Sex-specific computational models for blood pressure regulation in the rat

Modulation of blood pressure by dietary potassium and sodium: sex differences and modeling analysis

High Na+ intake has been linked to elevations in blood pressure, whereas K+ has the opposite effect. The underlying mechanisms involve complex interactions among renal function, fluid volume, fluid-regulatory hormones, vasculature, cardiac function, and the autonomic nervous system. These mechanisms are likely modulated by sex, given the known sex differences in blood pressure regulation and the higher prevalence of hypertension in men. The source of these observed sex differences may be traced to organ and tissue levels, given that kidney function, intrarenal renin-angiotensin system components, renal sympathetic nervous activity, and nitric oxide bioavailability all exhibit sex differences. To assess the functional impact of each of these sex differences, we developed sex-specific computational models to simulate whole-body Na+, K+, and fluid homeostasis, and the effects on blood pressure. The models describe the interactions among the renal system, cardiovascular system, gastrointestinal system, renal sympathetic nervous system, and renin-angiotensin-aldosterone system. Model simulations suggest that women's attenuated blood pressure response to hypertensive stimuli, including high Na+ intake, may be largely attributable to the female renal transporter abundance pattern. In addition, we investigated the causal link between high K+ intake and blood pressure reduction. The models simulate renal response to high K+ intake, including the immediate gastrointestinal feedforward signals to the kidneys to increase K+ excretion, and the longer-term response to decrease proximal fractional Na+ reabsorption and distal K+ reabsorption. With these assumptions, simulations of high K+ intake yielded kaliuresis, natriuresis, and a substantial reduction in blood pressure, even when combined with high Na+ intake.NEW & NOTEWORTHY Excessive dietary Na+ raises blood pressure, whereas a high K+ diet has the opposite effect. The underlying mechanisms are moderated by sex and involve multiple organs and tissues. How do high K+-induced alternations in kidney function lower blood pressure, and how do those mechanisms differ between men and women? To answer these questions, we conducted computer simulations to simulate whole-body fluid and electrolyte homeostasis, and the effects of Na+ and K+ intake on blood pressure.

We are all different: Modeling key individual differences in physiological systems

Mathematical models of whole-body dynamics have advanced our understanding of human integrative systems that regulate physiological processes such as metabolism, temperature, and blood pressure. For most of these whole-body models, baseline parameters describe a 35-year-old young adult man who weighs 70 kg. As such, even among adults those models may not accurately represent half of the population (women), the older population, and those who weigh significantly more than 70 kg. Indeed, sex, age, and weight are known modulators of physiological function. To more accurately simulate a person who does not look like that "baseline person," or to explain the mechanisms that yield the observed sex or age differences, these factors should be incorporated into mathematical models of physiological systems. Another key modulator is the time of day, because most physiological processes are regulated by the circadian clocks. Thus, ideally, mathematical models of integrative physiological systems should be specific to either a man or woman, of a certain age and weight, and a given time of day. We illustrate the importance of capturing these individual differences, using the blood pressure regulatory system as an example, and explain how that such models can be built.

Applications of model simulation in pharmacological fields and the problems of theoretical reliability

The use of mathematical models has become increasingly prevalent in pharmacological fields, particularly in drug development processes. These models are instrumental in tasks such as designing clinical trials and assessing factors like efficacy, toxicity, and clinical practice. Various types of models have been developed and documented. Nevertheless, emphasizing the reliability of parameter values is crucial, as they play a pivotal role in shaping the behavior of the system. In some instances, parameter values reported previously are treated as fixed values, which can lead to convergence towards values that deviate substantially from those found in actual biological systems. This is especially true when parameter values are determined through fitting to limited observations. To mitigate this risk, the reuse of parameter values from previous reports should be approached with a critical evaluation of their validity. Currently, there is a proposal for a simultaneous search for plausible values for all parameters using comprehensive search algorithms in both pharmacokinetic and pharmacodynamic or systems pharmacological models. Implementing these methodologies can help address issues related to parameter determination. Furthermore, integrating these approaches with methods developed in the field of machine-learning field has the potential to enhance the reliability of parameter values and the resulting model outputs.

