Marion Escudier

Jennifer Cautela

Nausicaa Malissen

Yann Ancedy

Morgane Orabona

Johan Pinto

Sandrine Monestier

Jean-Jacques Grob

Ugo Scemama

Alexis Jacquier

; Md

Morgane Orabona

MD ; Pinto

Johan Md

Sandrine ; Monestier

MD ; Grob

MD; Jacquier Alexis Md

PhD ; Lalevee

Nathalie Phd

; Barraud

Jeremie Md

; Peyrol

Michael Md

; Laine

Marc Md

; Bonello

PhD Laurent Md

Franck ; Paganelli

PhD ; Cohen

PhD Ariel Md

; Barlesi

PhD; Ederhy Fabrice Md

Stephane Md

Franck ; Thuny

MD Franck Thuny
email: franck.thuny@gmail.com

Clinical Features, Management, and Outcomes of Immune Checkpoint Inhibitor-Related Cardiotoxicity

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The medical records of patients with a clinical suspicion of ICI-related cardiotoxicity were reviewed from the databases of 2 cardio-oncology units between March 2015 and April 2017. The patients are managed according to similar protocols. Because no specific follow-up had previously been established for patients receiving ICIs during the study period, the oncologists referred patients receiving ICIs only on the basis of their clinical suspicion of cardiovascular events. These patients had a standardized evaluation including clinical consultation, ECG, transthoracic echocardiography, and measurement of brain natriuretic peptide and troponin I serum levels. The management of cardiotoxicity was left to the physician's discretion. The study was approved by our institutional review board, and informed consent has been obtained from the subjects. To create a pooled analysis, we also searched PubMed for English articles reporting cases of ICI-related cardiotoxicity until April 2017. We selected the cases reporting in detail the patient characteristics and the disease evolution. Among the selected cases, we excluded those for which data were considered insufficient to formally conclude that clinical manifestations were related to ICIs.

A total of 30 patients with ICI-related cardiotoxicity were finally analyzed in this study, including 12 newly diagnosed patients in the 2 cardio-oncology unit and 24 patients with sufficient data previously reported in 10 case series. The data of those 24 patients were summarized in a recent review 2 and in 2 additional case reports.3,4 The characteristics of the 30 patients are summarized in the Table . Cardiotoxicity was diagnosed at a median of 65 days (range, 2-454 days) after the initiation of ICIs and occurred after a median of 3 (range, 1-33) infusions. The rate of cardiotoxicity was higher after the first and third infusions, corresponding to the period after the first and third infusions. Dyspnea, palpitation, and signs of congestive heart failure were the most frequent clinical manifestations. Left ventricular systolic dysfunction was reported in 79% of patients, and Takotsubo syndrome-like appearance occurred in 14%. Atrial fibrillation, ventricular arrhythmia, and conduction disorders were observed in 30%, 27%, and 17% of patients, respectively. They were isolated (without left ventricular systolic dysfunction) in 3%, 7%, and 13% of patients, respectively. Concomitant signs of myositis were present in 23% of patients. Of the 18 patients with available data on left ventricular ejection fraction evolution, complete reversibility of left ventricular systolic dysfunction was significantly associated with corticosteroid therapy (8 of 12 [67%] versus 1 of 6 [17%]; P=0.04). Eight patients (27%) died of cardiovascular complications. The causes of death were refractory ventricular arrhythmia (n=3), heart failure (n=2), pulmonary embolism (n=1), sudden death (n=1), and cardiac arrest after the diagnosis of a conductive disorder (n=1). Cardiovascular mortality was significantly associated with conduction abnormalities (80% versus 16%; P=0.003) and ipilimumab-nivolumab combination therapy (57% versus 17%; P=0.04). Immune therapy was administered again after the first episode of cardiotoxicity only in the 4 patients (14%) without any recurrences.

The mechanisms of ICI-related cardiovascular events remain not well known, but this study provides a more comprehensive clinical description of this cardiotoxicity by analyzing a greater number of patients compared with previous studies. It shows that clinical manifestations are variable and associated with high cardiovascular mortality. Although we observed a higher incidence rate of cardiotoxicity during the first and third months of treatment, clinicians should keep in mind that cardiotoxicity can develop at any time; in our study, the interval varied from 2 to 454 days. Therefore, a comprehensive cardiac evaluation might be justified not only before the beginning of ICI therapy (as a reference) but also in cases of cardiovascular manifestations during treatment and systematically at the third month or after the third infusion. However, further data are needed to determine which cardiovascular investigations are relevant in this situation. In our analysis, cardiovascular mortality was high and significantly associated with the occurrence of conduction disorders.Although guidelines recommend a definite discontinuation of immune therapy in cases of life-threatening and severe adverse events,5 the management of each case should be individualized according to cancer status and the presence of toxicity regression. Indeed, corticosteroid use was associated with a higher probability of left ventricular function recovery, and no recurrence of cardiotoxicity was observed in the patients who underwent ICI readministration. This study has several limitations, including retrospective design, small sample size, and reporting bias.

In conclusion, this work provides new insights into the cardiotoxicity observed in patients treated with ICIs. Because the number of patients exposed to this new immune therapy is expected to dramatically increase in the near future, our study encourages further work to define guidelines for cardiovascular monitoring and management.


