Volodia Parol

Nikos Parlavantzas
email: nikos.parlavantzas@irisa.fr

Volodia Parol-Guarino
email: volodia.parol-guarino@inria.fr

GIRAFF: Reverse Auction-based Placement for Fog Functions

Keywords: Reverse Auction-based Placement for Fog Functions, Computer systems organization → Distributed architectures fog, FaaS, function-as-a-service, serverless, auction, SLA, servicelevel agreement, QoS, quality of service, testbed, Grid'5000

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INTRODUCTION

The rapid growth of data exchange creates significant scalability challenges, prompting the expansion of cloud computing into the fog computing domain [START_REF] Mahmud | Fog computing: a taxonomy, survey and future directions[END_REF]. Fog brings computing power closer to the border of the network where data is generated and consumed. This proximity alleviates bandwidth pressures on the cloud and enables low-latency application responses. A compelling programming model for developing fog applications is serverless computing [START_REF] Schleier-Smith | What serverless computing is and should become: the next phase of cloud computing[END_REF] using the FaaS model. FaaS applications are made up of stateless event-triggered functions that can be flexibly deployed along the continuum from the cloud to the Internet network border. Functions are dynamically provisioned and unprovisioned, ensuring that resources are allocated only when needed, thus promoting efficient utilization of infrastructure resources.

The delivery of FaaS applications that can optimally exploit fog infrastructures poses significant challenges. First, fog-based applications often have stringent Quality-of-Service (QoS) requirements, especially in terms of latency. For example, constrained-time use cases, such as augmented reality (AR) workloads [START_REF] Rausch | Towards a platform for smart city-scale cognitive assistance applications[END_REF], require controlled latency to ensure reliable and expected performance. Achieving such low-latency responses in the fog is difficult because fog resources are shared among highly dynamic workloads with ever-changing resource demands. Second, fog resources are owned and operated by multiple independent infrastructure providers, such as individuals, companies, communities, and established cloud and edge providers. These various providers may have different resource management strategies and should be incentivized to contribute their computational resources for hosting application functions.

Although initial research has explored the use of FaaS in fog environments [START_REF] Aslanpour | Serverless edge computing: vision and challenges[END_REF][START_REF] Bermbach | AuctionWhisk: Using an auction-inspired approach for function placement in serverless fog platforms[END_REF], currently no system effectively addresses the challenges mentioned above. The broader issue of placing computational tasks in the fog infrastructure has received significant research attention [START_REF] Sonkoly | Survey on placement methods in the edge and beyond[END_REF]. However, most of that research assumes resources are owned and managed by a single provider and ignores the realistic scenario of multi-provider infrastructures. Some research has addressed the multi-provider requirement by using market-based approaches [START_REF] Qiu | Applications of auction and mechanism design in edge computing: a survey[END_REF]. However, these systems primarily focus on economic aspects, are evaluated through simulations, and lack practical implementations that can be readily used in close-to-real-world fog deployments at scale. This article introduces a novel approach, named Global Integration of Reverse Auctions and Fog Functions (GIRAFF), to optimize the placement of FaaS applications in the fog taking into account economic concerns. The approach satisfies QoS requirements by exclusively reserving resources for functions for a specified duration while incentivizing resource providers through a market-based mechanism. In our proposed solution, clients submit function placement requests to a central marketplace. Function placement requests characterize functions through Service-Level Agreements (SLAs), which specify guarantees for network latency and required resources. The marketplace then organizes an auction in which fog nodes, owned by independent providers, compete for hosting functions by making bids. After the auction selects a fog node, the node allocates resources for a specified time to the client's function and receives payment from the client. The approach is evaluated in a close-to-real-world testbed by deploying a reproducible fog network on the Grid'5000 scientific infrastructure at scale. The article makes two main contributions:

• we propose an auction-based approach for placing FaaS functions in a multi-provider fog infrastructure; • we assess the effectiveness of our approach1 through reproducible experiments on the Grid'5000 testbed2 , comparing it with baseline algorithms, at scale.

The article continues with a review of related work (section 2) and the design section (section 3), which discusses the system model, our market-based algorithm, and its implementation.

The article then presents a comparison of the algorithm with two baselines in the evaluation section (section 4). Finally, section 5 concludes the article.

RELATED WORK

There is extensive research on the placement of computational entities in emerging fog infrastructures [START_REF] Sonkoly | Survey on placement methods in the edge and beyond[END_REF]. This research assumes that resources are issued and managed by a single entity. Some research targets multi-provider fog environments using auction-based approaches [START_REF] Qiu | Applications of auction and mechanism design in edge computing: a survey[END_REF]. However, these systems focus primarily on economic considerations, rely on simulations for evaluation, and lack practical implementations that can be readily deployed in fog environments.

In the following, we only consider work related to the placement of FaaS applications in fog environments. Bocci et al. [START_REF] Bocci | Placing faas in the fog, securely[END_REF] present a declarative approach for placing FaaS applications in a fog infrastructure using a Prolog engine. The approach considers hardware and software requirements, latency constraints, security constraints, and trust relationships between stakeholders. However, the economic goals of the stakeholders are not considered.

Rausch et al. [START_REF] Rausch | Optimized container scheduling for data-intensive serverless edge computing[END_REF] present a container scheduling system for placing FaaS functions on a fog cluster. The scheduler uses multi-objective optimization techniques, considering node capabilities, network topology, and data transfer requirements of functions. Similarly to our work, the prototype relies on OpenFaaS and Kubernetes. Unlike our approach, this scheduling system does not consider multiple clusters owned by different entities.

Bermbach et al. [START_REF] Bermbach | AuctionWhisk: Using an auction-inspired approach for function placement in serverless fog platforms[END_REF] present an auction-based function placement approach for FaaS applications running on fog platforms. In this approach, application developers specify bids on storage and processing resources, attached to function placement requests. Bids are processed in batches. Fog nodes then decide locally whether to serve the requests or offload the requests to the next node on the path towards the cloud. Unlike our approach, this work does not provide latency guarantees to clients.

Ascigil et al. [START_REF] Ascigil | Resource provisioning and allocation in function-as-a-service edge-clouds[END_REF] examine FaaS resource provisioning over computation spots distributed along the path to the cloud. This work uses simulations to evaluate various centralized and decentralized strategies for resource provisioning. Similarly to our work, FaaS functions have latency requirements. However, unlike our work, the contribution assumes that the computing infrastructure is owned by a single organization.

Baresi et al. [START_REF] Baresi | Neptune: network-and gpu-aware management of serverless functions at the edge[END_REF] propose NEPTUNE, a framework for managing serverless applications with response-time requirements on fog topologies. The framework supports function placement, request routing, function scaling, and GPU management using Mixed Integer Programming and control-theoretic techniques. NEPTUNE divides the fog topology into independent communities to simplify management but does not consider competition between these communities.

Finally, Smolka and Mann's [START_REF] Smolka | Evaluation of fog application placement algorithms: a survey[END_REF] survey analyzes 99 articles in the fog placement literature. In this survey, 88% of the articles use a simulator. Only 18% of analyzed articles tested their techniques on more than 100 fog nodes. Usually, the articles surveyed use a simulator for scaling, and they validate their results on a small testbed. One of the survey's conclusions is that most experiments are conducted on unrealistically small problem instances. In this article, we deploy up to 119 nodes. To the best of our knowledge, we are the first to experiment on a scaled-up, reproducible testbed.

GIRAFF DESIGN

This section presents our system model, the SLA contents, our auction-based placement method, the baseline methods, and the system implementation.

System Model

The actors in the system are the fog nodes, the clients, the end users, and the marketplace. Fog nodes contain resources and are owned by providers. Clients create and manage applications that use fog node resources. In our case, these applications are stateless functions that follow the FaaS paradigm. End users interact with client functions. The marketplace serves as a trusted intermediary between clients and fog nodes. It enables monetary and placement decisions using a reverse auction. In this auction, fog nodes are resource vendors, while clients are purchasers. A second-price auction [START_REF] Choi | Second-Price Auctions[END_REF] is held, in which the fog nodes submit bids, and the winner is the lowest bidder, yet gets paid the value of the secondlowest bid. This type of auction encourages fog nodes to bid their true resource cost, thus promoting economic efficiency.

The marketplace is aware of the fog topology and centralizes payment and placement mechanisms. This design choice is in line with existing security and authentication proposals [START_REF] Puthal | Secure and Sustainable Load Balancing of Edge Data Centers in Fog Computing[END_REF][START_REF] Shojafar | Internet of everything, networks, applications, and computing systems[END_REF] that aim to ensure the security of application data [START_REF] Bocci | Declarative Secure Placement of FaaS Orchestrations in the Cloud-Edge Continuum[END_REF].

Requests from end users to functions do not go through a central gateway [START_REF] Russo Russo | Serverledge: Decentralized Functionas-a-Service for the Edge-Cloud Continuum[END_REF].

