*Article* **Incorporating Fuzzy Logic in Harrod's Economic Growth Model**

**Joan Carles Ferrer-Comalat 1,\*, Salvador Linares-Mustarós 1 and Ricard Rigall-Torrent 2**

**Abstract:** This paper suggests the possibility of incorporating the methodology of fuzzy logic theory into Harrod's economic growth model, a classic model of economic dynamics for studying the growth of a developing economy based on the assumption that an economy with only savings and investment income is in equilibrium when savings are equal to investment. This model was the first precursor to exogenous growth models, which in turn gave rise to endogenous growth models. This article therefore represents a first step towards introducing fuzzy logic into economic growth models. The study concerned considers consumption and savings to depend on income by means of uncertain factors, and investment to depend on the variation of income through the accelerator factor, which we consider uncertain. These conditions are used to determine the equilibrium growth rate of income and investment, as well as the uncertain values for these variables in terms of fuzzy numbers. As a result, the new model is shown to expand the classical model by incorporating uncertainty into its variables.

**Citation:** Ferrer-Comalat, J.C.; Linares-Mustarós, S.; Rigall-Torrent, R. Incorporating Fuzzy Logic in Harrod's Economic Growth Model. *Mathematics* **2021**, *9*, 2194. https:// doi.org/10.3390/math9182194

Academic Editors: Jorge de Andres Sanchez and Laura González-Vila Puchades

Received: 29 June 2021 Accepted: 6 September 2021 Published: 8 September 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Keywords:** fuzzy logic; fuzzy arithmetic; extension principle; economic models; Harrod's growth


**Author details**

Indranil Biswas1 and Gausal A. Khan2 \*

1 Cardiovascular Biology Research Program, Oklahoma Medical Research Foundation, Oklahoma City, OK, USA

2 Department of Physiology, Fiji School of Medicine, Fiji National University, Suva, Fiji Islands

\*Address all correspondence to<EMAIL_ADDRESS>
© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


**Acknowledgements**

clinical diagnosis of schizophrenia. These findings implicate that the emotional salience detection of voices differentiate the negative and positive symptoms in neuropsychiatric

The emotional prosody was also examined in those with congenital amusia (a specific neu‐ rodevelopmental disorder featured as tone‐deafness, [32]). Lu et al. [32] presented emotional words spoken with declarative or the question voice to the amusics and their healthy control. The N1 was reduced and the N2 was increased in incongruent voice. The modulation of N1 was intact whereas the change in N2 was reduced in amusics, suggesting an impaired conflict processing in amusia. The authors argued that the impaired discrimination of speech intona‐ tion among amusic individuals may arise from an inability to access information extracted at

One application of these studies is to build an artificial intelligence to decode brain signals which contribute to socioemotion understanding. Most of the studies use the acted (posted) vocal expression as testing materials, which were produced by professional actors, public speakers, or amateurs to portray an intended emotion. In real‐life communication, the com‐ municators may use such emotional pose to achieve certain communicative goals. Some research purpose, for example, the cultural display in vocal expression communication, may be specifically favored by using posed stimuli. However, a call for research on naturalistic, ecological, and observation‐based stimuli is highly recommended. Therefore, a future study is to examine how the brain differentiates "real" vs. "fake" vocal expression by looking at the

Another implication of using EEG signals to study vocal emotion decoding is to test the effectiveness of speech‐coding strategies used in hearing aids for deaf listeners when they distinguish the emotions via prosody‐specific features of language [33, 34]. In Agrawal et al. [33], statements simulated with different speech‐encoding strategies differentiated the P200 in the happy expression and an early (0–400 ms) and late (600–1200 ms) gamma band power increase in vocal expressions of happiness, anger, and neutral. In Agrawal et al. [34], the P200 was differentiated by different simulation strategies in all types of emotions, and was larger in happiness than in other emotion types across speech‐encoding strategies. These studies emphasized the importance of vocoded simulation to better understand the prosodic cues which cochlear impairment users may be utilizing to decode emotion in the voice. Further studies will also draw upon the merits of multimodal recording and synchroniza‐ tion of neurophysiological and peripheral physiological responses to decoding vocal expres‐ sions, including eye movement, pupil dilation, heart rate tracking, etc., to understand how different systems support the understanding of social and emotional information in speech

disorders at the preattentive level.

