Effect of pregnancy and hypertension on kidney function in female rats: Modeling and functional implications

Abstract

During pregnancy, major adaptations in renal morphology, hemodynamics, and transport occur to achieve volume and electrolyte retention required to support a healthy pregnancy. Additionally, during pregnancies complicated by chronic hypertension, altered renal function from normal pregnancy occurs. The goal of this study is to analyze how inhibition of key transporters impacts gestational kidney function as well as how altered renal function during chronic hypertension impacts renal function during pregnancy. To do this, we developed epithelial cell-based computational models of solute and water transport in the kidneys of a female rat in mid- and late pregnancy. We simulated the effect of key individual pregnancy-induced changes on renal Na⁺ and K⁺ transport: proximal tubule length, Na⁺/H⁺ exchanger isoform 3 (NHE3) activity, epithelial Na⁺ channel activity (ENaC), K⁺ secretory channel expression, and H⁺-K⁺-ATPase activity. Additionally, we conducted simulations on the effects of inhibition and knockout of the ENaC and H⁺-K⁺-ATPase transporters on virgin and pregnant rat kidneys. Our simulation results predicted that the ENaC and H⁺-K⁺-ATPase transporters are essential for sufficient Na⁺ and K⁺ reabsorption during pregnancy. Last, we developed models to capture changes made during hypertension in female rats and considered what may occur when a rat with chronic hypertension becomes pregnant. Model simulations predicted that in hypertension for a pregnant rat there is a similar shift in Na⁺ transport from the proximal tubules to the distal tubules as in a virgin rat.

Introduction

Normal pregnancy is characterized by complicated and multifactorial adaptations in the maternal body in almost all physiological systems (1,2). These changes are dynamic, often competing, and, when considered in isolation, are sometimes counterintuitive. For example, despite a massive increase in plasma volume, which in isolation would significantly increase blood pressure, blood pressure typically decreases in a normal pregnancy due to changes in the cardiovascular system (3).

In a healthy pregnancy, a new organ, the placenta, develops which requires adequate blood flow to support sufficient fetal oxygenation, nutrition, and maturation (4). Notably, the placenta is an endocrine organ which secretes hormones that alter maternal body function (1,4). For example, progesterone levels rise about 100-fold and estrogen levels by about 50-fold by the end of gestation (5). Both hormones have significant impacts on many physiological systems and their massive increase in levels can largely be attributed to placental secretion (1,2,4). Remarkably, the maternal body adapts to not only support normal tissue and organ perfusion, but also the nutrient and electrolyte requirements of the rapidly growing fetus and placenta. Indeed, when the maternal body does not sufficiently adapt, dangerous gestational disorders, or fetal growth restriction may occur (6–9).

Chronic hypertension is one of the most common medical disorders globally (10). It affects about 45% of all U.S. adults and is estimated to occur in about 21% of women of reproductive age (10–12). In the context of pregnancy, chronic hypertension is defined as hypertension that is diagnosed pre-pregnancy or before 20 weeks gestation (11,13,14). Interestingly, due to normal vascular adaptations that occur during pregnancy, oftentimes women with chronic hypertension experience a decrease in blood pressure during pregnancy, sometimes being able to decrease medications or even become normotensive (13). Pregnancy has also been shown to be antihypertensive for spontaneously hypertensive rats (15,16). While many women who have chronic hypertension are able to sustain a healthy pregnancy, they do have increased risk of dangerous adverse health effects such as superimposed preeclampsia, fetal growth restriction, preterm birth, and placental abruption (11,13,17). For example, preeclampsia, which is one of the most dangerous complications of pregnancy, occurs in about 17-25% of pregnancies in women with chronic hypertension compared with 3-5% of pregnancies in the general population (13,18). Additionally, it has been shown that pregnancies complicated by chronic hypertension can have adverse health effects on the child through their lifetime (11,19–21). The prevalence of pregnancies complicated by chronic hypertension has doubled over the last decade and it is estimated that this trend will continue to increase as average maternal age and obesity rates increase among women of childbearing age (11,14,17,22). Indeed, it is important to have a full understanding of the impacts of chronic hypertension and pregnancy, not only for the perinatal health of the fetus and mother, but also to prevent impacts of future disease caused by prenatal insults.

The kidneys play an essential role in regulating body homeostasis, namely water, electrolyte, and acid-base balance (23). During pregnancy, the plasma volume of the mother must expand drastically to support the rapidly developing fetus and placenta (3). In a virgin or non-pregnant rat, almost all Na⁺ intake is excreted through urine, but in pregnancy this is not the case: there is net Na⁺ retention in a pregnant rat (24,25). Additionally, in late pregnancy, maternal net K⁺ retention occurs (24–27). These changes are supported by the kidneys, which are regulators of volume and electrolyte homeostasis, via major adaptations that are made in renal hemodynamics (28–35), morphology (29,30,36), and nephron transport (24,26,33,37–44). Specifically, this includes increased filtration to the kidneys, increased kidney volume, and altered transporter activity along the various nephron segments.

The kidneys play an essential role in long-term blood pressure control. Altered renal function in a rat occurs during hypertension (45–47). Specifically, in female rats, chronic hypertension has been shown to decrease Na⁺ transporter activity in the proximal segments as well as increase Na⁺ transporter activity in the distal segments (47). In this paper, we seek to predict how chronic hypertension impacts renal transport in a virgin female rat and pregnant rat using computational modeling.

In this study, we developed computational models of a full kidney in a pregnant rat to investigate the impact of key pregnancy-induced renal adaptations on Na⁺ and K⁺ handling in silico. We built two computational models: one that represents kidney function at mid-pregnancy and another that represents kidney function at late pregnancy. The female-specific rat kidney model developed by Hu et al. (48) is used as a virgin control in this study. Different models for mid- and late pregnancy stages were necessary because of the changes demands of a growing fetus and placenta through gestation. Using these models we investigated the impact of key pregnancy-induced renal adaptations on Na⁺ and K⁺ handling in a full kidney. Additionally, we considered the impact of epithelial Na⁺ channel and H⁺-K⁺-ATPase knockout and inhibition on kidney Na⁺ and K⁺ transport during pregnancy based on existing experimental studies (Refs. (43,49)). Finally, we extend the models to investigate how hypertension may affect kidney function in a virgin rat and during pregnancy. The objective of this study is to answer the following questions: (1) To what extent can individual pregnancy-induced renal adaptations impact renal Na⁺ and K⁺ handling? (2) How does distal segment transporter inhibition and knockout impact fine tuning of Na⁺ and K⁺ during pregnancy? (3) What differences in renal electrolyte handling are predicted when a hypertensive female rat become pregnancy?

Materials and Methods

In our previous work (Ref. (25)), we developed epithelial cell-based models of a superficial nephron in the kidney of a virgin, MP, and LP rat. While the superficial nephrons do make up about 2/3 of the total nephron population, in this study, to capture full kidney function, we consider various types of nephrons. More specifically, we consider both superficial and juxtamedullary nephrons. This type of model can be described as a multiple nephron model and has been extensively developed and used to study kidney function in non-pregnant rats (48,50,51). In this study we developed baseline pregnancy-specific multiple nephron models in MP and LP rats. Additionally, we developed models of hypertensive virgin (female rat) and considered what may happen in the kidneys when a hypertensive female becomes pregnant.

