Fig 1.
Schematic representation of the interactions between the blood pressure and Ca2+-Mg2+ homeostasis models.
Mauve nodes, plasma [Ca2+], [Mg2+], [1,25(OH)2D3], and [PTH]; yellow nodes, renal Na+, Ca2+, and Mg2+ handling; blue nodes, renin-angiotensin-aldosterone system. (Node colors match those in Fig 2.) Solid arrows indicate activation and dotted arrows indicate inhibition. Brown arrows indicate the direct links between components of the blood pressure regulation model and the Ca2+-Mg2+ homeostasis model. In this schematic, distal tubule includes the distal convoluted tubule, connecting tubule, and collecting duct. ACE, angiotensin-converting enzyme; AGT, angiotensinogen; ALD, aldosterone; Ang I, angiotensin I; Ang II, angiotensin II; AT1R-bound Ang II, angiotensin II type 1 receptor-bound angiotensin II; AT2R-bound Ang II, angiotensin II type 2 receptor-bound angiotensin II; PRC, plasma renin concentration.
Fig 2.
Schematic diagram of the integrative model.
(A) Blood pressure regulation model. Pink nodes denote variables that describe cardiovascular function; green nodes, renal hemodynamics; yellow nodes, renal Na+ and fluid handling; blue nodes, the renin-angiotensin-aldosterone system (RAAS). Solid arrows indicate activation and dotted arrows indicate inhibition. In this schematic, the proximal tubule includes also the loop of Henle. (B) Ca2+-Mg2+ homeostasis model. The model consists of five compartments: plasma, intestine, kidney, parathyroid gland, and bone. Solid arrows with open arrowheads indicate fluxes, solid arrows with closed arrowheads indicate activation, and dotted arrows indicate inhibition. All arrows are color coded. Green arrows, Ca2+; red arrows, Mg2+, blue arrows, parathyroid hormone (PTH); purple arrows, 1,25(OH)2D3. ACE, angiotensin-converting enzyme; AGT, angiotensinogen; ALD, aldosterone; Ang I, angiotensin I; Ang II, angiotensin II; AT1R-bound Ang II, angiotensin II type 1 receptor-bound angiotensin II; AT2R-bound Ang II, angiotensin II type 2 receptor-bound angiotensin II; PRC, plasma renin concentration.
Table 1.
Descriptions and values of new model parameters and variables at baseline for a male rat.
Table 2.
Changes in model parameters to simulate five model instances of hypertension, each with different primary trigger(s), labelled RSNA, Renin, ALD, AA, and Combined. RSNA, renal sympathetic nervous activity; ALD, aldosterone; AA, afferent arterial.
Fig 3.
Conducted by increasing individual parameters by 5%. The resulting percent change in model steady state concentrations from baseline is presented here. White indicates the resulting change was less than 1%. RSNA, renal sympathetic nervous activity; GFR, glomerular filtration rate; MAP, mean arterial pressure; [ALD], plasma aldosterone concentration; PRA, plasma renin activity; [PTH], plasma PTH concentration; [1,25(OH)2D3], plasma 1,25(OH)2D3 concentration; [Mg2+], plasma Mg2+ concentration; [Ca2+], plasma Ca2+ concentration.
Fig 4.
Effect of hypertensive stimuli.
Fractional change from baseline (denoted by grey line at zero) of model variables (A) and Ca2+-Mg2+ fluxes (B) under five hypertensive stimuli: overactive RSNA (HTN-RSNA), increased renin secretion (HTN-Renin), increased aldosterone secretion (HTN-ALD), increased vascular tone (HTN-AA), and a combination of these stimuli (HTN-Combined). Bone to plasma and plasma to bone fluxes represent the exchange of Ca2+ and Mg2+ between plasma and the fast bone pool; bone resorption represents the release of Ca2+ and Mg2+ from the slow bone pool into plasma. MAP, mean arterial pressure; [ALD], aldosterone concentration; PRA, plasma renin activity; [AT1R-Ang II], plasma AT1R-bound Ang II concentration; RSNA, renal sympathetic nervous activity; RVR; renal vascular resistance; RBF, renal blood flow; GFR, glomerular filtration rate; , extracellular fluid volume;
, total plasma sodium; [PTH], plasma PTH concentration; [1,25(OH)2D3,], plasma 1,25(OH)2D3 concentration; [Mg2+], plasma Mg2+ concentration; [Ca2+], plasma Ca2+ concentration.
Fig 5.
Effect of Mg2+, Ca2+, and vitamin D3 deficiency.
(A) Fractional change from baseline (denoted by grey line at zero) of model variables under 70% dietary Mg2+ intake () restriction, 70% dietary Ca2+ intake (
) restriction, and 70% 25(OH)D (precursor of 1,25(OH)2D3) deficiency for 1 month. (B) Interplay between key variables that are affected by dietary Mg2+, dietary Ca2+, and 25(OH)D deficiency. Each variable is accompanied by their change over time for each of the three cases. Maroon bar plots, dietary Mg2+ deficiency; blue bar plots, dietary Ca2+ deficiency; green bar plots, 25(OH)D deficiency. The Y-axis range is [–0.7, 0.7]. MAP, mean arterial pressure; CO, cardiac output; TPR, total peripheral resistance; [ALD], aldosterone concentration; PRA, plasma renin activity; [AT1R-Ang II], AT1R-bound Ang II concentration; RSNA, renal sympathetic nervous activity; RVR; renal vascular resistance; GFR, glomerular filtration rate; Vecf, extracellular fluid volume; [PTH], plasma PTH concentration; [1,25(OH)2D3], plasma 1,25(OH)2D3 concentration; [Mg2+], plasma Mg2+ concentration; [Ca2+], plasma Ca2+ concentration; AR, arterial resistance.
Fig 6.
Simulation results for primary hyperparathyroidism.
Fractional change from baseline (denoted by grey line at zero) of model variables (A, B) and Ca2+-Mg2+ fluxes (C) after increasing the baseline PTH synthesis rate () by factors of 2, 3, 5, 7, 10. [PTH], plasma PTH concentration; [1,25(OH)2D3], plasma 1,25(OH)2D3 concentration; [Mg2+], plasma Mg2+ concentration; [Ca2+], plasma Ca2+ concentration; MAP, mean arterial pressure; CO, cardiac output; TPR, total peripheral resistance; [ALD], aldosterone concentration; PRA, plasma renin activity; [AT1R-Ang II], AT1R-bound Ang II concentration; RSNA, renal sympathetic nervous activity; GFR, glomerular filtration rate;
, extracellular fluid volume.