54 Emotion and Attention Recognition Based on Biological Signals and Images

**7. Applications and future directions**

early processing stages.

neurophysiological responses.

and vocalizations.

Special thanks to Professor Dr. Marc D. Pell who leads the Neuropragmatics and Emotion Lab in the School of Communication Sciences and Disorders, the McLaughlin Scholarship and McGill MedStar by Faculty of Medicine, McGill University that were awarded to the author.


**7. Conclusions**

The problem of energy consumption optimization in manufacturing systems has received attention with the rising concern of sustainability. This paper reviews articles in the field of energy optimization of O&M of manufacturing systems, covering several aspects related to the optimization procedures such as model construction, solution methods, and application areas. The main contributions of this paper are as follows:

For the research related to energy optimization, we believe that it has high application value and vast research space. Through reasonable O&M scheduling, energy savings can be achieved without changing production system structures, which will pave the way for the progressive promotion of sustainable manufacturing paradigms. Research in this area is expected to achieve greater attention and policy preferences. The systematic review of this paper can provide some references for future studies.

**Author Contributions:** Conceptualization, methodology, investigation, writing—original draft preparation, X.A.; editing, visualization, G.S.; validation, formal analysis, Q.L.; writing—review, supervision, project administration, funding acquisition, T.X.; data curation, Y.L.; resources, funding acquisition, R.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key R&D Program of China (No. 2022YFF0605700), National Natural Science Foundation of China (No. 51875359 and 71971139), Natural Science Foundation of Shanghai (No. 20ZR1428600), Shanghai Science and Technology Innovation Center for System Engineering of Commercial Aircraft (No. FASE-2021-M7), Oceanic Interdisciplinary Program of Shanghai Jiao Tong University (No. SL2021MS008), and CSSC-SJTU Marine Equipment Forward Looking Innovation Foundation (No. 22B010432).

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors are indebted to the reviewers and editors for their constructive comments, which greatly improved the contents and exposition of this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.


*5.3.2. Fusarium*

*Fusarium* spp. are well known saprophytes in soil, as well as the cause of a range of plant diseases. However, they also often cause hyalohyphomycosis after traumatic inoculation in humans and seem to be an emerging pathogen in immuno-compromised patients [16]. In cetaceans, mycotic dermatitis caused by a *Fusarium* sp., was reported in a pygmy sperm whale and an Atlantic white-sided dolphin. These cetaceans were characterized by elevated, firm, erythematous, cutaneous tubercles mostly found on the heads, trunks and caudal portions of the cetaceans' bodies [31].


*2.2.2 APMC admin services*

APMC is advertising board set up by state government in India to guarantee reasonable promoting for the farmer's yield. The services offered by the APMC admin are as follows.

5.Insurance – It facilitates the admin to approve or reject the insurance claimed by the farmer by verifying the criteria.

In this section, the block diagram of the proposed model and description of its process flow is explained briefly. Detailed discussion and data flow diagrams of each module is explained in subsequent chapter. The soil nutrient and pH of irrigation water testing using IoT enabled sensor technology is explained.


**1. Introduction**

Breast cancer is one of the most common neoplasia in women, representing about 25% of all most cancer instances in women, and is the second main purpose of most cancer deaths in advanced countries [1]. The search for therapies for this pathology is an expanding field in medical research.

Melatonin is an indoleamine secreted in particular with the aid of using the pineal gland with circadian rhythmicity. Melatonin represents one of the links between circadian disruption and cancer development. The role of this hormone in the regulation of cancer cell growth has been extensively investigated and many studies have pointed out the oncostatic properties of melatonin against different neoplasia, including breast cancer, ovarian, skin, lymphomas, leukemia, sarcoma, hepatocarcinoma,

colorectal cancer, melanoma, lung cancer, endometrial and cervical cancer, prostate cancer, larynx carcinoma, neural tumors, and pancreatic cancer [2]. Melatonin production takes place mainly during the night in the pineal gland. However, its synthesis is also produced in other parts of the body, including gastrointestinal tract [3]. Specifically, gut cells synthesize great quantities of this indoleamine [4]. Apart from this, melatonin can be produced by gut microbiota directly or indirectly, since microbiota produces short-chain fatty acids (SCFAs), which stimulate serotonin production. Serotonin by the action of two enzymes (arylalkylamine-N-acetyltransferase (AANAT) together with 14–3-3 proteins for its stabilization, and acetylserotonin O-methyltransferase (ASMT)) is converted into melatonin [5].

