related to pathological changes in the M2R-GIRK signaling in SAN tissue.

Thus, the present study was designed to elucidate whether the responsiveness of SAN cells, tissue, and heart to parasympathetic stimulation is compromised under septic conditions due to modifications in the M2R-GIRK signaling, thereby potentially impairing HRV.

Results

LPS attenuates parasympathetic modulation of heart rate and its variability

We first induced sepsis in mice via intra-peritoneal (i.p.) injection of LPS (5 mg/kg), an endotoxin from gram-negative bacteria, and after 6 h, recorded ECGs from the isolated hearts under Langendorff's perfusion in relation to parasympathetic stimulation. We compared the beating rate and HRV measurements (SDNN, RMSSD, and pNN6, defined in the method section) calculated from ECGs on the hearts isolated from septic versus phosphate-buffered saline (PBS)-injected control mice. As illustrated in Fig. 1A, the beating rate of isolated hearts was unaffected by LPS injection in mice (414.22 ± 10.23 /min) compared to controls (399.58 ± 13.11 /min). Perfusion for 10 min with 0.1 µM carbachol (CCh), a muscarinic receptor agonist, significantly reduced the heart rate in controls by 39% (243.81 ± 12.06 /min). In contrast, CCh could marginally, albeit nonsignificant, reduce the beating rate in septic hearts (383.73 ± 14.08 /min, 7.4% reduction). LPS altered neither the SDNN (Fig. 1B, 0.81 ± 0.22 ms vs. 0.83 ± 0.12 ms) nor RMSSD (Fig. 1C, 0.69 ± 0.21 ms vs. 0.46 ± 0.09 ms) compared to controls. However, upon CCh perfusion, hearts from control mice exhibited significantly higher SDNN (Fig. 1B,2.88 ± 0.16 ms, 3.5 fold) and RMSSD (Fig. 1C,2.46 ± 0.39 ms, 5.4 fold). SDNN of hearts from LPS-injected mice also increased significantly following CCh perfusion (Fig. 1B,1.85 ± 0.31 ms, 2.3 fold) but to a much lesser extent than in controls, as evident from the significant interaction effect in the mixed two-way ANOVA (p=0.032). Meanwhile, the increase in RMSSD of hearts from LPS-injected mice did not reach significance (Fig. 1C, 1.19 ± 0.35 ms, 1.7 fold) following CCh perfusion. SDNN and RMSSD data together reflect that LPS attenuated the increase in total autonomic variability as well as short-term variation between successive heart beats in response to CCh. Further, baseline pNN6 data were zero in most of the control and LPS-injected mice. So, the difference or increase in pNN6 data between baseline and CCh response were compared in Fig. 1D. Clearly, the percentage increase in pNN6 following CCh perfusion was significantly higher in the hearts from control mice than those from LPS-injected mice (3.15% vs. 0.3%), which further reflects a lower response of heart rate to parasympathetic stimulation.

LPS dampens CCh-mediated negative chronotropic effect on Ca 2+ dynamics in SAN tissue

The heartbeat is generated by SAN pacemaker mechanism, which depends on the activity of the membrane and the calcium clocks. Cholinergic stimulation is known to modulate Ca 2+ homeostasis during SAN pacemaking and LPS impaired CCh effect on HR and HRV in isolated hearts (Fig. 1). So, we examined the effect of CCh on Ca 2+ dynamics in SAN tissues isolated from control and LPS-administered mice. Fig. 2A illustrates pacemaker activity reflected by automatic intracellular Ca 2+ -transients, expressed as change in fluorescence signal of Cal-520indicator over time in the SAN tissue of control vs. LPS-injected mouse in response to CCh. CCh perfusion for 10 min significantly reduced the rate of spontaneous Ca 2+ -transients in control SAN tissues by 25% (Fig. 2B, 284.76 ± 27.21 /min to 213.51 ± 32.19 /min), which correlates well to the reduced beating rate of isolated hearts as observed in Fig. 1A. Meanwhile, the rate of Ca 2+transients following CCh perfusion was also significantly reduced in SAN tissues from LPSinjected mice by 9.4% (Fig. 2B, 328.99 ± 32.29 /min to 298.17 ± 34.26 /min). However, the magnitude of reduction in LPS-treated SAN tissues was significantly lower than in control tissues, evident from the significant interaction effect in the mixed two-way ANOVA (p=0.015). CCh reduced the peak amplitude by 23.6% (Fig. 2C) and prolonged the relaxation time to 90% from peak (RT 90 ) by 15.5% (Fig. 2D) in the control SAN tissues whereas these parameters were unaffected in the SAN tissues of LPS-injected mice. Under basal conditions, there was no difference in these parameters between SAN tissues of LPS-injected mice and control mice (Fig. 2B-D), supporting the results obtained from isolated hearts (Fig. 1).

