Physiology of acid-base equilibrium

 

Physiology of acid-base equilibriumReminders about acid-base balance in humans:

The position of the problem of acid-base equilibrium in humans: the blood pH is maintained at 7.40, which corresponds to a concentration of H + in the very low extracellular sector, of 40 nmol / L. The pH is maintained alkaline in spite of the fact that the body produces large quantities of acid in two forms: a volatile acid, carbonic acid (H 2 CO 3 ), coming from CO 2; non-volatile acids, also known as metabolic acids.

TWO TYPES OF ACIDS:

– Carbonic acid (H 2 CO 3 ).

It is made from CO 2 , which is the end product of oxidative metabolism. It is a major source of acid: 13,000 to 20,000 mmol of CO 2 are formed per day.

When CO 2 is metabolized, it provides an H + ion according to two types of reactions:

– hydration of CO 2 :

CO 2 + H 2 O d H 2 CO 3 d H + + HCO 3-

This reaction can be carried out without the intervention of carbonic anhydrase;

– hydroxylation of CO 2 :

HOH d H + + OH  (dissociation of H 2 O);

OH  + CO 2 d HCO 3- (hydroxylation of CO 2 by carbonic anhydrase).

In both cases the final product is HCO 3 – and H + . The reactions take place to the left, with production of CO 2 which is rapidly eliminated by the lung, hence the notion of volatile acid.

– Non-volatile acids: they are produced from food and intermediate metabolism. The sources of non-volatile acids are dietary proteins and metabolism of phosphodiesters (see below).

BUFFING OF AN ACID LOAD:

Three lines of defense against acid attack can be schematically described: the physicochemical line of defense, of instantaneous action; the line of respiratory defense, rapid action; the line of kidney defense, slow action.

– Physicochemical line of defense: buffer systems.

The pH is the logarithm of the inverse of the concentration of H + ions (1 / [H + ]).

A buffer is a substance that captures H + ions in a solution to limit pH changes. A buffer consists of the combination of a weak acid and its conjugated base.

The prototype of the buffering reaction is as follows: strong acid + basic salt d neutral salt + weak acid

In the case of hydrochloric acid:

HCl + NaHCO 3 d NaCl + H 2 CO 3

The Henderson-Hasselbach equation is written:

pH = pK + log acid / base

For the buffer HCO 3 – / H 2 CO 3 , the reaction is written:

pH = pK + log [HCO 3 ] / [dissolved CO 2 ]

pH = 6.1 + log 24 / (0.03  PaCO 2 ) = 6.1 + log 24 / (0.03  40)

pH = 6.1 + log 24 mmol / 1.2 mmol = 6.1 + log 20 = 7.4

If 12 mmol of HCl is added to 1 L of extracellular fluid, the following reaction is obtained:

HCl + 24 NaHCO 3 d 12 NaCl + 12 NaHCO 3 + 12 H 2 CO 3 then 12 H 2 CO 3 d 12 CO 2 + 12 H 2 O

In the equation, the numerator is reduced by 12 and the denominator is increased by 12:

pH = 6.1 + log 12 / (1.2 + 12) = 6.1 + log 12 / 13.2 = 6.06

The buffers do not prevent the decrease of the pH but minimize the decrease of the pH.

– Line of respiratory defense.

If, in the preceding equation, the buffer system is considered to be open and the 12 CO 2 are eliminated by the lung, the equation becomes:

pH = 6.1 + log 12 / 1.2 = 6.1 + log 10 = 7.1

In fact, the lung does more, because acidosis causes alveolar hyperventilation which results in a decrease in PaCO 2 .

If the PaCO 2 falls down to 23 mmHg, the equation becomes:

pH = 6.1 + log 12 / (0.03 ’23) = 7.34

– Renal line of defense.

At this point, the pH is almost normalized. However, H + ions remain in the form of weak acids and the plasma concentration of HCO 3 is lowered by 12 mmol / L. The kidney then intervenes to restore the concentration of HCO 3-and eliminate the few remaining H + .

WHAT ARE THE BUFFERS IN HUMANS?

The extracellular buffers are represented essentially by the bicarbonate / carbonic acid buffer: HCO 3 / H 2 CO 3 d H 2O and CO 2 . Protein and phosphate buffers provide only 1% of the plasma buffering capacity.