Fan Zhang

Elise El Ahmar
email: elise.el_ahmar@mines-paristech.fr

Alain Valtz

Eric Boonaert

Christophe Coquelet

Antonin Chapoy

Phase Equilibrium of Three Binary Mixtures Containing NO and Components Present in Ambient Air

Keywords: Vapor -Liquid Equilibrium, low temperature, thermodynamic models, measurements, phase behavior

Air contains impurities, which must be removed before its transformation and utilization. In the present work, new isothermal Vapor-Liquid Equilibrium (VLE) data are reported for three binary systems containing NO with (CO, N 2 or Ar) at different temperatures (between 105 and 146 K) and pressures up to 4 MPa. The compositions of the coexisting phases were experimentally determined using an apparatus based on the "static-analytic" method. The Peng-Robinson Equation of State combined with different mixing rules (classical, Wong-Sandler and Huron-Vidal) were used to represent the phase diagram (P, x, y).

Introduction

Air is indispensable to life and an important resource at the same time. It is approximately a ternary mixture of nitrogen, oxygen, and argon. Nevertheless, it contains variable quantities of many other substances like rare gases, COx, hydrogen, methane, oxides of nitrogen, NOx, and of sulfur, SOx. To illustrate, Table 1 gives an example of an average volumetric distribution of the substances in the air mixture. In Table 1, distinction is made between fixed components and impurities [START_REF] Arpentinier | The technology of catalytic oxidations[END_REF] .

Air contains large amounts of nitrogen and oxygen. Cryogenic distillation of air is the oldest but most highly developed separation technology for the industrial production of oxygen and nitrogen. This technology has not changed fundamentally from that initially developed by Carl von Linde and Claude-Delorme at the beginning of the 20th century. The core of a conventional Air Separation Unit (ASU) is a system of two distillation columns and a reboiler-condenser in between working at about 100 K. The importance of this process depends heavily on its capability in providing extremely pure nitrogen (10 ppb of impurities) and oxygen (purity from 85% up to 99.7%) in both the liquid and vapor states. Cryogenic air separation is based on the principle of fractional distillation. This process involves liquid and vapor phases and air components are separated on the basis of differences in boiling point and of relative volatility. Consequently, the whole process is related to the VLE occurring within the distillation column, thus important information for the plant design are saturation lines of the main air components and the thermodynamics and phase equilibria of mixtures of nitrogen, oxygen, and argon. There are currently few data available in the open literature on the thermodynamic behavior of mixtures composed of fixed components + impurities as well as mixtures composed of two impurities. [START_REF] Houssin-Agbomson | Equipment using a "static-analytic" method for solubility measurements in potentially hazardous binary mixtures under cryogenic temperatures[END_REF] ) and N 2 -propane (VLLE, Houssin-Agbomson et al. [START_REF] Houssin-Agbomson | Equilibrium data for the oxygen + propane binary system at temperatures of[END_REF] ). NO, CO and Ar are also impurities present with CO 2 after the process of CO 2 capture. Development of thermodynamic model to design CO 2 transportation process requires binary interaction parameters (Coquelet et al. [START_REF] Coquelet | Transport of CO 2 : Presentation of New Thermophysical Property Measurements and Phase Diagrams[END_REF] ). These parameters are obtained from experimental data. In this work, VLE measurements of three binary mixtures composed of some impurities (Ar-NO, CO-NO and N 2 -NO,) will be presented at low temperature conditions. The Peng-Robinson Equation of State, commonly used in industry, is used to model the above systems.

Experimental set-up

Chemicals

Chemicals (nitrogen, argon, carbon monoxide and nitric oxide) were purchased from Air Liquide (France) and presented in Table 2. The chemicals were used without further purification.

Apparatus description

The set-up is based on the 'static-analytic' method, for measurements at temperatures down to the normal nitrogen boiling temperature. The measured properties are: pressure, temperature and vapor and liquid compositions. A Hastelloy C276 cell (43 cm [START_REF] De Stefani | Solubility measurements for carbon dioxide and nitrous oxide in liquid oxygen at temperatures down to 90[END_REF] ) is placed inside a cryostat partially filled with liquid nitrogen. If the desired temperature is the normal nitrogen boiling temperature, the cell is completely immersed in liquid nitrogen. Above this temperature, the level of liquid nitrogen is maintained below the bottom of the cell. In this way, liquid nitrogen acts as the cold reservoir while a rounded heating resistance connected to a PID thermal regulator is used to achieve temperature stability within 0.1 K. Two capillary samplers Rapid On-Line Sampler-Injector (ROLSI ® ) [START_REF] Armines | Procédé et dispositif pour prélever des microéchantillons d'un fluide sous pression contenu dans un container[END_REF] are fixed on the top of the cell, one for the liquid phase and one for the vapor phase, and allowing direct injection of samples into the carrier gas circuit of a gas chromatograph. Efficient stirring of mixtures inside the cell is achieved using a magnetic rod driven by an external rotating magnetic field. Its rotation speed is selected through a variable speed motor.

A detail description of the setup can be found in Baba-Ahmed et al. [START_REF] Baba-Ahmed | New equipment using a static analytic method for the study of vapour-liquid equilibria at temperatures down to 77 K[END_REF] and Houssin-Agbomson et al. [START_REF] Houssin-Agbomson | Equipment using a "static-analytic" method for solubility measurements in potentially hazardous binary mixtures under cryogenic temperatures[END_REF] .

