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(Hypertension. 1997;30:1318-1324.)
© 1997 American Heart Association, Inc.

Articles

A Mouse View of Hypertension

Oliver Smithies

From the Department of Pathology and Laboratory Medicine, University of North Carolina at Chapel Hill.

Correspondence to Oliver Smithies, D. Phil, Department of Pathology and Laboratory Medicine, University of North Carolina at Chapel Hill, CB #7525, 701 Brinkhous Bullitt Building, Chapel Hill, NC 27599-7525.

	Abstract

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
Abstract Essential hypertension probably results from combinations of genetic variations, not necessarily the same in all afflicted persons, which individually may not cause sufficient deviation from normality to be significantly harmful.

Genes contributing to hypertension are being sought by analytic experiments aimed at identifying candidate genes associated or segregating with the phenotype in humans and animals and by synthetic experiments in which changes are made in candidate genes in animals and their effects on blood pressure are determined.

We have used gene targeting to vary the amounts of angiotensinogen and angiotensin-converting enzyme (ACE) synthesized from their genes (Agt and Ace). These "gene titration" experiments establish that changes in Agt gene expression cause changes in the blood pressures of mice. Surprisingly, quantitative changes in Ace gene expression over a threefold range do not affect blood pressures.

Computer simulations with a simple version of the renin-angiotensin system predict that changes in Agt function alter the steady state levels of both angiotensin I (Ang I) and angiotensin II (Ang II). In contrast, modest changes in Ace function alter Ang I levels considerably but scarcely affect Ang II levels. Simulations over the ranges of ACE levels that can be achieved with ACE inhibitors predict that Ang II levels will decrease only when Ang I levels have plateaued.

Comparisons of the computer simulations with our genetic experiments and with prior work of others using wide dose ranges of ACE inhibitor show a satisfactory agreement and help reconcile the apparent contradictions between the genetic and pharmacological experiments.

Key Words: hypertension, essential • renin-angiotensin system • gene targeting • genetic variations

	Introduction

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
Essential hypertension—high blood pressure with no obvious cause—is an insidious condition in which the risk of disability or death increases progressively with blood pressure (reviewed by Pickering in Reference 1¹ ). Determinants of blood pressure include both environmental and genetic factors, with the latter accounting for somewhat more than half of the familial aggregation of blood pressure (reviewed by Ward in Reference 2² ). In a small percentage of hypertensive individuals, the disease is the consequence of defects in single genes that are inherited in a simple Mendelian fashion (reviewed by Lifton in Reference 3³ ). However, in the majority of cases, the pattern of inheritance is not clear, suggesting that, as with many other quantitative phenotypes, blood pressure is determined by the action of many genes. A likely hypothesis is that essential hypertension results from combinations of genetic variations that are not the same in all afflicted persons and that individually may not cause sufficient deviation from normality to be significantly harmful.

	Analytic Experiments

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
The tools available to investigators concerned with identifying genes that contribute to the hypertensive phenotype can usefully be categorized as either analytic or synthetic. Analytic experiments typically use one of two approaches. One approach is to study families (human or animal) in which some but not all of the offspring are hypertensive; the segregation pattern of a large number of genetic markers is then compared with the segregation of the hypertensive phenotype; chromosomal region(s) that cosegregate with the trait can thereby be recognized, candidate genes within the region can be identified, and differences between the candidate genes of the hypertensive and normotensive individuals can then be sought. This method of analysis is well illustrated by the work of Jacob et al⁴ and Hilbert et al,⁵ which aimed at identifying candidate genes in stroke-prone spontaneously hypertensive rats. A candidate gene (ACE) that both groups of investigators identified in this manner (using the same genetic crosses) codes for the angiotensin-converting enzyme (ACE), the key enzyme in generating Ang II from its immediate precursor, Ang I. (Here, and in what follows, I attempt to use the notations for genes that are applicable to the relevant species.) However, subsequent investigations by Kreutz et al⁶ showed that although molecular variants of the rat ACE gene cosegregate with plasma ACE activities, blood pressure does not cosegregate with these ACE variants.