The melatonergic pathway starts with the uptake of tryptophan (Trp) [6]. This important amino acid is needed for lifestyle and growth, however, is not synthesized via way of means of the organism. In the body, Trp is transported around the periphery either bounded to albumin (90%) or in free form (10%) [7]. Trp can act as a precursor of different pathways once in the central nervous system (CNS). First, kynurenine pathway constitutes the major catabolism route (95% of whole Trp dietary intake) [8]. In second place, 3% of Trp is converted into tryptamine by decarboxylation or into indol-3-pyruvic acid by transamination. Thirdly, about 1% of Trp is used for protein synthesis, and finally, the melatonergic pathway is over 1% of whole Trp intake, being this route through which serotonin and melatonin synthesis is done [9].

The kynurenine pathway begins with the action of the rate-limiting enzymes Trp-2,3-dioxygenase (TDO) and indoleamine-2,3-dioxygenase (IDO-1 and IDO-2) [10]. TDO is an enzyme that is mainly expressed in the liver, apart from other organs such as the brain, where it is found in low quantities. TDO expression is induced by oxidative stress [9, 10]. In contrast, IDO-1 is found primarily in extrahepatic tissues such as the lungs, brain, or kidneys [9, 10]. IDO-1 expression is induced by lipopolysaccharides (LPS), amyloid peptides, human immunodeficiency virus (HIV) proteins [10], tumor necrosis factor-alpha (TNF-α), interferon gamma (IFN-γ), and by different proinflammatory cytokines, including interleukin-1beta (IL-1 β), IL-6, and IL-18 [8]. Thanks to the action of TDO and IDO, Trp is converted into kynurenine (KYN), which activates the aryl hydrocarbon receptor (AhR) [9]. After this activation, AhR/cytochrome P450 (CYP1B1) pathway starts, being this pathway fundamental in breast cancer [11]. After, CYP1B1 stimulates N-acetylserotonin (NAS) conversion from melatonin, causing an increase in NAS/melatonin ratio and a reduction in melatonin levels [12]. NAS induces the dimerization and activation of tyrosine kinase B receptors (TrkB) and the stimulation of the AKT and extracellular signal-regulated protein kinases 1 and 2 (ERK1/2) pathways [13], which are implicated in the survival, proliferation, invasion, and migration of breast cancer cells and their resistance to the different therapies.

As previously described, the kynurenine pathway is implicated in the development of breast cancer. Apart from this, it has been implicated in a wide range of diseases and disorders, including inflammatory processes, infectious diseases, neurological disorders, Huntington's disease, affective disorders, autoimmune diseases, peripheral conditions, and cancer progression. A key indicator of cancer progression is often the upregulation in IDO-1, resulting in an accelerated and sustained degradation in Trp [8]. Tryptophan degradation products through the kynurenine pathway exhibit neuromodulatory and inflammatory effects and have been related to cancer development and tumor progression [9]. Glioblastoma sufferers with a high-ratio KYN/ Trp had a bad evolution and occasional survival as compared with sufferers with a decrease ratio [14].

#### *DOI: http://dx.doi.org/10.5772/intechopen.106068 A Promising Challenge in the Link between Melatonin and Breast Cancer…*

The importance of the kynurenine pathway during cancer development has encouraged recent studies on the use of IDO inhibitors as a therapeutic strategy for treatment of breast, lung, and ovarian cancer [9]. Suppression of IDO and TDO would lead to a decrease in kynurenine production [15]. It is a novel therapeutic target in cancer research and the results have been positive. Using transgenic mouse model of breast cancer, IDO-1 inhibitors, 1-methyltryptophan (1-MT), and methylthiohydantoin-tryptophan were able to potentiate the efficacy of chemotherapy drugs, promoting tumor regression without increasing the side effects [16]. 1-MT, a competitive IDO inhibitor, has been tested and approved in phase I clinical trials in patients with metastatic neoplasms as well as in lung, ovarian, Fallopian tube, and breast cancers displaying sickness stabilization in many cases [17–20].

In addition, the alterations in the melatonergic pathway that occurred in breast cancer cells produce changes in gut permeability and microbiome composition accompanied by a reduction in butyrate levels and an increase in LPS, leading to a pro-inflammatory response, and increasing the production of Trp catabolites, thus decreasing the melatonin production [21].

