Guillaume Rosinosky
email: guillaume.rosinosky@loria.fr

Samir Youcef
email: samir.youcef@loria.fr

François Charoy
email: francois.charoy@loria.fr

A genetic algorithm for cost-aware business processes execution in the cloud

Keywords: BPM, elasticity, cloud, optimization

With the generalization of the Cloud, software providers can distribute their software as a service without investing in large infrastructure. However, without an effective resource allocation method, their operation cost can grow quickly, hindering the profitability of the service. This is the case for BPM as a Service providers that want to handle hundreds of customers with a given quality of service. Since there are variations in the needed load and in the number of users of the service, the allocation and scheduling methods must be able to adjust the cloud resource quantity and size, and the distribution of customers on these resources. In this paper, we present a cost optimization model and an heuristic based on genetic algorithms to adjust resource allocation to the needs of a set of customers with varying BPM task throughput. Experimentations using realistic customer loads and cloud resources capacities show the gain of these methods compared to previous approaches. Results show that, in our case, using our algorithm on split groups of customers can provide better results.

Introduction

Consuming "Business Process Management as a Service" (BPMaaS) offer benefits that IT people widely acknowledge. It reduces the operational burden and allows to rely on the provider for the maintenance and provisioning of the service. However, from the BPMaaS provider point of view, it increases the operational complexity. The provider must ensure that all his customers receive the same attention and a defined quality of service at all time. He must also ensure that it operates at the best possible cost.

A Business Process Management System (BPMS) deployment is complex: it requires application servers, process engines and database management systems. Clustered installations requiring load balancers can also be deployed for high availability. Each customer has a different usage pattern and the number of tasks to execute evolves constantly. Each cloud compute resource is costly and has a capacity corresponding to its CPU, memory, storage and network speed, for a defined response time. In order to maintain an optimal infrastructure cost, processes executions must be distributed on different cloud resources. Figure 1 shows an example with two customers (or tenants). They require different capacity at each hour. We want to allocate the cheaper Cloud resources and distribute the process execution of tenants on these resources to optimize the operational cost. In order to optimize resource usage, we must sometimes migrate tenants from an installation to another. In figure 1, at time 5, tenant 1 is moved on the same resource as tenant 2 because both require less capacity and fit on this resource. A migration generates disruption of service on the customer side. We must stop the processes and move the data from one installation to the other [START_REF] Das | Live database migration for elasticity in a multitenant database for cloud platforms[END_REF]. We must find the best distribution of tenants on resources for each interval of time while controlling the number of migrations for each tenant. This problem becomes complex for a high numbers of tenants.

We propose an integer linear programming (ILP) model and a genetic algorithm that aims at finding the best allocation strategy while limiting the number of migrations per tenant. We improve our previous results [START_REF] Rosinosky | Efficient Migration-Aware Algorithms for Elastic BPMaaS[END_REF] with a method that provides a better cost elasticity.

In the next section, we describe our migration strategy model, our genetic algorithm approach coupled to a solving of our model, and our previous iterative heuristic. We then study experimental results on both of the approaches compared to a baseline approach. We also show how we achieve interesting experimental results. Then, we compare our results with the state of the art. The last part concludes and presents our future work.

A migration strategy based model

In this Section we present the context for BPMaaS, our hypothesis and our method to optimize resource cost. This can be seen as a resource allocation problem with a constraint regarding the number of reallocations. Moving a tenant from a resource to another generates a service disruption. We want to limit their number to ensure stable quality of service for the customers. Thus, one of our problems is to find the right time to move tenants. We call it the migration strategy.

Context and constraints

Our approach is tenant-centric. All customers (tenants) processes are executed on the same BPMS installation. It is easier to manage deployments by customers rather than by processes. Customer processes share business data and security configuration that we need to manage together. Our assumptions are the following :

BPMS do not scale infinitely.

There is no such thing as an infinitely scalable BPMS installation. Even clustered installation reach a limit due to the transactional nature of the database interactions. Thus, we use several BPMS installations. In our approach, we assume our tenants can fit on the "bigger" resource available.

Provisioning and deprovisioning takes time. We cannot change instantly tenant distribution, as computing instances instantiation, software installation, and data migration takes time. Thus we compute resource allocation in a discretized manner at fixed time interval or time slot. A time slot is a significant period of time for the provider: it could be a few seconds or an hour.

A tenant is a customer of the BPMaaS. Tenants run BPM processes composed of tasks. To execute them, the BPMS needs computing power, network bandwidth, disk and memory. It relies on separated compute instances for database systems for data persistence, and load balancers for clustered installations.

Task throughput is our performance metric. It corresponds to the number of BPM tasks executed for one period of time (e.g. per second). This metric is meaningful for the customers.

Our approach is offline. We assume we know the required BPM task throughput for each tenant and each time slot.

A cloud resource has a capacity expressed in BPM task throughput. A cloud resource (or resource) is one or several cloud compute instances that we use for the database tier, BPM system tier, load balancer tier, etc. It supports a full BPMS installation. A cloud resource can host several tenants. In our case, we assume a tenant fits on one resource: tenants won't be distributed on several cloud resources.

The number of migrations must be limited. We name migration the action of moving a tenant data and processes from one cloud resource to another. It requires the target cloud resource to be up and running. This action takes time to be executed. If all tenants of a cloud resource are migrated, it can be released. Migrations generate QoS breaks for the customers [START_REF] Das | Live database migration for elasticity in a multitenant database for cloud platforms[END_REF]. We limit their number for each tenant depending on the Service Level Agreement.

Without an optimization method, a solution to allocate tenant to resources would be to allocate each tenant on a resource that supports its maximum task throughput. We call this solution, baseline method. This method is often used in production, but can become very expensive.

We proposed in [START_REF] Rosinosky | Efficient Migration-Aware Algorithms for Elastic BPMaaS[END_REF] a method based on an iterative heuristic and time series segmentation. It computes the list of necessary cloud resources and a mapping of tenants on each resource, time slot per time slot. We present it in the next Section.

Allocation with an iterative heuristic and time series segmentation

In this part, we recall briefly our previous method [START_REF] Rosinosky | Efficient Migration-Aware Algorithms for Elastic BPMaaS[END_REF]. It has two parts: first, we choose a migration strategy i.e the time slots where each tenant can migrate, and, second, we apply a heuristic using resources prices and capacity, tenants needs, and their migration strategy in order to obtain the cloud resources and the placement of tenants. For the first part, a time series segmentation [START_REF] Lovrić | Algoritmic methods for segmentation of time series: An overview[END_REF] allows to select good migration times for each tenant. We present in figure 2 two examples of migration strategies, in red for two tenants. In this figure, Tenant 1 can only be migrated at the end of time slots 1 and 4. For Tenant 2, it is time slots 2 and 3. This means both tenants will be migrated at most 2 times. They will stay on their origin resource if there is no migration authorization.

For the second part, our iterative timeslot heuristic is based on Variable Cost and Size bin packing in which we added repacking steps. It takes as input the tenant throughput by timeslot, the cloud resource prices and capacity, and the migration strategies for the tenants.

This coupled approach provides better results than the baseline approach.

Still, the comparison with the solution computed with a solver showed that it is far from the optimal cost. It is possible to enhance this solution. We propose to use a genetic algorithm to find migration strategies that reduce the resource cost, and propose an alternative to the iterative timeslot heuristic based on integer linear programming. We present this model in the next Section.

An efficient model for migration strategies

Our problem is to find resource and tenant distributions for each time slot, for given tenants' loads, resource prices and capacity, and migration strategy. The model we propose answers to this problem. Our model principle is based on the absence of tenant migration when there no authorization to move. In this case, simple placement constraints should exist, and no constraint exist when there is an authorization to move in the migration strategy.

Let the following variables:

-T , the set of cloud resource types, with t its cardinality.

-I, the set of tenants with n its cardinality.

-J , is T ×I the set of all possible cloud resources associated with each tenant. its cardinality is m = t × n. -C j , and W j represent respectively the cost and the capacity in terms of BPM task throughput for the configuration j, with j in J . w i (k), the required capacity in terms of BPM task throughput for the tenant i during time slot k. -K defines all the time slots, from 0 to D, where D + 1 is the number of time slots. x j i (k), the assignment of tenant i to configuration instance j during time slot k.

y j (k), the activation of configuration j during time slot k.

-M , the maximum number of migrations of tenants between cloud resources on all time slots.

-h i (k) with 0 ≤ k ≤ D -1. h i (k) is equal to 0 if
h i (k) = M
where M is the number of migrations. This number depends on the SLA.

The objective is to minimize the total cost for all active cloud resources, for each time slot, as shows equation 1.

min j∈J j k∈K k C j y j (k) (1)
We must ensure that the following constraints are enforced:

∀i ∈ I, ∀k ∈ K j∈J j x j i (k) = 1 (2) ∀j ∈ J , ∀k ∈ K i∈I i w i (k)x j i (k) ≤ W j y j (k) (3) ∀j ∈ J , ∀i ∈ I, ∀k ∈ K|h i (k) = 0, x j i (k) = x j i (k + 1) (4) ∀i ∈ I, ∀j ∈ J , ∀k ∈ K, x i j (k) ∈ {0, 1}, y j (k) ∈ {0, 1} (5)
Equation 2 represents the obligation for a tenant to be placed at each time slot on an active cloud resource. Equation 3 means that the sum of the required capacity for each tenant on one cloud resource cannot exceed the capacity of the cloud resource. Equation 5represents the variables we use. Equation 4represent the migration strategy. The equality constraint means that for a tenant i and a time slot k, assignation values x i j (k) will stay the same on time slots k and k + 1. When a tenant is authorized to migrate between resources, there is no constraint for this tenant. Generalizing this on all resources produces the desired effect: tenants will be migrated from one resource to another only during the time slots specified by the migration strategy. The pre-defined migration strategy is symbolized here by the variable h i (k).

Finding cheap migrations strategies is primordial in our approach. This is the goal of our genetic algorithm. We present it in the following Section.

