We discuss here the relationship among glomerulotubular balance (GTB), tubuloglomerular feedback (TGF), and NaCl (salt) handling by the kidney. GTB refers to the direct positive effect of tubular flow rate on tubular reabsorption. TGF operates in the juxtaglomerular apparatus and confers an inverse dependence of single-nephron GFR on tubular fluid salt reaching the macula densa. GTB and TGF form a negative feedback system that stabilizes both single-nephron GFR and distal salt delivery. Most of our points are made by deduction.
EXISTENCE AND LIMITATIONS OF GTB
Tubular reabsorption is a random process, subject to statistical laws. Accordingly, more delivery translates to more chances for reabsorption, which translates to more total reabsorption. Ergo, GTB exists. But increasing the flow through a nephron segment also increases the opportunity for an individual molecule to transit the segment without being reabsorbed. From this we deduce the most perfect GTB can do no better than maintain a constant fractional reabsorption. In reality, GTB in the proximal tubule is approximately 70% efficient at holding fractional reabsorption constant.1 To put this in context, if a person in balance on a 180 mEq/d sodium intake with GFR 180 L/d and fractional reabsorption of 80% up to the macula densa were to experience a 10% increase in GFR, then 44% of the increment in filtered load would arrive at the macula densa. GTB downstream from the macula densa is difficult to quantify, but assuming constant fractional reabsorption (to wit perfect distal GTB), this 10% increase in GFR would effect a 22% increase in salt excretion.
The mechanisms of GTB have been argued since the 1930s and are not entirely clear, even today. GTB depends partly on parallel changes in peritubular capillary oncotic pressure that accompany changes in filtration fraction. Recently, a luminal mechanism has also been identified in which shear strain on the proximal tubule brush border activates apical co-transporters.2 In the loop of Henle, GTB is expected to result from the relatively low affinity of the bumetanide-sensitive salt transporter for chloride; however, our arguments here rely only on the existence and inherent limitations of GTB, which are deduced independent of present or future knowledge of its mechanisms.
The inherent limitation of GTB also does not apply to tubular effects of “natritropic” nerves and hormones regulating the total body salt through negative feedback. Instead, the natritropes, which include angiotensin, aldosterone, natriuretic peptides, and renal nerves, are constrained by the immutable requirement for salt balance to nullify any long-term disparity between salt intake and salt excretion. This requirement is immutable because the alternative advances an untenable notion of infinite total body salt.
COMBINING GTB WITH TGF
Because of the limitations of GTB, a portion of any change in GFR will pass along the nephron to elicit a TGF response, which will offset part of the original disturbance. The uncompensated portion of the original disturbance remains as an error signal. The ratio of the compensation to the error signal is termed the open loop gain (OLG). The OLG of any feedback loop equals the product of the slopes of its pair-wise relations (see Appendix). Typically, the negative OLG for the GTB-TGF system is approximately 2, which means that the system compensates for approximately 66% of an outside disturbance,3 so an outside disturbance that would increase GFR by 10% and salt excretion by 22% in the absence of TGF winds up as a 3% increase in GFR and a 7% increase in salt excretion. Current thinking on the mechanism of TGF is that the macula densa releases ATP in proportion to the tubular fluid salt concentration and this ATP binds to vasoconstrictor purinergic receptors on the afferent arteriole and/or converts to adenosine, which activates vasoconstrictor adenosine A1 receptors on afferent arterioles. The sensitivity of this feedback is susceptible to modulation by a variety of mediators, including nitric oxide, prostaglandins, and angiotensin II, among others.4
GTB, TGF, AND SALT HOMEOSTASIS
After a change in salt intake, salt excretion asymptotically catches up to the new intake and balance is restored at a new total body salt. Over time, total body salt varies directly with the salt intake, and the slope of this relationship is inversely related to how rapidly balance is restored after a change in salt intake. When balance is restored rapidly, the total body salt is less sensitive to long-term salt intake than when balance is restored slowly, so the efficiency of salt homeostasis boils down to how long it takes to restore balance after a change in salt intake. The most parsimonious explanation for observed behavior is a system in which salt excretion is driven not by salt intake but by the total body salt.5 This likens salt excretion to radioactive decay. The construct allows for the 4 to 7 d required to achieve salt balance while also allowing salt excretion to change rapidly after a sudden change in total body salt. In addition, this construct provides a fair literal representation, because activation of the major natritropes is tied to changes in the total body salt. The natritropic hormones and nerves make for a more stable total body salt, but, to the extent that they act by changing GFR or proximal reabsorption, their effectiveness is attenuated by TGF. In other words, when the object of homeostasis is the total body salt, TGF is antihomeostatic.
This, too, can be deduced: Any change in salt excretion equals a change in delivery to the macula densa minus a change in reabsorption downstream from the macula densa. Hence, there is potential for natritropes to speed up the salt balance by impinging both upstream and downstream from the macula densa. But TGF makes the distal delivery resistant to change. If GTB-TGF were perfectly efficient (OLG infinite), then total responsibility for salt balance would be relegated downstream from the macula densa. This competition between TGF and the natritropes results in a compromise between the efficient compensation for changes in salt intake and control of the distal salt delivery. The integration of this compromise is inherent and its details are revealed by solving a simple system of equations developed from the individual pair-wise relations between total body salt, the natritropes, and their effects on the various nephron segments (see Appendix).
