Mirela-Diana Ilie

Alexandre Vasiljevic

Dr Philippe Bertolino
email: philippe.bertolino@inserm.fr

Gérald Raverot
email: gerald.raverot@chu-lyon.fr

Gérald Pr

Raverot

Biological and Therapeutic Implications of the Tumor Microenvironment in Pituitary Adenomas

Keywords: tumor microenvironment (TME), tumor-infiltrating lymphocytes (TILs), tumor-associated macrophages (TAMs), angiogenesis, tumor-associated fibroblasts (TAFs), folliculostellate cells (FSCs), extracellular matrix

Pituitary adenomas are neoplasms derived from the endocrine cells of the anterior pituitary gland. Most frequently, they are benign tumors, but may sometimes display an aggressive course, and in some cases metastasize. Their biology, including their wide range of behavior, is only partly understood. In terms of therapeutic targeting, most pituitary adenomas are easily treated with the available medical treatments, surgery, and sometimes radiotherapy. Nevertheless, gonadotroph adenomas lack medical therapeutic options, and treatment of aggressive pituitary adenomas and pituitary carcinomas remains challenging.

Here, we present an overview of the implications of tumor microenvironment in pituitary adenomas, reviewing its composition and function, as well as published cases that have been treated thus far using tumor microenvironment-targeting therapies. Additionally, we discuss emerging views, such as the concept of non-angiogenic tumors, and present perspectives regarding treatments that may represent future potential therapeutic options. Tumor-infiltrating lymphocytes, tumor-associated macrophages, folliculostellate cells, tumor-associated fibroblasts, angiogenesis, as well as the extracellular matrix and its remodelling, all have complex roles in the biology of pituitary adenomas. They have been linked to hormone production/secretion, size, invasion, proliferation, progression/recurrence, and treatment response in pituitary adenomas. From a therapeutic perspective, immune-checkpoint inhibitors and bevacizumab have already shown a degree of efficacy in aggressive pituitary adenomas and pituitary carcinomas, and the use of numerous other tumor microenvironment-targeting therapies can be foreseen. In conclusion, similar to other cancers, understanding the tumor microenvironment improves our understanding of pituitary adenoma biology beyond genetics and epigenetics, and constitutes an important tool for developing future therapies.

Introduction

The environment within which a tumor exists, the tumor microenvironment (TME), is composed of vascular structures, non-tumor cells such as immune cells, and non-cellular components such as extracellular matrix (ECM) macromolecules. It has long been accepted that the TME impacts tumor biology and has clinical implications, both as a prognostic tool and a therapeutic target in numerous cancers [START_REF] Balkwill | The tumor microenvironment at a glance[END_REF][START_REF] Hui | Tumor microenvironment: Sanctuary of the devil[END_REF]. In pituitary adenomas (PAs), the importance of the TME has emerged more recently, but there is now a constantly growing literature on the subject, and growing evidence of the complex and intricate roles that the TME plays in the biology of PAs [START_REF] Ilie | The Microenvironment of Pituitary Tumors-Biological and Therapeutic Implications[END_REF][START_REF] Marques | The tumour microenvironment of pituitary neuroendocrine tumours[END_REF].

Here, we review the biological and therapeutic implications of the TME in PAs. Briefly, we provide an overview of the TME composition and function, and we review all of the published cases of aggressive PAs and pituitary carcinomas (PCs) that have been treated with therapies that target the TME. Additionally, we present perspectives regarding treatments that have not so far been used in PAs, but that may represent potential therapeutic options in the future. Given that both the mechanisms of tumorigenesis and the composition of the TME, along with its biological and clinical implications, might differ depending on the histological subtype of the adenoma, where possible the available data is summarized separately for each major adenoma subtype. Figure 1 depicts T cells, macrophages, blood vessels, and folliculostellate cells in four different histological subtypes of PAs.

Immune microenvironment

A. Biology a) T cells

Tumor-infiltrating lymphocytes (TILs) have complex roles within the TME, that can translate into either anti-tumorigenic or pro-tumorigenic effects [START_REF] Hui | Tumor microenvironment: Sanctuary of the devil[END_REF]. TILs that are considered to have an anti-tumorigenic effect include CD56+ natural killer cells, CD8+ cytotoxic T cells, CD8+ memory T cells (CD8+CD45RO+), and CD4+ T helper 1 T cells, while TILs generally considered to have an pro-tumorigenic effect include CD4+ T helper 2 T cells and CD4+CD25+FoxP3+ regulatory T cells [START_REF] Balkwill | The tumor microenvironment at a glance[END_REF][START_REF] Hui | Tumor microenvironment: Sanctuary of the devil[END_REF][START_REF] Fridman | The immune contexture in cancer prognosis and treatment[END_REF]. However, these anti-tumorigenic and pro-tumorigenic effects are context-dependent, varying across tumor types and tumor stages, and are dependent on the specific composition of the immune infiltrate of a tumor and composition of its TME in general, as well as the location of the TIL, i.e. at the tumor invasive margin versus the tumor center [START_REF] Fridman | The immune contexture in cancer prognosis and treatment[END_REF]. Indeed, although CD8+ T cells have been associated with a positive prognosis in most cancer types, they have been associated with a negative prognosis in renal cell carcinoma. Conversely, regulatory T cells were associated with a good prognosis in colorectal or gastric cancer [START_REF] Fridman | The immune contexture in cancer prognosis and treatment[END_REF]. Therefore, TILs along with the other TME components need to be characterized in detail in PAs, in order to understand their respective roles.

To date, the majority of studies in PAs [START_REF] Rossi | Mononuclear Cell Infiltrate and Hla-Dr Expression in 28 Pituitary Adenomas[END_REF][START_REF] Wang | The expression profile of PD-L1 and CD8+ lymphocyte in pituitary adenomas indicating for immunotherapy[END_REF][START_REF] Heshmati | Prevalence of Lymphocytic Infiltrate in 1400 Pituitary Adenomas[END_REF][START_REF] Sato | Analysis of Tumor Angiogenesis and Immune Microenvironment in Non-Functional Pituitary Endocrine Tumors[END_REF][START_REF] Lu | Immune Cell Infiltrates in Pituitary Adenomas: More Macrophages in Larger Adenomas and More T Cells in Growth Hormone Adenomas[END_REF][START_REF] Lupi | Tumor Infiltrating Lymphocytes But Not Serum Pituitary Antibodies Are Associated with Poor Clinical Outcome after Surgery in Patients with Pituitary Adenoma[END_REF][START_REF] Barry | Tumor microenvironment defines the invasive phenotype of AIP-mutation-positive pituitary tumors[END_REF][START_REF] Mei | Increased expression of programmed death ligand 1 (PD-L1) in human pituitary tumors[END_REF][START_REF] Principe | Immune Landscape of Pituitary Neuroendocrine Tumours Reveals Association between Macrophages and Gonadotroph-Tumour Invasion[END_REF][START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF][START_REF] Jacobs | Regulatory T cells and the PD-L1/PD-1 pathway mediate immune suppression in malignant human brain tumors[END_REF] have relied on only single/few immune markers, and the quantification of the immune infiltrate varied across these studies. Nonetheless, these studies already provide important information on the immune composition of the TME and its potential roles.

PAs have been shown to be infiltrated by CD3+, CD8+, CD4+, FoxP3+, CD45RO+, and CD56+ cells [START_REF] Heshmati | Prevalence of Lymphocytic Infiltrate in 1400 Pituitary Adenomas[END_REF][START_REF] Barry | Tumor microenvironment defines the invasive phenotype of AIP-mutation-positive pituitary tumors[END_REF][START_REF] Mei | Increased expression of programmed death ligand 1 (PD-L1) in human pituitary tumors[END_REF][START_REF] Principe | Immune Landscape of Pituitary Neuroendocrine Tumours Reveals Association between Macrophages and Gonadotroph-Tumour Invasion[END_REF][START_REF] Jacobs | Regulatory T cells and the PD-L1/PD-1 pathway mediate immune suppression in malignant human brain tumors[END_REF][START_REF] Kemeny | Targeting PD-L1 Initiates Effective Antitumor Immunity in a Murine Model of Cushing Disease[END_REF]. Compared to the normal pituitary gland (NPG), PAs had more CD4+ T cells and a lower CD8+/CD4+ cell ratio [START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF]. Functioning adenomas showed increased CD3+, CD8+, CD4+, and FoxP3+ IHC infiltrates in comparison to non-functioning (NF) PAs [START_REF] Mei | Increased expression of programmed death ligand 1 (PD-L1) in human pituitary tumors[END_REF][START_REF] Mei | Immune profiling of pituitary tumors reveals variations in immune infiltration and checkpoint molecule expression[END_REF]. Regarding the quantity of various T cell types relative to the different histological subtypes of adenomas, studies have thus far yielded contradictory results [START_REF] Wang | The expression profile of PD-L1 and CD8+ lymphocyte in pituitary adenomas indicating for immunotherapy[END_REF][START_REF] Lu | Immune Cell Infiltrates in Pituitary Adenomas: More Macrophages in Larger Adenomas and More T Cells in Growth Hormone Adenomas[END_REF][START_REF] Mei | Immune profiling of pituitary tumors reveals variations in immune infiltration and checkpoint molecule expression[END_REF]. In terms of the genetic background, amongst GH-secreting adenomas, those AIP-mutated had more FoxP3+ cells compared to sporadic adenomas [START_REF] Barry | Tumor microenvironment defines the invasive phenotype of AIP-mutation-positive pituitary tumors[END_REF]. The potential impact of T cells on aggressiveness-related characteristics [START_REF] Sato | Analysis of Tumor Angiogenesis and Immune Microenvironment in Non-Functional Pituitary Endocrine Tumors[END_REF][START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF][START_REF] Iacovazzo | Tumour-infiltrating cytotoxic T lymphocytes in somatotroph pituitary neuroendocrine tumours[END_REF] is summarized in Table 1 [START_REF] Marques | The tumour microenvironment of pituitary neuroendocrine tumours[END_REF][START_REF] Sato | Analysis of Tumor Angiogenesis and Immune Microenvironment in Non-Functional Pituitary Endocrine Tumors[END_REF][START_REF] Lu | Immune Cell Infiltrates in Pituitary Adenomas: More Macrophages in Larger Adenomas and More T Cells in Growth Hormone Adenomas[END_REF][START_REF] Lupi | Tumor Infiltrating Lymphocytes But Not Serum Pituitary Antibodies Are Associated with Poor Clinical Outcome after Surgery in Patients with Pituitary Adenoma[END_REF][START_REF] Barry | Tumor microenvironment defines the invasive phenotype of AIP-mutation-positive pituitary tumors[END_REF][START_REF] Mei | Increased expression of programmed death ligand 1 (PD-L1) in human pituitary tumors[END_REF][START_REF] Principe | Immune Landscape of Pituitary Neuroendocrine Tumours Reveals Association between Macrophages and Gonadotroph-Tumour Invasion[END_REF][START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF]. b) Tumor-associated macrophages (TAMs)

