His and her mathematical models of physiological systems

Sexual Dimorphism in Substrate Metabolism During Exercise

During aerobic exercise, women oxidize significantly more lipids and less carbohydrates than men. This sexual dimorphism in substrate metabolism has been attributed, in part, to the observed differences in epinephrine and glucagon levels between men and women during exercise. To identify the underpinning candidate physiological mechanisms for these sex differences, we developed a sex-specific multi-scale mathematical model that relates cellular metabolism in the organs to whole-body responses during exercise. We conducted simulations to test the hypothesis that sex differences in the exercise-induced changes to epinephrine and glucagon would result in the sexual dimorphism of hepatic metabolic flux rates via the glucagon-to-insulin ratio (GIR). Indeed, model simulations indicate that the shift towards lipid metabolism in the female model is primarily driven by the liver. The female model liver exhibits resistance to GIR-mediated glycogenolysis, which helps maintain hepatic glycogen levels. This decreases arterial glucose levels and promotes the oxidation of free fatty acids. Furthermore, in the female model, skeletal muscle relies on plasma free fatty acids as the primary fuel source, rather than intramyocellular lipids, whereas the opposite holds true for the male model.

Mathematical modeling of calcium homeostasis in female rats: An analysis of sex differences and maternal adaptations

Calcium plays a vital role in various biological processes, including muscle contractions, blood clotting, skeletal mineralization, and cell signaling. While extracellular calcium makes up less than 1% of total body calcium, it is tightly regulated since too high or too low extracellular calcium concentration can have dangerous effects on the body. Mathematical modeling is a well-suited approach to investigate the complex physiological processes involved in calcium regulation. While mathematical models have been developed to study calcium homeostasis in male rats, none have been used to investigate known sex differences in hormone levels nor the unique physiological states of pregnancy and lactation. Calcitriol, the active form of vitamin D, plays a key role in intestinal calcium absorption, renal calcium reabsorption, and bone remodeling. It has been shown that, when compared to age-matched male rats, females have significantly lower calcitriol levels. In this study we first seek to investigate the impact of this difference as well as other known sex differences on calcium homeostasis using mathematical modeling. Female bodies differ from male bodies in that during their lifetime they may undergo massive adaptations during pregnancy and lactation. Indeed, maternal adaptations impact calcium regulation in all mammals. In pregnant rodents, intestinal absorption of calcium is massively increased in the mother's body to meet the needs of the developing fetus. In a lactating rodent, much of the calcium needs of milk are met by bone resorption, intestinal absorption, and renal calcium reabsorption. Given these observations, the goal of this project is to develop multi-scale whole-body models of calcium homeostasis that represents (1) how sex differences impact calcium homeostasis in female vs. male rats and (2) how a female body adapts to support the excess demands brought on by pregnancy and lactation. We used these models to quantify the impact of individual sex differences as well as maternal adaptations during pregnancy and lactation. Additionally, we conducted "what if" simulations to test whether sex differences in calcium regulation may enable females to better undergo maternal adaptations required in pregnancy and lactation than males.

Understanding the Mechanisms and Treatment of Heart Failure: Quantitative Systems Pharmacology Models with a Focus on SGLT2 Inhibitors and Sex-Specific Differences

Heart failure (HF), which is a major clinical and public health challenge, commonly develops when the myocardial muscle is unable to pump an adequate amount of blood at typical cardiac pressures to fulfill the body's metabolic needs, and compensatory mechanisms are compromised or fail to adjust. Treatments consist of targeting the maladaptive response of the neurohormonal system, thereby decreasing symptoms by relieving congestion. Sodium-glucose co-transporter 2 (SGLT2) inhibitors, which are a recent antihyperglycemic drug, have been found to significantly improve HF complications and mortality. They act through many pleiotropic effects, and show better improvements compared to others existing pharmacological therapies. Mathematical modeling is a tool used to describe the pathophysiological processes of the disease, quantify clinically relevant outcomes in response to therapies, and provide a predictive framework to improve therapeutic scheduling and strategies. In this review, we describe the pathophysiology of HF, its treatment, and how an integrated mathematical model of the cardiorenal system was built to capture body fluid and solute homeostasis. We also provide insights into sex-specific differences between males and females, thereby encouraging the development of more effective sex-based therapies in the case of heart failure.