Cost optimization via genetic algorithms

A genetic algorithm is a well known meta-heuristic belonging to the family of evolutionary algorithms, and inspired by natural selection [START_REF] Whitley | A genetic algorithm tutorial[END_REF]. Its principle is to produce directed random evolutions on a population of individuals until it obtains one or several individuals with a good fitness value. Individuals are usually vectors of boolean values, whose corresponding fitness can be evaluated. Iterations are triggered until an end condition is reached.

We want to find the best migration strategy for all the tenants and time slots. Figure 3 shows our approach. The general principle is to use our iterative time slot heuristic (or the restricted model we have described in the previous Section) for evaluating migration strategies, until we find the best. To represent an individual, we vectorize a migration strategy by concatenating migration strategies of each |I| tenants (each one corresponding to a vector of D boolean values, D + 1 being the number of studied time slots). The size of the vector will be D × |I|, with each element being equal to zero or one. For instance with two tenants and three time slots, the first migrating on the second time slot and the second tenant on the third time slot, we will have the following representation: 0 1 0 0 0 1 . The reader will find in figure 4 a brief description of the different steps of a genetic algorithm. Compared to the traditional approach, we have switched the mutation phase and the crossover phase. The co-hosted mutation requires to know the cost of the migration strategy in the population. We compute the cost in the fitness evaluation phase. The crossover phase generates potentially unknown (not yet computed) migration strategies. Thus, we do it after the mu-tation phase. In our case, "parents" are mutated instead of the offspring. In the following, we describe the solution we designed.

Population initialization

We initialize the population with several segmentation algorithm combinations (as we described in Section 2.2), and with random individuals with the correct number of migrations for each tenant.

Fitness evaluation

We want to find the migration strategies that produces the lowest cost. The fitness score corresponds to the total cost of all the active resources on the time slots. To evaluate it on the different individuals, we compute the cloud resources allocation and placement of the tenants on it. In our case, we run our iterative time slot heuristic [START_REF] Rosinosky | Efficient Migration-Aware Algorithms for Elastic BPMaaS[END_REF] or a solver on our model presented in Section 2.4, for each individual (migration strategy) we need to evaluate. We keep the cloud resources and tenants assignation distribution in memory for the next steps, and the fitness score.

Termination condition We use a time limit termination condition. This allow us to compare different solutions based on this limit.

Parent selection For this step, we use a classical rank selection strategy. We sort the population by fitness and we select randomly, and with a higher priority, the individuals with the higher rank (lower fitness or price in our case) for parents.

A specific mutation: co-hosted tenant migration mutation strategy In classic approaches, mutation updates randomly individuals, depending on a mutation rate, switching scalar values from zero to one or the other way around [START_REF] Whitley | A genetic algorithm tutorial[END_REF].

Here, the goal is to generate brand new individuals in the population, with non tested configurations. In our case, we cannot use a totally random approach, as the number of migrations for each tenant is bounded. However, even a randomized approach keeping a fixed number of migrations will not provide the desired effects as we can see on the left side of figure 5. We have noticed that most of the times, resources are not liberated as only one of their tenants is authorized to migrate. It limits the savings of resources liberation. We developed an alternative mutation more suited to our problem.

It consists in shifting the authorization to migrate for each co-hosted tenant at the indicated time slot for the reference tenant's resource. To achieve this goal, for each tenant, we browse the past time slots until we find an authorization to migrate or until we reach the beginning of the time slot space. If we find one, we set it to zero while setting to one the "destination" time slot. If the "destination" time slot is already set to one, we ignore this behavior. The example on the right side of figure 5 describes this principle. There, it is possible to migrate all the tenants of resource R1 to the cheaper resource R2, and thus reduce costs1 .

Fig. 5. Basic tenant mutation vs cohosted mutation

Specific offspring generation: the tenant crossover strategy The crossover phase consists in randomly mixing individuals (parents) of the current population in order to generate new individuals (children) having characteristics of both parents. The crossover technique that we use consists in switching the migration time of random tenants. First, two children identical to two migration strategies parents are generated. Then, depending on the number of tenants specified, each one will see its migration times switched in the children.

Generational replacement

We replace the entire population with the offsprings, except for the best individuals from the original population (named elites). They replace the less fit offspring in the future population.

In the next Section, we present our experiments and the results.

Experimentation

We have conduct tests with the cloud resource prices and sizes, and the seeds of our previous work [START_REF] Rosinosky | Efficient Migration-Aware Algorithms for Elastic BPMaaS[END_REF]. We consider 12 configurations, each composed of two Amazon Web Services compute resources: one database resource (RDS) for the database, and one compute instance (EC2) for the application server. Prices are comprised between 0.177 $ per hour for a BPM task throughput of 16.4 tasks per second, and 4.126 $ per hour for a BPM task throughput of 129.279 tasks per second.

For the customer part, we vary the number of tenants (10, 25, 50 and 100), and we use different throughputs in terms of BPM task per second. These throughputs are based on usage of anonymous customers of the BPMS Bonita2 . We consider 6 configurations, needing a throughput respectively between 1 and 120, 14 and 16, 0 and 120, 1 and 3, 5 and 120, and 0 and 4 3 .

We generate each tenant's initial time slot throughput randomly following an uniform distribution between the two throughputs. Our next step is to generate the variation of throughput between time slots by adding or removing a random value limited to one quarter of the difference between the maximum and the minimum throughput. For our experiments, we used the Python library Inspyred [START_REF] Garrett | inspyred: Bio-inspired Algorithms in Python -inspyred 1.0 documentation[END_REF] for the genetic algorithm that integrated well with our environment.

Experiment Parameters In order to obtain significant and realistic results, we used the following parameters:

each test is launched for 10 different random seeds (i.e tenants' loads) a time slot size of one hour, as it was the reference duration of AWS cost model for computing instances at the time of the experiment. we choose to consider 4 migrations per day. A migration produces an interruption of around 10 seconds depending on the quantity of data. we consider a 2 days period (thus limiting migrations to 8, for 48 time slots).

we consider the following parameters for the genetic algorithm: the number of elites individuals to 5, a mutation rate of 0.4, a population size of 20, a number of mutation points corresponding to the number of tenants divided by 5. These parameters were chosen following tests on multiple values for a limited number of seeds each. Details on this choice cannot be included for space restriction reasons. we limit the genetic algorithm computation to 600 or 1800 seconds and the solver computation time to 5 seconds.

Results

Fig. 6. Mean genetic algorithm gain on best initial segmented population for 600 second of running time

In figure 6, we show the relative gain of this approach compared to our previous approach (segmented approach) in red (in the upper part of the figure), and to a baseline approach in blue (in the lower part of the figure). The gain is better for 10 tenants than for 100 tenants since the system has more time to search for the cheapest solution. For 10 tenants, we obtain more than 10 % enhancement compared to the previous approach, and more than 45 % compared to the baseline approach. However for 100 tenants, we have only a 1 % enhancement.

It appears that either the iterative usage of the heuristic, the genetic algorithm or the two of them is more efficient for a small number of tenants for the same number of generations. This is why we conducted experiments where we apply the proposition to subsets of the tenants and we aggregated the results as described in the next Subsection.

The splitting strategy

For this solution, we split the set of tenants into small groups selected randomly. We have tested different size of groups with various number of tenants and we applied the previous method keeping the same total computation time. Figure 7 shows the results we obtained with the genetic algorithm and the iterative heuristic. The x axis corresponds to the size of the groups of tenants. The y axis shows the relative gain compared to the results with no partition. A subset size with the same size as the number of tenants corresponds to no split, the gain is zero. We obtain the best results with partitions of 5 tenants in all cases. For the experiments we ran, the gain varies from 5% to 15%. We have no good expla-nation for this result that we can reproduce. Our tests with the solver give the same results for the size of the groups as with the heuristic. In the next Section we present our results with groups of 5 tenants.

Results for solver and iterative heuristic

We implemented our model (presented in Subsection 2.4) using the optimization library PuLP4 with the Gurobi solver 5 . For execution time and cost reasons, we were not able to test every set of parameters. For instance, with our current implementation, we managed to obtain results with the solver only up to a size of 25 tenants for the partition. Indeed, the duration of the initialization part and the required memory makes it impossible to run with more tenants. Thus we have limited our tests to parts of 5 tenants, for a total of 50 and 100 tenants. As we can see, the results stay close to the results of the heuristic. Figure 8 shows the absolute gain we obtained, and the corresponding percentage compared to the baseline approach cost, for 600 seconds and 1800 seconds of running time. We also present the non-split result for the segmented approach (results of the previous paper), and the split segmented approach where we apply time series segmentation on the groups of 5 tenants instead of all the tenants simultaneously. For 1800 seconds of execution time of the genetic algorithm, split heuristic give the best results. Mean distribution costs are 51.34 % for 50 tenants, and 51.72 % for 100 tenants compared to the cost of the intuitive approach. Using the solver gives good results but more expensive (respectively 55 % and 54.19 %). For 600 seconds of execution time, the results are more balanced: they vary between 54.2% and 55.64%. The genetic algorithm does not enhance the results a lot for both approaches after 600 seconds: 3% for the heuristic and less than 1 % for the solver. Still, it enhances the initial split segmented results from 61.3 % to 51.34% for 50 tenants, and from 59.34 % to 51.72 % for 100 tenants.

We observe that the split segmented approach allows to gain more than 2 % , and to unleash the results of the genetic algorithm. Without splitting we gain around 1 % for 600 seconds of genetic algorithm compared to the original population (non split segmented). When splitting, the genetic algorithm results in a gain of 7.1 % for 50 tenants, and 4.69 % for 100 tenants compared to the split segmented strategy. The absolute gain compared to the intuitive approach remains worthwhile for 2 days: we save 1702 $ for 50 tenants and 3319 $ for 100 tenants for a cost of respectively 3498$ and 6874$. The respective gain compared to our previous work is 425 $ and 763 $.