A second analytic approach requires the choice of a candidate gene on the basis of prior physiological or other data, followed by a study of segregation of the hypertensive phenotype with variants of the candidate gene or of markers in nearby DNA. Studies by Rapp et al⁷ illustrate this method. These investigators looked for and found restriction fragment length polymorphisms in the renin genes in the Dahl salt-sensitive and salt-resistant strains of rats. They then demonstrated segregation of the salt-sensitive–type length polymorphism with higher blood pressure in crosses between the two strains. However, once again, the difficulties inherent to this type of study are made apparent by subsequent work by St. Lezin et al,⁸ in which congenic Dahl salt-resistant rats carrying the salt-sensitive renin gene had lower blood pressures and renin levels than Dahl rats with the salt-resistant renin gene (The two congenic rat strains had been bred to be genetically identical except for the chromosomal region that includes the renin gene.) In humans, Jeunemaitre et al⁹ demonstrated in siblings cosegregation of a hypertensive phenotype with a specific marker (threonine at amino acid position 235) in the AGT gene, which codes for angiotensinogen (AGT). The authors also observed that individuals homozygous for the T235 allele had steady state plasma AGT levels approximately 20% higher than individuals homozygous for the alternate allele, M235, coding for methionine at 235; they went on to hypothesize that the increased AGT concentration might be the key determinant that leads to hypertension. Subsequent studies in a variety of populations have confirmed that the T235 allele segregates with either an increased AGT concentration¹⁰ or hypertension.¹¹ Also very recently, a single nucleotide difference was identified between the promoters of the T235 AGT gene (A at -6) and the M235 AGT gene (G at -6) that affects in vitro transcription in the expected direction.¹²

A difficult problem remains, however, even when a candidate gene has been identified by segregation and a specific variation in the candidate gene has been found. The problem is in going from the correlative stage, in which the hypertensive gene or gene variant segregates with the phenotype, to a proof of causation. This problem is particularly serious in the case of hypertension, for which observed quantitative changes may be either a consequence of the disease or a cause (see Smithies and Kim¹³ and Smithies and Maeda¹⁴ for further discussion). Synthetic experiments can remove substantial portions of this uncertainty when genetic factors are being investigated.

	Synthetic Experiments

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
Typical synthetic experiments require choosing a candidate gene either on the basis of previous analytic studies of human families/animal strain crosses or on a priori grounds such as the involvement of the product of the candidate gene in a relevant physiological/biochemical system. Attempts are then made to synthesize the phenotype of interest either by using gene targeting to make a predetermined change in the candidate gene or by adding a suitable transgene. Clearly, if the synthetic experiments are properly designed and executed, there is no longer any problem in assigning primary causation. However, the extent to which a chosen mutation will affect the phenotype of interest is difficult to estimate before execution of the experiment. For this reason, most synthetic experiments carried out by gene targeting have involved the generation of lack of function (null) mutations, in which the effects are likely to be severe. Yet, lack of function mutations are, by their nature, typically inherited as simple recessive Mendelian factors, a pattern of inheritance that, as discussed above, is not frequent in essential hypertension. So, in what follows, I discuss the results of using gene targeting to make genetic changes that are less drastic than absence of gene function and that match known quantitative human variations more closely than is possible with gene knockout animals and classic transgenic mice.

Our first experiments were designed to make precise and known genetic changes in mice to replicate the provocative observation by Jeunemaitre et al⁹ of a modest (20%) increase in plasma AGT associated with the T235 variant. In principle, a mutation could be introduced into the promoter of the mouse Agt gene to cause an increase in transcription without altering the general regulation of the gene. In practice, knowledge of the rules that govern fine details of promoter function is so limited that this course of action is not generally available. Dr Hyung-Suk Kim (at the University of North Carolina) and I therefore chose to increase the level of function of the mouse Agt gene by using gene targeting to duplicate the whole gene at its normal chromosomal location without altering the sequence of the resulting gene product or of any nearby cis-acting control elements.¹³ By having the duplication extend upstream and downstream of the known transcriptional region of the gene, we expected that the duplicated gene would yield roughly twice as much product as the normal singleton gene. Fig 1B illustrates the type of targeting used to duplicate the Agt target gene; details are given in Reference 13¹³ .

View larger version (20K): [in this window] [in a new window]   Figure 1. Two modes of gene targeting: A, gene disruption; B, gene duplication. The top lines in the two parts of the figure represent the target gene in its natural chromosomal context; the middle lines, the targeting constructs; the bottom lines, the modified genes. The thicker horizontal lines are mouse genomic DNA; the thinner lines, plasmid DNA. The dashed lines have no length. The selectable marker gene is neo, with its transcriptional orientation indicated by the enclosing open arrows. Regions where homologous crossing over occurs are shown by crosses. Note that although the targeting constructs for A and B use the same DNA fragments, their topological arrangements differ.

