J Oliveira

P Frey

H Morel

J M Reynes

J Burky

F Coccetti

F Iannuzzo

M Piton

Failure Degradation Similarities on Power SiC MOSFET Devices Submitted to Short-Circuit Stress and Accelerated Switching Conditions

The aim of this paper is to present a comparison between failure analyses results performed on power SiC devices. Various devices have been submitted to SC (Short-circuit) stress and ITASC (Inverter Test with Accelerated Switching Conditions) method. Some similarities have been detected, as well as the same failure mode represented by a gate-source shorted-circuit.

Introduction

Future electrification demands drastic improvements in power electronics by enhancing power density and efficiency, without a negative impact on reliability and lifetime for the industry and transport sectors like automotive, railways, aeronautics, and electric grids. High reliability and large robustness in extreme conditions are among the first requirements for power devices, including extreme operations [START_REF] Shoji | Dependence of short-circuit withstand capability of SiC MOSFETs on short-circuit failure time[END_REF]. However, both the lack of insight into SiC MOSFETs specific failuremechanism and ad-hoc tests covering real mission profiles are hindering their extensive adoption.

SiC MOSFETs present a significantly lower specific on-resistance (Ωcm 2 ) compared to silicon counterparts. Moreover, a higher short-circuit current is observed, which generates very high temperatures in a few microseconds [START_REF] Romano | A comprehensive study of short-circuit ruggedness of silicon carbide power MOSFETs[END_REF]. The same holds for the current density through bond wires, ending up in a systematic overcurrent through them [START_REF] Reigosa | A short-circuit safe operation area identification criterion for SiC MOSFET power modules[END_REF].

A lot of studies has been already done on this topic, including extensive accelerated testing. Thus, it is well-known that degradation mechanisms occur on SiC MOSFETs caused by short-circuit events, and hard switching conditions.

In this paper, repetitive SC have been performed

to lead the SiC device to failure, however not in complete destruction of the DUT (Device Under Test). ITASC method is used to define a hard switching condition up to device degradation. The operation point is located within SOA (Safe Operating Area) limits. An internal visual inspection have showed a fail-to-open (FTO) of the device, identified by a gate-source shorted-circuit.

Repetitive Short-circuit Stress

DUT and test bench used

This study is performed on ST Microeletronics TM device 1200 V, 75 mΩ, 33 A @TCase = 25 °C planartype device, in an automotive-grade 3-lead TO-247 case. The device was placed on the low side of a phase-leg power test bench presented in Fig. 1 [START_REF] Reigosa | Effect of short-circuit stress on the degradation of the SiO2 dielectric in SiC power MOSFETs[END_REF]. SC tests up to 900 V can be performed with the test bench. A protection system composed of circuit breaker is used to interrupt current in a case of thermal runaway.

Methodology and experimental results

A repetitive short-circuit test is applied to the DUT with a time between each pulse of 5 seconds. The test conditions are VDS = 600 V, Vbuffer = -5V/+18V and TCASE = room temperature. Previous studies [START_REF] Shoji | Dependence of short-circuit withstand capability of SiC MOSFETs on short-circuit failure time[END_REF][START_REF] Reigosa | A short-circuit safe operation area identification criterion for SiC MOSFET power modules[END_REF] have been performed to estimate the average TSCWT (Short-circuit Withstand Time), about 5 µs. Once this time is found, a percentage of 70%TSCWT (3.5 µs) is set for the pulse width. Thus, a thermal runaway and then a catastrophic drain-source failure-mode are prevented. All tested devices in SC showed gate-source degradation only.

In Fig. 2, the waveforms during a first shortcircuit event (#cycle1, blue lines), and the last (#cycle400, red lines), for this test are shown. The abnormal effect (current bump) observed on gate current (IG) is probably due to an electromagnetic disturbance caused by parasitic elements of the PCB (Printed Board Circuit), and associated common mode current.

The drain-source current peak decay between the first and last cycles is due to the self-heating of the device. A thermocouple is used to monitor temperature increase during repetitive cycles, by ensuring the definition of waiting time. Furthermore, it is important to mention that this effect it not a degradation. The gate current is also measured at the final of each pulse (3.5 µs instant) to verify any variation along the repetitive short-circuits. In additional, gate charge is calculated. These results are presented in Fig. 3.

