Silvia Ghilezan

Simona Kašterović
email: simona.k@uns.ac.rs

Luigi Liquori
email: luigi.liquori@inria.fr

Bojan Marinković
email: bojanm@mi.sanu.ac.rs

Zoran Ognjanović
email: zorano@mi.sanu.ac.rs

Tamara Stefanović
email: tstefanovic@uns.ac.rs

Federating Digital Contact Tracing using Structured Overlay Networks

Keywords: Covid-19, Digital Contact Tracing, Distributed Hash Tables, Structured Overlay Networks, Bluetooth, GPS

In this paper we present a comprehensive, yet simple, extension to the existing systems used for Digital Contact Tracing in Covid-19 pandemic. The extension, called BubbleAntiCovid19 (BAC19), enables those systems, regardless of their underlying protocol, to enhance their sets of traced contacts and to improve the global fight against pandemic during the phase of opening boarders and enabling more traveling. BAC19 is a structured overlay network, or better, a Federation of mathematical Distributed Hash Tables. Its model is inspired by the Chord and Synapse structured overlay networks. The paper presents the architecture of the Overlay Network Federation and shows that the federation can be used as a formal model of Forward Contact Tracing.

Introduction

One of the biggest challenges of today is to slow down the spreading of SARS-CoV-2 virus producing Covid-19 pandemic; Prevention, Testing and Tracing are the main pillars of the solution. Contact Tracing of an infected person is essential to control the spread of the disease.

Tracing. Contact tracing is the process of identifying, notifying, and monitoring people who came in close contact with an individual who was tested positive for an infectious disease, like Covid-19, while he/she was infectious. Contact tracing benefits the fight with the pandemic at multiple levels. Identifying and quarantining close contacts limits their ability to spread the disease. Therefore, in a period in which the disease and its effects are still being investigated, contact tracing plays a key role in preventing the further spread of the disease. Furthermore, contact tracing data helps medical experts to find the origin of the virus and learn more about the nature of the virus.

Manual Contact Tracing. Contact tracing has mostly been done manually since many centuries ago just by taking note on a simple piece of paper the list of persons and goods you get in contacts with (see e.g. La Peste by A. Camus [START_REF] Camus | La peste[END_REF]). In the actual days, manual contact tracing could be exploited using simple telephone calls. Identifying contacts is done through an interview with the person infected with the virus. Each person is then contacted by phone. Health Authorities should quickly alert people who are close contacts that they may have been exposed to the virus. The sooner the contacts are notified, the lower the risk of the spreading further. However, due to the highly contagious nature of the SARS-CoV-2 virus and the fact that symptoms can manifest after many days (or even never, e.g. asymptomatic cases), manual contact tracing does not give satisfactory results.

Health departments and authorities do not have enough employees to do manual contact tracing. It must be further emphasized that the SARS-CoV-2 can be transmitted not only by direct contact, but also by indirect contact. The reason is that infected people can leave virus droplets on any physical object they touch. In this case, manual contact tracing is ineffective. For the reasons stated above, digital contact tracing has been considered already at the beginning of the Covid-19 pandemic.

Problem

There is a plethora of digital contract tracing applications in use all over the world fighting the Covid-19 pandemic [START_REF]ETSI: Comparison of existing pandemic contact tracing systems[END_REF][START_REF] Martin | Demystifying COVID-19 Digital Contact Tracing: A Survey on Frameworks and Mobile Apps[END_REF]. They are developed on very different paradigms, centralized [START_REF] Castelluccia | ROBERT (ROBust and privacy-presERving proximity Tracing protocol)[END_REF] vs. decentralized [START_REF] Troncoso | Decentralized Privacy-Preserving Proximity Tracing[END_REF], GPS based (very few indeed because of a clear violation of privacy) vs. Bluetooth Low Energy based (the majority). The rush to make these applications work in the shortest time led to their great diversity. The most important open problem is their interoperability. There are many ongoing efforts to make a federation of these different systems. Herein, we address this problem and propose a solution based on mathematical models of overlay networks.

Contributions

We develop a formal federation overlay network, called BubbleAntiCovid19 (BAC19), for connecting different digital contact tracing applications, which are currently in use all over the world. The model is based on the well-known model of Structured Overlay Network protocols like e.g. Chord [START_REF] Stoica | Chord: A scalable peer-to-peer lookup service for internet applications[END_REF][START_REF] Stoica | Chord: a scalable peer-to-peer lookup protocol for internet applications[END_REF], Kademlia [START_REF] Maymounkov | Kademlia: A peer-to-peer information system based on the XOR metric[END_REF], Synapse [START_REF] Liquori | Synapse: A scalable protocol for interconnecting heterogeneous overlay networks[END_REF]. We prove that BAC19 provides a complete and fully exhaustive retrieving procedure of people that get in touch with other people having tested positive to the Covid-19 disease. Hence, BAC19 is proven to be a simple yet powerful interconnection of already existing digital contact tracing applications that -by construction -do not communicate with each others as such providing their efficient interoperability.

As far as we know, the mathematical model and techniques presented in this paper have not been considered in other approaches.

Overlay networks in a Nutshell.

Structured Overlay Networks are suitable models of scalable and efficient organization of resources on the Internet. They represent logical organizations, independent on underlying network infrastructure that physically connects available assets. Overlay networks have been proven as very resilient tool in the situation when some parts of the underlying infrastructure fail or become overloaded or corrupted.

Organization of the Paper

The rest of the paper is organized as follows. Section 2 presents classifications of digital contact tracing applications. Section 3 reviews Chord and Synapse protocols of overlay networks. Section 4 briefly reviews basic notions of Abstract State Machines and some related work by the authors. Section 5 introduces the BAC19 system and proves the completeness and full exhaustiveness of the retrieving procedure. Section 6 presents a discussion on other proposals for providing interoperable frameworks for digital contact tracing. Section 7 concludes the paper. Appendix give an overview of different digital contact tracing applications that are in current use against the pandemic.

Digital Contact Tracing Applications

Advances in digital technology have enabled smartphones and other digital devices to be used for contract tracing. Particularly, more and more countries are showing interest in digital contact tracing applications (DCT apps) implemented for smartphones. Despite the great variety among these applications, all contact tracing apps work on the principle of automatic data exchange with nearby devices. When a user of a particular contact tracing app is identified as infected, a special report is uploaded to the DCT app server. Based on that report, close contacts of the infected person (also DCT app users) are informed that they have been in a contact with a positive user and/or the app calculates their exposure risk. The identity of the infected persons is not disclosed in order to protect their privacy.

Existing contact tracing apps can be classified based on two criteria:

-Contact-tracing technology;

-System architecture.

More information about the classification of the existing contact tracing apps can be found in [START_REF] Ocheja | Quantifying the privacy-utility trade-offs in COVID-19 contact tracing apps[END_REF][START_REF] Tang | Privacy-preserving contact tracing: current solutions and open questions[END_REF].

Classification by Contact-Tracing Technology

In order for two people to be in close contact, they need to stay in the same place, at a short distance, for a long enough period of time. Therefore, the main data type used by the contact tracing apps is location data. There are various technologies for collecting and tracking location data, and contact tracing apps can be divided into two major categories depending on whether they track absolute or relative location:

-Absolute location apps -Apps that track the absolute location of their users are mostly based on GPS technology. Location data is stored in the form of geolocation coordinate pair. These apps are also known as Geolocation-based DCT apps.

-Relative location apps -Apps that track relative location of their users are mostly based on Bluetooth technology. These apps are also known as proximity DCT apps.

A boarding pass or a ticket for a specific event can also be considered as relative location data. In order to use this kind of data, some contact tracing apps deploy QR code technology.

Classification by System Architecture

Since the data is collected from users, their processing should be addressed. When it comes to DCT app data managing, the responsibility can be on a central authority or on each user individually. Therefore, contact tracing apps can be divided into three major categories depending on the architecture of the underlying system:

-Centralized apps -data are solely managed by a central server;

-Hybrid apps -multiple nodes can manage the data, but the control is centralized; -Decentralized apps -each user is managing his/her data.

In centralized apps, the central server is responsible for ID generation, risk analysis and notifications. In decentralized apps these functionalities are moved to the user devices and the central server is only an encounter point. The hybrid architecture proposes decentralized ID generation and centralized risk analysis. There are a few proposed hybrid contact tracing protocols, but their implementation in real contact tracing apps is still waiting. More about these protocols can be found in [START_REF] Ahmed | A Survey of COVID-19 Contact Tracing Apps[END_REF]. For that reason, we will focus on apps with centralized and decentralized architecture, and we will provide an overview of the existing contact tracing apps based on the above classifications in Appendix. A. The results are summarized in Figure 1, which is motivated by [START_REF] Ocheja | Quantifying the privacy-utility trade-offs in COVID-19 contact tracing apps[END_REF]. Two main advantages of geolocation-based DCT apps are the following: 1) Geolocation-based DCT apps are compatible with manual contact tracing. Compatibility of geolocation-based DCT apps and manual contact tracing has mutual benefits.

