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

Embracing sex-specific differences in engineered kidney models for enhanced biological understanding of kidney function

In vitro models serve as indispensable tools for advancing our understanding of biological processes, elucidating disease mechanisms, and establishing screening platforms for drug discovery. Kidneys play an instrumental role in the transport and elimination of drugs and toxins. Nevertheless, despite the well-documented inter-individual variability in kidney function and the multifaceted nature of renal diseases-spanning from their origin, trigger and which segment of the kidney is affected-to presentation, progression and prognosis, few studies take into consideration the variable of sex. Notably, the inherent disparities between female and male biology warrants a more comprehensive representation within in vitro models of the kidney. The omission of sex as a fundamental biological variable carries the substantial risk of overlooking sex-specific mechanisms implicated in health and disease, along with potential differences in drug responsiveness and toxicity profiles between sexes. This review emphasizes the importance of incorporating cellular, biological and functional sex-specific features of renal activity in health and disease in in vitro models. For that, we thoroughly document renal sex-specific features and propose a strategic experimental framework to integrate sex-based differences into human kidney in vitro models by outlining critical design criteria to elucidate sex-based features at cellular and tissue levels. The goal is to enhance the accuracy of models to unravel renal mechanisms, and improve our understanding of their impact on drug efficacy and safety profiles, paving the way for a more comprehensive understanding of patient-specific treatment modalities.

Renal calcium and magnesium handling during pregnancy: modeling and analysis

Pregnancy is associated with elevated demand of most nutrients, with many trace elements and minerals critical for the development of fetus. In particular, calcium (Ca2+) and magnesium (Mg2+) are essential for cellular function, and their deficiency can lead to impaired fetal growth. A key contributor to the homeostasis of these ions is the kidney, which in a pregnant rat undergoes major changes in morphology, hemodynamics, and molecular structure. The goal of this study is to unravel the functional implications of these pregnancy-induced changes in renal handling of Ca2+ and Mg2+, two cations that are essential in a healthy pregnancy. To achieve that goal, we developed computational models of electrolyte and water transport along the nephrons of a rat in mid and late pregnancy. Model simulations reveal a substantial increase in the reabsorption of Mg2+ along the proximal tubules and thick ascending limbs. In contrast, the reabsorption of Ca2+ is increased in the proximal tubules but decreased in the thick ascending limbs, due to the lower transepithelial concentration gradient of Ca2+ along the latter. Despite the enhanced transport capacity, the marked increase in glomerular filtration rate results in elevated urinary excretions of Ca2+ and Mg2+ in pregnancy. Furthermore, we conducted simulations of hypocalcemia and hypomagnesemia. We found that hypocalcemia lowers Ca2+ excretion substantially more than Mg2+ excretion, with this effect being more pronounced in virgin rats than in pregnant ones. Conversely, hypomagnesemia reduces the excretion of Mg2+ and Ca2+ to more similar degrees. These differences can be explained by the greater sensitivity of the calcium-sensing receptor (CaSR) to Ca2+ compared with Mg2+.NEW & NOTEWORTHY A growing fetus' demands of minerals, notably calcium and magnesium, necessitate adaptations in pregnancy. In particular, the kidney undergoes major changes in morphology, hemodynamics, and molecular structure. This computational modeling study provides insights into how these pregnancy-induced renal adaptation impact calcium and magnesium transport along different nephron segments. Model simulations indicate that, despite the enhanced transport capacity, the marked increase in glomerular filtration rate results in elevated urinary excretions of calcium and magnesium in pregnancy.

Predicting sex differences in the effects of diuretics in renal epithelial transport during angiotensin II-induced hypertension