Affected by cues coming from both tumor cells and TME cells, TAMs can acquire distinct phenotypes and have either anti-tumorigenic or pro-tumorigenic effects [START_REF] Maman | A history of exploring cancer in context[END_REF]. TAMs with an M2 phenotype are considered to be pro-tumorigenic and have been consistently associated with a negative prognosis across various cancers, while TAMs with an M1 phenotype are considered anti-tumorigenic and have been associated with a positive prognosis [START_REF] Fridman | The immune contexture in cancer prognosis and treatment[END_REF]. However, in some tumor types, the effect of TAMs on prognosis depends on their location, in the tumor stroma versus the tumor core [START_REF] Fridman | The immune contexture in cancer prognosis and treatment[END_REF].

PAs have been reported to contain more macrophages (CD68+), more M2-like macrophages (CD163+), and a CD163/HLA-DR ratio three-times higher when compared to NPG (the HLA-DR marker being indicative of M1-like TAMs) [START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF]. This is similar to what is seen in other cancers, where M2-like TAMs also predominate [START_REF] Fridman | The immune contexture in cancer prognosis and treatment[END_REF]. TAMs were also reported to be the most abundant immune cell in PAs [START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF][START_REF] Zhang | Lactate-induced M2 polarization of tumor-associated macrophages promotes the invasion of pituitary adenoma by secreting CCL17[END_REF][START_REF] Yeung | In silico analysis of the immunological landscape of pituitary adenomas[END_REF], most notably M2-like TAMs [START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF][START_REF] Yeung | In silico analysis of the immunological landscape of pituitary adenomas[END_REF]. The percentage of CD68+ TAMs showed a positive correlation with adenoma size in somatotroph, lactotroph, NFPAs [START_REF] Zhang | Lactate-induced M2 polarization of tumor-associated macrophages promotes the invasion of pituitary adenoma by secreting CCL17[END_REF], and gonadotroph adenomas [START_REF] Principe | Immune Landscape of Pituitary Neuroendocrine Tumours Reveals Association between Macrophages and Gonadotroph-Tumour Invasion[END_REF]. In terms of TAM infiltration relative to the different histological subtypes of adenomas, studies have thus far yielded contradictory results [START_REF] Lu | Immune Cell Infiltrates in Pituitary Adenomas: More Macrophages in Larger Adenomas and More T Cells in Growth Hormone Adenomas[END_REF][START_REF] Principe | Immune Landscape of Pituitary Neuroendocrine Tumours Reveals Association between Macrophages and Gonadotroph-Tumour Invasion[END_REF][START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF][START_REF] Mei | Immune profiling of pituitary tumors reveals variations in immune infiltration and checkpoint molecule expression[END_REF][START_REF] Zhang | Lactate-induced M2 polarization of tumor-associated macrophages promotes the invasion of pituitary adenoma by secreting CCL17[END_REF][START_REF] Yeung | In silico analysis of the immunological landscape of pituitary adenomas[END_REF]. Concerning the genetic background, amongst GH-secreting adenomas, those AIP-mutated had more CD68+ cells compared to sporadic adenomas [START_REF] Barry | Tumor microenvironment defines the invasive phenotype of AIP-mutation-positive pituitary tumors[END_REF].

The potential impact of TAMs on aggressiveness-related characteristics [START_REF] Sato | Analysis of Tumor Angiogenesis and Immune Microenvironment in Non-Functional Pituitary Endocrine Tumors[END_REF][START_REF] Lu | Immune Cell Infiltrates in Pituitary Adenomas: More Macrophages in Larger Adenomas and More T Cells in Growth Hormone Adenomas[END_REF][START_REF] Lupi | Tumor Infiltrating Lymphocytes But Not Serum Pituitary Antibodies Are Associated with Poor Clinical Outcome after Surgery in Patients with Pituitary Adenoma[END_REF][START_REF] Barry | Tumor microenvironment defines the invasive phenotype of AIP-mutation-positive pituitary tumors[END_REF][START_REF] Mei | Increased expression of programmed death ligand 1 (PD-L1) in human pituitary tumors[END_REF][START_REF] Principe | Immune Landscape of Pituitary Neuroendocrine Tumours Reveals Association between Macrophages and Gonadotroph-Tumour Invasion[END_REF][START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF][START_REF] Mei | Immune profiling of pituitary tumors reveals variations in immune infiltration and checkpoint molecule expression[END_REF][START_REF] Zhang | Lactate-induced M2 polarization of tumor-associated macrophages promotes the invasion of pituitary adenoma by secreting CCL17[END_REF][START_REF] Yagnik | Stratifying nonfunctional pituitary adenomas into two groups distinguished by macrophage subtypes[END_REF] is summarized in Table 1. Taking into account both TILs and TAMs, it appears that aggressiveness is associated with an immunosuppressive TME. From a mechanistic point of view, bidirectional interactions between tumor cells and TAMs take place, with tumor cells recruiting and polarizing TAMs preferentially towards an M2-like phenotype, while M2-like TAMs promote PA aggressiveness, and most notably PA invasiveness [START_REF] Barry | Tumor microenvironment defines the invasive phenotype of AIP-mutation-positive pituitary tumors[END_REF][START_REF] Principe | Immune Landscape of Pituitary Neuroendocrine Tumours Reveals Association between Macrophages and Gonadotroph-Tumour Invasion[END_REF][START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF][START_REF] Zhang | Lactate-induced M2 polarization of tumor-associated macrophages promotes the invasion of pituitary adenoma by secreting CCL17[END_REF][START_REF] Yagnik | Stratifying nonfunctional pituitary adenomas into two groups distinguished by macrophage subtypes[END_REF]. These findings are consistent with the reports of M2-like TAMs being implicated in tumor growth and development of an invasive phenotype in other types of cancer [START_REF] Fridman | The immune contexture in cancer prognosis and treatment[END_REF]. Moreover, bidirectional interactions take place between TAMs and other components of the TME, especially between M2-like TAMs and angiogenesis. For example, in several other cancers it has been shown that hypoxia leads to macrophage recruitment, which in turn facilitates angiogenesis [START_REF] Condeelis | Macrophages: Obligate Partners for Tumor Cell Migration, Invasion, and Metastasis[END_REF]. Figure 2 summarizes the roles and interactions of TAMs in PAs [START_REF] Barry | Tumor microenvironment defines the invasive phenotype of AIP-mutation-positive pituitary tumors[END_REF][START_REF] Principe | Immune Landscape of Pituitary Neuroendocrine Tumours Reveals Association between Macrophages and Gonadotroph-Tumour Invasion[END_REF][START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF][START_REF] Mei | Immune profiling of pituitary tumors reveals variations in immune infiltration and checkpoint molecule expression[END_REF][START_REF] Iacovazzo | Tumour-infiltrating cytotoxic T lymphocytes in somatotroph pituitary neuroendocrine tumours[END_REF][START_REF] Zhang | Lactate-induced M2 polarization of tumor-associated macrophages promotes the invasion of pituitary adenoma by secreting CCL17[END_REF][START_REF] Yagnik | Stratifying nonfunctional pituitary adenomas into two groups distinguished by macrophage subtypes[END_REF][START_REF] Fujiwara | Identification of M2 macrophages in anterior pituitary glands of normal rats and rats with estrogen-induced prolactinoma[END_REF].

c) Other immune cells

There is limited published data concerning other immune cells in PAs. PAs have been reported to contain fewer neutrophils than NPG [START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF]. Some studies have reported B cells to be only seen in exceptional cases [START_REF] Rossi | Mononuclear Cell Infiltrate and Hla-Dr Expression in 28 Pituitary Adenomas[END_REF][START_REF] Heshmati | Prevalence of Lymphocytic Infiltrate in 1400 Pituitary Adenomas[END_REF][START_REF] Lu | Immune Cell Infiltrates in Pituitary Adenomas: More Macrophages in Larger Adenomas and More T Cells in Growth Hormone Adenomas[END_REF], while other studies did identify B cells in PAs, but they were fewer compared to TAMs and T cells [START_REF] Principe | Immune Landscape of Pituitary Neuroendocrine Tumours Reveals Association between Macrophages and Gonadotroph-Tumour Invasion[END_REF][START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF][START_REF] Yeung | In silico analysis of the immunological landscape of pituitary adenomas[END_REF]. Somatotroph adenomas have been reported to have more B cells compared to NFPAs [START_REF] Zhou | Comprehensive analysis of the immunological landscape of pituitary adenomas: implications of immunotherapy for pituitary adenomas[END_REF], while NFPAs contained more neutrophils than somatotroph adenomas [START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF].