On the one hand, past geo-trajectories of a patient can be added to an app by the contact tracer even if the patient did not use the app. This enables the app to warn more users. On the other hand, the app can give the information about places with higher exposure risk to a contact tracer, so that the contact tracer can identify high-risk service workers.

2) Another advantage is that geolocation-based DCT apps can recognize patterns of disease's spreading and locations with higher exposure risk, and they can inform health authorities about it.

Nevertheless, geolocation-based DCT apps have also disadvantages. The major challenges are privacy concerns, which cause low adoption rate of these applications. User's privacy can be violated in several ways. Recording all user's trajectories can result in revealing user's personal information such as identity, home address, work address, the identity of the patient and revealing user's exposure risk to other users. These problems have been elaborated in more details in [START_REF] Cheng | KHOVID: interoperable privacy preserving digital contact tracing[END_REF].

Bluetooth-based Apps

Bluetooth-based DCT apps record direct contacts of the users. A device generates a unique, randomized identifier and assigns it to a user. There are two kinds of identifiers: static, identifiers do not change over time, and dynamic, identifiers change over time.

During a direct contact devices exchange identifiers and save received identifiers. Once a user is identified as positive in the application, other users can calculate their exposure risk by checking whether they received a patient's identifier. We give a brief review of the existing Bluetooth-based apps in Appendix A.2.

Depending on whether the exposure risk is calculated by the central server or the user's device, we have centralized and decentralized apps, respectively, see Figure 2, which is motivated by [START_REF] Huang | On the privacy and integrity risks of contacttracing applications[END_REF].

Centralized apps raise privacy concerns and questions about massive surveillance.

People often do not trust servers and as a consequence there is a low adoption rate of these applications. On the other hand, the advantage of centralized apps is the possibility for health authority to make a transmission graph and learn more about the virus. Also, the possibility of false positive users is reduced.

As we have already observed, privacy issues lead to low adoption rate and decrease the efficiency of the application. In order to solve the problem of distrust of the central server, decentralized apps were designed. However, decentralized methods also raise some privacy concerns, for example the identity of a patient can be easily revealed.

The major disadvantage is that Bluetooth-based DCT apps work only if both users have installed the same application.

In order to take advantage of both types of these apps, Bluetooth-GPS apps were designed, see Appendix A.3. Given the different characteristics of DCT apps, the question arises whether it is possible to aggregate their data in order to track contacts more effectively. The answer can be found in overlay networks.

Overlay Networks

Overlay networks are the way to organize available assets, as mentioned in Section 1. Some overlay networks are implemented in a form of Distributed-Hash-Tables (DHTs).

One of DHT protocols is the Chord protocol. It was introduced in [START_REF] Stoica | Chord: A scalable peer-to-peer lookup service for internet applications[END_REF][START_REF] Stoica | Chord: a scalable peer-to-peer lookup protocol for internet applications[END_REF]. Nodes that are part of a Chord system form a ring shaped network. The basic operations of a Chord node are entering and leaving the system and the mapping given key onto the corresponding node of the system using consistent hashing.

The correctness and efficiency of the Chord's protocol lookup procedure was in the focus of several papers, e.g. [START_REF] Marinković | Proving properties of the chord protocol using the ASM formalism[END_REF][START_REF] Marinković | Correctness of the chord protocol[END_REF][START_REF] Stoica | Chord: A scalable peer-to-peer lookup service for internet applications[END_REF][START_REF] Stoica | Chord: a scalable peer-to-peer lookup protocol for internet applications[END_REF]. However, these properties will not be in the focus of this paper. Our goal is to deliver information of every affected node, so we will not use any presented improvements to speed up the process of getting results, but to linearly pass every node in a Chord network, to be sure that no information is missed.

Interconnection of several overlay networks is a very hard problem since different networks may use different protocols, and even in the case of several DHT networks that use the same protocol (e.g. Chord) it is enough that every overlay network uses its own hash function and information between two of them cannot be exchanged. A proposal to solve this issue was given by defining the Synapse protocol in [START_REF] Liquori | Synapse: A scalable protocol for interconnecting heterogeneous overlay networks[END_REF]. Its performances were analyzed in [START_REF] Marinković | Analyzing the exhaustiveness of the synapse protocol[END_REF], whereas one real-life proof of concept was developed in [START_REF] Marinković | A distributed catalog for digitized cultural heritage[END_REF]. For the purpose of this paper we will consider the so-called, white-box version of the Synapse protocol that, in short, allows to consider all the keys as they were using the same hash table (see [START_REF] Liquori | Synapse: A scalable protocol for interconnecting heterogeneous overlay networks[END_REF] for details). Again, since we will use the linear search procedure in one Chord network we can be sure that information will be retrieved if it exists in the system.

Abstract State Machines and Chord

In this section, we briefly review basic notions of Abstract State Machines.

Abstract State Machine (ASM) [START_REF] Börger | Abstract State Machines. A Method for High-Level System Design and Analysis[END_REF][START_REF] Gurevich | Evolving algebras 1993: Lipari guide[END_REF] is a formalization method to model algorithms at the appropriate abstraction level. An ASM A is defined as a program P rog which consists of:

an at most countable set of states, its subset of initial states, and a finite number of transition rules, where states are first order structures over a fixed signature, whereas transitional rules:

update (:=), sequential (seq . . . endseq), conditional (if . . . then . . . else . . . endif ), parallel (par . . . endpar), nondeterministic (choose v ∈ U satisfying g(v) . . . endchoose) and universal (forall v with g . . . endforall) represent next-state functions. An execution of one of the last two types of rules introduces a variable v. In the case of nondeterministic rule, the transition is executed with a value of v which satisfies a guard g, while in the case of universal rule, the transition is executed simultaneously for all values v which satisfy a guard g. An ASM can interact with its environment using external functions (oracles) by providing arguments to oracles and receiving the corresponding results.

In a distributed case with many agents, every agent executes its own program and has its own partial view of a global state. The nullary function M e allows an agent to identify itself among other agents. The global program is the union of all agents' programs, whereas a transition between two states is obtained by an evaluation of transition functions of all agents.

An ASM A models a real system S in terms of evolution of states described by runs.

A run of A is a (in)finite sequence of S 0 , S 1 , S 2 , . . . where S 0 is an initial state, and every S i+1 is obtained from S i by executing a transitional rule. In this paper we consider only the runs in which states are global and agents' moves are atomic (instantaneous).

The most general kind of runs for a distributed ASM are partially ordered runs. To prove properties of partially ordered runs, thanks to the results proved in [START_REF] Gurevich | Evolving algebras 1993: Lipari guide[END_REF], the attention may be restricted to their linearizations that are sequential runs and satisfy the following fundamental properties:

-All linearizations of the same finite initial segment of a run have the same final state.

-A property holds in every reachable state of a run iff it holds in every reachable state of any of its linearization.

Note that this implies that it is enough to find only one sequence of transitions and the runs that are considered here and start from the same initial state will have the same final state.

The key notions introduced in [16, Definition 5.1] are:

stable states in a Chord network, where a state of a network is stable if the successor (predecessor) pointers of all nodes form an ordered ring, and regular runs, where a run is regular if it is a linearization such that nodes leave and enter the network only in stable states.

Having these notions, the paper [START_REF] Marinković | Proving properties of the chord protocol using the ASM formalism[END_REF] proves that the presented formalization of Chord consistently maintains the topological structure of rings and manipulates with distributes keys. In Section 5 we will explain that our model of BAC19 satisfies the mentioned constraints and that results from [START_REF] Marinković | Proving properties of the chord protocol using the ASM formalism[END_REF] hold also for BAC19.

On the other hand the papers [START_REF] Liquori | Synapse: A scalable protocol for interconnecting heterogeneous overlay networks[END_REF][START_REF] Marinković | Analyzing the exhaustiveness of the synapse protocol[END_REF] recognize the fact that the search procedure of the Synapse protocol is not complete and fully exhaustive. This is due to the fact that the lookup procedure of the Chord network can skip some of the synapse nodes, and thus not to spread the query to all networks that are reachable. To avoid this situation we redefine the lookup procedure with Algorithm 1, not to skip any node.

System BAC19

In this section, we propose the design of the system BubbleAntiCovid19 (BAC19), which is a formal federation overlay network for connecting different digital contact tracing applications that are currently in use all over the world. BAC19 federation (Figure 3) consists of several Chord networks:

a network for each person/device of his/her first contacts (black circles in Figure 3), dedicated red network to connect all infected persons (red circle in Figure 3), dedicated amber network to connect all the first contacts of infected persons (amber circle in Figure 3), and -Gateways (black rectangles in Figure 3) as the connections to the existing digital contact tracing systems (black rounded corners rectangles in Figure 3). The first connection between the proposed extension and an existing system for contact tracing is called Gateway. The purpose of a Gateway is to maintain communication between two parts and to transform messages in a way that both sides can communicate efficiently.

The most important thing is to maintain the mappings between identifiers (IDs) used on both sides of a Gateway. As we could see in Section 2, some systems periodically change IDs, so the possibility to trace those changes is vital for functioning of BAC19.