Note that the original nephron transport model equations (see Refs. (48,50,51)) are based on mass conservation which are also valid in pregnancy. Hence, those same equations are used in the MP, LP, and hypertensive models, but appropriate parameter values are changed to account for the appropriate renal adaptations. The parameter changes for the MP and LP models versus virgin are summarized in Table 1. The hypertensive virgin and MP model parameter changes are summarized in Table 2.

Table 1.

MP-to-virgin and LP-to-virgin ratios of parameter values used in the MP and LP models, respectively. Virgin model parameter values were used from Ref. (48) and changed by the respective ratio for the MP and LP models. Parameter values for the MP and LP models were chosen based on experimental literature and are discussed in Ref. (25). Distal segments refers to all segments after the PCT and S3 segments (i.e., after the PT). Ratios are from the respective MP or LP model to the virgin model parameter value. The ratios are the same for the juxtamedullary and superficial nephrons. PCT, proximal convoluted tubule; S3, proximal straight tubule; SDL, short descending limb; LDL, thin descending limb; LAL, thin ascending limb; mTAL, medullary thick ascending limb; cTAL, cortical thick ascending limb; DCT, distal convoluted tubule; CNT, connecting tubule; CCD, cortical collecting duct; OMCD, outer medullary collecting duct; IMCD, inner medullary collecting duct; PT, proximal tubule; P_f, water permeability; P_K, K⁺ permeability; NHE3, Na⁺/H⁺ exchanger isoform 3; ENaC, epithelial Na⁺ channel; NKCC2, Na⁺-K⁺-2Cl^- cotransporter 2; NaPi2, Na⁺-H₂PO^{4 -} cotransporter 2; NCC, Na⁺-Cl^- cotransporter; KCC, K⁺-Cl^- cotransporter.

Table 2.

Parameter changes made in the hypertensive virgin (female) and hypertensive mid-pregnant models given as ratios from the hypertensive (HT) model parameter to the normotensive (NT) model parameter. Parameter change ratios for hypertension are the same in both the hypertensive non-pregnant and hypertensive mid-pregnant models. Abbreviations are the same as listed in Table 1.

Multi-nephron epithelial transport model

Each nephron segment is modeled as a tubule lined by a layer of epithelial cells in which the apical and basolateral transporters vary depending on the cell type (i.e., segment, which part of segment, intercalated and principal cells). The model accounts for the following 15 solutes: Na⁺, K⁺, Cl^-, HCO₃^-, H₂CO₃, CO₂, NH₃, NH₄⁺, HPO₄^2-, H₂PO₄^-, H⁺, HCO₂^-, H₂CO₂, urea, and glucose. The model consists of a large system of coupled ordinary differential and algebraic equations, solved for steady state, and predicts luminal fluid flow, hydrostatic pressure, membrane potential, luminal and cytosolic solute concentrations, and transcellular and paracellular fluxes through transporters and channels. A schematic diagram of the various cell types, with MP and LP changes highlighted, is given in Figure 1.

Figure 1.

Schematic diagram of the nephrons represented in the models. The model includes a superficial nephron and five representative juxtamedullary nephrons scaled by the appropriate population ratio. Here only one superficial and one juxtamedullary nephron are illustrated. The juxtamedullary nephron is the nephron including the LAL and LDL segments. The diagram displays main Na⁺, K⁺, and Cl^- transporters as well as aquaporin water channels. Mid-pregnant adaptations from virgin values are indicated by pink arrows. Late-pregnant adaptations from virgin values are indicated by green arrows. Upward orientation indicates that the transporter is increased in the respective model. Details are shown in Table 1. CCD, cortical collecting duct; cTAL, cortical thick ascending limb; CNT, connecting tubule; DCT, distal convoluted tubule; IMCD, inner medullary collecting duct; LAL, thin ascending limb; LDL, thin descending limb; mTAL, medullary thick ascending limb; OMCD, outer medullary collecting duct; PCT, proximal convoluted tubule; SDL, short descending limb; SNGFR, single-nephron glomerular filtration rate; S3, proximal straight tubule. Cell and nephron diagram adapted from Refs. (25,51).

Superficial vs. juxtamedullary nephrons

Kidneys have multiple types of nephrons; superficial and juxtamedullary nephrons make up most of them (52–54). In a rat, about two-thirds of the nephron population are superficial nephrons: the remaining third are called juxtamedullary nephrons. These two nephron types have several key differences. The first major difference is that the juxtamedullary nephrons have loops of Henle that reach differing depths into the inner medulla. In contrast, the loops of superficial nephrons turn before reaching the inner medulla. To capture this, in the model there are six classes of nephrons: a superficial nephron (denoted by “SF”) and five juxtamedullary nephrons that are assumed to reach depths of 1, 2, 3, 4, and 5 mm (denoted by “JM-1”, “JM-2”, “JM-3”, “JM-4”, and “JM-5”, respectively) into the inner medulla. In the same way as in Ref. (51), the ratios for the six nephron classes are n_SF = 2/3, n_JM―1 = 0.4/3, n_JM―2 = 0.3/3, n_JM―3 = 0.15/3, n_JM―4 = 0.1/3, and n_JM―5 = 0.05/3 so that 2/3 of the nephrons are superficial and the juxtamedullary nephrons make up the remaining 1/3 of nephrons. Note that shorter juxtamedullary nephrons are the most common, thus turning in the upper portion of the inner medulla. We note that we do not consider mid-cortical nephrons in this model. These assumptions are used from Ref. (51) which were based on anatomical findings in Ref. (55).

The previously developed superficial nephron virgin, MP, and LP (see Ref. (25)) models include the proximal, short descending limb, thick ascending limb, distal convoluted tubule, connecting tubule, and the collecting duct. The juxtamedullary nephron models include all the same segments of the superficial nephron with the addition of the long descending limbs and ascending thin limbs; these are the segments of the loops of Henle that extend into the inner medulla. The length of the long descending limbs and ascending limbs are determined by which type of juxtamedullary nephron is being modeled.

It has been shown that the SNGFR for juxtamedullary nephrons is higher than the superficial nephron SNGFR (51,52). We assume that the juxtamedullary SNGFR is about 40% higher than the superficial SNGFR in the virgin model as done in Ref. (48) and reported in experimental studies in Refs. (52–54).

All other segments in the juxtamedullary nephrons are the same as the superficial nephrons except the length of the cortical thick ascending limb and the connecting tubule. Since the glomeruli of juxtamedullary nephrons are located lower in the cortex than the superficial nephron glomeruli, these segments do not have to be as long for the nephron to pass the glomerulus at the macula densa. Hence, these segments are modeled with a shorter length.

The connecting tubules of the five juxtamedullary nephrons and the superficial nephron coalesce into the cortical collecting duct. To model this, we compute the flows from the six nephrons at the start of the collecting duct. The remaining model is the collecting duct which does not have distinct nephron segments.

Pregnancy-specific models

We created pregnancy-specific models to simulate kidney function in MP and LP by using the virgin (female-specific) multiple nephron epithelial transport model developed in Ref. (48) and increasing or decreasing relevant virgin model parameter values based on experimental findings in the literature. The specific MP-to-virgin and LP-to-virgin parameter value ratios are listed in Table 1.

