The body images of social robots* Bing Li 1 , Oumayma Ajjaji 1 , Robin Gigandet 1

and Tatjana Nazir 1

Abstract-The rapid development of social robots has sparked a challenge for both robotics and cognitive sciences to comprehend how humans perceive the appearance of robots. This understanding is a crucial prerequisite for achieving successful human-robot symbiosis. To uncover people's perceptions and attitudes towards robots, we analyzed imageassociated words generated spontaneously by humans for 30 robots developed in the past decades. These words delineated a body image for each of the robots. We then used word affective scales and embedding vectors to provide evidence for links between human perception and the body images. Our findings revealed that the valence and dominance of the body images reflected human attitudes toward the general concept of robots. The study further demonstrated that the user-base and usage of robots significantly influenced people's impressions of individual robots. Moreover, we investigated the psychological and cultural implications of the body images by examining semantic distances between the robots and a humanrelated word, as well as gender-and age-distinguished words. This analysis revealed a relationship between the semantic distances to the word "person" and the robots' affects, as well as gender and age stereotypes towards the robots. Our study demonstrated that using words to build body images for robots is an effective approach to understanding which features are appreciated by people and what influences their feelings towards robots.

I. INTRODUCTION

Body image refers to the subjective perception and evaluation of one's own physical appearance, encompassing attitudes, feelings and cultural implications. Given the fast growth of robots in people's life, revealing what is implied in the body images of robots will help us improve the relationship between us and our artificial companions. The present study aims to understand how humans perceive robots and how they form semantic representations of the robots from purely visual characteristics. The term "body image" will be used to refer to the semantic understanding a person derives from viewing (images of) robots.

Neuroscientific research has shown that visual input to the brain is transformed into semantic representations through a default path [START_REF] Doerig | Semantic scene descriptions as an objective of human vision[END_REF]. Visual traits such as strokes, shapes, and colors are processed in the occipital lobe and then transmitted to the frontal and temporal lobes through pathways for semantic interpretation of the object [START_REF] Kar | Fast recurrent processing via ventrolateral prefrontal cortex is needed by the primate ventral stream for robust core visual object recognition[END_REF]. Importantly, significant traits such as faces and word forms are processed in dedicated regions close to occipital regions [START_REF] Hannagan | Emergence of a compositional neural code for written words: Recycling of a convolutional neural network for reading[END_REF], [START_REF] Tsao | Faces and objects in macaque cerebral cortex[END_REF], before *This project has received funding from the MEL (Métropole européenne de Lille) and the I-SITE ULNE (Université Lille Nord-Europe). Grant awarded to TAN (n • : R-Talent-20-006-Nazir). 1 The authors are affiliated with SCALAB, UMR CNRS 9193, Université de Lille, Lille, France. Address correspondence to Bing Li (bing.li@univ-lille.fr) or Tatjana Nazir (tatjana.nazir@univ-lille.fr) other semantic information is processed in the temporal lobe [START_REF] Patterson | Where do you know what you know? The representation of semantic knowledge in the human brain[END_REF]- [START_REF] Tong | A distributed network for multimodal experiential representation of concepts[END_REF]. Recently, a third pathway has been proposed that is specialized in processing social cues [START_REF] Pitcher | Evidence for a third visual pathway specialized for social perception[END_REF]. These pieces of evidence suggest that the human brain possesses a default system [START_REF] Doerig | Semantic scene descriptions as an objective of human vision[END_REF] that interprets visual inputs and generates semantic outputs. Therefore, the body image of a robot encompasses not only the visual appearance of the robot but also its semantic meaning and social significance.

Studies in semantics provided models about how concepts are organized in the brain's semantic system. In psycholinguistics, a commonly used model is the word embedding model [START_REF] Bhatia | Associative judgment and vector space semantics[END_REF]. This neural network model extract the likelihood of words appearing next to each other in large, naturally occurring texts typically found on the internet, and represents words using vectors. Research has shown that this model accurately reflects real-world semantic information [START_REF] Grand | Semantic projection recovers rich human knowledge of multiple object features from word embeddings[END_REF]. The spontaneous word association method can effectively uncover individuals' underlying perceptions and attitudes towards robots by analyzing the words they associate with them [START_REF] Nelson | What is free association and what does it measure?[END_REF]. Therefore, rather than focusing on the visual appearance of robots, which can often be difficult to quantify and interpret, incorporating a person's understanding of a robot's appearance into such a semantic framework could be more transparent and easier to implement.

With the goal of understanding human's mental representation of social robots, we propose to examine the characteristic features of robots from a semantic perspective. A free word-association task will be used to collect basic impressions about various robots and to model the data within a sematic space using word vectors. We will also quantify the affective dimensions of the words using "valence", "arousal" and "dominance" measurements from an affective lexicon [START_REF] Mohammad | Obtaining reliable human ratings of valence, arousal, and dominance for 20,000 english words[END_REF]. Moreover, we will determine how the word-vector that characterize a given robot relate to the word "person" within the semantic space, to assess how closely participants associate the robot with the human environment. Finally, we will investigate potential human stereotypes using two sets of opposing concepts (gender and age) to analyze the positioning of social robots on these semantic dimensions.

II. METHODS

A. The robot stimuli and human participants

We selected 30 robots from the robots available on the market or as prototypes in the past decades. To ensure a broad range of diverse features, the robots chosen for this study exhibit a wide variety of characteristics, including the presence or absence of a face, legs, arms, and resemblance to typical animal-or human-shapes. The robots included into the study are: Buddy, Eilik, Musio, Pico, Sima, example is quadrotor aircraft, or drones. While some may consider drones as robots, as evidenced by their inclusion in the IEEE Robotics & Automation Society's robots list 1 , others may perceive them simply as aircraft. However, the present study focuses on investigating the robot body image as a basis for human-robot interaction, a goal that does not align with the typical applications of drones. Therefore, drones were excluded from the current investigation.

The experiment was conducted on the Prolific platform 2 and built with psychJS [START_REF] De Leeuw | jspsych: A javascript library for creating behavioral experiments in a web browser[END_REF]. Before publishing the experiment task, we set pre-screening filters to only include native English speaker between 18 and 30 year old to maintain the homogeneity of the age span, within which people are very likely to grow up with internet, and more open to new technologies.

Before the tasks, participants were informed that they can quit the task at any moment during the task and will be compensated for the time spent on the task 3 . The task averagely took 14 minutes per participant. Compensation was of about C7.15/hour. Thirty participants were recruited into the experiment.

B. Experimental procedure

The experiment consisted of two distinct sessions aimed at 1) measuring attitudes towards robots and 2) constructing their corresponding body images.