ADVANTAGES TO COMPROMISING ON THE EFFICIENCY OF SALT HOMEOSTASIS
A stable internal environment is essential for normal functioning of the organs, so why incorporate TGF, which naturally lessens the efficiency of sodium homeostasis? Sodium is not the only important constituent of the body fluids. There is also potassium, acidity, and calcium to consider. Homeostasis of all of these moieties involves regulated transport downstream from the macula densa, which makes random fluctuations in distal delivery disruptive. Furthermore, not all changes in salt delivery to the macula densa help to stabilize total body salt. For example, if GFR, hence macula densa salt, were passively allowed to track short-term fluctuations in BP that occur independent of total body salt, then fluctuating salt excretion would follow, irrespective of total body salt. Or if proximal reabsorption were to decline in the aftermath of some injury to the tubule, then macula densa salt would increase independent of total body salt. The kidney invokes TGF to lessen the impact of such transient events on GFR and salt excretion,6 but this inevitably requires some sacrifice of salt homeostasis.
The relative contribution of proximal and distal nephrons to overall salt balance must vary according to the relative OLG of the GTB-TGF and natritropic feedback systems. A model for this is developed in the Appendix. When numbers derived from the published literature are applied to this model, it is revealed that eliminating TGF would lessen by 30% the impact of dietary salt on the total body salt.
TGF ADAPTATION: LIMITING THE COST OF TGF
Because of the inverse relationship imposed by TGF, glomerular filtration and distal salt delivery cannot change in the same direction unless there is resetting of the TGF curve. For example, acute plasma volume expansion, which increases both GFR and distal delivery, must cause rightward resetting of TGF.3 Furthermore, the natural tendency for tubular flow to align with the steepest part of the TGF curve suggests resetting at the level of each nephron, a phenomenon that has been confirmed.7,8 If TGF resets rightward during prolonged activation, then this will lessen its apparent OLG for buffering long-term (hours/days/weeks) relative to short-term (seconds/minutes) disturbances. Hence, the degree to which TGF interferes with salt homeostasis will be tempered to the extent that TGF resets rightward on a high-salt diet. The full details of TGF resetting are not known, but several lines of evidence point to nitric oxide synthase in the macula densa,9–12 and blocking this enzyme makes the BP sensitive to salt intake, which is tantamount to demonstrating that more persistent TGF causes less efficient salt homeostasis.13
TGF helps to overcome inherent limitations of GTB in stabilizing distal salt delivery. The added stability bestowed on nephron function by negative feedback from TGF inevitably incurs some cost in terms of less efficient salt homeostasis, but this cost is tempered by TGF resetting. These implications of the GTB-TGF interaction are revealed, mainly, by deduction.
GTB and TGF place the following conditions on GFR and macula densa chloride,
where ΔGFR and ΔMDsalt refer to residual changes in GFR and macula densa NaCl after compensation by GTB-TGF for an outside disturbance, δ, in GFR. αp is the change in MDsalt per unit change in GFR as a result of GTB. β is the negative slope of the TGF curve (see Figure 1A). The straightforward solution is as follows:
where αpβ is the negative open loop gain. There are constraints on αp as a result of the nature of GTB. These are discussed in the main text. Theoretically, β can assume any value from 0 to infinity where β = 0 is the absence of TGF. Typically, αpβ is approximately 2 in the rat.
The model in Figure 1B depicts the impact of GTB-TGF on salt homeostasis. The seven internal variables (e.g., total body salt [TBsalt], GFR, natritrope activity) represent changes as a result of outside disturbance (δ). In other words, for the system in steady state with no disturbance, these all are 0. Positive and negative influences are written such that all parameters (αp,d, β,γ, η1 to 3) are positive numbers. These represent slopes of the pair-wise relations. By conservation of mass:
The solution to the homogeneous equation is the simple decaying exponential:
where k is obtained from the model by algebraic substitution to express urinary sodium voided (UNaV) as a function of TBsalt. If δ is applied as a bolus at time 0, then C = δ and TBsalt will decay from δ to 0 with time constant k. Similarly, if δ is applied as a step increase in salt intake, then TBsalt will exponentially approach a new steady state value where TBsalt = δ/k, so salt balance is achieved more rapidly and salt homeostasis is more efficient when k is large.
Note the dependence of k on αpβ, which is the negative OLG for GTB-TGF. This is the main point of the exercise and reveals how GTB-TGF competes with the natritropes for control of GFR and macula densa salt. As GTB-TGF becomes more powerful relative to natritropes that act upstream of the macula densa (η1 to 2), overall salt homeostasis becomes less efficient and more dependent on feedback from TBsalt through natritropes acting on the distal nephron (η3). The impact on salt homeostasis of eliminating TGF is shown in Figure 1C, for which model parameters were given values derived from the literature.
This work was performed with funds provided by National Institute of Diabetes and Digestive and Kidney Diseases grants DK28602 and DK56248 and by the Department of Veterans Affairs Research Service.
Published online ahead of print. Publication date available at www.jasn.org.
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