Numerical Methods for Fluid-Structure Interaction — A Review - Volume 12 Issue 2 - Gene Hou, Jin Wang, Anita Layton

Background: Cells adapt their metabolism and activities in response to signals from their surroundings, and this ability is essential for their survival in the face of perturbations. In tissues a deficit of these mechanisms is commonly associated with cellular aging and diseases, such as cardiovascular disease, cancer, immune system decline, and neurological pathologies. Several proteins have been identified as being able to respond directly to energy, nutrient, and growth factor levels and stress stimuli in order to mediate adaptations in the cell. In particular, mTOR, AMPK, and sirtuins are known to play an essential role in the management of metabolic stress and energy balance in mammals. Methods: To understand the complex interactions of these signalling pathways and environmental signals, and how those interactions may impact lifespan and health-span, we have developed a computational model of metabolic signalling pathways. Specifically, the model includes (i) the insulin/IGF-1 pathway, which couples energy and nutrient abundance to the execution of cell growth and division, (ii) mTORC1 and the amino acid sensors such as sestrin, (iii) the Preiss-Handler and salvage pathways, which regulate the metabolism of NAD+ and the NAD+ -consuming factor SIRT1, (iv) the energy sensor AMPK, and (v) transcription factors FOXO and PGC-1α. Results: The model simulates the interactions among key regulators such as AKT, mTORC1, AMPK, NAD+ , and SIRT, and predicts their dynamics. Key findings include the clinically important role of PRAS40 and diet in mTORC1 inhibition, and a potential link between SIRT1-activating compounds and premature autophagy. Moreover, the model captures the exquisite interactions of leucine, sestrin2, and arginine, and the resulting signal to the mTORC1 pathway. These results can be leveraged in the development of novel treatment of cancers and other diseases. Conclusions: This study presents a state-of-the-art computational model for investigating the interactions among signaling pathways and environmental stimuli in growth, ageing, metabolism, and diseases. The model can be used as an essential component to simulate gene manipulation, therapies (e.g., rapamycin and wortmannin), calorie restrictions, and chronic stress, and assess their functional implications on longevity and ageing‐related diseases.

Diabetes increases the reabsorption of Na⁺(T_Na) and glucose via the sodium-glucose cotransporter SGLT2 in the early proximal tubule (S1-S2 segments) of the renal cortex. SGLT2 inhibitors enhance glucose excretion and lower hyperglycemia in diabetes. We aimed to investigate how diabetes and SGLT2 inhibition affect T_Naand sodium transport-dependent oxygen consumption [ ] along the whole nephron. To do so, we developed a mathematical model of water and solute transport from the Bowman space to the papillary tip of a superficial nephron of the rat kidney. Model simulations indicate that, in the nondiabetic kidney, acute and chronic SGLT2 inhibition enhances active T_Nain all nephron segments, thereby raising [ ] by 5–12% in the cortex and medulla. Diabetes increases overall T_Naand [ ] by ∼50 and 100%, mainly because it enhances glomerular filtration rate (GFR) and transport load. In diabetes, acute and chronic SGLT2 inhibition lowers [ ] in the cortex by ∼30%, due to GFR reduction that lowers proximal tubule active T_Na, but raises [ ] in the medulla by ∼7%. In the medulla specifically, chronic SGLT2 inhibition is predicted to increase [ ] by 26% in late proximal tubules (S3 segments), by 2% in medullary thick ascending limbs (mTAL), and by 9 and 21% in outer and inner medullary collecting ducts (OMCD and IMCD), respectively. Additional blockade of SGLT1 in S3 segments enhances glucose excretion, reduces [ ] by 33% in S3 segments, and raises [ ] by <1% in mTAL, OMCD, and IMCD. In summary, the model predicts that SGLT2 blockade in diabetes lowers cortical [ ] and raises medullary [ ], particularly in S3 segments.