B. Therapy a) Immune-checkpoint inhibitors

The immune-checkpoint inhibitors that have been used to date in aggressive PAs and PCs include: ipilimumab combined with nivolumab, used in six cases, and pembrolizumab, which was used in five cases [START_REF] Lin | Marked Response of a Hypermutated ACTH-Secreting Pituitary Carcinoma to Ipilimumab and Nivolumab[END_REF][START_REF] Lin | Synergism of Checkpoint Inhibitors and Peptide Receptor Radionuclide Therapy in the Treatment of Pituitary Carcinoma[END_REF][START_REF] Duhamel | Immunotherapy in Corticotroph and Lactotroph Aggressive Tumors and Carcinomas: Two Case Reports and a Review of the Literature[END_REF][START_REF] Sol | Immune Checkpoint Inhibitor Therapy for ACTH-Secreting Pituitary Carcinoma: a new emerging treatment?[END_REF][START_REF] Caccese | Rapid disease progression in patient with mismatchrepair deficiency pituitary ACTH-secreting adenoma treated with checkpoint inhibitor pembrolizumab[END_REF][START_REF] Lamb | Case Report: A Case of Pituitary Carcinoma Treated With Sequential Dual Immunotherapy and Vascular Endothelial Growth Factor Inhibition Therapy[END_REF][START_REF] Goichot | Should pituitary carcinoma be treated using a NET-like approach? A case of complete remission of a metastatic malignant prolactinoma with multimodal therapy including immunotherapy[END_REF][START_REF] Majd | Efficacy of pembrolizumab in patients with pituitary carcinoma: report of four cases from a phase II study[END_REF]. The mechanisms of action of these drugs are illustrated in Figure 3A. Their use in aggressive PAs and PCs has been extensively reviewed recently [START_REF] Ilie | Immunotherapy in aggressive pituitary tumors and carcinomas: a systematic review[END_REF].

Six corticotroph carcinomas and one aggressive corticotroph adenoma have been treated with immunecheckpoint inhibitors. In terms of the radiological response, four of the carcinomas showed a partial response that was maintained for 6 to 42 months (duration not available in one case), two of the carcinomas showed stable disease that was maintained for at least 12 months in one of the cases (data not available in the second), while the aggressive adenoma showed progressive disease (57-61,64,65) (Figure 4). In two of the cases that initially showed a partial response, a dissociated radiological response was later noted, and in both cases, continuation of immune-checkpoint inhibitors in combination with local treatment (radiotherapy, surgery, and radiofrequency ablation, respectively) proved to be a good therapeutic option [START_REF] Ilie | Immunotherapy in aggressive pituitary tumors and carcinomas: a systematic review[END_REF].

Three lactotroph carcinomas and one aggressive lactotroph adenoma have been treated with immunecheckpoint inhibitors. Regarding the radiological response, one carcinoma showed a complete response maintained for at least 13 months, one showed a partial response maintained for 8 months, the third showed progressive disease, while the aggressive adenoma also showed progressive disease (59,62-64) (Figure 4).

Of note, the carcinoma that progressed was initially treated with pembrolizumab, and was subsequently treated with programmed cell death protein 1 (PD-1)/programmed death-ligand 1 (PD-L1) pathway inhibitors, and showed continued progression [START_REF] Majd | Efficacy of pembrolizumab in patients with pituitary carcinoma: report of four cases from a phase II study[END_REF].

Regarding potential predictive factors of response, data is too scarce to allow firm conclusions. Currently, the most promising predictive factor appears to be a high tumor mutational burden. Negative PD-L1 immunohistochemical staining should not preclude the administration of immune-checkpoint inhibitors, since even negative cases responded well. Conversely, the presence of a mismatch repair deficiency did not guarantee a good response [START_REF] Ilie | Immunotherapy in aggressive pituitary tumors and carcinomas: a systematic review[END_REF]. Moreover, for corticotroph tumors, it appears important to achieve eucortisolism, since glucocorticoids have an immunosuppressive effect that could lessen the efficacy of treatment [START_REF] Ilie | Immunotherapy in aggressive pituitary tumors and carcinomas: a systematic review[END_REF]. Currently, too little data is available to reach a conclusion on the eventual superiority of combined immunotherapy over monotherapy [START_REF] Ilie | Immunotherapy in aggressive pituitary tumors and carcinomas: a systematic review[END_REF].

Concerning the tolerance of immune-checkpoint inhibitors, patients cumulatively experienced fatigue, diarrhea, nausea, vomiting, anorexia, fever, transaminitis, autoimmune hepatitis, autoimmune nephritis, rash, myalgia, and possible hypophysitis and progressive weight loss [START_REF] Lin | Marked Response of a Hypermutated ACTH-Secreting Pituitary Carcinoma to Ipilimumab and Nivolumab[END_REF][START_REF] Lin | Synergism of Checkpoint Inhibitors and Peptide Receptor Radionuclide Therapy in the Treatment of Pituitary Carcinoma[END_REF][START_REF] Duhamel | Immunotherapy in Corticotroph and Lactotroph Aggressive Tumors and Carcinomas: Two Case Reports and a Review of the Literature[END_REF][START_REF] Sol | Immune Checkpoint Inhibitor Therapy for ACTH-Secreting Pituitary Carcinoma: a new emerging treatment?[END_REF][START_REF] Caccese | Rapid disease progression in patient with mismatchrepair deficiency pituitary ACTH-secreting adenoma treated with checkpoint inhibitor pembrolizumab[END_REF][START_REF] Lamb | Case Report: A Case of Pituitary Carcinoma Treated With Sequential Dual Immunotherapy and Vascular Endothelial Growth Factor Inhibition Therapy[END_REF][START_REF] Goichot | Should pituitary carcinoma be treated using a NET-like approach? A case of complete remission of a metastatic malignant prolactinoma with multimodal therapy including immunotherapy[END_REF][START_REF] Majd | Efficacy of pembrolizumab in patients with pituitary carcinoma: report of four cases from a phase II study[END_REF]. As expected, monotherapy was better tolerated than combined treatment. Nevertheless, these adverse events were mostly mild, and led to interruption of dual immunotherapy in only two cases: in one in which progressive disease was simultaneously noted [START_REF] Duhamel | Immunotherapy in Corticotroph and Lactotroph Aggressive Tumors and Carcinomas: Two Case Reports and a Review of the Literature[END_REF], and in a second case, where treatment was continued with nivolumab alone [START_REF] Lamb | Case Report: A Case of Pituitary Carcinoma Treated With Sequential Dual Immunotherapy and Vascular Endothelial Growth Factor Inhibition Therapy[END_REF].

b) Perspectives

Potential leads for increasing the efficacy of immune-checkpoint inhibitors include a better patient selection, as well as combining immune-checkpoint inhibitors with angiogenesis-targeting drugs [START_REF] Sato | Analysis of Tumor Angiogenesis and Immune Microenvironment in Non-Functional Pituitary Endocrine Tumors[END_REF][START_REF] Rahma | The Intersection between Tumor Angiogenesis and Immune Suppression[END_REF][START_REF] Ramjiawan | Anti-angiogenesis for cancer revisited: Is there a role for combinations with immunotherapy?[END_REF], with radiotherapy [START_REF] Wilky | Immune checkpoint inhibitors: The linchpins of modern immunotherapy[END_REF][START_REF] Deng | Irradiation and anti-PD-L1 treatment synergistically promote antitumor immunity in mice[END_REF], or with peptide receptor radionuclide therapy [START_REF] Lin | Synergism of Checkpoint Inhibitors and Peptide Receptor Radionuclide Therapy in the Treatment of Pituitary Carcinoma[END_REF].

At the same time, given both the presence and the important role TAMs appear to play in PAs, targeting TAMs may prove to be a good option for PAs and PCs. This might be even more true for gonadotroph tumors, which are, at least in theory, less amenable to immune-checkpoint inhibitors than other types of PA [START_REF] Ilie | Treatment options for gonadotroph tumors: current state and perspectives[END_REF][START_REF] Wang | The Immune Profile of Pituitary Adenomas and a Novel Immune Classification for Predicting Immunotherapy Responsiveness[END_REF]. There are numerous TAM-targeting agents and TAM-targeting strategies, including preventing TAM recruitment by using, for example, colony stimulating factor 1 (CSF1)-CSF1 receptor inhibitors, C-C chemokine receptor (CCR)5-C-C motif chemokine ligand (CCL)5 inhibitors etc.; depleting TAMs by using CSF1-CSF1 receptor inhibitors, triggering receptor expressed on myeloid cells (TREM) inhibitors etc.; reprogramming TAMs by using CD40 agonists, TREM inhibitors etc.; exploiting the antitumor functions of TAMs by using tyrosine protein phosphatase non-receptor type substrate 1 (SIRPα)-CD47 inhibitors or sialic acid-binding immunoglobulin-like lectin (SIGLEC)10-CD24 inhibitors; and infusing macrophages that are engineered to eliminate tumor cells and/or reprogram the TME (72).