Fig. 3. The gate current (IG) remains nearly constant between @Cycle1 and @Cycle400. Gate charge (QG) about the same 71 µC for 400 cycles.

This test is part of an aging protocol that aim to verify the evolution of static and dynamic parameters such as leakage drain/gate current, output capacitance, etc. Threshold voltage (VTH) presented a maximum variation of about 5%, for example. TDDB (Timedependent Gate Oxide Breakdown) was not affected after aging.

ITASC method

Test bench used

The DST (Double Source Test) bench is an alternative to classical DPT (Double Pulse Test). It allows to stress a power device through a high voltage/current switching. Thanks to the electrical schematic of the test, it is possible to define a constant value for voltage and current on the DUT [START_REF] Garrab | On the extraction of PIN diode design parameters for validation of integrated power converter design[END_REF]. In this way, the main goal is to define an aging law, regarding different stressor parameters, such as: applied voltage/current (up to 1000 V and 100 A), switching speed (RG), number of cycles (10 5 ~10 6 ), negative/positive pre-conditioning, etc. In Fig. 4, the electrical schematic and the mounted test bench are presented. Fig. 4. Electrical schematic of the test bench [START_REF] Reigosa | Effect of short-circuit stress on the degradation of the SiO2 dielectric in SiC power MOSFETs[END_REF]. This platform is based in Ampere Laboratory in Lyon, and it was developed in collaboration with IRT Saint Exupery.

Methodology and experimental results

A repetitive hard switching test is performed with the DUT applying a time of 1 second between each pulse. This prevents any self-heating effect. The test conditions are VDS = 1000 V, IDS = 65 A, VDRV = -5V/+18V and initial temperature TCASE 1 = room temperature, and final temperature TCASE 2 = 52 °C. The test bench enables to increase the nominal switching energy by a ratio of 30. The phase of current rise in the DUT corresponds to about 2 ms, and it is also a high stress, however this operation point is inside SOA (Safe Operating Area) limits. In Fig. 5, the target stress condition can be seen. In addition to current rising, a higher gate resistance is also used. Some degradations have been observed for currents around 65 A at 1000 V. Tests on some specimens in this condition showed a maximum number of cycles of about 100, before total failure of device. In the observed degradations, a short-circuit between gate and source is always detected for all tested devices. Fig. 5. Switching energy comparison an example operation point (400V/20A), and the hard stress condition (1000V/65A). An increase greater than a factor of 30 is observed for the switching energy.

For lower current values, no static parameters (Rds(on), Vth, Igss, Idss, etc) variation was detected. A current of 50 A allows to achie 200k cycles without degradation. Seen that, the target current is increased until reaching SOA limits. In this case, the device presents total failure without any precursor previously.

Voltage and current waveforms of DUT can be seen in Fig. 6. The total stress is the result of two phase that are the conduction during current rising by inductor, and switching events. Total energy during one cycle of ITASC method has the same magnitude of SC test, some hundreds of milijoules. The charging time defined to reach the target current level is also an additional stress. Thus, some tests at low voltage (100 V) but with the same current level have been performed to attempt observing any degradations. The results are presented in Fig. 7.

During the test, after 6k cycles the switching is paused to perform a gate leakage current measurement. Thereafter, when the test is re-started, the initial current (at #cycle6000) is monitored and compared to its value at #cycle0. The current remains the same, therefore, there is probably no degradation of ON resistance. As seen in Fig. 7, the device has the same current capability (65 A) after 10k cycles, and none gate leakage current is detected. A preliminary conclusion is that the degradation is due to high power switching about 63 kW (at 1000 V). Fig. 7. ITASC method in low voltage level (100 V) applied to a SiC power device. Cold state represents to 10 minutes of waiting time, before re-starting tests.