Calibrations and uncertainty estimation

Calibration of pressure transducer is performed against a dead weight pressure balance (Desgranges & Huot 5202S, CP 0.3-40 MPa, Aubervilliers, France). Accuracies are estimated to be within 0.005 MPa. The two platinum resistance thermometer probes (100 Ω) are calibrated by measuring the oxygen vapor pressure at low temperatures and comparing this value to the one found in the open literature. These probes are coupled to a Hewlett Packard multi-meter. Accuracies are estimated to be within 0.1 K for both probes. The signals from the probes (temperatures and pressures) are transmitted to a data acquisition system (DAS) which is connected to a PC. The thermal conductivity detector (TCD) of a Perichrom gas chromatograph (PR-2100) is calibrated using known amounts of compounds introduced through syringes. The column used for this analytical work is a packed column molecular sieve 5A (60/80) (Restek, France).

To estimate the uncertainties in temperature, pressure and composition, we have followed the guidelines of NIST 8 . The uncertainty estimation procedure is fully described by Zhang et al. [START_REF] Zhang | An improved static-analytic apparatus for vapor-liquid equilibrium (PTxy) measurement using modified in-situ samplers[END_REF] .

Both measurements repeatability and calibration uncertainties are taken into account. All the expanded uncertainties U(x), U(y) with coverage factor, k=2) for experimental data are reported in section 4.

Experimental procedure

At room temperature, the equilibrium cell and its loading lines are vacuumed. The cell is first loaded with the component having the lowest vapor pressure (NO in our study). The temperature is then set to the desired point and the system is left to reach thermodynamic equilibrium. After recording the vapor pressure of this component, the second component is introduced step by step, leading to successive equilibrium mixtures of increasing overall compositions. The two-phase (liquid and vapor) envelopes are measured with about 6 to 10 liquid and vapor points. Phase equilibrium is assumed to be achieved while temperature and pressure readings stabilized for at least 30 min. For each equilibrium condition, several samples of each phase (vapor and liquid) are withdrawn using the capillary samplers ROLSI® and analyzed in order to determine the mole fraction of each phase and check for repeatability of measurements which must be closed or better than ± 1 %.

Modelling

For binary mixtures modelling, the critical parameters (temperature (T C ) and pressure (P C )), and acentric factor () for each of the pure components are provided in Table 3 [START_REF]Component plus software[END_REF] . The experimental VLE data were correlated using the Peng-Robinson cubic Equation of State (PR EoS) [START_REF] Peng | A new two constant equation of state[END_REF] with different mixing rules. These models were chosen in order to produce reliable correlation of the experimental data with reasonable accuracy comparable with experimental uncertainties and to represent at the best the both phases. -PR EoS incorporating the the Mathias-Copeman alpha function [START_REF] Mathias | Extension of the Peng-Robinson Equation of State to Complex Mixtures: Evaluation of Various Forms of the Local Composition Concept[END_REF] , combined with the classical mixing rules [START_REF] Van Der Waals | On the continuity of the gaseous and liquid state[END_REF] (PR-EoS) as implemented in in-house software developed at CTP. -PR EoS incorporating the Mathias-Copeman alpha function, with the Wong-Sandler mixing rules [START_REF] Wong | A Theoretically Correct Mixing Rules for Cubic Equations of State[END_REF] involving NRTL activity coefficient model [START_REF] Renon | Local Composition in Thermodynamic Excess Function for Liquid Mixtures[END_REF] (PR-WS-NRTL EoS) (with non-randomness parameter =0.3).

-PR EoS incorporating the Mathias-Copeman alpha function, with the Huron-Vidal mixing rules [START_REF] Huron | New Mixing Rules in Simple Equations of State for Representing Vapor-Liquid Equilibria of Strongly non-ideal Mixtures[END_REF] with a Wilson activity coefficient model [START_REF] Wilson | Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing[END_REF]

(PR-HV-Wilson EoS)

The Mathias-Copeman alpha function coefficients for all components are listed in Table 3 Where P corresponds to bubble pressure, exp corresponds to experimental and cal corresponds to calculated.

Results and discussion

VLE data for Ar-NO system

The experimental VLE data were determined at 135.80 and 146.22 K (see Table 4) and are plotted in Figure 1. The PR-EoS using the classical mixing rules is used to represent the phase diagram (P,x,y). The adjusted BIP (k ij ) with and without a temperature dependency are presented in Table 5.

In order to quantify the fit of the models to the experimental data, the average absolute deviation (AADU) is calculated for the pressure and the vapor phase mole fractions. The deviation is defined by:

       exp exp / / 100 U U U N AADU cal (eq.2)
Where N is the number of data points, cal corresponds to calculated value, exp corresponds experimental value and U = P 1 or y 1 . These indicators, which give information about the agreement between model and experimental results, are presented in Table 5. Regarding these indicators, taking into account a temperature dependent BIP does not improve significantly the calculated data obtained. In Figure 1, k ij values used for our calculations with the PR are those obtained with a temperature dependency. PR The AADU is less than 2.3%. This system has been studied by Scheunemann et al., (1985) [START_REF] Scheunemann | Eine Apparatur zur Bestimmung von Tieftemperatur-Flüssigkeits-Dampf-Gleichgewichten und Messungen im System N 2 -NO[END_REF] at 113.85 and 119.55 K. Our new experimental data were measured at 105.69 and 127.14 K (see Table 8). Table 9 presents the BIP obtained at each temperature. For this system, the PR-EoS with classical mixing rule have some difficulties in representing the liquid composition, particularly for N 2 rich mixtures (Figure 3

Conclusions

Phase equilibrium of binary mixtures NO with (CO, N 2 or Ar) for cryogenic air separation in this paper. New experimental VLE data for these three binary systems are presented at different temperatures. Experimental data for these systems have not been previously reported in the open literature at the studied temperature. The experimental setup using a 'staticanalytic' method is described and the uncertainties concerning the calibrations of pressure, temperature and gas chromatography detector are also given. The measured data were correlated using the PR-EoS with different mixing rules (classical, Wong-Sandler and Huron-Vidal) in function of the system studied. The new experimental data obtained in this work were used to adjust the binary interaction parameters and the chosen models seems to be adequate to fit these types of component and mixtures at these temperature conditions. As future work, we will be focusing on the improvement of PR-EoS in order to represent the thermodynamic behavior of air components.