The HCO 3 / H 2 CO 3 buffer is a good buffer because: on the one hand it belongs to an open system in relation to the lung which eliminates CO 2 and with the kidney which reabsorbs and regenerates HCO 3- , and on the other hand its concentration in the extracellular sector is high.

Intracellular buffers are proteins. In the red blood cells, the hemoglobin buffer, via the imidazole groups of the histidines, has a very high buffering capacity.

In the other cells, proteinate and phosphate buffers predominate. Moreover, the skeleton is an immense reservoir of alkaline salts. Bone dissolves under acute or chronic acidosis, releasing phosphate and carbonate buffers.

An acidic charge will be 40% buffered in the extracellular area by bicarbonate / carbonic acid buffer, and 60% by intracellular buffers of red blood cells, soft tissues and bone. These cell sites are storage sites for H + ions while waiting for their excretion through the kidneys. The buffer proteins carry out H + / Na + or H + / K + exchanges in the cell membranes. Renal excretion begins rapidly, but it takes 2 days for the acid charge to be eliminated.

An alkaline charge will be buffered to 60% in the extracellular sector, and 40% in the intracellular. In contrast, its renal excretion is faster than in acidosis.

CO2 TAMPERING AND LUNG ROLE:

Before CO 2 is removed from the lungs, the alkalinity of the serum is threatened during the time of transport of CO 2from the cells where it is produced to the lungs where it is excreted.

CO 2 is buffered to 80% by bicarbonate buffer in red cells, which are rich in carbonic anhydrase, and 11% by hemoglobin, while a very small proportion of CO 2 is in dissolved form. CO 2 buffer systems are very effective, as evidenced by the very low pH difference between venous blood and arterial blood (0.04 pH units).

The lungs remove CO 2 : this is one of the openings in the bicarbonate buffer system. Central and peripheral chemoreceptors analyze the arterial partial pressure of CO 2 (PaCO 2 ). PaCO 2 stimulates (in case of elevation) or inhibits (in case of decrease) the respiratory centers.

If the pH decreases, chemoreceptors will generate hyperventilation, and vice versa.

Principles of physiology concerning acid-base equilibrium:

CONCENTRATION IN PROTONS IN THE LIQUIDIAN SECTORS:

Blood pH is maintained within a very narrow range of 7.38 to 7.42. This corresponds to a very small amount of H +ions in the extracellular sector (40 nmol / L), with respect to the other ions. The ratio of the concentration of the other ions (Na + , K + , etc.) to H + is 10 5 to 10 6 . Small variations in this figure have important clinical consequences.

The concentration of H + in the cytosol is 80 to 100 nmol / L, the intracellular pH is more acidic than that of the plasma, varying from 6.8 to 7.2 depending on the tissues.

PRODUCTION AND CONSUMPTION OF PROTONS:

A metabolic process is a series of chemical reactions that start from an energetic substrate, either by the formation of adenosine triphosphate (ATP) or by the appearance of new energy-producing compounds (such as glycogen for example). The substrate is of food origin or comes from a stock (like triglycerides in adipocytes).

During metabolic processes, H + are systematically formed. Here are two examples:

– Formation and consumption of ATP ATP 4- d ADP 3- + Pi 2- + H +

This reaction takes place in the Na + / K + ATPases pumps, and releases energy.

ADP 3- + Pi 2- + H + d ATP 4-

This reaction is carried out in the mitochondria and makes it possible to regenerate ATP.

The resultant of the two reactions is zero for the proton balance.

Indeed, all the H + ions formed during catabolism of ATP are used to regenerate ATP.

– Use of energy-triglycerides

The normal use of triglycerides for an energetic purpose involves triglyceride metabolism of free fatty acids (LFA) in adipocytes, according to the following reaction: triglycerides d 3 palmitate  + 3 H + + glycerol

AGLs migrate to the liver where they are metabolized to ketones according to the reaction:

3 palmitates  + 3 H + + 18 O 2 d 12 ketone bodies + H +

Ketones are mainly used by the brain for energy purposes, according to the following reaction:

12 ketones + H + d CO 2 + H 2 O + ATP

If we consider the whole metabolic chain, we see that all the H + formed are used and that the net balance of H + is zero.