Service Level Agreement

The SLA specifies the constraints that must be met for a function to run as intended by the client. SLA constraints include the following: 𝑆𝐿𝐴 𝑒𝑛𝑡𝑟 𝑦𝑝𝑜𝑖𝑛𝑡 is the entry point, that is, the node where the end user is connected (this is the ideal node to provision the function). 𝑆𝐿𝐴 𝑚𝑎𝑥_𝑙𝑎𝑡 is the maximum latency allowed for the function; the latency is defined as the delay between the request of an end user entering 𝑆𝐿𝐴 𝑒𝑛𝑡𝑟 𝑦𝑝𝑜𝑖𝑛𝑡 and its reception by a function (when the network packets are reconstructed and the function is ready to unmarshal the data; see section 3.4). 𝑆𝐿𝐴 𝑑𝑢𝑟 is the duration of the reservation. 𝑆𝐿𝐴 𝐶𝑃𝑈 and 𝑆𝐿𝐴 𝑚𝑒𝑚 denote the CPU and memory constraints.

Algorithms

This section presents GIRAFF and two baseline placement methods.

GIRAFF approach.

The interactions between the marketplace and the fog nodes are illustrated in figure 1. First, the end user who desires to use a client application contacts the client representative service (running in the cloud) to authenticate and identify as a new user (Step 1, figure 1). The client representative then sends an SLA of the required function to the central marketplace (Step 2, figure 1). The marketplace then sends the SLA to 𝑆𝐿𝐴 𝑒𝑛𝑡𝑟 𝑦𝑝𝑜𝑖𝑛𝑡 , the ideal node to serve the end user, on the network border (Step 3, figure 1). Fog nodes transmit the SLA to their neighbors as long as the constraint 𝑆𝐿𝐴 𝑚𝑎𝑥_𝑙𝑎𝑡 is respected (Step 4, figure 1). When receiving an SLA, each node responds with a bid estimating the cost of the function if they were to provision it. This approach encourages competition among providers, each acting selfishly and autonomously to achieve their own goals, while competition is kept under control by the use of second-price auctions. The algorithms run by the marketplace and fog nodes are described next. GIRAFF marketplace accepts a client's SLA as input. It uses its knowledge of the fog network to find the IP address and send the SLA to the 𝑆𝐿𝐴 𝑒𝑛𝑡𝑟 𝑦𝑝𝑜𝑖𝑛𝑡 . This node then returns a list of bids made by nodes that meet the constraints described in the SLA. The algorithm proceeds with the second-price auction and validates function provisioning on the winning node.

GIRAFF participant evaluates the cost of the SLA for the node (expressed as bid) and forwards the SLA to neighbors of the node for further evaluation. The process repeats itself. Additionally, the node increments a variable that measures the accumulated latency between the first SLA reception by a fog node and the current node. This variable is included in the request to ensure adherence to the 𝑆𝐿𝐴 𝑚𝑎𝑥_𝑙𝑎𝑡 constraint. If this constraint cannot be met, the SLA is not sent to the neighbor.

Baseline placement methods.

This subsection introduces the two baseline placement methods with which we compare our GIRAFF method; that is, the edge-furthest and edgeward methods. These methods follow a collective approach in which the fog nodes collaboratively manage their resources, disregarding their interests.

Edge-furthest seeks to anticipate future placements. The SLA is accepted by a single node, the furthest possible, while still adhering to the SLA. The motivation is to keep available resources closer to entry points, allowing more constrained functions to be accepted as they arrive. This algorithm was chosen as a straightforward approach to increase the utilization of the fog platform while respecting SLAs.

Edge-ward is an algorithm implemented in iFogSim [START_REF] Gupta | Ifogsim: a toolkit for modeling and simulation of resource management techniques in the internet of things, edge and fog computing environments[END_REF]. It establishes a path between the 𝑆𝐿𝐴 𝑒𝑛𝑡𝑟 𝑦𝑝𝑜𝑖𝑛𝑡 and the cloud. It attempts to greedily allocate the SLA at each layer, stopping at the first positive response. The algorithm ignores the latency constraint in the SLA.

Implementation

As described in section 3.3.1, our system is divided into the marketplace and fog node software. The first acts as the fog network's gateway for clients and coordinates function provisioning. The second runs on each fog node that participates in the fog network and is implemented on top of OpenFaaS3 running on K3S4 . The entire project is managed with Nix5 .

Nix is used to generate deterministic and reproducible virtual machines (VMs) for our experiments.

EVALUATION

This section discusses experimental settings, the adopted cost model, and comparisons between GIRAFF and the two baselines concerning placement quality, client spending, and deployment time.

Experimental settings

The experiments were run on Grid'5000. The servers use Intel Xeons Gold 5220 from 2019, each of which has 36 SMT threads and 96 GiB of RAM. Each server runs multiple VMs that act as fog nodes. Depending on its location in our 4layer deep fog network, each VM can use from 2 vCPUs and 4 GiB of RAM up to 16 vCPUs and 46 GiB of RAM when the node is located closer to the cloud. In our experiments, we used up to 20 servers for 119 fog nodes. The number of nodes and the network's topology are randomly generated to fit onto a certain number of servers.A fog network requires that latency be set between all pairs of VMs. To this end, we employ Netem6 , wrapped by Enoslib7 (the deployment library that we use for Grid'5000). Then, a dedicated VM acting as all end users (cf. figure 1) generates a load for 300 seconds. This load is low (low-load; one request sent every 1000 ms) or high (high-load; one request sent every 8 ms). Furthermore, the submitted functions are divided in low-latency (10𝑚𝑠 ≤ 𝑆𝐿𝐴 𝑚𝑎𝑥_𝑙𝑎𝑡 ≤ 16𝑚𝑠) and high-latency (80𝑚𝑠 ≤ 𝑆𝐿𝐴 𝑚𝑎𝑥_𝑙𝑎𝑡 ≤ 125𝑚𝑠). 𝑆𝐿𝐴 𝑚𝑎𝑥_𝑙𝑎𝑡 is randomly set between the given intervals.

Cost model

In our experiments, fog nodes adopt a cost model similar to the pricing model used by most cloud offerings (e.g., a fixed cost per vCPU per second). Allocating a resource unit at a given fog node incurs a fixed cost per second; we call this the unit cost. The unit cost typically decreases as the nodes are closer to the cloud [START_REF] Farzin | FLEX: A Platform for Scalable Service Placement in Multi-Fog and Multi-Cloud Environments[END_REF]. Thus, a fog node 𝑖 can estimate the cost of running a client's function for 𝑆𝐿𝐴 𝑑𝑢𝑟 seconds using:

𝑐𝑜𝑠𝑡 𝑖 (𝑆𝐿𝐴) = 𝑆𝐿𝐴 𝑑𝑢𝑟 × ∑ [𝐶𝑃𝑈 ,𝑚𝑒𝑚] 𝑟𝑒𝑠 𝑆𝐿𝐴 𝑟𝑒𝑠 × 𝑈 𝑛𝑖𝑡𝐶𝑜𝑠𝑡 𝑟𝑒𝑠,𝑖

Placement quality

This section evaluates the quality of the function placement produced by the methods. We first examine the placed function ratio. This is defined as the number of provisioned functions over the number of submitted functions. Second, we look at the satisfaction rate, defined as the ratio of the number of requests that arrive under the 𝑆𝐿𝐴 𝑚𝑎𝑥_𝑙𝑎𝑡 +1𝑚𝑠 threshold8 over the total received number requests per function.

Figure 2 shows the placed function ratio split into two buckets (≈ 30 and ≈ 100 nodes). We use a two-way analysis of variance (ANOVA) test followed by a Tuckey honest significant difference test to reveal differences between the placement methods for the buckets. Differences are highlighted by the use of the compact letter display procedure, in which variables are statistically indistinguishable if and only if they share at least one letter. Edge-ward is the only method that provisions significantly fewer functions when the size of the network grows. Meanwhile, GIRAFF successfully places 80% of the functions on average, which is statistically indistinguishable from the other baselines, independently of the size of the network. Figure 3 displays the mean satisfaction rate.

A one-way ANOVA followed by a Tuckey's test was used to analyze the data. It shows that in the case of both highlatency and low-latency functions, GIRAFF is indistinguishable from edge-furthest. In the case of high-latency functions, the GIRAFF satisfaction rate is 98.8% and edge-ward is 99.6%. However, in the case of low-latency functions, our method serves 94.7% of requests against 63.7% for edge-ward.

In conclusion, GIRAFF reliably places as many functions as the other baselines, regardless of the size of the fog network. Furthermore, GIRAFF manages to satisfy 49% more requests directed to low-latency functions than edge-ward.

Client spending

This section examines economic performance from the point of view of the client. The economic performance of each placement method is given by the mean monetary spending to provision a function; it is displayed in figure 5. The figure features a one-way ANOVA test followed by a Tuckey's test for each function category. When considering high-latency functions, the client spends the least using GIRAFF. For the case of high-latency high-load functions, GIRAFF is on par with edge-ward. For high-latency low-load functions, edge-ward's client spending is 3 times that of GIRAFF. Low-latency lowload functions do not show any difference between the methods. Lastly, for low-latency high-load functions, our method is similar to edge-furthest, but results in 75% more spending than edge-ward. This is expected since edge-ward does not enforce the 𝑆𝐿𝐴 𝑚𝑎𝑥_𝑙𝑎𝑡 constraint. Since low-latency functions can be provisioned on fog nodes closer to the cloud, they have lower prices (cf. section 4.2), and edge-ward shows lower spending but fails to deliver proper SLA satisfaction, as shown in figure 3. The valid comparison for that category of functions is against edge-furthest, which is similar in client spending to our method.

