The integration of the physiological systems that conform the human body and its operation can be considered an open structure with characteristics of a complex system that are the result of the large number of system components that comprise it, and the coupling and interactions between them (Bashan et al., 2012). The non-linear interaction of these components, their self-organization, emergent behavior, scale invariance, in addition to their adaptability, support the functional balance required for life (Rivera et al., 2020). In this context, proper functionality and adaptability are necessary to maintain health. Homeostasis is given by the balance between robustness, which define a system and its conformation, and adaptability (which is the ability of the system to respond to changes in the environment) while preserving its functionality (Fossion et al., 2018). Loss of this balance leads to disease. The systemic interactions within human physiology change as a function of many factors, age and sex being prominent examples. Here, by “sex” we refer to “the classification as male or female according to reproductive organs and functions assigned by the chromosomal complement” (Institute of Medicine (US) Committee on Understanding the Biology of Sex and Gender Differences, 2001). The expression of this sexual differentiation produces changes in many organ systems and across the lifespan of the individual, influencing how our bodies interact with the environment to determine health (Rich-Edwards et al., 2018). In this way, sex is recognized as a genetic modifier of disease pathophysiology, resulting in variations which should be considered in the biomedical enterprise (Mauvais-Jarvis et al., 2020).

There is ample evidence that the mechanisms underlying the regulation of various homeostatic processes are different in men and women. Physiologically, differences have been found in the function and morphology, for example, of the distribution and metabolism of adipose tissue (Palmer and Clegg, 2015), leading to the development of different types of obesity in women and men (Lumish et al., 2020). At the central nervous system level, morphological differences have been demonstrated in terms of structures and information processing: For instance, the thickness of the cortical mantle is greater in women than in men; also, memory consolidation is also different between sexes (Maren et al., 1994; Piefke et al., 2005). Other examples of physiological differences are specific pathologies such as neurodevelopmental disorders and neurodegenerative diseases, which are more frequent in men than in women (Hanamsagar and Bilbo, 2016), while on the other hand it is known that women have a greater predisposition to develop autoimmune diseases (Ngo et al., 2014), or gastrointestinal problems such as achalasia (Furuzawa-Carballeda et al., 2015; Rivera et al., 2021). The response to different pathogens also seems to depend on sex (McClelland and Smith, 2011). In the cardiovascular system, various studies provide evidence that men have a greater predisposition to develop cardiovascular diseases (Lloyd-Jones et al., 1999), greater cardiovascular mortality due to them (Regitz-Zagrosek, 2006), such that the risk factors between men and women are different. For example, while the average age at which women tend to experience myocardial infarction is higher than that of men, variables such as hypertension, diabetes and smoking result in significantly higher hazard ratios of myocardial infarction in women than in men (Mauvais-Jarvis et al., 2020). Metabolic syndrome may also develop differently due to physiological sexual dimorphism, as has been seen in other animals (Velasco et al., 2020).

Sex-based differences in normal physiology, including those dependent on the endocrine system, are present and have been described in isolation for many physiological systems. However, to examine system-wide properties and interactions, new methodologies are necessary. Here we use time series analysis (Fossion et al., 2018) and network theory applied to data mining (Stephens et al., 2020) as two complementary approaches to study relations between physiological variables and their variability (Fossion et al., 2017). Cardiovascular coupling is a representative example of homeostatic regulation between different systems influenced by sex that is easily captured by several physiological time series. According to the control theory applied to homeostasis, physiological control systems are able to maintain the values of regulated variables that are vital for the organism within “normal” ranges because of the physiological responses of the corresponding effector variables which increase their variability (Fossion et al., 2018). In the cardiovascular system, heart rate serves as a regulatory variable and blood pressure as a regulated variable to sustain perfusion in the tissues. Different conditions and variations in metabolic activity induce changes in frequency and amplitude of the pulmonary and cardiac cycles in conjunction with vascular resistance and capacitance to provide an adequate constant oxygen supply. Modulation of these couplings is multidirectional in order to preserve homeostasis, and both acute and chronic diseases change this modulation through different pathophysiological mechanisms. This physiological modulation exhibits sex-based differences, and cyclic changes along the ovarian cycle phases (Figure 1). By examining differences in this modulation through time series analysis, different aspects of coupling are studied.