Overall, H + are produced in the case of conversion of a neutral compound into an anion: fatty acids d 4 ketone bodies + 4 H +

+ is consumed when converting an anion into a neutral compound, or by the generation of a new cation:

– lactate  + H + d glucose (conversion anion to neutral compound);

– glutamine d glucose + NH 4 + + HCO 3 + CO 2 + H 2 O (generation of a new cation, reaction taking place in the kidney).

Other reactions do not consume or produce protons: glucose d glycogen + CO 2 + H 2 O

During the metabolism of carbohydrates and lipids, there is no accumulation of H + as generation is equal to consumption.

– For carbohydrates: glycogen d glucose d CO 2 + H 2 O (in the Krebs cycle).

The only exception is lactate anion. But in physiology, the H + formed are rapidly metabolized with the anion by the liver into neutral compounds: glucose, CO 2 , H 2 O, glycogen.

– For lipids: fatty acids and ketone bodies are anions whose formation generates H + , but during the normal metabolism they are consumed and do not accumulate.

– For proteins:

– 13 out of 20 amino acids are neutral; their metabolism provides neutral compounds (H 2 O, CO 2 , urea, glucose).There is no net gain of H + ions;

– five amino acids have a metabolism that generates H + : the three cationic amino acids (lysine, arginine and histidine), as well as the two sulfur amino acids (cystine and methionine);

– glutamate and aspartate are two anionic amino acids which generate HCO 3- .

– Phosphodiesters: Organic phosphates are the main anions of the intracellular medium (ribonucleic acid [RNA], deoxyribonucleic acid [DNA], phospholipids, ATP …). The products of their metabolism are HPO 4 2- and H + . The divalent phosphate anion (HPO 4 2- ) is filtered by the kidney. As the pH of the tubular fluid tends to acidify and pass below the HPO 4 2- pK, HPO 42- and H + will recombine to form H 2 PO 4 . This corresponds to titratable acidity (TA) (see below).

It can be seen that organic phosphates generate an H + production but with a “partner” which promotes its elimination.

WHAT ARE THE SOURCES OF ACIDS AND BASES?

– The sources of acids are therefore proteins and phosphodiesters.

Cystine and methionine are a source of H + ions resulting from the oxidation of the sulfur contained in these amino acids to sulfuric acid, according to the following reaction:

5 H 11 NO 2 S + 15 O 2 d 4 H + + 2 SO 4 – + CO (NH 2 ) 2 + 7 H 2 O + 9 CO 2

The cationic amino acids (lysine, arginine and histidine) release H + ions in the form of hydrochloric acid (HCl).

– The catabolism of phosphoproteins and phospho-aminolipids results in urinary excretion of phosphate.

– Catabolism of carbohydrates and lipids produces lactates and ketones that are metabolized in physiology, so that the net production of H + ions is very low. Urinary excretion of organic anions reflects this source of H + .

The production of H + from carbohydrates or lipids can however increase considerably in certain physiological or pathological situations:

– muscular exercise or hypoxia generates lactic acid;

– unbalanced diabetes generates ketone bodies.

– The sources of bases are proteins and metabolizable anions:

– the catabolism of proteins which provides anionic amino acids: aspartate and glutamate;

– the catabolism of metabolizable organic anions (citrate, lactate, gluconate …) provides bicarbonates.

Role of the kidney in the acid-base balance:

The kidney is the exclusive organ of H + regulation.

In fact, its role is two-fold: reabsorb 3- filtered HCOs, regenerate HCO 3- by excreting the acidic charge in the form of NH 4 + and AT.

The free H + ions are found in very small amounts and determine the pH of the urine.

REABSORPTION OF FILTERED BICARBONATES:

Mechanisms of proximal reabsorption of HCO 3 -:

HCO 3- are freely filtered at the glomerular level.

Filtered amount: 0.120 L / min ’60 min  24 hours  26 mmol / L = 4,500 mmol / d

The tubular reabsorption of HCO 3 is 99.9% of the amount filtered, which means that only 2 mmol of HCO 3 is excreted in the urine per day.

The reabsorption of HCO 3 – is very limited, because as soon as the plasma concentration is 28 mmol / L, bicarbonate appears in the urine. This ability to excrete HCO 3 – for concentrations just above plasma concentrations reflects the effective protection of the organism from alkaline loading.

The reabsorption of the HCO 3- takes place essentially at the level of the proximal bypass tube.