In the virgin model, the superficial SNGFR is 24 nL/min and the juxtamedullary SNGFR is 33.6 nL/min. During pregnancy, there is a significant increase in GFR compared to the virgin values (3,29,32,35,56–58). Specifically, in rats, the GFR is increased by about 30% in MP and drops in LP to 20% above pre-gestational (virgin) GFR (3,29,32,35). The GFR is the total filtration by a kidney, hence is a total combination of the SNGFR of the superficial and juxtamedullary nephrons (denoted by SNGFR_sup and SNGFR_jux respectively) so that where n_sup and n_jux denote the total number of superficial and juxtamedullary nephrons in a rat kidney. In our previously developed pregnancy-specific superficial nephron models (see Ref. (25)), SNGFR_sup was increased by 30% in MP and 20% in LP based on Ref. (32). Then using Eq. 1 we can note that to have a 30% and 20% increase in the MP and LP GFR, respectively, that SNGFR_jux must also be increased by 30% and 20% in the MP and LP models, respectively (see Table 1). We note that it has been shown that increased GFR in pregnancy has been attributed to increased renal blood flow (31,35), so then a similar increase in filtration in both the superficial and juxtamedullary nephrons would be supported by this hypothesis.

Other parameter changes were changed in the same way as in the pregnancy-specific superficial nephron models we previously developed in Ref. (25). See Table 1 for the full list of MP and LP model changes from virgin model parameters. It is assumed that the activity levels of the transporters in the juxtamedullary nephrons are changed in the same way as in the superficial nephrons.

Simulating transporter inhibition and knockout

We conducted ENaC and H⁺-K⁺-ATPase inhibition in silico experiments using our baseline NP, MP, and LP models. In the EnaC inhibition experiment we inhibited the ENaC by 70% and also full knockout (i.e., inhibit by 100%) based on the chronic ENaC blockade experimental processes conducted by West et al. (43).

In the H⁺-K⁺-ATPase experiments we ran two types of H⁺-K⁺-ATPase experiments. In the first one we fully knocked out the H⁺-K⁺-ATPase transporter only (referred to as HKA-KO) for each of the virgin, MP, and LP models. In the second experiment (referred to as HKA-KO-preg) we also added changes to the MP and LP H⁺-K⁺-ATPase knockout experiments so that the NCC and Pendrin transporters were unchanged from virgin values and the ENaC increase during pregnancy was decreased by half. These changes were made based on the observations by Walter et al. (49) that pregnant H⁺-K⁺-ATPase knockout mice had altered renal adaptations from normal pregnancy renal adaptations.

Simulating hypertension in virgin females and pregnancy

To study the impact of hypertension in a virgin female as well as during pregnancy we developed models that captured renal changes during angiotensin II-induced hypertension. We note that during pregnancy there are multiple types of hypertensive disorders of pregnancy. In this study we simulate what happens when a female rat that is hypertensive (pre-gestation) gets pregnant. Therefore, we simulate the hypertensive mid-pregnant rat as the hypertensive virgin rat model with then adding the mid-pregnancy changes to the parameters. Note that we model hypertension based on studies using mostly angiotensin II-dependent hypertension (45,47).

The parameter changes made to simulate hypertension were based largely on the hypertensive female (virgin) rat results in Veiras et al. (47), which investigated the effect of hypertension on female and male rats. Additionally, we make parameter changes using the results from Abreu et al. (33), who investigated the effects of hypertensive virgin and hypertensive mid-pregnancy on renal Na⁺ and aquaporin (AQP) transporters. The exact parameter changes made are listed in Table 2 and are described here. Parameters not listed in Table 2 were not changed in the hypertension models.

Proximal segment changes

The fluid inflow at the start of the PT is assumed to be the same as the normotensive virgin and MP models in the hypertensive virgin (virgin-HTN) and hypertensive MP (MP-HTN) models in the same way as Edwards and McDonough (46). We note that this would be assuming a similar plasma volume status in chronic hypertension with pregnancy since the pregnancy-induced increase in SNGFR has been shown to be induced by increased renal plasma flow.

Located on the basolateral side of every cell type in every segment along the nephron, the Na⁺-K⁺-ATPase pump is a key driver of Na⁺ transport. Na⁺-K⁺-ATPase abundance has been shown to be decreased in the medullary thick ascending limb during hypertension (45,47). Na⁺-K⁺-ATPase abundance in the proximal and distal tubules, as well as the cortical part of the ascending limb was largely unchanged (45,47). To incorporate this into the model, we decreased Na⁺-K⁺-ATPase activity in the medullary thick ascending limb and left the activity unchanged in the other segments in the hypertensive models (see Table 2).

The Na⁺/H⁺ exchanger isoform 3 (NHE3) is located along the apical side of the epithelial cells in the PT and thick ascending limb. This transporter plays a major role in Na⁺ reabsorption along these early segments of the nephrons. During hypertension, there is blunted pressure-natriuresis which often is attributed to lower NHE3 activity. Abreu et al. (33) showed that in MP rats, there was decreased expression of NHE3.Veiras et al. (47) found that along the PT and the medullary thick ascending limb, NHE3 activity in hypertensive rats was decreased from normotensive NHE3 activity. We chose a value slightly higher for the virgin (female) rats from the parameter change chosen in Edwards and McDonough (46) since hypertensive females seemed to have slightly higher NHE3 activity than hypertensive males in Ref. (47). In the cortical segment of the thick ascending limb, it has been shown that the NHE3 activity is largely unchanged in a hypertensive rat, hence we did not change the NHE3 activity in that segment in the hypertensive models (45). See Table 2 for exact changes made in the virgin-HTN and MP-HTN models.

The Na⁺/P_i cotransporter 2 (NaPi2) is located along the PT. Veiras et al. (47) found in hypertensive rats that NaPi2 expression was decreased compared to normotensive rats. As such, we decreased NaPi2 activity in the hypertensive models (Table 2).

The Na⁺-K⁺-2Cl^- cotransporter (NKCC2) is located on apical membrane along the thick ascending limb. During hypertension, NKCC2 activity is different in the medullary and cortical segments (45–47). Specifically, in the cortex, NKCC2 activity is increased, while in the medulla, NKCC2 is significantly decreased (45–47). We altered NKCC2 activity in the hypertensive models accordingly (Table 2).

Distal segment changes

The Na⁺-Cl^- cotransporter (NCC) is in the distal convoluted tubule. During hypertension, NCC abundance and phosphorylation has been found to increase significantly (45–47). Parameter changes in NCC activity in the hypertensive models is listed in Table 2.

Abreu et al. (33) found a major decrease in the expression of the renal outer medullary K⁺ channel (ROMK) during hypertension for both virgin and MP. To capture this, we significantly decreased K⁺ permeability in the late distal convoluted tubule (DCT2) and the connecting tubule (see Table 2).

During hypertension, ENaC activity is increased (45–47). Since the female ENaC increase appears slightly higher than males, as shown by Veiras et al. (47), we chose to increase the ENaC activity more than done in the previous hypertensive male model by Edwards & McDonough (46). The hypertensive model parameter change is given in Table 2.

Abreu et al. (33) showed major changes in aquaporin 2 (AQP2) expression in the collecting duct. Specifically, in the hypertensive virgin results, the AQP2 expression increased from normotensive virgin levels. We changed the water permeability in the collecting duct segments based on this result (see Table 2).