LPS inhibits CCh-mediated increase in steady-state current density and I KACh in isolated SAN cells

Since LPS blunted CCh-induced reduction in heart rate and frequency of spontaneous Ca 2+ transients (Fig. 1 and2), we investigated the impact of CCh on membrane current in SAN cells isolated from control and LPS-injected mice. In whole-cell patch-clamp recordings, a ramp protocol from -100 mV to +40 mV was applied over 1.5 s to elicit quasi steady-state current before and after 0.1 µM CCh perfusion (Fig. 3A andB). The major differences between control and LPS groups in response to CCh were noticeable at negative and positive voltages (Fig. 3C and S1A-E). Upon CCh perfusion, control SAN cells showed significant increase in the inward current density at -100 mV (Fig. 3C), -90 and -80 mV (Fig. S1A andB) as well as the outward current density at +20, +30, and +40 mV (Fig. S1C-E). In contrast, CCh perfusion failed to alter the current density in inward and outward direction in SAN cells from LPS-injected mice, except for reduction at -80 mV. In Fig. S1F, plotting the difference between CCh and basal current (I CCh -I basal , referred as CCh-induced) revealed that I KACh mediated CCh effect at both negative and positive voltages, and showed inward rectifying properties in control SAN cells. In contrast, LPS suppressed the CCh-induced inward current at negative voltages and abrogated most of the difference current at positive voltages. The inward current was further confirmed to be mediated by I KACh in a separate set of experiments where a GIRK channel inhibitor tertiapin-Q [START_REF] Lyashkov | Cholinergic receptor signaling modulates spontaneous firing of sinoatrial nodal cells via integrated effects on PKA-dependent Ca(2+) cycling and I(KACh)[END_REF][START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF] at 300 nM significantly attenuated CCh-mediated increase in current density at -100 mV (Fig. 3D).

We next evaluated I KACh at -35 mV holding potential, as reported previously [START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF]. Fig. 3E illustrates representative current recordings, demonstrating prominent activation of I KACh within few seconds upon CCh perfusion in a control cell but negligible activation in a cell from LPSinjected mouse. Averaged data plotted in Fig. 3F show that CCh significantly increased I KACh in control SAN cells (1.24 ± 0.23 pA/pF) compared to cells from LPS-injected mice (0.35 ± 0.11 pA/pF). We further investigated if LPS diminished I KACh activation independent of Gβγ-coupled M2R stimulation by CCh. To do so, we used ML297 and 3hi2one-G4, direct activators of heteromeric GIRK1/4 and homomeric GIRK4 channels respectively [START_REF] Kaufmann | ML297 (VU0456810), the first potent and selective activator of the GIRK potassium channel, displays antiepileptic properties in mice[END_REF][START_REF] Cui | A novel small-molecule selective activator of homomeric GIRK4 channels[END_REF], for measuring I KACh at -100 mV in ramp recordings. 3 µM ML297 significantly increased the inward current density at -100 mV in the control SAN cells but not in the cells from LPS-injected mice (Fig. S1G), suggesting disruption of GIRK1/4 channel function and/or expression. In contrast, 30 µM 3hi2one-G4 failed to elicit I KACh at -100 mV in the cells from both control and LPS-injected mice (Fig. S1H), suggesting that in SAN cells, GIRK4 forms functional heterotetramers with GIRK1 but not GIRK4 homotetramers.

LPS reduces expression of M2R and GIRK channels involved in parasympathetic regulation of heart rate

GIRK1 and GIRK4 channels are integral components of membrane delimited M2R-induced activation of I KACh [START_REF] Behar | The Autonomic Nervous System Regulates the Heart Rate through cAMP-PKA Dependent and Independent Coupled-Clock Pacemaker Cell Mechanisms[END_REF][START_REF] Lyashkov | Cholinergic receptor signaling modulates spontaneous firing of sinoatrial nodal cells via integrated effects on PKA-dependent Ca(2+) cycling and I(KACh)[END_REF][START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF]. So, we investigated whether LPS administration could alter expression of M2R and/or GIRK channel isoforms accounting for loss of I KACh and reduced response to CCh in SAN pacemaker cells, intact SAN tissues and whole hearts isolated from LPS-injected mice in the functional assays described above. Western blots of SAN tissues from LPS-injected mice indeed showed significantly lower expression of GIRK1 (0.33 ± 0.05 fold), GIRK4 (0.51 ± 0.09 fold), and M2R (0.49 ± 0.09 fold) compared to the SAN tissues from control mice (Fig. 4A). Next, we investigated if LPS directly impacts the expression of these receptors and ion channels in intact SAN tissues in situ in addition to the above in vivo effects. Invitro incubation of the isolated SAN tissues with LPS for 6 h also significantly reduced the expression of GIRK1 (0.65 ± 0.04 fold), GIRK4 (0.74 ± 0.05 fold), and M2R (0.69 ± 0.04 fold) compared to the control SAN tissues (Fig. 4B), however, the effect was less pronounced than in the SAN tissues from LPS-injected mice. Next, we evaluated the expression of M2R and GIRK1/4 channels in the human right atrial appendages (RAA) from septic patients and similarly observed reduced expression of GIRK1 (0.43 fold), GIRK4 (0.45 fold), and M2R (0.55 fold) compared to the control human tissues (Fig. S2), which corroborates the findings in the SAN tissues from mice following invivo or invitro LPS treatment.