List of figures

List of tables

Table 1: Example of Air composition from Arpentinier et al. [START_REF] Arpentinier | The technology of catalytic oxidations[END_REF] . Table 2: Details of the chemicals. Table 3. Critical parameters, acentric factor and Mathias-Copeman Coefficients for the PR [START_REF]Component plus software[END_REF] . Table 4. Vapor-liquid equilibrium pressures and phase compositions for Ar (1) -NO ( 2) mixture (composition: y for Vapor phase and x for liquid phase, n: samples number). Table 5. BIP values and deviations obtained in fitting experimental VLE data with PR-EoS (bubble pressure calculation) for Ar (1) -NO (2) mixture. Table 6. Vapor-liquid equilibrium pressures and phase compositions for CO (1) -NO (2) mixture (composition: y for Vapor phase and x for liquid phase, n: samples number). Table 7. BIP values and deviations obtained in fitting experimental VLE data with PR-EoS (bubble pressure calculation), PR-WS-NRTL EoS (with non-randomness parameter =0.3) and PR-HV-Wilson EoS for CO (1) -NO (2) mixture. Table 8. Vapor-liquid equilibrium pressures and phase compositions for N 2 (1) -NO (2) mixture (composition: y for Vapor phase and x for liquid phase, n: samples number). Table 9. BIP values and deviations obtained in fitting experimental VLE data with PR-EoS (bubble pressure calculation), PR-WS-NRTL EoS (with non-randomness parameter =0.3) and PR-HV-Wilson EoS for N 2 (1) -NO (2) mixture.

  Since 1990's, the Centre of Thermodynamics of Processes has been involved in the study of the thermodynamic behavior (experimental measurements and thermodynamic calculation) of such mixtures. As examples of results obtained, we can mention the study of phase equilibria of several binary systems, O 2 -N 2 , O 2 -Ar and Ar-N 2 (VLE, Baba-Ahmed et al. 2 , O 2 -CO 2 , O 2 -N 2 O (solid solubility in liquid oxygen, De Stefani et al. 3 ), O 2 -propane (VLLE, Houssin-Agbomson et al.

  [START_REF]Component plus software[END_REF] .Binary Interaction Parameters (BIP, kij) were determined directly from the VLE data by minimizing the following objective function (eq.1):

Figure 1 .

 1 Figure 1. Phase diagrams (P-x-y) for Ar (1) -NO (2) mixture (symbols: this work, □: 146.42 K, ○: 135.80 K, Black lines: PR-EoS with a temperature dependent BIP).

Figure 2 .

 2 Figure 2. Phase diagrams (P-x-y) for CO (1) -NO (2) mixture (symbols: this work, □: 127.32 K, ○: 105.89 K, Black lines: PR-EoS with a temperature dependent BIP. a-With classical mixing rule

Figure 3 .Figure 4 .

 34 Figure 3. Phase diagrams (P-x-y) for N 2 (1) -NO (2) mixture (symbols: experimental work, □: data measured in this work at 127.14 K, ○: data measured in this work at 105.69 K, ×: Data from Scheunemann and Wagner measured at 119.55K 18 , +: Data from Scheunemann and Wagner measured at 113.85K 18 , Black lines: PR-EoS with a temperature dependent BIP).

Figure 4 .

 4 Figure 1. Phase diagrams (P-x-y) for Ar (1) -NO (2) mixture (symbols: this work, □: 146.42 K, ○: 135.80 K, Black lines: PR-EoS with a temperature dependent BIP).Figure 2. Phase diagrams (P-x-y) for CO (1) -NO (2) mixture (symbols: this work, □: 127.32 K, ○: 105.89 K, Black lines: PR-EoS with a temperature dependent BIP).Figure 3. Phase diagrams (P-x-y) for N 2 (1) -NO (2) mixture (symbols: experimental work, □: data measured in this work at 127.14 K, ○: data measured in this work at 105.69 K, ×: Data from Scheunemann and Wagner measured at 119.55K 18 , +: Data from Scheunemann and Wagner measured at 113.85K 18 , Black lines: PR-EoS with a temperature dependent BIP).Figure 4. BIP's values with PR-WS-Wilson EoS as function of temperature. (symbols: experimental work, ○: 12 , □: 21) for N 2 (1) -NO (2) mixture.

  1. Phase diagrams (P-x-y) for Ar (1) -NO (2) mixture (symbols: this work, □: 146.42 K, ○: 135.80 K, Black lines: PR-EoS with a temperature dependent BIP).

	Figure 2. Phase diagrams (P-x-y) for CO (1) -NO (2) mixture (symbols: this work, □: 127.32
	K, ○: 105.89 K, Black lines: PR-EoS with a temperature dependent BIP).
	Figure 3. Phase diagrams (P-x-y) for N 2 (1) -NO (2) mixture (symbols: experimental work,
	□: data measured in this work at 127.14 K, ○: data measured in this work at 105.69 K, ×: Data
	from Scheunemann and Wagner measured at 119.55K 18 , +: Data from Scheunemann and
	Wagner measured at 113.85K 18 , Black lines: PR-EoS with a temperature dependent BIP).