Research Ethics

There was no use of animal or human subjects in this study.

Results

Baseline MP and LP models predict a balance of the marked increase in filtered loads and pregnancy-induced enhancement in transport capacity

Solute and fluid volume reabsorption along specific nephron segments depends on activity of membrane transporters, permeability of the apical and basolateral membrane, as well as tubular morphology. Many changes occur in almost all nephron segments during pregnancy. To investigate the impact of pregnancy-induced changes on renal transport, we developed baseline models to represent kidney function in a virgin, mid-pregnant (MP), and late-pregnant (LP) rat. The models are based on our previous work (see Ref. (25,48)) and are described in Materials and Methods. A model schematic is shown in Figure 1.

In the MP and LP models, the filtration to the nephrons is assumed to be 30% and 20% higher than the virgin model values, respectively (Table 1). This yields a proportional increase in total fluid and solute delivery at the start of the proximal tubule (PT) in the MP and LP model predictions (Figure 2). Model predictions indicate that, due to tubular hypertrophy (i.e., increased transport area) and upregulation in the Na⁺/H⁺ exchanger isoform 3 (NHE3) and the K⁺-Cl^- cotransporter (KCC), predicted net Na⁺ and Cl^- reabsorption in the PT of the MP and LP models is significantly larger than in the virgin rat model (Figure 3A; Figure 3C). Specifically, MP and LP models predicted a 27% and 16% increase in net Na⁺ reabsorption along PT when compared to virgin. The increase in Na⁺ reabsorption is about the same proportion increase as the in GFR in both the MP and LP models, hence glomerulotubular balance in the PT appears to hold in pregnancy, with a fractional reabsorption of Na⁺ about 60% for each of the virgin, MP, and LP models along the PT. Analogous results are obtained for Cl^- and fluid volume along the PT (see Figure 2; Figure 3).

Figure 2.

Delivery of key solutes (A-E) and fluid volume (F) to the beginning of individual nephron segments in the virgin, mid-pregnant (MP), and late pregnant (LP) rat models. The colored bars denote the superficial nephron values, and the white bars denote the weighted totals of the juxtamedullary nephrons (five representative model nephrons) where total bar height is the sum of the delivery to superficial and juxtamedullary nephrons. Note that since the model assumes that the superficial-to-juxtamedullary nephron ratio is 2:1, the superficial delivery values are generally higher. Additionally, the juxtamedullary and superficial nephrons merge at the collecting duct so the urine output is combined. PT, proximal tubule; DL, descending limb; LAL, thin ascending limb; mTAL, medullary thick ascending limb; DCT, distal convoluted tubule; CNT, connecting tubule; CCD, cortical collecting duct. Insets: reproduction of distal segment values.

Figure 3.

Net segmental transport of key solutes (A-E) and volume (F) along the individual nephron segments in the virgin, MP, and LP models. Transport is positive out of the nephron segment, i.e., positive transport indicates net reabsorption and negative transport indicates net secretion along that segment. Colored bars denote the superficial nephron values and white bars denote juxtamedullary values computed as a weighted sum of the five representative juxtamedullary nephrons. PT, proximal tubule; DL, descending limb; LAL, thin ascending limb; TAL, thick ascending limb; DCT, distal convoluted tubule; CNT, connecting tubule; CD, collecting duct. Insets: reproductions of distal segment values.

Downstream of the PT, the thick ascending limb reabsorbs much of the Na⁺ and Cl^- remaining in the lumen. In the MP model, Na⁺ delivery to the thick ascending limb is 16% higher than virgin model values due to the increased filtered load of Na⁺ along with similar fractional reabsorption of Na⁺ by the PT (Figure 2A). Reabsorption along the thick ascending limb increases by about 16% in MP (Figure 3A). Analogous results are obtained for Cl^-. In the end, urinary Na⁺ excretion for both MP and LP is about 16% higher than virgin values and urinary Cl^- excretion is increased by 4% and 6% in the MP and LP models, respectively. The increase in natriuresis and Cl^- excretion in the pregnancy models versus the virgin model are within reported ranges (37,59).

Along the PT, the increased Na⁺ reabsorption provides the driving force for increased water reabsorption along the PT by 34% and 24% in the MP and LP models, respectively, when compared to virgin model values (Figure 3F). In the segments after the macula densa and the collecting duct, fluid reabsorption is also increased by 22% and 12% in the MP and LP models, respectively when compared to virgin model fluid reabsorption (Figure 3F). This is likely driven by increased AQP2 expression in the collecting duct, increased nephron diameter and length, as well as increased fluid volume delivery to these segments.

About 58% of the filtered K⁺ is reabsorbed along the PT in the virgin model. During LP, the fractional reabsorption of K⁺ in the PT increases to about 63% (Figure 3B). This is due to the massive increase in delivery of K⁺ from a combination of 30% increase in plasma K⁺ concentration (26,60), increased GFR, and increased K⁺ transport capacity (Table 1). Distal segment K⁺ secretion along the distal convoluted tubules (DCT) and connecting tubules (CNT) is decreased by about 8% in the MP and LP models from virgin model values despite known kaliuretic factors such as increased Na⁺ delivery (Figure 3B). This is due to the decreased K⁺ channel permeability in these segments (see Table 1). In all, K⁺ urinary excretion is predicted to be 2.4, 3.0, and 2.9 mmol/day in the virgin, MP, and LP models, respectively. The increase in kaliuresis from virgin values in the MP and LP models is within reported ranges (26,59).

Proximal tubule hypertrophy and the upregulation of epithelial Na⁺ channel and H⁺-K⁺-ATPase play key roles in maintaining Na⁺ and K⁺ balance during pregnancy

Using our baseline LP computational model, we conducted what-if simulations to predict how key individual changes impact renal transport during late pregnancy. To do this we considered the renal adaptations that have a major impact on nephron transport from our analysis of a superficial nephron (see Ref. (25)) and conducted simulations of LP kidney function without such adaptation (i.e., respective parameter value at the virgin model value). Transport of Na⁺ and K⁺ for adaptations that effect the proximal segments of the nephron (i.e., PT length, NHE3 activity, and Na⁺-K⁺-ATPase activity) are shown in Figure 4 and adaptations that effect only the distal segments (i.e., ENaC activity, K⁺ channel permeability, H⁺-K⁺-ATPase activity) are shown in Figure 5.

Figure 4.

Impact of key pregnancy-induced proximal segment renal adaptations on net segmental transport and urine excretion of Na⁺ (A) and K⁺ (B) along individual nephron segments in the baseline LP model and LP model with one pregnancy-induced change (as labeled) set to the respective virgin parameter value: NHE3 activity, PT length, and Na⁺-K⁺-ATPase activity. Transport orientation and abbreviations for the PT, DL, LAL, TAL, DCT, CNT, and CD are the same as in Figure 3. Delivery of urine is same convention as in Figure 2. NHE3, Na⁺/H⁺ exchanger isoform 3; NKATPase, Na⁺-K⁺-ATPase.

Figure 5.