To assess the effects on blood pressure of a genetic decrease in the amounts of AGT, we used animals having only one functional copy of the Agt gene instead of the usual two copies.¹⁵ Such single-copy animals are readily generated as the heterozygotes from a conventional gene knockout experiment. Fig 1A illustrates the type of targeting procedure used to disrupt (knockout) the Agt target gene; details are in Reference 15¹⁵ . Because gene copy numbers are being changed in these experiments, we refer to them as "gene titrations."

	An Agt Gene Titration

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
Fig 2 shows the three chromosomes that were used: the zero-copy (knockout) chromosome; the one-copy (normal) chromosome; and the two-copy (duplication) chromosome. By suitable breeding, animals having zero, one, two, three, or four functional copies of the Agt gene were generated.

View larger version (8K): [in this window] [in a new window]   Figure 2. The three forms of murine Agt gene used for gene titration (modified from References 13 and 15). A, The disrupted Agt locus having no functional gene copy. B, The wild-type Agt locus having one functional gene copy. C, The duplicated Agt locus having two functional gene copies.

Fig 3A shows the steady state plasma AGT concentrations of the one-copy, two-copy, three-copy, and four-copy animals.^{13 15} As can be seen, the range covers the levels observed by Jeunemaitre et al⁹ in the hypertensive patients and their normotensive siblings.

View larger version (12K): [in this window] [in a new window]   Figure 3. The effects of Agt gene copy number on: A, steady state plasma AGT as percent of that in wild type, two-copy animals (modified from References 13 and 15); B, mean arterial blood pressure (modified from Reference 15). *Assumed.

The blood pressures of the one- through four-copy mice were then measured,¹⁵ either by an indwelling carotid catheter on unrestrained conscious animals or by a computerized tail-cuff method on restrained but unoperated animals.¹⁶ Fig 3B shows the carotid arterial pressures as a function of Agt gene copy number. The change in pressure (approximately 8 mm Hg per gene copy) is significant and reproducible. A firm conclusion can therefore be drawn that genetically determined changes in the level of expression of the Agt gene directly cause changes in the blood pressures of mice and that this change is observable in animals that have all their normal homeostatic mechanisms intact.

	An Ace Gene Titration

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
There are many reasons for asking whether genetically controlled differences in the synthesis of ACE might also affect blood pressures. These reasons include the importance of ACE in catalyzing the conversion of Ang I to the vasoconstricting peptide Ang II in the renin-angiotensin system and in catalyzing the inactivation of the vasodilating peptides kallidin and bradykinin in the kallikrein-kinin system; the efficacy of ACE inhibitors in the management of many hypertensive patients; the existence of genetically determined quantitative differences in the amount of circulating ACE in normal humans¹⁷ ; and the genetic linkage experiments with the stroke-prone hypertensive rats described above.

Dr John H. Krege (at the University of North Carolina) and I therefore carried out a gene titration experiment in mice with the Ace gene.¹⁸ Fig 4A shows the serum ACE activities of the resulting animals as a function of Ace gene copy number. The variation in levels is considerable and is remarkably close to being directly proportional to gene copy number. Yet, as shown in Fig 4B, the tail-cuff blood pressures of the animals are unaffected by the threefold differences in ACE activity caused by the genetic changes. This result is paradoxical when one considers that ACE inhibitors lower blood pressure in mice (see, for example, Reference 16¹⁶ ) as well as in humans.

View larger version (18K): [in this window] [in a new window]   Figure 4. The effects of Ace gene copy number on: A, steady state serum ACE activities (modified from Reference 18 plus unpublished data, 1996); B, mean tail-cuff blood pressure (modified from Reference 18 plus unpublished data, 1996).

One possible explanation of the paradox is that homeostasis (for example, by changes in renin production) with the Ace gene variations may for unknown reasons be more effective than with the Agt gene variations. However, this possibility is made very unlikely by our observation¹⁸ that kidney renin mRNA is increased less (about 30% above normal) in the Ace one-copy animals with normal blood pressures than in the Agt one-copy animals with lower than normal blood pressures (their kidney renin mRNA is more than 100% above normal; H.-S. Kim, personal communication, 1997).