To determine whether LPS-induced reduction of GIRK1/4 expression in the SAN tissues is reflected at the membrane levels, we performed fluorescence immunolabeling of SAN cells isolated from control and LPS-injected mice. We also assessed the membrane expression of other ion channels involved in SAN pacemaking, such as Ca v 1.3 channels ( 14) and I f -conducting HCN4 [START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF]. Fig. 4C shows the immunolabeled GIRK1, GIRK4, Ca v 1.3, and HCN4 homogenously localized in discrete clusters at the membrane in both conditions, suggesting that LPS does not alter the overall channel distribution. However, quantitative analysis of fluorescence intensity (Fig. 4D) revealed significant reduction of GIRK1 (0.57 ± 0.04 fold) and GIRK4 (0.86 ± 0.05 fold) membrane levels in SAN cells from LPS-injected mice compared to controls, indicating that LPS diminishes the amount of functional GIRK channels at the surface. The membrane amount of Ca v 1.3 was also significantly decreased (0.55 ± 0.06 fold) whereas HCN4 showed strong variability with no significant change. Low magnification images of the SAN cells from which the enlarged regions in Fig. 4C were isolated are provided in Fig. S3 and display their typical thin and elongated morphology. Fig. S4 clarifies the membrane localization of the analyzed channels as a rim surrounding the intracellular region. Although some intracellular labeling consistent with organelle localization was observed (arrowheads), this was segregated in restricted regions and clearly distinguishable from the cell membrane rim (arrows). This differs from the homogeneously distributed clusters represented in Fig. 4C, consistent with membrane ion channels segregated in functional domains.

Since the intermediate G-protein subunits, namely Gα i and Gβγ, mediate cAMP-PKA pathway inhibition and I KACh activation respectively upon M2R stimulation by CCh [START_REF] Lyashkov | Cholinergic receptor signaling modulates spontaneous firing of sinoatrial nodal cells via integrated effects on PKA-dependent Ca(2+) cycling and I(KACh)[END_REF], we checked if LPS affects the expression of Gα i2 and Gβ too. However, we did not observe any change in expression from western blots of SAN tissues from LPS-injected mice compared to those from control mice (Fig. S5). We further checked whether the reduced expression in SAN is mediated by common pro-inflammatory cytokines like tumor necrotic factor-alpha (TNF-α), interleukin-1 beta (IL-1β) or interleukin-6 (IL-6). Elevated level of these cytokines has been previously shown to promote systemic inflammation [START_REF] Borovikova | Vagus nerve stimulation attenuates the systemic inflammatory response to endotoxin[END_REF][START_REF] Schulte | Loss of vagal tone aggravates systemic inflammation and cardiac impairment in endotoxemic rats[END_REF] and is associated with reduced HRV in septic rodents [START_REF] Fairchild | Endotoxin depresses heart rate variability in mice: cytokine and steroid effects[END_REF]. We incubated SAN tissues with TNF-α (50 ng/mL), IL-1β (10 ng/mL) or IL-6 (10 ng/mL) for 6 h. These cytokines did not affect expression of M2R and GIRK1/4 channels compared to the control tissues (Fig. S6A andB), suggesting that cytokine elevation in sepsis may not directly affect expression of channels involved in I KACh in the SAN tissues.In addition, we investigated if I KACh activation by CCh in SAN cells was affected upon incubation with 10 ng/ml IL-6 for 2 h. IL-6-incubated cells showed similar increase in CCh-activated I KACh density at -100 mV compared to control cells (Fig. S6C), indicating no direct effect of cytokines like IL-6 on GIRK channel activation in addition to expression.

Discussion

To the best of our knowledge, our study is the first to present evidence of impaired M2R-GIRK signaling pathway in the SAN tissues of LPS-injected septic mice. As summarized in Fig. 5, LPSreduced expression of key ion-channels and receptors (GIRK1, GIRK4, and M2R). This diminished expression led to diminished parasympathetic regulation of pacemaker activity at multiple levels namely, (i) I KACh activation in SAN cells, (ii) reduction in the frequency of spontaneous Ca 2+ transients of SAN tissues, and (iii) lowering of heart rate and increase in HRV parameters.

Our findings are in line with previous studies showing that genetic ablation of GIRK4 channels and hence lack of I KACh in isolated SAN tissue and atrial myocytes attenuated the effect of vagal stimulation, namely lowering of heart rate and increase in HRV, in isolated hearts as well as conscious mice [START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF][START_REF] Wickman | Abnormal heart rate regulation in GIRK4 knockout mice[END_REF]. We further revealed substantial reduction in expression of GIRK1, GIRK4, and M2R in RAA of septic patients, which might in turn contribute to the diminished vagal response and impaired HRV observed in these patients [START_REF] Schmidt | Autonomic dysfunction predicts mortality in patients with multiple organ dysfunction syndrome of different age groups[END_REF][START_REF] Chen | Heart rate variability measures as predictors of in-hospital mortality in ED patients with sepsis[END_REF]. However, LPS did not affect the expression of M2R-coupled Gβ subunit that directly activates I KACh in mouse SAN tissues but attenuated Gβγ-independent and direct GIRK1/4 channel activation by ML297 in mouse SAN cells, which indicates that LPS impairs GIRK1/4 channel function and expression independent of regulation of Gβ expression. Our group has previously reported impairment of I f in human RAAs following LPS incubation without affecting HCN2/4 expression, which further compromises cardiac pacemaking in response to autonomic inputs [START_REF] Zorn-Pauly | Endotoxin impairs the human pacemaker current If[END_REF][START_REF] Scheruebel | I(f) blocking potency of ivabradine is preserved under elevated endotoxin levels in human atrial myocytes[END_REF]. Here, we did not observe change in membrane expression of HCN4 channels in the SAN cells from LPS-injected mice, in line with our previous report. In addition, our data show that SAN cells most likely conduct I KACh via functional heterotetramers of GIRK1/4 but not GIRK4 homotetramers since GIRK4-specific activator, 3hi2one-G4, failed to elicit I KACh in the SAN cells from both control and LPS-injected mice. Moreover, this evidence further supports LPS-induced reduction of I KACh in SAN cells is due to concomitant down regulation of GIRK1 and GIRK4.