Sour Tamarind Is More Antihypertensive than the Sweeter One, as Evidenced by In Vivo Biochemical Indexes, Ligand-Protein Interactions, Multitarget Interactions, and Molecular Dynamic Simulation

This research investigated the antihypertensive effects of tamarind products and compared their potentials based on an animal model's data verified by molecular docking, multitarget interactions, and dynamic simulation assays. GC-MS-characterized tamarind products were administered to cholesterol-induced hypertensive albino rat models. The two-week-intervened animals were dissected to collect their serum and organs and respectively subjected to analyses of their hypertension-linked markers and tissue architectures. The lead biometabolites of tamarinds interacted with eight target receptors in the molecular docking and dynamic simulation studies and with multitarget in the network pharmacological analyses. The results show that the serum alanine aminotransferase (ALT), aspartate aminotransferase (AST), alkaline phosphatase (ALP), C-reactive protein (CRP), troponin I, and lipid profiles were maximally reinstated by the phenolic-enriched ripened sour tamarind extract compared to the sweet one, but the seed extracts had a smaller influence. Among the tamarind's biometabolites, ϒ-sitosterol was found to be the best ligand to interact with the guanylate cyclase receptor, displaying the best drug-likeliness with the highest binding energy, -9.3 Kcal. A multitargeted interaction-based degree algorithm and a phylogenetic tree of pathways showed that the NR3C1, REN, PPARG, and CYP11B1 hub genes were consistently modulated by ϒ-sitosterol to reduce hypertension and related risk factors. The dynamic simulation study showed that the P-RMSD values of ϒ-sitosterol-guanylate cyclase were stable between 75.00 and 100.00 ns at the binding pocket. The findings demonstrate that ripened sour tamarind extract may be a prospective antihypertensive nutraceutical or supplement target affirmed through advanced preclinical and clinical studies.

Sex matters: the frequently overlooked importance of considering sex in computational models

Personalised medicine and the development of a virtual human or a digital twin comprises visions of the future of medicine. To realise these innovations, an understanding of the biology and physiology of all people are required if we wish to apply these technologies at a population level. Sex differences in health and biology is one aspect that has frequently been overlooked, with young white males being seen as the "average" human being. This has not been helped by the lack of inclusion of female cells and animals in biomedical research and preclinical studies or the historic exclusion, and still low in proportion, of women in clinical trials. However, there are many known differences in health between the sexes across all scales of biology which can manifest in differences in susceptibility to diseases, symptoms in a given disease, and outcomes to a given treatment. Neglecting these important differences in the development of any health technologies could lead to adverse outcomes for both males and females. Here we highlight just some of the sex differences in the cardio-respiratory systems with the goal of raising awareness that these differences exist. We discuss modelling studies that have considered sex differences and touch on how and when to create sex-specific models. Scientific studies should ensure sex differences are included right from the study planning phase and results reported using sex as a biological variable. Computational models must have sex-specific versions to ensure a movement towards personalised medicine is realised.

The intrarenal renin-angiotensin system in hypertension: insights from mathematical modelling

The renin-angiotensin system (RAS) plays a pivotal role in the maintenance of volume homeostasis and blood pressure. In addition to the well-studied systemic RAS, local RAS have been documented in various tissues, including the kidney. Given the role of the intrarenal RAS in the pathogenesis of hypertension, a role established via various pharmacologic and genetic studies, substantial efforts have been made to unravel the processes that govern intrarenal RAS activity. In particular, several mechanisms have been proposed to explain the rise in intrarenal angiotensin II (Ang II) that accompanies Ang II infusion, including increased angiotensin type 1 receptor (AT1R)-mediated uptake of Ang II and enhanced intrarenal Ang II production. However, experimentally isolating their contribution to the intrarenal accumulation of Ang II in Ang II-induced hypertension is challenging, given that they are fundamentally connected. Computational modelling is advantageous because the feedback underlying each mechanism can be removed and the effect on intrarenal Ang II can be studied. In this work, the mechanisms governing the intrarenal accumulation of Ang II during Ang II infusion experiments are delineated and the role of the intrarenal RAS in Ang II-induced hypertension is studied. To accomplish this, a compartmental ODE model of the systemic and intrarenal RAS is developed and Ang II infusion experiments are simulated. Simulations indicate that AT1R-mediated uptake of Ang II is the primary mechanism by which Ang II accumulates in the kidney during Ang II infusion. Enhanced local Ang II production is unnecessary. The results demonstrate the role of the intrarenal RAS in the pathogenesis of Ang II-induced hypertension and consequently, clinical hypertension associated with an overactive RAS.