Regarding IDs, our goal is to have one identifier per one person/device regardless of how many systems it appears in. We argue that this is possible to achieve. First, it is possible to use sufficiently large codomain of the hash function (e.g. 2 128 ). Also, it is possible to select enough parameters of a person/device so that it can be uniquely identified. We are not storing any other attribute of a person/device except a newly introduced identifier in our extension.

More precisely, with respect to the specifications that are provided in [START_REF] Marinković | Analyzing the exhaustiveness of the synapse protocol[END_REF][START_REF] Marinković | Proving properties of the chord protocol using the ASM formalism[END_REF] we need to introduce the following changes:

- To obtain completeness and full exhaustiveness of the retrieval procedure the rule FIND-SUCCESSOR, which finds a responsible node for a given ID, is changed as in the way presented in Algorithm 1.

With this proposal we are not compromising performances of the extension by much.

Since the number of contacts of a person is relatively small, it is manageable to allow increasing the complexity of the worst case retrieval from O(logN ) to O(N ). In the predefined time-slots our extension will receive the following information from a system:

all identified infected cases since the last import (Algorithm 2), all confirmed cases that are not infected anymore since the last import (Algorithm 3), all identified contacts since the last import in the form of the tuple id i , id j , t with the meaning that persons id i and id j had a risk contact at t timestamp. For the purpose of providing privacy protection timestamp should be kept at the precision of days.

Unfortunately, this type of communication is not possible with the systems that are categorized as decentralized Bluetooth systems, since the fact that contact tracing computation is performed at users' devices and not shared with the central storage.

These systems can only share newly identified cases and their time of recovery (see Algorithm 4).

Algorithm 4: Set contact time par

Set contacttime(idi, idj) = t Set contacttime(idj, idi) = t endpar Also, if needed it is possible to introduce the new Gateway with the purpose to enter manually recognized contacts to the system. When information is received from origin systems, as the first step BAC19 will connect all newly recognized infected cases to the red network, as well as to remove all cured.

A node will remain in the red network until its recovering is confirmed. All IDs that are recognized as the risk contacts of a person/device (e.g. id i ) will be added to its bubble.

They will stay there until t + 14 days, where t is the time of their contact. If the id i is the member of the red network all the members of its network will be added to the amber network and stay there during the same time frame t + 14 days. If a contact is already in the amber network timestamp will be updated to the higher value (Algorithm 5).

During the opposite way of communication, BAC19 will pass on information to all nodes in the amber network to Gateways. If an identifier is recognized in the set of mappings for the particular origin system, the corresponding information is transferred to the origin system to alert (if not already) the person/device that she/it had risk contact with an infected person at stored timestamp. Also, BAC19 is capable to send information on the second level contacts (the result is stored in the set Result, Algorithm 6).

Algorithm 5: Leave of network

For all net id i ∈ N etwork\{red} For all idj ∈ net id i if contacttime(idi, idj) + 14 days > currentdate() then Invoke LEAVE Of Network idj for idi Algorithm 6: Get all nodes seq Invoke GET all nodes from amber and store the result in Amber For all id ∈ Amber Invoke GET all nodes from net id and append the result to Result endseq Namely, for all nodes of the amber network it is possible to go through every origin bubble and pass those identifiers to the Gateways. Then the origin systems can inform those persons that they should increase their awareness since they are second level contacts.

Using the results from [START_REF] Marinković | Analyzing the exhaustiveness of the synapse protocol[END_REF][START_REF] Marinković | Proving properties of the chord protocol using the ASM formalism[END_REF] we prove the following statement:

Theorem 1 The proposed extension stores and retrieves only up-to-date information on Covid-19 positive cases (identified by the origin systems) and their contacts and makes it available to all origin systems. Proof. It is shown in the paper [START_REF] Marinković | Proving properties of the chord protocol using the ASM formalism[END_REF] that it might happen that stable states in a Chord network cannot be achieved if Leave and/or Put rules are fired in unstable states. Thus, to avoid that in BAC19, it is necessary to ensure that the executions of each of Algorithm 2 -Algorithm 6 do not intertwine.

Executions of the proposed extension are performed in the controlled environment.

Due to the scheduled time intervals for running different tasks, the nodes' leaving from the bubbles will not happen during the unstable states, i.e., there will be only runs compatible with conditions of [START_REF] Marinković | Proving properties of the chord protocol using the ASM formalism[END_REF]Theorems 5.3,5.4 and 5.7]. Also, the fact that the rule FIND-SUCCESSOR is changed guarantees that all nodes will be contacted during the search procedure, and that the retrieving procedure of the Synapse protocol [START_REF] Marinković | Analyzing the exhaustiveness of the synapse protocol[END_REF] is complete and fully exhaustive.

As a consequence of the mentioned adaptations of the proposed Chord model, all possible execution of BAC19 fulfill conditions from [16, Theorems 5.3, 5.4 and 5.7]. So, with these modifications starting from the given state BAC19 will always reach the stable state, and the retrieved information will be up-to-date and valid.

Discussion

The paper [START_REF] Vukolic | On the interoperability of decentralized exposure notification systems[END_REF] proposes building a common API. This approach is rather similar to the extension proposed in this paper. However, these approaches have also two significant differences:

while [START_REF] Vukolic | On the interoperability of decentralized exposure notification systems[END_REF] building API connection points between each of two different origin systems that are connected, our extension proposes a version to common bus where each of the origin systems communicates with the proposed extension and in this way reduces and simplifies the number of connection points that needs to be maintained when several origin systems are connected;

with BAC19 we are simplifying also information that is being exchanged, and we do not violate privacy in the origin systems (since our extension does not collect information of origin DCT system).

ETSI GS-E4P presents in [START_REF]ETSI: Pandemic proximity tracing systems: Interoperability framework[END_REF] an interoperability framework for pandemic contact tracing systems which allows the centralized and decentralized modes of operation to fully interoperate.

A guideline on Interoperability specifications for cross-border transmission chains between approved apps by the European Community [START_REF]eHealth Network: Interoperability specifications for cross-border transmission chains between approved apps[END_REF] proposes a Federation Gateway Service for synchronizing the diagnosis keys (keys of infected users) across backend servers of each national app. However, this approach focuses only on Google/Apple exposure notification apps because the majority of European countries have developed this kind of apps, and also because one Google/Apple exposure notification app can detect the contact with a user of another Google/Apple exposure notification app. In this paper we do not focus on a certain type of DCT apps, we want to achieve the connection between them regardless the contact-tracing technology and their system architecture. We leave to the the reader to envisage the following scenario:

-Alice lives in the region which has centralized DCT System A, while Bob lives in the region which has centralized DCT System B. Bob has spent some time in the region A, and both of them are traveling together side by side with negative RT-PCR tests. However, Bob developed symptoms of Covid-19 after couple of days and was confirmed as positive.

If System A and System B are part of BAC19, it would be enough that only one of Alice and Bob had installed system from the other region just in the time of travel for Alice to be informed that she is the first contact of an infected person.

Conclusions

In this paper we have presented BAC19 a new and efficient overlay network connecting existing systems for digital contact tracing. The advantages of BAC19 (its usage) are:

a person does not install anything new on his/her mobile device (except a new application which is used in the region that this person is visiting); the overlay does not store any personal sensitive information; the overlay is independent regarding how the origin system calculated contacts or is it based on Bluetooth or GPS technology;

the overlay supports manual entry of recognized contacts; there are no new highly complicated calculations of possible contacts beside those that are performed by the original contact tracing systems.

The presented extension BAC19 is the so-called forward tracing system (finding all contacts of an infected person). We plan to explore the possibilities to adapt BAC19 to also enable backward tracing (finding the source of infection using contacts).

Acknowledgment. This work was partly supported by: the Science Fund Republic of Serbia #6526707 AI4TrustBC.

A. DCT apps -overview

A.1. Geolocation-based DCT apps Home Quarantine. At the beginning of the Covid-19 pandemic, Ministry of Digital Affairs of Poland developed the Home Quarantine app. More details about this app can be found in [START_REF]Data justice and COVID-19: Global perspectives[END_REF]. This is a typical example of a centralized app which deploys GPS technology.

It is developed to support the authorities, especially the police and social services, with adequate information about people undergoing mandatory home quarantine. Users are also required to upload their digital photos. So, aside the GPS technology the app also uses face recognition. The app is mandatory for anyone who has developed coronavirus symptoms. It should be emphasized that Poland also developed the ProteGO Safe app for alerting users of close contact with an infected person based on The (Google/Apple) Exposure Notification (GAEN) system.

The Shield (HaMagen). In March 2020, Israeli Ministry of Health developed The Shield app [START_REF] Altshuler | Digital Contact Tracing and the Coronavirus: Israeli and Comparative Perspectives[END_REF]. This is a typical example of a decentralized app which deploys GPS technology. Location data is stored in the phone. If a user tests positive, he/she can upload his/her location history to the central server. Once the user uploaded his/her location history, it is added into a JSON file that is updated with new data on an hourly basis. Matching the locations happens on the phone. If the match is found, the app shows you the exact time and location. The app is later updated to work with Bluetooth technology but on a voluntary basis, every user can choose whether to use the proximity data or not.