Related work

Many researchers have studied elasticity in the cloud and elasticity for BPM or orchestration systems. Schulte and al. [START_REF] Schulte | Elastic Business Process Management: State of the art and open challenges for BPM in the cloud[END_REF] did a general review on the topic and gave directions for future research. In this paper, we focus on the resource allocation and scheduling problem and use a tenant-centric approach based on BPM task throughput, instead of the BPM process-centric from other approaches. Rekik et al. [START_REF] Rekik | A Linear Program for Optimal Configurable Business Processes Deployment into Cloud Federation[END_REF] propose an integer programming model based on general hardware metrics for BPM elasticity on the cloud. They base their approach on resource allocation and BPM task scheduling. They do not consider multiple time slots, tenant migration or multi-tenancy. Other attempts on BPM elasticity in the cloud exist such as [START_REF] Euting | Scalable Business Process Execution in the Cloud[END_REF], [START_REF] Xu | Resource Management for Business Process Scheduling in the Presence of Availability Constraints[END_REF], [START_REF] Hoenisch | Cost-Efficient Scheduling of Elastic Processes in Hybrid Clouds[END_REF]. Though not cloud-related, Djedovic et al. propose in [START_REF] Djedović | Optimization of business processes by automatic reallocation of resources using the genetic algorithm[END_REF] a genetic algorithm for BPM task scheduling to their corresponding resources. It uses a representation of each resource. They want to minimize the waiting time and the global resource cost. Junhke et al. [START_REF] Juhnke | Multi-objective Scheduling of BPEL Workflows in Geographically Distributed Clouds[END_REF] propose a task focused genetic algorithm for BPEL workflows scheduling in distributed Clouds.

On other subjects than BPM, the machine reassignment problem6 is close to our problematic. It considered software reassignment problem on virtual machines including the migration cost. Gavranovic et al. [START_REF] Gavranović | Variable Neighborhood Search for Google Machine Reassignment problem[END_REF] obtained the better results to this challenge. However, this problem is based on hardware metrics, and aggregate migration cost in the objective function. Our problem is not exactly virtual machine allocation since the hardware is already defined. Numerous other attempts target virtual machines, such as [START_REF] Chen | Tradeoffs Between Profit and Customer Satisfaction for Service Provisioning in the Cloud[END_REF]. Automated approaches based on cloud offers retrieval and hardware requirement for software such as [START_REF] García | Automated Analysis of Cloud Offerings for Optimal Service Provisioning[END_REF] are also valuable.

These works do not consider simultaneously multi-tenancy, multiple instance types, and migrations, except in the form of data transfer cost for [START_REF] Hoenisch | Cost-Efficient Scheduling of Elastic Processes in Hybrid Clouds[END_REF] or aggregated migration cost for [START_REF] Gavranović | Variable Neighborhood Search for Google Machine Reassignment problem[END_REF]. In this paper, we present an evolution of our previous work [START_REF] Rosinosky | Efficient Migration-Aware Algorithms for Elastic BPMaaS[END_REF]. We have based our approach on time series segmentation for deducing the "good" time slots to migrate tenants, and on the iterative use of an enhanced version of our time slot heuristic [START_REF] Rosinosky | An Efficient Approach for Multitenant Elastic Business Processes Management in Cloud Computing Environment[END_REF]. We also presented the corresponding ILP (Integer Linear Programming) model. Results were encouraging compared to a baseline approach, but could be improved regarding the results that we obtain with a solver. We could not compare with other approaches since most of them do not consider migrations of data as an issue. They scale up by adding compute resources to the process engine, considering that access to the database is not a problem. From our experience, at some point, the database is always a bottleneck.

Conclusion

In this paper, we proposed a method for cost optimization of BPMaaS deployment based on tenant migration strategies and a genetic algorithm. We presented a new integer programming optimization model. Both allows to obtain substantial gains for BPMaaS providers. The result we obtain when we group the tenants is interesting. It may be explained by the size of the objective space. The fact that it is reproducible for different number of tenants shows that testing multiple sizes may allow providers to save on the operation cost. Moreover, using other metaheuristics such as simulated annealing or hill climbing could provide even better results.

Our method was tested with BPM task throughput but could work with other metrics that can be expressed as a scalar for both the cloud resources and the tenants. We can consider for instance the number of processes, or the number of HTTP requests that lead to transactional processing. Our methods can then be generalized on systems non related to BPMS using multi-tenancy and tenant-related persisted data. A BPMS execution engine behaves more or less like a transactional web application. Our approach is offline and require to anticipate on the tenant load. For many business cases, this is a valid assumption. The server load is relative to the number of employees and the number of cases they can execute everyday or hour with little variations. A next obvious step would be to couple our algorithm with prediction systems. This would provide an effective online algorithm. It could adapt to unforeseen variations.

Fig. 1 .

 1 Fig. 1. Multi tenant resource allocation and distribution tenants

Fig. 2 .

 2 Fig. 2. Exemple of a migration strategy

Fig. 3 .Fig. 4 .

 34 Fig. 3. A genetic algorithm to find better strategies

Fig. 7 .

 7 Fig. 7. Gain depending on splitting strategy for various split quantities.

Fig. 8 .

 8 Fig. 8. Mean cost comparison for 50 and 100 tenants per group of 5

  the tenant i is not allowed to be migrated between time slot k and k+1, and equal to 1, if it is allowed. The set of all h i (k) (for each tenant and each time slot) is a migration strategy.migration strategies assume the maximum number of migrations allowed per tenant: ∀i ∈ I

	k∈K
	k

The simple approach on the left of figure5keeps tenants on resource R1, it can never be freed

http://www.bonitasoft.com/

The data and the results are available at: https://doi.org/10.5281/zenodo. 1173617. The source code of the framework is not public, except for the segmentation library, available at https://github.com/guillaumerosinosky/Segmentation/.

https://pythonhosted.org/PuLP/

http://www.gurobi.com/

http://www.roadef.org/challenge/2012/en/

Acknowledgment

The authors would like to thank Gurobi for the usage of their optimizer, and Amazon Web Services for the EC2 instances credits (this paper is supported by an AWS in Education Research Grant Award).


Simone Hemm-Ode

Daniela Pison
email: daniela.pison@fhnw.ch

Fabiola Alonso

Ashesh Shah

Jerome Coste

Jean-Jacques J Lemaire

Erik Schkommodau

Karin Wårdell
email: karin.wardell@liu.se

Dr Simone Hemm
email: simone.hemm@fhnw.ch

Prof Karin Wårdell

A method for electric field simulations and acceleration measurements for intraoperative test stimulation

Background

Despite an increasing use of deep brain stimulation (DBS), the fundamental mechanisms underlying therapeutic and adverse effects as well as the optimal stimulation site remain largely unknown. Computer simulations of electric entities such as electric field or current density are more and more used to try to identify the stimulated volume around implanted DBS electrodes. So far simulations for intraoperatively obtained test stimulation data have not been considered. The aim of the present work was to propose a methodology allowing an optimal exploitation of test stimulation data including a quantitative assessment of the clinical outcome by acceleration measurements. Patient-specific electric field simulations for stimulation amplitudes at different anatomical positions might provide supplementary data about implicated structures and the mechanism of action. In order to illustrate technical and clinical feasibility, the presented methodology has been applied to two patients.

Methods

Results

• 108 electric field simulations performed for the eight trajectories • Simulation-based versus classical approach (Fig. 2): VO and VCM appear more often; DL appears only with the simulation based approach. • Low versus high improvement (Fig. 2): Differences in appearance especially in VO, VIM and VCM SURGICAL PROTOCOL • Preoperative manual outlining of VIM and its anatomic neighbors using iPlan (Brainlab, Feldkirchen, Germany) and choice of target • Intraoperative microelectrode recording (MER) and test stimulations -in 24 (patient 1) and 30 positions (patient 2) (4 traj. per patient) -clinically evaluated using 3-axis accelerometer [Shah, 2013] DATA ANALYSIS

Discussion

• Workflow and methodology for e-field simulations on manually outlined anatomical structures have been designed. • First results seem to confirm published data hypothesizing that the stimulation of other structures than the VIM might at least partially be responsible for good clinical effects: Vassal et al. [START_REF] Vassal | [END_REF] already suggested that parts of the ventro-oral nucleus (VO) could be appropriate targets as well. • New concept including a detailed analysis of the isofield maps will allow the analysis of a high amount of intraoperative data which might help to elucidate the mechanism of action of DBS. • Highest improvement at positions were the following structures where present in stimulated volume: VO (69  21%), VCM (67  24%), VIM (50  19%) • E-field maps show as well that not always best intraoperative clinical results can be observed in the Vim but in the surrounding regions (Fig. 3)

E-FIELD SIMULATION

Input: T1 MRI dataset, stereotactic CT, target coordinates, stimulation position and amplitude Electric field simulations: Patient specific modeling based on MRI Output: Electric field isosurface for 0.2V/mm [Dicsfalusy, 2013]

Figure 1 :

 1 Figure 1: Workflow for generation of patient-specific electric field simulations on patient specific anatomy

Figure 2 :

 2 Figure 2: Differences in the number of appearance between simulation-based and classical approach and between low and high improvement for the simulation based approach

Figure 3 :

 3 Figure 3: E-fields visualised for highest obtained clinical improvement at a specific position in patient 1 (red to yellow colour scale) superimposed to anatomical structures: sagital view (right side) (A) and axial views, inferior to superior (B to F). Clinical improvement is higher outside the VIM (=gray structure) (A, E, F) than inside (B, C, D).

  • Simulation-based approach clearly brings in supplementary information compared to the classical one. But the analysis of more data is necessary to draw any final conclusion.