Impact of key pregnancy-induced adaptations in the distal segments on net segmental transport and urine excretion of Na⁺ (A) and K⁺ (B) along individual nephron segments in the baseline LP model and LP model with one pregnancy-induced change set to the respective virgin value: ENaC activity, P_K, and H⁺-K⁺-ATPase activity. Transport orientation and abbreviations for the DCT, CNT, and CD are the same as in Figure 3. Delivery of urine is same convention as in Figure 2. Only the distal segment results are shown because these changes only affect distal segments. HKATPase, H⁺-K⁺-ATPase; ENaC, epithelial Na⁺ channel; P_K, permeability of K⁺.

Most reabsorption in the kidneys occurs in the proximal segments, which include the PT and the loop of Henle. During LP, the PT length is increased by about 17% from the baseline virgin model nephron length (Table 1; Refs. (25,29,30)), which increases transport capacity along the PT of the nephrons. Without this change, we predict that the PT reabsorbs 11% less Na⁺ than the baseline LP model (Figure 4A). While reabsorption along the thick ascending limbs and distal segments is increased, it is not enough to make up for the loss resulting in an increase of about 77% in urine excretion of Na⁺ (Figure 4A). Similarly, without the PT length increase, K⁺ reabsorption is significantly decreased in the PT segment, ultimately resulting in a 46% increase in urinary K⁺ excretion.

The distal segments account for much of the fine tuning of fluid concentrations in the kidney nephrons before excreting what is remaining through urine. In our analysis of a superficial nephron, we predicted that key distal segment adaptations seem to play a role in gestational nephron function (25). The ENaC is increased in abundance during pregnancy (37,43), likely contributing to increased ENaC activity. Additionally, key K⁺ transporters are altered, namely the activity of key distal segment K⁺ channels, the renal outer medullary K⁺ channel (ROMK) and big K⁺ channel (BK), are significantly decreased (26). (Note that this is represented by P_K in Table 1.) These channels are secretory meaning that they secrete K⁺ into the lumen along the distal segments. Additionally, the activity of the H⁺-K⁺-ATPase transporter is significantly increased (26,27,42,49). We conducted simulations of the LP model without such changes and present the results for Na⁺ and K⁺ transport as well as urinary excretion in Figure 5.

The ENaC plays a key role in reabsorbing Na⁺ along the late DCT, CNT, and collecting duct (CD). Without a large increase in ENaC activity in the LP model, Na⁺ reabsorption in the DCT and CNT decreased by 13%. This yielded a 22% increase in urinary Na⁺ excretion (Figure 5A). Notably, increased ENaC activity is a known kaliuretic factor. Without a pregnancy-induced increase in ENaC activity we predict a 15% decrease in urinary K⁺ excretion (Figure 5B).

The abundance of K⁺ secretory channels is massively decreased during LP. Without this change in the LP model, K⁺ secretion along the DCT increased by 26%. Decreased CNT K⁺ makes up for some of this extra K⁺ loss, but model simulations predict an increase in K⁺ excretion by about 8%. The other K⁺ transporter altered during LP is H⁺-K⁺-ATPase activity, which is significantly increased (Table 1). Without this change, both the distal tubule and CD K⁺ secretion more than doubles (Figure 5B). This results in urinary K⁺ increase by 19%.

Other pregnancy-induced renal adaptations such as the activity of the NHE3 and Na⁺-K⁺-ATPase transporters effect urinary excretion in a significant way. Decreasing NHE3 activity to the virgin value results in a 2% decrease in PT reabsorption. This change is not made up for in the late segments and results in a 17% increase in urinary Na⁺ excretion and 8% increase in urinary K⁺ excretion (Figure 4). The effect of pregnancy on Na⁺-K⁺-ATPase activity in the kidneys is region-specific (38). Setting the Na⁺-K⁺-ATPase activity in each segment to the virgin value resulted in a 16% decrease in urinary excretion of Na⁺ and a 5% decrease in K⁺ excretion (Figure 4).

Epithelial Na⁺ channel activity is essential for sufficient Na⁺ reabsorption during pregnancy

West et al. (43) conducted experiments to test the effect of inhibition of the ENaC on pregnancy and found that a chronic ENaC blockade ablated the normal pregnancy Na⁺ retention. We conducted simulations to test the impact of a 70% ENaC inhibition and a full ENaC knockout (i.e., 100% inhibition) on our model predictions. Results are given in Figure 6 and Figure 7, respectively.

Figure 6.

Impact of epithelial Na⁺ channel (ENaC) inhibition (70%) on distal segment net segmental transport of Na⁺ (A) and K⁺ (B) along individual nephron segments in the virgin, mid-pregnant (MP), and late pregnant (LP) models. Transport orientation and labels are the same as in Figure 3. The last bar shows delivery of urine which is the same as in Figure 2. Only the distal segments are shown because ENaC inhibition only affects distal segments.

Figure 7.

Impact of epithelial Na⁺ channel (ENaC) knockout on distal segment net segmental transport of Na⁺ (A) and K⁺ (B) along individual nephron segments in the virgin, mid-pregnant (MP), and late pregnant (LP) models. Transport orientation and labels are the same as in Figure 3. The last bar shows delivery of urine which is the same as in Figure 2. Only the distal segments are shown because ENaC inhibition only affects distal segments.

When the ENaC is inhibited by 70% in the MP and LP models, there is a 19% and 21% reduction in Na⁺ reabsorption along the DCT and CNT, respectively, when compared to the respective baseline MP and LP models. Collecting duct Na⁺ reabsorption does increase in both models, but this loss results in a 48% and 38% increase in urinary Na⁺ excretion, respectively (Figure 6A). ENaC inhibition has an opposite effect on K⁺. Specifically, K⁺ secretion is decreased by ENaC inhibition so much so that the models predict a net K⁺ reabsorption along the CNT for each of the virgin, MP, and LP models. This significant change results in a net reduction in K⁺ secretion along the distal segments of 82% in the MP model. In the end urinary excretion of K⁺ is reduced by about 26% when compared to the baseline MP and LP models (Figure 7B).

A full ENaC knockout leads to even more drastic effects on Na⁺ and K⁺ handling in each of the virgin, MP, and LP model predictions when compared to 70% inhibition. Specifically, the CNT has net secretion of Na⁺ with net reabsorption of K⁺. This happens likely because the ENaC is the primary Na⁺ transporter along this segment. As a result, urinary Na⁺ excretion is predicted to more than double while urinary K⁺ excretion is about 25% of baseline for the virgin, MP, and LP models (Figure 7).

Adaptations in pregnant H⁺-K⁺-ATPase knockout animals decreases excess K⁺ loss while increasing Na⁺ excretion

Walter et al. (49) conducted experiments to test the effect of H⁺-K⁺-ATPase knockout (HKA-KO) on Na⁺ and K⁺ regulation in pregnant mice and found that pregnant HKA-KO mice had only a modestly expanded plasma volume and altered K⁺ balance when compared to pregnant wild-type mice.

We conducted two types of HKA-KO experiments. In the first simulation we did a full 100% inhibition of the H⁺-K⁺-ATPase transporter only. We will refer to this simulation as HKA-KO. Results are shown in Figure 8. In the second simulation we also added a changes in Na⁺-Cl^- cotransporter, ENaC, and Pendrin transporter activities as reported in Walter et al. (49) (see Materials and Methods). We will refer to this simulation as HKA-KO-preg. These results are shown in Figure 9.

Figure 8.

