Abstract Simple Summary The recent success of immunotherapy treatments against cancer relies on helping our own body’s defenses in the fight against tumours, namely reinvigorating the cancer killing action of T cells. Unfortunately, in a large proportion of patients these therapies are ineffective, in part due to the presence of other immune cells, macrophages, which are mis-educated by the cancer cells into promoting tumour growth. Here we start from an existing model of macrophage polarization and extend it to the specific conditions encountered inside a tumour by adding signals, receptors, transcription factors and cytokines that are known to be the key components in establishing the cancer cell-macrophage interaction. Then we use a mathematical Boolean model applied to a gene regulatory network of this biological process to simulate its temporal behaviour and explore scenarios that have not been experimentally tested so far. Additionally, the KO and overexpression simulations successfully reproduce the known experimental results while predicting the potential role of regulators (such as STAT1 and EGF) in preventing the formation of pro-tumoural macrophages, which can be tested experimentally. Abstract The tumour microenvironment is the surrounding of a tumour, including blood vessels, fibroblasts, signaling molecules, the extracellular matrix and immune cells, especially neutrophils and monocyte-derived macrophages. In a tumour setting, macrophages encompass a spectrum between a tumour-suppressive (M1) or tumour-promoting (M2) state. The biology of macrophages found in tumours (Tumour Associated Macrophages) remains unclear, but understanding their impact on tumour progression is highly important. In this paper, we perform a comprehensive analysis of a macrophage polarization network, following two lines of enquiry: (i) we reconstruct the macrophage polarization network based on literature, extending it to include important stimuli in a tumour setting, and (ii) we build a dynamical model able to reproduce macrophage polarization in the presence of different stimuli, including the contact with cancer cells. Our simulations recapitulate the documented macrophage phenotypes and their dependencies on specific receptors and transcription factors, while also unravelling the formation of a special type of tumour associated macrophages in an in vitro model of chronic lymphocytic leukaemia. This model constitutes the first step towards elucidating the cross-talk between immune and cancer cells inside tumours, with the ultimate goal of identifying new therapeutic targets that could control the formation of tumour associated macrophages in patients. Keywords: Boolean model, tumour associated macrophage, macrophage polarization, nurse-like cells, chronic lymphocytic leukaemia 1. Introduction As all living cells, macrophages perceive and respond to intra- and extracellular signals in order to maintain their functions (endocytic, phagocytic and secretory, for example) by displaying a wide spectrum of specific phenotypes (polarizations) in different inducer environments. Based on their activity and the expression of specific proteins, markers and chemokines, two major subsets of macrophages have been identified, namely classically activated macrophages (M1) exhibiting a pro-inflammatory response, and alternatively activated macrophages (M2, themselves subdivided into 4 subclasses: M2a, M2b, M2c, M2d [[40]1,[41]2,[42]3]) exhibiting an anti-inflammatory response. Additionally, multiple studies support the idea that M1 and M2 macrophages represent, in fact, the extremes of a continuous polarization spectrum of cells deriving from the differentiation of monocytes [[43]4]. Their plastic gene expression profile is determined by the type, concentration and duration of exposure to the polarization stimuli in an inflammatory environment [[44]3,[45]5,[46]6,[47]7,[48]8]. Macrophages are also found inside tumors, as part of the tumor micro-environment (TME), a complex collection of cells that are found surrounding cancer cells including also other immune cells, such as lymphocytes and neutrophils, as well as other normal cells. In many tumors, infiltrated macrophages display mostly an M2-like phenotype, which provides an immunosuppressive microenvironment. In cancer, these tumor associated macrophages (TAMs) secrete several cytokines, chemokines and proteins which promote tumor angiogenesis, growth and metastasis [[49]9,[50]10,[51]11,[52]12]. Interestingly, it was observed that in established tumors, signals originating from cancer cells can cause phenotypic shifts in macrophages, leading to alternative functions that do not correspond to either M1 or M2 phenotypes [[53]13]. Several studies have demonstrated that TAMs directly suppress CD8 [MATH: + :MATH] T cell activation in vitro [[54]14,[55]15,[56]16,[57]17]. Mechanisms that orchestrate this process, either directly or indirectly, remain unclear [[58]18] and warrant further exploration due to macrophages’ important impact on tumor progression. The TME can be defined as an ecological system given the presence of diverse types of cells that interact in specific ways with each other. To name a few, cytotoxic T lymphocytes can attack cancer cells and kill them, while macrophages can phagocyte apoptotic or dead cells. However, complex feedback relations exist between the signals produced by some cell types and the phenotypic transitions that are induced by these signals in other cells. For example, due to the high density of leukemic B cells, monocytes residing in lymph nodes from CLL patients