Chronic angiotensin II (ANG II) infusion is an experimental model that induces hypertension in rodents. The natriuresis, diuresis, and blood pressure responses differ between males and females. This is perhaps not unexpected, given the rodent kidney, which plays a key role in blood pressure regulation, exhibits marked sex differences. Under normotensive conditions, compared with males, the female rat nephron exhibits lower Na+/H+ exchanger 3 (NHE3) activity along the proximal tubule but higher Na+ transporter activities along the distal segments. ANG II infusion-induced hypertension induces a pressure natriuretic response that reduces NHE3 activity and shifts Na+ transport capacity downstream. The goals of this study were to apply a computational model of epithelial transport along a rat nephron 1) to understand how a 14-day ANG II infusion impacts segmental electrolyte transport in male and female rat nephrons and 2) to identify and explain any sex differences in the effects of loop diuretics, thiazide diuretics, and K+-sparing diuretics. Model simulations suggest that the NHE3 downregulation in the proximal tubule is a major contributor to natriuresis and diuresis in hypertension, with the effects stronger in males. All three diuretics are predicted to induce stronger natriuretic and diuretic effects under hypertension compared with normotension, with relative increases in sodium excretion higher in hypertensive females than in males. The stronger natriuretic responses can be explained by the downstream shift of Na+ transport load in hypertension and by the larger distal transport load in females, both of which limit the ability of the distal segments to further elevate their Na+ transport.NEW & NOTEWORTHY Sex differences in the prevalence of hypertension are found in human and animal models. The kidney, which regulates blood pressure, exhibits sex differences in morphology, hemodynamics, and membrane transporter distributions. This computational modeling study provides insights into how the sexually dimorphic responses to a 14-day angiotensin II infusion differentially impact segmental electrolyte transport in rats. Simulations of diuretic administration explain how the natriuretic and diuretic effects differ between normotension and hypertension and between the sexes.

A modeling analysis of whole body potassium regulation on a high-potassium diet: proximal tubule and tubuloglomerular feedback effects

Potassium (K+) is an essential electrolyte that plays a key role in many physiological processes, including mineralcorticoid action, systemic blood-pressure regulation, and hormone secretion and action. Indeed, maintaining K+ balance is critical for normal cell function, as too high or too low K+ levels can have serious and potentially deadly health consequences. K+ homeostasis is achieved by an intricate balance between the intracellular and extracellular fluid as well as balance between K+ intake and excretion. This is achieved via the coordinated actions of regulatory mechanisms such as the gastrointestinal feedforward effect, insulin and aldosterone upregulation of Na+-K+-ATPase uptake, and hormone and electrolyte impacts on renal K+ handling. We recently developed a mathematical model of whole body K+ regulation to unravel the individual impacts of these regulatory mechanisms. In this study, we extend our mathematical model to incorporate recent experimental findings that showed decreased fractional proximal tubule reabsorption under a high-K+ diet. We conducted model simulations and sensitivity analyses to investigate how these renal alterations impact whole body K+ regulation. Model predictions quantify the sensitivity of K+ regulation to various levels of proximal tubule K+ reabsorption adaptation and tubuloglomerular feedback. Our results suggest that the reduced proximal tubule K+ reabsorption under a high-K+ diet could achieve K+ balance in isolation, but the resulting tubuloglomerular feedback reduces filtration rate and thus K+ excretion.NEW & NOTEWORTHY Potassium homeostasis is maintained in the body by a complex system of regulatory mechanisms. This system, when healthy, maintains a small extracellular potassium concentration, despite large fluctuations of dietary potassium. The complexities of the system make this problem well suited for investigation with mathematical modeling. In this study, we extend our mathematical model to consider recent experimental results on renal potassium handling on a high potassium diet and investigate the impacts from a whole body perspective.

How the kidney regulates magnesium: a modelling study

The kidneys are crucial for maintaining Mg2+ homeostasis. Along the proximal tubule and thick ascending limb, Mg2+ is reabsorbed paracellularly, while along the distal convoluted tubule (DCT), Mg2+ is reabsorbed transcellularly via transient receptor potential melastatin 6 (TRPM6). TRPM6 and other renal transporter expressions are regulated by sex hormones. To investigate renal Mg2 handling, we have developed sex-specific computational models of electrolyte transport along rat superficial nephron. Model simulations indicated that along the proximal tubule and thick ascending limb, Mg2+ and Na+ transport occur parallelly, but they are dissociated along the DCT. In addition, our models predicted higher paracellular Mg2+ permeability in females to attain similar cortical thick ascending limb fractional Mg2+ reabsorption in both sexes. Furthermore, DCT fractional Mg2+ reabsorption is higher in females than in males, allowing females to better fine-tune Mg2+ excretion. We validated our models by simulating the administration of three classes of diuretics. The model predicted significantly increased, marginally increased and significantly decreased Mg2+ excretions for loop, thiazide and K-sparing diuretics, respectively, aligning with experimental findings. The models can be used to conduct in silico studies on kidney adaptations to Mg2+ homeostasis alterations during conditions such as pregnancy, diabetes and chronic kidney disease.