Impact of H⁺-K⁺-ATPase knockout (KO) study on distal segment net segmental transport of Na⁺ (A) and K⁺ (B) along individual nephron segments in the virgin, mid-pregnant (MP), and late pregnant (LP) models. Transport orientation and labels are the same as in Figure 3. The last bar shows delivery of urine which is the same as in Figure 2. Only the distal segments are shown because HKA inhibition only affects distal segments.

Figure 9.

Impact of pregnancy-specific H⁺-K⁺-ATPase knockout (KO) study on distal segment net segmental transport of Na⁺ (A) and K⁺ (B) along individual nephron segments in the virgin, mid-pregnant (MP), and late pregnant (LP) models. Pregnancy models also include changes to the pregnancy-specific renal adaptations of the Na⁺-Cl^- cotransporter, epithelial Na⁺ channel, and Cl^--HCO^3- exchanger. Transport orientation and labels are the same as in Figure 3. The last bar shows delivery of urine which is the same as in Figure 2. Only the distal segments are shown because HKA inhibition only affects distal segments.

Net K⁺ secretion along the DCT and CNT is predicted to increase by 85% and 77% in the MP HKA-KO and LP HKA-KO simulations, respectively, when compared to the baseline MP and LP models. This results in about a 60% increase in urinary K⁺ excretion for both the MP and LP HKA-KO model simulations. The virgin HKA-KO model predicts an increase in K⁺ secretion along these segments, but by a smaller fraction of 34%, yielding a 41% increase in urinary K⁺ excretion when compared to the baseline virgin model (Figure 8). Na⁺ handling is slightly altered resulting in about a 5% increase in urinary Na⁺ excretion for each of the virgin, MP, and LP model simulations.

Walter et al. (49) found that in pregnant H⁺-K⁺-ATPase type 2 knockout mice, the Na⁺-Cl^- cotransporter, ENaC, and Pendrin transporter were altered as well from normal pregnancy adaptations. We conducted simulations with these observed changes and called these simulations the HKA-KO-preg simulations (see Figure 9). The additional adaptations alter how Na⁺ and K⁺ is handled along the distal segments when compared to the HKA-KO only simulations (see Figure 8). Specifically, in the HKA-KO-preg MP simulations, K⁺ secretion along the DCT and CNT is 32% higher than baseline MP simulations. Similarly, the HKA-KO-preg LP simulation predict a 19% increase in K⁺ secretion along these segments when compared to baseline LP. This is likely due to the decreased ENaC activity because increased ENaC activity would increase K⁺ secretion in these segments. In the end urinary K⁺ excretion for the HKA-KO-preg MP and LP simulations is 42% higher than the respective baseline MP and LP model predictions. Additionally, since there is Na⁺ transporter changes, Na⁺ handling is altered such that urinary Na⁺ excretion is increased by about 24% in both the HKA-KO-preg MP and HKA-KO-preg LP models when compared to the respective baseline MP and LP model predictions.

Chronic hypertension induces a shift in Na⁺ load to distal segments in virgin and MP rat kidneys

We developed hypertensive virgin and MP models using the changes listed in Table 2 and described in Materials and Methods. We denote the hypertensive virgin model by virgin-HTN and the hypertensive MP model by MP-HTN. Delivery of Na⁺, K⁺, and fluid volume to each segment for the baseline virgin, virgin-HTN, baseline MP, and MP-HTN models are shown in Figure 10. Net segmental transport predictions for each of the normotensive and hypertensive virgin and MP models is given in Figure 11.

Figure 10.

Delivery of key solutes (A-E) and fluid volume (F) in the normotensive and hypertensive virgin and mid-pregnant (MP) models. The colored bars denote the superficial nephron values, and the white bars denote the weighted totals of the juxtamedullary nephrons (five representative model nephrons). PT, proximal tubule; DL, descending limb; LAL, thin ascending limb; mTAL, medullary thick ascending limb; cTAL, cortical thick ascending limb; DCT, distal convoluted tubule; CNT, connecting tubule; CCD, cortical collecting duct. Insets: reproduction of distal segment values.

Figure 11.

Net segmental transport of key solutes (A-E) and volume (F) along the individual nephron segments in the normotensive and hypertensive virgin and mid-pregnant (MP) models. Transport is positive out of the nephron segment, i.e., positive transport shows net reabsorption and negative net secretion along that segment. Colored bars denote the superficial nephron values and white bars denote juxtamedullary values computed as a weighted sum of the five representative juxtamedullary nephrons. PT, proximal tubule; DL, descending limb; LAL, thin ascending limb; mTAL, medullary thick ascending limb; cTAL, cortical thick ascending limb; DCT, distal convoluted tubule; CNT, connecting tubule; CD, collecting duct. Insets: reproductions of distal segment values.

Due to pressure natriuresis, PT Na⁺ reabsorption is decreased slightly (about 4%) in the virgin-HTN and MP-HTN models from the respective normotensive model predictions (Figure 11A). The virgin-HTN and MP-HTN models predict a 5% and 3% decrease in PT K⁺ reabsorption when compared to the respective normotensive models (Figure 11B). Net fluid volume reabsorption along the PT decreased by about 3% for both the virgin-HTN and MP-HTN models when compared to the respective normotensive baseline models (Figure 11C). The lower fluid volume reabsorption results in increased volume delivery to each of the segments along the nephron. These changes in Na⁺, K⁺, and volume transport along the PT are driven by the decreased NHE3 and NaPi2 activity in the hypertensive models (see Table 2).

Region-specific changes in the Na⁺-K⁺-2Cl^- cotransporter (NKCC2), NHE3, and Na⁺-K⁺-ATPase activity (Table 2) lead to differential alterations in transport in the medullary and cortical segments of the thick ascending limb. In the medullary thick ascending limb of both hypertensive models, NKCC2, NHE3, and Na⁺-K⁺-ATPase activity are assumed lowered decreased (Table 2). Consequently, Na⁺ reabsorption along the medullary thick ascending limb decreases by 12% in the virgin-HTN model and 8% in the MP-HTN model relative to the respective normotensive models (Figure 11A). As such, more Na⁺ reaches the cortical thick ascending where, unlike the medullary thick ascending limb, transport capacity is enhanced: NKCC2 activity is increased from normotensive values in the hypertensive models, while NHE3 and Na⁺-K⁺-ATPase activity is unchanged from normotensive values (Table 2). This results in about a 27% increase in Na⁺ reabsorption along this segment in both the hypertensive models (Figure 11A).

The reduced PT K⁺ reabsorption leads to a 7% and 5% increase in K⁺ delivery to the thick ascending limb in the virgin-HTN and MP-HTN models, respectively, when compared to the respective normotensive model (Figure 10B). Along the medullary thick ascending limb, K⁺ transport is increased by about 15% in the hypertensive models compared to the respective normotensive models (Figure 11B). This increased transport in the medullary thick ascending limb results in decreased cortical thick ascending limb K⁺ delivery in the hypertensive models compared to the respective normotensive models for both the virgin-HTN and MP-HTN models.