Deployment time

This section examines the deployment time of functions. This is the time between the arrival of the client's SLA at the marketplace (step 2, figure 1) and the start of function provisioning on the selected node (step 5, figure 1). Figure 4 illustrates the mean deployment time for high-latency and low-latency functions. A one-way ANOVA test followed by a Tuckey's test reveals that the GIRAFF mean deployment time is 2 times that of edge-ward, with an average overhead of under 300ms in this experiment. However, this difference

High-latency

Low-latency

CONCLUSION

This article proposes the GIRAFF approach to FaaS application placement in a multi-provider fog infrastructure. The approach uses an auction mechanism to distribute functions among independent fog nodes while ensuring that the latency and resource requirements of these functions are satisfied. The approach was assessed using a reproducible opensource testbed running on Grid'5000. Within this environment, we run experiments with up to 119 fog nodes. In these experiments, we evaluated GIRAFF in comparison to two baseline methods, that is, edge-ward [START_REF] Gupta | Ifogsim: a toolkit for modeling and simulation of resource management techniques in the internet of things, edge and fog computing environments[END_REF] and edge-furthest. We found that GIRAFF reduced by up to 3 times client spending on a function while maintaining the expected client's QoS. We also found that GIRAFF increased deployment time, specifically for functions with relaxed latency requirements. In conclusion, this study shows that the GIRAFF approach, featuring independent, competing fog providers, does not adversely affect performance compared to collaborative baselines. Our method makes the client spend less when possible, without being detrimental to the QoS.

The study has revealed numerous avenues for further research. We first intend to investigate the placement of directed acyclic graphs of functions. We also intend to allow for a more opportunistic approach to executing functions, in addition to always reserving resources. These additions will increase the versatility and applicability of our proposed system to more realistic fog computing scenarios.

1 . 6 6 Figure 1 :

 1661 Figure 1: Provisioning function 𝑓

Figure 2 :

 2 Figure 2: Ratio of placed functions for 𝑛-node fog networks

Figure 3 :-Figure 4 : 3 -𝜇 = 0. 3 -Figure 5 :

 34335 Figure 3: Mean satisfaction rate

https://github.com/VolodiaPG/giraff; version used here is tagged 1.0.0 and is also available in the release section along with the raw data used in section 4.

www.grid5000.fr

www.openfaas.com

k3s.io is a lightweight distribution of Kubernetes

nixos.org is a package manager for reproducibility and determinism

www.linux.org/docs/man8/tc-netem.html

discovery.gitlabpages.inria.fr/enoslib/index.html

1𝑚𝑠 is added to compensate for the lack of precision of the NTP clock and proxy overhead, cf. figure1.

ACKNOWLEDGMENTS

The experiments presented in this paper were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER, and several universities as well as other organizations. GNU parallel [20] has been used to ease parallelization across the contribution.

We thank the reviewers whose valuable comments improved the paper.


domain: info.info-bi chim sdv

text:
Pierre Couvineau

Hugo De Almeida

Bernard Maigret

Catherine Llorens- Cortes
email: c.llorens-cortes@college-de-france.fr

Xavier Iturrioz
email: xavier.iturrioz@college-de-france.fr

Involvement of arginine 878 together with Ca 2+ in mouse aminopeptidase A substrate specificity for N-terminal acidic amino-acid residues

Aminopeptidase A (APA) is a membrane-bound zinc metalloprotease cleaving, in the brain, the N-terminal aspartyl residue of angiotensin II to generate angiotensin III, which exerts a tonic stimulatory effect on the control of blood pressure in hypertensive animals. Using a refined APA structure derived from the human APA crystal structure, we docked the specific and selective APA inhibitor, EC33 in the presence of Ca 2+ . We report the presence in the S1 subsite of Arg-887 (Arg-878 in mouse APA), the guanidinium moiety of which established an interaction with the electronegative sulfonate group of EC33. Mutagenic replacement of Arg-878 with an alanine or a lysine residue decreased the affinity of the recombinant enzymes for the acidic substrate, α-L-glutamyl-β-naphthylamide, with a slight decrease in substrate hydrolysis velocity either with or without Ca 2+ . In the absence of Ca 2+ , the mutations modified the substrate specificity of APA for the acidic substrate, the mutated enzymes hydrolyzing more efficiently basic and neutral substrates, although the addition of Ca 2+ partially restored the acidic substrate specificity. The analysis of the 3D models of the Arg-878 mutated APAs revealed a change in the volume of the S1 subsite, which may impair the binding and/or the optimal positioning of the substrate in the active site as well as its hydrolysis. These findings demonstrate the key role of Arg-878 together with Ca 2 + in APA substrate specificity for N-terminal acidic amino acid residues by ensuring the optimal positioning of acidic substrates during catalysis.

Introduction

Aminopeptidase A (APA; EC 3.4.11.7) is a 160 kDa homodimeric type II Zn 2+ membranebound aminopeptidase [START_REF] Danielsen | Proteins of the kidney microvillar membrane. Aspartate aminopeptidase: purification by immunoadsorbent chromatography and properties of the detergent-and proteinase-solubilized forms[END_REF][START_REF] Glenner | A mammalian peptidase specific for the hydrolysis of N-terminal alpha-Lglutamyl and aspartyl residues[END_REF]. APA cleaves the N-terminal glutamyl or aspartyl residue from peptide substrates such as angiotensin II (AngII) and cholecystokinin-8 and is activated by Ca 2+ [START_REF] Healy | Localization of immunoreactive glutamyl aminopeptidase in rat brain. II. Distribution and correlation with angiotensin II[END_REF][START_REF] Nagatsu | Purification of aminopeptidase A in human serum and degradation of angiotensin II by the purified enzyme[END_REF]. Ca 2+ not only enhances the hydrolysis by APA of N-terminal acidic amino acid residues from substrates, but also decreases the hydrolysis of N-terminal neutral or basic residues [START_REF] Feracci | Enzymatic and immunological properties of the protease form of aminopeptidase N and A from pig and rabbit intestinal brush border[END_REF]. APA is expressed in various tissues, including the brush border of intestinal and renal epithelial cells and the vascular endothelium [START_REF] Lojda | Study on aminopeptidase A[END_REF]. This enzyme is also expressed in several brain nuclei involved in the control of body fluid homeostasis and cardiovascular function, together with other components of the brain renin-angiotensin system [START_REF] Zini | Aminopeptidase A: distribution in rat brain nuclei and increased activity in spontaneously hypertensive rats[END_REF]. Studies with the specific and selective APA inhibitor EC33 [(S)-3-amino-4-mercapto-butyl sulfonic acid] [START_REF] Chauvel | Differential inhibition of aminopeptidase A and aminopeptidase N by new beta-amino thiols[END_REF] have shown that, in the brain, APA generates angiotensin III (AngIII) [START_REF] Zini | Identification of metabolic pathways of brain angiotensin II and III using specific aminopeptidase inhibitors: predominant role of angiotensin III in the control of vasopressin release[END_REF] which exerts a tonic stimulatory action on the control of blood pressure in hypertensive animals and increases arginine vasopressin release [START_REF] Zini | Identification of metabolic pathways of brain angiotensin II and III using specific aminopeptidase inhibitors: predominant role of angiotensin III in the control of vasopressin release[END_REF][START_REF] Reaux | Aminopeptidase A inhibitors as potential central antihypertensive agents[END_REF][START_REF] Mc | Brain renin-angiotensin system blockade by systemically active aminopeptidase A inhibitors: a potential treatment of salt-dependent hypertension[END_REF]. Thus, the inhibition of brain APA with specific and selective inhibitors normalizes blood pressure in conscious hypertensive rats [START_REF] Reaux | Aminopeptidase A inhibitors as potential central antihypertensive agents[END_REF][START_REF] Mc | Brain renin-angiotensin system blockade by systemically active aminopeptidase A inhibitors: a potential treatment of salt-dependent hypertension[END_REF][START_REF] Bodineau | Orally active aminopeptidase A inhibitors reduce blood pressure: a new strategy for treating hypertension[END_REF][START_REF] Marc | Central antihypertensive effects of orally active aminopeptidase A inhibitors in spontaneously hypertensive rats[END_REF]. These studies suggest that brain APA constitutes a promising target for the treatment of hypertension [START_REF] Iturrioz | Aminopeptidase Inhibitors as Anti-Hypertensive Drugs[END_REF][START_REF] Ferreira | Aminopeptidase A: could it be a novel target for neurogenic hypertension?[END_REF][START_REF] Gao | A new strategy for treating hypertension by blocking the activity of the brain renin-angiotensin system with aminopeptidase A inhibitors[END_REF]. This justifies the development of potent and selective APA inhibitors crossing the blood-brain barrier after oral administration for use as centrally-acting antihypertensive agents. With this aim, we have pursued our studies on the APA active site organization by molecular modeling and site-directed mutagenesis. First, using the crystal structure of leukotriene-A4 hydrolase (LTA4H; EC 3.3.2.6) [START_REF] Thunnissen | Crystal structure of human leukotriene A(4) hydrolase, a bifunctional enzyme in inflammation[END_REF] as a template and the functional information collected from previous site-directed mutagenesis studies on APA [START_REF] Wang | Histidine residue in the zinc-binding motif of aminopeptidase A is critical for enzymatic activity[END_REF][START_REF] Vazeux | Identification of glutamate residues essential for catalytic activity and zinc coordination in aminopeptidase A[END_REF][START_REF] Vazeux | A tyrosine residue essential for catalytic activity in aminopeptidase A[END_REF][START_REF] Vazeux | A glutamate residue contributes to the exopeptidase specificity in aminopeptidase A[END_REF][START_REF] Iturrioz | Histidine 450 plays a critical role in catalysis and, with Ca2+, contributes to the substrate specificity of aminopeptidase A[END_REF][START_REF] Iturrioz | Study of asparagine 353 in aminopeptidase A: characterization of a novel motif (GXMEN) implicated in exopeptidase specificity of monozinc aminopeptidases[END_REF][START_REF] Rozenfeld | Contribution of molecular modeling and sitedirected mutagenesis to the identification of two structural residues, Arg-220 and Asp-227, in aminopeptidase A[END_REF], we built a three-dimensional (3D) model of the mouse APA (mAPA) ectodomain from residue 79 to 559 [START_REF] Gao | A new strategy for treating hypertension by blocking the activity of the brain renin-angiotensin system with aminopeptidase A inhibitors[END_REF][START_REF] Rozenfeld | Contribution of molecular modeling and sitedirected mutagenesis to the identification of two structural residues, Arg-220 and Asp-227, in aminopeptidase A[END_REF], including the catalytic domain. We subsequently docked into the APA active site, specific and selective APA inhibitors, such as Glu-PO 3 H 2 (4-amino-4-phosphonobutyric acid) a transition state analog [START_REF] Lejczak | Inhibition of aminopeptidases by phosphonic acid and phosphinic acid analogues of aspartic and glutamic acids[END_REF].