1) The robot attitude scale: To assess attitudes, we designed a questionnaire, the Robot Attitude Questionnaire (RAQ). The RAQ was adapted from a study by Lee and Sabanović [START_REF] Lee | Culturally variable preferences for robot design and use in south korea, turkey, and the united states[END_REF] that explored cross-cultural differences in attitudes towards robots. The questionnaire comprised statements pertaining to the willingness of participants to seek assistance from robots in various situations and used a Likert scale rating (see Tab. I). Participants were required to select the option that best represented their attitude on a 5-point Likert scale ranging from 0 -"Strongly disagree" to 4 -"Strongly agree". To calculate the overall attitude score of a participant, scores from all the statements were averaged. Participants completed the Robot Attitude Questionnaire (RAQ) prior to engaging in the free association task. Therefore, the term "robot" in the RAQ did not refer to any specific robot model but instead represented the general concept of robots.

2) Free association: To construct the robot's body images we used a free association task [START_REF] Nelson | What is free association and what does it measure?[END_REF], [START_REF] De Deyne | Better explanations of lexical and semantic cognition using networks derived from continued rather than single-word associations[END_REF]. Following completion of the questionnaire, participants were instructed to provide 6 words that came to their minds in response to each of 10 sequentially presented images. The images were presented at the top of the screen, followed by 6 text boxes for each image. The participants were required to enter the words in a sequential manner, from the 1st to the 6th text box, and click on the "Finished" button to proceed to the next image. To expedite the process of moving to the next word after entering a word, participants used the "Enter" key. For each image, participants were required to enter all 6 words, and skipping any text box was not permitted. The "Auto fill-in" functionality of the psychJS program utilized in the study was disabled.

To mitigate the potential for intra-correlation among participants, whereby individuals might demonstrate similar behaviors across the observed robots, a randomized robot selection procedure was implemented. The randomization approach is detailed in [START_REF] Hollis | Scoring best-worst data in unbalanced many-item designs, with applications to crowdsourcing semantic judgments[END_REF]. As a result of this method, each participant viewed a distinct subset of 10 robots.

Tab. II displays the top 30 most commonly reported words.

C. Word vectors and affect measurements

To represent words as vectors, the Word2vec model pretrained on Wikipedia news by FastText was utilized 4 . The resulting vectors possessed 300 dimensions. Given that a robot is associated with multiple words, the vectors for the different words were averaged to create a single 300dimension vector for each robot, as illustrated in Fig. 2. To quantify the affective dimensions of words, the valence, arousal, and dominance (VAD) measurements from Mohammad's [START_REF] Mohammad | Obtaining reliable human ratings of valence, arousal, and dominance for 20,000 english words[END_REF] affective lexicon were used. This lexicon contains VAD ratings for 20,000 English words based on best-worst scaling [START_REF] Mohammad | Obtaining reliable human ratings of valence, arousal, and dominance for 20,000 english words[END_REF], [START_REF] Hollis | Scoring best-worst data in unbalanced many-item designs, with applications to crowdsourcing semantic judgments[END_REF].

After data collection, the responses were pre-processed. This involved converting plural words into their singular forms and converting capitalized words to lowercase. For compound words and phrases, the most representative word was primarily extracted. For example, "canfly" was replaced with "fly" and "car-like" was replaced with "car". However, in cases where representativeness was difficult to determine, such as "artificial intelligence", the entire compound was omitted.

Due to the limited size of the VAD lexicon, some adjectives were not present in the VAD lexicon, but their synonyms were. For example, "gangly" was not in the lexicon, but "awkward" was present and used instead. In such cases, synonyms were obtained from the Merriam-Webster thesaurus 5 . After pre-processing, the VAD lexicon covered 92.33% of the responses. In the lexicon, the values of the affective dimensions ranged between 0 to 1, with a higher value indicating a higher affective rating.

III. RESULTS

A. Word affects predicts subjective attitude

At participant-level, we investigated whether the general attitude towards robots can be predicted by affective measures of the associated words. Three linear mixed-effect (LME) models were built with attitude scores as the dependent variable and affective measures as the only fixedeffect independent variable respectively. Robots with random intercepts were included as the maximized random-effect structure.

The results showed that valence is a strong predictor for attitude (likelihood ratio test, LRT χ 2 = 15.577, p < .000), and dominance is a strong predictor for attitude (LRT χ 2 = 19.529, p < .000). However, arousal did not predict attitude (LRT χ 2 = 2.101, p = .146). Figure 1 illustrates the relationships between attitudes and affective measures. The values of the affective measures for each of the three features (valence, dominance, arousal) were averaged across words for each participant. Each dot in the figure represents one participant. The results show that the semantic associations of a robot's body image are reflective of the attitude of the observer.

B. The graph of body images

Robot classification methods generally vary and can include shape, function, and usage. However, the extent to which these features influence human perception of robots has not been extensively studied. Here, we created a graph of the 30 robots based on the average word vectors associated with each of the robots. We then used pair-wise cosine similarity to connect each robot to its three most similar robots (as shown in Fig. 2 and Fig. 3D). The graph identified the robot types commonly known as humanoids, robot assistants, and robot pets. However, some robots were not clearly classified into a category. For example, Aibo, often referred to as a "robot dog", was found to be more similar to Eilik than to Spot. Similarly, Neubie, which is shaped like a trolley or a locomotive, was more strongly connected with humanoid robots than with similarly shaped robots (e.g. Parky) or other wheel-based robots (e.g. Pico and Astro).

The most distinct categories of robots are identifiable by cliques, which refer to fully connected components in the graph. We have highlighted the 4-cliques (4 fully connected robots) that exist in the graph, representing the categories of (A) robot pets, (B) humanoids, and (C) robot kids (in Fig. 3). The robot Nao falls into the category of children-oriented robots, which includes "robot pets" and "robot kids." Thus, individuals evaluating Nao immediately associate it with the user-base and usage. In contrast, Neubie's indefinite body image makes it challenging to connect it to a particular userbase or usage. Overall, the identified robot categories based on their semantic relationships suggest that people tend to form body images based on the anticipated user-base and usage of the robot, rather than its shape. The diagram shows the distance between a robot and the target word "person", simplified in a 2-dimensional plaine for better illustration. The peripheral dots represents words in the original semantic space, the dots of the same color indicated in the vicinity of the circles around the word. The outer circle is the distance proximity of the robot NAO and the inner circle is the distance proximity of the robot Pico. Due to the bias towards the distance between words and human-related words, the words that are closer to the human-related words (the red dots) are systematically different from the words that are further than the human-related words (the orange dots). Therefore the affect values of the words on the proximity circles are used as baselines for the respective robots; (B-D) The x-axis is the distance between robot body images and the word "person"; the y-axes are standardized valence, arousal and dominance.

C. The distance to human related words predicts affect of robots' body images

The distance between a robot's body image (the words that characterize the robot) and human-related words may provide insight into how closely the robot is associated with human life in a semantic sense. Here, we took the averaged word vectors for each of the robots, and computed their distance from the word "person" using the cosine distance. Specifically, we used the formula 1similarity cos (v 1 , v 2 ), where v 1 and v 2 are the vectors abstracting a robot and the target word "person".