		InL	DL		VO	VIM	VCM	LaCM	VCL
	Approach	Low	High	Low	High	Low	High	Low	High	Low	High	Low	High	Low	High
		impr.	impr.	impr.	impr.	impr.	impr.	impr.	impr.	impr.	impr.	impr.	impr.	impr.	impr.
	Simulation-based	9	13	8	11	10	16	9	20	10	21	3	5	1	4
	Classic	7		0		10	17	7		3		2


Ashesh Shah
email: ashesh.shah@fhnw.ch

Jerome Coste

Jean-Jacques J Lemaire

Erik Schkommodau

Dr Simone Hemm
email: simone.hemm@fhnw.ch

S Hemm-Ode

Correlation analysis between quantitatively analyzed stimulation effects and anatomical position during deep brain stimulation surgery

published or not. The documents may come

Correlation analysis between quantitatively analyzed stimulation effects and anatomical position during deep brain stimulation surgery

Background

Deep Brain Stimulation (DBS) is a routinely performed surgical procedure for treatment of movement disorders like Essential Tremor (ET). However, the target selection in DBS is not fully optimized. Incomplete knowledge of the mechanisms of action being one of the reasons, we believe, suboptimal usage of information during surgery is another. We have previously demonstrated the use acceleration sensors to quantify changes in patient tremor during deep brain stimulation surgery [START_REF] Shah | A method to quantitatively evaluate changes in tremor during deep brain stimulation surgery[END_REF]. We analyzed the correlation of the acceleration data results with the different deep brain structures. We present in this paper the result from 6 ET patients implanted in the ventrointermediate nucleus (VIM) of the thalamus.

Methods

PATIENTS

-5 patients with Essential tremor (ET) participated in a clinical study -bilateral implantation of DBS electrodes was performed in the ventrointermediate nucleus (VIM) region. SURGICAL PROTOCOL -Preoperative manual outlining of Vim and its anatomic neighbors was done using iPlan (Brainlab, Feldkirchen, Germany) and the target point was selected (Fig 1). -Intraoperative microelectrode recording (MER) and test stimulations (Fig 2 ) : -124 test stimulations in total, were performed for 5 patients.

-Maximum reduction in tremor and the corresponding amplitude were noted for all positions using visual symptom evaluation. -Acceleration data were recorded and evaluated for all test stimulations (Fig 3

Results

-The 124 test stimulations were distributed over 7 different thalamic regions : Centre Median (CM), Intermediolateral (IML), VIM, Ventrocaudal lateral (VCL), Ventrocaudal medial (VCM), Ventro-oral (VO) and also in Preleminiscale Radiations (PreR) -In the VCM and the VO, the improvements described by the neurologist for the same amplitude is higher than that for the VIM, and in the IML, VCL and the VO, the improvements measured by the acceleration data for the same amplitude is higher (Fig 4, Table 1). For the VO, the improvement is higher compared to the VIM when evaluated by both methods. -For similar amount of tremor reduction,

Discussion

• Quantitative analysis suggests VCL, IML and VO might be better targets than VIM with lower side effects and better reduction in tremor for less current. This is not observed with visual evaluation method (Fig 4). • Quantitative evaluation of patient tremor assists in identifying stimulation target structures. • New and more effective targets can be identified using quantitative evaluation along with visual evaluation. • Higher reduction in tremor at lower stimulation amplitude will benefit patients in multiple ways : less side effects, longer stimulator battery life etc. • More evaluations for CM are required to increase the significance of the results. • However, one structure per stimulation position is not optimum, as stimulation creates a 3D volume of Electric Field. Further analysis necessary by considering electric field stimulations

  ) -One thalamic sub-structure was attributed to every test stimulation position[START_REF]Direct stereotactic targeting of the ventrointermediate nucleus of the thalamus based on anatomic 1.5-T MRI mapping with a white matter attenuated inversion recovery (WAIR) sequence[END_REF].DATA ANALYSIS-Statistical features were calculated from acceleration data for quantitative tremor evaluation. -For every test stimulation, change in acceleration features was calculated for the data corresponding to the visually identified effective stimulation amplitude. -Stimulation amplitudes were also identified based on acceleration data where the change in acceleration features was equivalent to the change observed visually during the surgery. -Data for all stimulation positions were then grouped based on the thalamic substructure associated with it. Institute for Medical and Analytical Technologies, Head: Prof. Dr.-Ing. Erik Schkommodau, Gründenstrasse 40 et al. hnw.ch/lifesciences

Fig 1 :

 1 Fig 1: Patient images with marked thalamic structures

Fig 3 :

 3 Fig 3 : Tremor acceleration data along with stimulation amplitude.

Table 1

 1


Michaël Hermoso
email: michael.hermoso@sorbonne-universite.fr

Fabrice Minoletti

Mass and Fine-Scale Morphological Changes Induced by Changing Seawater pH in the Coccolith Gephyrocapsa oceanica

High resolution microscopic analyses of coccolith biominerals cultured under pH ranging from 7.4 to 9.0.

• Detection of ultrastructural changes within the biominerals to provide a mechanistic understanding of the effect of pH on biomineralization.

• Decrease in calcite mass at lowest pH corresponds to a strong reduction of the breadth of the central tube of the coccoliths.

Abstract

Coccolithophores have been extensively studied to understand the environmental control on calcification in a key biological group influencing the alkalinity of seawater. Previous studies have established that bulk calcification scales with cell division rates under a wide range of pH conditions. Yet, the fine scale ultrastructural changes of the coccoliths and therefore the pH-sensitive underlying mechanisms altering biomineralization of the coccoliths remain largely under-constrained. Using circularly polarized light and high-resolution microscopy, we have generated mass estimates of cultured Gephyrocapsa oceanica coccoliths grown in media with pH values ranging from 7.4 to 9.0. These mass estimates representing a bulk calcification response were related to the morphological changes within the coccoliths. From optimal (pH 8.6) down to pH 7.4 conditions, we have observed that impaired cell growth and lower calcite quota are accompanied by a 35% decrease in mean coccolith mass. The data further show that seawater acidification does not homogenously affect calcification of the coccoliths, as a clear decrease of the breadth of the tube (a structure surrounding the central area of the coccoliths) was detected, whereas all other ultrastructural components were far less impacted. We discuss this specific sensitivity to acidification as the possible consequence of the altered interaction of the acidic polysaccharides used for biomineralization and ambient concentration of protons released by calcification that substantially modify the growth patterns, the morphology, and ultimately the mass of the coccoliths.

Plain Language Summary

Anthropogenic rise in CO2 concentrations induces ocean acidification, which represents a threat for marine organisms. As calcium carbonate is sensitive to pH, those organisms secreting calcite shells, such as the coccolithophores (unicellular microalgae) are particularly exposed to ongoing climate change. Previous studies have documented that the coccoliths, the calcite biominerals produced intracellularly by the coccolithophores, will be adversely affected by decreased ambient pH values. Yet, how this reduction operates at the scale of the coccolith remains elusive and we are thus lacking an understanding of the intracellular mechanisms behind undercalcification, which is essential to anticipate the response of marine calcifiers in a changing planet. We analyzed the morphometric parameters of coccoliths grown under the pH range 7.4 -9.0. Our data show a clear reduction in coccolith mass in more acidic conditions, and we explain this change by altered growth of calcite at an early stage of the formation of the biomineral. This study suggests that certain organic molecules used to promote intracellular calcification are perturbed by decreased local pH, and that less calcified coccoliths produced within the cell cannot be the result of a post mortem process that may occur when calcite is bathed in relative low pH environments after their secretion outside the cells.

Introduction

Calcification by coccolithophore microalgae occurs in the oceans since the Late Triassic (~200 Ma) and has offered a valuable deep sea climatic archive that paleoceanographers study to reconstruct ancient climates. By mineralizing dissolved inorganic carbon and alkaline earth cations, the production of the coccoliths in sunlit oceanic waters is influential on the carbonate chemistry of seawater, which in turn controls, with temperature and salinity, the dynamics of the exchange of CO2 between the atmosphere and the surface oceans, and hence climates [START_REF] Sigman | Glacial/interglacial variations in atmospheric carbon dioxide[END_REF][START_REF] Ridgwell | A Mid Mesozoic Revolution in the regulation of ocean chemistry[END_REF]. With raising concerns about the future climate of the Anthropocene, there is a need to quantitatively and mechanistically understand the effect of decreasing pH values of the surface oceans on oceanic phytoplankton (e.g. [START_REF] Doney | Ocean Acidification: The Other CO2 Problem[END_REF]. Under a perturbed environment, the environmental, physiological and genetic parameters -and the interplay thereof-controlling cellular calcite quota in the coccolithophores remain largely under-constrained beside a bulk response that has been achieved thus far. Overall, culture studies of the coccolithophores have been overwhelmingly focused on Emiliania huxleyi and showed reduced bulk calcification at the lowest pH [START_REF] Riebesell | No Title[END_REF][START_REF] Iglesias-Rodriguez | Phytoplankton calcification in a high-CO2 world[END_REF][START_REF] Rickaby | Perturbing phytoplankton: response and isotopic fractionation with changing carbonate chemistry in two coccolithophore species[END_REF][START_REF] Langer | The morphological response of Emiliania huxleyi to seawater carbonate chemistry changes : an inter-strain comparison[END_REF][START_REF] Hoppe | Emiliania huxleyi shows identical responses to elevated pCO2 in TA and DIC manipulations[END_REF][START_REF] Bach | Influence of changing carbonate chemistry on morphology and weight of coccoliths formed by Emiliania huxleyi[END_REF][START_REF] Sett | Temperature Modulates Coccolithophorid Sensitivity of Growth, Photosynthesis and Calcification to Increasing Seawater pCO2[END_REF][START_REF] Riebesell | Competitive fitness of a predominant pelagic calcifier impaired by ocean acidification[END_REF][START_REF] Müller | Independence of nutrient limitation and carbon dioxide impacts on the Southern Ocean coccolithophore Emiliania huxleyi[END_REF]. In addition, changes in bulk calcite production under pH/pCO2 perturbation experiments was previously documented for the ubiquitous coccolithophore species Gephyrocapsa oceanica [START_REF] Rickaby | Perturbing phytoplankton: response and isotopic fractionation with changing carbonate chemistry in two coccolithophore species[END_REF][START_REF] Sett | Temperature Modulates Coccolithophorid Sensitivity of Growth, Photosynthesis and Calcification to Increasing Seawater pCO2[END_REF][START_REF] Hermoso | Control of ambient pH on growth and stable isotopes in phytoplanktonic calcifying algae[END_REF]. Specifically, it has been showed that cell division rates of Gephyrocapsa oceanica (µ) and µ-normalized calcite quotas scaled linearly: Cells dividing more frequently (high µ) have higher calcite quota (calcite produced per cell and per day) [START_REF] Sett | Temperature Modulates Coccolithophorid Sensitivity of Growth, Photosynthesis and Calcification to Increasing Seawater pCO2[END_REF]. However, a much more limited number of studies have approached this problem by characterizing changes in finescale morphometrics of the coccoliths [START_REF] Bollmann | Morphological and Physiological Characteristics of Gephyrocapsa oceanica var. typica Kamptner 1943 in Culture Experiments: Evidence for Genotypic Variability[END_REF][START_REF] Young | Morphology of Emiliania huxleyi coccoliths on the northwestern European shelfis there an influence of carbonate chemistry?[END_REF]. In this study, we dissect the effect of changing ambient pH values on calcification patterns of individual coccoliths through laboratory cultures of Gephyrocapsa oceanica. The overarching question addressed in our work is to determine whether calcification is homogenously affected at the scale of the coccolith and to establish how the discrete ultrastructural parts of the biomineral (the shields, the elements of the tube and of the bridge, and the central area) specifically respond to acidification (Figures 1 and2).