Na⁺ transport along the DCT and CNT exhibits a substantial increase in both hypertensive models (69% and 42% increase, respectively, in the virgin-HTN and MP-HTN above baseline normotensive model predictions), due to elevated delivery as well as the enhanced Na⁺-Cl^- cotransporter and ENaC activity (Figure 11A). Major K⁺ secretion occurs along the DCT and CNT. During hypertension, the expression of K⁺ secretory channel ROMK is significantly decreased (Table 2). In the late DCT, the reduced K⁺ secretion from the ROMK leads to 8% and 25% lower K⁺ secretion in the DCT for the virgin-HTN and MP-HTN models, respectively when compared to the respective normotensive virgin and MP models. This is where the virgin-HTN and MP-HTN models seem to differ. Connecting tubule K⁺ secretion is increased in the virgin-HTN model when compared to virgin so that in total the K⁺ secretion along the DCT and CNT is 45% higher than virgin distal tubule K⁺ secretion. This increase is likely driven by the effect of increased Na⁺ flow in the CNT and increased ENaC activity (a known kaliuretic factor). The increased Na⁺ in the CNT creates a favorable electrical potential gradient which in turn increases K⁺ secretion. K⁺ secretion in the MP-HTN model along the DCT and CNT is predicted to be about the same as normotensive MP distal tubule K⁺ secretion. This is likely due to the already significantly decreased ROMK channel permeability in the normotensive MP model (Table 1).

In summary, decreased Na⁺ transport in the proximal segments effects the early K⁺ reabsorption which leads to higher K⁺ flow to the distal segments. Further along the nephron in the distal segments K⁺ secretory channels are reduced to lower K⁺ secretion despite high Na⁺ flow and kaliuretic factors such as increased ENaC activity.

Discussion

What are the physiological implications of the renal adaptations that occur during pregnancy? How does altered expression and activity of renal transporters impact kidney function in a female with hypertension? How does pregnancy alter transport along the nephrons in a hypertensive female rat? To answer these questions, we developed baseline computational models of full kidney function of a rat during mid- and late pregnancy. Additionally, we developed a female-specific hypertension model as well as a model that predicts kidney function during mid-pregnancy for a female rat with chronic hypertension. We focus on mid-pregnant hypertension since there have not been any studies to date that investigated nephron function in late pregnant hypertensive rats.

Kidney function during pregnancy

The kidneys play a key role in maintaining body homeostasis. Pregnancy is unique in that plasma volume expansion and electrolyte retention is required in the maternal body to sufficiently supply the rapidly developing fetus and placenta. Without a massive plasma volume expansion, it is likely that fetal growth restriction will occur (3,28,61–66). Gestational disorders such as gestational hypertension and preeclampsia are also associated with low plasma volume expansion (3,63–65). Indeed, renal adaptations must occur to be able to support such a significant change in the maternal body.

Pregnancy-induced renal adaptations are complex and dynamic. Starting from early pregnancy, filtration to the nephrons is massively increased due to increased plasma flow (31). This requires major adaptations in the nephron segments to sufficiently reabsorb this increased load (24,25). The proximal tubule is the first segment of the nephron and reabsorbs a majority of the filtered load. During pregnancy, the tubule length is increased which leads to more transport capacity (25,30,67). Without this change, excess natriuresis and kaliuresis will likely occur, due to inadequate Na⁺ reabsorption by the proximal tubule (Figure 4). This result is similar to our previous study where we investigated the effects of individual pregnancy-induced adaptations on urinary excretion of a single superficial nephron (25).

Similarly, we hypothesize that NHE3 activity increases during pregnancy (25). This has not been reported experimentally, but our simulation results indicate that some increase in NHE3 activity must occur to reabsorb the excess filtered Na⁺ load to the nephrons (see Figure 4). Without NHE3 upregulation, proximal tubule Na⁺ reabsorption is insufficient, resulting in increased urinary Na⁺ excretion.

Distal segment transporters also seem to play a key role in maintaining sufficient Na⁺ retention during pregnancy (25,26,37,43,60). West et al. (43) showed that with chronic EnaC blockade, pregnant rats were unable to sustain sufficient Na⁺ and water retention and were poor reproducers (i.e., pup weight was significantly lower than control). This result together with modeling simulations presented here and in our study on superficial nephron transport (see Ref. (25)) emphasize the importance of this transporter in pregnancy.

Several kaliuretic factors act on the kidneys of a pregnant female: elevated aldosterone levels (3,68,69), decreased NCC activity (60), and increased ENaC activity (37,43,69). However, through pregnancy the maternal body is able to maintain K⁺ homeostasis and even retain K⁺ in late pregnancy (24,26). The K⁺ secretory channels in the distal segments, which in a virgin rat vigorously secrete K⁺, are downregulated (26). In addition, the K⁺ transporter, H⁺-K⁺-ATPase has been shown to be significantly upregulated (26,27,42,49). Although it is not the key focus of this study, we note that the upregulated H⁺-K⁺-ATPase activity likely plays a key role in acid-base regulation in pregnancy which has been shown to be altered as well (26,42,70). Together these transport changes prevent excess K⁺ loss.

Female rats, pregnant or not, express more Na⁺ transporters along the distal nephron segments compared to males (48,71,72). While the proximal tubule reabsorbs the bulk of the volume and electrolytes, the distal segments are responsible for “fine-tuning” tubular transport, to yield the target urinary excretion. Placing a larger transport load on the distal segments enables the females to adapt to the changing electrolyte and volume homeostasis more easily in pregnancy and lactation. In pregnancy, GFR and filtered Na⁺ load is increased as is their respective transport; these two competing factors yield urinary excretion that nearly equals intake. Overall, there is a net whole-body Na⁺ retention, and in late pregnancy, net K⁺ retention; nevertheless, plasma Na⁺ concentration decreases largely due to the massive increase in plasma volume. Given the large amount of fluid and solutes handled by the kidneys, minute adjustments in transport are sufficient to yield the almost imperceptible difference in intake and urinary excretion, to attain the net volume and electrolyte retention seen in pregnancy. That kind of fine-tuning can best be achieved via signalling to the distal segments.

As previously noted, the marked increase in renal hemodynamics is remarkable. Studies have suggested roles for nitric oxide synthase, prostaglandins, endothelin, and relaxin. This area of research is exciting, as unraveling why glomerular filtration rate and renal plasma flow increase in pregnancy may eventually benefit patients with acute and chronic renal function loss.

Effect of distal tubule transporter inhibition on pregnancy

West et al. (43) found that chronic renal ENaC blockade (both pharmacological and genetic inhibition) ablated normal Na⁺ retention found in pregnant rats. Without this Na⁺ retention, there was significant fetal growth restriction with a decrease in maternal blood pressure and body weight, all essential to a healthy pregnancy (43). Our model simulations on renal Na⁺ transport with both 70% ENaC inhibition as well as full ENaC knockout (i.e., 100% inhibition) predict a massive increase in Na⁺ urinary excretion in both mid- and late pregnancy (Figure 6A; Figure 7A). Without this key Na⁺ transporter, excess natriuresis would certainly occur. Additionally, K⁺ handling in the distal segments is significantly impacted by the ENaC. Specifically, K⁺ secretion is decreased leading to ultimately decreased urinary K⁺ excretion (Figure 6B; Figure 7B). This could lead to excess K⁺ retention in the body leading to potential hyperkalemia without other balancing mechanisms.