Therefore, a bidirectional flow is observed between alterations in the composition of the microbiota (dysbiosis), the production of melatonin levels (circadian disruption), and breast cancer. Thus, in this chapter, we will deal with the properties of melatonin, highlighting its antiestrogenic properties, and its relationship with the microbiota and breast cancer.

#### **2. Melatonin interaction molecules**

Melatonin has different actions depending on its binding to specific receptors. On the one hand, melatonin activates MT1, MT2, and MT3 cell membrane receptors coupled to Gi protein [22]. This hormone binds to these receptors, reducing cAMP levels, thus counteracting the estrogen-induced estrogen receptor alpha (ERα) transcriptional activity by interacting with the cAMP signaling cascade [22] and thus suppressing adenylate cyclase [23].

On the other hand, melatonin binds to calmodulin (CaM), behaving as an antagonist capable of binding and inactivating the Ca2+/CaM complex. CaM is important in the activation of ERα, by facilitating its association with other coactivators and binding to the estrogen response element (ERE) [24]. Melatonin inactivates the Ca2+/CaM complex, inhibiting CAM-dependent estradiol-induced transactivation of the ER [25].

Besides, melatonin interacts with the retinoic Z receptor/retinoid, receptor-related orphan nuclear receptor alpha and beta (RZR/RORα and RORβ) superfamily. The estrogen-induced transcriptional activity of ERα is due to the overexpression of these receptors and its effects can be inhibited by melatonin by the activation of MT1 or by inhibiting CaM [26].

Finally, melatonin is described as an antioxidant. It transfers electrons to hydroxyl radicals, superoxide anions, hydrogen peroxide, hypochlorous acid, nitric oxide, and peroxynitric anions [27]. Furthermore, melatonin stimulates the expression of antioxidant enzymes, being a powerful free radical scavenger [28, 29].

#### **2.1 Melatonin actions in cancer**

Melatonin has been widely described in the literature as a potential antitumor agent due to its several antitumoral properties [30]. Firstly, melatonin is a powerful antioxidant molecule that neutralizes the free radicals that induce carcinogen modifications in the DNA and cause cell nuclear damage, preventing the appearance of cancer [31].

Secondly, melatonin is known to prevent circadian disruption that occurs frequently in women who work night shifts by exposure to artificial light at night (ALAN) [32]. Therefore, this hormone synchronizes the circadian rhythms with ambient light [33].

Furthermore, melatonin regulates fat metabolism since it prevents the linoleic acid adsorption. This fatty acid activates the epidermal growth factor (EGF), mitogenactivated kinases (MAPK), and ERK1/2 pathways, promoting the proliferation and growth of the tumor. Thus, melatonin can prevent cancer by inhibiting the acid linoleic adsorption [30].

On the other hand, melatonin is known to regulate cell cycle. The Trp-derivated causes the arrest of cell cycle by lengthening the GAP1 (G1) growth phase, thus delaying the entrance to the synthesis (S) and mitosis (M) phases [34]. For this reason, melatonin has antiproliferative actions. Besides, melatonin stimulates apoptosis process of the tumoral cells by increasing p53 expression [35, 36].

Also, low levels of melatonin are related to alterations in the immune system [33]. Melatonin stimulates immune system mediated by interleukins and other cytokines in monocytes and lymphocytes, reducing tumor cell survival and proliferation [28].

Apart from these antitumoral actions, melatonin inhibits angiogenesis by avoiding the different steps in this process. In fact, this hormone inhibits invasion, migration [37], and metastasis of tumoral cells [38], thus preventing tumoral cells from entering to the vascular system and inhibiting tumoral angiogenesis [39].

Additionally, melatonin also inhibits telomerase activity, which is stimulated in breast cancer cells [40]. Telomerase activity is responsible to maintain the DNA stability, contributing to the cancer cells' immortality, and providing an unlimited capacity for the division of neoplastic cells [30]. Melatonin prevents the action of estrogen, cadmium, or estradiol-induced telomerase reverse transcriptase (hTERT) transcription in the breast cancer cells and reduces the transactivation of hTERT initiated by ERα [41].

 In the next section, we will deal with the actions of melatonin behaving as a selective estrogen modulator (SERM) or selective estrogen enzyme modulator (SEEM) in detail.

