Physics, Chemistry and Biology of WATER The Tenth Annual Water Conference Bulgaria, October 1-4. 2015

Carlos U. Häubi Segura, PhD [email protected]  Homeopathy  Memory of water  Messages from water  Bulk water vs.  structured water vs. EZ  Energy from light?  Chronic dehydration  And what about …pH?

“Discovery is seeing what everybody else has seen, and thinking what nobody else has thought.” Albert Szent-Györgi  Canadian physiologist http://www.acidbase.org/  University of Manitoba (1943) .  MSc in physics and mathematics (1949)  PhD in biophysics (1951)  Emory University , Physiology (1954)  Brown University , Medical science (1965-1983)

 Stewart, P.A. (1981). How to Understand Acid-Base. A Quantitative Acid-Base Primer for Biology and Medicine, Elsevier Nordholland, New York http://issuu.com/acidbase/docs/htuab

 Stewart, P.A. (1983). Modern quantitative acid-base chemistry. Can J Physiol Pharmacol. 61: 1444-1461  Kellum, John A; Elbers, Paul WG, eds. (2009). Stewart's Textbook of Acid-Base. ISBN 978-1-4092-5470-6 If the data does not fit the theory, it is time to change the theory What is an acid diet? What is an alkaline diet? What makes it acid? What makes it alkaline?

What are biological limits? Blood? What is biologicaly apt pH? Cells?  Acids taste sour  Bases taste bitter  acids change blue litmus to red  feel slippery or soapy  their aqueous (water) solutions  bases turn red (acidified) litmus conduct electricity back to blue  react with bases to form salts  their aqueous (water) solutions and water as the only products conduct electricity

 evolve hydrogen gas (H2) upon  react with acids to form salts reaction with an active metal, and water as the only products such as alkali metals, alkaline  An alkali is a substance which earth metals, zinc, iron, forms OH- ions as the only aluminum, forming a salt as the negative ion in aqueous only other product solution.  An acid is a substance which A base is an insoluble forms H+ ions as the only hydroxide. positive ion in aqueous solution Author A theory of Hydrogen A theory of Oxygen PARACELSUS Discovers Hydrogen upon (S.XV) acting on a metal ROBERT BOYLE (Pointy corpuscules?) (1671) ANTOINE LAVOISIER Oxy = acid (1777) All acids contain “O” HUMPHREY DAVY Not all acids contain “O” (1800) Hydracids (HCl, HF, HI) “H” = Principle of acidification J.P. DULONG Union of an electronegative (1820) compound (Oxygen, halogen) with an electropositivo compound (H) and this can be substituted by a metal J.J. BERZELIUS Oxides of metaloides (1830) produce acids in water Oxygen = Sauerstoff (German for “acid substance”) JUSTUS VON LIEBIG An acid contains a H-atom (1838) which can be subtituted by a metal GRAHAM Monobasic and polibasic (1880) acids: H is subsituted by a base  Arrhenius (1887) ◦ An acid is a substance which forms H+ ions as the only positive ion in aqueous solution. HCl ---> H+ + Cl- ◦ An alkali is a substance which forms OH- ions as the only negative ion in aqueous solution. A base is an insoluble hydroxide  Brønsted-Lowry (1923) HCl(g) + NH3(g) ---> NH4Cl(s) ◦ An acid is a proton donor. 2HCl + MgO ---> MgCl2 + H2O A base is a proton acceptor.  Lewis (1923) ◦ An acid is an electron acceptor, and a base is an electron donor. ◦ This totally removes the concept of hydrogen ions being a pre-requisite for an acid. But like the Brønsted-Lowry definiton above, it still includes every acid and base under the Arrhenius definition, and all those under the Brønsted-Lowry definition. + 2- Zn(OH)2 + 2NaOH(aq) ---> 2Na (aq) + [Zn(OH)4] (aq)  Water is an acid or a base?

 Bicarbonate is a base or an acid?

-  Where does HCO3 come from?

From NaHCO3

 Where does the OH- come from? From NaOH

 H2CO3 is an acid or a conjugated acid?