In the 3D model of APA, the Zn 2+ atom is coordinated by the two histidine residues (His385 and His389) of the HEXXH motif, a water molecule, glutamate 408 (Glu408) of the WLNEG motif and either by one of the oxygen atoms of the phosphate of GluPO 3 H 2 [START_REF] Rozenfeld | Contribution of molecular modeling and sitedirected mutagenesis to the identification of two structural residues, Arg-220 and Asp-227, in aminopeptidase A[END_REF]. The water molecule bound to the Zn 2+ atom also interacts with Glu-352 and Glu-386 side chains [START_REF] Vazeux | Identification of glutamate residues essential for catalytic activity and zinc coordination in aminopeptidase A[END_REF][START_REF] Vazeux | A glutamate residue contributes to the exopeptidase specificity in aminopeptidase A[END_REF]. Ca 2+ was then introduced in the APA 3D model. The Ca 2+ atom was localized at the bottom of the S1 subsite, as suggested previously by Danielsen et al. [START_REF] Danielsen | Proteins of the kidney microvillar membrane. Aspartate aminopeptidase: purification by immunoadsorbent chromatography and properties of the detergent-and proteinase-solubilized forms[END_REF]. The Ca 2+ atom interacts with the acidic side chains of Asp-213 and Asp-218, the carbonyl group of Glu-215 and three water molecules, one of them being engaged in a hydrogen bond with the negatively charged carboxylate side chains of the inhibitors [START_REF] Claperon | Asp218 participates with Asp213 to bind a Ca2+ atom into the S1 subsite of aminopeptidase A: a key element for substrate specificity[END_REF]. Site-directed mutagenesis of Asp-213 and Asp-218 (Asp-221 in human APA (hAPA)) showed that their negative charges are required for the presence of the Ca 2+ atom that ensures acidic APA substrate specificity [START_REF] Claperon | Asp218 participates with Asp213 to bind a Ca2+ atom into the S1 subsite of aminopeptidase A: a key element for substrate specificity[END_REF][START_REF] Goto | Asparatic acid 221 is critical in the calcium-induced modulation of the enzymatic activity of human aminopeptidase A[END_REF]. More recently, the X-ray structure of human APA (residues 76 to 956) was resolved [START_REF] Yang | Structural insights into central hypertension regulation by human aminopeptidase A[END_REF] and its comparison with the APA 3D model showed a perfect overlap of the catalytic regions.

In the present study, we have therefore taken advantage of the X-ray-derived structure of human APA to build a new system comprising the complete refined APA 3D structure complexed with EC33, an APA inhibitor exhibiting a inhibitory potency of 10 -7 M on APA and 100-fold less active on APN [START_REF] Chauvel | Differential inhibition of aminopeptidase A and aminopeptidase N by new beta-amino thiols[END_REF]. We visualized, in the S1 subsite, Arg-878 (Arg-887 in hAPA), which interacts with the electronegative sulfonate moiety of EC33 as observed by Yang et al in the crystal structure of human APA bound to a Glu, exhibiting an inhibitory potency of 7 x 10 -3 M on APA [START_REF] Lalu | Characterization of three aminopeptidases purified from maternal serum[END_REF]. The first data obtained by these authors on the role of Arg-887 in the absence of Ca 2+ suggested an involvement in hAPA substrate specificity [START_REF] Yang | Structural insights into central hypertension regulation by human aminopeptidase A[END_REF]. However, the Ca 2+ increases APA preference for acidic substrates and this Ca 2+ -modulated APA substrate specificity is deemed physiologically relevant since the concentrations of Ca 2+ that modulate APA activity, are in the same range as those found in brain fluid (i.e. 1-2 mM) [START_REF] Jones | Brain fluid calcium concentration and response to acute hypercalcaemia during development in the rat[END_REF]. Taking into account that Ca 2+ plays a major role in APA substrate specificity, the aim of our work was to deepen the role of Arg-878 of mAPA together with Ca 2+ in substrate/inhibitor binding and substrate specificity of APA for N-terminal acidic amino acid residues. For this purpose, we replaced Arg-878 with an alanine or a lysine residue and checked that the mutated enzymes displayed similar processing and subcellular distribution to wild-type mAPA. We then biochemically and kinetically characterized the purified recombinant wild-type and mutated enzymes with various substrates and determined their sensitivity to Ca 2+ and various inhibitors exhibiting different side chains targeting the S1 subsite of APA.

Materials and methods

Materials

Restriction endonucleases Dpn1 was obtained from New England Biolabs Inc (Evry, France) and was used according to the manufacturer's instructions. The PfuUltra High-fidelity DNA Polymerase was purchased from Agilent (les Ulis, France). The liposomal transfection reagent, Lipofectamine 2000, the pcDNA 3.1-His vector and the monoclonal anti-Xpress antibody were purchased from Life Technologies (Cergy-Pontoise, France). CHO-K1 cells were obtained from American Type Culture Collection (Manassas, VA, USA). The horseradish peroxidaseconjugated sheep anti-mouse antibody was purchased from Sigma-Aldrich (Saint Quentin Fallavier, France). The cOmplete, EDTA-free Protease Inhibitor Cocktail was purchased from Roche (Mannheim, Germany). Immobilized cobalt affinity columns (Talon) were obtained from Clontech (Heidelberg, Germany). The synthetic substrates, GluNA, AspNA, AlaNA and LysNA were purchased from Bachem (Bunderdorf, Switzerland).

Molecular docking and molecular dynamics simulations

The Crystallographic structure of human aminopeptidase A complexed with glutamate and calcium (PDB ID: 4KXD) was used to perform docking and molecular dynamics simulations. The 3D-structure was first treated to remove the Glu ligand, as well as the N-Acetyl-D-Glucosamine chains and non-conserved water molecules. Zn 2+ and Ca 2+ atoms were kept, and a loop was added for residues missing from crystallographic data (residues 608 to 611) using the software MODELLER [START_REF] Webb | Protein structure modeling with MODELLER[END_REF]. Reference inhibitors developed by our group were docked into our 3D-model using GOLD v5.1 [START_REF] Jones | Development and validation of a genetic algorithm for flexible docking[END_REF], with the ChemPLP scoring function selected and several penalties added based on the analysis of available crystallographic structures. The list of docked molecules and the applied penalties can be found in S3 and S4 Tables, respectively. In order to analyze if the predicted interactions would be conserved in a physiological and dynamical molecular system, compounds EC33 and GluPO 3 H 2 were chosen to be parametrized, and poses obtained from the automated docking process above were submitted to molecular dynamics (MD) simulations using NAMD. Briefly, small ligands were parametrized with Discovery Studio Visualizer 4.5 (BIOVIA) using CHARMm 36 forcefields [START_REF] Best | Optimization of the additive CHARMM allatom protein force field targeting improved sampling of the backbone phi, psi and side-chain chi(1) and chi(2) dihedral angles[END_REF][START_REF] Mackerell | All-atom empirical potential for molecular modeling and dynamics studies of proteins[END_REF], with atom types being assigned manually. Ligand-protein complexes were generated with VMD autopsf plug-in using the BIOVIA provided topology files. The MUTATOR plugin was used to build systems with mutated hAPAs (R887A and R887K). The obtained systems were then included in a water-box using the VMD solvate plug-in, followed by charge neutralization through the ionize plug-in. The final systems comprising ~80,000 atoms were then subjected to three stages of conjugate gradient energy minimization of 6400 steps each. The first stage had the ligandprotein complex fixed, and allowed only water to move freely. The second stage allowed ligand motions, and the last stage consisted of the energy minimization of the entire system. Those systems were then subjected to a short MD simulation of 500 ps in order to equilibrate pressure and the temperatures before proceeding to production runs. Each MD production run simulation was carried out in the NPT ensemble, with periodic boundary conditions, Particle Mesh Ewald for treating electrostatic interactions and 1 fs per time step for 50,000,000 steps, generating a trajectory of 50 ns. Trajectory analyses were performed with VMD, pair interaction calculations with NAMD and ligand binding site volume with MDPOCKET.