Walter et al. (49) studied the effects of pregnancy on H⁺-K⁺-ATPase type 2 knockout mice. They found that H⁺-K⁺-ATPase type 2 knockout mice not only had altered K⁺ balance but also had significantly inhibited plasma volume expansion (49). We note that this is a rat model, however adaptations that happen during pregnancy in rats and mice are similar, so we conducted simulations in a similar way here. First, we conducted simulations with a full knockout of the H⁺-K⁺-ATPase transporter only (denoted by HKA-KO) and then conducted simulations that included other altered transporters (see Materials and Methods) observed by Walter et al. (49) in the MP and LP knockout simulations (denoted by HKA-KO-preg).

The HKA-KO simulation resulted in a higher increase in urinary K⁺ excretion than the HKA-KO-preg simulations when compared to the respective baseline models for both MP and LP (Figure 8B; Figure 9B). A similar change occurred in Na⁺ handling; HKA-KO simulations resulted in only a small increase in urinary Na⁺ excretion when compared to the respective baseline models while the HKA-KO-preg simulations had a significant increase in urinary Na⁺ excretion.

During normal pregnancy, ENaC activity is massively upregulated from virgin values (24,37,43,69). Walter et al. (49) observed a lower increase in ENaC activity in pregnancy H⁺-K⁺-ATPase type 2 knockout mice when compared to the pregnant wild-type mice. It is known that enhanced ENaC activity increases K⁺ secretion along the distal segments, hence by having less ENaC activity during pregnancy in H⁺-K⁺-ATPase type 2 knockout mice there is less K⁺ secretion leading to lower urinary K⁺ excretion. However, this also comes at the cost of not reabsorbing the same amount of Na⁺. Since pregnancy-induced plasma volume expansion is driven by Na⁺ retention, it appears that the observed loss in plasma volume expansion (see Ref. (49)) in H⁺-K⁺-ATPase type 2 knock out mice may be driven by compensatory changes in the nephrons. The altered Na⁺ transporters from normal pregnancy values in the pregnancy-specific H⁺-K⁺-ATPase type 2 knockout mice (captured in HKA-KO-preg simulations) may work to prevent excess kaliuresis at the cost of losing more Na⁺ and hence resulting in lower plasma volume expansion that is known to be driven by Na⁺ retention.

The model simulations presented here with the experimental results of Refs. (43,49) demonstrate the importance of distal segments transporters, specifically H⁺-K⁺-ATPase and ENaC, during pregnancy.

Hypertension in females and pregnancy

Hypertension is a highly complex disease with many underlying pathophysiological mechanisms, some of which remain to be fully understood. Hypertension affects over 30% of the global adult population and is the leading cause of cardiovascular disease (10). It is estimated that the prevalence of hypertension will continue to rise due to ageing populations, increases in the exposure to high Na⁺ and low K⁺ diets, and a lack of physical activity (10).

During hypertension, inhibited pressure natriuresis reduces NHE3 activity and proximal tubular Na⁺ reabsorption, which leads to a higher Na⁺ load to the distal segments. Interestingly, the medullary and cortical thick ascending limbs exhibit differential regulation of NKCC2, with the transporter down- and up-regulated in these two segments, respectively (45,47). Simulation results obtained for the hypertensive non-pregnant and mid-pregnant female models indicate that this differential regulation of NKCC2 minimizes Na⁺ retention while preserving K⁺ (Figure 11), consistent with results obtained in a modeling study of angiotensin II-induced hypertension in the male rat (see Ref. (46)). Differential regulation of NKCC2 in pregnancy may be attributed to that angiotensin II stimulates NKCC2 in the cortex but not in the medulla.

Along the distal segments, the activity of Na⁺ transporters the Na⁺-Cl^- cotransporter (NCC) and the ENaC are both upregulated in hypertension (see Table 2). In both the hypertensive virgin and hypertensive MP models, this change led to increased Na⁺ reabsorption in the distal segments.

In hypertension, both with and without pregnancy, there is a shift in Na ⁺ transport from the proximal tubules to the distal tubules (see Figure 11). Given that the proximal tubules are more efficient than distal tubules in transporting Na⁺ (73), in that less oxygen is consumed to reabsorb a given amount of Na ⁺, the downstream shift implies an increase in overall oxygen demand. The elevated metabolic demand, if accompanied by maternal endothelial dysfunction that negatively impacts renal oxygen supply, may lead to renal hypoxia and kidney damage.

Future work

Studying hypertensive disorders of pregnancy is complicated in that there are multiple types: chronic hypertension, chronic hypertension with superimposed pre-eclampsia, gestational hypertension, and pre-eclampsia (8,74). In this study we chose to investigate chronic hypertension due to little experimental data on nephron function in gestational hypertension and pre-eclampsia. Abreu et al. (33) investigated only mRNA data on a few transporters in hypertensive and normotensive pregnant rats. Hu et al. (75) investigated altered expression of renal Na⁺ transporters using urinary vesicles in pregnant women with pre-eclampsia. In a similar way to Refs. (76,77), human-specific models of kidney function during pregnancy may be developed to study the functional implications of this altered renal function.

Another common complication of pregnancy that may affect the kidney is gestational diabetes (6). Gestational diabetes is diagnosed by hyperglycemia that develops in the third trimester (of human pregnancy) and resolves post-parturition. Jiang et al. (78) investigated the impact of high-fat diet induced gestational diabetes on the SGLT2 and GLUT2 transporters in mice nephrons. The present model can be modified to simulate gestational diabetes and its functional implications on kidney function.

As average maternal age increases and the rates of comorbidities such as hypertension and diabetes increase in the population of women of childbearing age, rates of pregnancies complicated by a disorder will increase (6,7,11). However, our understanding of pregnancy physiology and especially gestational disorders remains limited. The study of pregnancy and its related pathologies has been historically limited by the fetal risks and ethical implications of running clinical trials on pregnant women (2,79). However, this limitation may be overcome, in part, by using computational models to test hypotheses, unravel complicated mechanisms, and potentially test the efficacy for therapies for gestational diseases in silico with the use of pregnancy-specific models as developed in this study. Indeed, there is much more computational work that can be done in understanding pregnancy physiology as well as gestational diseases as we recently reviewed in Ref. (2).

Limitations of the study

Epithelial transport models have been extensively developed to provide an accurate accounting of solute and water transport to yield insights along with experimental evidence for the complicated transport pathways, driving forces, and coupling mechanisms that are involved in kidney function. These models have been used to study the functional implications of sexual dimorphisms (48,72,76,77,80–82), interspecies differences (81), diabetes (77,83), hypertension (46), and hyperkalemia (84), circadian rhythms (82), and others. However, there are limitations that often stem from the paucity of experimental data as well as model structure as discussed in Refs. (50,85,86).

One key limitation is that in the models presented in this study it is assumed that the interstitial fluid composition is known a priori. There are changes in these models that may affect interstitial fluid composition, but since there is no evidence that has measured these changes, we did not include those changes in our model assumptions. Interactions among nephron segments and the renal vasculature can be modelled using the approaches in Refs. (87–90).

Similar to the limitations in our previous study (25), gestational kidney physiology has not been fully studied as there are some parameters that had to be assumed rather than directly based on experimental evidence. A similar limitation is there for the hypertension models. We used experimental evidence from Ref. (47) to inform our model parameter choices, however this study only investigated Na⁺ transporters. It is likely that there are other renal alterations that are impacted by hypertension. As more experimental evidence on renal transporter function during pregnancy and hypertension becomes available these models can be improved.