This reabsorption has two components, one linked to Na + and the other to H + .

Na + component:

The very low concentration of Na + in the cytosol of the proximal tubular cell, maintained by the action of the basolateral Na + / K + ATPases, allows Na + to enter the cell along its physicochemical gradient.

The counter-transport Na + / H + in the luminal membrane causes the H + to flow out using the energy created by the Na + input into the cytosol.

+ component:

The output of the H + ions of the cell is essentially achieved by the Na + / H + luminal counter-transport, but also under the action of the luminal H + ATPases. The H + combines with the HCO- 3 in the tubular lumen, which forms H 2 CO 3,then H 2 O and CO 2 under the action of the carbonic anhydrase located in the brush border. CO 2 diffuses into the cell where it recombines to OH  , which forms HCO 3 under the action of cytoplasmic carbonic anhydrase. On the basolateral membrane, a single channel allows the exit of HCO 3 with Na + , in anionic form (Na (HCO 3 ) 3 2- ).

Regulation of the proximal reabsorption of bicarbonates:

Four factors control the proximal reabsorption of HCO 3- .

– HCO 3- filtered charge.

In the case of metabolic acidosis, the filtered amount of HCO 3 decreases.

This reduces the secretion of H + ions, thus maintaining acidosis.

– H + luminal concentration.

When treated with acetazolamide (carbonic anhydrase inhibitor), the concentration of H + in the light rises and stops the reabsorption of HCO 3- well before the usual percentage of reabsorption is reached.

– Concentration of H + in tubular cells.

As the intracellular concentration of H + increases as in acidosis, there is an increase in activity of the Na + / H +transporter. This system, however, is not very effective in removing the acid charge, as the decrease in the filtered amount of HCO 3 limits the potential increase in Na + / H + counter-transport activity.

Conversely, in the case of metabolic alkalosis, there is a decrease in the intracellular H + concentration, which limits the secretion of H + by the Na + / H + countertransport, despite the elevation of acceptors in the tubular fluid. This is another factor (with the renal threshold of HCO 3- 28 mmol / L) explaining that an alkaline charge is rapidly excreted.

– Avidity of tubular cells to reabsorb Na + .

The volumic contraction favors the reabsorption of 3- HCO. It is a very important factor in the maintenance of metabolic alkalosis when it is associated with extracellular dehydration.

Volemic expansion has the opposite effect. Indeed, as expected, if the tubular cells reabsorb less Na + , the H +secretion capacity is reduced.

Proximal tubular acidosis is therefore characterized by a decrease in the blood concentration of HCO 3- by renal leakage and by an inability to increase the blood concentration of HCO3 in case of perfusion of HCO3 due to the less reabsorption .

Ten to 15% of the 3- filtered HCOs leave the proximal bypass tube and are reabsorbed into the pars recta of the proximal tube and the wide ascending limb of Henle. The secretion of H + is always carried out by a Na + / H +counter-transport.

REGENERATION OF HCO 3 -:

The kidneys reconstitute the pool of HCO 3- by excretion of NH 4 + and excretion of AT.

In both cases, the HCO 3 formed in the renal tubular cell passes into the peritubular blood with Na + which has been filtered.

Formation of titratable acidity:

– Definition of TA.

TA represents protons buffered by salts of weak urinary acids other than bicarbonate.

– Tubular location of AT formation.

It appears essentially:

– in the proximal tube: 60% of total urinary TA;

– in the distal tubule;

– in the collecting tube (40% of excretion).

– Buffers involved in AT training.

The main buffer is disodium inorganic phosphate (Na 2 HPO 4 ) which is reabsorbed to 70%. Creatinine and urate do not participate in TA because their urinary concentrations are low and their pK is low, which makes them operative only at very acidic urinary pH values.

– TA training mechanisms.

The starting point is the dissociation of a molecule of water. OH  will combine with the CO 2 present in the cytosol under the action of carbonic anhydrase to form an HCO 3- which passes into the peritubular blood. In the tubular lumen, the secreted proton combines with HPO 4 to form the excreted H 2 PO 4 2 in the urine.

The released Na + is reabsorbed by the cell and combines with the HCO 3- .

In total, the excretion of an H + promotes the entry of a 3- HCO into the circulation.

– Factors regulating TA.