The objective of this study was to investigate how physiological, pharmacological, and pathological conditions that alter sodium reabsorption (T_Na) in the proximal tubule affect oxygen consumption (QO₂) and Na⁺transport efficiency (T_Na/QO₂). To do so, we expanded a mathematical model of solute transport in the proximal tubule of the rat kidney. The model represents compliant S1, S2, and S3 segments and accounts for their specific apical and basolateral transporters. Sodium is reabsorbed transcellularly, via apical Na⁺/H⁺exchangers (NHE) and Na⁺-glucose (SGLT) cotransporters, and paracellularly. Our results suggest that T_Na/QO₂is 80% higher in S3 than in S1–S2 segments, due to the greater contribution of the passive paracellular pathway to T_Nain the former segment. Inhibition of NHE or Na-K-ATPase reduced T_Naand QO₂, as well as Na⁺transport efficiency. SGLT2 inhibition also reduced proximal tubular T_Nabut increased QO₂; these effects were relatively more pronounced in the S3 vs. the S1–S2 segments. Diabetes increased T_Naand QO₂and reduced T_Na/QO₂, owing mostly to hyperfiltration. Since SGLT2 inhibition lowers diabetic hyperfiltration, the net effect on T_Na, QO₂, and Na⁺transport efficiency in the proximal tubule will largely depend on the individual extent to which glomerular filtration rate is lowered.

Sodium and its associated anions are the major determinant of extracellular fluid volume, and the reabsorption of Na⁺by the kidney plays a crucial role in long-term blood pressure control. The goal of this study was to investigate the extent to which inhibitors of transepithelial Na⁺transport (T_Na) along the nephron alter urinary solute excretion and T_Naefficiency and how those effects may vary along different nephron segments. To accomplish that goal, we used the multinephron model developed in the companion study (28). That model represents detailed transcellular and paracellular transport processes along the nephrons of a rat kidney. We simulated the inhibition of the Na⁺/H⁺exchanger (NHE3), the bumetanide-sensitive Na⁺-K⁺-2Cl⁻transporter (NKCC2), the Na⁺-Cl⁻cotransporter (NCC), and the amiloride-sensitive Na⁺channel (ENaC). Under baseline conditions, NHE3, NKCC2, NCC, and ENaC reabsorb 36, 22, 4, and 7%, respectively, of filtered Na⁺. The model predicted that inhibition of NHE3 substantially reduced proximal tubule T_Naand oxygen consumption (QO₂). Whole-kidney T_Naefficiency, as reflected by the number of moles of Na⁺reabsorbed per moles of O₂consumed (denoted by the ratio T_Na/QO₂), decreased by ∼20% with 80% inhibition of NHE3. NKCC2 inhibition simulations predicted a substantial reduction in thick ascending limb T_Naand QO₂; however, the effect on whole-kidney T_Na/QO₂was minor. Tubular K⁺transport was also substantially impaired, resulting in elevated urinary K⁺excretion. The most notable effect of NCC inhibition was to increase the excretion of Na⁺, K⁺, and Cl⁻; its impact on whole-kidney T_Naand its efficiency was minor. Inhibition of ENaC was predicted to have opposite effects on the excretion of Na⁺(increased) and K⁺(decreased) and to have only a minor impact on whole-kidney T_Naand T_Na/QO₂. Overall, model predictions agree well with measured changes in Na⁺and K⁺excretion in response to diuretics and Na⁺transporter mutations.

The goal of this study is to investigate the functional implications of the sexual dimorphism in transporter patterns along the proximal tubule. To do so, we have developed sex-specific computational models of solute and water transport in the proximal convoluted tubule of the rat kidney. The models account for the sex differences in expression levels of the apical and basolateral transporters, in single-nephron glomerular filtration rate, and in tubular dimensions. Model simulations predict that 70.6 and 38.7% of the filtered volume is reabsorbed by the proximal tubule of the male and female rat kidneys, respectively. The lower fractional volume reabsorption in females can be attributed to their smaller transport area and lower aquaporin-1 expression level. The latter also results in a larger contribution of the paracellular pathway to water transport. Correspondingly similar fractions (70.9 and 39.2%) of the filtered Na⁺ are reabsorbed by the male and female proximal tubule models, respectively. The lower fractional Na⁺ reabsorption in females is due primarily to their smaller transport area and lower Na⁺/H⁺ exchanger isoform 3 and claudin-2 expression levels. Notably, unlike most Na⁺ transporters, whose expression levels are lower in females, Na⁺-glucose cotransporter 2 (SGLT2) expression levels are 2.5-fold higher in females. Model simulations suggest that the higher SGLT2 expression in females may compensate for their lower tubular transport area to achieve a hyperglycemic tolerance similar to that of males.