Failure Analysis Comparison

The failure analysis have been performed by Alter Technology Laboratory. After short-circuit stress, an analysis was performed. Four different Aluminum (Al) reconstruction levels were observed at source pad edge and wedge bond edge. The highpower stress applied on the component makes a thermal-mechanical stress on ILD (Inter Layer Dielectric) leading to aluminum propagation in the crack inducing electrical leakage [START_REF] Garrab | On the extraction of PIN diode design parameters for validation of integrated power converter design[END_REF][START_REF] Cavallaro | Capability of SiC MOSFETs under short-circuit tests and development of a thermal model by finite element analysis[END_REF]. Fig. 8 shows the crack observed at ILD level after 636 cycles, under the conditions previously mentioned (section 2.2). This generates a path for the melted Al-metallization causing a short-circuit between gate and source. The metal crack can happen due to a temperature gradient between active and edge area. Two contributors seems to be significant in Al source reconstruction phenomenon: the very high temperature gradient at border of active area, and the melting of source metal in active area. This phenomenon has been already observed in the literature [START_REF] Cavallaro | Capability of SiC MOSFETs under short-circuit tests and development of a thermal model by finite element analysis[END_REF][START_REF] Ceccarelli | A survey of SiC power MOSFETs shortcircuit robustness and failure mode analysis[END_REF]. It is important to mention that SC leads the DUT to operate outside the SOA.

ITASC method allows for a hard stress with 65 kW of power peak on the device, but inside the SOA. After certain failure analysis, it was observed the same failure mode: gate-source short-circuited. However, the mechanism is distinct when compared to SC stress. In Fig. 9, it is possible to see an aluminium migration near of source and gate. This causes the gate-source short-circuit. Furthermore, it is observed Al reconstruction likewise for the SC stress, what shows some similarities. Therefore, it could be estimated a surface temperature near 660 °C, melting point of Al. This is local phenomenon (in the center), and probably if the gate finger was not present, this failure would not arise.

Conclusions

The failure analysis performed on power SiC MOSFET devices after two different stress tests (SC and ITASC) shows a same failure mode: shorted gatesource. It is important to mention that the failure are related to a high dissipated power on the DUT. In addition, for both stresses an aluminum reconstruction has been observed, but not at the same location. After SC events, the Al migration occurs towards the cracked ILD, however after ITASC stress this migration happens on border region of the surface pad, located in center of active area. Thus, both stresses present different failure mechanisms.

Results for ITASC method at low voltage have been presented. This allowed to show that the degradation is only due to the high switching power (65 kW), and not the current charging phase.

Another issue will be to better address in the future the SOA in such short and high power stresses because they strongly differ from whose observed in silicon devices.

  Gate-source voltage (VGS) and output-drive voltage (Vbuffer) are measured with a Rohde & Schwarz RT-ZP10-400V, 500 MHz bandwidth probe. Drainsource voltage (VDS) is measured with a Testec HV 250-2500 V, 300 MHz bandwidth probe. Drain-source current (IDS) is measured through a shunt T&M Research SDN-414-01, 6 J, 400 MHz coaxial shunt. The drop voltage on gate resistance is used to estimate gate current (IG).

Fig. 1 .

 1 Fig. 1. Electrical schematic of the test bench [1], and the Pulse Tester User Interface developed at IRT Saint Exupery.

Fig. 2 .

 2 Fig. 2. Gate-source (VGS) voltage, gate current (IG), drainsource current (IDS), and drain-source voltage (VDS) during short-circuit event.

Fig. 6 .

 6 Fig. 6. Switching transients of a Power SiC MOSFET for an example operation point (400V/20A), and the hard stress condition (1000V/65A).

Fig. 8 .

 8 Fig. 8. Fusing point between PolySilicon layer & Source ohmic contact. ILD damaged until Ti barrier.

Fig. 9 .

 9 Fig. 9. Aluminum melted and displaced near edge of source gate (orange arrow).

Acknowledgements

This work was carried out in the framework of the IRT Saint Exupéry's project SiCRET (SiC Reliability Evaluation for Transport). We acknowledge the financial support from the SICRET's industrial and academic members and the financial support from the French National Research Agency (ANR).

SiCRET's Industrial members: Alstom, Alter Technology, Emotors, Liebherr, Nucletudes, Safran, SuperGrid Institute, Thales, Vitesco Technologies.