A.2. Bluetooth-based DCT apps

Blue-Trace protocol apps. Singapore's Government Technology Agency in collaboration with Ministry of Health in March 2020 released the TraceTogether app that allows digital contact tracing using the custom BlueTrace protocol. Australia has later adopted the protocol and released the CovidSafe app. More details about these apps can be found in [START_REF] Abbas | COVID-19 Contact Trace App Deployments: Learnings From Australia and Singapore[END_REF].

Contact tracing is done using Bluetooth Low Energy and proximity data is encrypted and stored only on the users phone. Users in the contact log are identified using anonymous time-shifting "temporary IDs". If a user tests positive for the infection, the Ministry of Health requests his/her contact log. The user has the right to choose whether to share the contact log or not. If the user chooses to share the log, the contact log is uploaded to a central server and the health authority is then responsible for matching the log to contact detail and informing close contacts of the infected user. These apps are examples of Bluetooth-based centralized apps. It should also be noted that Singapore solved the problem of tracing people who don't use smartphones by enabling the app to work with Token -a physical Bluetooth-based device.

ROBERT protocol app. The French National Assembly released the StopCovid app in May 2020 [START_REF] Montagni | The French Covid-19 contact tracing app: knowledge, attitudes, beliefs and practices of students in the health domain[END_REF]. The app has later been renamed to TousAntiCovid. It allows digital contact tracing using the ROBust and privacy-presERving proximity Tracing protocol (ROBERT protocol). It also deploys Bluetooth technology and belongs to the category of centralized apps. The difference between this app and apps based on the BlueTrace protocol relates to confirmation of positive users. More precisely, in France when a person is confirmed to be positive, the lab gives a patient a QR code and the scanned code is the proof for the app that you are infected. It is up to you to share this information with the app, and if you choose to share this information with a central server, the server is responsible for alerting your close contacts.

Google/Apple exposure notification apps. In April 2020 Google and Apple announced the joint work on decentralized Bluetooth-based protocol named The (Google/Apple) Exposure Notification (GAEN) system [START_REF] Hoepman | A Critique of the Google Apple Exposure Notification (GAEN) Framework[END_REF]. Many states then developed different apps using the Google/Apple Exposure Notification framework including Austria (Stopp Corona app), Germany (Corona-Warn-App), Italy (Immuni), Canada (COVID Alert ) etc. The principle by which applications work is as follows. During a close contact, user's phones exchange random Bluetooth identifiers. These identifiers change frequently and the information about exchanged ID's is stored on the user's phone. When a user gets infected, he/she can decide to upload ID's he/she was using the last 14 days to the server. Phones of all users periodically download the list of ID's which belong to the infected users and does the matching locally.

A.3. Bluetooth-GPS apps

Apps that deploy both Bluetooth and GPS technology are rare. One app of this kind is the Aarogya Setu app [START_REF] Basu | Effective Contact Tracing for COVID-19 Using Mobile Phones: An Ethical Analysis of the Mandatory Use of the Aarogya Setu Application in India[END_REF], developed by National Informatics Centre that comes under the Ministry of Electronics and Information Technology, Government of India. Aarogya Setu is following the centralized approach, and is one of the world's fastest growing applica-

Fig. 1 .

 1 Fig. 1. Classification of analyzed applications

Fig. 2 .

 2 Fig. 2. Centralized vs Decentralized Bluetooth-based apps

Fig. 3 .

 3 Fig. 3. BAC19 Federation Overlay Network

  the set N etwork = {red, amber, net 1 , . . . , net N }, N ∈ N to denote all possible networks, where N is the number of possible persons/devices in the proposed extension; the set T ime and the function contact time() : (Chord ∪ {amber}) × Chord → T ime to denote the time of the contact between two persons; the external function current date() to get the current date.

  tions. The app mainly uses proximity data and GPS data are recorded only once in 30 minutes. The location data is mainly used to identify the locations where you might have caught the infection and identify potential hotspots that may be developing when multiple infected people visit the same place. Interaction between users is recorded by exchange of Device Identification Numbers (DiD's) which are static. Contact tracing data is kept on the phone. Council of Medical Research (ICMR) shares the list of Covid-19 positive persons with the Aarogya Setu server, and information about contact tracing is uploaded to the server only if you are tested positive. The central server is then responsible for alerting your close contacts.

Algorithm 2 :

 2 PutFor all inf ∈ N ewCases Invoke PUT Of Network red To Store inf For all id ∈ net inf if contacttime(amber, id) < t or contacttime(amber, id) = undef then Set contacttime(amber, id) = t

	Algorithm 3: Leave
	For all inf ∈ Healed
	Invoke LEAVE Of Network red for inf

Silvia Ghilezan et al.


Sara Bocanegra Rodríguez

Carmens Molins-Legua

Pilar Campíns-Falcó

Fabien Giroud

Andrew J Gross
email: andrew.gross@univ-grenoble-alpes.fr

Serge Cosnier
email: serge.cosnier@univ-grenoble-alpes.fr

] S Bocanegra Rodríguez

] F Giroud

Monofunctional pyrenes at carbon nanotube electrodes for direct electron transfer H 2 O 2 reduction with HRP and HRP-bacterial nanocellulose

Keywords: Direct electron transfer, horseradish peroxidase, biofuel cell cathode, nanocellulose electrode, bioelectrocatalysis, electrochemical sensor

The non-covalent modification of carbon nanotube electrodes with pyrene derivatives is a versatile approach to enhance the electrical wiring of enzymes for biosensors and biofuel cells. We report here a comparative study of five pyrene derivatives adsorbed at multi-walled carbon nanotube electrodes to shed light on their ability to promote direct electron transfer with horseradish peroxidase (HRP) for H 2 O 2 reduction. In all cases, pyrene-modified electrodes enhanced catalytic reduction compared to the unmodified electrodes. The pyrene N-hydroxysuccinimide (NHS) ester derivative provided access to the highest catalytic current of 1.4 mA cm -2 at 6 mmol L -1 H 2 O 2 , high onset potential of 0.61 V vs. Ag/AgCl, insensitivity to parasitic H 2 O 2 oxidation, and a large linear dynamic range that benefits from insensitivity to HRP "suicide inactivation" at 4 to 6 mmol L -1 H 2 O 2 . Pyrene-aliphatic carboxylic acid groups offer better sensor sensitivity and higher catalytic currents at ≤ 1 mmol L -1 H 2 O 2 concentrations. The butyric acid and NHS ester derivatives gave high analytical sensitivities of 5.63 A M -1 cm -2 and 2.96 A M -1 cm -2 , respectively, over a wide range (0.25 to 4 mmol -1 ) compared to existing carbon-based HRP biosensor electrodes. A bacterial nanocellulose pyrene-NHS HRP bioelectrode was subsequently elaborated via "one-pot" and "layer-bylayer" strategies. The optimised bioelectrode exhibited slightly weaker voltage output, further enhanced catalytic currents, and a major enhancement in 1-week stability with 67% activity remaining compared to 39% at the equivalent electrode without nanocellulose, thus offering excellent prospects for biosensing and biofuel cell applications.

Introduction

The development of enzymatic electrodes based on carbon materials with electrically-wired oxidoreductases is of great importance for biosensor and biofuel cell applications (Bollella and Katz, 2020;Gross et al., 2018). Carbon-based enzymatic electrodes have already shown remarkable commercial success for portable and wearable self-monitoring glucose sensors, and have tremendous potential for body-integrated and portable biofuel cells for low power electronics (Abreu et al., 2018a;Bollella et al., 2020;Chen et al., 2019;Lee et al., 2021). To date the glucose/O 2 biofuel cell is the most commonly reported and arguably most practical biofuel cell type; nevertheless, there are still important limitations relating to the stability and activity of the bioelectrodes as well as limited substrate availability. The oxygen reduction reaction at the cathode is typically achieved using the multicopper oxidases (MCOs) laccase or bilirubin oxidase (BOx), but such enzymes are degraded or inhibited by ubiquitous hydrogen peroxide and halogens such as chloride (Antiochia et al., 2019;Valles et al., 2020).

Oxygen-dependent oxidases such as glucose oxidase (GOx) unfortunately generate hydrogen peroxide in the presence of oxygen. Chloride on the other hand is common in biological or artificial biofuel cell electrolytes. Laccases generally demonstrate good activity at acidic pH but low activity and/or stability at neutral pH (Goff et al., 2015). BOx is generally bettersuited to neutral pH but BOx-based cathodes typically exhibit a ca. 100-200 mV lower onset potential (E 1/2(T1) = 0.52 V vs. Ag/AgCl (sat. KCl) at pH 7.0) compared to laccases (Gross et al., 2017). Another prominent issue for MCO-based cathodes is related to the low concentration of dissolved oxygen (oxidant) in biological fluids: ca. 45-70 µmol L -1 in blood and cerebrospinal fluid and ca. 200 µmol L -1 in aqueous quiescent solutions (Gross et al., 2017;Zebda et al., 2018). The development of improved bioelectrode interfaces to address stability and substrate limitations whilst maintaining good mass and electron transport for effective catalytic activity is therefore highly desirable, not just for biofuel cells, but also for electrochemical biosensors.