Three factors influence the formation of AT:

– Buffer Availability: Increased urinary phosphate excretion by itself increases H + ion secretion. Moreover, since the pH of the tubular fluid changes from 7.4 (at the entrance of the proximal bypass tube) to 4.4 (minimum possible pH), the Na 2 HPO 4 converts to NaH 2 PO 4 ;

– influence of the pK of the buffers: the creatinine can not have an important influence on the secretion of AT, because its pK is close to the maximum threshold of acidification of the urine;

– influence of urine pH: if the pH of the tubular fluid is decreased from 7.4 to 4.4 (minimum figure), the creatinine buffer increases the excretion of H + in the form of AT.

Overall, the excretion of H + in the form of TA is very poorly adaptable and insufficient quantitatively to eliminate the daily acid charge.

Formation of NH 4+:

NH 4 + is the molecule that will allow renal excretion of the acid charge.

Proton secretion by the distal nephron:

A single cell type is involved in H + secretion. These cells, called alpha spacer cells, are located in the collecting channel. They have H + ATPase pumps on their luminal membrane. + acceptors in the tubular lumen are required to maintain the activity of the pumps, as the pH of the tubular fluid can not drop below 4.4. The secretion of a proton in the tubular lumen is accompanied by the basolateral exit of an HCO 3- by the HCO 3- / Cl  countertransport.

In addition to the active secretion of H + by alpha intercalated cells, there is also a voltage-dependent H + secretion, which is dependent on the difference of negative light transtubular potential. The main cells of the cortical collector tube are mainly involved in Na + reabsorption and K + secretion. Electrogenic reabsorption of Na + via the amiloride sensitive channel of the luminal membrane increases the transepithelial potential difference with more negative tubular lumen. This promotes the secretion of cations (K + and H + ), by specific channels located in the luminal membrane.This dependent H + -dependent secretion is sensitive to aldosterone, which increases the probability of opening amiloride-sensitive sodium channels and activates the basolateral Na + / K + ATPase on which Na + reuptake depends.

The beta type intercalated cells secrete HCO 3 ions in the tubular lumen. They are located in the collecting channel.They have the inverse structure of the alpha-type intercalated cells, with H + ATPases pumps located on the basolateral membrane and a counter-transport Cl  / HCO 3 in the luminal membrane.

Tubular location of NH 4 + formation :

Urinary NH 4+ is derived from renal synthesis. The formation of NH 4 + can be schematized in three steps.

· First step: formation of NH 4 + in the proximal tube

Almost all of the NH 4 + present in the final urine is already formed in the proximal tube, according to the following reaction: proteins glutamine ® 2 NH 4 + + alphacetoglutarate alphacetoglutarate ® glucose + 2 HCO 3-

The metabolism of alphacetoglutarate occurs in the mitochondria within the Krebs cycle, which provides ATP, CO 2and H 2 O. Any generation of NH 4 + is therefore accompanied by ATP.

On the luminal side, NH 4 + is secreted in the tubular lumen, taking the place of an H + on the counter-transport Na + / H + .

The two HCO 3 formed will pass into the peritubular fluid through the basolateral membrane through a Na + / HCO 3-cotransport.

The fact that the formation of NH 4 + is necessarily accompanied by a generation of ATP has three consequences:

– Since ATP can not be stored, it is produced in response to a request. In practice, in the kidney, this demand is mainly sustained by the reabsorption of Na + . During chronic renal failure, the filtered amount of Na + decreases, as does the reabsorbed portion. This leads to a reduction in the need for ATP, and thus for NH 4 + production , which explains the decrease in urinary excretion of NH 4 + and thus acidosis;

– the synthesis of NH 4 + may be limited if other fuels are supplied to the Krebs cycle (eg, ketones during fasting or parenteral nutrition);

– synthesis of NH 4 + takes place mainly in the proximal tube, since it consumes the most ATP.

There are two stimuli at the entrance of glutamine in mitochondria: metabolic acidosis and hypokalaemia. These two clinical situations are characterized by elevated urinary excretion of NH 4 + .