Cloning and site-directed mutagenesis

The cDNA encoding mouse APA [START_REF] Iturrioz | Histidine 450 plays a critical role in catalysis and, with Ca2+, contributes to the substrate specificity of aminopeptidase A[END_REF] was used as a template for the generation of mutants by PCR-based site-directed mutagenesis. The arginine residue at position 878 was replaced with either an alanine or a lysine residue. The mutated primers A (forward) and B (reverse) were:

A (5'-CAATCAATGACGCATACCTTGGCCGGATCG-3') and B (5'-GGCCAAGGTATGCG TCATTGATTGTAAATC-3') for R878A A (5'-CAATCAATGACAAATACCTTGGCCGGATCG-3') and B (5'-GGCCAAGGTATTTG TCATTGATTGTAAATC-3') for R878K

The underlined bases encode the new amino acid residue and replace the naturally occurring codon at position 2634. Nucleotide numbering corresponds to the mAPA sequence deposited in the GenBank/EBI database (accession number M29961). PCR was performed with PfuUltra High-fidelity DNA Polymerase to make a full-length plasmid PCR product. The methylated plasmid used as the template was then specifically digested with Dpn1 and Top 10 E. coli were transformed to obtain the mutated cDNA. Sequences of all constructs were checked by DNA Sequencing (GATC Biotech, Mulhouse, France).

Cell culture and establishment of stable CHO-K1 cell lines producing wild-type and mutated His-mAPAs Chinese Hamster Ovarian (CHO-American Type Culture Collection) cells were cultured in Ham's F-12 medium supplemented with 10% fetal calf serum, 0.5 mM glutamine, 100 units/ml penicillin and 100 μg/ml streptomycin (all from Life Technologies) at 37˚C in a humidified atmosphere of 5% CO 2 , 95% air. The cells were transfected with either 2.5 μg of plasmid containing the Xpress-polyHis-tagged wild-type or the Xpress-polyHis-tagged mutated mAPA cDNAs using Lipofectamine 2000 following manufacturer instructions. Stable cell lines producing the wild-type and mutated His-APAs were established as previously described [START_REF] Iturrioz | Study of asparagine 353 in aminopeptidase A: characterization of a novel motif (GXMEN) implicated in exopeptidase specificity of monozinc aminopeptidases[END_REF].

Immunofluorescence analysis of stably transfected CHO cells

Stable transfected CHO cells producing wild-type and mutated His-mAPAs were seeded (100,000 cells) onto 14-mm-diameter coverslips and grown for 24h. Then, the cells were fixed and permeabilized in 100% ice-cold methanol for 5 min on ice. After blocking with 0.5% BSA in 0.1 M PBS, coverslips were incubated with the anti-Xpress antibody (1:1000) in 0.5% BSA in PBS for 2h at 20˚C, washed thrice with cold PBS and then incubated with a 1:500 dilution of AlexaFluor 488-conjugated polyclonal anti-rabbit antibody in 0.5% BSA in PBS for 2 h at 20˚C. The coverslips were then mounted in Mowiol. The cells were examined with a Leica TCS SP V (Leica Microsystem, Heidelberg, Germany) confocal laser scanning microscope equipped with an argon/krypton laser and configured with a Leica DM IRBE inverted microscope. AlexaFluor was detected after 30% excitation at 488 nm. The images (1024 x1024 pixels) were obtained with a 63x magnification oil-immersion objective. Each image corresponded to a cross-section of the cells.

Purification and western blot analysis of wild-type and mutated recombinant His-mAPAs

Stable transfected CHO cells (3x10 9 cells) were harvested and a crude membrane preparation was obtained, as previously described [START_REF] Iturrioz | Study of asparagine 353 in aminopeptidase A: characterization of a novel motif (GXMEN) implicated in exopeptidase specificity of monozinc aminopeptidases[END_REF]. Crude membrane preparation was solubilized overnight in 50 ml of 20 mM Tris-HCL buffer (pH 8) containing 100 mM NaCl and 1% nonidet P-40 (loading buffer, 1 ml/10 6 cells ratio). The solubilized membrane preparation was centrifuged at 100,000 x g for 90 min and the supernatant was subjected to metal affinity chromatography with a metal chelate resin column (Talon Co 2+ , Clontech). The wild-type or mutated His-mAPAs were eluted with loading buffer containing 250 mM imidazole. The eluted fractions were loaded into Pierce Protein Concentrators, 150K MWCO (ThermoFisher) to concentrate the fraction and to replace the elution buffer with 20 mM Tris-HCl buffer (pH 7.4) containing 100 mM NaCl and 0.1% nonidet P-40. Protein concentrations were determined with the BCA assay kit (Calbiochem). The purity of the final preparation was assessed by NuPAGE (4-12% polyacrylamide gels, Invitrogen) and SilverQuest Silver staining (all from Life Technologies). Purified wild-type and mutated His-mAPAs were resolved by 4-12% SDS-PAGE and the proteins were transferred on a nitrocellulose membrane. His-tagged recombinant proteins were detected with the anti-Xpress antibody (1:5000 dilution). The resulting immune complex was detected with an anti-mouse antibody coupled to HRP (GE Healthcare, 1:10,000) and revealed with the ECL Plus Western blotting detection system (GE Healthcare) and image was acquired with an ImageQuant LAS 4000 (GE Healthcare).

Enzyme assay

Enzyme assays were carried out for wild-type and mutated His-mAPAs in 50 mM Tris-HCl buffer, pH 7.4, with or without 4 mM CaCl 2 , by monitoring the rate of hydrolysis of GluNA, as previously described [START_REF] Vazeux | Identification of glutamate residues essential for catalytic activity and zinc coordination in aminopeptidase A[END_REF]. The sensitivity to Ca 2+ of purified wild-type and mutated His-mAPA was determinated by incubating 0.5 mM GluNA with 0 to 4 mM CaCl 2 in a final volume of 100 μl of 50 mM Tris-HCl buffer, pH 7.4. All the assays were performed in black 96-well plates (solid black 96-well flat-bottomed non-treated plates with no lid; Corning Costar). All of the enzymatic studies were performed such that substrate hydrolysis rates were maintained below 10% (initial rate conditions). The kinetic curves were monitored by following the increase in fluorescence at 460 nm (l ex = 330 nm), induced by the release of the βnaphthylamide fluorogenic part of the substrate by APA. Fluorescence signals were monitored by counting photons with a spectrophotometer (Fusion universal microplate analyser; Packard) equipped with a temperature control device and a plate shaker. The kinetic parameters (K m and k cat ) were determined from Michaelis-Menten plots, using GraphPad Prism 4 software (GraphPad) with a final concentration of substrate (GluNA) from 0.005 to 5 mM with or without 4 mM Ca 2+ . For evaluation of the substrate specificity of APA with or without 4 mM Ca 2+ , the rate of hydrolysis of two additional substrates, α-L-aspartate-β-naphthylamide (AspNA), α-L-alanine-β-naphthylamide (AlaNA) and basic α-L-lysine-β-naphthylamide (LysNA), was determined under the same experimental conditions as described for GluNA. The sensitivity of wild-type and mutated His-mAPAs to inhibition by [(3S)-3-amino-4-sulfanyl-butane-1-sulfonic acid] (EC33), glutamate-thiol (GluSH), glutamate-phosphonic-acid (GluPO 3 H 2 ), methionine-thiol (MetSH) and lysine-thiol (LysSH) was determined by establishing dose-dependent inhibition curves for a final GluNA concentration of 0.5 mM in the presence or absence of 4 mM CaCl 2 . These compounds being linear competitive inhibitors, their K i were calculated from the formula

K i = IC 50 / (1+ [GluNA]/K m ).

Statistical analysis

Statistical comparisons were carried out with Student's unpaired t-test. Differences were considered significant if p was less than 0.05.

Results and discussion

APA belongs to the monozinc aminopeptidase family, which requires Zn 2+ for catalytic activity. In addition, the substrate specificity of APA, unlike that of other monozinc aminopeptidases, is enhanced by Ca 2+ . Indeed, APA preferentially hydrolyzes peptides with N-terminal acidic amino acids and this is due in part to the presence of Ca 2+ in the S1 subsite of the APA active site [START_REF] Iturrioz | Histidine 450 plays a critical role in catalysis and, with Ca2+, contributes to the substrate specificity of aminopeptidase A[END_REF][START_REF] Claperon | Identification of threonine 348 as a residue involved in aminopeptidase A substrate specificity[END_REF]. In the present work, we used the recent crystal structure of human APA to build a 3D model of APA complexed with EC33, a specific and selective APA inhibitor targeting the S1 subsite to explore if other residues, in addition to Ca 2+ , participate to APA acidic substrate specificity.