#### **2.2 Melatonin as a natural antiestrogen molecule**

Melatonin is a molecule that modifies the estrogen levels by altering the estrogen synthesis pathway preventing breast cancer. This hormone has direct actions at the level of the tumoral cell, behaving as a SERM [42]. On the one hand, it counteracts the effects of estrogen acting as a natural antiestrogen. Besides, melatonin binds to the MT1 receptor and avoids the binding between the estradiol (E2)-ERα complex to ERE and the initiation of transcription [25]. In addition, the literature has described another mechanism by which melatonin binds to calmodulin (CaM), preventing the binding of the E2-ERα complex to ERE and thus its transcription [25].

On the other hand, melatonin modulates the expression and activity of the different enzymes implies in the synthesis of estrogens (SEEM), thus reducing its levels. In concrete, melatonin reduces the expression and activity of aromatase, sulfatase

*DOI: http://dx.doi.org/10.5772/intechopen.106068 A Promising Challenge in the Link between Melatonin and Breast Cancer…*

(STS), and 17β-hydroxysteroid dehydrogenase (17βHSD) enzymes and enhances the expression and activity of estrogen sulfotransferase (EST). Aromatase is the enzyme responsible to convert the androgens into estrogens by the stimulation of its different promoters (promoter II, I.3 and I.4) [43]. Melatonin is able to inhibit this enzyme by inhibiting cyclooxygenase-2 (COX-2) and decreasing the production of prostaglandin E2 (PGE2), which reduces the levels of cAMP and indirectly decreases the activation of aromatase promoters and finally decreases the aromatase expression and activity, which will reduce the estrogen levels [44]. 17βHSD and sulfatase enzymes are the responsible for the conversion of biologically inactive estrogens into their active form. EST is the enzyme responsible to do the opposite action, converting the steroids into the active form [45]. Therefore, melatonin by modulating the expression and activity of these enzymes can prevent the development of breast cancer by reducing theestrogen levels [43].

Finally, melatonin has indirect actions on the hypothalamus-hypophysis-gonads axis, lowering the synthesis of ovarian estrogens and prolactin, which are fundamental in mammary growth [28].

#### **3. Melatonin and breast cancer**

Cohen et al. proposed that a reduction in melatonin levels induced an increase in estrogen levels, being the cause of the development of breast cancer [46]. Since then, there are numerous research that display the association between melatonin levels, estrogens and cancer progression [39]. There are studies in which women with low levels of circulating melatonin, suffer from breast cancer [28]. Specially, women with tumors with positive receptors to estrogen or progesterone, have lower nocturnal levels of melatonin than those with negative hormone receptors [47]. Furthermore, lower levels of 6-sulfatexymelatonin in the urine of breast cancer patients are observed, in comparison with women with benign pathologies [48]. Apart from this, it is described that shift work produces circadian disruption, reducing the production of melatonin and thus increasing the risk of breast cancer [30].

The uses of melatonin are demonstrated *in vitro*, *in vivo* and in some clinical trials. In regard to the *in vitro* studies, melatonin inhibits the proliferation of MCF-7 breast cancer cells through the inhibition of ERα [30]. Regarding the *in vivo* studies, most of them were performed in mice with mammary adenocarcinomas induced by chemical carcinogens [49]. In these studies, mice treated with melatonin, showed inhibition of mammary tumor growth [50]. Finally, most of the clinical trials with melatonin in cancer patients have been made by Lissoni and colleagues [51]. They demonstrated that melatonin can extend survival in metastatic cancer patients [51].

#### **3.1 Fat tissue, estrogens and breast cancer**

The link between obesity and breast cancer has been widely described in the literature. Obesity consists of excessive fat accumulation in white adipose tissue (WAT) in addition to hyperplasia and hypertrophy of adipocytes. These events cause chronic inflammation of WAT, constituting an important adipokines and triglycerides source which will be related with breast cancer development [52]. There are several adipokines secreted by adipose tissue that are implied with breast cancer [53]. Specially, increased leptin levels are related not only with breast cancer but also with obesity [54]. Leptin is the responsible for the mammary glands development and lactation, in addition to the breast cancer proliferation and invasion [55]. In fact, higher levels of leptin have been observed in women with breast cancer compared to healthy women. On the other hand, it has been described that adiponectin levels are inversely proportional to adiposity, exerting an inhibitory action on tumor growth and proliferation as well as stimulating apoptosis [56]. That is why lower levels of this adiponectin have been observed in patients with obesity [52]. Regarding insulin, obese and breast cancer women present higher circulating levels. Insulin induces proliferation of the breast cancer cells with ER+ by realizing growth factors that stimulate mitosis and inhibit apoptosis [57].  This protein binds to sex steroids, regulating their bioavailability in the bloodstream. Therefore, this is the reason by which obese women with breast cancer have elevated levels of estrogen in their breast tissues.