Folliculostellate cells

Apart from immune cells, the TME of PAs includes a number of additional cells, including folliculostellate cells and tumor-associated fibroblasts. Folliculostellate cells are non-endocrine cells that are found in the NPG, where they account for ~5% of the cells of the anterior lobe [START_REF] Hofler | Immunohistochemistry of folliculo-stellate cells in normal human adenohypophyses and in pituitary adenomas[END_REF][START_REF] Allaerts | History and perspectives of pituitary folliculo-stellate cell research[END_REF]. These cells are recognized by their morphology and by immunopositivity for S100B protein [START_REF] Nakajima | S100 protein in folliculostellate cells of the rat pituitary anterior lobe[END_REF][START_REF] Morris | Folliculo-stellate Cells: Paracrine Communicators in the Anterior Pituitary[END_REF]. Through both paracrine [START_REF] Morris | Folliculo-stellate Cells: Paracrine Communicators in the Anterior Pituitary[END_REF][START_REF] Denef | Paracrinicity: the story of thirty years of cellular pituitary crosstalk[END_REF] and physical actions [START_REF] Fauquier | Folliculostellate cell network: A route for long-distance communication in the anterior pituitary[END_REF][START_REF] Hodson | Roles of connexins and pannexins in (neuro)endocrine physiology[END_REF], folliculostellate cells exert numerous roles in the NPG, including a supportive role, phagocytic properties, regulation of hormone secretion, and the production of growth factors and cytokines (vascular endothelial growth factor (VEGF), interleukin 6, basic fibroblast growth factor, follistatin, transforming growth factor β etc.) [START_REF] Allaerts | History and perspectives of pituitary folliculo-stellate cell research[END_REF][START_REF] Denef | Paracrinicity: the story of thirty years of cellular pituitary crosstalk[END_REF][START_REF] Devnath | An Insight to Pituitary Folliculo-Stellate Cells[END_REF][START_REF] Claudius | Phagocytotic removal of apoptotic endocrine cells by folliculostellate cells and its functional implications in clusterin accumulation in pituitary colloids in helmeted guinea fowl (Numida meleagris)[END_REF]. A role as a stem/progenitor cell has also been often discussed, however it is still debated whether the S100B/SOX2 positive cells, considered to be the stem/progenitor cells, are a subset of folliculostellate cells or an entirely different population that happens to also be positive for S100B protein [START_REF] Allaerts | History and perspectives of pituitary folliculo-stellate cell research[END_REF][START_REF] Kato | New insights into the role and origin of pituitary S100β-positive cells[END_REF].

PAs have been consistently shown to contain fewer folliculostellate cells than the NPG [START_REF] Ilie | Intratumoural spatial distribution of S100B + folliculostellate cells is associated with proliferation and expression of FSH and ERα in gonadotroph tumours[END_REF][START_REF] Hofler | Immunohistochemistry of folliculo-stellate cells in normal human adenohypophyses and in pituitary adenomas[END_REF][START_REF] Iwaki | Proliferating potential of folliculo-stellate cells in human pituitary adenomas: Immunohistochemical and electron microscopic analysis[END_REF].

However, heterogeneity between tumors exists, and although the vast majority of tumors had very low percentages of S100B+ cells, other tumors were rich in S100B+ cells [START_REF] Ilie | Intratumoural spatial distribution of S100B + folliculostellate cells is associated with proliferation and expression of FSH and ERα in gonadotroph tumours[END_REF]. Concerning their potential roles in PAs, consistent with their role in the NPG, folliculostellate cells appear to potentially modulate hormone production/secretion: in acromegaly patients, relationships were shown between S100B+ cells and both growth hormone and prolactin levels [START_REF] Voit | Folliculo-stellate Cells in Pituitary Adenomas of Patients with Acromegaly[END_REF], while in gonadotroph tumors a positive correlation between S100B staining and FSH staining was identified [START_REF] Ilie | Intratumoural spatial distribution of S100B + folliculostellate cells is associated with proliferation and expression of FSH and ERα in gonadotroph tumours[END_REF]. A role of folliculostellate cells in maintaining a more functional, differentiated state, thus closer to the normal state of gonadotroph tumor cells has also been proposed [START_REF] Ilie | Intratumoural spatial distribution of S100B + folliculostellate cells is associated with proliferation and expression of FSH and ERα in gonadotroph tumours[END_REF]. Another proposed role for folliculostellate cells in PAs, consistent with a similar role proposed for a subset of folliculostellate cells in the NPG [START_REF] Allaerts | History and perspectives of pituitary folliculo-stellate cell research[END_REF][START_REF] Allaerts | Immunohistochemical, Morphological and Ultrastructural Resemblance between Dendritic Cells and Folliculo-Stellate Cells in Normal Human and Rat Anterior Pituitaries[END_REF], is an antigen presentation function, this proposition being based on the spatial proximity of immune cells and folliculostellate cells co-expressing the S100 protein and MHC class II antigens that was observed in three PAs [START_REF] Vajtai | Folliculo-stellate cells of "true dendritic" type are involved in the inflammatory microenvironment of tumor immunosurveillance of pituitary adenomas[END_REF]. The potential impact of folliculostellate cells on aggressiveness-related characteristics [START_REF] Ilie | Intratumoural spatial distribution of S100B + folliculostellate cells is associated with proliferation and expression of FSH and ERα in gonadotroph tumours[END_REF] is summarized in Table 1. Therefore, it appears that folliculostellate cells might play important roles in tumorigenesis-related processes in PAs, but these roles need to be further studied. Hopefully, ways in which these cells could be therapeutically targeted/modulated will be developed in the future.

Tumor-associated fibroblasts

Tumor-associated fibroblasts are phenotypically and functionally heterogeneous cells, that are seen as a key TME component across various cancers [START_REF] Ziani | Alteration of the Antitumor Immune Response by Cancer-Associated Fibroblasts[END_REF][START_REF] Kalluri | The biology and function of fibroblasts in cancer[END_REF]. Tumor-associated fibroblasts have been mostly associated with tumor progression, but they can also exhibit cancer-restraining functions [START_REF] Kalluri | The biology and function of fibroblasts in cancer[END_REF][START_REF] Lebleu | A peek into cancer-associated fibroblasts: origins, functions and translational impact[END_REF]. Through the secretion of cytokines, chemokines and growth factors, as well as extracellular matrix components and remodeling enzymes, tumor-associated fibroblasts have been shown to be implicated in tumor growth, ECM remodeling, angiogenesis, tumor invasion, metastasis, immune and metabolic reprogramming of the TME, as well as in chemoresistance [START_REF] Balkwill | The tumor microenvironment at a glance[END_REF][START_REF] Ziani | Alteration of the Antitumor Immune Response by Cancer-Associated Fibroblasts[END_REF][START_REF] Kalluri | The biology and function of fibroblasts in cancer[END_REF][START_REF] Lebleu | A peek into cancer-associated fibroblasts: origins, functions and translational impact[END_REF].

Tumor-associated fibroblasts have also been identified in PAs [START_REF] Marques | Pituitary tumour fibroblast-derived cytokines influence tumour aggressiveness[END_REF], and although the literature is, so far, scarce, promising biological and therapeutic implications can be foreseen. Cultured tumor-associated fibroblasts, derived from PAs with cavernous sinus invasion, expressed higher levels of VEGF and interleukin 6 compared to those derived from PAs without cavernous sinus invasion [START_REF] Lv | Invasive Pituitary Adenoma-Derived Tumor-Associated Fibroblasts Promote Tumor Progression both In Vitro and In Vivo[END_REF][START_REF] Marques | Pituitary tumour fibroblast-derived cytokines influence tumour aggressiveness[END_REF]. Moreover, coinjecting GH3 cells with tumor-associated fibroblasts derived from PAs with cavernous sinus invasion resulted in xenografts with higher VEGF expression (expressed mainly by tumor cells) compared to coinjecting GH3 cells with tumor-associated fibroblasts derived from PAs without cavernous sinus invasion [START_REF] Lv | Invasive Pituitary Adenoma-Derived Tumor-Associated Fibroblasts Promote Tumor Progression both In Vitro and In Vivo[END_REF]. In addition, cultured tumor-associated fibroblasts derived from PAs secreted CCL2 -a molecule with an angiogenic function, whose levels were strongly positively correlated with the microvessel area of PAs [START_REF] Marques | Pituitary tumour fibroblast-derived cytokines influence tumour aggressiveness[END_REF]. The potential impact of tumor-associated fibroblasts on aggressiveness-related characteristics [START_REF] Lv | Invasive Pituitary Adenoma-Derived Tumor-Associated Fibroblasts Promote Tumor Progression both In Vitro and In Vivo[END_REF][START_REF] Marques | Pituitary tumour fibroblast-derived cytokines influence tumour aggressiveness[END_REF] is summarized in Table 1. These findings point towards a potential role of tumor-associated fibroblasts in angiogenesis, tumor growth and tumor invasion, consistent with the roles observed for these cells in other cancers.

From a therapeutic perspective, the somatostatin (SST) type1 receptor was shown to be the predominant SST receptor expressed in tumor-associated fibroblasts from PAs, shown at the mRNA level, and pasireotide was able to decrease the release of interleukin 6 and CCL2 from these cells [START_REF] Marques | Pituitary tumour fibroblast-derived cytokines influence tumour aggressiveness[END_REF]. This suggests that pasireotide may exert its role by acting on both pituitary tumor cells and tumor-associated fibroblasts.

In pancreatic cancers, pasireotide was also shown to inhibit protein synthesis in tumor-associated fibroblasts, and in combination with gemcitabine it reduced the chemoresistance triggered by the tumorassociated fibroblast-derived secretome, as well as reducing tumor growth [START_REF] Duluc | Pharmacological targeting of the protein synthesis MTOR /4E-BP 1 pathway in cancer-associated fibroblasts abrogates pancreatic tumour chemoresistance[END_REF]. Lastly, numerous other therapeutic strategies are emerging for targeting of tumor-associated fibroblasts, ranging from cell depletion (via targeting of cell surface markers), to altering their activation and/or their function, to tumor-associated fibroblasts normalization [START_REF] Chen | Turning foes to friends: targeting cancer-associated fibroblasts[END_REF].