	Computer Simulations

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
Dr Marshall H. Edgell (at the University of North Carolina) and I have recently been using computer simulations to explore another possibility—namely, that the apparently contradictory responses of the mice to changes in Agt versus Ace gene function are not caused by some special biological compensation but are rather the natural outcome of steady state relationships between substrates and products that are applicable to any multistep pathway. A literature search identified a collection of experiments in which mathematical modeling of a complex genetic system was attempted. These experiments concentrated on the effects in neurospora and yeast of mutations in genes needed for the synthesis of arginine and tryptophan, which are essential for growth. The relevant synthetic pathways are comprised of several consecutive steps catalyzed by enzymes that are specified by individual genes. The overall effects of variations in the individual genes on the net flux (ie, synthesis of the final metabolite) have been the subject of both theoretic and experimental investigations dating back more than 20 years (reviewed by Kacser and Burns in Reference 19¹⁹ ). A central conclusion from these studies is the flux summation theorem,^{19 20} symbolized as:

This theorem states that the sum of the ratios (C) of the fractional change in flux (J) caused by a fractional change in the activity (E) of each of n enzymes in a steady state pathway is equal to unity. The predicted practical effect of this theorem is that when the activities of any of the individual enzymes in the pathway are changed, the net effect on the total flux tends to be small. This prediction was tested by Niederberger et al²⁰ who found that increases of between 10- and 50-fold in the activities of four individual enzymes in the yeast tryptophan pathway resulted in increases in tryptophan flux of at most 30%. Individual enzyme decreases in activity to one fourth of normal in a tetraploid yeast strain also had small effects on total flux, at most a decrease of 25%.

In the complex mammalian disease, essential hypertension, which we are considering, total fluxes are usually less important than the steady state levels of key intermediates. A form of theoretical treatment is therefore called for in which the steady state levels of different intermediates can be computed when changes occur in the genes comprising the system. To this end, we have carried out computer simulations of the circulatory arm of the renin-angiotensin system with the help of a commercially available program (STELLA, High Performance Systems, Inc) of general use for modeling the behavior of complex interacting systems. This program allows the specification of the starting values of many items and then computes how these values change with time as the items are incrementally used, destroyed, or replaced following paths and equations specified by the investigator. Branching paths are permissible, as are feedback loops. The final, steady state values of all variables can be computed for systems as they come to a dynamic equilibrium. Our experience with this program suggests that it is eminently suitable for modeling complex genetic systems, in which several genes affect the production and use or turnover of enzymes and substrates interconnected in a specifiable manner.

In modeling the genetics of the renin-angiotensin system, we started by specifying the number of genes coding for AGT and the amount of AGT produced per gene per unit time. Consumption of AGT occurs in two ways, as a consequence of its use as a substrate by renin and as a consequence of turnover and clearance of the type expected for any protein. We assumed that the use follows Michaelis-Menten kinetics with an explicit K_m and k_cat. We assumed that the amount of AGT cleared per unit time follows first-order kinetics and so can be calculated from the concentration of AGT multiplied by a clearance constant, which we must specify. A steady state level of AGT will be achieved when a balance is reached between production, use, and clearance. If any of these items change, the steady state level will change. Renin and ACE production and clearance must also be specified, as must the formation and removal of specific receptor(s) for Ang II. The steady state level of the peptide intermediate Ang I will depend on the rate of its formation from AGT, on its use by conversion to Ang II via the action of ACE, and on its clearance by other peptidases and excretion via the kidney. Ang II levels will depend on its rate of formation from Ang I, on its use and removal by binding to its receptors, and on its clearance by peptidases and excretion. Equations are required to specify the interaction of Ang II with its receptors. The relationship between receptor-occupancy and cellular response (such as smooth muscle contraction) must also be defined. For simplification, we have initially assumed that the phenotypic response is proportional to the concentration of the ligand (Ang II), but as elements distal to the ligand are considered (such as the levels of synthesis of different receptors), the model must be expanded. Feedback loops and their sensitivities require specification. For example, a vast body of previous work in the renin-angiotensin system, which is confirmed in all of our current genetic experiments, requires that renin synthesis at the very least be subject to positive feedback regulation when Ang II levels and/or blood pressure decrease.