Influence of administration time and sex on natriuretic, diuretic, and kaliuretic effects of diuretics

Sex differences in renal function and blood pressure have been widely described across many species. Blood pressure dips during sleep and peaks in the early morning. Similarly, glomerular filtration rate, filtered electrolyte loads, urine volume, and urinary excretion all exhibit notable diurnal rhythms, which reflect, in part, the regulation of renal transporter proteins by circadian clock genes. That regulation is sexually dimorphic; as such, sex and time of day are not two independent regulators of kidney function and blood pressure. The objective of the present study was to assess the effect of sex and administration time on the natriuretic and diuretic effects of loop, thiazide, and K⁺-sparing diuretics, which are common treatments for hypertension. Loop diuretics inhibit Na⁺-K⁺-2Cl^- cotransporters on the apical membrane of the thick ascending limb, thiazide diuretics inhibit Na⁺-Cl^- cotransporters on the distal convoluted tubule, and K⁺-sparing diuretics inhibit epithelial Na⁺ channels on the connecting tubule and collecting duct. We simulated Na⁺ transporter inhibition using sex- and time-of-day-specific computational models of mouse kidney function. The simulation results highlighted significant sex and time-of-day differences in the drug response. Loop diuretics induced larger natriuretic and diuretic effects during the active phase. The natriuretic and diuretic effects of thiazide diuretics exhibited sex and time-of-day differences, whereas these effects of K⁺-sparing diuretics exhibited a significant time-of-day difference in females only. The kaliuretic effect depended on the type of diuretics and time of administration. The present computational models can be a useful tool in chronotherapy, to tailor drug administration time to match the body's diurnal rhythms to optimize the drug effect.NEW & NOTEWORTHY Sex influences cardiovascular disease, and the timing of onset of acute cardiovascular events exhibits circadian rhythms. Kidney function also exhibits sex differences and circadian rhythms. How do the natriuretic and diuretic effects of diuretics, a common treatment for hypertension that targets the kidneys, differ between the sexes? And how do these effects vary during the day? To answer these questions, we conducted computer simulations to assess the effects of loop, thiazide, and K⁺-sparing diuretics.

A mathematical model of potassium homeostasis: Effect of feedforward and feedback controls

Maintaining normal potassium (K+) concentrations in the extra- and intracellular fluid is critical for cell function. K+ homeostasis is achieved by ensuring proper distribution between extra- and intracellular fluid compartments and by matching K+ excretion with intake. The Na+-K+-ATPase pump facilitates K+ uptake into the skeletal muscle, where most K+ is stored. Na+-K+-ATPase activity is stimulated by insulin and aldosterone. The kidneys regulate long term K+ homeostasis by controlling the amount of K+ excreted through urine. Renal handling of K+ is mediated by a number of regulatory mechanisms, including an aldosterone-mediated feedback control, in which high extracellular K+ concentration stimulates aldosterone secretion, which enhances urine K+ excretion, and a gastrointestinal feedforward control mechanism, in which dietary K+ intake increases K+ excretion. Recently, a muscle-kidney cross talk signal has been hypothesized, where the K+ concentration in skeletal muscle cells directly affects urine K+ excretion without changes in extracellular K+ concentration. To understand how these mechanisms coordinate under different K+ challenges, we have developed a compartmental model of whole-body K+ regulation. The model represents the intra- and extracellular fluid compartments in a human (male) as well as a detailed kidney compartment. We included (i) the gastrointestinal feedforward control mechanism, (ii) the effect of insulin and (iii) aldosterone on Na+-K+-ATPase K+ uptake, and (iv) aldosterone stimulation of renal K+ secretion. We used this model to investigate the impact of regulatory mechanisms on K+ homeostasis. Model predictions showed how the regulatory mechanisms synthesize to ensure that the extra- and intracelluller fluid K+ concentrations remain in normal range in times of K+ loading and fasting. Additionally, we predict that without the hypothesized muscle-kidney cross talk signal, the model was unable to predict a return to normal extracellular K+ concentration after a period of high K+ loading or depletion.