Angiogenesis

A. Biology

Angiogenesis, i.e. the outgrowth of new blood vessels from pre-existing vessels, is a complex process that involves numerous signaling pathways and molecules [START_REF] Donnem | Non-angiogenic tumours and their influence on cancer biology[END_REF][START_REF] Viallard | Tumor angiogenesis and vascular normalization: alternative therapeutic targets[END_REF]. Of these, the VEGF/VEGF-receptor (VEGFR) pathway has remained, thus far, the most studied and most targeted pathway [START_REF] Ramjiawan | Anti-angiogenesis for cancer revisited: Is there a role for combinations with immunotherapy?[END_REF][START_REF] Ferrara | Vascular Endothelial Growth Factor: Basic Science and Clinical Progress[END_REF], including in PAs. These newly formed blood vessels are immature, disorganized, and with impaired functionality, leading to poor tumor perfusion, hypoxia, and decreased immune cell infiltration and activity. These characteristics further facilitate the acquisition of an aggressive phenotype by tumor cells, reduce the antitumoral immune response, but also decrease the beneficial effects of both chemotherapy and radiotherapy [START_REF] Maman | A history of exploring cancer in context[END_REF][START_REF] Viallard | Tumor angiogenesis and vascular normalization: alternative therapeutic targets[END_REF]. Therefore, a strategy of vascular normalization, which aims to restore the normal perfusion and oxygenation of the tumor, has emerged in order to mitigate the aforementioned negative effects of angiogenesis [START_REF] Viallard | Tumor angiogenesis and vascular normalization: alternative therapeutic targets[END_REF]. It is noteworthy that while angiogenesis plays pivotal roles in tumorigenesis-related processes [START_REF] Maman | A history of exploring cancer in context[END_REF][START_REF] Folkman | Tumor Angiogenesis: Therapeutic Implications[END_REF], a growing body of literature demonstrates that numerous human tumors in fact lack angiogenesis, suggesting that their blood supply is acquired either by vascular co-option or by vasculogenic mimicry [START_REF] Donnem | Non-angiogenic tumours and their influence on cancer biology[END_REF]. These either completely non-angiogenic tumors or partly angiogenic/partly non-angiogenic tumors, display biological differences compared to angiogenic tumors, which has important therapeutic implications [START_REF] Donnem | Non-angiogenic tumours and their influence on cancer biology[END_REF]. A better characterization of the blood supply of PAs is therefore needed.

The vascularization of PAs (the microvessel density and area, but also the number and percentage of endothelial cells) was found to be lower compared to that of the NPG (49,96-99), and higher in PCs compared to PAs [START_REF] Jugenburg | Vasculature in nontumorous hypophyses, pituitary adenomas, and carcinomas: A quantitative morphologic study[END_REF][START_REF] Vidal | Microvessel density in pituitary adenomas and carcinomas[END_REF], suggesting a potential role of angiogenesis during tumor progression and malignant transformation of PAs. The exception to this is invasive macroprolactinomas, which have been reported to have vascular densities similar to those of the NPG [START_REF] Turner | Angiogenesis in pituitary adenomasrelationship to endocrine function, treatment and outcome[END_REF]. VEGF expression, on the other hand, was reported to be either lower in PAs compared to the NPG (100,101), or at similar levels [START_REF] Viacava | Microvascular density and vascular endothelial growth factor expression in normal pituitary tissue and pituitary adenomas[END_REF]. Regarding vascular densities and the expression of angiogenesis-related molecules relative to the different histological subtypes of adenomas, studies have so far yielded contradictory results (49,50,96-98,100,102,103). The potential impact of angiogenesis and of angiogenesis-related molecules on aggressiveness-related characteristics [START_REF] Sato | Analysis of Tumor Angiogenesis and Immune Microenvironment in Non-Functional Pituitary Endocrine Tumors[END_REF][START_REF] Iuchi | Proliferation, Vascular Endothelial Growth Factor Expression and Cavernous Sinus Invasion in Growth Hormone Secreting Pituitary Adenomas[END_REF][START_REF] Karabid | Angpt2/Tie2 autostimulatory loop controls tumorigenesis[END_REF][START_REF] Turner | Angiogenesis in pituitary adenomasrelationship to endocrine function, treatment and outcome[END_REF][START_REF] Cai | Dopamine agonist resistance-related endocan promotes angiogenesis and cells viability of prolactinomas[END_REF][START_REF] He | Relationship between RSUME and HIF-1α/VEGF-A with invasion of pituitary adenoma[END_REF][START_REF] Sánchez-Ortiga | Over-expression of vascular endothelial growth factor in pituitary adenomas is associated with extrasellar growth and recurrence[END_REF][START_REF] Wang | Endothelial cell-specific molecule-1 as an invasiveness marker for pituitary null cell adenoma[END_REF][START_REF] Matano | Endocan, a new invasion and angiogenesis marker of pituitary adenomas[END_REF][START_REF] Miao | A comparative analysis of ESM-1 and vascular endothelial cell marker (CD34/CD105) expression on pituitary adenoma invasion[END_REF][START_REF] Jia | Vascular endothelial growth inhibitor (VEGI) is an independent indicator for invasion in human pituitary adenomas[END_REF][START_REF] Cornelius | Endothelial Expression of Endocan Is Strongly Associated with Tumor Progression in Pituitary Adenoma: Endocan in Pituitary Adenoma[END_REF][START_REF] Jugenburg | Vasculature in nontumorous hypophyses, pituitary adenomas, and carcinomas: A quantitative morphologic study[END_REF][START_REF] Vidal | Microvessel density in pituitary adenomas and carcinomas[END_REF][START_REF] Gruppetta | Expression of cell cycle regulators and biomarkers of proliferation and regrowth in human pituitary adenomas[END_REF] is summarized in Table 1.

B. Therapy a) Anti-VEGF-A and anti-VEGFRs therapies

The anti-angiogenic therapies used to date in aggressive PAs and PCs include: bevacizumab, an anti-VEGF-A monoclonal antibody, which has been used in 21 cases; sunitinib, a tyrosine kinase inhibitor that targets multiple tyrosine kinases, including VEGFRs, and which was used in two cases; and apatinib, a tyrosine kinase inhibitor that is primarily a VEGFR2 inhibitor, and which was used in one case [START_REF] Ilie | The Microenvironment of Pituitary Tumors-Biological and Therapeutic Implications[END_REF][START_REF] Majd | Efficacy of pembrolizumab in patients with pituitary carcinoma: report of four cases from a phase II study[END_REF](104)(105)(106)(107). The mechanisms of action of these drugs are illustrated in Figure 3B.

The 15 patients who received monotherapy with one of these molecules had all previously received at least one course of temozolomide, while for the nine patients receiving concomitant temozolomide, this included both first-course and second-course temozolomide (3,64,104-107). Given the already proven response to temozolomide, the response to combination treatments does not give a clear illustration of the potential efficacy of bevacizumab, therefore in Figure 4 we present only the radiological response to monotherapy.

Bevacizumab

Five corticotroph carcinomas and three aggressive corticotroph adenomas received bevacizumab alone (six cases) or combined with temozolomide (two cases) [START_REF] Ilie | The Microenvironment of Pituitary Tumors-Biological and Therapeutic Implications[END_REF]104,106,108). Of the six cases treated with bevacizumab alone, the radiological response was reported in 4 cases, with two showing stable disease [START_REF] Ilie | The Microenvironment of Pituitary Tumors-Biological and Therapeutic Implications[END_REF]104,106) maintained for at least 26 months in one case (109), and for an unknown duration in the second (110), one showed progressive disease (108) (Figure 4), while the fourth patient died shortly after an MRI performed following 2 cycles of bevacizumab showed radiological stable disease (106). Regarding the cases receiving concomitant temozolomide, one corticotroph carcinoma received bevacizumab, temozolomide, and radiotherapy, and demonstrated radiological complete response, while one corticotroph carcinoma received bevacizumab and temozolomide, and demonstrated radiological stable disease (104).

Following ICI failure, one lactotroph carcinoma and one aggressive lactotroph adenoma received bevacizumab alone and showed stable disease. Stable disease was maintained for at least 2 months in one case (59) (Figure 4), while in the second case stable disease was demonstrated 6 months after the administration of three cycles of bevacizumab (62) (Figure 4). A third case of a lactotroph carcinoma, progressed after ICI failure on combined therapy with bevacizumab, temsirolimus, and valproic acid [START_REF] Majd | Efficacy of pembrolizumab in patients with pituitary carcinoma: report of four cases from a phase II study[END_REF].

One aggressive somatotroph adenoma received concomitant bevacizumab and temozolomide, and showed partial response (111).

One aggressive non-immunoreactive adenoma was treated with bevacizumab monotherapy, and showed stable disease, which was maintained for 18 months (106) (Figure 4).

Four tumors of unknown subtype were treated with bevacizumab alone and showed partial response in one case, stable disease in one case, and progressive disease in one case (3) (Figure 4). The duration of maintained partial response, and stable disease, respectively, were not reported. The radiological outcome is unknown in the fourth case ( 112). An additional four tumors of unknown subtype were treated with combined bevacizumab and temozolomide. The radiological responses consisted of a partial response in two cases, progressive disease in one case, and unknown radiological response in the fourth case [START_REF] Ilie | The Microenvironment of Pituitary Tumors-Biological and Therapeutic Implications[END_REF].

The potential benefit of adding bevacizumab to first-course temozolomide is hard to evaluate at this time because of the generally good efficacy of first-course temozolomide, combined with the small number of cases that have been published with combination therapy. However, regarding the combination of bevacizumab with second-course temozolomide, in the European Society for Endocrinology survey, out of 18 patients who received second-course temozolomide, only two patients showed partial response, of whom one received concomitant bevacizumab (113). Therefore, if second-course temozolomide is envisioned, given the generally poor response that has been reported, addition of bevacizumab might be considered.