 Classical theories of acids Old theories are ◦ Theory of dissociation, Arrhenius-Ostwaldt (1887) ◦ pH scale (pH = -log [H+]), Sørenson (1909) still actual? ◦ Henderson-Hasselbalch equation (1916) ◦ Proton donors, Brønsted-Lowry (1923) ◦ Electron donars, Lewis acids (1923)

 General definitions of solvents Any new theories? ◦ Effects of solutes on the solvent (Germann, 1925) ◦ Quantitative theory of acids (Stewart,1981)  Concepts of acids in Medicine Iatrogenic? ◦ Dissociation of strong acids and bases

◦ Partial pressure of CO2 (PCO2) ◦ Buffers Qualitative or ◦ Henderson-Hasselbalch – only one variable Quantitative? --  -- O H +  Water is really weird... 104.5° H + It forms a permanent dipole d+ - ◦ H d d+ - + O H d d d- O H H + - d+ - ◦ It hydrates other molecules, even other O d H d H H d H + - O O d H d + - + - molecules of water H d H d H d H d d+ - O + H d H d d- O + - O H H d H d H ◦ It forms liquid crystals with moving electric O O H d+ - + - O H d H d H d H charges O O H H  It dissociates with difficulty (Kd) but re- H H + associates rapidly (K ) : H3O O a Protonic H ◦ It is the main donador and receptor of hydrogen H jumps O ions (= protons: H+) and hydroxile ions (OH-) H + H ◦ Protons (H ) cannot live freely; they associate O

+ and hydrate : H3O (H2O)n H H + O H O ◦ Water has a high concentration of H2O: 55.5 M 3 H  One molecule in each 10 million dissociates spontaneously: ◦ 0.1 ppm , 1/107 , 10-7 (pH=7) How is this possible?

 The reaction is the following:

+ - + + H2O  H + OH H + H2O  H3O

 The proton binds to another molecule of water

H + - O  + O - H + H  + + + H3O H  H  - + H + + O  H  O -H  H +

+ O - O -H  OH- H + H +

Theory of dissociation, Arrhenius-Ostwaldt (1887) General definitions of solvents

The neutral charge El protón no tiene vida libre, se forma el ion H + + O - in water is always hidrogenion H3O + H  C C maintained H + - + O  + O - H  H  Matriz de agua: H + Donador y receptor ÁcidoÁcido no disociado:-disociado: H2O de protones NoCarga tiene (carga-) = anión H O+ 3 y iones OH-

H + H + - - O  - Saltos protónicos O  H + O  + + + H  H  + Dónde quedó la bolita? H  - H  + O  H  + O - O - H   Ac H H+ + H + H + H + H + - - O  O  H + Cristal de agua tiene carga H + Acido orgánico se protoliza: neutra se forma un anión solvatado Por cada carga negativa se genera un protón H+  According to Germann (1925)

+ ◦ Cation of water (H3O ): “Lyonium” ◦ Anion of water (OH-): “Lyate”

 For a given solvent:

◦ Acid: a substance that increments the concentration of the “Lyonium” ion and reduces the concentration of the “Lyate” ion ◦ Base: a substance that increases the concentration of the “Lyate” ion and decreases the concentration of “Lyonium” ion.

 In the case of water, acids and bases can be defined as :

◦ Acid: A negative charge that produces a mayor dissociation of water and an increase in the concentration of protons, [H+] ◦ Base: A positive charge that produces a mayor dissociation of water molecules and an increase in the concentration of hydroxile ions, [OH-] Three factors that affect pH but could not be reconciled... now braught together by a quantitative method

Cationes P CO2 Na+ fuertes SID= Variables dependientes Strong ? pH [A-] ? PCO2= Ion - + HCO + 2+ [HA] 3 - HA Ca Difference [H ] OH H3O Presiуn [OH-] Parcial de - ? + Henderson-Hasselbalch A = [HCO ] K CO TOT 3 pH = pKa + Log [A-]/[HA] ? 2 2- - Total de A [CO3 ] ? 2- 2- Mg2+ aniones CO SO4 3 dйbiles Aniones Aniones dйbiles Seis ecuaciones fuertes Cl- ? simultбneas