Fig 5 shows the interrelations of these various factors in our simplified version of the renin-angiotensin system modeled with the STELLA software. Note that in making a start at modeling this system, we have reduced its complexity by restricting the model to the endocrine aspects of the system and by using Ang II level as the phenotype (rather than blood pressure). I emphasize that in setting up this computer model, the aim is not to simulate known elements of behavior of the real system (although it should do this) but is rather to use the computer model to develop a better understanding of the system. I have found that this second aim can be partly achieved despite the absence of sufficient information to specify the precise forms of the equations for each step (for example, the equation for describing renin feedback) or the exact constants in the known equations (for example, the exact values of K_m and k_cat for all of the enzymes). I hope in what follows to make clear the types of insight that even relatively simple models of this type can generate.

View larger version (33K): [in this window] [in a new window]   Figure 5. A computer model of a simplified renin-angiotensin system (based on STELLA).

Initial steps in developing the model consisted largely of testing the effects on the levels of AGT, renin, ACE, Ang I, and Ang II of changes in individual elements in the model, including gene copy numbers, protein per gene specifications, clearance constants, K_ms, etc. By trial and error, values were assigned to the adjustable elements to eliminate meaningless situations (such as when the final steady state was only achieved when the level of some gene product or intermediate fell to zero) and to keep the steady states of the substrates in roughly the same ratios to the K_ms of their enzymes as occur in vivo. (For example, the plasma concentration of AGT in the mouse is close to the K_m of renin; that of Ang I is well below the K_m of ACE.) Tests were then made of varying the copy numbers of the Agt genes over a fourfold range in conjunction with varying the amount of ACE protein over an eightfold range. These and other tests showed that simulated changes in the number of Agt genes had a much greater effect on the Ang II levels than comparable changes in the number of Ace genes.

Fig 6 presents graphically the outcome of two simulations in which the numbers of copies of either the Agt gene (Fig 6A) or the Ace gene (Fig 6B) were varied. These two simulations are therefore respectively equivalent to the animal experiments illustrated in Figs 3 and 4, except that in place of the steady state levels of AGT or ACE and the blood pressures shown in the earlier figures, Fig 6 shows the computed steady state levels of Ang I and Ang II relative to the corresponding levels for wild-type animals having two copies of each gene. As can be seen, the steady state levels of Ang II change progressively and modestly (solid line in Fig 6A) when the simulation changes the number of copies of the Agt gene over the range one to four. In contrast, when the simulation is repeated but with changes now in the number of copies of the Ace gene, the steady state levels of Ang II are insensitive (solid line in Fig 6B) to the changes in gene copy number. (Note that nothing other than the gene under consideration is changed between the two simulations.) Thus, the simulations lead to the same conclusions as the genetic experiments: variations in Agt gene copy number affect blood pressure, but variations in Ace gene copy number do not. The second of these conclusions is similar to that, described above, reached by Niederberger et al²⁰ after their genetic manipulations of individual enzymes in the tryptophan biosynthetic pathway of yeast.

View larger version (12K): [in this window] [in a new window]   Figure 6. Relative levels (simulated) of Ang I (hashed line) and Ang II (solid line) as a function of: A, Agt gene copy number, with Ace gene copy number constant and set at 2; B, Ace gene copy number, with Agt gene copy number constant and set at 2. The levels corresponding to wild-type animals with two copies of both genes are taken as 1.

Clues to the conceptual framework that underlie these results are provided by noting how the steady state levels of Ang I vary. As can be seen, the computed levels of Ang I progressively and modestly increase (hashed line in Fig 6A) as a function of Agt gene copy number. Because ACE levels are not varying in this "experiment," this progressive increase in Ang I causes a corresponding progressive increase in the steady state levels of Ang II (and, thence, of blood pressure). In contrast, the computed levels of Ang I vary inversely and markedly (hashed line in Fig 6B) with the number of Ace gene copies. This inverse relationship compensates almost completely for the changes in ACE function, and so the Ang II levels are not significantly altered.

The basis for the inverse relationship can be understood by recalling that the renin-angiotensin system is a steady state system. When a steady state system is at equilibrium, the levels of all intermediates self-stabilize at values such that the sum of the rates of their conversion to the next intermediate and of their clearance by other means exactly balances the rate of their production. In the Ace gene titration experiment when the ACE level is reduced to 50% normal (as it is when there is only one copy of the gene), Ang I accumulates and its level rises. As the level of Ang I rises, the rate of its conversion to Ang II will also rise following Michaelis-Menten kinetics, in which an increase in substrate concentration leads to an increase in reaction velocity. A new steady state is eventually reached when the level of Ang I has risen sufficiently for the sum of the conversion of Ang I to Ang II and the clearance of Ang I by other means to be restored to its initial value. The net result is that the level of Ang II in the one-copy animals is restored to close to the two-gene copy level without the need to invoke substantial homeostatic changes in renin production.