SiCRET's academic members: Ampère, LAAS, IES, LAPLACE.

The authors would also like to thank Francesco Pintacuda from STMicroelectronics and ST Microelectronic Automotive Discrete Group (ADG) for the valuable support (components and expertise).

The authors would also like to thank Sylvain Jouanolle from the French MoD (DGA) for the valuable support (physical analysis).


Julien Y Dutheil
email: dutheil@evolbio.mpg.de

Diyar Hamidi

Basile Pajot

The Site/Group Extended Data format and tools

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

Introduction

Evolutionary comparative sequence analysis can unravel information about the evolutionary processes that shape the observed genetic diversity. When applied to gene sequence alignments, dedicated statistical methods detect positions that evolved under a particular evolutionary scenario, such as negative/positive selection or coevolution [START_REF] Yang | Computational Molecular Evolution[END_REF][START_REF] Pollock | Coevolving protein residues: maximum likelihood identification and relationship to structure[END_REF]. Further insights into the functional role of these positions in the molecule and organism can be obtained by mapping them onto the three-dimensional structure of the encoded molecule and assessing their structural properties.

Mapping evolutionary predictions onto three-dimensional structures requires translating positions between three distinct reference systems: alignment positions, individual sequences, and three-dimensional structures. While software that allows the joint visualisation of sequence alignments, phylogenies and protein structures is available [START_REF] Meng | Tools for integrated sequence-structure analysis with UCSF Chimera[END_REF][START_REF] Waterhouse | Jalview Version 2-a multiple sequence alignment editor and analysis workbench[END_REF], it requires manual interaction to visualize the results of evolutionary analyses, restricting their usage to case studies and preventing their use in genomic pipelines. Furthermore, each analysis software outputs results in its distinct format, complicating the development of generic analysis tools.

We designed the Site/Group Extended Data (SGED) format to facilitate the cross-analysis of sequence sites and their annotations. We introduce the SgedTools package, which contains utilities to manipulate and analyse SGED files. Lastly, we demonstrate their application on a classic example of positively selected sites in Primates lysozyme sequences.

The Site/Group Extended Data (SGED) format

We propose generalising the text tabular format to account for site coordinates. The Site/Group Extended Data (SGED) format is based on the widely used comma-separated values (CSV) and tab-separated values (TSV) formats, where columns represent variables and rows, data points -here in the form of (groups of) sites in a sequence or alignment. The SGED file contains one or several columns to store coordinates (e.g. a site's position in the alignment), with a dedicated syntax: the coordinates are specified within square brackets, and coordinates are separated by semi-columns (see Table 1). Other columns represent any measure or statistic for the corresponding groups. The SgedTools offers a collection of programs that specifically deal with the coordinates of the groups. They also compute statistics that will be added as columns in the SGED files.

As SGED files are CSV/TSV files, they can be easily generated and edited, either manually or with dedicated software, such as spreadsheets, R, or the Python package pandas. The format is supported natively by programs using the Bio++ libraries, outputting various alignment statistics [START_REF] Guéguen | Bio++: Efficient Extensible Libraries and Tools for Computational Molecular Evolution[END_REF]. The SgedTools contains several conversion utilities that generate SGED files from the output of programs for sequence and structure analysis (Supplementary Table 1). SGED files can be further manipulated by dissociating sites within groups or combining sites into groups according to the content of a column. Finally, the columns of two SGED files can be merged based on the groups coordinates.

Indexing and coordinate translation

A prerequisite for analysing candidate positions in a sequence or sequence alignment is the conversion of coordinates to a common reference (Supplementary Table 1). The most basic conversion is between sequences within an alignment and is easily achieved by indexing each sequence position according to their alignment column (Figure 1A). Another sequence-only conversion task is when sequences or alignments are concatenated, for instance, to reconstruct a joint phylogeny, jointly estimate model parameters on multiple genes, or perform an inter-gene coevolution analysis. Positions in the super-alignment subsequently need to be converted back to the original sequence coordinates for further analysis (Figure 1B).