Dissociation of strong acids and bases SID – Strong Ion Difference

Partial pressure of CO2 – PCO2 Partial pressure of CO2 – PCO2 Dissociation of weak acids ATOT – Total of weak anions Strong Ion Difference: Protein concentration Atot] Na + K + Ca +Mg pCO : 2 Phosphates, ammonia, etc. -Cl – strong ions = SID Weak acids: VFA Lactate

Chemistry laws: - Mass action: - Electro-neutrality: - Dissociation of: water, carbonic acid, weak acids, weak bases, ammonia, etc.

+ - - 2- - [H ] [OH ] [HCO3 ] [CO3 ] [A ] [Pi] [VFAs] [Lactates] Stewarts theory is based on the effect of three basic principles of chemistry, on the balance of electrical charges in aqueous solutions:

1) Principle of electro-neutrality, 2) Law of Mass Action, 3) Law of Mass Conservation 1) Principle of electro-neutrality

the sum of all positive charged ions must equal the sum of all the negatively charged ions:

[Na+] + [K+] + [Ca2+] + [Mg2+] + [H+] - [Cl-] – - - - 2- [Anion ]-[OH ] - [HCO3 ] - [CO3 ] = 0 160 OH- 140 Pi 120 Atot 100 HCO3- 80 Otros Aniones

mmol/L 60 Cl- 40 H+ Ca2+ 20 K+ 0 Na+ Cationes Aniones 2) Law of Mass Action

States that all incompletely dissociated substances reach a dissociation equilibrium:

[A] * [B] = K * [C]

where K is the rate constant for the reaction.

Water has a very small dissociation constant: -14 KW (KW = 1*10 )

but a very large association constant: 14 (1/KW = 1*10 ) 3) Law of Mass Conservation

States that the amount of a substance remains constant unless it is added, removed, generated or destroyed:

- [HA] + [A ] = [ATOT]

The total of a weak acid (ATOT) is an independent variable and can be present as a dissociated acid (A-) or non-dissociated (HA),

both being dependent variables. The dissociation of water into H+ ions (pH) and OH- and the behavior of other weak acids (organic acids, carbonates, phosphates and proteins) and bases (ammonia), depends on three independent variables:

1) The Strong Ion Difference (SID)

+ + 2+ 2+ - 2- Na + K + Ca + Mg - Cl - SO4

2) The partial pressure of carbon dioxide (PCO2)

+ - + 2- CO2 + H2O  H2CO3  H + HCO3  2 H + CO3

3) The total amount of weak anions (ATOT) - HAlb + Alb = AlbTOT Water is the primary and inexhaustible source and sink for hydrogen ions.

+ - [H2O]* KW = [H ] * [OH ]

The dissociation constant KW is very small ( 4.3 * 10-16Eq/l at 37 oC).

KW varies with temperature

-16 (e.g., at 25 °C, KW is about 1.8 * 10 Eq/l)

The approximate value of KW' is:

-10 (-1.0^1*10^6) / T^2) KW' = 8.754 * 10 * e where temperature T is expressed in degrees Kelvin This can be done with the solution of six simultaneous equations:

+ - [H ] * [OH ] = KW‘ Equation #0

+ - [H ] * [A ] = KA * [HA] Equation #4

- [HA] + [A ] = [ATOT] Equation #5

+ - [H ] * [HCO3 ] = KC * PCO2 Equation #8

+ 2- - [H ] * [CO3 ] = K3 * [HCO3 ] Equation #9

and finally, to maintain electrical neutrality:

+ - - 2- - [SID] + [H ] - [HCO3 ] - [A ] - [CO3 ] - [OH ] = 0 Equation #10 This makes the solution for the hydrogen ion concentration [H+] possible with the aid of computers:

+ + + [SID] + [H ] - KC * PC / [H ] - KA * [ATOT] / (KA + [H ]) – K3 * + 2 + KCPC / [H ] - KW' / [H ] = 0 Equation #10