While the principle supply of estrogen in premenopausal women is the ovaries, in postmenopausal women estrogen synthesis is located in peripheral tissues along with WAT (which include mammary glands) and endothelial tissue [59]. In this case, estrogens are synthesized by transformation of androgenic precursors of adrenal origin or biologically inactive estrogens. Adipose tissue from mammary glands is composed of fibroblasts and endothelial cells. Breast cancer risk is correlated to the increased amount of adipose tissue, particularly in undifferentiated fibroblasts, due to this tissue has high aromatase activity, responsible for stimulating the synthesis of estrogens, and its promoters [60]. In normal breast tissue there is a high concentration of inactive steroids and the expression and activity of EST tend to be increased. In contrast, in breast tumor tissue, aromatase, 17βHSD, and steroid sulfatase (STS) tend to be overexpressed while EST expression and activity is decreased, resulting in an accumulation of 17beta-estradiol in breast tumor tissues [61, 62].

Estrogens are necessary to the malignant epithelial cells' growth. These cells produce antiadipogenic cytokines (IL-6, IL-11 and TNF-α and PGE2), that increase the cAMP levels which stimulate the aromatase promoters, giving place an up-regulation of aromatase expression in the preadipocytes. This is the reason why there are a great number of estrogens in adipose tissue fibroblasts. Furthermore, the antiadipogenic cytokines are responsible for the inhibition of the adipogenic cytokines, PPARγ and C/EBPα, stopping the differentiation of preadipocytes into mature adipocytes [63]. All these processes are known as desmoplastic reaction [64].

#### **3.2 Melatonin and desmoplastic reaction**

Melatonin stimulates the adipogenic cytokines, peroxisome proliferator-activated receptor gamma (PPARγ) and CCAAT-enhancer-binding proteins (C/EBPα), promoting the differentiation of preadipocytes into mature adipocytes [65]. Besides, melatonin inhibits the expression of aromatase promoters lowering the estrogen circulating levels [64]. This hormone is able to inhibit cyclooxygenase activity, thus reducing PGE2 levels, and decreasing intracellular cAMP. This fact will inhibit the aromatase promoters in peritumoral fibroblasts, reducing the expression and activity of aromatase and, therefore, the local estrogen levels in breast tissue [66]. Finally, melatonin reduces the antiadipogenic cytokines production in malignant epithelial cells, being related this with the aromatase expression.

As already has been described in a previous section, melatonin acts as a SEEM and SERM, reducing the estradiol concentrations in tumors, and therefore reducing the risk of breast cancer [42, 43, 67, 68].

### **4. Melatonin and the estrobolome in breast cancer**

It is known that both changes in the production of melatonin (circadian disruption) and the imbalance in the composition of the microbiota (dysbiosis) produce alterations in estrogen levels, which is one of the main risk factors for the development of breast cancer.

Bacterial composition of estrobolome in turn is probably affected by different factors, which can exert selective pressures on bacterial populations and can cause an imbalance or dysbiosis, which increases the risk of breast cancer due to elevated levels of circulating estrogens in postmenopausal women [69]. Melatonin modulates the composition of the microbiota and suppresses pathogenic bacteria in the gut due through its antioxidant activities [70]. Additionally, significantly, enteric cells and gut microbiota produce large amounts of melatonin. Circadian disruption, caused by sleep deprivation or exposure to constant light, causes an alteration in the composition of intestinal bacteria (dysbiosis) and affects the levels of melatonin [70]. Some authors demonstrated that exogenous melatonin supplementation restores microbiota composition [71] by reducing oxidative stress and the inflammatory response by suppressing toll-like receptor 4 (TLR4) expression, suggesting that melatonin may interact directly with gut microbiota. Thus, since melatonin modulates microbiota composition, involved in the pathogenesis of various cancers, a link exists between melatonin, microbiota, and the pathogenesis of cancer caused by dysbiosis [70].