A comparative modeling study of the mitochondrial function of the proximal tubule and thick ascending limb cells in the rat kidney

To reabsorb >99% of the glomerular filtrate, the metabolic demand of the kidney is high. Interestingly, renal blood flow distribution exhibits marked inhomogeneity, with typical tissue oxygen tension (Po2) of 50-60 mmHg in the well-perfused cortex and 10-20 mmHg in the inner medulla. Cellular fluid composition and acidity also varies substantially. To understand how different renal epithelial cells adapt to their local environment, we have developed and applied computational models of mitochondrial function of proximal convoluted tubule cell (baseline Po2 = 50 mmHg, cytoplasmic pH = 7.20) and medullary thick ascending limb (mTAL) cell (baseline Po2 = 10 mmHg, cytoplasmic pH = 6.85). The models predict key cellular quantities, including ATP generation, P/O (phosphate/oxygen) ratio, proton motive force, electrical potential gradient, oxygen consumption, the redox state of key electron carriers, and ATP consumption. Model simulations predict that close to their respective baseline conditions, the proximal tubule and mTAL mitochondria exhibit qualitatively similar behaviors. Nonetheless, because the mTAL mitochondrion has adapted to a much lower Po2, it can sustain a sufficiently high ATP production at Po2 as low as 4-5 mmHg, whereas the proximal tubule mitochondria would not. Also, because the mTAL cytosol is already acidic under baseline conditions, the proton motive force (pmf) exhibits higher sensitivity to further acidification. Among the different pathways that lead to oxidative phosphorylation impairment, the models predict that both the proximal tubule and mTAL mitochondria are most sensitive to reductions in Complex III activity.NEW & NOTEWORTHY Tissue fluid composition varies substantially within the mammalian kidney. The renal cortex is well perfused and pH neutral, whereas some medullary regions are hypoxic and acidic. How do these environments affect the mitochondrial function of proximal convoluted tubule and medullary thick ascending limb cells, which reside in the cortex and medulla, respectively? This computational modeling study demonstrates that these mitochondria can adapt to their contrasting environments and exhibit different sensitivities to perturbations to local environments.

Sex differences in renal transporters: assessment and functional consequences

Mammalian kidneys are specialized to maintain fluid and electrolyte homeostasis. The epithelial transport processes along the renal tubule that match output to input have long been the subject of experimental and theoretical study. However, emerging data have identified a new dimension of investigation: sex. Like most tissues, the structure and function of the kidney is regulated by sex hormones and chromosomes. Available data demonstrate sex differences in the abundance of kidney solute and electrolyte transporters, establishing that renal tubular organization and operation are distinctly different in females and males. Newer studies have provided insights into the physiological consequences of these sex differences. Computational simulations predict that sex differences in transporter abundance are likely driven to optimize reproduction, enabling adaptive responses to the nutritional requirements of serial pregnancies and lactation - normal life-cycle changes that challenge the ability of renal transporters to maintain fluid and electrolyte homeostasis. Later in life, females may also undergo menopause, which is associated with changes in disease risk. Although numerous knowledge gaps remain, ongoing studies will provide further insights into the sex-specific mechanisms of sodium, potassium, acid-base and volume physiology throughout the life cycle, which may lead to therapeutic opportunities.

Coupling of renal sodium and calcium transport: a modeling analysis of transporter inhibition and sex differences

Ca2+ transport along the nephron occurs via specific transcellular and paracellular pathways and is coupled to the transport of other electrolytes. Notably, Na+ transport establishes an electrochemical gradient to drive Ca2+ reabsorption. Hence, alterations in renal Na+ handling, under pathophysiological conditions or pharmacological manipulations, can have major effects on Ca2+ transport. An important class of pharmacological agent is diuretics, which are commonly prescribed for the management of blood pressure and fluid balance. The pharmacological targets of diuretics generally directly facilitate Na+ transport but also indirectly affect renal Ca2+ handling. To better understand the underlying mechanisms, we developed a computational model of electrolyte transport along the superficial nephron in the kidney of a male and female rat. Sex differences in renal Ca2+ handling are represented. Model simulations predicted in the female rat nephron lower Ca2+ reabsorption in the proximal tubule and thick ascending limb, but higher reabsorption in the late distal convoluted tubule and connecting tubule, compared with the male nephron. The male rat kidney model yielded a higher urinary Ca2+ excretion than the female model, consistent with animal experiments. Model results indicated that along the proximal tubule and thick ascending limb, Ca2+ and Na+ transport occurred in parallel, but those processes were dissociated in the distal convoluted tubule. Additionally, we conducted simulations of inhibition of channels and transporters that play a major role in Na+ and Ca2+ transport. Simulation results revealed alterations in transepithelial Ca2+ transport, with differential effects among nephron segments and between the sexes.NEW & NOTEWORTHY The kidney plays an important role in the maintenance of whole body Ca2+ balance by regulating Ca2+ reabsorption and excretion. This computational modeling study provides insights into how Ca2+ transport along the nephron is coupled to Na+. Model results indicated that along the proximal tubule and thick ascending limb, Ca2+ and Na+ transport occur in parallel, but those processes were dissociated in the distal convoluted tubule. Simulations also revealed sex-specific responses to different pharmacological manipulations.