Coordinates are required to cross results between different analyses, particularly evolutionary analyses (alignment-based) and functional analyses (single-sequence-based). A class of widely used functional analyses involve the three-dimensional structure of the encoded molecule, RNA [142; 144; 158; 335] 0.648215 0.09130 [145; 347; 200; 242] 0.610141 0.29092 [198; 248; 329; 217; 312] 0.563759 1 [139; 232; 236; 150; 202; 205] or protein. Three-dimensional structures can be obtained experimentally or predicted computationally. In both cases, some data may be missing so that the structure of some part of the sequence could not be obtained. Furthermore, the individual sequence used to predict the structure is rarely the same as the one used for the evolutionary analysis, possibly from a different species. Mapping candidate sites from evolutionary analyses onto a protein or RNA structure is a challenging task that requires sequence alignment between reference sequences (Figure 1C).

The create-structure-index program from the SgedTools permits the automation of such a task. Using a set of PDB structures, it aligns each sequence in a sequence alignment with the sequence of every chain in every PDB entry provided as input. Using the best matching pair of sequences, it then creates an alignment-structure index that maps all alignment positions onto the selected three-dimensional structure with minimal data loss. The sequence alignment is done using methods from the BioPython package [START_REF] Cock | Biopython: freely available Python tools for computational molecular biology and bioinformatics[END_REF]. Structure-mapped positions can then be used to extract structural properties.

Adding structural properties

Information about the functional relevance of predicted sites can be obtained by knowledge of their three-dimensional position. Relevant structural characteristics include location in secondary structure motifs, solvent exposure, number of residue contacts and inter-residue distances. Some information is directly accessible from the three-dimensional structure file; others can be predicted with dedicated software. The structure-infos program uses the BioPython.PDB package [START_REF] Hamelryck | PDB file parser and structure class implemented in Python[END_REF] to automatically retrieve structural properties from PDB and mmCIF files, such as secondary structure motives (Supplementary Table 1). It can also compute three-dimensional distances between sets of residues. structure-infos, and can further retrieve information about residues's RSA and depth using the BioPython.PDB parsers for the DSSP [START_REF] Kabsch | Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features[END_REF] and MSMS [START_REF] Sanner | Reduced surface: an efficient way to compute molecular surfaces[END_REF] programs.

structure-infos further includes an algorithm computing the number of residue clusters in a group of sites. It first generates the matrix of pairwise distances between all pairs of residues in a group. A hierarchical clustering tree is then computed from the distance matrix, using the nearest linkage algorithm, as implemented in the cluster.hierarchy.single function in the SciPy package [START_REF] Virtanen | SciPy 1.0 Contributors. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python[END_REF]. A distance threshold is then used to obtain clusters of residues. To assess the significance of structural statistics, we need to compare their observed values to their expectation under a null model. Such expectations can be derived using randomization procedures.

6 Advanced hypothesis testing using randomization

The randomize-groups program (Supplementary Table 1) generates random groups from two input SGED files: a first file with test groups, whose characteristics will be reproduced in the randomly generated groups and a second file providing the list of sites to sample from, with their properties. Each site can only be sampled once in each test group, but a site can be sampled multiple times between test groups if several are provided.

randomize-groups can perform a conditional sampling by selecting sites with similar properties to those in the tested group. This is achieved by specifying a conditional variable, provided as a dedicated column in the list of sites to sample. Continuous variables are discretized, and a bias correction for skewed distributions is implemented, as described in [START_REF] Chaurasia | The Structural Determinants of Intra-Protein Compensatory Substitutions[END_REF]. In section 8, we demonstrate how the SgedTools can be used to statistically analyse the structural properties of sites detected to evolve under positive selection, using conditional sampling to disentangle the effect of RSA and residue dispersal.

Program installation and usage

The SgedTools package is a collection of independent scripts written in Python (version 3.1 minimum). It makes use of several Python packages:

pandas for CSV/TSV file reading, manipulating and writing [The pandas development team, 2020], numpy and scipy for numerical calculations and statistics [START_REF] Harris | Array programming with NumPy[END_REF], Virtanen et al., 2020],

biopython for sequence and three-dimensional structures manipulation [START_REF] Cock | Biopython: freely available Python tools for computational molecular biology and bioinformatics[END_REF].