Materials and Methods

Culture Material

We analyzed cultured coccoliths of the species Gephyrocapsa oceanica (strain RCC 1314) that were grown and geochemically measured in an earlier study aiming at understanding the biological isotopic fractionation in coccolith calcite [START_REF] Hermoso | Control of ambient pH on growth and stable isotopes in phytoplanktonic calcifying algae[END_REF]. The raw medium was made from natural seawater from the English Channel with chemical amendments following the K/2 recipe [START_REF] Keller | Media for the culture of oceanic ultraphytoplankton[END_REF]. Temperature was kept constant at 15 °C. Light irradiance was 150 μmol photons m -2 s -1 with an illuminated period of 14 h and a dark period of 10 h.

The final pH values ranged from 7.4 to 9.0 pH units (total scale). Full procedure of the implementation of the cultures can be found in [START_REF] Hermoso | Control of ambient pH on growth and stable isotopes in phytoplanktonic calcifying algae[END_REF]. The shift in carbonate equilibrium in media induced by H + or OH -addition made to reach the targeted pH values, and in particular the availability of CO2 aq for cell growth, is depicted on Fig 1a . The saturation state of the medium with respect to calcite (ΩCaCO3) ranged from 1.1 to 16.6 from the lowest to the highest pH values.

Smear Slide Preparation

The culture residues comprising the coccospheres and detached coccoliths were not oxidized / bleached in order to avoid calcite dissolution during sample processing. About 2 mg of culture residues were dispersed in 4 mL neutralized deionized water. The glass vial containing this very diluted suspension was exposed to gentle and brief ultrasonic treatment (30 W / 25 kHz for approximately 20 s) to disaggregate the coccospheres and avoid clusters of materials in the suspension. The method for smear slide preparation followed that described by [START_REF] Koch | A simple weighing and dilution technique for determining absolute abundances of coccoliths from sediment samples[END_REF]. A volume of 0.25 mL of the suspension was pipetted out and deposited onto a 22 × 32 mm microscope slide. The preparation was dried on a hot plate and mounted using a UV light-reticulable NOA 61 glue (Norland Products Inc.).

Optical Microscopy and Evaluation of Calcite Thickness

The smear slides were processed and analyzed using a Zeiss Axio Imager M1 optical microscope fitted with a circular polarizer at Sorbonne Université, Paris. Individual coccoliths were photographed by a digital camera Axiocam MRc5 attached to the trinocular tube. The combination of a ×63 objective with a ×2.5 additional lens resulted in a resolution of one pixel width representing 0.034 µm. Preparing a very dilute suspension as described above was essential to ensure that the coccoliths were flat lying. Overlapping specimens or crooked coccoliths were disregarded from the analyses. The resulting 256 × 256 pixel-width frames containing one single coccolith per field-of-view were subsequently converted into 8-bit grayscale images for processing (Figure 2a). Transmitted light was set using Kohler illumination with 50% of the LED illumination power and a 400 ms exposure time resulting in background gray levels comprised between values of 32 to 44.

Gray level values and calcite thickness scale over the range of the first order birefringence color of the Michel-Lévy Chart and can be used to calculate calcite thickness, provided they are measured perpendicularly to the coccolith plane [START_REF] Beaufort | Weight estimates of coccoliths using the optical properties (birefringence) of calcite[END_REF]. Conversion between gray levels and thickness was made applying the polynomial regression recast from the dataset by Bollmann (2014) (equation 1).

Calcite thickness = 0.0000004 × MGL 2 + 0.0033 × MGL + 0.0072

(1)

where calcite thickness estimates are in micrometer, and the mean gray level (MGL) of a considered area is a dimensionless value comprised between 0 and 255.

We are fully aware that many technical parameters may complicate the application of equation ( 1) to transfer measured gray levels into estimates of calcite thickness (see, e.g., discussion by Linge Johsen [START_REF] Johnsen | Interactive comment on "An empirical method for absolute calibration of coccolith thickness[END_REF]. Indeed, the microscope optics, camera characteristics, the light source (halogen versus LED), and the exposure time are instrument specific, and hamper interlaboratory comparison in the evaluation of calcite thickness. This potential caveat induces that the equation 1 can in theory only be used if the measurements were made under the same analytical conditions as in [START_REF] Bollmann | Technical Note: Weight approximation of coccoliths using a circular polarizer and interference colour derived retardation estimates (The CPR Method)[END_REF]. In any case, whichever equation linking gray level and thickness is used, both parameters are proportional, and they are linearly related within the range of the measurements of the present study. With this in mind, we only interpreted variations of the estimates of height (thickness) of the tube and the coccolith shields to decipher fine-scale changes in the morphometrics of the coccoliths grown at distinct pH. Nevertheless, coccolith thicknesses computed via equation

(1) in our study appear to be realistic when comparing them with published data generated with other analytical conditions and transfer equations (see later discussion).

Detection of Fine-Scale Ultrastructure Within the Coccolith

The monocrystalline calcite elements within Noëlaerhabdaceae coccolithsa family to which G. oceanica belongs-are radially arranged with their crystallographic c-axis in the direction of the coccolith plane [START_REF] Young | Crystal assembly and phylogenetic evolution in heterococcoliths[END_REF]. This crystallographic feature allows full detection and quantification of calcite elements using circularly polarized light that eliminates the extinction patterns [START_REF] Bollmann | Technical Note: Weight approximation of coccoliths using a circular polarizer and interference colour derived retardation estimates (The CPR Method)[END_REF][START_REF] Beaufort | Optical measurements to determine the thickness of calcite crystals and the mass of thin carbonate particles such as coccoliths[END_REF][START_REF] Fuertes | The use of circularly polarized light for biometry, identification and estimation of mass of coccoliths[END_REF]. As a result, calcite crystals are consistently birefringent with gray levels values greater (i.e., brighter) than the background values without the black cross that appears under cross polarized light. In our analyses and under the analytical settings, the presence of a particle was detected with a threshold at 44 gray levels, the upper limit of background values defined above.

On average, the mean measurements presented in this study originate from 30 different coccolith specimens and the error bars correspond to one standard deviation (1 SD) of the data around the mean. Morphometric measurements of the coccoliths were achieved from the images using a routine developed on the Fiji software [START_REF] Schindelin | Fiji: an open-source platform for biologicalimage analysis[END_REF]. The routine was designed to detect (i) the external edge of the distal shield (Figure 2) with values greater than 44 gray levels (i.e., the maximum value of the black background) and (ii) the external edge of the tube with gray level values greater than 100 (thickness greater than 0.38 µm). The surface area of the latter structure may also include the innermost part of shields, and when present, the ascending part of the bridge that crowns the central area. The discrete fine-scale ultrastructural parts of the coccoliths being investigated here (see Table 1).

For both the whole coccolith and the tube, the routine automatically measured the surface area (Table 1; Parameters P1 and P5) and mean gray level or MGL (Table 1; Parameters P2 and P6) that were used to estimate the calcite thickness using equation (1) (Table 1; Parameters P3 and P7). Volume estimates were obtained by multiplying the surface area by the thickness, and lastly converted into calcite weight using a density of calcite of 2.71 (Table 1; Parameters P4 and P8).

Table 1. Coccolith Morphometric Parameters Defined in Text and Used in the Present Study.

We also analyzed fine-scale ultrastructure within the biominerals, such as the morphometrics of the central area, the tube that connects the two cycles, and the radial shields (Figure 2). The axial ratio of the tube (length over width; Figure 2b) was determined by processing the gray level profiles of 96 radial segments across this structure, and determining each local maximum gray level. These local maxima were computed to fit an ellipse that accurately reflects the shape of the tube. From this outline, the major and minor axes (Table 1; parameters P10 and P11, respectively) were used to calculate the axial ratio of the tube, and that of the encircled central area. The morphometrics of the central area (P13, P14, P15) were derived from the parameters of this ellipse since the central area has the same shape and is slightly smaller (0.4 µm on average) than the length and width of the determined ellipse.

The tube breadth was inferred by combining the surface area and the size (length and width) of the tube by idealizing two ellipses derived from the local maxima, thus defining the distance between the edge of the central area and the external perimeter of the tube (Figure 2c). The surface area of the shield was calculated as the difference between the surface area of entire coccolith, and those of the tube and the central area (P16) (Figure 2).