Horseradish peroxidase (HRP) is a robust and readily available heme-containing glycoprotein capable of direct electron transfer (DET) bioelectrocatalytic 2 e -/2 H + reduction at carbon electrodes such as graphite (Andreu et al., 2007;Ferapontova and Puganova, 2002), singlewalled (Shu et al., 2016), double-walled (Agnès et al., 2013), and multi-walled carbon nanotubes (Abreu et al., 2018b;Elouarzaki et al., 2015) (MWCNTs), 3D printed graphene (López Marzo et al., 2020), and nanofiber composites (Jia et al., 2010). HRP is therefore an excellent candidate for the development of reagentless third generation H 2 O 2 electrochemical biosensors (Xu et al., 2015). HRP bioelectrodes are also of interest to simplify biocathodes for biofuel cell applications, offering mediator-free bioelectrocatalysis at a high onset potential.

The DET H 2 O 2 reduction reaction with immobilised HRP has generally been obtained at potentials of ca. +100 to -50 mV vs. Ag/AgCl, although higher onset potentials up to ca. +400-600 mV vs. Ag/AgCl have been reported at oxygenated porous carbon and carbon nanotube electrodes (Jia et al., 2010;Ruff et al., 2017). Schuhmann, Stoica and coworkers made important developments on carbon fiber/CNT composites, highlighting the important roles of the hierarchically porous structure and the chemical functionalities, pyrene hexanoic or butyric acid, to achieve H 2 O 2 reduction as high as +600 mV vs. Ag/AgCl (Jia et al., 2010;Ruff et al., 2018). Several studies highlighted the benefit of introducing oxygenated functionalities to the carbon surface, including specifically carboxylic acid groups, to improve hydrophilicity for DET bioelectrocatalysis (López Marzo et al., 2020;Yamamoto et al., 2003). Alternatively, we and others have demonstrated the possibility to obtain effective DET bioelectrocatalysis with HRP simply at nonfunctionalised MWCNTs that contain low levels of oxygen (ca. 1%) [15,16] .

As is also the case for MCO bioelectrodes, HRP bioelectrodes are limited by the low presence of endogenous substrate present in biological fluids for energy harvesting body-integrated biofuel cells, for example, operating in blood or sweat (Forman et al., 2016;Jia et al., 2012).

An original approach in biofuel cell design to circumvent or minimise issues with low H 2 O 2 concentration involves generating hydrogen peroxide in-situ, for example, via enzymatic reactions. Hydrogen peroxide may be continuously generated in situ from GOx (Abreu et al., 2018b;Elouarzaki et al., 2015;Jia et al., 2012;Gorton et al., 1991) or other oxidases such as pyranose oxidase (Lidén et al., 1998) or alcohol oxidase (AOx) (Ruff et al., 2017). Over 30 years ago, Kulys and Schmid demonstrated the concept of bienzyme electrodes based on peroxidase mixed with GOx, AOx or choline oxidase (Kulys and Schmid, 1990). Over 20 years ago Willner, Katz and coworkers demonstrated this original concept with GOx in solution at a microperoxidase-11 cathode compartment where GOx reduced O 2 to H 2 O 2 (Willner et al., 1998). Lo gorton and coworkers provided a review showcasing the use of a whole series of H 2 O 2 producing oxidases with HRP at electrodes (Ruzgas et al., 1996). More recent developments focused on bi-enzymatic biocathodes with immobilised GOx/HRP (Agnès et al., 2013;Elouarzaki et al., 2015;Jia et al., 2012) and AOx/HRP (Ruff et al., 2017) where H 2 O 2 was immediately generated in the vicinity of the cathode. At physiologicallyrelevant glucose concentrations in phosphate buffer saline (PBS, pH 7.4), without externally added peroxide, a practical current density of over 1 mA cm -2 and a respectable 15 days storage stability was achieved for a co-immobilised GOx/HRP biocathode (Elouarzaki et al., 2015). More recently, we reported a flow-through portable biofuel cell in which unwired GOx at the anode generated H 2 O 2 in-situ at the anode that was then transported to a HRP-based cathode, again, without the need to add peroxide from an external source. A respectable open circuit voltage (OCV) of 0.6 V and maximum power output of 0.7 mW for a single biofuel cell validated the potential of HRP-based cathodes as an alternative to O 2 biocathodes in glucose biofuel cells (Abreu et al., 2018b). Schuhmann and coworkers earlier validated the alternative AOx/HRP biocathode, relying on DET between MWCNTs and HRP, that was then integrated with a nicotinamide adenine dinucleotide (NAD) + -dependent alcohol dehydrogenase bioanode for a self-powered biofuel cell-biosensor (Ruff et al., 2017). A high OCV of 0.66 V and relatively low maximum power density of 8.9 µW cm -2 were observed in air-saturated 0.5 M ethanol buffer solution. Another advantage for HRP biocathodes is their demonstrated high resistance to physiological concentrations of chloride at neutral pH (Jia et al., 2012;Shu et al., 2016). A direct comparative study showed better stability for HRP compared to laccase in the presence of chloride (Elouarzaki et al., 2015).

In the present work, we explore the use of several functional pyrene derivatives adsorbed at multi-walled carbon nanotube electrodes to shed new light on the influence of contrasting organic surface functionalities on DET bioelectrocatalysis with immobilised HRP.

Concentration effects on catalytic current as well as voltage output and stability performance are considered for biocathode and biosensor applications. The construction of a new type of HRP bioelectrode incorporating hydrated nanocellulose as an environmentally friendly and sustainable component was subsequently investigated and the resulting sensor and catalytic stability performance evaluated.

Experimental Section

Materials and chemicals

Sodium phosphate dibasic (Na 2 HPO 4 , ≥ 99%), sodium dihydrogen phosphate (NaH 2 PO 4 , ≥ 99%), hydrogen peroxide (≥ 30% w/w in H 2 O), 1-methyl-2-pyrrolidone (NMP, ≥ 99%), pyrene (98%, py), 1-pyrenebutyric acid N-hydroxysuccinimide ester (pyNHS, 95 %), 1pyrenemethylamine hydrochloride (pyNH 2, 95 %), 1-pyrenebutyric acid (pyBA, 97%), 1pyreneacetic acid (pyAA, 97 %), and horseradish peroxidase from Armoracia rusticana (type II, 150-250 units/mg solid) were purchased from Sigma Aldrich and used as received without further purification. The enzyme was stored at -20 °C when not in use. Distilled water was purified to a minimum resistivity of 15 MΩ cm -1 using a Millipore Ultrapure system.

Commercial grade thin multi-walled carbon nanotubes (MWCNTs, Ø = 9.5 nm, 90% purity, NC7000, batch 1166) were obtained from Nanocyl and used as received without purification.

High purity oxygen and argon were obtained from Messer. N, N-Dimethylformamide (DMF, 99.8%) was obtained from Carlo Erba reagents (France). Acetonitrile (ACN) was obtained from VWR chemicals (France). The 1 % bacterial cellulose nanofibers gel was obtained from Nano Novin Polymer Co. (99%, average 40 nm diameter) and used as received.

Electrochemistry

Electrochemical measurements were performed at room temperature using a Biologic VMP3 Multi Potentiostat operated with EC-lab software. A three-electrode cell was used comprising a carbon nanotube film-modified glassy carbon (GC) working electrode (Ø = 3 mm), a silversilver chloride reference electrode (Ag/AgCl with saturated KCl), and a Pt wire counter electrode. GC electrodes were polished using a Presi polishing cloth with 1 µm alumina or diamond slurry then sonicated for 5 min in distilled water prior to use. Electrochemical experiments were performed in 0.1 mol L -1 phosphate buffer (pH 7.0) in the absence of oxygen. Oxygen was removed by purging the solution with argon for 15 min. A gentle argon flow was maintained in the air space above the solution during experiments. Amperometric data was recorded at E p = 0 V vs. Ag/AgCl (sat. KCl). Bioelectrodes were stored in fresh buffer solution between stability experiments performed on different days at 4°C in the fridge.

Current densities were estimated based on the geometric surface area of the working electrode (0.071 cm 2 ).

Preparation of film-modified multiwalled carbon nanotube electrodes

5 mg of MWCNTs were first added to 2 mL of NMP in a sealed glass vial and the resulting suspension sonicated for 60-120 min to achieve a homogeneous dispersion. 20 µL of the MWCNT dispersion (2.5 mg mL -1 ) was subsequently drop-casted onto the GC electrode to obtain a densely and homogeneously coated MWCNT layer after drying, based on our previously reported method (Gross et al., 2020). The modified electrode was dried under vacuum for ca. 2 hours then rinsed with 0.1 mol L -1 phosphate buffer (pH 7.0) prior to use.

Preparation of pyrene-modified MWCNT electrodes

The modified MWCNT electrodes were obtained by immersion of the electrode in a sealed vial containing 100 µL of 5 mmol L -1 modifier solution containing the pyrene derivative in DMF. After 60 min, the electrode was gently removed from the modifier solution then rinsed with DMF followed by ACN to remove weakly adsorbed species. The modified electrodes were rinsed gently with 0.1 mol L -1 phosphate buffer (pH 7.0) prior to use.