Sex differences are widespread across physiology, and may be classified as sex chromosome effects as well as hormonal effects that are either organizational or activational (Arnold et al., 2009). Therefore, physiological differences between men and women also occur in systems that are not easily recordable by continuous monitoring, and are instead widely approached through transversal studies of human populations. To take advantage of the wide selection of physiological variables available for transversal studies, correlation matrices in narrow-age cohorts can be used to construct complex inference networks (Hofer and Sliwinski, 2001; Batushansky et al., 2016; Barajas-Martínez et al., 2020, 2021; Cohen et al., 2021). Complex inference networks allow to find and explore statistical associations from the perspective of network theory, which provides a natural way to describe the relationships between a large set of entities (Stephens et al., 2018). Through networks, biological systems can be described by both graph-theoretical metrics as well as visual analysis (Aittokallio and Schwikowski, 2006; Merico et al., 2009; Pavlopoulos et al., 2011). This approach provides the possibility of observing the aggregate behavior of the system, offering insights on the function and structure of the system (Arnold et al., 2009; Jansson, 2020).

Historically, basic and clinical research has been carried out preferably in men or male animals. The bias to use male animals is based on reasons that have to do with the practicality of the study. For example, the preference for using male animals may be due to the fact that individuals are usually larger and therefore easier to manipulate when dissecting, or having better access in neurological studies for example. Another justification is that they do not have estrous cycles that strongly alter various physiological variables. There are also specific considerations such as the possibility of a differential response to treatment between men and women, and it is specifically for this reason that gender disparities should not be overlooked (Buoncervello et al., 2017). From preclinical studies (in animal models) to clinical studies, the study of the mechanisms involved in the appearance of many pathologies must consider the existence of different behavior and regulatory mechanisms between sexes, which is why there are explicit recommendations to include both sexes in preclinical studies (Sandberg et al., 2015) and to consider it in clinical treatment and evaluation (Mauvais-Jarvis et al., 2020). The aim of this study is to explore differences in the properties of the physiological systems of women and men using integrative approaches.

The present contribution analyzes the differences that exist in physiological regulation mechanisms between women and men. To see these differences on one physiological variable (cardiac frequency) was studied by the time series obtained from electrocardiographic records of men and women from the Fantasia database of Physionet (Iyengar et al., 1996; Goldberger et al., 2000). To see systemic differences, a network analysis of biochemical and anthropometric biomarkers was carried out using a database of healthy men and women, using the physiological network model previously reported by our research group in Barajas-Martínez et al. (2021).

Significant differences on the physiology of men and women were found using two complementary analysis: a univariate physiological time series study carry-on in heart rate variability (section “Analysis of Heart Rate Variability Using the Physionet Fantasia Database”) and a systemic approach by a physiological network construction (section “Physiological Network”).

There is a close relationship between indices of sympathetic activity and vascular resistance in men as a function of age (Joyner et al., 2016). This relationship is absent in young women, but is noticeable in postmenopausal women. These sex and age differences are related to vascular resistance, and are the result of changes in the balance between the receptors responsible for arterial tone, i.e., vasoconstriction and vasodilation (Joyner et al., 2016). In young men, there is a relationship between neuromuscular sympathetic activity (NSA) and total peripheral resistance (TPR). However, this relationship is not associated with blood pressure, but is due to the fact that cardiac output is inversely proportional to NSA and TPR. In contrast, in young women, there is no relationship between NSA and TPR, due to the vasodilator mechanism of B-adrenergic receptors, which counteract the vasoconstriction of A-adrenergic receptors. Therefore, blood pressure is not related to NSA in young women (Joyner et al., 2016).

Sympathetic activity also affects the cardiovascular system; thus, it would produce different heart rate variability signals depending on age and sex. The cardiovascular system is one of the most regulated systems in the human body, and its study sets the tone for a great tradition of research and innovation. In the context of this characteristic integration of several systems, it has been established that significant differences occur between men and women in physiological regulation. The analysis of the time series of cardiac activity provides indicators of the functioning of the system and also of the effect of the parasympathetic and vagal modulation to which it may be subjected. The analysis of these fluctuations allows to know the state of these oscillators with respect to sympathetic and vagal modulation (Berntson et al., 1997). The analysis of the statistical moments provides indicators of the degree of rigidity or adaptability of the physiological system (Rivera et al., 2016, 2018).