Lastly, the size normalized thickness or SNT (Table 1; Parameter P9) is a dimensionless parameter that corresponds to a three dimensional aspect ratio of the tube, as calculated in (2)

Scanning Electron Microscopy

An aliquot of a suspension containing the cultured coccoliths used for the preparation of the smear slides was poured onto a 2 μm polycarbonate membrane and dried out at room temperature. A 1 cm 2 piece of this membrane was mounted onto a stub, carbon coated, and introduced in a Zeiss Ultra 55 Field Emission Scanning Electron Microscope at Sorbonne Université, Paris. The working accelerating voltage was 15 keV. On the scanning electron microscope (SEM) images, no overgrowth of secondary calcite on the coccoliths or non biogenic carbonate phases, such as aragonite needles, were observed. We did not observe notable malformation or etching features on G. oceanica coccoliths, although some specimens exhibited slit-like structures on the distal shield or incomplete bridges. We did not attempt estimates of the frequency of malformed coccoliths, as in the work by [START_REF] Langer | The morphological response of Emiliania huxleyi to seawater carbonate chemistry changes : an inter-strain comparison[END_REF] in which malformed E. huxleyi seemed to be much more frequent than observed for G. oceanica in our study.

Results

Influence of pH on Division Rates

The division rates of G. oceanica strain RCC 1314 previously measured by [START_REF] Hermoso | Control of ambient pH on growth and stable isotopes in phytoplanktonic calcifying algae[END_REF] were found to be highly sensitive to ambient pH values. Over the entire 7.4 -9.0 spectrum, the relationship between pH and µ values was described by a second order polynomial relationship (bell curve) exhibiting an optimum between pH 8.2 and 8.4 (Figure 1b). These conditions correspond to the acclimation conditions of the strain, which is maintained in vitro for nearly 20 years and also to seawater pH in the Arcachon Bay (France) where this strain was collected. The results for this strain match the reported µ values under varying pH (7.35 to 8.93) from the experiments conducted at 15 °C by [START_REF] Sett | Temperature Modulates Coccolithophorid Sensitivity of Growth, Photosynthesis and Calcification to Increasing Seawater pCO2[END_REF] on another strain of the coccolithophore G. oceanica (RCC 1303). Both strains correspond to the morphotype Large sensu [START_REF] Bollmann | Morphological and Physiological Characteristics of Gephyrocapsa oceanica var. typica Kamptner 1943 in Culture Experiments: Evidence for Genotypic Variability[END_REF] and originate from the same temperate region of the Atlantic Ocean. Ecological and biogeochemical model predicts that in unicellular algae, the faster division rate, the smaller the cell size [START_REF] Marañón | Cell Size as a Key Determinant of Phytoplankton Metabolism and Community Structure[END_REF][START_REF] Aloisi | Covariation of metabolic rates and cell size in coccolithophores[END_REF]. However, in the experiments, there was no clear influence of ambient pH and the induced change in µ on the diameters of the coccospheres with relatively steady values ranging from 6.4 to 7.4 µm across [START_REF] Hermoso | Control of ambient pH on growth and stable isotopes in phytoplanktonic calcifying algae[END_REF]. The study by [START_REF] Sett | Temperature Modulates Coccolithophorid Sensitivity of Growth, Photosynthesis and Calcification to Increasing Seawater pCO2[END_REF] did not document coccosphere or cell sizes.

However, the authors have provided key parameters pertaining to bulk calcification, and showed that the calcite quotas (expressed as pg C cell -1 day -1 ) were linearly related to the specific growth rates (µ) at 15 °C according to equation (3):

Calcite quota

[pg C cell -1 day -1 ] = (22.6 × μ [day -1 ]) -0.49 (r 2 = 0.93) (3) Table 2.
Means and standard deviations of the measurements and calculated parameters (P1 to P17) defined in Table 1. Note: commas are used for decimal points.

Changes in Whole Coccolith Surface Area

As observed for the cellular divisions rates, the total surface area of the coccoliths is correlated with pH following a second order polynomial regression (Fig 3a). Although the mean of measurements corresponding to pH 8.2 seems to depart from the bell curve with slightly lower values than expected, it appears that the largest coccoliths are produced by the coccolithophores dividing the faster. Decreasing ambient pH from 8.6 (optimum calcification) down to 7.4 leads to smaller surface areas of the coccoliths with values dropping from 18 to 14 µm 2 on average. Under more basic conditions compared to the optimum, a sharp decrease in the surface area of the coccoliths is also observed up to pH 9.0 (coccolith surface areas on the order of 14 µm 2 ). 2) and therefore shows the mass of the coccoliths and that of the tube and shields taken separately. Note that no mass quantification has been made for the central area.

Changes in Whole Coccolith Thickness

The effect of lowering ambient pH from pH 8.6 down to 7.4 led to a progressive decrease of the calcite thickness of the coccoliths (Table 2). The magnitude of this change is appreciable, representing a loss of 25% of calcite thickness with mean values falling from 0.31 to 0.24 µm.

We emphasize that this result of our study corresponds to differences in MGLs and that the relative changes in calcite thickness do not depend on the calibration shown in equation (1).

On the 8.6 -7.4 pH range, the decrease appears to be linear with a statistically significant regression coefficient (r 2 = 0.95; p-value < 0.0005). The two highest pH conditions, namely 8.8 and 9.0, depart from this regression line with a mean thickness around 0.29 µm, thus are lowered compared to the maximum value observed at pH 8.6. These values reflect an integrated thickness of the total surface area of the coccoliths, and as such, these estimates may be influenced by changes of the constitutive crystallographic and ultrastructural parts forming the coccoliths (see below). From a methodological point of view (see section 2.3), coccolith surface area and thickness presented in this study for pH around 8 are in line with previous estimates inferred using another technique (SYRACO) and obtained from strain RCC 1314 grown in the same conditions also at the Oxford Biogeochemistry Laboratories [START_REF] Mcclelland | Calcification response of a key phytoplankton family to millennial-scale environmental change[END_REF].

Changes in Whole Coccolith Mass

At the level of individual coccoliths, that is, regardless of cell division rates and µ-normalized calcite quota, there is appreciable variation of the degree of calcification of the biominerals produced by G. oceanica at distinct pH spanning from 9 to nearly 15 pg (Figure 3b). The results show that the average coccolith mass is minimum at both the lowest and highest pH values, whereas calcite biominerals are more heavily calcified at intermediate pH with an optimum between pH 8.4 and 8.6. On the entire pH spectrum, the pH/coccolith mass relationship follows a second order polynomial law (r 2 = 0.76). Disregarding the two highest pH conditions (8.8 and 9.0), the two parameters linearly correlate (r 2 = 0.94; p-value < 0.0005): The lower the pH from 8.6 to 7.4, the lower the average mass of calcite per coccolith. This trend, once again, parallels cell growth rates with a regression coefficient (r 2 ) of 0.69 (p-value < 0.005).

Morphological Changes Within the Coccoliths

Changes Within the Coccolith Plane

We did not observe any statistically significant changes in the size of the central area for coccoliths precipitated from distinct ambient pH conditions, as measurements for each pH condition are indistinguishable from each other considering the standard deviation of the data.

The mean value for all measurements (3.06 ±0.67 µm 2 ; Figure 3a) matches the measurements conducted by [START_REF] Bollmann | Morphological and Physiological Characteristics of Gephyrocapsa oceanica var. typica Kamptner 1943 in Culture Experiments: Evidence for Genotypic Variability[END_REF] based on SEM analyses with a mean of 3.81 µm 2 for strain ARC03, which also belongs to the morphotype Large and originates from the same region than the strain RCC 1314 being analyzed here. By contrast, calcite constitutive of the shields and the tube exhibits pronounced changes in their surface area, but the response of these two structures is contrasting. There is a progressive decrease in the surface area of the shield of the coccoliths with increasing pH (Figure 3a). This negative trend (r 2 = 0.53; p-value < 0.05) corresponds to a decrease from 9.5 to 7.5 µm 2 of the surface area of the distal shield (Figure 3a).

The most prominent change in the morphology of the coccoliths is the surface area of the tube that sharply and continuously decreases from pH 8.6 to 7.4 (r 2 = 0.90; p-value < 0.005). This decrease of 70% of the surface area is considerable with mean values falling from 6.1 to 1.8 µm 2 . The larger tubes (in the coccolith plane) are thus observed specimens grown at pH 8.6. At the highest pH (8.8 and 9.0), the tube becomes smaller (~4 µm 2 ) and narrower (~1.2 µm), compared to maximum values observed at pH 8.6.

Changes Perpendicular to the Coccolith Plane (Height and Thickness)

The tube height, as the thickness of the shield, both exhibit a decrease from pH 8.6 to 7.4

(r 2 = 0.86; p-value < 0.005; r 2 = 0.97; p-value < 0.005 for the tube and shield, respectively).

For the tube, the mean values drop from 0.49 µm down to 0.42 µm over this pH range, thus representing a 14% decrease in height (or thickness). For the shields, we observed a 20% decrease with values falling from 0.39 to 0.31 µm.

Changes in the Tube Aspect Ratio

The axial ratio of the tube (length/width in the coccolith plane; Table 1) is found to be relatively invariant with a mean value of 1.38 ±0.01 (1 SD) combining all measurements (data not shown). This result is in line with the aforementioned study by [START_REF] Bollmann | Morphological and Physiological Characteristics of Gephyrocapsa oceanica var. typica Kamptner 1943 in Culture Experiments: Evidence for Genotypic Variability[END_REF] on wild G. oceanica specimens that also reported the steady nature of the roundness -the inverse of the axial ratio-of the central area with changing temperature and also among morphotypes of this species.

Comparing the relative evolution of the surface area and height is not straightforward and requires normalization, as the two parameters have different dimensions. This can be achieved by introducing the SNT that corresponds to a three-dimensional aspect ratio of the tube according to equation ( 2). The data indicate a progressive increase in the SNT of the tube with lowering pH from 8.6 to 7.4. Less heavily calcified tubes with more acidic ambient conditions are therefore primarily accounted for by a reduction of the breadth and therefore the surface area of this structure. Meanwhile, the height of the tube is relatively less variable (Figure 4b).

Summary of Coccolith Changes

The diminution of calcite mass at the scale of the whole coccolith is primarily due to diminished radial extension of the tube on the 8.6 -7.4 pH spectrum. The decrease in the mass of calcite in the tube at the highest pH (8.8 and 9.0) is due to the same morphological change within the coccoliths. Altogether, the data show that the breadth of the tube is the most sensitive parameter to pH-driven changes in intracellular calcification.