Preparation of HRP-modified MWCNT bioelectrodes

Aliquots of enzyme solution were first prepared at 5 mg mL -1 in 0.1 mol L -1 phosphate buffer (pH 7.0) and stored at -20°C. Prior to use, the aliquot was carefully thawed to room temperature then immediately used for bioelectrode preparation. The pyrene-modified MWCNT electrode was immersed in a sealed vial containing 40 µL of the enzyme solution then left overnight at 4°C in the fridge. Prior to electrochemistry or further modification, the bioelectrode surface was rinsed gently with 0.1 mol L -1 phosphate buffer (pH 7.0) to remove weakly adsorbed species.

Preparation of nanocellulose-modified HRP MWCNT bioelectrodes 2.6.1. Layer-by-layer method

The HRP modified bioelectrodes were first prepared as described in Section 2.5. 10 µL of the as-received nanocellulose gel (1% nanocellulose) was then mixed with 30 µL of 0.1 mol L -1 phosphate buffer (pH 7.0) in a vial for 60 s by vortexing. 20 µL of the mixture was then drop-casted onto the bioelectrode. The electrode was left to dry at room temperature for 1 h then gently rinsed with the buffer solution prior to use.

One-pot method

0.4 mg of HRP, 10 µL of nanocellulose gel (1% nanocellulose) and 30 µL of 0.1 mol L -1 phosphate buffer (pH 7.0) were mixed together in a vial for 60 s by vortexing. After prerinsing of the pyrene-modified MWCNT electrode (Section 2.4) with the buffer, either 5 µL or 20 µL of the mixed enzyme/nanocellulose solution was drop-casted on the surface of the electrode. The electrode was left to dry at room temperature for 1 h then gently rinsed with the buffer solution prior to use.

Results and discussion

Bioelectrocatalyis of HRP/pyrene-modified MWCNT bioelectrodes

The pyrene and functionalised pyrenes employed for non-covalent modification of the MWCNT electrodes, and the subsequent preparation of HRP bioelectrodes for H 2 O 2 reduction, are schematically illustrated in Figure 1. (Berglund et al., 2002).

The MWCNT electrodes were obtained according to our reported strategy that allows the formation of highly stable and reproducible MWCNT coatings on GC electrodes with a film thickness of ca. 6 µm (Gross et al., 2020;Lalaoui et al., 2016). The pyrene-modified MWCNT electrodes were prepared by a simple immersion protocol using a DMF modifier solution with 5 mmol L -1 of the pyrene derivative, followed by rinsing to remove weakly adsorbed species (Section 2.4). The effective adsorption of pyrenes including mono/polycyclic and ionisable/non-ionisable derivatives to CNTs occurs via physical interactions, particularly pi-pi stacking interactions between CNT sidewalls and the aromatic system of the molecules (Chunping et al., 2014;Haddad et al., 2010;Sheng et al., 2010). This non-covalent modification strategy is attractive for electrochemical biosensor and biofuel cell applications due to its simplicity, the ability to preserve the aromatic systems and therefore electronic properties of the nanotubes, and the possibility to introduce a wide range of surface functionalities in a straightforward manner (Gross et al., 2017;Haddad et al., 2010;Gutiérrez-Sánchez et al., 2012). For example, carbon nanotube electrodes modified with pyrene derivatives have been used to yield direct electron transfer with oxidoreductase enzymes such as laccase (Gutiérrez-Sánchez et al., 2012) and bilirubin oxidase (Mazurenko et al., 2016).

To achieve efficient DET bioelectrocatalysis with metalloenzymes it is necessary to optimise enzyme orientation and immobilisation. Recent studies have highlighted the importance of electrode functionalisation with ionisable, hydrophilic/hydrophobic, reactive tether, and/or substrate-like functional groups (Blanford et al., 2007;Lalaoui et al., 2016;Ramasamy et al., 2010;Tominaga et al., 2008). Concerning DET bioelectrocatalysis with HRP, several reports have shown the importance of surface oxygen functionalities and/or carboxylic acid groups to improve performance compared to unmodified carbon and CNT electrodes (Abreu et al., 2018b;Jia et al., 2010;López Marzo et al., 2020;Ruff et al., 2018;Shu et al., 2016;Yamamoto et al., 2003). Little progress has been made regarding the influence of charge and/or other surface functionalities to promote DET bioelectrocatalysis with immobilised HRP. The commercial HRP has a stated isoelectric point (pI) of approximately 3 to 9 owing to the presence of several isozymes. Nevertheless, important studies by Radola and Delincée on the fractionation of commercially-sourced HRP shows that the predominant isozyme pI is 9.1 (Delincée and Radola, 1975;Delincée and Radola, 1978). At pH 7.0 we therefore expect HRP to be positively charged. As depicted in Scheme 1, we explored the use of a "classical" pyrene-aliphatic carboxylic acid, pyrene butyric acid (pyBA, pK a 4.8), as well as the shorter chain equivalent, pyrene acetic acid (pyAA, pK a 4.2), a pyrene aliphatic amine (pyNH 2 , pK b ~ 10), pyrene, and a pyrene-NHS ester derivative. With all aqueous experiments performed in 0.1 mol L -1 phosphate buffer (pH 7.0), this set of derivatives enabled the comparison of positive (protonated amine), negative (deprotonated carboxylic acid) and neutral (pyrene) charged surface species. Furthermore, the pyNHS derivative comprises the succinimidyl group that may react with amino residues at the surface of the enzyme to form strong covalent bonds, therefore enabling comparison of a "tether" functionality (Karachevtsev et al., 2011).

The use of pyrene-NHS has proven to be very effective for DET bioelectrocatalysis with multicopper oxidases for O 2 reduction (Gross et al., 2018;Ramasamy et al., 2010) and is therefore an interesting alternative to electrostatic enzyme immobilisation.

Catalytic cyclic voltammetry experiments were performed in argon-saturated 0.1 mol L -1 phosphate buffer (pH 7.0) for the unmodified and pyrene-modified electrodes after immobilisation of HRP by an immersion protocol then gentle rinsing (Section 2.5). Figure 2 shows the first-scan cyclic voltammograms (CVs) recorded at the MWCNT bioelectrodes from open circuit potential to 0 V vs. Ag/AgCl (sat. KCl) in the presence of "low" 0.5 mmol L -1 and "high" 4 mmol L -1 H 2 O 2 . CVs recorded in the absence of H 2 O 2 showed no reduction processes beyond the background signal of the MWCNT bioelectrode (data not shown). In the presence of 0.5 mmol L -1 H 2 O 2 , a large catalytic reduction peak is observed at all electrodes, including the unmodified electrode, consistent with DET bioelectrocatalysis between adsorbed HRP and the MWCNT electrodes (Figure 2A). Based on previous findings, the reaction occurs via the oxyferryl iron-porphyrin pi-cation radical species, Fe IV =O,P +• , of the active site of HRP Compound 1 (Jia et al., 2010). Similar catalytic current maximums of -21 to -24 µA are observed for the different pyrene-modified electrodes compared to a slightly lower current of -20 µA for the unmodified MWCNTs electrode, consistent with surface modification leading to a minor enhancement in DET at 0.5 mmol L -1 H 2 O 2 . The pyBA bioelectrode exhibited the highest catalytic current but with unattractively low peak and onset potentials of 0.1 V and 0.49 V, respectively. PyNHS-and pyAA-modified bioelectrodes provided access to the highest onset potentials of 0.61 V and 0.60 V, respectively. The onset potentials are very close to the formal potential of 0.63 V for the redox conversion of HRP compound 1/ferric HRP at pH 7.0 vs. Ag/AgCl (Csöregi et al., 1993). The catalytic improvements observed with pyNHS, pyBA and pyAA indicate that hydrophilic and negatively-charged functionalities, or tether group functionalities, are more favorable compared to positively-charged or entirely hydrophobic modifications at "low" H 2 O 2 concentration. Nevertheless, the hydrophobic bioelectrode prepared with pyrene still exhibited enhanced bioelectrocatalysis compared to the unmodified MWCNT electrode. The negatively-charged functionalities that provide catalytic improvements compared to positively-charged functionalities highlight the beneficial electrostatic interactions at pH 7 that favor DET bioelectrocatalysis between positively-charged HRP enzymes and deprotonated aliphatic acids at the electrode. Figure 2 also shows the variable presence of an apparent redox couple at 0.1 V. Control experiments in Figure 2C and Figure S1 performed at CNT electrodes in the absence and presence of adsorbed HRP, respectively, indicate that these redox peaks originate from the carbon nanotubes. The redox peaks are tentatively attributed to surface quinone functionalities with a nature similar to those observed at MWCNT and graphite electrodes (Gusmão et al., 2015;Csöregi, 1993;Blanchard 2019). At 4 mmol L -1 H 2 O 2, markedly different bioelectrocatalytic voltammograms with a more complex wave shape were observed (Figure 2B). The H 2 O 2 concentration became sufficiently high that notable differences in maximum catalytic currents were observed between the modified electrodes. Generally, with an increase in substrate, higher catalytic currents were observed, particularly at lower potentials of ca. 0 to 0.1 V. The catalytic wave onset potential observed for pyNHS and pyAA again starts at ca. 0.6 V vs. Ag/AgCl, as observed at the "low" H 2 O 2 concentration, which favorably compares to the 0.55 V vs. Ag/AgCl (pH 7.5) (Ruff et al., 2016) and 0.6 V maximum (pH 7) vs. Ag/AgCl (Jia et al., 2010) observed at previous high performing MWCNT DET HRP biocathodes. Such biocathodes clearly offer improved voltage performance compared to cross-linked CNT/HRP on thiol-modified gold (Kafi et al., 2018) with onset potentials starting at -0.05 V vs. Ag/AgCl at pH 7. The second reduction wave is characteristic of a catalytic "boost" linked to an increase in enzymatic activity with driving force. A similar wave shape with a "boost" at low potential was reported by Armstrong and coworkers for fumarate reductase at a graphite electrode in the presence of high substrate concentration (Hudson et al., 2005). It may be that the DET mechanism takes a different route depending on the potential but this was not studied further. The possibility of an MET or mixed DET/MET mechanism at low potential involving the proposed surface quinone at bare CNTs is not ruled out (Csöregi, 1993). A control experiment performed at a MWCNT electrode without HRP in the presence of 4 mmol L -1 H 2 O 2 did not show any reductive currents, confirming that the second reduction wave observed in Figure 2B is not due to H 2 O 2 reduction at unmodified MWCNTs (Figure 2C). PyNHS and pyAA bioelectrodes exhibited the highest catalytic currents of -94 µA and -78 µA compared to -24 µA observed at the unmodified MWCNT bioelectrode. This represents a 3-4 factor catalytic enhancement and the possibility to achieve up to ca. 1.1 to 1.3 mA cm -2 current densities for the tether function and shorter chain acid function. PyBA bioelectrodes produced a mediocre current maximum of -50 µA and globally weaker bioelectrocatalysis compared to the pyNHS and pyAA bioelectrode. The pyrene and pyNH 2 behaved similarly to the pyBA bioelectrodes, thus at "high" 4 mmol L -1 concentration, the positive, negative and neutral charges do not play a key role on enhanced DET bioelectrocatalysis. There is no obvious trend due to the use of different aliphatic chain lengths. For reference, voltammograms were not investigated at lower potentials of ≥ -0.15 V where deactivation of the HRP is observed (Csöregi et al., 1993).