Noteworthy, there are several human-related words sharing similar contexts from which we can choose, with a nuanced difference in their contexts though, including "adult", "child", "woman", "man", "human", "people" and "person".

We selected the word "person" as the target word due to the consideration that, primarily, this word has a context that is more general to human life. Since the training objective of Word2vec is to maximize the probability of the occurrence of a word given its context, or the occurrence of a context given its word, a word contains the information about the contexts where the word is commonly used. The context of the word "person" is also less discriminatory towards genders or age, which makes it a more representative term for human life.

Another consideration was that "person" has a larger number of words in proximity to the distance between it and the word vector that characterize the robot (see the dots of the same color indicated in the vicinity of the circles around the word "Person" in Fig. 4A). This helps to control for affective biases induced by the distance between human- related words and other words. An example of such a bias is the valence score of words, which is negatively correlated with the distance to the word "person". The other affective scores of words (arousal and dominance) also tend to show systemic relationships with their distance to the target word "person". To eliminate this bias, we subtracted a baseline from its affective score. In our analysis, a baseline for a robot was the mean affective level of all words at a similar distance between the robot and the target word (see 4A). There were fewer baseline words centered on the words "human" and "people" than on the word "person", making "person" the most robust choice for the target word.

In Figure 4B-D, we analyzed the relationship between the perceived affective level (in terms of valence, arousal, and dominance) of robots' body images and their distance from the target word "person". Our results indicate that valence and dominance are both correlated with the distance to the target word. Specifically, the valence scores of words associated with the robots initially increase with distance, then plateau with a slight drop at a level higher than the baseline. Similarly, dominance scores increase monotonously with distance to the target word. However, we did not find a clear relationship between arousal scores and distance to the target word.

Interestingly, we found that most of the humanoids were located further away from the target word "person" than the other robots. For example, Atlas, Optimus, Pepper, Musio, Hitchbot, Talos, iCub, and Asimo were the most distant robots, while Aquanaut, Jibo, Spot, Aibo, Pico, Pyxel, and Buddy were the closest. These results could suggest that being more human-like may not necessarily lead to better integration of robots into human environments.

D. The stereotypes about gender and age towards robots

Aside from the literal meanings of individual words, such as those related to humans, semantic space also incorporates complex cultural and social associations that distinguish between opposing concepts. To investigate potential stereotypes as perceived by human participants, we utilized two sets of opposing concepts to analyze the body images of our robots.

The first set of opposing concepts examined the effect of gender, using words such as "females", "female", "girls", "girl", "women", "woman", "ladies", "lady", "actress", and "actresses" for one end of the dimension, and "males", "male", "boys", "boy", "men", "man", "gentlemen", "gentleman", "actors", and "actor" for the other end. The word vectors for each set were then averaged to respectively represent"female" and "male", and this allowed for the positioning of the robots on the gender dimension. The results are presented in the left column of Fig. 5, where the upper plot shows the relationship between"manliness" and valence, and the lower plot shows the relationship between"manliness" and dominance. Note, the manliness scores on the x-axis were calculated by subtracting the distance between the robots to the female concepts from that to the male concepts, with greater values representing shorter distances to the male concepts. We found that manliness was positively related to dominance, and the humanoids were mostly on the more manliness side of the dimension. Notably, as shown in the inset, all robots were positioned on the male side of the semantic space, suggesting a stereotype of robots as males.

The second set of opposing concepts was about age, with one end consisting of the words "young", "child", "children", and the other consisting of "old", "elderly", "adult", "adults". The results are shown in the right column of Fig. 5. We found that the humanoids were positioned closer to the "older" end of the age dimension, while the robot pets and robot kids were closer to the "younger" end. While this finding was in line with our expectations, we found that the robot vectors crossed the equilibrium line between young and old. This was a notable difference from the gender dimension, where no robot crossed the equilibrium line between female and male. The relationship between "oldness" and valence on the one hand, and "oldness" dominance on the other hand shows that robots that are perceived as older have lower valence scores and are perceived as more dominant.

IV. DISCUSSION

The field of psycholinguistics provides a wealth of knowledge about the nature of words. In this study, we introduce a paradigm that leverages this knowledge to investigate human-robot interaction. Specifically, we analyzed the words associated with the visual image of robots to gain insight into human perception of them. We found that the affective connotations of these words (valence and dominance) are predictive of people's attitudes towards robots. Additionally, we were able to group robots based on their intended user-base and appearance, using the associated words as a guide. A third key finding underscored the importance of a robot's body image in shaping its potential integration into the human environment. Specifically, we found that humanoids were often positioned further away from the target word "person" than other types of robots, suggesting that being more human-like may not necessarily lead to better integration into human environments. Lastly, we used opposing concepts to characterize our robots on the genderand age-dimensions, with a notable finding that our robots were associated more with words pertaining to masculinity, which was correlated with dominance.

Our paradigm consists of two procedures. The first procedure involves associating robots with a set of words, which allows us to infer the perceived emotions of the robots based on the degree of valence and the degree of dominance of the words as determined in existing lexicons (e.g., Mohammad's 2018 [START_REF] Mohammad | Obtaining reliable human ratings of valence, arousal, and dominance for 20,000 english words[END_REF]). Fig. 1 demonstrates how word-related valence and dominance can be utilized to predict human attitudes towards robots obtained from Likert scale ratings. Note, a recent study on social robots [START_REF] Brondi | What do we expect from robots? social representations, attitudes and evaluations of robots in daily life[END_REF] also employed free association to investigate participants' word associations with the written word "robot" and used factor analysis to categorize the mental representation of robots as social entities. Our study shares a similar theoretical foundation with this prior research, but with a more specific focus on individual robots rather than a general robot concept or its social presence.

In the second procedure, the words associated with the robots are transformed into 300-dimensional vectors, representing the robots in a robust semantic space. Fig. 3 shows that although the grouping of robots is based on their associated words, members of a group also exhibit similarities in their physical appearance and derived features. For example, humanoid robots are grouped around the blue clique on the left side of the figure, next to the quadrupedal robots, while child-oriented robots are clustered in the green and light blue cliques. As the number of robots increases, these patterns are likely to become even clearer. These findings provide support for the idea that a robot's body image comprises interconnected visual, semantic, and potentially social features, which are all inferred from the robot's morphology.

Our paradigm allows for a rich description of how humans perceive robots, with the potential for exploring various lexical and semantic features. This detailed understanding can shed light on the ways in which robots relate to one another and to other concepts within the semantic space. This can be done by two approaches. Firstly, by computing the distance between the robots to words that encompass a broad context in semantic space, i.e. "person", we exhibited how valence and dominance are related to a robot's proximity to the concept of "person" (Fig. 4). Secondly, by computing the distance between the robots and features such as gender and age in semantic space, we exhibited how people anthropomorphize, and even disambiguate, robots. This analysis revealed that the set of robots used in our study was generally perceived as more masculine, and robots that were perceived as younger had a more positive valence (Fig. 5). These results highlight the importance of a robot's body image in shaping its interactions with humans and its potential integration into human environments.