In previous reports, elevated common pro-inflammatory cytokines like TNF-α, IL-1β, and IL-6 have been associated with blunted anti-inflammatory vagal tone leading to cardiac inflammation and reduced HRV in LPS-induced sepsis in rodents [START_REF] Schulte | Loss of vagal tone aggravates systemic inflammation and cardiac impairment in endotoxemic rats[END_REF][START_REF] Fairchild | Endotoxin depresses heart rate variability in mice: cytokine and steroid effects[END_REF]. Among the common cytokines, IL-6 was previously found to be highly elevated in plasma of LPS-administered mice within 1 h (30) and IL-6 incubation of atrial-SAN tissues isolated from control mice for 30 minutes reduced CCh response on beating rate by 4.7 fold [START_REF] Hajiasgharzadeh | Interleukin-6 impairs chronotropic responsiveness to cholinergic stimulation and decreases heart rate variability in mice[END_REF]. However, direct incubation of SAN tissues isolated from control mice with these common cytokines for 6 h in the present study did not affect the expression of M2R and GIRK channels. Moreover, isolated control SAN cells in direct contact with IL-6 for 2 h failed to alter CCh-activated I KACh . These findings together suggest that the common cytokines interfere with the vagal response associated with reduced HRV in sepsis most likely via indirect systemic mechanism(s), rather than directly targeting M2R-GIRK1/4 function and expression. However, we cannot exclude that less-known cytokines may contribute to direct effect of LPS and further mechanistic studies are required to establish the effect of the other cytokines on HRV during sepsis.

Tachycardia and reduced HRV are mostly detected in septic patients [START_REF] Chen | Heart rate variability measures as predictors of in-hospital mortality in ED patients with sepsis[END_REF][START_REF] De Castilho | Heart rate variability as predictor of mortality in sepsis: A prospective cohort study[END_REF][START_REF] Pong | Combining Heart Rate Variability with Disease Severity Score Variables for Mortality Risk Stratification in Septic Patients Presenting at the Emergency Department[END_REF] and reported in LPS-administered rats in vivo though the basal beating rate of SAN-atrial tissue isolated from these rats was unaffected [START_REF] Gholami | Endotoxemia is associated with partial uncoupling of cardiac pacemaker from cholinergic neural control in rats[END_REF]. Besides, conscious GIRK4 knockout mice showed no change in basal heart rate but reduction in HRV in telemetry [START_REF] Wickman | Abnormal heart rate regulation in GIRK4 knockout mice[END_REF]. Under our ex vivo experimental conditions, we did not observe significant change in basal beating rate and HRV of isolated hearts and in basal Ca 2+ transient rate of isolated SAN tissues from LPS-injected mice compared to controls. The impact of LPS-induced endotoxemia on heart rate and HRV as well as GIRK4 knockout on HRV in previous findings in the whole animal likely requires additional factors like elevated sympathetic inputs and/or eicosanoids [START_REF] Gholami | Endotoxemia is associated with partial uncoupling of cardiac pacemaker from cholinergic neural control in rats[END_REF][START_REF] Takayama | Thromboxane A2 and prostaglandin F2alpha mediate inflammatory tachycardia[END_REF], which were absent in our experiments designed to investigate parasympathetic inputs on the isolated SAN cell/tissue and heart. The parasympathetic inhibition of chronotropic action on SAN tissues and heart isolated from LPSinjected mice was compromised, as evident from the diminished effect of a muscarinic agonist, CCh, on the rate of spontaneous Ca 2+ transients in the SAN and heart rate. This functional impairment of negative chronotropic effect is likely a direct consequence of reduced expression of M2R and GIRK channels in SAN tissues. This outcome is consistent with previous studies that have documented the inhibitory role of M2R-GIRK pathway on action potential firing rate in isolated SAN cells and heart rate [START_REF] Lyashkov | Cholinergic receptor signaling modulates spontaneous firing of sinoatrial nodal cells via integrated effects on PKA-dependent Ca(2+) cycling and I(KACh)[END_REF][START_REF] Van Borren | Effects of muscarinic receptor stimulation on Ca2+ transient, cAMP production and pacemaker frequency of rabbit sinoatrial node cells[END_REF][START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF][START_REF] Wickman | Abnormal heart rate regulation in GIRK4 knockout mice[END_REF].

In addition to slowing action potential firing rate in isolated SAN cells, Gα i -coupled M2R stimulation attenuates SR-Ca 2+ release and reuptake via inhibition of cAMP-PKA-mediated phosphorylation of downstream ion-channels and pumps [START_REF] Lyashkov | Cholinergic receptor signaling modulates spontaneous firing of sinoatrial nodal cells via integrated effects on PKA-dependent Ca(2+) cycling and I(KACh)[END_REF]. We observed these effects in SAN tissues isolated from control mice as reduced peak amplitude and longer RT 90 of Ca 2+ -transients following CCh administration. However, these effects were absent in the SAN tissues of LPSinjected mice with lower expression of M2R and Ca v 1.3 but not Gα i2 , suggesting that cAMP-PKA downstream signaling could not be inhibited independent of Gα i2 expression. LPS-induced reduction in membrane expression of Ca v 1.3 channels in the SAN cells is in line with previous findings of reduced expression of Ca v 1.3 in the atrial tissues isolated from LPS-injected guinea pigs [START_REF] Aoki | Role of ion channels in sepsis-induced atrial tachyarrhythmias in guinea pigs[END_REF]. This warrants investigation of LPS effect on cAMP-PKA cascade and L-type Ca v 1.3 currents in SAN cells/tissues in future studies.