Reported adverse events consisted of epistaxis and hypertension in one case [START_REF] Duhamel | Immunotherapy in Corticotroph and Lactotroph Aggressive Tumors and Carcinomas: Two Case Reports and a Review of the Literature[END_REF], nephritis in another case [START_REF] Lamb | Case Report: A Case of Pituitary Carcinoma Treated With Sequential Dual Immunotherapy and Vascular Endothelial Growth Factor Inhibition Therapy[END_REF], and petechia and fatigue in a third case (106).

Tyrosine kinase inhibitors

Two tumors, one corticotroph carcinoma and a tumor of unknown type, were treated with sunitinib monotherapy and showed progression (3,108) (Figure 4). Any eventual adverse events were not reported.

An aggressive somatotroph adenoma treated concomitantly with apatinib and temozolomide showed radiological partial response. Adverse events included hypertension, and hand and foot syndrome (107).

b) Perspectives

While the VEGF/VEGFR pathway has been thus far the most targeted pathway in cancer, tumors can be inherently resistant or can become resistant to inhibition of the VEGF/VEGFR axis [START_REF] Ramjiawan | Anti-angiogenesis for cancer revisited: Is there a role for combinations with immunotherapy?[END_REF], and thus additional therapeutic strategies are needed, for example vascular normalization [START_REF] Viallard | Tumor angiogenesis and vascular normalization: alternative therapeutic targets[END_REF]. Strategies to achieve vascular normalization include the use of agonists of dopamine receptor type 2, which have been found to have an effect on both pericytes and endothelial cells [START_REF] Viallard | Tumor angiogenesis and vascular normalization: alternative therapeutic targets[END_REF]114,115). Interestingly, in a mouse prolactinoma model, bromocriptine not only blocked tumor growth, but also restored the balance between anti-angiogenic and pro-angiogenic factors, and normalized blood vessels (116). Of note, in the same prolactinoma model, axitinib (a TKI inhibiting VEGFRs) restrained tumor growth and improved vascular remodeling, while when bromocriptine was combined with axitinib, intratumoral hemorrhage was suppressed and blood vessel perfusion was restored (116). This is consistent with the complementary effect that VEGF/VEGFR pathway inhibitors and drugs targeting alternative angiogenesis pathways were shown to have, and highlight the role that combination therapies might have when targeting angiogenesis (116-118).

Interestingly, the angiopoietin-2/angiopoietin-1 receptor axis, classically regarded as an endothelial cell axis, was recently also shown to be active in pituitary tumor cells. Both in vitro and in vivo evidence indicated that this axis was an exploitable therapeutic target in PAs, most notably in NFPAs, and therefore the use of anti-angiopoietin biologicals or angiopoietin-1 receptor inhibitors might be warranted in these tumors [START_REF] Karabid | Angpt2/Tie2 autostimulatory loop controls tumorigenesis[END_REF].

Extracellular matrix and its remodeling

The ECM consists of a dynamic 3D network of macromolecules (proteins, proteoglycans, glycosaminoglycans etc.), in which soluble factors (cytokines, growth factors etc.) are embedded [START_REF] Balkwill | The tumor microenvironment at a glance[END_REF](119)(120)(121). The ECM is implicated in the differentiation, adhesion, migration, proliferation, and survival of cells in both physiological and pathological conditions (121-123). In cancer, the ECM might also influence treatment efficacy, for example, ECM attachment to cancer cells might lead to resistance to apoptosis, a desmoplastic stroma might represent a physical barrier for chemotherapy, while soluble factors might activate survival signaling pathways resulting in resistance to cell death [START_REF] Maman | A history of exploring cancer in context[END_REF].

Regarding the presence and distribution of ECM macromolecules and of integrins (cell membrane receptors that transduce ECM signals to cells), differences have been shown to exist between PAs and the NPG [START_REF] Kuchenbauer | Laminin inhibits lactotroph proliferation and is reduced in early prolactinoma development[END_REF]124,125). For example, vitronectin was found in PA TME, but not in the NPG, while tumor cells showed a greater range of expression of integrin subunits, simultaneously with the downregulation of α3β1 expression and the loss of α6β4 expression compared with the NPG (125). From a functional viewpoint, laminin expression was found to gradually decrease from the NPG stage to the lactotroph hyperplasia stage and then to the prolactinoma stage, and, in addition, laminin was found to inhibit GH3 and AtT-20 cell proliferation [START_REF] Kuchenbauer | Laminin inhibits lactotroph proliferation and is reduced in early prolactinoma development[END_REF][START_REF] Kuchenbauer | Extracellular matrix components regulate ACTH production and proliferation in corticotroph tumor cells[END_REF]. Several other ECM macromolecules were also found to impact tumor cell proliferation, invasion and migration [START_REF] Azorín | The invasion mode of GH3 cells is conditioned by collagen subtype, and its efficiency depends on cell-cell adhesion[END_REF][START_REF] Kuchenbauer | Extracellular matrix components regulate ACTH production and proliferation in corticotroph tumor cells[END_REF] -see Table 1, suggesting ECM macromolecules might indeed play a role in PA tumorigenesis. Moreover, ECM macromolecules (laminin, collagen I, and fibronectin) were found to inhibit hormonal production/secretion [START_REF] Kuchenbauer | Laminin inhibits lactotroph proliferation and is reduced in early prolactinoma development[END_REF][START_REF] Kuchenbauer | Extracellular matrix components regulate ACTH production and proliferation in corticotroph tumor cells[END_REF]. Interestingly, the same ECM macromolecules did not impact the hormonal production/secretion of normal rat pituitary cells, suggesting a potential change in integrin expression during tumorigenesis [START_REF] Kuchenbauer | Laminin inhibits lactotroph proliferation and is reduced in early prolactinoma development[END_REF][START_REF] Kuchenbauer | Extracellular matrix components regulate ACTH production and proliferation in corticotroph tumor cells[END_REF].

Regarding ECM remodeling, numerous studies have looked at matrix metalloproteinases (MMPs), enzymes that degrade and remodel the ECM, while in the process releasing the molecules that are embedded in it, and also at tissue inhibitors of metalloproteinases (TIMPs), molecules that regulate MMPs (1). Lower TIMP levels and higher levels of MMP activity were found in PA-derived conditioned medium compared to normal pituitary explant-derived conditioned medium [START_REF] Paez-Pereda | High Levels of Matrix Metalloproteinases Regulate Proliferation and Hormone Secretion in Pituitary Cells1[END_REF]. TIMP-3 expression was associated with the deposition of fibrous matrix in PAs (126). In both PAs and PCs, MMPs and TIMPs have been linked to multiple characteristics related to aggressiveness [START_REF] Paez-Pereda | High Levels of Matrix Metalloproteinases Regulate Proliferation and Hormone Secretion in Pituitary Cells1[END_REF][START_REF] Turner | Role of Matrix Metalloproteinase 9 in Pituitary Tumor Behavior[END_REF][START_REF] Knappe | Expression of serine proteases and metalloproteinases in human pituitary adenomas and anterior pituitary lobe tissue[END_REF][START_REF] Hui | Expression of MMP14 in invasive pituitary adenomas: relationship to invasion and angiogenesis[END_REF][START_REF] Liu | Matrix metalloproteinase 2 and 9 expression correlated with cavernous sinus invasion of pituitary adenomas[END_REF][START_REF] Guo | Expressions of Matrix Metalloproteinases-9 and Tissue Inhibitor of Metalloproteinase-1 in Pituitary Adenomas and Their Relationships with Prognosis[END_REF] -see Table 1. In addition, by releasing growth factors embedded in a synthetic matrix (matrigel), MMPs were shown, in vitro, to have a role in hormone secretion by pituitary tumor cell lines [START_REF] Paez-Pereda | High Levels of Matrix Metalloproteinases Regulate Proliferation and Hormone Secretion in Pituitary Cells1[END_REF]. MMPs have also been linked to angiogenesis in PAs, with MMP-9 positive prolactinomas showing higher vascular densities than MMP-9 negative prolactinomas [START_REF] Turner | Role of Matrix Metalloproteinase 9 in Pituitary Tumor Behavior[END_REF]. These data are consistent with the roles the MMP-system plays in other cancers, notably in progression and angiogenesis (127). Other than MMPs, the urokinase plasminogen activator (uPA) system is another key player in ECM remodeling and has been shown to be involved in cancer progression, including in cell growth, cell migration, epithelial-mesenchymal transition, and angiogenesis (128). uPA, uPA receptor, tissue-type plasminogen activator, and plasminogen activator inhibitor-1, were also found to be expressed in PAs, and a higher uPA expression was noted in PAs when compared to the NPG [START_REF] Knappe | Expression of serine proteases and metalloproteinases in human pituitary adenomas and anterior pituitary lobe tissue[END_REF]. The potential impact of the uPA-system, as well as of other ECM components, on aggressiveness-related characteristics [START_REF] Marques | The tumour microenvironment of pituitary neuroendocrine tumours[END_REF][START_REF] Kuchenbauer | Laminin inhibits lactotroph proliferation and is reduced in early prolactinoma development[END_REF][START_REF] Azorín | The invasion mode of GH3 cells is conditioned by collagen subtype, and its efficiency depends on cell-cell adhesion[END_REF][START_REF] Paez-Pereda | High Levels of Matrix Metalloproteinases Regulate Proliferation and Hormone Secretion in Pituitary Cells1[END_REF][START_REF] Turner | Role of Matrix Metalloproteinase 9 in Pituitary Tumor Behavior[END_REF][START_REF] Knappe | Expression of serine proteases and metalloproteinases in human pituitary adenomas and anterior pituitary lobe tissue[END_REF][START_REF] Kuchenbauer | Extracellular matrix components regulate ACTH production and proliferation in corticotroph tumor cells[END_REF][START_REF] Hui | Expression of MMP14 in invasive pituitary adenomas: relationship to invasion and angiogenesis[END_REF][START_REF] Liu | Matrix metalloproteinase 2 and 9 expression correlated with cavernous sinus invasion of pituitary adenomas[END_REF][START_REF] Guo | Expressions of Matrix Metalloproteinases-9 and Tissue Inhibitor of Metalloproteinase-1 in Pituitary Adenomas and Their Relationships with Prognosis[END_REF][START_REF] Xing | Study on the expression levels of CXCR4, CXCL12, CD44, and CD147 and their potential correlation with invasive behaviors of pituitary adenomas[END_REF][START_REF] Wu | Significance of TNF-α and IL-6 expression in invasive pituitary adenomas[END_REF][START_REF] Qiu | The expression of interleukin (IL)-17 and IL-17 receptor and MMP-9 in human pituitary adenomas[END_REF][START_REF] Wang | The expression of integrinβ1 and FAK in pituitary adenomas and their correlation with invasiveness[END_REF] is summarized in Table 1. Therefore, both the ECM and ECM remodeling appear to have important roles in the biology of PAs, and may constitute potential treatment targets. Appealing candidates include the targeting of the MMP-system (129,130) and targeting of integrins (131,132).