Finally, our study provides valuable insights for commercial robot development, as we discovered that human attitudes towards robots can be predicted from the valence and dominance of the words associated with them. For example, robots such as Jibo and Buddy, which are low in dominance and closer to the concept of "person", may be more appealing for consumers compared to humanoids. As we continue to expand our dataset of robots, we anticipate even greater insights into the complex dimensions of robots and their impact on human behavior and response.

Fig. 1 .

 1 Fig. 1. The relationships between the attitudes and dominance, valence, arousal. The dashed line indicates the insignificance in the corresponding LME analyses.

Fig. 2 .

 2 Fig. 2. Clustering of the robots based on their cosine similarities. The outermost circle is the robots in the present study. The intermediate circle indicates the vector abstraction of the robots, colored with the three clusters identified by hierarchical clustering of the cosine similarities between robots. And the innermost network is comprised of the connections between each robot and its 3 closest neighbors.

Fig. 3 .

 3 Fig. 3. The network of robots based on their body images. (A-C) Three 4-cliques in the network. (D) the whole network of all the 30 robots. The colors of the cliques correspond to the colors in the network.

Fig. 4 .

 4 Fig. 4. The relationship between affects and human distance. (A)The diagram shows the distance between a robot and the target word "person", simplified in a 2-dimensional plaine for better illustration. The peripheral dots represents words in the original semantic space, the dots of the same color indicated in the vicinity of the circles around the word. The outer circle is the distance proximity of the robot NAO and the inner circle is the distance proximity of the robot Pico. Due to the bias towards the distance between words and human-related words, the words that are closer to the human-related words (the red dots) are systematically different from the words that are further than the human-related words (the orange dots). Therefore the affect values of the words on the proximity circles are used as baselines for the respective robots; (B-D) The x-axis is the distance between robot body images and the word "person"; the y-axes are standardized valence, arousal and dominance.

Fig. 5 .

 5 Fig. 5. The stereotypes about gender and age towards robots. (A) and (B) are the stereotype about gender; (C) and (D) are the stereotype about age; (A) and (C) are the relationships between the robot scores and valence; (B) and (D) are the relationships between the robot scores and dominance. The inset on the left side shows the positons of the robots around the sex equilibrium line, where the area below the equilibrium line is where male likeness score ¿ female likeness score. The blue lines are the equilibrium lines splitting the sides of the opposing concepts.

https://robots.ieee.org/robots/ (April 18,

2023).[START_REF] Kar | Fast recurrent processing via ventrolateral prefrontal cortex is needed by the primate ventral stream for robust core visual object recognition[END_REF] https://app.prolific.co[START_REF] Hannagan | Emergence of a compositional neural code for written words: Recycling of a convolutional neural network for reading[END_REF] The study was approved by the ethics committee at the University of Lille with the reference number 2023-663-S113.

https://fasttext.cc/docs/en/english-vectors.html

https://www.merriam-webster.com/thesaurus/


Sujith Sritharan

Raphaelle Versini

Jules Petit

Emmanuelle Bayer

Antoine Taly
email: taly@ibpc.fr

Deep Learning-Based Prediction of A. thaliana's MCTP4 Structure and Exploration of Transmembrane Dynamics using Coarse-Grained Molecular Dynamics Simulations

Multiple C2 Domains and Transmembrane region Proteins (MCTPs) in plants have been identified as important functional and structural components of plasmodesmata cytoplasmic bridges, which are vital for cell-cell communication. MCTPs are endoplasmic reticulum (ER)-associated proteins which contain three to four C2 domains and two transmembrane regions. In this study, we created structural models of Arabidopsis MCTP4 ER-anchor transmembrane region (TMR) domain using several prediction methods based on deep learning. This region, critical for driving ER association, presents a complex domain organization and remains largely unknown. Our study demonstrates that using a single deep-learning method to predict the structure of membrane proteins can be challenging. Our deep learning models presented three different conformations for the MCTP4 structure, provided by different deep learning methods, indicating the potential complexity of the protein's conformational landscape. For the first time, we used simulations to explore the behaviour of the TMR of MCTPs within

INTRODUCTION

Plasmodesmata (PD) are intercellular channels found in plants that allow for the communication and transport of molecules between adjacent cells. [START_REF] Tilsner | Staying Tight: Plasmodesmal Membrane Contact Sites and the Control of Cell-to-Cell Connectivity in Plants[END_REF] PD have a unique membrane organization characterized by tight membrane contact sites, consisting of two concentric membranes -the plasma membrane (PM) and the endoplasmic reticulum (ER).. [START_REF] Tilsner | Staying Tight: Plasmodesmal Membrane Contact Sites and the Control of Cell-to-Cell Connectivity in Plants[END_REF] The regulation of intercellular trafficking through these channels is essential for plant growth, development, and defense against biotic and abiotic stresses. [START_REF] Petit | Dare to change, the dynamics behind plasmodesmata-mediated cell-to-cell communication[END_REF] The ER-PM tethering machinery of membrane contact sites in plasmodesmata has been hypothesised to play a crucial role in PD formation, reshaping, and proper function. [START_REF] Tilsner | Staying Tight: Plasmodesmal Membrane Contact Sites and the Control of Cell-to-Cell Connectivity in Plants[END_REF][START_REF] Petit | Dare to change, the dynamics behind plasmodesmata-mediated cell-to-cell communication[END_REF] Members of the MCTP family are plasmodesmata-localised and act as ER-PM tethers. [START_REF] Brault | Multiple C2 domains and transmembrane region proteins (MCTPs) tether membranes at plasmodesmata[END_REF] These tethering proteins selectively concentrate at plasmodesmata, bind membranes together, and were hypothesised to control the exchange of information between cells. [START_REF] Petit | Dare to change, the dynamics behind plasmodesmata-mediated cell-to-cell communication[END_REF] MCTP proteins consist of two transmembrane regions and three or four tandem C2 domains. The C2 domains act as PM docking sites through interaction with anionic sites, while the transmembrane domain insert into the ER membrane. This structural organization is essential for their function in PD. While C2 domains are relatively conserved and the 3D structure is more easily accessible, the TMR presents a complex domain organization that

has not yet been elucidated. [START_REF] Brault | Multiple C2 domains and transmembrane region proteins (MCTPs) tether membranes at plasmodesmata[END_REF] Recently, a variety of novel protein structure prediction tools, namely Alphafold and RosettaFold, as well as new strategies based on large language models, including ESMFold and OmegaFold, have emerged. [START_REF] Jumper | Highly accurate protein structure prediction with AlphaFold[END_REF][START_REF] Baek | Accurate prediction of protein structures and interactions using a threetrack neural network[END_REF][START_REF] Wu | High-resolution de novo structure prediction from primary sequence[END_REF][START_REF] Lin | Evolutionary-scale prediction of atomic level protein structure with a language model[END_REF] These tools are powerful and trained to recognize evo-2 lutionary preserved structural motifs. However, they are also very recent, and we are just beginning to understand their limitations. One such limitation is that membrane proteins are underrepresented in the training datasets, which could lead to uncertain models. On the other hand, new methods based on language models, such as the one developed by Lin et al. (2022), are not limited by experimental data. [START_REF] Lin | Evolutionary-scale prediction of atomic level protein structure with a language model[END_REF] These methods employ the protein sequence, potentially generating more accurate predictions for membrane proteins.