In summary, our findings demonstrate a pivotal role of downregulation of M2R-GIRK signaling in SAN pacemaking and HRV in a murine sepsis model and likely contribution to the diminished vagal response and reduced HRV observed in septic patients. Furthermore, our data support the emerging practice to monitor HRV as an early prognostic marker for sepsis [START_REF] Schmidt | Autonomic dysfunction predicts mortality in patients with multiple organ dysfunction syndrome of different age groups[END_REF][START_REF] Chen | Heart rate variability measures as predictors of in-hospital mortality in ED patients with sepsis[END_REF][START_REF] De Castilho | Heart rate variability as predictor of mortality in sepsis: A prospective cohort study[END_REF][START_REF] Pong | Combining Heart Rate Variability with Disease Severity Score Variables for Mortality Risk Stratification in Septic Patients Presenting at the Emergency Department[END_REF][START_REF] Quinten | Protocol of the sepsivit study: a prospective observational study to determine whether continuous heart rate variability measurement during the first 48 hours of hospitalisation provides an early warning for deterioration in patients presenting with infection or sepsis to the emergency department of a Dutch academic teaching hospital[END_REF]. Within 6 h of LPS administration, expression of M2R and GIRK channel is reduced with consequences on vagal responsiveness and HRV. Hence, HRV monitoring at the onset of sepsis, when clinical symptoms are subtle and can easily be overlooked, is a non-invasive and efficient tool for timely diagnosis and therapeutic intervention of this fatal disease in patients.

Materials and Methods

Animals

The experimental procedure and number of animals used were approved by the ethics committee of the Medical University of Graz and Federal Ministry of Science, Research, and Economy of the Republic of Austria (BMWFW-66.010/0101-WF/V/3b/2016), and the University of Montpellier and the French Ministry of Agriculture (protocol no: 2017010310594939). The experiments were conducted according to the Directive of the European Parliament and of the Council of September 22, 2010 (2010/63/EU). C57BL/6 wild-type mice (both sexes, 14-20 weeks old) were administered with LPS (5 mg/kg, i.p.) to elicit a septic response for 6 h as reported previously [START_REF] Fairchild | Endotoxin depresses heart rate variability in mice: cytokine and steroid effects[END_REF] and compared to PBS-injected controls.

Human right atrial appendages (RAA)

The use of human tissue was approved by the ethics committee of the Medical University of Graz, Austria (19-109 ex 07/08) and all patients gave prior informed consent according to the WMA Declaration of Helsinki, 2013. RAA were obtained from 2 septic and 2 non-septic (control) patients undergoing cardiac surgery.

Reagents

All reagents used were of molecular biology grade and purchased from Sigma-Aldrich or Carl Roth unless specified otherwise.

Langendorff perfusion

Mice were injected with heparin (1000 U/kg, i.p.) and anaesthetized with ketamine (80 mg/kg, i.p.) and xylazine (10 mg/kg, i.p.). Depth of anesthesia was monitored by toe pinch reflex and mice were sacrificed by cervical dislocation. Hearts were rapidly excised and arrested in ice-cold Krebs-Henseleit buffer. After cannulation of the aorta with a 20-gauge needle, retrograde perfusion was established at a constant flow of 20 ml/min/g wet weight with a modified Krebs-Henseleit bicarbonate buffer (in mM: 118 NaCl, 25 NaHCO 3 , 1.2 KH 2 PO 4 , 4.8 KCl, 1.2 MgSO 4 , 1.25 CaCl 2 , 11 glucose, pH 7.4) using the ISO-HEART perfusion system (Hugo Sachs Elektronik) as described previously with slight modifications [START_REF] Koyani | Dipeptidyl peptidase-4 independent cardiac dysfunction links saxagliptin to heart failure[END_REF]. The perfusate was filtered through a 5 µm filter before reaching the heart and continuously gassed with carbogen (95% O 2 , 5% CO 2 ). Heart temperature was maintained at 37°C throughout the experiments, monitored with a physitemp probe (Physitemp Instruments). After removal of the left auricle, a tiny fluid-filled balloon made of a small square of polyethylene film was inserted into the left ventricle and connected to a pressure transducer via a 4F biluminal monitoring catheter (Vygon). An epicardial ECG was recorded throughout the experimental period with the use of two stainless steel electrodes attached directly to the base of the right atrium and left ventricle, respectively. Hearts were perfused for 30 min to establish stable baseline conditions, followed by 15 min perfusion with 0.1 µM CCh.