Molecular modeling of human APA and docking of the APA inhibitor EC33

Using the recent crystal structure of hAPA (PDB ID 4KXD, [START_REF] Yang | Structural insights into central hypertension regulation by human aminopeptidase A[END_REF]), with a bound Glu (Fig 1A and1C), we built a 3D model of hAPA complexed with EC33 (Fig 1B and1D). EC33 interacted in the S1 subsite of the APA active site with the Zn 2+ atom via its thiol group and Glu-215, Glu-352 and Glu-408 (Glu-223, Glu-360 and Glu-416 in hAPA) via their free alpha amino group. [START_REF] Rozenfeld | Contribution of molecular modeling and sitedirected mutagenesis to the identification of two structural residues, Arg-220 and Asp-227, in aminopeptidase A[END_REF]. In addition, the sulfonate group of EC33 was embedded at the bottom of the S1 subsite formed by Asp 221 and Asp 226, which bind the Ca 2+ atom. All these interactions were previously visualized in the 3D model of the mouse APA ectodomain from residues 79 to 559 that we generated by homology using the X-ray crystal structure of leukotriene A4 hydrolase (LTA4H; EC 3.3.2.6) as a template and the functional data collected from site-directed mutagenesis studies on APA [START_REF] Thunnissen | Crystal structure of human leukotriene A(4) hydrolase, a bifunctional enzyme in inflammation[END_REF].

The crystal structure of APA with a bound Glu showed the presence of Arg-878 (Arg-887 in hAPA) at the bottom of the S1 subsite, interacting with the electronegative carboxylate of Glu. We also visualized the presence of this residue in the S1 subsite of the 3D model of human APA/EC33 complex, the guanidinium moiety of which established an interaction with the sulfonate groups of EC33. Moreover, multiple sequence alignments of monozinc aminopeptidases (Fig 1E) demonstrated the presence of this Arg residue exclusively in APA.

Yang et al substituted this residue by an Ala and showed a decrease in GluNA hydrolysis and an increase in ArgNA hydrolysis by the mutated APA versus wild-type APA, all these experiments being performed in the absence of Ca 2+ [START_REF] Yang | Structural insights into central hypertension regulation by human aminopeptidase A[END_REF], suggesting that Arg-878 could participate to APA substrate specificity. However, when conducting these experiments in the absence of Ca 2+ might influence the results since one of the key features of APA is its stimulation by Ca 2+ [START_REF] Danielsen | Proteins of the kidney microvillar membrane. Aspartate aminopeptidase: purification by immunoadsorbent chromatography and properties of the detergent-and proteinase-solubilized forms[END_REF]. The enzymatic activity of APA with substrates bearing acidic amino acids at their N-terminal part increases 5 to 7-fold when the Ca 2+ concentration rises from 0 to 4 mM [START_REF] Glenner | A mammalian peptidase specific for the hydrolysis of N-terminal alpha-Lglutamyl and aspartyl residues[END_REF][START_REF] Iturrioz | Histidine 450 plays a critical role in catalysis and, with Ca2+, contributes to the substrate specificity of aminopeptidase A[END_REF]. Ca 2+ not only enhances the hydrolysis by APA of N-terminal acidic residues from substrates, but also reduces the hydrolysis of neutral or basic residues [START_REF] Feracci | Enzymatic and immunological properties of the protease form of aminopeptidase N and A from pig and rabbit intestinal brush border[END_REF]. Furthermore, we have shown, by molecular modeling and site-directed mutagenesis studies, that Asp-218 and Asp-213 bind the Ca 2+ atom into the S1 subsite [START_REF] Claperon | Asp218 participates with Asp213 to bind a Ca2+ atom into the S1 subsite of aminopeptidase A: a key element for substrate specificity[END_REF] and that Ca 2+ interacts with the side chain carboxylate of the P1 residue, ensuring the substrate specificity of APA for N-terminal acidic amino acid residues. The high degree of sequence identity (77%) between hAPA and mAPA (S1 Fig) suggested that both proteins have closely related structures. We therefore investigated the role of Arg-878 of mAPA together with Ca 2+ by molecular modeling and site-directed mutagenesis.

Site-directed mutagenesis, expression and purification of recombinant wild-type and mutated His-mAPAs

For this purpose, we replaced Arg-878 with an alanine (R878A) or a lysine (R878K) residue by site-directed mutagenesis. Wild-type and mutated His-mAPAs were then stably expressed in CHO cells. We first verified that the mutations did not affect the production and the processing of the recombinant proteins by investigating the subcellular distribution of wild-type and mutated His-mAPAs in stably transfected CHO cells by immunofluorescence staining. Confocal microscopy analysis of wild-type and mutated His-mAPAs showed that all recombinant His-mAPAs were located at the plasma membrane consistent with the correct processing of these enzymes (Fig 2A). Wild-type and mutated His-mAPAs stably expressed in CHO cells were then purified by metal affinity chromatography and purified proteins were subjected to SDS-PAGE/silver staining analysis (Fig 2B ) and Western blot analysis (Fig 2C). We showed that all recombinant His-mAPAs displayed a major mature form of 180-kDa (Fig 2B and2C) that corresponded to the mature monomeric glycosylated APA sorted from the Golgi apparatus. SDS-PAGE and silver staining analysis showed that the enzymes reached a purity higher than 90% with an overall yield of 72% and a purification factor of 118-fold.

Enzymatic activity of purified wild-type and mutated His-mAPAs

We then determined the Ca 2+ activation profile of purified recombinant wild-type and mutated His-mAPAs, using an acidic substrate, α-L-glutamyl-β-naphthylamide (GluNA) as previously described [START_REF] Iturrioz | Histidine 450 plays a critical role in catalysis and, with Ca2+, contributes to the substrate specificity of aminopeptidase A[END_REF]. We observed that wild-type mAPA was strongly activated by Ca 2+ (EC 50 = 22 ± 5 μM), with enzymatic activity increasing by 7-fold as the Ca 2+ concentration raised from 0 to 4 mM, as previously reported [START_REF] Iturrioz | Histidine 450 plays a critical role in catalysis and, with Ca2+, contributes to the substrate specificity of aminopeptidase A[END_REF]. The replacement of Arg-878 by a lysine residue, conserving the positive charge, did not change the ability of this enzyme to be activated by Ca 2+ when compared to that of the wild-type. By contrast, the replacement of Arg-878 by an alanine, a neutral residue devoid of charge, very slightly reduced activation by Ca 2+ (Fig 3A). This finding is consistent with the localization of Arg-878 (Arg-887 in hAPA) into the APA active site 3D model, but showed that Arg-878 does not contribute to Ca 2+ binding in the S1 subsite. However, the maximal enzymatic activities of R878A and R878K mutated mAPAs measured in the presence of a supramaximal concentration of Ca 2+ were significantly decreased (by a factor of 2.4 and 1.7, respectively, (Fig 3B) when compared to wild-type mAPA. Since these mutated enzymes exhibited a similar pattern of membrane expression when compared to wild-type mAPA, these defect suggest that Arg-878 could contribute to substrate recognition and hydrolysis.

Kinetic parameters for purified recombinant wild-type and mutated His-mAPAs

This led us to determine the kinetic parameters (K m and k cat ) for wild-type and mutated His-APAs in the absence or presence of 4 mM Ca 2+ using GluNA as a substrate. The results are summarized in Table 1. In the absence of Ca 2+ , the cleavage efficiency (k cat /K m ) of the mutated enzymes for the acidic substrate, GluNA was clearly reduced when compared to that of the wild-type, but less markedly (by a factor 25) for R878A than for R878K (by a factor 281). This was due to a net decrease in the affinity of the mutated enzymes for GluNA together with a slight decrease in hydrolysis velocity. The addition of Ca 2+ enhanced wild-type APA activity by increasing the affinity of the enzyme for GluNA as well as substrate hydrolysis velocity, increasing cleavage efficiency (k cat /K m ) by 25-fold. In the same conditions, a lower cleavage efficiency of the mutated enzymes for GluNA was observed when compared to wild-type but less markedly than in the absence of Ca 2+ , by a factor 21 for R878A and a factor 4 for R878K. This was due to a decrease in the affinity of both mutated enzymes for GluNA (by a factor 6) but also to a decrease in hydrolysis velocity for R878A (by a factor 4) whereas the k cat for R878K was unchanged. These findings suggested that Arg-878 of mAPA participates in the establishment of the Michaelis complex as well as in catalysis either in the presence or in the absence of Ca 2+ .

Inhibitory potency of various classes of compounds against GluNA on purified recombinant wild-type and mutated His-mAPAs

To further investigate the functional role of Arg-878, we evaluated the binding mode of various inhibitors mimicking the Michaelis complex such as the β-amino thiol inhibitors, EC33, GluSH, LysSH and MetSH by measuring their inhibitory potencies (K i ) against GluNA hydrolysis by wild-type and mutated His-mAPAs in the absence or in the presence of 4 mM Ca 2+ . These compounds interact with the amine binding site, within the S1 subsite via their acidic, basic, or neutral side chains, and with the Zn 2+ atom via their chelating thiol group. We also used the inhibitor, GluPO 3 H 2 which behaves as an analog of the transition state, mimicking the interaction of the substrate with the enzyme at the transition state by its phosphonate group that mimics the tetrahedral intermediate formed during catalysis. The structures of the inhibitors and the results are summarized in Table 2 and Table 3.