Discussion

4.1 Carbonate Chemistry, Cell Growth, and Calcite Quota Calcification in coccolithophores occurs intracellularly in a highly buffered and chemically regulated microenvironment within the coccolith vesicle [START_REF] Brownlee | Calcification in coccolithophores: A cellular perspective[END_REF][START_REF] Taylor | Coccolithophore Cell Biology: Chalking Up Progress[END_REF] 3)), indicating that the faster the division rate, the highest the calcification rates. It has been suggested that H + released from calcification have a cellular function for the cell machinery, as they counterbalance basification of the microenvironment due to CO2 aq carbon fixation by photosynthesis, therefore potentially explaining the link between the rates of calcification and photosynthesis [START_REF] Flynn | The role of coccolithophore calcification in bioengineering their environment[END_REF]. At the optimum pH that corresponds to the acclimation conditions of this strain, not only do the cells divide faster, but also each cell produced more heavily calcified coccoliths (Figure 3b). On the more basic side (pH 8.4 -9.0), CO2aq limitation was put forward as the main factor responsible for lower division and calcification rates [START_REF] Hermoso | Control of ambient pH on growth and stable isotopes in phytoplanktonic calcifying algae[END_REF]. Yet undercalcification at the lowest pH remains to be explained as the DIC resource (CO2 aq and HCO3 -) are at highest concentrations.

Our data indicate that coccoliths precipitated from ambient conditions with high [CO3 2-] and ΩCaCO3 are undercalcified, an observation that challenges some previous reports (e.g., [START_REF] Beaufort | Sensitivity of coccolithophores to carbonate chemistry and ocean acidification[END_REF], while it has to be acknowledged that the range of pH in our study exceeds the natural variability examined for these parameters of the carbonate system by [START_REF] Beaufort | Sensitivity of coccolithophores to carbonate chemistry and ocean acidification[END_REF]. Our finding is, however, in line with previous suggestions for the lack of a direct control by ambient CO3 2-on the degree of intracellular calcification [START_REF] Smith | Predominance of heavily calcified coccolithophores at low CaCO3 saturation during winter in the Bay of Biscay[END_REF][START_REF] Young | Morphology of Emiliania huxleyi coccoliths on the northwestern European shelfis there an influence of carbonate chemistry?[END_REF][START_REF] Marañón | Coccolithophore calcification is independent of carbonate chemistry in the tropical ocean[END_REF]. The apparent effect of pH on growth, calcification, and coccolith weight are asymmetrical on both sides of the optimum, suggesting that distinct mechanisms are at play under acidic and basic conditions, respectively. This contrasting behavior is apparent on Figure 5 where the combined effect of pH on calcite quota and averaged individual coccolith mass are plotted. In coccolithophores, the translocation of protons to the external milieu is allowed by the proton permeation of coccolithophore cells using voltage gated H + channels [START_REF] Suffrian | Cellular pH measurements in Emiliania huxleyi reveal pronounced membrane proton permeability[END_REF][START_REF] Taylor | A voltage-gated H + channel underlying pH homeostasis in calcifying coccolithophores[END_REF]. The lower the pH, the lower the electrochemical gradient, and the less calcified coccoliths, as the efflux of protons is hampered (Figures 3b and5). The severe decrease in calcification and coccolith mass from pH 8.2 down to 7.4 can be tentatively explained by the challenge faced by the cell to translocate protons in an environment relatively enriched in protons [START_REF] Brownlee | Calcification in coccolithophores: A cellular perspective[END_REF][START_REF] Suffrian | Cellular pH measurements in Emiliania huxleyi reveal pronounced membrane proton permeability[END_REF][START_REF] Brownlee | Coccolithophore biomineralization: New questions, new answers[END_REF]. Yet which process of the cell machinery related to the biomineralization toolbox is affected remains to be explored. Relevant to ocean acidification research, lowering ambient pH from 8.2 down to 7.4 leads to a decrease of 35% of the weight of the coccoliths on average that is mainly attributable to diminished calcification of the tubea biogeochemical feature that we will discuss in the following account.

Figure 5. Comparison between inferred bulk calcification derived from the cellular growth rates of Gephyrocapsa oceanica strain RCC 1314 and average coccolith mass cultured as a function of ambient pH. Bulk calcification estimates reported in the y axis were obtained using our specific division rates and equation 3 in text. The estimates appear to be linearly correlated on the 7.4-8.4 pH range (regression not shown on the scatterplot).

Insights Into Coccolith Biomineralization

We have shown that calcification of the coccolith at the scale of the entire biomineral is not homogenously affected by change in ambient pH and induced alteration of physiologically relevant parameters. The way that the ultrastructure of the coccoliths changes among different carbonate chemistry on either side of the pH 8.2 -8.6 optimum range is contrasting. Indeed, if the average masses of coccoliths measured for pH 7.8 and 9.0 are apparently similar, the morphometrics of the biominerals differ. The morphology of the inner parts of the coccoliths (central area and tube) is not affected by the alteration of ambient pH compared to the optimum conditions. This feature, which has been previously observed for the close relative species E. huxleyi [START_REF] Bach | Influence of changing carbonate chemistry on morphology and weight of coccoliths formed by Emiliania huxleyi[END_REF], confirms that the implantation of the protococcolith ring on the organic baseplate is not sensitive to the physiological status of the cell induced by ambient pH or CO2 aq availability. In the growth pattern of coccolithogenesis, it is the baseplate that will ultimately delimit the position of the tube in the final coccolith [START_REF] Westbroek | Mechanism of calcification in the marine alga Emiliania huxleyi [and Discussion[END_REF], and as such will control the surface area and the axial ratio of the central area.

After the formation of the protococcolith ring, the radial propagation of the tube in the plane of the organic baseplate is the growth pattern that is the most altered by acidification. This feature is evidenced in our dataset by the fact that the tube becomes narrower while its elevation (height or thickness) remains unchanged at lowest pH compared to normal coccolith specimens. Thus, the SNT or three-dimensional axial ratio of the tube (equation ( 2)) is at a maximum at the lowest pH, indicating that radial expansion of the calcite within this structure is impaired by acidification, while the distal elongation of the crystals (height) is relatively unchanged.

From a crystallographic perspective, the tube expands distally perpendicular to the direction of the c axis. Hence, new calcite forms from the obtuse kink sites, whereas radial propagation is made with crystal elongating in the direction of the c axis. This crystallographic difference represents a possible explanation for the change in morphology of the tube related to the biomineralizing molecules. The organic compounds, and specifically acidic polysaccharides in coccolithophores, have a stereochemical function on substrate-crystal interfaces for calcite nucleation and dictate the overall and fine-scale organization of the biomineral [START_REF] Borman | The Role in CaCO3 Crystallization of an Acid Ca 2+ -Binding Polysaccharide Associated with Coccoliths of Emiliania huxleyi[END_REF][START_REF] Westbroek | Coccolith production in the marine alga Emiliania huxleyi[END_REF][START_REF] Borman | Coccolith-associated polysaccharides from cells of Emiliania huxleyi (Haptophyceae)[END_REF][START_REF] Giuffre | Polysaccharide chemistry regulates kinetics of calcite nucleation through competition of interfacial energies[END_REF][START_REF] Lee | The uronic acid content of coccolith-associated polysaccharides provides insight into coccolithogenesis and past climate[END_REF].

Studies by [START_REF] Henriksen | Biological control on calcite crystallization: AFM investigation of coccolith polysaccharide function[END_REF] and [START_REF] Payne | Calcite crystal growth orientation: implications for trace metal uptake into coccoliths[END_REF] experimentally showed that the role of acidic polysaccharides was to block the acute surface kinks, promoting growth of faces with lower angles to the c axis. Thus, the relative inhibition of the radial expansion of the tube (breadth) through calcification on acute kinks can arise from higher activity of the acidic polysaccharides under more acidic conditions microlocally at the site of calcification. Indeed, polysaccharides operate a control on biomineralization using an acid binding function of Ca 2+ ions. It was recently suggested that the polysaccharide charge density, which arguably relates to ambient H + concentrations, exerts a control on calcite precipitation in coccolithophores [START_REF] Lee | The uronic acid content of coccolith-associated polysaccharides provides insight into coccolithogenesis and past climate[END_REF]. This hypothesis would imply that biomineralization is adversely affected by the metabolic load of protons released incrementally from calcification, and that the relationship between site specific attachment to crystallographic steps, growth patterns, and ultimately ultrastructure are highly influential on the bulk sensitivity of calcification within the biominerals.

Radial growth of the shields mostly corresponds to the widening of crystals that have a c axis in the direction of the elongation of the crystal. We did not observe such a significant decrease of surface area of the shield at the lowest pH compared to the tube. However, still from a crystallographic point of view, calcite of the elements forming the shield has comparable orientation of their c-axis than the crystals grown radially within the tube. Under optimal growth and calcification conditions between pH 8.2 and 8.6 (Figure 1b) and equation

(3), the mass of calcite constituting the tube and the shields are relatively similar (around 7 to 8 pg per coccolith). The shields do not exhibit significant changes in their appearance, nor in the absolute mass of calcite when pH decreases from 8.2 to 7.4. This feature indicates that this component of the coccolith is not affected by the acidification of the culture medium conversely to the tube (CaCO3 greater than unity for all conditions). From this, it emerges that change in the degree of calcification of the coccoliths grown in relatively low pH conditions cannot be accounted for by post mortem dissolution of coccolith calcite. This conclusion is also supported by the lack of significant dissolution features of the coccoliths observed under the SEM.