RR intervals (1000 baseline and 1000 after 10 min of CCh perfusion) were extracted using HRV module of LabChart 7 Pro software (ADInstruments). Each RR interval was plotted as a function of time (tachogram) or as a function of the preceding RR (Poincaré plot) to select the normal RR intervals excluding artifact and ectopic beats, as reported previously [START_REF] Thireau | Heart rate variability in mice: a theoretical and practical guide[END_REF]. Heart rate and timedomain statistical measures of HRV (SDNN, RMSSD, and pNN6) were calculated from RR interval using MATLAB TM . SDNN, the standard deviation of all normal RR intervals (in ms), estimates the total HRV arising from autonomic nervous system. RMSSD denotes the square root of the mean of the sum of the squares of differences between adjacent normal RR intervals (in ms), quantifying short-term variation between two successive beats as a measure of parasympathetic regulation. pNN6 is the percentage of consecutive normal RR intervals differing more than 6 ms, and reflects the relatively abrupt and fast changes in HR, attributed to cardiac parasympathetic activity.

Isolation of sinoatrial node (SAN) cells

SAN cells were isolated as described previously [START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF][START_REF] Mangoni | Properties of the hyperpolarization-activated current (I(f)) in isolated mouse sino-atrial cells[END_REF]. Briefly, mice were heparinized (250 U, i.p., Gilvasan Pharma), anesthetized with ketamine (100 mg/kg, i.p.) and xylazine (10 mg/kg, i.p.

Electrophysiological Recordings

Electrophysiological recordings were performed in the whole-cell configuration of the patch-clamp technique using Axopatch 200B or Multiclamp amplifiers connected to Digidata 1550B interface (Molecular Devices) and Clampex v11.1 software. For IL-6 group, control SAN cells were incubated with 10 ng/ml IL-6 for 2 h before recordings. SAN cells were harvested on a custommade glass-bottom dish and mounted on the stage of an inverted microscope (Zeiss Axiovert 135) with a 40x/0.75 objective. Pre-warmed (37 °C) Tyrode's solution was perfused near the cell using a multi-MPRE8 heating pen and cFlow perfusion controller (Cell MicroControls). Only elongated, spontaneously beating cells were patched with patch pipettes filled with intracellular solution containing (in mM): 80 K + -aspartate; 50 KCl, 3 Na + -ATP, 2 CaCl 2 , 1 MgCl 2 , 5 HEPES, and 5 EGTA (adjusted to pH 7.2 with KOH), and a tip resistance of 2-3 MΩ. The current was recorded from a holding potential of -80 mV using a voltage ramp protocol (1.5 s in duration) from -100 mV to +40 mV (37) before and after perfusion with 0.1 µM CCh, 300 nm tertiapin-Q (Alomone Labs) or 3 µM ML297 in Tyrode's solution. For measuring I KACh [START_REF] Mesirca | The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation[END_REF], the current was recorded at -35 mV holding potential and after reaching a stable current (baseline), 0.1 µM CCh was added and the current was recorded till it reached a plateau, usually within a few seconds.

I KACh was calculated as the difference between the baseline and the plateau current. Current density was calculated by dividing the current amplitudes with cell membrane capacitance to allow comparison among cells of different size.

Ca 2+ imaging of SAN tissue

Intact SAN/atrial tissue was isolated from the excised mouse heart in Tyrode's solution prewarmed to 37°C as described previously [START_REF] Torrente | Burst pacemaker activity of the sinoatrial node in sodium-calcium exchanger knockout mice[END_REF][START_REF] Ahammer | Sinoatrial Beat to Beat Variability Assessed by Contraction Strength in Addition to the Interbeat Interval[END_REF]. The right and the left atria were pinned flat to the bottom of 35 mm cell culture dish coated with Sylgard (Sylgard 184 Silicone elastomer kit; Dow Corning) of ~2 mm thickness. The tissue was loaded with 5 µM Cal-520 AM dye (Biozol) and 0.02% Pluronic F-127 (Thermo Fisher Scientific) in the Tyrode's solution at 20-22°C for 1 h in dark, washed twice with fresh Tyrode's solution and kept for 15 min to allow de-esterification of Cal-520 AM. The dish with Cal-520-loaded tissue was then mounted on an upright microscope (Olympus BX51WI) with a 5x/0.75 objective and perfused with Tyrode's solution at 37 o C using dual automatic temperature controller (Warner Instruments). The SAN area was excited with 470 nm LED of Omicron LEDHUB (Omicron-Laserage Laserprodukte GmbH) and the fluorescent images were captured at 100 frames/s in Visiview v5.0 software (Visitron Systems) using 530/43 nm emission filter (Semrock) with an ORCA-Flash 4.0 v2 CMOS camera (Hamamatsu). The fluorescence intensity (F) proportional to the intracellular Ca 2+ concentration in the SAN region was analyzed after background subtraction and normalized to baseline fluorescence F b (F/F b ).

The Ca 2+ -transient parameters (transients/min, peak amplitude, RT 90 ) were calculated using peak analysis module of LabChart 7 Pro software (ADInstruments).

Western blot

Western blot was performed as described previously [START_REF] Koyani | Dipeptidyl peptidase-4 independent cardiac dysfunction links saxagliptin to heart failure[END_REF]. SAN tissues were used immediately after isolation except when incubated with TNF-α (50 ng/mL), IL-1β (10 ng/mL) or IL-6 (10 ng/mL) (Peprotech) for 6 h. The isolated tissue was homogenized in 50-100 µl ice-cold lysis buffer (50 mM HEPES, 150 mM NaCl, 1 mM EDTA, 1% Triton X-100, 10% glycerol, pH 7.4 adjusted with NaOH) containing protease inhibitor cocktail tablet (Roche) with Precellys 24 tissue homogenizer (2 × 20 s, 6,500 rpm) and then was centrifuged at 13,000 rpm, 4°C for 15 min. Protein estimation of solubilized tissue lysates was performed using BCA protein assay kit (Thermo Fischer Scientific). 25-30 µg protein was added to 10 µl of 4x NuPAGE LDS sample buffer containing 2 µl sample reducing agent (Thermo Fisher Scientific), resolved by electrophoresis in NuPAGE 4-12% Bis-Tris gel and transferred to nitrocellulose membranes (Thermo Fisher Scientific).