Once the packages are available in the Python environment, each script can be copied and run 'as is' without any further installation needed. The programs are run from the command line, using options which are specified using standard short (e.g. -a) or long arguments (e.g.

--alignment). The SgedTools package is distributed with detailed example analyses that can serve as templates for developing dedicated pipelines.

8 Application example: structural analysis of positively selected sites.

To illustrate the use of the SgedTools, we evaluate the results of the positive selection analysis of [START_REF] Yang | Codon-substitution models for detecting molecular adaptation at individual sites along specific lineages[END_REF]. This data set serves as an example for the widely used package PAML [START_REF] Yang | PAML 4: phylogenetic analysis by maximum likelihood[END_REF]. The PAML output file can be converted to the SGED format using the paml2sged program, keeping only the seven sites with a posterior probability calculated by the empirical Bayesian method and at least equal to 0.7: Using the Colobus sequence as a reference, we search the protein data bank (PDB) [START_REF] Berman | The Protein Data Bank[END_REF] for three-dimensional structures of lysozymes. After downloading the ten best matching PDB files, we use the create-structure-index program to align all chains from all structures and find the best alignment, which is used to create a structure index :

Group PDB amino_acid probability [14] [A:ARG14] R 0.859 [21] [A:ARG21] R 0.858 [23] [A:ILE23] I 0.853 [41] [A:ARG41] R 0.71 [50] [A:ARG50] R 0.704 [87] [A:ASP87] D 0.869 [126] [A:GLN126] Q 0.71
The translated coordinates can be used to visualize the candidate sites with software like PyMol [Schrödinger, LLC, 2015] or ChimeraX [START_REF] Meng | UCSF ChimeraX: Tools for Structure Building and Analysis[END_REF] (Figure 2A). The positively selected sites are located at the protein's surface and seem to be spread. We can statistically assess this by measuring the mean pairwise distance between the α carbons (C α ) of the residues and their mean relative solvent accessibility (RSA). We first need to create an SGED file where all sites are listed as a single group: We then compute the structural properties of this group using the structure-info program, using the best-matching PDB entry: The program computes two statistics for the group, the C α distance (argument --measure AlphaDist)

and several summary statistics generated by the DSSP program (argument --measure DSSPsum).

The resulting mean C α distance is 22.06 Å, and the mean relative solvent accessibility is 51.27%.

We then compare these statistics to their null expectation, obtained by sampling groups of sites in the protein structure using the program randomize-groups. We need to provide the list of sites to sample from using the structure-list program: The two observed statistics appear larger than their random expectation (Figure 2 B and C).

We compute an upper bound for the P value as

P value = |S sim ≥ S obs | + 1 10, 000 + 1, (1)
where |S sim ≥ S obs | represents the number of simulated groups with a statistic at least equal to the observed value (one-tail test). This gives 0.0304 for the solvent exposure and 0.0444 for the C α distance, both significant at the 5% level.

These results indicate that the surface exposure of the candidate sites is likely linked to their function. We further ask whether their dispersal is also possibly a signature of their function or whether it is a by-product of their location at the surface of the protein. We perform a conditional sampling by sampling exclusively sites with a solvent exposure similar to the candidate sites.

For this, we first compute the exposure of every residue of the structure: The distribution to the average RSA is now centered on the observed value, showing that the exposure effect is accounted for (Figure 2D). However, the C α distance is no longer significant (Figure 2E), P value = 0.2674, indicating that the apparent residues' dispersal results from a spurious correlation with the RSA.

Availability

The SgedTools are distributed under the GNU General Public Licence version 3 (GPL3) and can be downloaded from GitHub.com at https://jydu.github.io/sgedtools/.

Conclusion

We introduced a set of generic tools that permit integrating results from various evolutionary analyses with functional annotations, including three-dimensional structures. This interoperabil-ity is made possible by a generic file format for storing position-specific sequence annotations.

The format supports annotations for single sites and groups of sites while being simple and flexible. Besides basic data manipulation, the SgedTools implement more complex algorithms, for mapping three-dimensional structures to sequence alignments and a conditional sampling of sites for the statistical testing of hypotheses. The tools can be combined as modules to create pipelines for testing functional and structural hypotheses from evolutionary predictions.

