Conceptual Analogies Between Multi-Scale Feeding and Feedback Cycles in Supermassive Black Hole and Cancer Environments

Adopting three physically-motivated scales (“micro” – “meso” – “macro”, which refer to mpc – kpc – Mpc, respectively) is paramount for achieving a unified theory of multiphase active galactic nuclei feeding and feedback, and it represents a keystone for astrophysical simulations and observations in the upcoming years. In order to promote this multi-scale idea, we have decided to adopt an interdisciplinary approach, exploring the possible conceptual similarities between supermassive black hole feeding and feedback cycles and the dynamics occurring in human cancer microenvironment.


INTRODUCTION
Several scientific problems show complexities that can be understood only through a multi-scale approach, in which apparently disjointed processes are linked together across multiple scales. One of such examples is the astrophysical study of supermassive black holes (SMBHs), which resides at the core of virtually every galaxy in the universe. Feeding of matter from galactic distances onto SMBHs is thought to be the physical process powering active galactic nuclei (AGN), which are observed up to extremely large distances due to their large luminosities and are supposed to impact the evolution of their host galaxies through mechanical feedback from winds and jets (1)(2)(3).
It is important to remind that the typical scale associated with a SMBH is in units of its Schwarzschild radius rs = 2GM BH /c 2 , where G is the gravitational constant, c is the speed of light, and M BH is the mass of the SMBH. For a value of the SMBH mass of ≃ 10 10 times that of our Sun, this corresponds to a scale in units of parsec of 1 mpc = 10 −3 pc ≃ 10 14°c m. This scale is larger than the distance between our Earth and the Sun, but it is negligible when compared to the size of a typical galaxy that can span a radius of more than 10 kpc. Therefore, the study of AGN and their host galaxies is inherently a multi-scale problem.
It has been recently assessed that adopting three physicallymotivated scales ("micro" -"meso -macro, which refer tompckpc -Mpc, respectively) is paramount for achieving a unified theory of multiphase AGN feeding and feedback, and it represents keystone for astrophysical simulations and observations in the upcoming years (4). In order to promote this multi-scale idea, we have decided to adopt an interdisciplinary approach, exploring the possible conceptual similarities between SMBH feeding and feedback cycles and the dynamics occurring in human cancer microenvironment.
To this end, analogously to the three major scales ("micro", "meso" and "macro") identified in the aforementioned astrophysical investigation, we defined three distinct scales within the tumor microenvironment: (1) micro ≡intratumor network; (2) meso≡ intercellular exchanges between tumor and immune cells; and (3) macro ≡extracellular vesicles-based communication between primary tumor and distant premetastatic niches. In these three contexts, cell-to-cell communication is mediated by exosomes, nano-sized vesicles (40-100 nm in diameter) enclosed by a lipid bilayer and released by cells under healthy or pathological conditions (5) (Figure 1). Exosomes contain a variety of biomolecules that include oncogenic proteins, signaling molecules, glycans, lipids, metabolites, RNA, and DNA (6).

MICRO: EXOSOME-BASED INTRATUMOR COMMUNICATION
Studies focused on a variety of distinct cancer cells reported that tumor-derived exosomes can promote tumor cell proliferation. An autocrine induction of cellular proliferation was reported in chronic myeloid leukemia (7), gastric cancer (8), bladder cancer (9), glioblastoma (10) and melanoma (11). Furthermore, exosomes-based intratumor communication is also fundamental for the acquisition of migratory properties in cancer cells from the primary tumor. This phenomenon has been reported in both nasopharyngeal carcinoma (12) and prostate cancer (13), where exosomes released by primary tumor cells can increase the invasiveness and motility of other recipient malignant cells ( Figure 2).
A single cancer cell can produce and release in the blood from 2000 to 7000 exosomes (14). In 2018, Professor Avner Friedman and Professor Wenrui Hao (15) developed a mathematical model that resumes the production of tumor exosomes and the release of their content upon encountering cancer cells: where E c identifies the exosomes produced by cancer cell over time, t = time, D Ec is the diffusion coefficient of E C , l Ec is the production rate of E c , C means Cancer cell density and Kc indicates cancer cell saturation.
Exosomes released by tumor cells provide a paracrine signaling mechanism for cancer progression. Exosomes contain microRNAs (miRNAs), lipids and proteins that are cell type specific. The secretion and delivery of exosomal miRNAs are the basis for cancer cell-to-cell communication and contribute as signaling molecules to the creation of a tumor-promoting environment (16). The transfer of exosomal miRNAs can confer also acquired drug resistance by encoding proteins that can lead to chemoresistance in the recipient tumor cells (17). miR-21 is one of the most studied (18) and enhances tumor growth when is released by exosomes through the encounter between E c and cancer cells, as expressed by the equation (15): where D miR-21 is the diffusion coefficient of miR21once released by exosomes, estimated at 0.130 cm 2 /day (19), l miR21Ec represents the production rate of miR-21 by Ec, Kc indicates cancer cell saturation (estimated at 0.4 g/cm 3 ) (20) and d miR21 the degradation rate of miR-21.