Table 1 :

 1 Example of Air composition from Arpentinier et al. 1 .

	Component	Volumetric composition
		Fixed components
	N 2	78.084 ± 0.004%
	O 2	20.964 ± 0.002%
	Ar	0.934 ± 0.001%
	CO 2	0.033 ± 0.003%
	Ne	1.8 ± 0.04 ppm
	He	5.2 ± 0.05 ppm
	Kr	1.14 ± 0.01 ppm
	Xe	0.086 ± 0.001 ppm
	H 2	0.05 ppm
	Impurities (In ambient air, including dust, pollen and local
		pollutants.)
	H 2 O	0.1-2.8%
	CH 4	1-6 ppm
	CO	0.06-1 ppm
	SOx	0.1-1.0%
	NOx	0.52 ppm
	O 3 Rn	0.01-1 ppm 6 × 10 -3 ppq

Table 2 :

 2 Details of the chemicals.

	Chemical	Symbol	CAS number	Purity/volume% (by weighing)
	Argon	Ar	7440-37-1	99.999
	Nitrogen	N 2	7727-37-9	99.995
	Carbon dioxide	CO	630-8-0	99.995
	Nitric oxide	NO	10102-43-9	99.000

Table 3 .

 3 Critical parameters, acentric factors and Mathias-Copeman Coefficients for the PR-EoS 10 .

	Chemical	T c /K	P c /MPa		MC1	MC2	MC3
	Ar	150.86	4.8980	0	0.397483	-0.282393	0.796288
	N 2	126.20	3.4000	0.0377	0.448322	-0.156813	0.468652
	CO	132.92	3.4990	0.0481	0.451344	-0.0791691	0.464029
	NO	180.15	6.4800	0.5829	1.153810	0.243750	-0.043201

Table 4 .

 4 Vapor-liquid equilibrium pressures and phase compositions for Ar (1) -NO (2) mixture (composition: y for vapor phase and x for liquid phase, n: samples number). U(T)= 0.1 K, U(P)=0.005 MPa.

			T/K = 135.80
	P/MPa	y 1	x 1	U (y 1 )	U(x 1 )	ny 1 ; nx 1
	0.4109	0	0
	0.6432	0.3613	0.0282	2E-04	1E-04	4;6
	0.8844	0.5431	0.0636	2E-04	1E-04	6;5
	1.0634	0.6173	0.0944	3E-04	1E-04	5;7
	1.4012	0.7006	0.173	2E-04	2E-03	6;7
	1.7597	0.768	0.312	1E-03	1E-04	6;8
	1.9230	0.788	0.392	1E-03	4E-03	4;4
	2.0315	0.809	0.478	1E-03	4E-04	6;6
	2.1587	0.831	0.581	1E-03	5E-04	5;4
	2.2484	0.851	0.671	1E-03	2E-04	6;6
	2.6056	1	1
			T/K = 146.22
	0.9878	0	0
	1.5678	0.36283	0.0698	3E-05	9E-04	6;4
	1.7377	0.4235	0.0924	1E-04	2E-03	6;5
	2.0521	0.51394	0.1475	7E-05	1E-03	7;5
	2.5374	0.61724	0.2698	4E-05	3E-03	6;7
	3.0786	0.70481	0.4680	3E-05	4E-03	6;6
	3.2953	0.74408	0.5728	2E-05	3E-03	4;5
	3.5934	0.8028	0.7120	1E-04	1E-03	6;5
	3.8280	0.8617	0.8206	1E-04	2E-03	5;4
	4.0289	1	1

Table 5 .

 5 BIP values and deviations obtained in fitting experimental VLE data with PR-EoS (bubble pressure calculation) for Ar (1) -NO (2) mixture.

		PR-EoS with classical mixing rules
	T/ K	kij	AAD P (%) AAD y1 (%)
	135.80	0.1144	1.68	2.20
	146.22	0.1247	1.05	1.74
	no temperature dependency 0.1177	1.86	1.30

Table 6 .

 6 Vapor-liquid equilibrium pressures and phase compositions for CO (1) -NO (2) mixture (composition: y for vapor phase and x for liquid phase, n: samples number). U(T)= 0.1 K, U(P)=0.005 MPa.