Figure 1 :

 1 Figure 1: Distinct coordinate systems. A) Sites (= alignment columns) correspond to distinct positions within each aligned sequence. B) When alignments are concatenated, one needs to keep track of the original alignment coordinates in the concatenated alignment. C) To map alignment positions onto a three-dimensional structure, the sequence of each chain must be aligned with each sequence of the alignment to find the best match.

Figure 2 :

 2 Figure 2: Analysis of positively selected sites in the lysozyme. A) Three-dimensional structure of the human lysozyme (PDB structure 134l). Residues corresponding to sites evolving under a positive selection scenario with a posterior probability higher or equal to 70% are shown in full (labelled residues). B-E: Histograms of distributions over 10,000 random groups. Vertical lines show the corresponding observed values. B, D: average relative solvent accessibility (RSA). C, E: average pairwise C α distance. B, C: sampling over all residues in the structure. D, E: sampling conditioned on the RSA value of each residue.

  l y s o z y m e L a r g e _ P d b I n d e x . txt \ --exclude -incomplete We use a gap-opening penalty of -2 to maximize the overlap of the structure with the selected sequence, as they are not from the same species. Incomplete structures are excluded from the comparison. Chain A from the 134L PDB entry was selected as the closest match. We then use the generated index to obtain the coordinates of the positively selected sites in the protein structure: python3 sged -translate -coords . py \ --sged lysozymeLarge -possel . sged \ --output lysozymeLarge -possel_PDB . sged \ --index l y s o z y m e L a r g e _ P d b I n d e x . txt \ --name PDB resulting in the SGED file:

  lysozymeLarge -possel -group . sged resulting in the following SGED file: Group [A:ARG14;A:ARG21;A:ILE23;A:ARG41;A:ARG50;A:ASP87;A:GLN126]

  lysozymeLarge -possel -group_PDB_infos . sged

  134 l_residues . sged We generate 10,000 random groups: python3 sged -randomize -groups . py \ --sged -groups lysozymeLarge -possel -group . sged \ --sged -sites 134 l_residues . sged \ --number -replicates 10000 \ --output lysozymeLarge -possel -group_random . sged Finally, we compute the structural properties of the random groups, as it was done for the group of positively selected sites: python3 ../../ src / sged -structure -infos . py \ --sged lysozymeLarge -possel -group_random . sged \ --pdb 134 l . pdb \ --pdb -format PDB \ --measure AlphaDist \ --measure DSSPsum \ --output lysozymeLarge -possel -g r o u p _ r a n d o m _ P D B _ i n f o s . sged

--

  python3 sged -structure -infos . py \ --sged 134 l_residues . sged \ --pdb 134 l . pdb \ --pdb -format PDB \ --measure DSSP \ --output 134 l_residues_infos . sged and then condition on the RSA of each site, which is stored in the "Rsa" column of the 134l_residues_infos.sged file: python3 sged -randomize -groups . py \ --sged -groups lysozymeLarge -possel -group . sged \ --sged -sites 134 l_residues_infos . sged \ lysozymeLarge -possel -group_random -rsa . sged We finally compute the structural characteristics of the random groups: python3 sged -structure -infos . py \ --sged lysozymeLarge -possel -group_random -rsa . sged \ lysozymeLarge -possel -group_random -rsa_PDB . sged

Table 1 :

 1 Example of SGED file showing group statistics and their associated P values. The group coordinates are specified in the 'Group' column.

	Group	Statistic P value
	[147; 157]	0.816295 0.04376
	[334; 363]	0.533308 0.05941
	[178; 316]	0.289917 0.99998
	[167; 170; 186]	0.581136 0.04328
	[154; 172; 162]	0.534361 0.27306

11 Acknowledgments JYD acknowledges funding from the Max Planck Society. 12 Author's contributions JYD: Conceptualization, Methodology, Software, Data Curation, Writing -Original Draft, Writing -Review & Editing, Visualization, Supervision DH: Software, Data Curation, Writing -Review & Editing, Visualization BP: Software, Data Curation, Writing -Review & Editing