Despite these challenges, in this study, we employed several available deep learning algorithms in the literature to test for convergence, aiming to overcome potential limitations and obtain reliable predictions for the MCTP4 ER-anchor TMR domain. First, we generated different models using various deep learning-based prediction tools, such as Alphafold(AF), Alphafold multimer(AFM), RosettaFold(RF), Tr-RosettaFold(TR), ESMFold(ESM), and OmegaFold(OF).. [START_REF] Jumper | Highly accurate protein structure prediction with AlphaFold[END_REF][START_REF] Baek | Accurate prediction of protein structures and interactions using a threetrack neural network[END_REF][START_REF] Wu | High-resolution de novo structure prediction from primary sequence[END_REF][START_REF] Lin | Evolutionary-scale prediction of atomic level protein structure with a language model[END_REF][START_REF] Evans | Protein complex prediction with AlphaFold-Multimer[END_REF][9] We compared the results of these different prediction tools to ensure the reliability of the generated models. Finally, we employed molecular dynamics (MD) simulations with Martini 3 coarse-grained force fields and principal component analysis. We examine the structure and temporal flexibility of the TMR, as well as its behavior within a lipid bilayer. We find that MD explores the conformational space sampled by DL tools and beyond.

MATERIAL AND METHODS

Jupyter Notebook

All of the analysis and data used in this study have been documented and made available for reference and reuse. These scripts are hosted in Jupyter Notebooks, a popular open-source web application that allows for the creation and sharing of documents. The notebooks can be accessed from the associated GitHub repository at https://github.com/Jouffluu/Molecularmodelling-MCTP.

Predicted Models

The three-dimensional structure of the full-length Arabidopsis thaliana MCTP4 also called FT-interacting protein 4 (Uniprot: Q9C8TM3) was obtained using deep-learning prediction tools. We utilized Alphafold (version 2.2),, [START_REF] Jumper | Highly accurate protein structure prediction with AlphaFold[END_REF] Alphafold multimer (version 2.2), [START_REF] Evans | Protein complex prediction with AlphaFold-Multimer[END_REF] Omegafold (version 1.1.0), [START_REF] Wu | High-resolution de novo structure prediction from primary sequence[END_REF] and ESMfold (version 1.0.3), [START_REF] Cabezudo | Scaling protein-water interactions in the Martini 3 coarse-grained force field to simulate transmembrane helix dimers in different lipid environments[END_REF] which were run on a local cluster. For Rosettafold, we used the public webserver (https://robetta.bakerlab.org/submit.php), [START_REF] Baek | Accurate prediction of protein structures and interactions using a threetrack neural network[END_REF] and for Tr-rosetta, we utilized the webserver (https://yanglab.nankai.edu.cn/trRosetta). 9

System preparation

We utilized the Charmm GUI web server for system construction and mapping of atomistic structures to the coarse-grained (CG) Martini 3 models. [START_REF] Jo | CHARMM-GUI: A web-based graphical user interface for CHARMM[END_REF] We selected residues 550:776 for our simulations, which encompassed 50 residues preceding the transmembrane domain, the transmembrane (TM) helix domains (600:750), and extended to the end of the protein. To probe the stability of the TM helix, we conducted simulations in PIPC/PIPE (80:20) bilayer membranes. Each model was oriented using the PPM server, incorporating the topology of the N-terminus of the first chain from the PDB file. [START_REF] Lomize | OPM database and PPM web server: resources for positioning of proteins in membranes[END_REF] Each system was subsequently solvated in water and neutralized, and 0.15 M NaCl was added.

CG-MD simulations

In all simulations, GROMACS 2021.5 simulation package was used with the Martini 3 force field. [START_REF] Van Der Spoel | GROMACS: fast, flexible, and free[END_REF][START_REF] Souza | Martini 3: a general purpose force field for coarse-grained molecular dynamics[END_REF] The protocol consisted of an initial energy minimization phase, followed by a multi-stage equilibration process, and concluded with a production simulation. Energy minimization was carried out for two iterations of 5,000 steps each using the steepest descent method. The simulations were subsequently equilibrated through five stages, employing time steps of 2, 5, 10, 15, and 20 fs. A target temperature of 300 K was maintained with the v-rescale thermostat, with a coupling constant of 1 ps. An semiisotropic pressure of 1 bar was maintained using the Parrinello-Rahman barostat, [START_REF] Parrinello | Polymorphic transitions in single crystals: A new molecular dynamics method[END_REF] with a compressibility of 4.5 × 10-5 bar-1 and a relaxation time constant of 12 ps. Long-range interactions were treated with a cutoff radius of 1.1 nm for both van der Waals and Coulombic interactions, using a switching function from 1.0 nm for van der Waals. The production simulations were performed using an NPT ensemble with a time step of 20 fs for a total simulation time of 3 microseconds.

Multiple replicates were conducted for the system, and the final phase of the simulation was executed with no restraints.

Contact analysis

To quantify contacts between transmembrane (TM) helices among the different models predicted by the algorithms, we used the MDAnalysis library to calculate distances between the centers of mass of the residues. [START_REF] Gowers | A Python package for the rapid analysis of molecular dynamics simulations[END_REF][START_REF] Michaud-Agrawal | A Toolkit for the Analysis of Molecular Dynamics Simulations[END_REF] During the simulations, contacts between the beads representing the helices were defined using a cutoff distance of 12 Å, and contact occupancies were calculated for each bead pair. Subsequently, a contact map was generated using the R language for statistical computing (R Core Team, 2022) for each model. [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF] (data not shown)

Principal Component Analysis and Clustering

To reveal the most important motions in the TM helices, we employed principal components analysis (PCA) using the tools provided in the GROMACS software package. [START_REF] Van Der Spoel | GROMACS: fast, flexible, and free[END_REF] For all models, we first fitted the trajectories where the transmembrane (TM) helix part was stable within the membrane for 3 microseconds to ensure that the phosphates of the membrane remained in the same position. We then concatenated these adjusted trajectories.The covariance matrix was calculated on the backbone atoms of the residues located under the membrane (HP1 and HP2). The first two principal components were then plotted using the matplotlib library for statistical visualization. [START_REF] Hunter | Matplotlib: A 2D graphics environment[END_REF] The results of the PCA were clustered using the K-Medoids method. Utilizing the KMedoids class from the scikit-learn-extra library, [START_REF] Learn-Extra Developers | Scikit-learn-extra: A set of tools for scikit-learn[END_REF] we specified five clusters for categorization. We determined this optimal number of clusters using the elbow method. After fitting the model to the PCA data, the coordinates of the cluster centroids were determined.