Regarding breast cancer, gut microbiome is fundamental for the regulation of steroid hormone metabolism. It is crucial in the development of hormone receptorpositive breast cancer, whose circulating estrogen levels are the most important risk factor. Alterations in the bacterial composition of the estrobolome favor bacteria with β-glucuronidase activity, which deconjugate estrogens, favoring their enterohepatic circulation, causing their reabsorption and increasing the total estrogen load, and therefore increasing the risk of breast cancer [72].

On the other hand, melatonin increases the expression and activity of EST and reduces the expression and activity of STS, increasing the concentration of conjugated estrogens (biologically inactive) that are excreted in the bile and reducing the amount of deconjugated (biologically active) estrogens [44]. Therefore, this neurohormone exerts an activity opposite to the β-glucuronidase activity of intestinal bacteria, reducing the number of estrogens and lowering the risk of developing breast cancer [21].

Apart from this effect, changes in the intestinal microbiota activate the kynurenine pathway, moving Trp away from the melatonergic pathway and reducing the amount of melatonin and thus increasing the risk of breast cancer. In addition, butyrate favors the melatonergic pathway, so a reduction in this SCFA will produce a decrease in melatonin, increasing the NAS/melatonin ratio. NAS activates TrkB,

activating the PI3K/AKT, MAPK, and PLC/PKC pathways, which are involved in cancer cell survival, migration, invasion, and metastasis. Therefore, dysbiosis leads to lower concentrations of butyrate and melatonin, which can result in inflammation and an increase in estrogens in the bloodstream and, therefore, an increase in breast cancer risk [73].

## **5. Gut permeability, intestinal dysbiosis, and circadian disruption**

Dysbiosis and circadian disturbances induce the appearance of various diseases, including cancer. These disorders are characterized by an increase in gut permeability, which allows the passage of compounds such as LPS that interact with the immune system, causing inflammatory gut diseases [74].

A diet rich in fats and sugars causes an imbalance in bacteria composition, favoring the appearance of pathologies that are further pronounced by the circadian disruption [74]. This kind of diet has been shown to increase the abundance of Firmicutes, Proteobacteria, and Verrucomicrobia, and decrease the abundance of Bacteroidetes [74]. This dysbiosis is associated with a reduction in SCFAs production (especially butyrate) and an increase in the LPS levels, inducing gut permeability. Butyrate is related to the maintenance of gut barrier and the increased natural killer cytotoxicity, allowing the removal of viruses and cancer cells [75].

Increase in intestinal permeability is related to a reduction of calcium absorption produced by a vitamin D decreased [76], which produces a reduction in intestinal motility. This situation will allow the transfer of LPS to the circulation, which will activate the CD14/TLR2/4/MD2 pathogen recognition system [77]. The activation of this complex activates the Nuclear Factor kappa-light-chain-enhancer of activated B cells (NFkβ), activating the inflammatory cytokines and thus triggering strong autoimmune inflammatory activity that will be associated with cancer [76, 77]. Melatonin reduces the levels of these proinflammatory cytokines and inhibits NFkβ, modulating inflammation and reducing permeability [75, 78]. Furthermore, melatonin is able to reduce permeability by preserving mitochondrial-function mechanism [79] and releasing acetylcholine in the vagus nerve, which activates α7nAChR in intestinal cells [75, 80]. Apart from this, melatonin inhibits NOD-like Receptor 3 (NLRP3) and NOD-like Receptor pyrin domain-containing-6 (NLRP6), decreasing permeability [77]. Butyrate may also act as NLRP3 inhibitor, behaving similarly to melatonin [73].

On the other hand, circadian disruption induces an increase in proinflammatory cytokines, causing the loosening of tight junctions in intestinal epithelial cells and also increasing permeability [75]. When circadian disruption occurs, a significant increase in de abundance of Firmicutes is observed and this abundance was even higher when this situation is combined with a diet rich in fats and sugars. In addition, an increase in Ruminococcus and Sporosarcina was observed, accompanied by a reduction in Desulfosporosinus and Desulfotomocalum. Alternatively, melatonin can restore microbiota composition, reducing Clostridiales abundance and increasing Lactobacillus [81]. It is important to highlight that when circadian disruption occurs, there is an increase in the pro-inflammatory bacteria Ruminococcus and a reduction in the antiinflammatory bacteria Lactobacillus, which is associated with the NFkβ inhibition. All this suggests that circadian disruption favors inflammation and permeability, which are characteristics of cancers [74].