MESO: EXOSOME-BASED DIALOGUE BETWEEN TUMOR AND IMMUNE CELLS
The ability to develop strategies to escape from host immune surveillance is one of the hallmarks of cancer (21). It has been shown that tumor-derived exosomes can down-regulate CD3z and Janus kinase 3 (JAK3) expression in primary activated Tcells, mediate the apoptosis of CD8 + T-cells and the conversion of CD4 + CD25 -T-cell into CD4 + CD25(hi)FOXP3 + regulatory T-cells, (which express interleukin 10, transforming growth factor b1 and cytotoxic T-lymphocyte antigen 4 that effectively mediate suppression) (22) (Figure 2).

E c produced by tumor cells release their content through the encounter with a variety of immune cells including Th1 cells (T 4 ), CD8+ cells (T 8 ), regulatory T cells (T r ) and dendritic cells (D):
where T 4, T 8 ,T r and D express different immune cell density, while K indicate cell saturation estimated at 2 x 10 −3 g/ml for T 4 and T 8 , 5 x 10 −4 g/ml for T r (20,23) and 4 x 10 −6 g/cm 3 for D (24)(25)(26). The complex interactions of T 8, D and tumor cells (T) within the tumor has been described by Depillis and colleagues (27), who extended the model previously elaborated by Ludewig et al. (28) by adding a tumor compartment. In particular, they took into account tumor-immune system parameters such as immune cell trafficking rates to and from the tumor, effector cell deactivation rates by tumor cells, effector cell death rates, intrinsic tumor growth rates, and tumor cell kill rates by effector cells (27). The interactions of T 8, D and T were described by:

Interactions between CD8 + and tumor cells
where E a tumor is the number of CD8 + cells within the tumor, T is the number of tumor cells, m BTE is the T-dependent rate at which effector cells enter the tumor compartment from the blood, E a blood is the number of CD8 + cells in the blood, a EaT is the death rate of activated CD8 + in the tumor [estimated at 0.462/day (29)], c is the rate at which activated CD8 + are inactivated by T [estimated at 9.42 x 10 -12 cells x day (27)];

Interations between tumor and dendritic cells
where D tumor is the number of tumor-infiltrating dendritic cells, m is the maximum recruitment rate of DCs to tumor site [estimated at 2.4388 x 10 4 cells/day (27)], q is the value of T necessary for half-maximal DC recruitment [estimated at 100 cells (27)], m TB is the rate of dendritic cell transfer from tumor to blood [estimated at 0.0011/day (27)], and a D is the natural death rate of dendritic cells [0.2310/day (28)].

MACRO: EXOSOME-BASED COMMUNICATION BETWEEN PRIMARY TUMOR AND METASTASES
As reported above, tumor-derived exosomes promotes the invasiveness and motility of tumor cells from the primary site to metastatic niches (12,13) (Figure 2). By analyzing different cell lines, Yu et al. (31) observed 79 proteins that were differently expressed in exosomes between more and less metastatic tumors, and these proteins were implicated in cell adhesion, invasion, growth, metabolism and metastasis (31). Tumor-derived exosomes are crucial for the formation of pre-metastatic niches (32), which are necessary for the creation of a suitable environment for circulating tumor cells (CTCs) colonization and growing within a secondary site (33). The choice of metastatic sites is orchestrated by the primary tumor through secreted factors, with exosomes representing the main extravescicular population that mediates long-range signaling during metastasis (34)(35)(36). Exosome proteomics revealed distinct integrin expression patterns that could be used to predict organspecific metastasis (37). For example, exosomalintegrinsa6b4 and a6b1 were linked to lung metastases, while avb5 was associated to liver metastases (37), supporting the organotropism of tumor-derived exosomes.
If we assume that the production of tumor exosomes E c and the release of their content upon encountering cancer cells can be described by: We can derive that the diffusion of tumor-derived exosomes from primary tumor to pre-metastatic niches (D Ec DE c ) can be described by:

Diffusion of exosomes from primary tumor to metastastic cells
Where l Ec is the production rate of E c and Kc indicates cancer cell saturation.
The diffusion of tumor-derived exosomes (D Ec ) from the primary tumor the pre-metastatic niche can be estimated through considering the average diameters of exosomes (70 nm) at1.23 x 10 -4 cm 2 /day (15). The release of E c promotes the initial phases of tumor invasion and metastatization, described by the model we adapted from that proposed by Lai and Friedman (38):

Tumor apoptosis
where D c is the diffusion coefficient of cancer cells, c∇ (C ∇C)