Data analysis and visualisation

Some basic analysis tasks, such as the calculation of the root mean square deviation (RMSD) or the distances between centers of the geometry of the two helices, were performed using the tools provided in the GROMACS 2021.5 software package. [START_REF] Van Der Spoel | GROMACS: fast, flexible, and free[END_REF] For visualization purposes, we constructed a density plot to provide a view of the distribution of data points within the first two principal components (PC1 and PC2). More complex analyses, such as the tilt angle calculation, were implemented in the Python programming language with extensive use of the MDAnalysis (https://github.com/rversin/MD-TMtools). VMD [START_REF] Humphrey | VMD -Visual Molecular Dynamics[END_REF] were used to visualise the trajectories and ChimeraX was used to analyse alphafold output. [START_REF] Pettersen | UCSF ChimeraX: Structure visualization for researchers, educators, and developers[END_REF]

RESULTS

Models of MCTP4 ER-TMR domain

We generated six models of MCTP4 ER TMR domain using six different prediction methods, in addition to a partial model of MCTP4 TMR domain previously constructed by Modeller and used as a reference. [START_REF] Petit | Membrane Tethering in Plant Intercellular Communication : Structure-Function of Multiple C2 domains and Transmembrane Region Proteins (MCTP) at Plasmodesmata ER-PM Membrane Contact Site[END_REF] This work utilized bioinformatic tools, hydrophobic clusters analysis and molecular dynamics, to delineate transmembrane helices within the MCTP4 protein. [START_REF] Petit | Membrane Tethering in Plant Intercellular Communication : Structure-Function of Multiple C2 domains and Transmembrane Region Proteins (MCTP) at Plasmodesmata ER-PM Membrane Contact Site[END_REF] We decided to use the resulting definition of membrane domains. Therefore, we extracted the 550-776 region from each model. We previously identified five putative subdomains within the approximately 200-residue sequence of MCTP4 transmembrane domain (TMR). These subdomains include an N-term amphipathic helix (APH1), a putative transmembrane domain (TMD0), a hairpin transmembrane domain (HP1) composed of two transmembrane helices (TM1 and TM2), a second, longer amphipathic helix (APH2), and another hairpin transmembrane domain (HP2) which is also composed of two transmembrane 6 Subsequently, an alignment and Root Mean Square Deviation (RMSD) calculation were 7 performed on the extracted regions and on the whole model. The results of this analysis are displayed in Table 1 and Figure 3(g-i).

Table 1: RMSD values for the transmembrane domain (550-776) (upper half) and for the alpha carbon of entire models (lower half). For each pair of models, the RMSD value is indicated for each measurement. The PLDDT score was used to assess the confidence of the 3D structure prediction algorithms. A low PLDDT score indicates low confidence in the 3D structure, while a high score indicates higher confidence. Confidence scores varied among the models, particularly in the membrane region, as illustrated in Supplementary Figure 6. Among the prediction methods, ESM appeared to be the most confident in its predictions for both TM domains, while AlphaFold (AF2) seemed to be less confident in the HP2 domain compared to the other methods (Figure 2). The other methods showed relatively high confidence in their predictions. When comparing the contact maps, which are two-dimensional representations of threedimensional structures, [START_REF] Fakhoury | Generating protein folding trajectories using contact-map-driven directed walks[END_REF] of the models predicted by each method, we observed that ESM, TR, RF, and AFM predictions showed a similar pattern (Figure 3 a-b,d-e). In these conformations, the TM2-TM3 helices (615-635, 715:735) were found to be in close proximity. On the other hand, the models made by AF2 and OF displayed different conformations in the membrane domain. In AF2's model, the TM2-TM3 helices were separated by more than 8

AF AFM Rose

angstroms with almost no contact (Figure 3e/i). Furthermore, it's root mean square deviation (RMSD) was high, over 13 angstrom, compared to other models (Table 1). This shows that AF2's model was quite different in terms of structure. When looking at the conformation obtained by OF, the close connection was between helices TM1 and TM4 (residues 600:615, 735:750), as seen in Figure 3f/h. OF's model also had a high RMSD, around 15, compared to the other models (Table 1). These large RMSD values and different helix arrangements highlight the range of protein conformations predicted by different methods.

Dimers

We wanted to determine whether the ER-domain of MCTP4 has the potential to form dimers. The analysis of the dimer produced by Alphafold multimer revealed that intrasubunits contacts were similar to those found in the ESM, RF, and TR models. In the TMR, contacts are found between the M1 helix of one monomer and the M4 helix of the other one (Figure 4 a/c). Furthermore, the algorithm exhibits high confidence in the intradomain but also in the inter-subunits-interactions (Figure 4 b/d).

10 In every model, the MCTP4 TMR incorporates two hairpins predicted to be in the bilayer membrane. While four of the models converge on similar arrangements and distances between the hairpins, two models provide notably different configurations. To investigate the stability of each model and whether they would interconvert, we studied them using molecular dynamics simulations.

11

We performed coarse-grained molecular dynamics simulations with the Martini 3 force field, to investigate the behaviour of the TMR domains of each model, produced by the deep learning methods, included in a lipid bilayer that mimics the composition of the ER, as detailed in the materials and methods section. Ten replicates were conducted for each model, each lasting 3 microseconds. During the initial replicates, we observed that certain TM domains (HP1 or HP2 or both) exited the membrane, which could potentially introduce variability in our analyses (see Supplementary Material 9). To ensure consistency, we decided to exclude these simulations from our analysis. We then repeated the simulations until we obtained four simulations for each starting model, where the TM domains remained inside the membrane throughout the entire simulation. This approach allowed us to obtain a consistent dataset for further analysis.

Interestingly, out of the four simulations conducted for each of the AF2 and ESM models, one simulation from each model exhibited significant variations in the distances between the TM2 (HP1) and TM3 (HP2) helices during the simulation, with both proximity and separation observed. Despite these movements, these particular simulations demonstrated stability within the membrane, indicating that the helices were not confined to a single conformation (see Supplementary Materials 9). This also show that the system's movement was not ballistic, which suggest that the simulations might have converged to equilibrium.

To gain a deeper understanding of the dynamic behaviour of these helices within the membrane, we conducted further characterization using principal component analysis, to get insights into the conformational dynamics of TM domains in lipid bilayer membranes.