"Hi, how can i help you?": embracing artificial intelligence in kidney research

In recent years, biology and precision medicine have benefited from major advancements in generating large-scale molecular and biomedical datasets and in analyzing those data using advanced machine learning algorithms. Machine learning applications in kidney physiology and pathophysiology include segmenting kidney structures from imaging data and predicting conditions like acute kidney injury or chronic kidney disease using electronic health records. Despite the potential of machine learning to revolutionize nephrology by providing innovative diagnostic and therapeutic tools, its adoption in kidney research has been slower than in other organ systems. Several factors contribute to this underutilization. The complexity of the kidney as an organ, with intricate physiology and specialized cell populations, makes it challenging to extrapolate bulk omics data to specific processes. In addition, kidney diseases often present with overlapping manifestations and morphological changes, making diagnosis and treatment complex. Moreover, kidney diseases receive less funding compared with other pathologies, leading to lower awareness and limited public-private partnerships. To promote the use of machine learning in kidney research, this review provides an introduction to machine learning and reviews its notable applications in renal research, such as morphological analysis, omics data examination, and disease diagnosis and prognosis. Challenges and limitations associated with data-driven predictive techniques are also discussed. The goal of this review is to raise awareness and encourage the kidney research community to embrace machine learning as a powerful tool that can drive advancements in understanding kidney diseases and improving patient care.

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.

Sex differences in renal electrolyte transport

PURPOSE OF REVIEW

Women experience unique life events, for example, pregnancy and lactation, that challenge renal regulation of electrolyte homeostasis. Recent analyses of nephron organization in female vs. male rodent kidneys, revealed distinct sexual dimorphisms in electrolyte transporter expression, abundance, and activity. This review aims to provide an overview of electrolyte transporters' organization and operation in female compared with the commonly studied male kidney, and the (patho)physiologic consequences of the differences.

RECENT FINDINGS

When electrolyte transporters are assessed in kidney protein homogenates from both sexes, relative transporter abundance ratios in females/males are less than one along proximal tubule and greater than one post macula densa, which is indicative of a 'downstream shift' in fractional reabsorption of electrolytes in females. This arrangement improves the excretion of a sodium load, challenges potassium homeostasis, and is consistent with the lower blood pressure and greater pressure natriuresis observed in premenopausal women.

SUMMARY

We summarize recently reported new knowledge about sex differences in renal transporters: abundance and expression along nephron, implications for regulation by Na + , K + and angiotensin II, and mathematical models of female nephron function.

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.

Novel method for kinetic analysis applied to transport by the uniporter OCT2

The kinetics of solute transport shed light on the roles these processes play in cellular physiology, and the absolute values of the kinetic parameters that quantitatively describe transport are increasingly used to model its impact on drug clearance. However, accurate assessment of transport kinetics is challenging. Although most carrier-mediated transport is adequately described by the Michaelis-Menten equation, its use presupposes that the rates of uptake used in the analysis of maximal rates of transport (Jmax) and half-saturation constants (Kt) reflect true unidirectional rates of influx from known concentrations of substrate. Most experimental protocols estimate the initial rate of transport from net substrate accumulation determined at a single time point (typically between 0.5 and 5 min) and assume it reflects unidirectional influx. However, this approach generally results in systematic underestimates of Jmax and overestimates of Kt; the former primarily due to the unaccounted impact of efflux of accumulated substrate, and the latter due to the influence of unstirred water layers. Here, we describe the bases of these time-dependent effects and introduce a computational model that analyzes the time course of net substrate uptake at several concentrations to calculate Jmax and Kt for unidirectional influx, taking into account the influence of unstirred water layers and mediated efflux. This method was then applied to calculate the kinetics of transport of 1-methyl-4-phenylpryridinium and metformin by renal organic cation transporter 2 as expressed in cultured Chinese hamster ovary cells.NEW & NOTEWORTHY Here, we describe a mathematical model that uses the time course of net substrate uptake into cells from several increasing concentrations to calculate unique kinetic parameters [maximal rates of transport (Jmax) and half-saturation constants (Kt)] of the process. The method is the first to take into consideration the common complicating factors of unstirred layers and carrier-mediated efflux in the experimental determination of transport kinetics.