For the case of Fantasia database, statistical moments shows that in young women RR is more rigid and less variable than for men, and that in old age the variability presented by men is lost, becoming a rigid system. With respect to Poincare’s plots, young men have the most elliptic distributions, related with low correlations, and old men the most linear ones indicating stronger correlations, rigid distributions. Women statistical parameters change less than the ones of men, suggesting that the heart rate variability is more “robust” and correlated.

In contrast, Shannon’s entropy for young subjects is in the same region for women and men, and it is statistically significant different between old women and men. The change of entropy between young and old women is small compare with the suffer by men. Considering Shannon’s entropy as a measure of the facility to transmit information on the time series, for a constant signal the value will be zero (that corresponds to a “death” subject), and the larger the value better information transmission will be in the system. Similar values of entropy for young subjects indicate a “good” homeostatic balance independent of sex, with aging this entropy have a slow decrease for women, but a stronger change in men, that goes for old men close to zero. This may be one of the many factors that made heart rate variability a vulnerability factor for death incidence greater in old men.

We have reported previously how node centrality measures show the role of physiological variables within the physiological networks, how these roles change with age (Barajas-Martínez et al., 2020), and how topological and algorithmic community detection reveals functional clusters (Barajas-Martínez et al., 2021). Through this methodology, we have constructed physiological networks to describe how the changes in the coupling between regulated variables and those regulatory systems that try to maintain homeostasis may differ between young healthy men and women. Here we interpret the lack of correlation as one variable not being dependent on another. Some correlations are suggestive of a vulnerability of the system to develop a pathologic state (even when all values are within normal parameters and disease onset has yet to happen), while others indicate a healthy physiological coordination. In the differential network we found sex-dependent differences in several nodes. We found that for men urea levels are correlated with BMI and related anthropometric indicators but not for women, being both equally young healthy subjects that have urea, creatinine, and eGFR within the normal range (Figures 6, 8). Likewise, for men creatinine was related to insulin and HOMA, but not for women. This is notable in the context of the urea/creatinine ratio, an indicative of acute muscle catabolism, being higher for women (Figure 11). This reinforces the hypothesis, as previously suggested in the literature, that men have a greater difficulty in maintaining homeostasis between food intake and uremic solute clearance for the same level of eGFR (Nitsch, 2014). Another difference we found between sexes was the correlation between blood pressure and hemoglobin in men (Figures 6, 8). This correlation has been found for both men and women in a large cohort of Dutch voluntary blood donors and was attributed to erythropoietin, renin-angiotensin-aldosterone system or the mechanic effects of blood viscosity (Atsma et al., 2012). It is possible that a larger sample is required to observe the effect on both sexes, or that the age difference with our sample is behind this discrepancy. Nonetheless, we notice that both erythropoietin responsiveness and renin-angiotensin-aldosterone have sex differences that may also play a role (Ifudu et al., 2001; Komukai et al., 2010). Only in men, plycometric measurement of skinfolds was correlated with HDL, estimated average glucose and HbA1c (Figures 6, 8), even when both sexes had similar glucose variability (Figure 11). Glucose and lipid metabolism are directly modulated by sexual hormones, resulting in different combinations of the clustering of metabolic syndrome factors (Regitz-Zagrosek et al., 2007; Kuk and Ardern, 2010). Finally, we observed different correlations of neutrophils in men and women. While neutrophil variables were associated with insulin, HOMA and plycometry in women, they were correlated with body composition measurements by bioimpedance in men. This may be due to differences in the adipose tissue patterns that depend on sex, with subcutaneous fat being more abundant in women and visceral fat in men (Lumish et al., 2020). These proinflammatory associations in neutrophils have been found for both sexes (Ibáñez et al., 2005; Xu et al., 2015). It is important to mention that the correlations discovered in this work are the result of a network that has been filtered using a p-value threshold. Other strategies, however, are possible. For example, a multiple comparison correction could be added to aid in the selection of significant correlations. Another strategy is to use a bootstrap value threshold to identify correlations that occur frequently and are thus more robust. Row bootstrap or pair bootstrap methods can be used for this purpose (Musciotto et al., 2018). We use a row bootstrap approach to determine whether the differences in topological properties between sexes are robust. This same procedure could be used to further filter the network’s correlations.