In the absence of Ca 2+ , we showed that R878A was slightly better inhibited (maximally inhibited by a factor of 2) by basic (LysSH) or neutral (MetSH) inhibitors than wild-type APA whereas R878K was less inhibited by acidic (GluSH) or neutral inhibitors than wild-type. The presence of 4 mM Ca 2+ enhanced GluSH inhibitory potency on wild-type mAPA, R878A and R878K mutants by 5.0, 1.7 and 6.6-fold, respectively, when compared to the corresponding K i values obtained in the absence of Ca 2+ . In contrast, the presence of Ca 2+ decreased the inhibitory potency of MetSH and LysSH on wild-type and mutated APAs by a factor of 12 and 42 for wild-type, 7 and 64 for R878A and 4 and 37 for R878K when compared to the K i values obtained in the absence of Ca 2+ . This showed that the presence of Ca 2+ partially restored inhibitor specificity of the mutated mAPAs for inhibitors with a N-terminal acidic amino acid residue (GluSH>MetSH>LysSH), demonstrating that the Ca 2+ atom is a major component of APA acidic inhibitor specificity. However, the affinity of EC33 and GluSH for the mutated enzymes (R878A and R878K) remains weaker (factor 3 to 9) than that for the wild-type suggesting that the interaction between the acidic side-chain of the inhibitors with APA required the positive charge of Ca 2+ in the S1 subsite but not only. Indeed, our data showed that the conservative charge of the lysine substitution is not enough to maintain an optimal positioning of the acidic inhibitors into the active site versus wild-type mAPA. This can be explained by a different orientation of the inhibitor due to the longer side chain of the lysine residue when compared to that of the arginine. Since our data showed that Arg-878 plays a role not only in the establishment of the Michaelis complex but also in catalysis, we investigated the effects of the mutations of Arg-878 on GluPO 3 H 2 binding. GluPO 3 H 2, in the presence of Ca 2+ , inhibited R878A 87-times less efficiently than wild-type, whereas it inhibited R878K 8-times less efficiently than wild-type. This different behavior of GluPO 3 H 2 regarding the mutated enzymes is in agreement with data obtained on the hydrolysis of GluNA. Altogether, our data suggested that Arg-878 played a key role in substrate specificity of mAPA towards substrates with a Nterminal acidic amino acid residue by contributing with the Ca 2+ in the S1 subsite to interactions with the electronegative charge of the P1 substrate side chain.

Molecular dynamics simulation analysis

To better understand the effects of mutations on inhibitor binding and substrate accessibility, we performed MD simulations with wild-type and mutated hAPAs in the presence of Ca 2+ and various inhibitors. Pair interaction analysis revealed that the docked inhibitors (EC33 and GluPO 3 H 2 ) were kept stable at the active site of wild-type hAPA during the entire simulation (Fig 4A ) and the average interaction energies between the inhibitor and the protein versus those obtained between the inhibitor and the solvent were determined (Fig 4A). Wild-type displayed an average interaction energy of -270.1 ± 17.5 kcal/mol for EC33, and -299.5 ± 17.6 kcal/mol for GluPO 3 H 2 . Following virtual mutation, those energies became less spontaneous (less negative), but still favorable for inhibitor binding, agreeing with our experimental data. The substitution of Arg-887 by an alanine (R878A mutant in mAPA) decreased the binding of the inhibitors with an average interaction energy of -278.1 ± 8.9 kcal/mol for EC33 and of -254.5 ± 13.3 kcal/mol for GluPO 3 H 2 . Regarding the more conservative R887K mutation, interaction energies were close to those of the wild-type model (-225.6 ± 10.9 kcal/mol for EC33 and -298.9 ± 11.6 kcal/mol for GluPO 3 H 2 ). Indeed, the substitution of Arg-887 by an alanine leads to a strong decrease in the energy of interaction of GluPO 3 H 2 with the hAPA active site that can be due to a major modification of the electropositive environment of the S1 subsite. In addition, the higher interaction between GluPO 3 H 2 and the solvent observed with the R887A mutant led to a decrease in the affinity of the inhibitor towards the R887A mutated enzyme. On the other hand, the fact that the inhibitory potency of GluPO 3 H 2 towards the R878K mutant is less impacted than that towards R878A mutant, could be explained by the fact that the ε amine moiety of the lysine residue maintains the electropositive environment of the S1 subsite. This hypothesis is further supported by the fact that isolated pair interaction analysis performed between single residues and the inhibitors revealed that the Lys-887 substitute is able to interact spontaneously with both EC33 and GluPO 3 H 2 (Fig 4B able to interact with the EC33 inhibitor, Lys-887 is not as efficient as Arg-887 from the wildtype APA. We then analyzed the effect of the mutations on the volume of the S1 subsite. For this purpose, we extracted the binding site volume information from our MD simulations trajectories (Fig 4C, S1, S2 and S3 Movies). Although the lysine being a bulkier amino acid than alanine, the binding site volume of this mutant was significantly higher than that of R887A or wild-type hAPA, regardless of the inhibitor (EC33 or GluPO 3 H 2 ). The binding pocket volume averages for the APA + EC33 simulation were, 1194 ± 196 Å 3 , 821 ± 130 Å 3 and 1828 ± 253 Å 3 for wild-type, R887A and R887K, respectively. For the hAPA + GluPO 3 H 2 system, those values were 831 ± 137 Å 3 , 833 ± 149 Å 3 and 1634 ± 206 Å 3 for wild-type, R887A and R887K, respectively. The change in the volume of the S1 subsite observed with the R878K mutant, may impair the binding and/or the optimal positioning of the substrate as well as its hydrolysis, resulting in a lower cleavage efficiency (k cat /K m ) of GluNA and a lower inhibitory potency of GluPO 3 H 2 with the R878K mutated enzyme when compared to the wild-type enzyme. This strengthened the conclusion that Arg-878 is located in the mAPA S1 subsite and therefore may drive APA substrate specificity for N-terminal acidic amino acid residues. These changes were more marked in the absence than in the presence of Ca 2+ , supporting that Arg-878 together with Ca 2+ plays a crucial role in APA acidic substrate specificity.

Hydrolysis of various substrates by wild-type and mutated His-mAPAs

To strengthen the hypothesis that Arg-878 is involved in substrate specificity for N-terminal acidic amino acid residues, we evaluated the efficiency of hydrolysis of the wild-type and mutated His-mAPAs with various substrates differing by their side-chains. We therefore determined the kinetic parameters of wild-type and the mutated enzymes for the substrates, GluNA, AspNA, AlaNA and LysNA, in the absence or presence of Ca 2+ and we compared their substrate hydrolysis profiles (Fig 5, S1 and S2 Tables). In the absence of Ca 2+ , the substrate hydrolysis profile for wild-type mAPA was GluNA = AspNA > LysNA > AlaNA. This profile was changed by Arg-878 substitutions. The substrate profile for R878A was LysNA > AlaNA > GluNA = AspNA and for R878K AlaNA = LysNA >> GluNA > AspNA. The analysis of the kinetics parameters of wild-type and mutated mAPAs showed that the modifications in the substrate hydrolysis profile observed for the mutated mAPAs were due to an increased substrate hydrolysis velocity and to a better affinity of the mutated enzymes for AlaNA and LysNA when compared to that for GluNA or AspNA. The addition of Ca 2+ amplifies the preference of wild-type mAPA for acidic substrates. Thus, GluNA and AspNA were much more efficiently hydrolyzed than LysNA, which was hydrolyzed more efficiently than AlaNA (GluNA > AspNA >> LysNA > AlaNA). This profile was partially maintained in R878K with the conservative mutation. In contrast, the R878A mutant in the presence of Ca 2+ , similarly hydrolyzed GluNA, AspNA, AlaNA and LysNA. Altogether, these data confirmed that Arg-878 participates with Ca 2+ to APA acidic substrate specificity. Additionally, in the presence of Ca 2+ , the hydrolysis efficiency of GluNA by R878K and R878A remained 4-and 21-fold weaker than that of the wild-type, respectively. Since in the cerebrospinal fluid, the Ca 2+ concentration fluctuates from 4.3 mM to 5.9 mM [START_REF] Robertson | Ionized calcium in body fluids[END_REF], which is 40 times higher than the EC 50 of Ca 2+ for APA. This suggests the constant presence of Ca 2+ in the S1 subsite of endogenous APA, which consequently recognizes only APA substrates or inhibitors with an N-terminal acidic side chain, highlighting the key role of Arg-878 with Ca 2+ in APA substrate specificity.

In conclusion, we showed that the guanidium moiety of Arg-878 in the mAPA S1 subsite interacts with the N-terminal acidic amino acid residue of the substrate or inhibitor, participating with Ca 2+ to the substrate specificity of APA for N-terminal acidic amino acid residues. We also showed that Arg-878 contributes to ensure an optimal positioning of the substrate during catalysis, thereby optimizing the hydrolysis of the substrate scissile peptide bond. In addition, our work showed that, whereas Arg-878 is far from the consensus sequence HEXXH and other active site contributing residues in term of primary sequence, this residue is very close from the active site with regard to the 3D structure. Indeed, the X-ray structure of APA shows that the C-terminal domain that contains the Arg-878 residue is in close contact to the region of the active site and complement by this way the structure of the S1 subsite. These new insights into the organization of the APA S1 subsite showed that this subsite is at the interface of the N-and C-terminal domains of APA and that the C-terminal domain has not only a chaperone activity as previously demonstrated but also a functional role in the S1 subsite, in substrate recognition [START_REF] Iturrioz | Histidine 450 plays a critical role in catalysis and, with Ca2+, contributes to the substrate specificity of aminopeptidase A[END_REF][START_REF] Rozenfeld | The C-terminal domain of aminopeptidase A is an intramolecular chaperone required for the correct folding, cell surface expression, and activity of this monozinc aminopeptidase[END_REF].