Membranes were blocked with 5% (w/v) non-fat milk in Tris-buffered saline containing 0.1% Tween 20 (TBST, 25˚C, 1 h) and cut till 80 KDa protein ladder since all the detected proteins were below 80 KDa molecular weight and limited amount of working batch of antibodies could be utilized for incubation. The following primary antibodies (diluted in 5% [w/v] BSA-TBST) were used for incubation overnight at 4˚C: rabbit anti-GIRK1 (1:1,000, Alomone Labs Cat# APC-005, RRID: AB_2040113), rabbit anti-GIRK4 (1:500, Alomone Labs Cat# APC-027,RRID: AB_2039943), rabbit anti-CHRM2 (1:500, Alomone Labs Cat# AMR-002, RRID: AB_2039995), rabbit anti-Gα i2 (1:2000, GeneTex Cat# GTX101779, RRID: AB_10721709), and mouse anti-Gβ (1:500, Santa Cruz Biotechnology Cat# sc-166123, RRID: AB_2109632). For normalization, membranes were stripped with stripping buffer (58.4 g/L NaCl, 7.5 g/L glycine, pH 2.15 adjusted with HCl) and incubated with anti-GAPDH (1:10,000, Proteintech Cat# 60004-1-Ig, RRID: AB_2107436) as a primary antibody. After washing, the membranes were incubated with HRPconjugated goat anti-rabbit IgG (1:20,000, Thermo Fisher Scientific Cat# 31460, RRID: AB_228341) or goat anti-mouse IgG (1:10,000, Jackson ImmunoResearch Labs Cat# 115-035-146, RRID: AB_2307392) in 4% [w/v] nonfat milk-TBST (25˚C, 1 h). Immunoreactive bands were visualized using SuperSignal West Pico Chemiluminescent Substrate (Thermo Fisher Scientific) in ChemiDoc MP Imaging System (Bio-Rad) and densitometric evaluation was performed using Image Lab 6.0 software (Bio-Rad). The relative expression for each protein was calculated by normalizing to the control samples and GAPDH as a loading control.

Quantitative fluorescence immunolabeling

Fixed cells were immunolabeled for fluorescence imaging as described previously [START_REF] Di Biase | Resolving sub-synaptic compartments with double immunofluorescence labeling in hippocampal neurons[END_REF]. SAN cells were isolated from 3 control and 3 LPS-injected mice, as described above and plated on poly-llysine-coated glass coverslips with 18 mm diameter at plating density of 25-30 cells/100 µl. Two hours later, the cells were fixed with 4% paraformaldehyde, 4% sucrose in PBS at room temperature for 10 min. The fixed cells were incubated in 5% normal goat serum in PBS containing 0.1% BSA and 0.2% Triton X-100 (PBS/BSA/Triton) for 30 min. Cells were then exposed to the primary antibodies in PBS/BSA/Triton at 4°C overnight, washed and incubated with the fluorochrome-conjugated secondary antibodies at room temperature for 1 h. The primary antibodies used were rabbit anti-GIRK1 (1:1000, Alomone Labs Cat# APC-005, RRID: AB_2040113), rabbit anti-GIRK4 (1:1000, Alomone Labs Cat# APC-027, RRID: AB_2039943), guinea-pig anti-Ca V 1.3 (1:500, Alomone Labs Cat# ACC-005-GP, RRID: AB_2756614), and guinea-pig anti-HCN4 (1:500, Alomone Labs Cat# APC-052-GP, RRID: AB_2340957). The secondary antibodies goat anti-rabbit Alexa-594 (Thermo Fisher Scientific Cat# A-11012, RRID: AB_2534079) and goat anti-guinea-pig Alexa-647 (Thermo Fisher Scientific Cat# A-21450, RRID: AB_2735091) were used at 1:4000. Coverslips were mounted in p-phenylenediamine glycerol to retard photo bleaching and observed with a conventional inverted epifluorescence IX3 microscope (Olympus) using a 60x/1.42 apochromat oil-immersion objective lens (UPLXAPO60XO, Olympus) and SOLA LED solid-state light engine (Lumencor) light source.

Images were acquired with a sCMOS Prime BSI camera (Teledyne Photometrics) using the same acquisition time for all pictures. Two images were captured for each cell, one at the level of the cell membrane adhering to the coverslips and another at the longitudinal focal plane passing through the cell showing the membrane as a rim around the cell. unless specified otherwise, mixed two-way ANOVA was applied to evaluate interaction and main effects followed by simple effects. The between-group factor was treatment (Control vs. LPS) and the within-group, repeated measure factor was baseline (-CCh) vs. CCh response. In case of pNN6 data, the baseline values in both control and LPS groups were mostly zeroes, thus the difference between baseline and CCh response for control and LPS groups was calculated and the medians of the delta values were compared by the R function medpb2 as described by Wilcox in Chapter 7. 5.3 (43). This function uses the percentile bootstrap method to account for tied values. Data from two independent groups were analyzed by unpaired bootstrap t-test. Data from more than two paired groups were analyzed by repeated measure one-way ANOVA followed by within group effect analysis with Bonferroni adjustment. Western blot data were analyzed using one-sample t-test, with reference value for control samples set to one. All tests were two-tailed and p values < 0.05 were considered significant. Normally distributed data were plotted using OriginPro 2018 (OriginLab Corporation) as scatter plots along with mean ± SEM, otherwise median with first and third quartile were plotted.