I can summarize this part of our analysis by the statement that changes in Ace gene copy number are computed to affect Ang I levels markedly but to have essentially no effects on Ang II levels; in contrast, changes in Agt gene copy are computed to affect the levels of both peptides. We are currently in the middle of an experiment to test these predictions in mice with differing numbers of Agt and Ace genes.

	ACE Inhibitors

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
An obvious problem remains. If modest changes in ACE produced by genetic variations have little effect on blood pressure, why do ACE inhibitors lower pressure? In an attempt to answer this question, we have used our computer model to simulate the effects of doses of an inhibitor that reduce ACE function to values substantially lower than the 50% achieved in the gene titration experiment with animals. In presenting the results of these simulations, I need to remind you that (1) Ang I levels increase when ACE function decreases (as illustrated in Fig 6B) and (2) this increase effectively compensates for the decrease in ACE function that caused it, so Ang II levels change only slightly. However, this compensation, which makes the system insensitive to decreases in ACE function, does not continue when ACE is more severely inhibited. This is because the concentration of Ang I cannot increase indefinitely. It will eventually reach a plateau when the clearance of Ang I from the system by means other than its conversion to Ang II becomes so large that it consumes essentially all of the Ang I that renin generates from AGT. (We assume, as we did for the proteins, that clearance of Ang I follows first-order kinetics and so is proportional to its concentration.) Once the concentration of Ang I has plateaued, further decreases in ACE function will no longer be compensated for and Ang II levels will become sensitive to additional ACE inhibition.

Fig 7 displays, as a function of the percentage of ACE inhibition, the computed levels of Ang II (solid line) and Ang I (hashed line) relative to the normal level of Ang II with no ACE inhibition. Renin concentration (dashed line) is kept constant in this simulation. As can be seen, the level of Ang II is insensitive to decreases in the level of ACE function down to about 90% inhibition. However the level of Ang II becomes sensitive to ACE function when the enzyme inhibition greatly exceeds this percentage. The exact numeric value at which this change in sensitivity occurs in Fig 7 should not be interpreted too literally because it depends on the choice of constants used in the simulation, some of which are arbitrary. The existence of a crossover from insensitivity to sensitivity as ACE function decreases is, however, not arbitrary, because it is not materially affected by the numeric values chosen for the simulation. Likewise, it is not arbitrary that Ang I levels eventually plateau at the point at which the loss of Ang I by clearance accounts for essentially all of its generation from AGT by renin. This plateauing of Ang I levels is necessary (and sufficient) to cause Ang II levels to become fully proportional to ACE function.

View larger version (21K): [in this window] [in a new window]   Figure 7. Relative levels (simulated) of Ang I (hashed line) and Ang II (solid line) as ACE function is progressively inhibited over a wide range with renin concentration (broken line) kept constant. The peptide and renin levels are presented relative to the level of Ang II and renin, respectively, in the absence of any ACE inhibition. The computed effects when renin feedback is included are shown by the vertical arrows.

Our computer model allows us to explore the effects of including homeostatic feedback, such that decreases in Ang II levels cause increases in renin production and thence of Ang I production. The results are again clear but are rather unexpected. Until ACE function has decreased to close to the crossover point, renin concentration does not increase significantly (vertical arrows in lower part of Fig 7) because Ang II levels are not changing substantially. At ACE levels beyond the crossover point, when Ang II levels begin to fall more rapidly, the feedback causes renin levels to increase substantially (vertical arrows in Fig 7). However this increase does not materially affect the levels of Ang II, which still decrease. (The Ang II curve with renin feedback is the same as that without.) In effect, the additional Ang I that is generated by the greater renin levels ends up being cleared from the system by means other than conversion to Ang II. The amount of Ang I generated from AGT cannot, of course, increase indefinitely as renin increases, because the rate of Ang I synthesis eventually becomes limited by the rate at which AGT is synthesized.