On the level of whole network analysis, we found that despite the apparent differences in connections between sexes, each physiological variable played similar roles in terms of influence (eigencentrality) and intermediation (betweenness). Additionally, algorithmic clustering was similar for both physiological networks (Table 4). Furthermore, the hierarchical arrangement of nodes shows a similar structure for both sexes (Figure 9). This suggests that global functions of the systems are largely the same. The most notable difference in topology results from the density and modularity of the network, as a result the physiological network of men has a greater small-world index (Figure 7). Consequently, the physiological network of men was more vulnerable to degree-directed attacks, and women’s physiological network was resilient to random failure (Figure 10). Lastly, deviation from normality was higher for physiological variables of men than those for women (Figure 11). All things considered, the physiological network of women indicates a more resilient homeostatic regulation that restrains regulated variables within strict ranges, and as a result, network properties such as small-world and modularity are decreased. Taking into account this assortment of approaches, we suggest important differences in the resilience and adaptability of physiological systems in men and women. In the context of the network representation of physiological systems, a network is resilient to attacks if it contains a large number of alternative paths that maintain the system’s connectedness and thus coordination. This increase in a system’s robustness comes at the expense of its component’s flexibility. An adaptable network has a higher modularity, allowing components to operate independently while retaining the small world topology that enables rapid communication within the network. This, however, exposes the network to targeted attacks. Figure 10 is a simulation of a directed attack with the purpose of highlighting differences between men and women in the structural response to attack in networks. One real-world example may be the different structural response to an infection with SARS-CoV2, where being male has been considered as a risk factor (Peckham et al., 2020), possibly due to a less resilient physiological network with respect to women.

It is important here to point out that the aim of our work is to characterize the function and properties of physiological systems in men and women. In this sense, the meaning of the words “adaptable,” “robust,” and “resilient” are not intended to describe individuals but the physiological systems. Additionally, when searching for sex differences, caution is advised in “big data” approaches to consider confounding factors that may be involved due to the risk of finding sex differences where none exist (type I error) (Rich-Edwards et al., 2018). To attenuate this risk, we performed a narrow-age cohort from a specific population, the participants were then filtered by health criteria presented on Tables 1, 2 to ensure a well-defined sample as much as possible. The database from which these healthy young subjects were selected has also an extensive questionnaire on socio-economic status and health risks. Finally, by using a network approach, conclusions are drawn in the context of the whole instead of relying in any single correlation in isolation. Despite the fact that bivariate similarity tests are easy to understand and represent, higher-order correlations cannot be taken into account by this analysis. As a result, in order to inspect these correlations, other methodologies would need to be added.

We examined the differences between the sexes in the coordination of physiological systems by means of two methodologies: time series analysis of the specific variable of heart interbeat intervals and physiological networks constructed from point measurements of 62 different variables (50 variables directly measured related to anthropometry, bioimpedance, hematic biometry, blood chemistry, and 12 derived variables). We show consistency in the existence of sex differences both in the dynamics of heart rate as in the architecture of physiological networks. In youth, men have higher heart rate variability than women, as measured, e.g., with standard deviation or SD1 and SD2 of Poincaré plots, but with aging this variability is lost at a more rapid rate in men than in women. This effect is even more evident using Shannon entropy, which shows that entropy of heart interbeat intervals tends to be conserved in women but decreases drastically with aging in men. With respect to physiological networks, women have a higher connectedness, density and clustering coefficients, whereas men have higher modularity, eigencentrality and small-world index. Efficiency, node strength and measures that depend on the path structure of the network were similar for men and women. There were no differences in susceptibility to random failure between men and women, but the network of men was more vulnerable to directed attacks than the network of women. Both methodologies suggest that the physiological system of women has a greater number of connections, which translates into redundant regulation mechanisms and, on the other hand, has less variability with respect to that of men, that is, it is a more resilient system.

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author/s.

The studies involving human participants were reviewed and approved by the Ethics Committee of the Facultad de Medicina of the Universidad Nacional Autónoma de México (UNAM) under project FM/DI/023/2014. The patients/participants provided their written informed consent to participate in this study.

AB-M, EI-C, and AR performed the network modeling and wrote the manuscript. CS did the conceptualization of the project for dataset of Project_42 and funding acquisition. AB-M and JL-R participated in data collection. AR, JL-R, RL, and JG did the data curation. AB-M, EI-C, JL-R, RL, JG, and AR performed the data analysis. AR, AB-M, EI-C, RF, JT-R, BE, OR-A, and AF participated in the complexity interpretation and analysis of the results. VM-G, GT-S, CA-S, BE, NT, AT, and MH participated in the medical interpretation. All authors contributed with the manuscript revision, read, and approved the final version of the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.