Conclusions

Similar to the case in other cancers, the TME represents a promising lead for understanding of PA biology beyond genetics and epigenetics, and promises to be an important tool for therapeutic purposes. TILs, TAMs, folliculostellate cells, tumor-associated fibroblasts, angiogenesis, as well as the ECM and ECM remodelling, all have complex roles in the biology of PAs, being linked to their functionality, size, invasion, proliferation, progression/recurrence, and to their response to treatment. From a therapeutic viewpoint, immune-checkpoint inhibitors and bevacizumab have already shown some efficacy in treating aggressive PAs and PCs, and the use of numerous other TME-targeting therapies can be foreseen. Further work is still required for a better understanding of TME composition, its roles, and of the extensive crosstalk that takes place between adenoma cells and the TME, as well as between the different components of the TME.

Ideally, future studies will integrate a more intricate and complete view of the network of interactions that may exist between tumor cells and the components of the PA TME. Additionally, given the potential differences in TME composition and involvement in different subtypes of PAs, it will be important to study each of the histological subtypes of PA separately. Angiopoientin-2 promoted the pf. of GH3 cells [START_REF] Karabid | Angpt2/Tie2 autostimulatory loop controls tumorigenesis[END_REF] TAFs derived from PAs with CS inv. promoted pf. of GH3 cells in vitro, as well as the growth of GH3-derived xenografts in mice ( 23 with fewer S100B+ cells [START_REF] Ilie | Intratumoural spatial distribution of S100B + folliculostellate cells is associated with proliferation and expression of FSH and ERα in gonadotroph tumours[END_REF] Progression after surgery as. with higher VEGF expression [START_REF] Sánchez-Ortiga | Over-expression of vascular endothelial growth factor in pituitary adenomas is associated with extrasellar growth and recurrence[END_REF] Less progression-free time as. with higher VEGFR2 expression [START_REF] Sánchez-Ortiga | Over-expression of vascular endothelial growth factor in pituitary adenomas is associated with extrasellar growth and recurrence[END_REF]

Figure 1 .

 1 Figure 1. Immunohistochemical stainings depicting T cells (CD3+), macrophages (CD68+), blood vessels

Figure 2 .

 2 Figure 2. Roles and interactions of tumor-associated macrophages (TAMs) in pituitary adenomas. Derived

Figure 3 .

 3 Figure 3. Schematic representation of the mechanism of action of immune-checkpoint inhibitors (A), and

  ) TAF-conditioned medium induced morphology changes, EMT activation, & increased inv. & migration of GH3 cells (24) Laminin inhibited GH3 cell pf. (25) Different collagen subtypes impacted differently GH3 cell inv. & migration strategy (26) MMP inhibition decreased GH3 cell pf. (27) IL-2, IL-6, BMP-4 & CXCL12 stimulated, while TGF-β inhibited GH3 cell pf. (4) CXCL12 stimulated, while TGF-β inhibited GH4 cell pf. (4) Lactotroph F: Inv. macroprolactinomas as. with higher microvessel density than non-inv. macroprolactinomas (28) F: Inv. macroprolactinomas expressed more MMP-9 than non-inv. macroprolactinomas (29) F: Resistance to bromocriptine as. with higher endothelial expression of endocan (30) Corticotroph F: CS inv. as. with lower tPA expression (31) Collagen IV, fibronectin & activation of β1 integrin stimulated, while collagen I & laminin inhibited AtT-20 cell pf. (32) TIMP-1 inhibited AtT-20 cell inv. & migration (33) MMP inhibition decreased AtT-20 cell pf. (27) RSUME silencing inhibited inv. of AtT-20 cells (34) IL-1 & IL-2 stimulated, while IFN-γ & LIF inhibited AtT-20 cell pf. (4) Gonadotroph CS inv. as. with more CD68+ & CD163+ TAMs, & less thick & thin collagen fibers (14) Ki67 index ≥3%, mitosis > 2/10 HPFs & proliferative status as.

Table 1 .

 1 Potential impact of tumor microenvironment on aggressiveness-related characteristics of pituitary adenomas and carcinomas. Derived from data from[START_REF] Marques | The tumour microenvironment of pituitary neuroendocrine tumours[END_REF][START_REF] Sato | Analysis of Tumor Angiogenesis and Immune Microenvironment in Non-Functional Pituitary Endocrine Tumors[END_REF][START_REF] Lu | Immune Cell Infiltrates in Pituitary Adenomas: More Macrophages in Larger Adenomas and More T Cells in Growth Hormone Adenomas[END_REF][START_REF] Lupi | Tumor Infiltrating Lymphocytes But Not Serum Pituitary Antibodies Are Associated with Poor Clinical Outcome after Surgery in Patients with Pituitary Adenoma[END_REF][START_REF] Barry | Tumor microenvironment defines the invasive phenotype of AIP-mutation-positive pituitary tumors[END_REF][START_REF] Mei | Increased expression of programmed death ligand 1 (PD-L1) in human pituitary tumors[END_REF][START_REF] Principe | Immune Landscape of Pituitary Neuroendocrine Tumours Reveals Association between Macrophages and Gonadotroph-Tumour Invasion[END_REF][START_REF] Marques | Chemokines modulate the tumour microenvironment in pituitary neuroendocrine tumours[END_REF].

	844
		Invasion (Patients)	Proliferation (Patients)	Progression/Recurrence/Resistance to treatment (Patients)	In vivo/in vitro
					Macrophage-conditioned media induced
					morphology changes, EMT activation & increased
					inv. of GH3 cells (12,15)
					CCL17 promoted increased EMT changes,
			F: Higher Ki-67 index in PAs		migration, inv. & pf. of GH3 cells (21)
	Somatotroph	F: CS inv. as. with less CD8+ cells (19) & more CD68+ TAMs (14)	with high VEGF expression vs. PAs with no VEGF expression	F: Resistance to first-generation SRLs as. with less CD8+ cells (19)
			(20)

This work has been supported by the Fondation ARC pour la recherche sur le cancer (PJA 20181207935 and ARCMD-DOC12020020001361), the Ligue contre le cancer (CCAURA), the Région Rhone-Alpes-Auvergne (HypoMeT), and the Société Française d'Endocrinologie (FRIEMM).

death-ligand 1 (PD-L1), cytotoxic T-lymphocyte-associated protein 4 (CTLA-4), vascular endothelial growth factor A (VEGF-A), VEGF-receptor (VEGFR). [START_REF] Ilie | The Microenvironment of Pituitary Tumors-Biological and Therapeutic Implications[END_REF][START_REF] Ilie | Immunotherapy in aggressive pituitary tumors and carcinomas: a systematic review[END_REF]104,105). Abbreviation: non-immunoreactive (NIR), immune-checkpoint inhibitors (ICIs).

Unspecified or combined NFPAs

CS inv. as. with more CD163+ TAMs (9), M2like/M1-like TAMs ratio >1 (37) & higher FoxP3/CD8 ratio [START_REF] Sato | Analysis of Tumor Angiogenesis and Immune Microenvironment in Non-Functional Pituitary Endocrine Tumors[END_REF] CS inv. as. with more VEGF & VEGFR1 [START_REF] Sato | Analysis of Tumor Angiogenesis and Immune Microenvironment in Non-Functional Pituitary Endocrine Tumors[END_REF] Inv. of hormone-negative PAs as. with high endothelial expression of endocan [START_REF] Wang | Endothelial cell-specific molecule-1 as an invasiveness marker for pituitary null cell adenoma[END_REF] Higher MMP-9 expression in recurrent NFPAs (for the second surgery compared to the first) [START_REF] Turner | Role of Matrix Metalloproteinase 9 in Pituitary Tumor Behavior[END_REF] Cultured M2 versus M1 macrophages promoted increased inv., motility & pf. of primary NFPA cultures (37)

Combined histological subtypes

Knosp grades cor. with CD68+ TAMs number [START_REF] Lu | Immune Cell Infiltrates in Pituitary Adenomas: More Macrophages in Larger Adenomas and More T Cells in Growth Hormone Adenomas[END_REF] Tumor Microenvironment Implications in Pituitary Adenomas

Graphical Abstract

Click here to access/download;Graphical Abstract;graphical_abstract.pdf

Extracellular matrix

Collagen degradation (MMP9, ?)

CD163:HLA-DR ratio + cor. microvessel density & area Higher CD163 expression as. higher VEGF expression Higher CD68 expression as. higher VEGFR2 expression Endothelial endocan expression as. more CD68+ cells M2-like TAM infiltrate increased parallely with neovascularization, & then, hemorrhage*  Tumor-infiltrating lymphocytes have been linked to invasion and proliferation of pituitary adenomas, and to the response to treatment of somatotroph adenomas.