In addition to the bioelectrocatalytic H 2 O 2 reduction behaviour, an oxidative response was also observed at the pyrene-modified MWCNT electrodes, as shown in Figure 2. The oxidative response corresponds to direct electrochemical oxidation of H 2 O 2 , as previously reported at carbon electrodes (Jia et al., 2010). The H 2 O 2 oxidation occurring at ≥ 0.52 V therefore competes with the reduction process and diminishes the H 2 O 2 reduction current at these bioelectrodes. Considering both 0.5 mmol L -1 and 4 mmol L -1 concentrations, the most effective bioelectrodes for the parasitic H 2 O 2 oxidation are pyBA and pyNH 2 while the least effective was the pyNHS bioelectrode. The insensitivity of the pyrene-NHS bioelectrode towards H 2 O 2 is consequently one of the important factors that permits high catalytic H 2 O 2 reduction performance, particularly at the "high" peroxide concentration.

The steady-state amperometric current responses of the unmodified and pyrene-modified HRP bioelectrodes were subsequently measured at 0 V vs. Ag/AgCl under hydrodynamic conditions from 0.25 mmol L -1 to 9 mmol L -1 . Figure 3 shows the current-concentration response curves obtained from the amperometric experiments. The unmodified and modified electrodes show the same general trend with a linear increase in current to a plateau followed by a drop-off in current. Linear calibration curves (r 2 ≥ 0.98) from 0.25 mmol L -1 to between 1 mmol L -1 and 4 mmol L -1 were observed, depending on the pyrene derivative used (Figure S2). The pyNHS and pyAA bioelectrodes delivered the highest catalytic currents of 98.5 µA (1.4 mA cm -2 ) and 86.5 µA (1.2 mA cm -2 ) at 6 mmol L -1 , respectively. Beyond 6 mmol L -1 the catalytic current decreases as a result of enzyme deactivation. Such HRP "suicide inactivation" has previously been observed at low millimolar concentrations of H 2 O 2 , occurring when the peroxide converts Compound 2 of HRP into a highly reactive peroxy iron(III) porphyrin free radical that subsequently decomposes (Malomo et al., 2011). For a biocathode or biosensor targeting the highest catalytic current or wider dynamic range, the pyNHS is the optimal electrode. If higher catalytic currents or better sensor sensitivity is required at ≤ 1 mmol L -1 concentrations, then the pyBA or pyAA bioelectrode is the better choice. The sensitivities for pyBA and pyNHS bioelectrodes are 5.63 A M -1 cm -2 (0.40 A M -1 ) and 2.96 A M -1 cm -2 (0.21 A M -1 ) (Figure S2). These analytical sensitivities are high performance compared to estimated values of 0.15 A M -1 at activated graphene (López Marzo et al., 2020), 0.298 A M -1 cm -2 at cross-linked Os redox polymer and modified graphite (Bollella et al., 2018), 0.12 A M -1 cm -2 at carbon microspheres with integrated chitosan (Chen et al., 2008), or ca. 0.0026 A M -1 at a polymer-based CNT electrode (Moyo et al., 2013), or 0.34 A M -1 at a cross-linked CNT on thiol-modified Au electrode (Kafi et al., 2018). The pyBA bioelectrode notably also offers improved analytical sensitivity compared to the high sensitivity of 4.25 A M -1 cm -2 achieved at an ultramicroelectrode DET biosensor integrating ionic liquid, carbon fibers and single-walled CNTs (Ren et al., 2017), or a DET biosensor based on commercial screen-printed carbon electrodes with single-walled CNTs (Chekin et al., 2015) that yielded 0.0051 A M -1 cm -2 .

Bioelectrocatalysis of pyrene-NHS modified HRP bioelectrodes with nanocellulose

Towards the development of eco-friendlier biosensor and biofuel cell devices with improvements in properties such as biocompatibility and stability, we explored the development of HRP bioelectrodes integrating bacterial nanocellulose. Bacterial nanocellulose is a natural cellulosic fibrous material that offers advantages such as excellent biocompatibility, biodegradability, hydrophilicity and hydrogel-forming properties at very low solid content via -OH groups, high specific surface area and porous nanofibrillar network, eco-friendly processing, and low production costs (Abol-Fotouh et al., 2020;Stanisławska, 2016). Tominaga and coworkers reported the construction of a "one-pot" nanocellulose/CNT laccase biocathode, citing the possibility to improve electrode flexibility and proton conductivity; however, performance was limited compared to other biocathodes and no stability or biocompatibility data was reported (Tominaga et al., 2020). Slaughter and coworkers integrated bacterial nanocellulose sheets with bioelectrodes as a flexible and biocompatible layer to contact with skin (Yuen et al., 2019). The nanocellulose was however not exploited as part of the catalytic matrix to enhance bioelectrocatalysis. Zhang and coworkers developed a second-generation HRP biosensor based on gold nanoparticles with a quinone mediator and bacterial cellulose that offered high performance with a sensitivity of 0.61 A M -1 cm -2 (Wang et al., 2011). The absence of comparative data limits makes it difficult to define the enhancement effects specifically related to the nanocellulose.

We developed a nanocellulose bioelectrode design that is illustrated in Figure 4A. The pyrene-NHS modified MWCNT electrode was chosen due to the promising results observed for both biocathode and biosensor applications. Two strategies were investigated: (i) "layerby-layer" with nanocellulose added as an outer layer to the pyNHS HRP bioelectrode, and (ii) a "one-pot" strategy with a mixture of nanocellulose and enzyme first prepared then added as a mixed layer to the pyNHS electrode (see Section 2.6). Figure 4B shows the CVs obtained at the optimised nanocellulose/pyNHS bioelectrode prepared by the one-pot (5 µL) method. The CVs were obtained from 0.6 V to 0 V before after the addition of increasing amounts of H 2 O 2 from 0.4 mmol L -1 to 8 mmol L -1 . At concentrations ≤ 2 mmol L -1 , well-defined catalytic reduction peaks are observed that are followed by a slightly lower but constant current, consistent with the current not being diffusion limited, despite the presence of cellulosic material in the catalytic layer. The CVs recorded at "low" and "high" millimolar H 2 O 2 concentrations for the one-pot (5 µL)

nanocellulose/pyNHS HRP bioelectrode (Figure 4B) are similar to those observed at the pyNHS HRP bioelectrode without nanocellulose (Figure 2A), except for a few differences at 4 mmol L -1 H 2 O 2 . First, a higher catalytic current of 110 µA (1.6 mA cm -2 ) and the highest in this study was observed at the one-pot (5 µL) nanocellulose/pyNHS HRP bioelectrode, representing a 17% increase compared to the pyNHS HRP bioelectrode output at the same H 2 O 2 concentration. The other difference is that CVs observed at one-pot (5 µL) nanocellulose/pyNHS HRP bioelectrode at 4 mmol L -1 (and 6 mmol L -1 ) exhibited two unusual voltage cross-over points at low potential, but their nature is unclear. The crossed CVs may be related to changes in nucleation and/or conductivity of the cellulosic fibers, or result from enzyme activation and deactivation processes that switch abruptly at certain potentials.