			T/K = 105.89
	P/MPa	y 1	x 1	U(y 1 )	U(x 1 )	ny 1 ; nx 1
	0.0136	0	0
	0.7847	0.99460	0.9607	4E-05	1E-04	4;4
	0.8026	0.99632	0.9776	4E-05	2E-04	4;5
	0.7905	0.99508	0.9653	2E-05	3E-04	4;4
	0.3739	0.9671	0.10236	7E-04	6E-05	4;5
	0.4236	0.97249	0.1270	1E-05	5E-04	4;5
	0.4947	0.97742	0.1727	3E-05	9E-04	4;6
	0.6552	0.98341	0.442	7E-05	1E-03	5;5
	0.6930	0.98489	0.624	4E-05	3E-03	4;5
	0.7141	0.98588	0.729	3E-05	4E-03	4;5
	0.7200	0.98707	0.762	2E-05	3E-03	3;5
	0.7300	0.9881	0.817	1E-04	1E-03	4;5
	0.8300	1	1
			T/K = 127.32
	0.1883	0	0
	0.3852	0.5034	0.0198	5E-04	4E-04	5;4
	0.5011	0.618	0.0329	1E-03	2E-04	4;6
	0.8348	0.754	0.0763	2E-03	5E-04	6;5
	1.0907	0.8092	0.1190	7E-04	2E-04	4;5
	1.4696	0.85953	0.211	3E-05	1E-03	4;5
	1.7178	0.8815	0.314	2E-04	1E-03	5;5
	1.9145	0.8946	0.449	3E-04	1E-03	5;9
	2.0645	0.9018	0.5794	2E-04	2E-04	4;4
	2.1381	0.9084	0.6493	2E-04	2E-04	4;4
	2.1879	0.9137	0.7082	5E-04	2E-04	4;4
	2.2484	0.92010	0.74575	7E-05	9E-05	4;5
	2.4190	0.9421	0.86122	2E-04	4E-05	4;5
	2.5146	0.9590	0.9157	3E-04	5E-04	4;8
	2.6820	1	1

Table 7 .

 7 BIP values and deviations obtained in fitting experimental VLE data with PR-EoS (bubble pressure calculation), PR-WS-NRTL EoS (with non-randomness parameter =0.3) and PR-HV-Wilson EoS for CO (1) -NO (2) mixture.

		PR-EoS with classical mixing rule			PR-WS-NRTL EoS
	T/ K	kij	AAD P (%) AAD y1(%)	kij	 12 / J.mol -1	 21 / J.mol -1 AAD P (%) AAD y1 (%)
	105.89	-0.0081	4.89	0.49	-0.34795	3178.80	1235.00	1.60	0.53
	127.32	0.0374	4.52	0.93	0.24814	61.69	1304.80	1.35	0.73
						PR-HV-Wilson EoS
			T/ K		 12	 21	AAD P (%)	AAD y1(%)
			105.89	0.30286	0.14462	1.0	0.32
			127.32	0.14462	0.1164	0.89	1.55

Table 8 .

 8 Vapor-liquid equilibrium pressures and phase compositions for N 2 (1) -NO (2) mixture (composition: y for vapor phase and x for liquid phase, n: samples number). U(T)= 0.1 K, U(P)=0.005 MPa.

			T/K = 105.69
	P/MPa	y 1	x 1	U(y 1 )	U(x 1 )	ny 1 ; nx 1
	0.3008	0.9713	0.0328	3E-04	4E-04	5;4
	0.3558	0.9751		3E-04		4
	0.4653	0.9794		2E-04		5
	0.5379	0.9828	0.0774	2E-04	8E-04	4;5
	0.6207	0.9845	0.0912	2E-04	9E-04	5;5
	0.7078	0.9893	0.105	1E-04	1E-03	3;4
	0.8226	0.99222	0.147	9E-05	1E-03	4;4
	0.8555	0.99244	0.159	9E-05	2E-03	4;5
	0.8922	0.99410	0.180	7E-05	2E-03	3;4
	0.9474	0.99447	0.225	6E-05	2E-03	3;5
	0.9791	0.99304	0.259	8E-05	2E-03	3;4
			T/K = 127.14
	0.5568	0.667	0.0236	3E-03	3E-04	5;6
	0.8751	0.783	0.0474	2E-03	5E-04	5;6
	1.1304	0.829	0.0695	2E-03	7E-04	5;9
	1.4500	0.862	0.104	1E-03	1E-03	5;6
	1.7464	0.879	0.141	1E-03	1E-03	5;5
	1.9861	0.891	0.184	1E-03	2E-03	5;5
	2.3211	0.906	0.282	1E-03	2E-03	6;5
	2.5660	0.9130	0.450	9E-04	3E-03	5;7
	2.6573	0.9151	0.561	9E-04	3E-03	3;5
	2.7213	0.9185	0.632	8E-04	3E-03	4;9
	2.7482	0.9206	0.644	8E-04	3E-03	3;4
	2.7944	0.9221	0.703	8E-04	2E-03	3;5

Table 9 .

 9 BIP values and deviations obtained in fitting experimental VLE data with PR-EoS (bubble pressure calculation), PR-WS-NRTL EoS (with non-randomness parameter =0.3) and PR-HV-Wilson EoS for N 2 (1) -NO (2) mixture.

		PR-EoS with classical mixing rule			PR-WS-NRTL EoS
	T/ K	kij	AAD P (%) AAD y1(%)	kij	 12 / J.mol-1	 21 / J.mol-1	AAD P (%)	AAD y1 (%)
	105.69 -0.0004	8.02	1.31	0.0803	974.50	1244.80	1.67	1.01
	113.83 0.0241	6.81	0.63	0.2368	403.22	1307.00	1.77	0.08
	119.56 0.0307	7.25	0.90	0.2198	644.32	1034.50	1.75	0.09
	127.14 0.0430	5.52	2.74	0.2780	-138.28	1843.70	0.29	0.78
						PR-HV-Wilson EoS
			T/ K		 12	 21	AAD P (%)	AAD y1(%)
			105.69		0.2233	0.0186	3.30	1.14
			113.83		0.2413	0.0598	1.69	0.58
			119.56		0.3051	0.0619	3.07	1.08
			127.14		0.2782	0.1164	1.94	3.14

b-With Wong-Sandler mixing rule and NRTL activity coefficient model

Acknowledgments

This work was funded by Chevron, Linde, GALP, OMV, PETEX, Statoil, TOTAL and UK National Grid, whose support is gratefully acknowledged.