Implications for Naturally Occurring Assemblages

The degree and rate of calcification by the coccolithophores estimated from the analyses of wild assemblages reflect a mixed population signal. Altogether the individuals forming such populations in the water column or coccoliths in sediments have, by essence, greater plasticity and a potential adaptation to environmental changes compared to the clones grown during short term experiments in the laboratory. Specific to calcification, this feature is evidenced by distinct optima (division and calcification rates) by morphotypes of E. huxleyi and G.

oceanica subjected to perturbation experiments [START_REF] Blanco-Ameijeiras | Phenotypic Variability in the Coccolithophore Emiliania huxleyi[END_REF]Hermoso et al., 2016). In the natural environment, analyses of the morphometrics of coccoliths and estimates of calcification state through time series therefore reflect changes in the nannofloral composition transcending the strain specific level [START_REF] Beaufort | Sensitivity of coccolithophores to carbonate chemistry and ocean acidification[END_REF]. Climate changes and particularly ongoing oceanic acidification favor the most adapted morphotypes [START_REF] Blanco-Ameijeiras | Phenotypic Variability in the Coccolithophore Emiliania huxleyi[END_REF][START_REF] Rickaby | Environmental carbonate chemistry selects for phenotype of recently isolated strains of Emiliania huxleyi[END_REF]. Studies by [START_REF] Beaufort | Sensitivity of coccolithophores to carbonate chemistry and ocean acidification[END_REF] and [START_REF] Smith | Predominance of heavily calcified coccolithophores at low CaCO3 saturation during winter in the Bay of Biscay[END_REF] have shown the occurrence of heavily calcified E. huxleyi coccoliths at relatively low pH and low ΩCaCO3. In our study, such a pattern is not observed on cultured G. oceanica, but this response has to be regarded as a snapshot of the plasticity of calcification.

Two key studies have constrained the calcification state at the scale of the gephyrocapsid coccoliths in core top sediments from a wide array of biogeographical and climatic realms [START_REF] Bollmann | Global calibration of Gephyrocapsa coccolith abundance in Holocene sediments for paleotemperature assessment[END_REF][START_REF] Bollmann | Morphological and Physiological Characteristics of Gephyrocapsa oceanica var. typica Kamptner 1943 in Culture Experiments: Evidence for Genotypic Variability[END_REF]. Our study reveals that strain specific plasticity (calcification and biometric parameters, such as the axial ratio) exceeds the range of variability within the morphotypes Large of naturally occurring G. oceanica and laboratory specimens cultured at distinct temperatures. In both cases, temperature had relatively little effect on calcification compared to the larger scale perturbation of the environment induced by changes in the carbonate chemistry (and pH). The difference between these studies lies on the relatively small variability of the environment and in particular the status of chemistry of seawater compared to the substantial alteration of these parameters applied in our study.

Another line of evidence that carbonate chemistry exerts a primary control on calcification in G. oceanica originates from the study by [START_REF] Beaufort | Sensitivity of coccolithophores to carbonate chemistry and ocean acidification[END_REF], who have shown a decrease in the average weight by 25% since the last glacial maximum. Inference of seawater pH during the LGM is not straightforward, yet boron isotope measurements from planktonic foraminifera indicate a value nearing 8.4 in the surface waters [START_REF] Foster | Seawater pH, pCO2 and [CO2-3] variations in the Caribbean Sea over the last 130 kyr: A boron isotope and B/Ca study of planktic foraminifera[END_REF]. The pH offset between the LGM and modern values thus correspond to a drop by 0.3 pH units, which is indeed accompanied by decreased calcification of G. oceanica in our results. At face value using the linear regression line shown in Figure 5, our data indicate a loss by 10% in the averaged weight of G. oceanica coccoliths. Although such a comparison between sedimentary and culture data may be biased by many environmental factors [START_REF] Hermoso | Environmental control of the isotopic composition of subfossil coccolith calcite: Are laboratory culture data transferable to the natural environment?[END_REF], it appears that the intrinsic plasticity within a given strain is insufficient to account for the variations observed in fossil (downcore sediments) and subfossil (core tops) assemblages. [START_REF] Beaufort | Sensitivity of coccolithophores to carbonate chemistry and ocean acidification[END_REF] have suggested that coccolith mass can be used as a proxy for calcification. From our single strain study, although it has to be mentioned that the inter strain response to environmental perturbation within G. oceanica is relatively minor compared to E.

huxleyi, we can infer that such a correlation is only observed between pH 7.4 and 8.2 (Figure 5). Within the supposed range of seawater pH values that we can infer across glacial/interglacial cycles (8.4 to 8.1; see discussion above), we do not observe any correlation between inferred bulk calcification and average coccolith mass, leaving the number of coccolith produced per cell the most likely controlling parameter of coccolithophorid biomineralization in more saturated waters.

Conclusion

We have shown that the link between [CO3 2-] and calcification in coccolithophore is only apparent and is best explained by the covariation between ambient concentrations of protons and aqueous CO2. Calcification optima for G. oceanica are obtained at pH 8.4 and 8.6. Both at relatively higher and lower pH values, we observe a decrease in the ability of this species to The increasing use of birefringence color to determine the plasticity of calcification in a grainto-globe approach in literature warrants a unified effort in the community to establish a unique calibration overcoming existing limitations with a view to allow meaningful interlaboratory comparisons. We also call for future biological work that will have to test the effect of proton concentrations in the coccolith vesicle by, for example, perturbing the organic molecules enabling intracellular calcification by the coccolithophores. This could be achieved through inhibition of transmembrane proton channels or by the perturbation of the capability of acidic polysaccharidesthe latter would be implementable by inorganic precipitation experiments as a first, yet valuable step.

Figure 1 .

 1 Figure 1. Change in cellular division rates of the coccolithophore Gephyrocapsa oceanica (strain RCC 1314) with changes in ambient pH. (a) The status of the carbonate chemistry in medium (relative abundance of dissolved inorganic carbon species (DIC)) as a function of pH. (b) The changes in cell division rates induced by alteration of pH and speciation of the DIC species for Gephyrocapsa oceanica. Data from Hermoso (2015).

Figure 2 .

 2 Figure 2. Parameters (morphometrics) of Gephyrocapsa oceanica coccoliths analyzed in the present study. (a) A micrograph of a coccolith observed using circularly polarized light. Scale bar is inset. (band c) The discrete fine-scale ultrastructural parts of the coccoliths being investigated here (see Table1).

McClelland

  et al. (2016) on the entire coccolith. It was calculated by dividing the tube height (P7) by the square root of the tube surface area (P5) to homogenize the 1-D (height) and 2-D (surface area) dimensions of the two variables (equation (2)). Tube size normalized thickness [dimensionless] = Tube height [µm] √Tube surface area [µm 2 ]

Figure 3 .

 3 Figure 3. Changes in mean surface area and mass of the coccoliths cultured at various pH. (a) How the surface area of the coccoliths and of their discrete ultrastructural parts (central area, tube and shield) evolved. (b) Data presented in panel a and calcite thickness (raw data presented in Table2) and therefore shows the mass of the coccoliths and that of the tube and shields taken separately. Note that no mass quantification has been made for the central area.

Figure 4 .

 4 Figure 4. Dissecting the morphometric changes of the coccolith tube with changing ambient pH. (a) A bidirectional comparison between the elongation of the tube in the coccolith plane (defined as the breadth in text) and perpendicular to this direction (height or thickness). (b) The formalization of this comparison by the size normalized thickness (formula is inset top right). Overall, the data show a relative decrease of the tube breadth under lowest pH conditions.

  calcify, as reflected by the reduced coccolith mass of individual specimens. This change is more pronounced in acidic than in basic conditions when considering the optimum at pH 8.6 as a reference. From pH 8.6 down to 7.4, a range encompassing Cenozoic conditions, the coccoliths exhibit a loss of 35% of their average mass, primarily due to a reduction in the breadth of the tube of the coccoliths. Intrinsically to intracellular biomineralization in the coccolithophore G. oceanica, fine-scale observations within the coccolith indicate that radially grown calcite in the direction of the crystallographic c axis is the most affected growth pattern as a result of presumed elevated proton concentrations in the coccolith vesicle, and we have hypothesized that this crystallochemical feature can result from changing Ca 2+binding ability of the acidic polysaccharides. By contrast, all the parameters set by the calcite nucleation of the protococcolith (hence the two-dimensional morphology of the central area) are insensitive to environmental changes, and as such can be regarded as under a strict control of the biomineralization toolbox. An implication of our work is that the morphometrics of central area and of the tube can be used as a supplementary biometric tool to explore the genotypic variability within Noëlaerhabdaceae coccoliths, as they convey a genetic signal, and are insensitive to post mortem and diagenetic alteration compared to the whole coccoliths and especially the shields, which are more classically measured.

  . The link between ambient carbonate chemistry and the degree of calcification cannot be examined by the mere comparison between pH ([H + ]), [CO2 aq], and the saturation state ΩCaCO3 ([CO3 2-]). It is well argued that unicellular eukaryotic algae are unable to source CO3 2-ions from the external environment. Data by[START_REF] Sett | Temperature Modulates Coccolithophorid Sensitivity of Growth, Photosynthesis and Calcification to Increasing Seawater pCO2[END_REF] from G. oceanica grown

	at 15 °C indicate a linear relationship between growth rate and µ-normalized calcite quota
	(equation (

Acknowledgements

We are very grateful to Amélie Guittet (Sorbonne Université, Paris) for assistance in smear slide preparation and to Pascal Huang (Undergraduate research assistant at Sorbonne Université) for help with the acquisition and digital processing of the images. Omar Boudouma and Alexandre Lethiers (both at Sorbonne Université) are warmly thanked for running the SEM and advices in figure drafting, respectively. We are also grateful to Ian Probert (Station Biologique de Roscoff, France) for providing the strain of Gephyrocapsa oceanica. The authors thank two anonymous reviewers for valuable inputs. MH acknowledges financial support from the French National Research Agency (ANR) -Project "CARCLIM" under reference ANR-17-CE01-0004. Both authors are grateful to the CNRS-INSU Program INTERRVIE for financial support (Project "PRO-KIeC") and to the host Research Unit (Institut des Sciences de la Terre de Paris, UMR SU-CNRS 7193) for funds attributed within the Coup de Pouce scheme to set up the culture labs. All the data generated in this study are provided in Table 2 and as Supporting Information Data Set S1.

Supplementary Information

Data Set S1. Raw numerical dataset.