Sex differences in circadian regulation of kidney function of the mouse

Kidney function is regulated by the circadian clock. Not only do glomerular filtration rate and urinary excretion oscillate during the day, but the expressions of several renal transporter proteins also exhibit circadian rhythms. Interestingly, the circadian regulation of these transporters appears to be sexually dimorphic. Thus, the goal of the present study was to investigate the mechanisms by which the kidney function of the mouse is modulated by sex and time of day. To accomplish this, we developed the first computational models of epithelial water and solute transport along the mouse nephrons that represent the effects of sex and the circadian clock on renal hemodynamics and transporter activity. We conducted simulations to study how the circadian control of renal transport genes affects overall kidney function and how that process differs between male and female mice. Simulation results predicted that tubular transport differs substantially among segments, with relative variations in water and Na+ reabsorption along the proximal tubules and thick ascending limb tracking that of glomerular filtration rate. In contrast, relative variations in distal segment transport were much larger, with Na+ reabsorption almost doubling during the active phase. Oscillations in Na+ transport drive K+ transport variations in the opposite direction. Model simulations of basic helix-loop-helix ARNT like 1 (BMAL1) knockout mice predicted a significant reduction in net Na+ reabsorption along the distal segments in both sexes, but more so in males than in females. This can be attributed to the reduction of mean epithelial Na+ channel activity in males only, a sex-specific effect that may lead to a reduction in blood pressure in BMAL1-null males.NEW & NOTEWORTHY How does the circadian control of renal transport genes affect overall kidney function, and how does that process differ between male and female mice? How does the differential circadian regulation of the expression levels of key transporter genes impact the transport processes along different nephron segments during the day? And how do those effects differ between males and females? We built computational models of mouse kidney function to answer these questions.

Sex and species differences in epithelial transport in rat and mouse kidneys: Modeling and analysis

The goal of this study was to investigate the functional implications of sex and species differences in the pattern of transporters along nephrons in the rat and mouse kidney, as reported by Veiras et al. (J Am Soc Nephrol 28: 3504–3517, 2017). To do so, we developed the first sex-specific computational models of epithelial water and solute transport along the nephrons from male and female mouse kidneys, and conducted simulations along with our published rat models. These models account for the sex differences in the abundance of apical and basolateral transporters, glomerular filtration rate, and tubular dimensions. Model simulations predict that 73% and 57% of filtered Na+ is reabsorbed by the proximal tubules of male and female rat kidneys, respectively. Due to their smaller transport area and lower NHE3 activity, the proximal tubules in the mouse kidney reabsorb a significantly smaller fraction of the filtered Na+, at 53% in male and only 34% in female. The lower proximal fractional Na+ reabsorption in female kidneys of both rat and mouse is due primarily to their smaller transport area, lower Na+/H+ exchanger activity, and lower claudin-2 abundance, culminating in significantly larger fractional delivery of water and Na+ to the downstream nephron segments in female kidneys. Conversely, the female distal nephron exhibits a higher abundance of key Na+ transporters, including Na+-Cl− cotransporters in both species, epithelial Na+ channels for the female rat, and Na+-K+-Cl−cotransporters for the female mouse. The higher abundance of transporters accounts for the enhanced water and Na+ transport along the female rat and mouse distal nephrons, relative to the respective male, resulting in similar urine excretion between the sexes. Model simulations indicate that the sex and species differences in renal transporter patterns may partially explain the experimental observation that, in response to a saline load, the diuretic and natriuretic responses were more rapid in female rats than males, but no significant sex difference was found in mice. These computational models can serve as a valuable tool for analyzing findings from experimental studies conducted in rats and mice, especially those involving genetic modifications.

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.

Sex differences in solute and water handling in the human kidney: Modeling and functional implications

The kidneys maintain homeostasis by controlling the amount of water and electrolytes in the blood. That function is accomplished by the nephrons, which transform glomerular filtrate into urine by a transport process mediated by membrane transporters. We postulate that the distribution of renal transporters along the nephron is markedly different between men and women, as recently shown in rodents. We hypothesize that the larger abundance of a renal Na+ transport in the proximal tubules in females may also better prepare them for the fluid retention adaptations required during pregnancy and lactation. Also, kidneys play a key role in blood pressure regulation, and a popular class of anti-hypertensive medications and angiotensin converting enzymes (ACE) inhibitors have been reported to be less effective in women. Model simulations suggest that the blunted natriuretic and diuretic effects of ACE inhibition in women can be attributed, in part, to their higher distal baseline transport capacity.