Figure 5 shows the current-concentration response curves for the unmodified and pyrene-NHS modified HRP bioelectrode vs. the one-pot (5 µL) nanocellulose/pyNHS HRP bioelectrodes. Figure 5A and Figure 5B reveal either similar or enhanced catalytic current output as well as better sensitivity performance (3.51 A M -1 cm -2 ) across the current range from 0.25 mmol L -1 to 8 mmol L -1 for the optimised nanocellulose bioelectrode compared to the pyNHS and unmodified bioelectrodes without nanocellulose. Current-concentration responses for the alternative one-pot (20 µL) and layer-by-layer nanocellulose/pyNHS HRP bioelectrodes are reported in Figure S3. Significantly smaller catalytic currents were observed for these alternative configurations. The most important difference between the alternative nanocellulose preparations and the optimised preparation is that 300% more enzyme and nanocellulose were used for the alternative nanocellulose electrodes. Therefore, it seems likely that the nanocellulose at the alternative electrodes, possibly involving a synergetic effect with enzyme, hinders effective orientation and electron transport between the HRP and the pyNHS-modified CNTs. The alternative one-pot (20 µL)

bioelectrode gave approximately two-fold higher catalytic currents compared to the alternative "layer-by-layer (20 µL)" bioelectrode prepared using the same amounts of enzyme and nanocellulose (Figure S3). The incorporation of nanocellulose in the enzyme layer (onepot) as opposed to on the enzyme layer (layer-by-layer) therefore has a drastic positive effect on the catalytic current. The superior catalytic currents at layer-by-layer compared to one-pot can be explained by two important effects. The first, that the one-pot electrode has increased hydrophilicity and therefore hydration across the bulk nanocellulose-CNT matrix that increases the amount of electrochemically-wired HRP in the porous electrode structure. And second, a steric and/or electrically insulating barrier effect for the layer-by-layer electrode that limits H 2 O 2 permeation and enzyme wiring, respectively.

Next our attention focused on evaluating the open-circuit potential (OCP) as an indicator of effective bioelectrocatalysis and as a useful parameter of a biocathode for estimating the maximum possible operating voltage of a biofuel cell. The OCP is the potential adopted by the electrode at zero current and in this case reflects the highest potential at which the enzyme is capable of DET with the electrode, being typically close to the onset potential for bioelectrocatalytic reduction (Mano and de Poulpiquet, 2017). Figure 6A shows the loss in OCP at an increasingly slower rate with increasing additions of H 2 O 2 for the one pot (5 µL) nanocellulose bioelectrode. A high and stable OCP and onset potential is highly desirable, particularly for biocathodes with the objective of boosting the voltage output of biofuel cells.

Despite the slightly weaker OCP performance by ca. 5%. for the nanocellulose bioelectrode, the OCP values of between 0.5 to 0.62 V at ≤ 6 mmol L -1 H 2 O 2 remain in a very practical range for a biocathode. Bioelectrocatalytic stability experiments were performed over a 9-10 day period at the modified electrodes. Figure 6B shows a plot of the catalytic currents measured in the presence of 4 mmol L -1 H 2 O 2 at 0 V vs. Ag/AgCl from cyclic voltammograms recorded at 10 mV s -1 from 0.6 V to 0 V. The bioelectrodes were stored in 0.1 M phosphate buffer (pH 7) solution free of H 2 O 2 in the fridge at 4°C. The stability profiles for the pyNHS and nanocellulose/pyNHS bioelectrodes show the same general trend. However, of particular interest, the nanocellulose bioelectrodes exhibit a dramatic enhancement in stability with an average of 67% of the initial activity remaining after 7 days compared to 39% after 7 days for the pyNHS modified bioelectrode without nanocellulose.

Conclusion

The non-covalent modification of multi-walled carbon nanotube electrodes with various pyrene derivatives is a simple and versatile method to promote DET bioelectrocatalysis with immobilised HRP for H 2 O 2 . Surface modification with NHS ester and butyric acid groups proved the most effective for both high and low "catalytic boost" potential bioelectrocatalytic H 2 O 2 reduction, and most resistant to parasitic H 2 O 2 electro-oxidation. Integration of bacterial nanocellulose by a straightforward one-pot protocol is an extremely promising method that not only enhanced catalytic current output while maintaining a very respectable open circuit potential performance, but also significantly improved the catalytic stability, offering 72% more stability, compared to the equivalent electrode without the nanocellulose. The nanocellulose strategy in principle can be used with any other enzyme at functionalised MWCNT electrodes to improve the activity and stability of a wide range of catalytic bioelectrodes for biosensor and biofuel applications. The nanocellulose biocathode, and future nanocellulose bioelectrodes, may also provide attractive biocompatibility, biodegradability, and mechanical properties for body-integrated applications but this remains to be explored.

Future work integrating HRP and HRP bi-enzymatic electrodes for biofuel cell applications is envisioned.

Figure 1 .

 1 Figure 1. Schematic representation showing the five pyrene compounds used to obtain pyrenemodified MWCNT bioelectrodes with adsorbed HRP for the two-electron bioelectrocatalytic reduction of H 2 O 2 to water. Enzyme structure pdb1H55 of HRP from Armoracia rusticana(Berglund et al., 2002).

Figure 2 :

 2 Figure 2: (A, B) CVs recorded at MWCNT-HRP bioelectrodes at 10 mV s -1 in 0.1 mol L -1 phosphate buffer (pH 7.0) with (A) 0.5 mmol L -1 and (B) 4 mmol L -1 H 2 O 2 : (ꟷ) unmodified; (ꟷ) py; (ꟷ) pyNHS; (ꟷ) pyAA; (ꟷ) pyBA; (ꟷ) pyNH 2 . (C) CV recorded from open-circuit potential at unmodified MWCNT without HRP at 10 mV s -1 in 0.1 mol L -1 phosphate buffer (pH 7.0) with 4 mmol L -1 H 2 O 2 .

Figure 3 :

 3 Figure 3: Amperometric current-concentration response curves recorded at MWCNT-HRP electrodes in 0.1 mol L -1 phosphate buffer (pH 7.0) before and after additions of H 2 O 2 at increasing concentrations: (A, •) unmodified; (B, •) py; (C, •) pyNHS; (D, •) pyAA; (E, •) pyBA; (F, •) pyNH 2 . Current values obtained at 0 V vs. Ag/AgCl. Error bars correspond to standard deviation from n = 3 samples.

Figure 4 :

 4 Figure 4: Schematic representation of the MWCNT-HRP electrodes modified with pyNHS and nanocellulose. (B) Representative CVs recorded at 10 mV s -1 at the one-pot (5 µL) nanocellulose/pyNHS HRP bioelectrode in 0.1 mol L -1 phosphate buffer (pH 7.0) (ꟷ) before and after addition of H 2 O 2 at (ꟷ) 0.4; (ꟷ) 0.6; (ꟷ) 1; (ꟷ) 2; (ꟷ) 4; (ꟷ) 6; and (ꟷ) 8 mmol L -1 .

Figure 5 .

 5 Figure 5. Current-concentration (A) full range and (B) linear dynamic range response curves recorded at MWCNT-HRP electrodes in 0.1 mol L -1 phosphate buffer (pH 7.0) before and after increasing additions of H 2 O 2 : (•) unmodified; (•) pyNHS; (•) one pot (5 µL) nanocellulose/pyNHS. Current values obtained at 0 V vs. Ag/AgCl. Error bars correspond to standard deviation from n = 3 samples.

Figure 6 :

 6 Figure 6: (A) Open circuit voltage-concentration plot recorded at MWCNT-HRP electrodes in 0.1 M phosphate buffer (pH 7.0) before and after increasing additions of H 2 O 2 : (•) unmodified; (•) pyNHS; (•) pyNHS-nanocellulose. (B) Bioelectrocatalytic current from CVs recorded at (•) pyNHS and (•) pyNHS-nanocellulose modified MWCNT-HRP electrodes in 0.1 mol L -1 phosphate buffer (pH 7.0) in 4 mmol -1 H 2 O 2 : (•) unmodified; (•) pyNHS; (•) nanocellulose/pyNHS. Current values obtained at 0 V vs. Ag/AgCl.

Acknowledgments

The authors would like to thank the Generalitat Valenciana (PROMETEO Program 2016/109 and 2020/078) for financial support. SB expresses her gratitude to the PROMETEO program for her pre-doctoral grant and the GV-Union Social Fund for the foreign research visit grant (BEFPI19). The authors gratefully acknowledge support from the platform Chimie NanoBio ICMG FR 2607 (PCN-ICMG), and financial support from the French Agence Nationale de la Recherche (ANR) under reference ANR-20-CE05-0006-01 (JCJC), and LabEx ARCANE (ANR-11-LABX-003-01) and CBH-EUR-GS (ANR-17-EURE-0003).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.