For Table of Contents Only:


Jinming Lyu

Paul G Chen

Gwenn Boedec

Marc Leonetti

Marc Jaeger
email: marc.jaeger@centrale-marseille.fr

A coupled hybrid continuum-coarse-grained RBC membrane model

).

Introduction

The human red blood cells (RBCs) at rest are normally biconcave discocytes, and its membrane is composed of a lipid bilayer supported from inside by a two-dimensional (2D) triangular spectrin network of cytoskeletal proteins. The aim of this work is to see if adding a spring network to a vesicle dynamics model (based on boundary element method in a Stokes flow) could be a possible way to build a RBC model.

The Model

-The lipid bilayer (position x, velocity u) as a vesicle dynamics model (Boedec et al. 2011)

dx dt = u, div S (u) = 0, u = PGf + u ∞ , f = f b + f γ + f e
G the Green operator due to the Stokeslet, P the projector onto a subspace of surface divergencefree vectors to satisfy the incompressibility constraint on the lipid's flow, f b the bending force, f γ the surface-tension-like force resulting from the Lagrange multiplier of the surface divergence-free constraint, f e the elastic force exerted by the spring network.

-The cytoskeleton (position y, velocity v) and its interaction with the bilayer (Lyu et al. 2018)

dy dt = v, v • n = u • n, Π tg [C f (v -u) + f e ] = 0
The operator Π tg = Id -Π n the projector onto the tangent plan of the membrane surface, with Π n = n ⊗ n the projector in the normal direction given by the normal vector n pointing toward the outside bulk fluid, C f the friction coefficient.

-The cytoskeleton elasticity -the FENE-POW spring model (Fedosov et al. 2010)

f e n = p 4µ S √ 3 2y 2 0 1-y 2 0 + α + 1 1 -y 2 0 1 -y 2 np - y α+1 0 y α+1 np (y p -y n ),
We set α = 2 and the ratio y 0 = 1/2.05. For a given shear modulus µ S , and on the basis of the triangulation of cell membrane (y np = l np y 0 /l 0 = l np y 0 /l 0 np ) and its stress-free mesh (l 0 = l 0 np ), the elastic force f e n at node n by the edge np exerted by the spring network on the lipid bilayer can be obtained. The length of the link connecting vertices n and p is defined as l np = |y n -y p |.

Numerical Examples A Sedimentation

The first simulation example deals with a settling vesicle in combination with an underlying discrete spring network in an unbounded flow. Our objective here is to evaluate how effectively a cytoskeleton can influence the final shape of a settling vesicle. In the case of a vesicle (µ S = 0 µN/m), there is a finger-like shape that disappears if we increase the value of the shear modulus µ S . For high values of the shear modulus (µ S > 50 µN/m), the final shape is close to the initial reference one -a prolate ellipsoid. Coordinates are normalized with the equivalent radius of the vesicle R 0 . From this numerical experience, it is concluded that the emergence of long finger-like shapes can be observed only for vesicle sedimentation, since in the case of RBCs, even for large values of Bo, the cytoskeleton prevents the finger from appearing, indicating a significant interplay between vesicle dynamics and the cytoskeleton.

B RBC stretching

As a second numerical example, we perform RBC stretching simulations and compare our numerical results with the experimental data of RBC deformations by optical tweezers (Suresh et al. 2005). As could be expected, the deformations of the RBC membrane in response to the applied stretching forces depend largely on the value of the shear modulus used in a numerical model.

C Motion of a single RBC in a capillary

The third simulation example concerns a single RBC in capillary flows. For practical issues, the transport of BRCs inside a capillary is a more relevant situation to consider. Two specificities of this class of flows contribute to RBC deformation: curvature of the Poiseuille type flow profile and confinement.

Towards a RBC model Coordinates are normalized with the equivalent radius of the RBC. The finite-element meshes, i.e. the state of the cytoskeleton corresponding to the shape profiles for β = 0.5 are shown on the right. A vesicle (red profiles) takes a typical parachute-like shape whose curvature increases with confinement and which can deviate from the axial symmetry. When the effect of a cytoskeleton is considered, even for a very weak shear modulus (µ S = 0.5 µN/m), large deformations of the parachute shape are reduced substantially, and the asymmetry of the cell becomes less significant. As the cytoskeleton strength is further increased (µ S = 5 µN/m) the cell recovers the discocyte shape typical of RBCs at rest. That means that hydrodynamic forces are not strong enough to oppose to cytoskeletal forces in order to allow shape deformation, and that the biconcave shape is more resistant to the flow stress.

Conclusions

• A hybrid RBC model, based on a combination of a spring network with a vesicle dynamics model, is proposed for the prediction of RBCs dynamics in a flow. • The FENE-POW spring law is used for modeling the shear resistance of the cytoskeleton.

• The mechanical interaction between the bilayer and the cytoskeleton is explicitly computed.

• The model includes the fundamental mechanical properties of the RBC membrane: fluidity and bending rigidity of the lipid bilayer, and shear elasticity of the cytoskeleton while maintaining surface-area and volume conservation constraint. • This work fills the gap between continuum mechanical modeling and coarse-grained modeling of RBC membranes by fusing these two approaches. • There is a need for further development regarding the limitations that the test cases evidenced (stability issues, kinks).

Figure 1 :

 1 Figure 1: (a) A healthy human RBC and its membrane structure. (b) The cytoskeleton modeled as a spring network; the mechanical interaction between the spring network and the lipid bilayer at anchoring points (black beads).