 Folliculostellate cells have been linked to hormone production/secretion and to the proliferation of pituitary adenomas.

 Angiogenesis and angiogenesis-related molecules have been linked to invasion, proliferation, and the progression/recurrence of pituitary adenomas, as well as to response to treatment in lactotroph adenomas.

 The extracellular matrix and its remodeling have been linked to hormone production/secretion, to the invasion and proliferation of pituitary adenomas -most notably to their invasion.

 Substantial crosstalk takes place between adenoma cells and the tumor microenvironment, as well as between the different components of the tumor microenvironment.

 Immune-checkpoint inhibitors and bevacizumab have already shown some efficacy in treating aggressive pituitary adenomas and pituitary carcinomas.

Essential Points


Astrid Klipfel
email: klipfel@cril.fr

Zied Bouraoui
email: zied.bouraoui@cril.fr

Yaël Frégier
email: yael.fregier@univ-artois.fr

Adlane Sayede
email: adlane.sayede@univ-artois.fr

Equivariant graph neural network for crystalline materials

Materials generation is an essential task in material science that aims to discover new materials. While most of the existing models have shown interesting results in simulation, they struggle to produce new original and stable materials. This paper discusses the salient properties required for material generation and studies the difficulties related to material pattern repetition, which impacts the stability of the generated structures.

Introduction

Crystalline materials are involved everywhere in our modern society. From metal alloy to semi-conductor, several technological objects contain crystalline materials. Discovering new materials remains a difficult task in material science. While existing algorithms can search for new structures in the materials space [START_REF] Pickard | Ab initio random structure searching[END_REF], searching for a new material with a given set of desirable properties is not a trivial task. The set of potential candidate materials is not countable by a computer, and the portion of stable materials (i.e. materials that can exist without self-destructing) is small. Moreover, estimating the properties of a single material with chemical simulation as Density Functional Theory (DFT) is computationally expensive. To this end, methods based on evolutionary algorithms (e.g. [START_REF] Oganov | How evolutionary crystal structure prediction works-and why[END_REF]) are introduced for generating new materials from existing datasets composed of stable materials. However, most of these approaches work by hybridization and mutation of existing materials. As a consequence, these methods are not able to find complex materials.

Discovering new materials is a challenging problem. But contrary to most generation problems, theoretical chemistry provides a powerful set of tools to analyse synthetic and real data. As a matter of fact, simulation techniques like hartree-fock or DFT are able to estimate the properties of a given structure by applying physics laws. Consequently, the stability of the materials can be estimated through simulation. These methods can also be used to perform the relaxation of crystalline materials. Relaxation is the process of minimizing the energy of a crystalline structure by deforming it. This process is very common in material science to study a given ma-Figure 1: The energy of a structure is given by its geometry and chemistry. Stable structures are the local minima of the energy (green dots). Relaxing a structure is the process of modifying the geometry of a structure to minimize its energy (an unstable structure represented as a red dot converge to the nearest stable minima) terial. It permits the discovery of new materials since minimizing the total energy of the structure allows it to be more stable. Consequently, the local minima of the energy corresponding to stable materials and relaxation lead to producing stable crystalline structures from an initially unstable crystal around the stable structures in the materials space. This is illustrated in Figure 1.

Several methods were recently introduced for chemical simulation either by enhancing current algorithms with machine learning techniques (e.g. [START_REF] Yang | Machine-learning accelerated geometry optimization in molecular simulation[END_REF]) or by using end-to-end models (e.g. [START_REF] Kelvinius | Graph-based machine learning beyond stable materials and relaxed crystal structures[END_REF]). Most of these approaches focus on accelerating DFT by approaching relaxation as a supervised task. End-to-end models generally require expensive labels to be trained as interaction forces. However, these labels are generally not available and need to be produced through DFT calculation. Thus, the benefits of end-to-end models is limited because such models required data from atomistic simulation. Finally, even if the relaxation may lead to a crystalline structure, there is no guaranty on its stability. In fact, most of the random structures do not result in stable structures. Consequently, approaches based on simulation for new materials discovery are limited.

Another direction consists in directly generating stable crystalline structures using machine learning techniques.

In this case, the generative process can be performed with successive actions applied to the structure [START_REF] Xie | Crystal diffusion variational autoencoder for periodic material generation[END_REF]. This process doesn't require strictly following physics laws as long as the stable points (i.e. local minima of the energy) learned by the machine learning models remain the same as the real stable points. This fact can be advantageous in some cases because the realistic relaxation of a random structure is not guaranteed to converge to a stable material. As a result, learning realistic stable points without realistic physics can help machine learning models produce stable structures.

Indeed, graph neural networks (GNN) have already been used for the representation and generation of organic molecules [START_REF] Satorras | E(n) equivariant graph neural networks[END_REF]. However, crystalline materials are known to be more difficult to generate since they generally have more complicated chemistry. Also, they contain repetitive patterns defined by the lattice of the crystals, which make them harder to process. In this paper, we present how graphs representation of materials are defined. We also discuss some important properties required for generative models.

Problem statement

Crystalline systems As molecules, crystalline systems can be defined as coloured point clouds. However, as crystals are periodic structures, additional information about how the point could is repeated in the space is required to represent it. The periodicity of the material can be then represented as a network where a group of points is repeated by discrete translation, which is equivalent to tiling space with a parallelepiped containing a cloud of atoms as illustrated in Figure 2.

As a result, a periodic system can be describe as atomic positions 𝑥𝑖 ∈ [0, 1[ 3 with an associated feature space representing the chemical information of each atom 𝑧𝑖 ∈ ℱ and a lattice 𝜌 ∈ GL3(R) representing the periodicity of the material. The infinite point cloud generated by this representation can be defined as

{( 𝜌•(𝑥𝑖 +𝜏 ), 𝑧𝑖 ) |𝜏 ∈ Z 3 , 1 ≤ 𝑖 ≤ 𝑛 } ⊆ R 3 ×𝐹 (1)
Where 𝜏 act like a Z 3 vector that translate the point cloud.

Material graph There are multiple ways to define the graph of a material. Chemical bonds can be used to build the set of edges, but generally, edges are built from the atoms under a given threshold distance of from the 𝑘 nearest neighbourhood [START_REF] Xie | Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties[END_REF]. The resulting graph is a multi-graph because the local environment of an atom can be on a translated point cloud near the border of the lattice as depicted in Figure 2. As a result, an edge can have multiple edges between a pair of nodes and between a node with itself.

Figure 2:

The periodic structure of a material is represented as a lattice (in dotted lines). The multi-graph associated with a material (blue arrow) can overlap on the adjacent repetition of the lattice and a pair of nodes can be connected multiple time.

Material deformation

To tackle the crystalline system generation problem, we should define action on the geometry of the material. This action can be seen as an action on the lattice of the material 𝜌 resulting in the updated lattice 𝜌 ′ and action on the atomic positions 𝑥𝑖 resulting in the updated atomic position 𝑥 ′ 𝑖 .

{ 𝜌 ′ = 𝑔𝜌 𝑥 ′ 𝑖 = [𝑥𝑖 + 𝑔𝑖] . (2)
In this case, the goal is to predict the action 𝑔 ∈ GL3(R) on the lattice and the actions 𝑔𝑖 ∈ R 3 on the atomic position. The atomic positions are brought back into the lattice of the crystal by truncation.

Method

Equivariance To obtain meaningful actions applied to a material, we should satisfy the equivariance property. Indeed, translations and rotations have no impact on the material's properties. Consequently, a machine learning model acting on the material should not be dependent on the orientation and position of the structure but only be dependent on its geometry as shown in Figure 3. Actions on the lattice When 𝑔 acts on 𝑟ℎ𝑜 the lattice of the crystal, we would restrain 𝑔 to the group of actions deforming the structure. However, any matrix in R 3×3 can be decomposed as a sum of a symmetric and an antisymmetric matrix. As we define the action of 𝑔 in GL(3), the anti-symmetric part of the transformation can be seen as a rotation. But as we discussed earlier, applying rotations on a crystal doesn't act on a material as the rotated material is equivalent to the original material. This is illustrated in Figure 4. Consequently, it is better to restrain 𝑔 to GL(3) ∖ SO(3). In other words, to restrain 𝑔 to the subset of matrices of GL(3) that are symmetric.

Figure 4:

The SO(2) group doesn't act on the materials but only rotates them without deformation.

Acting on the crystalline structure To act on both the lattice and the atomic position, we can define actions on the edge of the graph. These actions can be then decomposed into a global action on the lattice of the crystal and local action on the atomic position. In order to define these actions, the contributions of all edges are aggregated to compute the action on the lattice. To act on the atomic positions, only the actions of the edges connected to the node are taken into account.

Conclusion

Crystalline materials are difficult to process because of the complexity and the variety of their chemistry, but also because of their repetitive structure. However, materials can be represented as graphs containing both chemical and geometrical information about the structures. Consequently, geometric machine learning techniques such as graph neural networks can be used in a wide variety of tasks including supervised and unsupervised learning. But in order to enhance the generalization capability of machine learning models, some properties such as the symmetry of the actions on the lattice or the equivariance can be beneficial.

Figure 3 :

 3 Figure 3:Equivariance between the action applied on the material 𝑔 and the actions of translation and rotation group ℎ ∈ R 3 ∪ SO(3). 𝑀 and 𝑀 ′ denoting the original material and the material after having applied the action 𝑔.

Acknowledgments

This work has been supported by HPC resources from GENCI-IDRIS (Grant 2021-[AD011013288]) and FEI INS2I 2022-EMILIE.

Figure 5: Actions defined on the edges of the graph can be decomposed into action on the atomic positions and action on the lattice of the crystalline material.