tend to differentiate into a pro-tumoral state, which is able in turn to promote survival of cancer cells through the secretion of anti-apoptotic signals, rather than eliminating them. These complex interrelations between cells are typical of predator-prey systems in ecology and can be modelled using similar approaches in which the possible final states (attractors) of the system define which populations will dominate [[59]19]. In any given environment, the cellular processes that determine a cell’s phenotype consist in a cascade of interactions, which can be represented as a regulatory network, in which nodes represent proteins, enzymes, chemokines, etc., while the connections represent the type (activation or inhibition) and direction of interactions of different types (transcriptional and post-translational activations). Network modelling has found numerous applications in studying the structure and dynamic behaviour of different biological systems in response to environmental stimuli and internal perturbations [[60]20,[61]21,[62]22,[63]23]. Several computational models of different pathways involved in the inflammatory immune response have been previously published, such as: continuous, logical and multi-scale models of T cell differentiation [[64]24,[65]25,[66]26], logical models of macrophage differentiation in pro- and anti-inflammatory conditions [[67]27], multi-scale models of innate immune response in tumoral conditions [[68]28], etc. Macrophages are extremely plastic cell types, whose phenotypes can easily switch depending on conditions. Since the specific macrophage state that protects cancer cells from undergoing apoptosis is fundamental in the development of resistance to treatments in CLL and solid tumors, we turned to study it as a polarization state. An important computational model of macrophage polarization was able to detect 3 different M2 subgroups of macrophages, as a result of various combinations of pro- and anti-inflammatory extra-cellular signals [[69]27], using exclusively literature-based knowledge of the intra-cellular regulatory interactions and pathways involved in the polarization process. In a more recent work, Ramirez et al. [[70]29] used temporal expression profiles of in vitro macrophage cytokines to infer logical models of macrophage polarization (M1 and 3 subcategories of M2: M2a, M2b and M2c) in the presence of different stimuli. Nevertheless, many important questions remain to be explored regarding the polarization states, especially in a tumor setting. More specifically, it is important to identify the pathways involved in TAM formation and to understand to what extent the macrophage plasticity facilitates this process inside a tumor. On the other hand, despite the wealth of quantitative information from bulk and single-cell sequencing datasets, the inference of regulatory networks based on experimental data remains a difficult challenge, with most approaches proposing a combination of both literature- and data-driven methods [[71]29,[72]30,[73]31,[74]32]. In Chronic Lymphocytic Leukemia (CLL), a B-cell malignancy in which patients accumulate large quantities of malignant CLL cells in their lymph nodes, an interesting ecology of cancer cells and immune cells is established. CLL cells are able to educate surrounding monocytes, through direct contact and cytokine signals, turning them into TAMs, which in this disease are referred to as Nurse Like Cells (NLCs) [[75]33]. NLCs are derived from CD14 [MATH: + :MATH] monocytes and are characterised by a distinct set of antigens (CD14lo, CD68hi, CD11b, CD163hi) [[76]34,[77]35]. Moreover, NLCs express stromal-derived-factor-1alpha, a chemokine which promotes chemotaxis and activates mitogen activated protein kinases, ultimately leading to more aggressive cancers and better survival of these cells in vitro. Through direct contact, the NLCs are able to protect the cancer CLL cells from apoptotic signals, and stimulate environment mediated drug resistance. Interactions between NLCs and CLL cells appear to be mediated by the B cell receptor, which, when stimulated, activates production of CCL3/4, initiating the recruitment of other cells, including CD4 [MATH: + :MATH] T cells and more NLCs. Another pathway that has been associated with NLCs and TAMs more in general is that of CSF-1 (MCSF). Patients with high expression of this factor usually show faster CLL progression and this gene was implicated in the production of NLCs. Also the more M1- or M2-like profile of NLCs in specific patients correlates with active and controlled disease, respectively. Analyses of the transcriptomic profile of NLCs suggest their high similarity to the macrophage M2 profile described in solid tumors, which makes studying the formation of NLCs all the more relevant in the quest of controlling TAMs in other malignancies. The main characteristics of these 3 types of macrophages are given in [78]Table 1. Considering the close phenotypic similarity between M2 and NLC/TAM macrophages, we consider that the NLC/TAM components should include the M2 ones. Here we indicate in blue the components that have been used in our model and in bold the ones that were taken as signature components for each phenotype. A schematic diagram of M1 and M2 (with 4 subcategories) macrophages can be found in [[79]2], whereas a short description of the profiles for the main macrophage phenotypes is given in [80]Appendix A. More detailed explanations of the mechanisms, pathways and components involved in the polarization process can be found in the cited papers and the references therein.