Supporting information

S1

Fig 1 .

 1 Fig 1. Human Aminopeptidase A with bound glutamate in the crystallographic structure and the proposed binding mode of the inhibitor EC33 after molecular docking in the 3D-model of human APA. (A and C), S1 subsite visualized in the crystallographic structure of APA co-crystallized with the glutamate (green) (PDB ID 4KXD). (B and D), S1 subsite visualized in the 3D-model of human APA after molecular docking of EC33 (orange). Protein residues either blocking the visualization or interacting with ligands are represented with a transparent surface. Predicted hydrogen or metallic bonds are drawn as dashed lines. Interacting protein residues are labeled (C and D) accordingly to the human APA numeration. (E), Alignment of the human and mouse APA amino acid sequences with the sequences of other monozinc aminopeptidases from the M1 family. Residues in bold are the Arg-887 of human APA and the Arg-878 of mouse APA. APA, Aminopeptidase A; APN, Aminopeptidase N; APB, Aminopeptidase B; LTA4H, Leukotriene A4 hydrolase; TRHDE, Thyrotropin releasing degrading enzyme; IRAP, Insulin regulated aminopeptidase. https://doi.org/10.1371/journal.pone.0184237.g001

Fig 2 .

 2 Fig 2. Expression and purification of wild-type and mutated mouse recombinant His-APAs. (A), Transfected CHO cells stably expressing the wild-type or mutated Xpress-His-mAPA construct were fixed and immunolabeled with a mouse monoclonal anti-Xpress primary antibody, which was detected with an Alexa 488-conjugated anti-mouse secondary antibody. Immunofluorescence was monitored by confocal microscopy. The bar indicates 10 μm. (B and C), Purified recombinant wild-type and mutated Xpress-His-mAPA were analyzed by SDS-PAGE 4-12% and proteins were silver stained (B) or transferred into nitrocellulose membrane and subjected to Western blot analysis using mouse monoclonal anti-X-press antibody (C). The arrows indicate the monomeric form of APA. https://doi.org/10.1371/journal.pone.0184237.g002

Fig 3 .

 3 Fig 3. Effects of the divalent cation Ca 2+ on recombinant wild-type and mutated mouse APAs enzymatic activities. Purified mAPAs (2 μg) were incubated at 37˚C for 30 min with 0.5 mM GluNA with various concentrations of CaCl 2 in a final volume of 100 μl of 50 mM Tris-HCl buffer (pH7.4). (A), APA enzymatic activities expressed as a percentage of maximal hydrolysis velocity obtained with 4 mM Ca 2+ for each purification vs log of Ca 2+ concentration. (B), Effect of increasing Ca 2+ concentration on APA enzymatic activities. https://doi.org/10.1371/journal.pone.0184237.g003

Fig 4 .

 4 Fig 4. Analysis of the molecular dynamics simulations trajectories reveals loss of inhibitor affinity for the mutated hAPAs and a larger active site pocket for the R887K mutant. (A), The pair interaction energies analysis between inhibitor and protein (blue) or inhibitor and solvent (red) indicate less spontaneous interactions between inhibitors and the mutant R887A when compared to wild-type hAPA. (B) Pair interaction energies analysis between residue 887 in the wild-type or mutated hAPAs and the inhibitors shows that the Arg-887 from the wild-type APA and the Lys-887 of the R887K mutant spontaneously interact with EC33 and GluPO 3 H 2 . (C), Pocket volume was extracted from the trajectories after removing the docked inhibitors, showing that the R887K mutant exhibits a larger binding pocket. Each point in the scatter plots correspond to the values calculated from a different frame in the MD trajectories, vertical bars illustrate the minimum and maximum values for each calculation, horizontal bars correspond to the means. https://doi.org/10.1371/journal.pone.0184237.g004

Fig 5 .

 5 Fig 5. Hydrolysis of various substrates, GluNA, AspNA, AlaNA and LysNA, by recombinant mAPAs. Recombinant wild-type and mutated mAPAs hydrolysis efficiencies were evaluated using GluNA, AspNA, AlaNA and LysNA as a substrate in the absence (A) or presence (B) of 4 mM Ca 2+ . The data are the mean ± S.E of five to seven experiments performed in duplicate. *** p< 0,001; ** p< 0,01; * p< 0,05 and n.s (not significant) when compared with the value obtained for GluNA. https://doi.org/10.1371/journal.pone.0184237.g005

Table 1 . Kinetic parameters for wild type and mutated mAPAs in the absence or presence of Ca 2+ using HGluβNA as a substrate.

 1

	Recombinant APAs		No Ca 2+			4 mM Ca 2+
		K m	k cat	k cat /K m	K m	k cat	k cat /K m
		(μM)	(s-1)	(s-1/mM)	(μM)	(s-1)	(s-1/mM)
	Wild type	165 ± 13.5	13.9 ± 0.1	84.3	39.1 ± 3.9	81.7 ± 4.0	2090
	R878A	1500 ± 79.6***	4.95 ± 0.1***	3.3	221 ± 4.0***	22.4 ± 0.1***	102
	R878K	12500 ± 1450***	3.12 ± 0.4***	0.3	269 ± 5.1***	135 ± 1.3***	502
	K

m and k cat values are the mean ± S.E.M from six to eight separate experiments performed in duplicate *** p<0.001, significant when compared to the corresponding wild type value https://doi.org/10.1371/journal.pone.0184237.t001

Table 2 . Ki values (nM) for several inhibitors with wild-type and mutated recombinant mAPAs targeting the S1 subsite in absence of calcium.

 2 Ki values are the mean ± S.E.M from seven separate experiments with duplicate determinations *** p<0.001 and n.s (not significant) when compared with the corresponding wild type values https://doi.org/10.1371/journal.pone.0184237.t002

		WT	R878A	R878K
	GluSH	1570 ± 270	1720 ± 190 n.s	> 10000
	MetSH	750 ± 46	475 ± 140***	1250 ± 57***
	LysSH	317 ± 30	118 ± 13***	378 ± 20 n.s

Table 3 . Ki values (nM) of several inhibitors with wild-type and mutated mAPAs targeting the S1 subsite in presence of calcium.

 3

		WT	R878A	R878K
	GluSH	314 ± 33	983 ± 160***	2100 ± 440***
	EC33	268 ± 22	2000 ± 200***	1520 ± 126***
	GluPO 3 H 2	74 ± 7.7	6500 ± 240***	619 ± 21***
	MetSH	9180 ± 770	3220 ± 200***	5140 ± 560***
	LysSH	13400 ± 1700	7510 ± 660***	13900 ± 390 n.

s Ki values are the mean ± S.E.M from seven separate experiments with duplicate determinations *** p<0.001 and n.s (not significant) when compared with the corresponding wild-type values https://doi.org/10.1371/journal.pone.0184237.t003

  ). For the EC33 inhibitor, the calculated energies were -59.64 ± 5.05 kcal/mol for the Arg-887 of the wild-type hAPA, -6.58 ± 1.35 kcal/mol for the Ala-887 of the R887A mutant and -27.19 ± 6.35 kcal/mol for the Lys-887 of the R887K mutant. For the GluPO 3 H 2 inhibitor, the calculated values were -59.26 ± 9.32 kcal/mol for the Arg-887 of the wild-type hAPA, -11.15 ± 1.03 kcal/mol for the Ala-887 of the R887A mutant, and -20,22 ± 3.58 kcal/mol for the Lys-887 of the R887K mutant. Furthermore, the distance between the ε nitrogen atom from the Lys-887 sidechain of the R887K mutant and the sulfonate moiety of the EC33 inhibitor fluctuated from 3.06 to 6.39 Å during the entire simulation, suggesting that this substitution was not engaged in a stable conformation with the EC33 inhibitor (S2 Fig), which might explain why this mutant was still impacted regarding inhibitor binding. Together those results imply that, despite still being

Table. Kinetic parameters for wild type and mutated mAPAs in absence of calcium, using different synthetic substrates

  . K m and k cat values are the mean ± S.E.M from six to eight separate experiments performed in duplicate. (DOCX)

PLOS ONE | https://doi.org/10.1371/journal.pone.0184237 September 6, 2017

Acknowledgments

We thank Je ´re ´mie Teillon of the CIRB for microscopy core facility. We acknowledge GENCI, as part of the molecular dynamics simulations were performed thanks to an allocation of computer time on the CINES supercomputer OCCIGEN.

This work was supported by the Institut National de la Sante ´et de la Recherche Me ´dicale, the Centre National de la Recherche Scientifique, the Collège de France. P. C. and H. D. A. were supported by fellowships from the Agence Nationale pour la Recherche RPIB and LabCom. P.C. has been also supported by a fellowship from Labex MemoLife (Paris Sciences et Lettres). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

All relevant data are within the paper and its Supporting Information files.

S2 Table. Kinetic parameters for wild type and mutated mAPAs in presence of