· Second stage: NH 4 + / NH 3 corticopapillary interstitial gradient

The maintenance of a corticopapillary gradient in NH 3 is necessary for the excretion of H + in the form of NH 4 + . In the fine descending branch of the loop of Henle, due to the alkalization of the tubular fluid (about 90% of the HCO 3were reabsorbed in the proximal tube) and water extraction, NH 4 + is transformed into NH 3 which accumulates in the medulla. In the broad ascending branch of Henle, NH 4 + is reabsorbed by taking the place of K + on the Na + / K + / 2 Cl  cotransport of the apical membrane. The reabsorption in the loop of Henlé makes it possible to extract approximately 70% of the NH 4 + formed in the proximal tube. After reabsorption, NH 4 + converts to NH 3 and H + in the ascending branch cell. NH 3 diffuses out of the cell and accumulates in the medulla. The H + is secreted and combines with the HCO 3 present in the light, which will form H 2 CO 3 , then CO 2 and H 2 O. The CO 2 is then delivered to the alpha intercalated cells.

In the case of hyperkalemia, there is competition between NH 4 + and K + for reabsorption, which reduces the NH 3concentration in the interstitium and thus the excretion of NH 4 + , which explains why hyperkalaemia favors acidosis.

· Third step: second NH 4 + formation in the collector tube

The CO 2 delivered to the alpha intercalated cells is converted to H + and HCO 3 by the carbonic anhydrase. These cells possess H + ATPases which secrete H + . These transform NH 3 into NH 4 + which is eliminated in the urine.

The pK of the reaction: NH 4 + NH 3 + H + is 9.2. At the pH of the tubular fluid between 4.4 and 7.4, 98% of the NH 3is in the form of NH 4 + .

Review of factors regulating urinary excretion of NH 4+:

– PH blood.

Blood acidosis causes cellular acidosis, which increases the production of NH 4 + , as the entry of glutamine into the mitochondria is favored. In addition, the Na + / H + counter-transport in the proximal tube, and the activity of the H +ATPase pumps of the collector tube are stimulated. In the case of alkalosis, the opposite effects are observed.

– PaCO 2 .

In the event of a decrease in PaCO 2 , a metabolic and then cellular alkalosis appears, which leads to a decrease in H + secretion in the proximal tube and the collecting tube. This is the metabolic compensation of hypocapnia. In the event of an increase in PaCO 2 , decreased plasma pH decreases the cellular pH, which increases the excretion of H + . This is the metabolic compensation of hypercapnia.

– Aldosterone.

It promotes the secretion of protons in the collecting tube: by the elevation of the voltage-dependent secretion of the H + linked to the reabsorption of Na + ; by directly stimulating the H + ATPases pumps of the alpha-type intercalating cells in the collecting tube.

A hyperaldosteronism is therefore associated with an alkalosis.

– Cortisol.

It stimulates the Na + / H + cotransport of the proximal tube, which raises the NH 4 + secretion.

– Extracellular volume and sodium flow.

Acute expansion of extracellular volume decreases reabsorption of HCO 3

 in the proximal tube (the reverse is true), and generates an acidosis called “dilution”. Chronic expansion of the extracellular sector by a salt-rich diet increases the amount of sodium in the cortical collector tube, which increases excretion of H + if aldosterone is fixed. In fact, in this situation, aldosterone is low, which limits the voltage-dependent secretion of H + .

– Potassium.

Hyperkalaemia favors acidosis by decreasing the excretion of NH 4 + (the reverse is true) by two mechanisms: less use of glutamine, competition for the reabsorption of NH 4 + in the cove of Henle.

– Antidiuretic hormone (ADH).

ADH stimulates H + secretion in the cortical collector tube, resulting in a decrease in urinary pH.

– Effect of diuretics.

Acetazolamide inhibits carbonic anhydrase in the lumen of the proximal tube and cytosol in the cells bordering the proximal tube, which reduces the reabsorption of HCO 3- and promotes metabolic acidosis.

Loop diuretics and thiazides increase the amount of Na + delivered to the cortical collector tube, which promotes the voltage-dependent distal secretion of H + .

+ -detecting diuretics block the corpus epithelial sodium channel and generate acidosis by decreasing the voltage-dependent H + secretion.

In total, the net excretion of acid is given by:

– excretion = NH 4 + + H 2 PO 4- d HCO 3-

– In the normal state, there is no bicarbonate in the urine for a urinary pH lower than 6.

The excretion of H + is one-third in the form of TA and two-thirds in the form of NH 4 + , knowing that in the case of acidosis only the excretion of NH 4 + can adapt multiplied by five).

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