Materials and Data Availability

All study data are included in the article and/or supporting information.

  ), and sacrificed by cervical dislocation. The beating heart was quickly removed and transferred to the Tyrode's solution (37°C) containing (in mM): 140 NaCl, 5.4 KCl, 1.8 CaCl 2 , 1 MgCl 2 , 5 HEPES-NaOH, and 5.5 d-glucose (adjusted to pH 7.4 with NaOH). The SAN tissue was excised by cutting along the crista terminalis and the interatrial septum, and transferred into a low-Ca 2+ , low-Mg 2+ solution containing (in mM): 140 NaCl, 5.4 KCl, 0.5 MgCl 2 , 0.2 CaCl 2 , 1.2 KH 2 PO 4 , 50 taurine, 5.5 d-glucose, 5 HEPES, and 1 mg/ml bovine serum albumin (BSA) (adjusted to pH 6.9 with NaOH). The tissue was enzymatically digested by adding 0.15 mg/ml Liberase TH (Roche) and 0.5 mg/ml elastase (Worthington Biochemical Corporation) for ~24 min at 37°C. The digested tissue was washed and transferred to a modified Kraftbrühe solution containing (in mM): 100 K + -L-glutamate, 10 K + -aspartate, 25 KCl, 10 KH 2 PO 4 , 2 MgSO 4 , 20 taurine, 5 creatine, 0.5 EGTA, 20 glucose, 5 HEPES, and 1 mg/ml BSA (pH 7.2 with KOH). Single cells were manually dissociated in Kraftbrühe solution at 37°C using a Pasteur pipette. Physiological extracellular Na + and Ca 2+ concentrations were re-established by adding aliquots of solutions containing (in mM): 10 NaCl, 1.8 CaCl 2 , and subsequently, Tyrode's solution containing 1 mg/ml BSA. Cells were used on the day of isolation.

  Quantitative fluorescence analysis was performed with the ImageJ-based open-source software package Fiji (ImageJ 1.53t)[START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF]. For each SAN cell, membrane and background regions were selected from the image at the level of the cell membrane adhering to the coverslips using the polygon selection tool, and mean fluorescence values were measured. Since HCN4 or GIRK1 immunostaining displayed distinct membrane localization, they were used as reference to observe the membrane and its regions adhering to the coverslip. The membrane regions with the co-stained GIRK4 and Ca v 1.3 respectively were co-imaged and analyzed accordingly. Membrane fluorescence values were background subtracted, obtaining one value for each cell representing the channel levels at the membrane. Absolute fluorescence values were normalized to the average fluorescence of control cells. For data presentation, representative membrane regions were selected and assembled in a composite using Photoshop version 24.1.0.Statistical analysisDatawere analyzed using IBM SPSS Statistics 27 (IBM Corporation), R version 4.1.0 (2021-05-18) and RStudio version 1.4.1717. N represents the number of cells or tissues from at least 6 mice unless specified otherwise. The approximate normal distribution of data was assessed by zvalue of skewness and kurtosis, and p-value of Shapiro-Wilk test. If normally distributed and

Figure legends \includegraphics Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .

 \includegraphics12345 Figure legends \includegraphics Fig. 1. LPS attenuates parasympathetic modulation of heart rate and its variability. Scatter plots showing mean ± SEM for (A) heart rate, (B) SDNN and (C) RMSSD in the absence (-) and presence (+) of 0.1 µM CCh and median with first and third quartile for (D) difference in pNN6 following 0.1 µM CCh perfusion in the isolated heart from LPS-injected mice vs controls. N = 6; **p < 0.01, ***p < 0.001, ns p > 0.05; mixed two-way ANOVA followed by simple effect analysis in A, B, C; percentile bootstrap based test of equal medians in D. \includegraphics Fig. 2. LPS dampens CCh-mediated negative chronotropic effect on Ca 2+ dynamics in SAN tissue. (A) Representative traces of Ca 2+ -sensitive Cal-520 fluorescence (F/F b ) depicting baseline-corrected intracellular Ca 2+ -transients over time in the SAN tissue isolated from control (left) and LPS-injected (right) mice in the absence (-) and presence (+) of 0.1 µM CCh. Scatter plots showing mean ± SEM for (B) Ca 2+ -transients/min, (C) peak amplitude and (D) RT 90 in the absence (-) and presence (+) of 0.1 µM CCh in the isolated SAN tissues from LPS-injected mice

Acknowledgements

This work was supported by research grants from the Austrian Science Funds [Hertha Firnberg T1066 and Zukunftskolleg ZK17 to S.S., stand-alone project P33225 to V.D.B.], and the Fondation Leducq [TNE FANTASY 19CVD03 to M.E.M.]. We acknowledge Diomedes E.

Logothetis for providing 3hi2one-G4.

heart rate and increase in HRV. LPS-induced sepsis reduces expression of M2R, GIRK1 and 677 GIRK4 channels, which diminishes the above mentioned effects of CCh stimulation.