Sex-Specific Computational Models of Kidney Function in Patients With Diabetes

The kidney plays an essential role in homeostasis, accomplished through the regulation of pH, electrolytes and fluids, by the building blocks of the kidney, the nephrons. One of the important markers of the proper functioning of a kidney is the glomerular filtration rate. Diabetes is characterized by an enlargement of the glomerular and tubular size of the kidney, affecting the afferent and efferent arteriole resistance and hemodynamics, ultimately leading to chronic kidney disease. We postulate that the diabetes-induced changes in kidney may exhibit significant sex differences as the distribution of renal transporters along the nephron may be markedly different between women and men, as recently shown in rodents. The goals of this study are to (i) analyze how kidney function is altered in male and female patients with diabetes, and (ii) assess the renal effects, in women and men, of an anti-hyperglycemic therapy that inhibits the sodium-glucose cotransporter 2 (SGLT2) in the proximal convoluted tubules. To accomplish these goals, we have developed computational models of kidney function, separate for male and female patients with diabetes. The simulation results indicate that diabetes enhances Na⁺ transport, especially along the proximal tubules and thick ascending limbs, to similar extents in male and female patients, which can be explained by the diabetes-induced increase in glomerular filtration rate. Additionally, we conducted simulations to study the effects of diabetes and SGLT2 inhibition on solute and water transport along the nephrons. Model simulations also suggest that SGLT2 inhibition raises luminal [Cl^–] at the macula densa, twice as much in males as in females, and could indicate activation of the tubuloglomerular feedback signal. By inducing osmotic diuresis in the proximal tubules, SGLT2 inhibition reduces paracellular transport, eventually leading to diuresis and natriuresis. Those effects on urinary excretion are blunted in women, in part due to their higher distal transport capacity.

The mixed blessing of AMPK signaling in Cancer treatments

Background

Nutrient acquisition and metabolism pathways are altered in cancer cells to meet bioenergetic and biosynthetic demands. A major regulator of cellular metabolism and energy homeostasis, in normal and cancer cells, is AMP-activated protein kinase (AMPK). AMPK influences cell growth via its modulation of the mechanistic target of Rapamycin (mTOR) pathway, specifically, by inhibiting mTOR complex mTORC1, which facilitates cell proliferation, and by activating mTORC2 and cell survival. Given its conflicting roles, the effects of AMPK activation in cancer can be counter intuitive. Prior to the establishment of cancer, AMPK acts as a tumor suppressor. However, following the onset of cancer, AMPK has been shown to either suppress or promote cancer, depending on cell type or state.

Methods

To unravel the controversial roles of AMPK in cancer, we developed a computational model to simulate the effects of pharmacological maneuvers that target key metabolic signalling nodes, with a specific focus on AMPK, mTORC, and their modulators. Specifically, we constructed an ordinary differential equation-based mechanistic model of AMPK-mTORC signaling, and parametrized the model based on existing experimental data.

Results

Model simulations were conducted to yield the following predictions: (i) increasing AMPK activity has opposite effects on mTORC depending on the nutrient availability; (ii) indirect inhibition of AMPK activity through inhibition of sirtuin 1 (SIRT1) only has an effect on mTORC activity under conditions of low nutrient availability; (iii) the balance between cell proliferation and survival exhibits an intricate dependence on DEP domain-containing mTOR-interacting protein (DEPTOR) abundance and AMPK activity; (iv) simultaneous direct inhibition of mTORC2 and activation of AMPK is a potential strategy for suppressing both cell survival and proliferation.

Conclusions

Taken together, model simulations clarify the competing effects and the roles of key metabolic signalling pathways in tumorigenesis, which may yield insights on innovative therapeutic strategies.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12885-022-09211-1.

Adaptive Changes in single-nephron GFR, Tubular Morphology, and Transport in a Pregnant Rat Nephron: Modeling and Analysis

Normal pregnancy is characterized by massive increases in plasma volume and electrolyte retention. Given that the kidneys regulate homeostasis of electrolytes and volume, the organ undergoes major adaptations in morphology, hemodynamics, and transport to achieve the volume and electrolyte retention required in pregnancy. These adaptations are complex, sometimes counterintuitive, and not fully understood. In addition, the demands of the developing fetus and placenta change throughout the pregnancy. For example, during late pregnancy, K⁺ retention and thus enhanced renal K⁺ reabsorption is required despite many kaliuretic factors. The goal of this study is to unravel how known adaptive changes along the nephrons contribute to the ability of the kidney to meet volume and electrolyte requirements in mid- and late pregnancy. We developed computational models of solute and water transport in the superficial nephron of the kidney of a rat in mid- and late pregnancy. The mid-pregnant and late-pregnant rat superficial nephron models predict that morphological adaptations and increased activity of the sodium hydrogen exchanger 3 (NHE3) and epithelial sodium channel (ENaC) are essential for enhanced Na⁺ reabsorption observed during pregnancy. Model simulations showed that for sufficient K⁺ reabsorption, increased H ⁺-K ⁺-ATPase activity and decreased K⁺ secretion along the distal segments is required in both mid- and late-pregnancy. Furthermore, certain known sex differences in renal transporter pattern (e.g., the higher NHE3 protein abundance but lower activity in the proximal tubules of virgin female rats compared to male) may serve to better prepare the female for the increased transport demand in pregnancy.