Modeling within-Host SARS-CoV-2 Infection Dynamics and Potential Treatments

The goal of this study was to develop a mathematical model to simulate the actions of drugs that target SARS-CoV-2 virus infection. To accomplish that goal, we have developed a mathematical model that describes the control of a SARS-CoV-2 infection by the innate and adaptive immune components. Invasion of the virus triggers the innate immunity, whereby interferon renders some of the target cells resistant to infection, and infected cells are removed by effector cells. The adaptive immune response is represented by plasma cells and virus-specific antibodies. The model is parameterized and then validated against viral load measurements collected in COVID-19 patients. We apply the model to simulate three potential anti-SARS-CoV-2 therapies: (1) Remdesivir, a repurposed drug that has been shown to inhibit the transcription of SARS-CoV-2, (2) an alternative (hypothetical) therapy that inhibits the virus' entry into host cells, and (3) convalescent plasma transfusion therapy. Simulation results point to the importance of early intervention, i.e., for any of the three therapies to be effective, it must be administered sufficiently early, not more than a day or two after the onset of symptoms. The model can serve as a key component in integrative platforms for rapid in silico testing of potential COVID-19 therapies and vaccines.

A Computational Model of Kidney Function in a Patient with Diabetes

At the onset of diabetes, the kidney grows large and the glomerular filtration rate becomes abnormally high. These structural and hemodynamics changes affect kidney function and may contribute to the development of chronic kidney disease. The goal of this study is to analyze how kidney function is altered in patients with diabetes and the renal effects of an anti-hyperglyceamic therapy that inhibits the sodium-glucose cotransporter 2 (SGLT2) in the proximal convoluted tubules. To accomplish that goal, we have developed a computational model of kidney function in a patient with diabetes and conducted simulations to study the effects of diabetes and SGLT2 inhibition on solute and water transport along the nephrons. Simulation results indicate that diabetes-induced hyperfiltration and tubular hypertrophy enhances Na+ transport, especially along the proximal tubules and thick ascending limbs. These simulations suggest that SGLT2 inhibition may attenuate glomerular hyperfiltration by limiting Na+-glucose transport, raising luminal [Cl-] at the macula densa, restoring the tubuloglomerular feedback signal, thereby reducing single-nephron glomerular filtration rate.

Impact of sex and pathophysiology on optimal drug choice in hypertensive rats: quantitative insights for precision medicine

Less than half of all hypertensive patients receiving treatment are successful in normalizing their blood pressure. Despite the complexity and heterogeneity of hypertension, the current antihypertensive guidelines are not tailored to the individual patient. As a step toward individualized treatment, we develop a quantitative systems pharmacology model of blood pressure regulation in the spontaneously hypertensive rat (SHR) and generate sex-specific virtual populations of SHRs to account for the heterogeneity between the sexes and within the pathophysiology of hypertension. We then used the mechanistic model integrated with machine learning tools to study how variability in these mechanisms leads to differential responses in rodents to the four primary classes of antihypertensive drugs. We found that both the sex and the pathophysiological profile of the individual play a major role in the response to hypertensive treatments. These results provide insight into potential areas to apply precision medicine in human primary hypertension.

Use of Angiotensin-Converting Enzyme Inhibitors and Angiotensin II Receptor Blockers During the COVID-19 Pandemic: A Modeling Analysis

Angiotensin-converting enzyme inhibitors (ACEi) and angiotensin II receptor blockers (ARB) are frequently prescribed for a range of diseases including hypertension, proteinuric chronic kidney disease, and heart failure. There is evidence indicating that these drugs upregulate ACE2, a key component of the renin-angiotensin system (RAS) and is found on the cells of a number of tissues, including the epithelial cells in the lungs. While ACE2 has a beneficial role in many diseases such as hypertension, diabetes, and cardiovascular disease, it also serves as a receptor for both SARS-CoV and SARS-CoV-2 via binding with the spike protein of the virus, thereby allowing it entry into host cells. Thus, it has been suggested that these therapies can theoretically increase the risk of SARS- CoV-2 infection and cause more severe COVID-19. Given the success of ACEi and ARBs in cardiovascular diseases, we seek to gain insights into the implications of these medications in the pathogenesis of COVID-19. To that end, we have developed a mathematical model that represents the RAS, binding of ACE2 with SARS-CoV-2 and the subsequent cell entry, and the host's acute inflammatory response. The model can simulate different levels of SARS-CoV-2 exposure, and represent the effect of commonly prescribed anti-hypertensive medications, ACEi and ARB, and predict tissue damage. Model simulations indicate that whether the extent of tissue damage may be exacerbated by ACEi or ARB treatment depends on a number of factors, including the level of existing inflammation, dosage, and the effect of the drugs on ACE2 protein abundance. The findings of this study can serve as the first step in the development of appropriate and more comprehensive guidelines for the prescription of ACEi and ARB in the current and future coronavirus pandemics.