Principal Component Analysis and Clustering

We employed principal component analysis (PCA) as a statistical method to elucidate the most significant motions of the TM helices within the lipid bilayer. In PCA, the Cartesian coordinates (X, Y, Z) of each atom were used as descriptors to capture the accessible degrees of freedom of the protein. Specifically, we selected the residues of the TM helices located in the membrane to perform the PCA. The resulting conformations from the simulations were projected onto the first two principal components, which accounted for 49% of the variability observed in our simulations (see Figure 5a). Each data point in the figure represents a conformation from the trajectory of an MCTP TMR model obtained through different methods, with the respective starting points of each model also displayed. Despite distinct starting points for each model, the conformations generated by the simulations appear to convergence towards two distinct basins (see Figure 5c). The main basin regroups the four similar models (ESM, RF, TR and AFM) and most of the structures including some coming from simulations started from AF2 and OF. The second basin does not include any of the starting structures but is formed by structures extracted from the simulations started from various models (AF2, ESM, RF and TR).

To identify the centers of these basins, we performed clustering using the k-meloids algorithm on the two principal components extracted from PCA. This allowed us to identify five distinct clusters within the conformational space (see Figure 5b). From each cluster, we extracted representative structures that best represented the characteristics of that particular cluster.

For the first cluster (Cluster A), we obtained a representative structure that closely resembled the initial "consensus" starting point of the simulation. This cluster is part of the main basin, suggesting that the simulation explored a conformational space similar to the initial structure throughout most of the simulation time.

In the second cluster (Cluster B), we obtained a representative structure that exhibited significant structural changes compared to the initial starting points. In this structure, helices TM2 are in contact with both TM3 and TM4 helices, which is novel and not captured by deep learning methods (see Figure 5d). This suggests that the simulation explored a different conformational space and underwent substantial structural rearrangements.

In the third cluster (Cluster C), which is also part of the main basin, the representa-13 tive structure shows contacts corresponding to the TM1-TM4 and TM2-TM3 helices. This indicates a unique conformation not present in the initial models, further highlighting the simulation's ability to explore alternative conformations.

For the cluster four, (Cluster D), the representative structure illustrates contacts between TM1-TM3 and TM1-TM4 helices. This suggests a distinct conformation, emphasizing the diversity of conformations accessible to the system.

Finally, in the fifth cluster (Cluster E), the representative structure corresponds to a conformation where the TM domains are separated (5d). This suggests that this simulation explored a wider range of conformational space, further highlighting the dynamic nature of the system under study. The PCA and clustering analysis have provided deeper insights into the structure and dynamics of the MCTP4 TMR. Our findings indicate that the MCTP4 TMR is not rigid, but displays substantial potential for structural rearrangement within the bilayer. There's a prominent convergence towards two main conformational basins, signifying two key structural states that the TMR can adopt. Furthermore, we identified certain novel helical contacts, implying that the MCTP4 TMR can explore a broad conformational space. This underscores the dynamic and versatile nature of the MCTP4 TMR in its biological context.

Discussion

Our study revealed that the MCTP4 TMR domain, located within the ER, consists of two hairpin, each containing two helices. These hairpin are deeply embedded within the lipid bilayer of the ER. The arrangement of these hairpins and their proximity to each other varied, reflecting the complexity and dynamism of the MCTP4 TMR structure within ER-mimicking bilayer.

Exploration of the conformational landscape by deep learning models.

In this study, we generated six distinct models of MCTP4 TMR using various prediction methods, which allowed us to explore the conformational landscape of the protein. Notably, PLDDT scores revealed varied confidence levels in the predictions of MCTP4's TMR 3D structure, with ESM showing the highest confidence in its predictions for both TM domains.

It is interesting to note that four of the prediction methods (ESM, TR, RF, and AFM) converged on a similar MCTP's transmembrane domain, where helices TM2 and TM3 are in close proximity. This suggests that this particular conformation might be a reliable representation of the protein's actual structure. However, AF2 and OF produced distinct models with different helical arrangements. These divergences could indicate the flexibility of MCTP4 TMR and the presence of alternative conformations. This also raises the importance of using multiple prediction methods in parallel to explore the conformational landscape of a protein. By relying on a consensus among several methods, we can potentially obtain a more accurate and reliable picture of the protein's structure. [START_REF] Graille | Best Practices of Using AI-Based Models in Crystallography and Their Impact in Structural Biology[END_REF] This approach is particularly relevant given the complexity of protein structure prediction and the possibility that different tools have complementary strengths and weaknesses. By combining the results, individual errors can be mitigated, and more robust conclusions can be drawn regarding the likely structure of a protein.

Simulations Behavior with Martini 3

During our simulations, we investigated the dynamic behaviors of the TM helices of MCTP4 within a lipid bilayer membrane designed to mimic the composition of the endoplasmic reticulum. With Martini 3, we were able to observe TM Helices that show spatial flexibility.

Nevertheless, among the 10 replicas for each model, we observed a diverse range of helix behaviors within the membrane. Some helices were coming out of the membrane (Supplementary Material Figure 101112131415). Consequently, we repeated the simulations multiple times to obtain a consistent and stable set of results within the membrane. In order to ensure the reliability of our analysis, we excluded simulations in which the TM domains exited the membrane. The Martini 3 force field has been developed in part to solve the issue identified with martini2, that tends overestimate protein-protein interactions. [START_REF] Souza | Martini 3: a general purpose force field for coarse-grained molecular dynamics[END_REF] However Martini3 is conversely associated with too hydrophobic alpha-helices. Therefore modifications to the scaling of interactions within the Martini 3 force field have been proposed to solve this issue.

Thomasen et al., proposed adjusting protein-protein interaction parameters to 88% of their original value in the Martini 3 force field. 26 The authors found that this scaling leads to that are closer to experimentally observed protein-membrane interactions, compared to a different scaling factor that modifies protein-water interactions. This did not solve the issue in our case (data not shown).

The plus of Molecular dynamics run on top of Deep-Learning Models

Three starting points were generated by deep learning methods and for each model, 4 times 3us simulations were launched. This allowed the exploration of a conformational landscape with two basins. The center of the first basin is very close to the conformation majorly found by deep learning algorithms. However, the other clusters present representative structures with contacts that are not found in deep learning methods, suggesting that with MD sim-ulation, we were able to explore new conformations which are not found by deep learning methods. It's also interesting to see that the AF2 and OF models start right at the edge of the consensus basin and then move into it. This shows how useful it is to use the physicsbased MD simulations together with models made by deep learning. By using both methods, we can benefit from their strengths and attain a more robust result.

Monomer versus Dimer contacts

Analyzing the predictions of deep learning models, we have observed significant differences between the TMR models of AF2, OF, and those that have converged, namely RF, AFM, TR, and ESM.

In the TMR model of AF2, the two helices of each transmembrane hairpin do not come into contact. This feature stands in stark contrast with those observed in other models.

In the TMR model from OF, it's noteworthy that helices TM1 and TM4 are in contact.

Similarly, the converged models exhibit a distinct contact between helices TM2 and TM3.

This analysis thus reveals a variety of structural configurations predicted by different deep learning models, underscoring the complexity of transmembrane interactions of MCTP4.

Through the use of coarse-grained molecular dynamics simulations, we found that the interaction between TM2 and TM3 tended to be more stable. This observation is supported by our density map, which reveals two distinct basins. Models that display these interactions are predominantly found in the larger of the two basins.