Two summary statements can be made from this part of our analysis. First, reductions in ACE function as a consequence of either genetic changes or the use of a converting enzyme inhibitor will appear to have a threshold (at around the crossover point described above) beyond which Ang II levels will progressively decrease. Second, increases in renin will be induced by postthreshold reductions in ACE function but will be accompanied by a decrease in Ang II levels.

	Comparison With Previous Experiments

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
A study by Campbell et al²¹ provides experimental data suitable for comparison with the simulations illustrated in Figs 6 and 7, which were made without reference to their data. These investigators examined, among other things, the dose-related effects of ACE inhibitors on circulating and tissue levels of the angiotensin peptides in normal rats on a normal diet. Comparison of their results with our simulations are very encouraging. Thus, the animal experiments showed that plasma Ang II levels were insensitive to increasing levels of an ACE inhibitor (perindopril) until the dose was equal to or greater than 0.467 (mg/kg per day), effectively a threshold. In contrast, Ang I levels increased progressively from the lowest dose of 0.006 to a dose of 0.467. Ang I levels plateaued at the 0.467 dose, and thereafter, Ang II levels became sensitive to further ACE inhibition. As the authors state "when Ang I levels were unable to increase further, higher [inhibitor] doses caused plasma Ang II levels to fall." The simulation in Fig 7 shows the same transition from insensitivity to sensitivity beyond a threshold decrease in ACE function and provides a clear conceptual framework for its existence.

The way in which renin levels change with ACE function during our simulations is also in general agreement with the experimental observations of Campbell et al.²¹ They observed modest increases in renin levels with increases in perindopril until the dose of 0.467 was reached. Thereafter, renin levels increased markedly to 20 times control, and at the highest doses of inhibitor (12.6), plasma renin was almost 100 times control. Yet, plasma Ang II levels decreased at inhibitor doses greater than 0.467, despite the large increases in renin levels. The simulation in Fig 7 likewise shows that when renin feedback is included in the analysis (vertical arrows), decreases in Ang II still occur as renin levels rise. (A caveat is again necessary that the exact numeric values achieved in the simulations are somewhat arbitrary and dependent on the choice of constants. The interrelationships between the variables are, however, not materially affected by the chosen values.)

	Concluding Remarks

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
The computer model presented in Fig 5 and used for the simulations in Figs 6 and 7 obviously represents a great oversimplification of the renin-angiotensin system. For example, the model does not include the complexities of the known receptors for Ang II. Also, it does not include the inactivation by ACE of the blood pressure–lowering kinins (kallidin and bradykin). Likewise, the model does not consider the effects of the renin-angiotensin system on the secretion by the adrenal glands of aldosterone with its controlling influence on sodium retention by the kidney. Also, involvement of the tissue renin-angiotensin system is not included in the model. Each of these complications, and many others, must be considered before the modeling process can be regarded as complete. We have learned enough from the current relatively simple treatment of steady states in the renin-angiotensin system to give us the confidence to try the more complex analyses and also to apply the treatment to other systems that affect blood pressure and blood volume. However, there is much left to learn and many more experiments to do before the effects on blood pressure of genetic variations and their interactions with each other or with the environment are fully understood.

In closing, I would also add that when thriving and mature disciplines come together, each goes through a learning phase. As a geneticist, I am having to relearn anatomy, physiology, biochemistry, and pharmacology. If, as a result of the incompleteness of this process, I have failed to refer to prior work by others in these disciplines, I ask their indulgence. Time, in any case, allows me to acknowledge this prior work only in general terms, which I gladly do. I should also stress that a literature search will yield a wealth of other experiments related to the genetics of hypertension in addition to those I have described here.

	Selected Abbreviations and Acronyms

 

ACE = angiotensin-converting enzyme AGT = angiotensinogen Ang I = angiotensin I Ang II = angiotensin II

	Acknowledgments

 
This work is supported by grants from the National Institutes of Health (HL49277 and GM20069) and by a grant from the W.M. Keck Foundation for work with animal models. I thank Tom Coffman, Marshall Edgell, Ariel Gomez, John Hagaman, Hyung-Suk Kim, John Krege, Nobuyo Maeda, and Nobuyuki Takahashi for their help, data, and counsel in preparing this lecture.

Received July 23, 1997; first decision July 30, 1997; accepted July 30, 1997.

	References

Top Abstract Introduction Analytic Experiments Synthetic Experiments An Agt Gene Titration An Ace Gene Titration Computer Simulations ACE Inhibitors Comparison With Previous... Concluding Remarks References

 
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