Figure 2 :

 2 Figure 2: Stationary shape profiles of a vesicle-cytoskeleton model with reduced volume ν = 0.9 for several values of µ S and of the Bond number in the sedimentation simulations. (a) Bo = 40, (b) Bo = 220.In the case of a vesicle (µ S = 0 µN/m), there is a finger-like shape that disappears if we increase the value of the shear modulus µ S . For high values of the shear modulus (µ S > 50 µN/m), the final shape is close to the initial reference one -a prolate ellipsoid. Coordinates are normalized with the equivalent radius of the vesicle R 0 . From this numerical experience, it is concluded that the emergence of long finger-like shapes can be observed only for vesicle sedimentation, since in the case of RBCs, even for large values of Bo, the cytoskeleton prevents the finger from appearing, indicating a significant interplay between vesicle dynamics and the cytoskeleton.

Figure 3 :

 3 Figure 3: Variation of the axial D A and transverse D T diameter (µm) of RBC membrane as a function of stretching forces (pN) for two values of the shear modulus, S = 5 µN/m and µ S = 50 µN/m. Simulation results are compared with the optical-tweezers experiment (Suresh et al. 2005) and numerical predictions by a spectrin-level modeling (Li et al. 2005).As could be expected, the deformations of the RBC membrane in response to the applied stretching forces depend largely on the value of the shear modulus used in a numerical model.

Figure 5 . 8 :Figure 5 Figure 4 :

 5854 Figure 5.8: Cross section of RBC final shapes in a capillary for increasing values of the membrane shear modulus. The confinement is β = 0.33 for the figure on the top and β = 0.5 on the bottom. In both cases Ca = 10. Filled circles and open ones represent the cross section on the xz and yz plane respectively.

Acknowledgements

We acknowledge financial support from Labex MEC (grant no. ANR-11-LABX-0092), from A*MIDEX (grant no. ANR-11-IDEX-0001-02) and from CNES. J.M. Lyu is sponsored by China Scholarship Council (CSC). This work was granted access to the HPC resources of Aix-Marseille Université financed by the project Equip@Meso (ANR-10-EQPX-29-01).


María Inés

Fariello Rico

Simon Boitard

Sabine Mercier

Magali San

Integrating single marker tests in genome scans for selection : the local score approach

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Open Archive TOULOUSE Archive Ouverte (OATAO)

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.

MOTIVATION

• Detect genomic regions with high genetic differentiation between populations, signatures of adaptive selection.

• Single-marker statistics have a large variance and ignore LD (Linkage Disequilinrium).

• Haplotype-based tests require individual data, not availale when sequencing DNA pools (Pool-seq).

• Window-based tests: how to choose window size? Statistical significance of a window?

• Local score: detects regions statistically enriched in markers with high genetic differentiation, without defining fixed windows.

DEFINITION

• For each marker m, score X m = -log10(p m ) -ξ (black points), p m p-value of a test for selection (i.e. rejecting neutrality).

• Cumulate scores using the Lindley process (solid line)

h 0 = 0, h m = max(0, h m-1 + X m )
• Excursions above 0 of the Lindley process, indicate genomic regions enriched in high scores / low p-values (green interval).

• Here p m is the p-value of the FLK test (Bonhomme et al, 2010).

IMPORTANT FEATURES

• One single tunning parameter: ξ, p-value threshold in log10 scale.

→ High values put emphasis on high scores: strong selection.

→ Low values put emphasis on extended regions: recent selection.

→ ξ = 1 recommended to optimize detection power.

• Statistical significance of an excursion depends on:

→ the number of markers in the sequence (M )

→ the auto-correlation of scores (ρ).

• Two new approaches to compute it, as a function of M and ρ:

→ analytical formula: valid if single-marker p-values are uniform under neutrality.

→ re-sampling approach: valid for all datasets.

SIMULATION RESULTS

• Two divergent populations, one neutral and one under selection.

• • Observed type I error 6% for SLgT, 5% for other tests. • Chromosome 1: much clearer signal with the local score.

• Ten significant regions genome-wide, with relevant candidate genes related to autistic disorders or behavorial traits in Humans.

CONCLUSIONS

• The local score accounts for LD whithout individual genotypes.

• Statistical significance of candidate regions easy to compute.

• Increased detection power compared to single-marker, windowbased or haplotype-based tests.

  fr/ Eprints ID : 19674 To cite this version : Fariello Rico, María Inés and Boitard, Simon and Mercier, Sabine and San Cristobal, Magali Integrating single marker tests in genome scans for selection : the local score approach. (2017) In: Mathematical and Computational Evolutionary Biology, 12 June 2017 -16 June 2017 (Porquerolles, France). (Unpublished) Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr Integrating single marker tests in genome scans for selection : the local score approach María Inés Fariello 1 , Simon Boitard 2 , Sabine Mercier 3 , Magali San Cristobal 4 (1) Univ. de la República, Montevideo, Uruguay. (2) GenPhySE, INRA Toulouse, France. (3) IMT, Univ. Toulouse, France. (4) Dynafor, INRA Toulouse, France.

  Methods: single-marker test (FLK), haplotype-based test (hapFLK, Fariello et al, 2013), window-based FLK tests (mean, diffx, prob >2), local score, detection threshold computed from our re-sampling approach (SLgT) or neutral simulations (SLgE).

F=0•

  Divergent selection on behaviour, pool-seq from each line (G50).