In contrast, the models produced by AlphaFold (AF) and OpenFold (OF) are positioned away from these basins. This positioning suggests that these models may represent an intermediate state. Further insights can be gleaned from studying the dimeric form of the protein.

Interestingly AF2 and AFM provided different results. This prompted us to explore further the difference. Noteworthy, AF2 showed significant deviations and obtained a low PLDDT score, particularly in the TM regions. This implies that AlphaFold's monomeric predictions are not always reliable or accurate for certain protein domains. The variation observed between monomeric and multimeric predictions could indicate that the formation of the dimeric structure involves additional interactions or structural rearrangements not captured in the monomeric prediction. A key capability of AF2 is to allow the prediction of contacts from sequence alignments. 27,[START_REF] Bouatta | Protein structure prediction by AlphaFold2: are attention and symmetries all you need?[END_REF] The relationship between sequences and contacts is however partially ambiguous, which has been shown in the case of conformational changes.

This in turn triggered the creation of strategies to explore the conformational landscape with AF2 and RoseTTAFold. [START_REF] Mitrovic | Reconstructing the transport cycle in the sugar porter superfamily using coevolutionpowered machine learning[END_REF][30][START_REF] Stein | Sampling protein ensembles and conformational heterogeneity with Alphafold2[END_REF][START_REF] Wayment-Steele | Prediction of multiple conformational states by combining sequence clustering with AlphaFold2[END_REF][START_REF] Schlessinger | Exploring the conformational diversity of proteins[END_REF][START_REF] Del Alamo | Sampling alternative conformational states of transporters and receptors with[END_REF] It is therefore tempting to speculate that evolutionary signals are not necessarily captured by AlphaFold's monomeric models for membrane proteins that form homo-oligomers. In the case of AF2, the model might be subject to conflicting constraints corresponding to intra-subunit and inter-subunit contacts. In agreement with that observation, the inter-subunit contacts between TM1 from one subunit and TM4 helix from the other subunit are evaluated to be positive (Figure 4).

The model produced by OF shows contacts between TM1 and TM4 helices that rather appear to be inter-subunit contacts with AFM. This is coherent with the notion that there are conflicting constraints, based on coevolution, corresponding to intra-subunit and intersubunit contacts in homo-oligomers, in particular using a monomeric prediction tool such as OF. Interestingly, the exploration of this model with a physics-based method like molecular dynamics could help resolve these conflicting constraints.

Finally, predicting the structures of multimers is a complex task, as assessing interfaces increases the difficulty compared to monomers. This raises a debate on whether to treat interfaces separately, as suggested by Zhu and colleagues. [START_REF] Zhu | Evaluation of AlphaFold-Multimer prediction on multi-chain protein complexes[END_REF] Furthermore, this leads to the question of whether multimeric proteins should be modeled as monomers or oligomers.

Oligomeric proteins could benefit from more precise treatment as oligomers rather than monomers, as part of the evolutionary pressure or signal might be associated with interfaces.

Overall, our study on the MCTP4 protein's transmembrane domain showed that predicting protein structures is complicated and needs a mix of methods. By using different tools, including deep learning and MD simulations, we got a detailed view of how this part of the protein moves and changes conformation. We also learned that it's crucial to think about how proteins group together and that simple models like AlphaFold might not always get it right. This study shows that using multiple approaches is key to understanding protein structures, especially for the parts that are in cell membranes.

Figure 1 :

 1 Figure 1: a) MCTP4 TMR having 5 elements: 2 transmembrane hairpins (HP1 and HP2) and 3 amphipathic helices (AH1, TM0 and AH2). b) AF MCTP4 model oriented in the lipid bilayer by OPM server.

Figure 2 :

 2 Figure 2: Evaluation of model predictions using the pLDDT score as a function of residues in the HP1 (left) and HP2 (right) regions. The curves of different colors represent models predicted by various prediction methods: AlphaFold (AF, red), OmegaFold (OF, blue), TR (green), ESM (yellow), and AlphaFold Multimer (AFM, magenta)

Figure 3 :

 3 Figure 3: Contact maps between the residues of transmembrane HP1 and HP2 of different protein structures: a) ESM, b) AFM, c) AF, d) TR, e) RF and f) OF. The distances were calculated using the alpha carbon atoms. Heat map coloring indicates the distance between residues, ranging from dark purple for short distances to white for longer distances(12 A). g) superposition of ESM, AFM, TR and RF transmembrane domain models. h) and j) are OF and AF transmembrane domains.

Figure 4 :

 4 Figure 4: a)AlphaFold multimer prediction of TMR MCTP4 protein. The HP1 domain is represented in orange and the HP2 domain in purple. The pLDDT score between residues of interchain domains is represented by lines, with the blue color indicating a high score. b) Predicted Aligned Error (PAE) for the MCTP4 dimer. PAE provides an estimate of the error in the predicted alignment of residues. c) Inter-chain contact map of TMR. d) Close-up view of the PAE for the TMR of MCTP4

Figure 5 :

 5 Figure 5: Principal Component Analysis (PCA) plots, clustering and density representation. a) The plot shows a projection based on the first two principal components (PCs) from a PCA. Large points represent the starting points of each simulation for each model, and small points are conformations generated by the simulation in each model. Each model is represented by its own colour: AlphaFold (AF, red), OmegaFold (OF, blue), TR-rosetta (TR, green), ESMFold (ESM, yellow), and AlphaFold Multimer (AFM, magenta). b) The centroids of each basin have been determined using the K-means clustering method. c) A density plot showing the projection of the two PCs, where each point corresponds to the starting point of each model. d) The representative structure of a basin is shown with a contact map corresponding to contacts between transmembrane domains.

Figure 6 : 25 (

 625 Figure 6: Evaluation of model predictions using the pLDDT score. The curves of different colors represent models predicted by various prediction methods: AlphaFold (AF, red), OmegaFold (OF, blue), TR (green), ESM (orange), and AlphaFold Multimer (AFM, purple)

Figure 7 :

 7 Figure 7: Variance explained by each Principal Component (PC) in a Principal Component Analysis (PCA).

Figure 8 :

 8 Figure 8: Projection of the first principal components (PC1 against PC2, PC3 and PC4). Each point represents an observation. Colors represent different models: Aqua for Rose, Lime Green for TR, Violet for AFM, Gold for ESM, Navy Blue for OMEGA, and Red for AF2

Figure 9 :Figure 10 :Figure 11 :Figure 12 :Figure 13 :Figure 14 :

 91011121314 Figure 9: Distance between HP1 and HP2 domains over the course of an AlphaFold simulation.

Acknowledgments

This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (project n°772103-BRIDGING .), labex DYNAMO (11-LABX-0011) and ANR projects DIVCON (ANR-21-CE13-0016-01) and MITOFUSION (ANR-19-CE11-0018).

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