 PC = PCO2 mmHg  Constants are: -14  KW = 4.40*10 (Eq/L) -11 2 -1  KC = 2.34 * 10 (Eq/L) mmHg -11  K3 = 6.0*10 Eq/L -7  KA = 1.64*10 Eq/L (rest) -7  KA = 1.98*10 Eq/L (exercise)

 KC = K * S ◦ where K = 7.42*10-7 Eq/L, K is the constante of dissolution; ◦ S = 0.0351 Eq/L mmHg-1 a 37°C y 300 mOsm, S is the constant of Solubility. The algebra to solve these six simultaneous equations gives a fourth-order polynomial. The exact solution for [H+] is:

+ 4 + 3 [H ] + ([SID] + KA) x [H ] +

+ 2 (KA x ([SID] – [ATOT]) – K’W – KC x PCO2) x [H ]

+ - (KA x (K’W + KC x KCO2) – K3 x KC x PCO2) x [H ] – KA x K3

x KC x PCO2 = 0

There are four possible solutions  PROGRAM STARTS: ◦ TOO_SMALL = 4.4 * 10-14 ◦ TOO_BIG = 1.0 ◦ CLOSE_ENOUGH = 0.000001  BEGIN: ◦ MY_GUESS = ROOT ( TOO_SMALL * TOO_BIG ) ◦ RESULT = F(MY_GUESS) ◦ IF ABS(RESULT) LESS THAN CLOSE_ENOUGH THEN RETURN MY_GUESS ◦ IF RESULT IS POSITIVE THEN  TOO_BIG = MY_GUESS  OTHERWISE  TOO_SMALL = MY_GUESS  GO TO BEGIN  PROGRAM ENDS:

Written by J. van Schalkwyk, 1999, from the website: http://www.anaesthetist.com/icu/elec/ionz/Stewart.htm  University of South Carolina, School of Medicine

http://ppn.med.sc.edu/watson/Acidbase/Acidbase.htm

 No free-living protons (H+):

 The acidity of the bicarbonate ion

 The volatility of the bicarbonate ions

 The effect of acids on EZ-water

Let’s start with this one! Initial state  Fig. 5.9 Time course of pH-dye distribution

as current flows between wire electrodes

immersed in a water bath containing pH-

sensitive dye.

high pH  Cathode (-): low pH

◦ Purple corresponds to high pH

◦ Attracts cations (+), Produces OH-

 Anode (+):

◦ Orange corresponds to low pH

+ + ◦ Attracts anions (-), Produces H , H3O Fig. 5.5 Addition of microspheres alters water’s pH. (a) Carboxylate microspheres, 1 μm diameter. Increasing microsphere concentration changes dye color toward red, indicating lower pH. (b) Positively charged amino microspheres change dye color toward green, indicating higher pH.  Does Stewart help explain EZ after formation or depletion?

 Pollack (2013):

 “an H3O+ combining with a

lattice-structural unit (OH-), which yields two water molecules (Fig. 6.11). This erosive action loosens the EZ’s hexameric structure.”  Sufficiently acidic pH does diminish EZ size.

 Salts erode the EZ similarly.

 Consider NaCl:

+  The Cl– component can combine with H3O in

the bulk to yield HCl + H2O,

 Na+ can invade the negative lattice, and go on to

create NaOH by extracting a lattice OH– unit.

 The EZ erodes and adds a water molecule to the “an H3O+ combining with a lattice- bulk water. Wherever the lattice is open, positive - structural unit (OH ), which yields two ions of any sort can enter and cause EZ erosion. water molecules (Fig. 6.11). This erosive action loosens the EZ’s hexameric structure.” According to Stewart: - + + • Cl increases [H ], therefore [H3O ] • Na+ ion reduces [H+] and increases [OH-] • Question to Jerry: Effect of NaOH on EZ?  The no free-living existence of protons (H+):

◦ Protons disociate and re-associate from the water matrix in order to maintain the principle of electroneutrality

◦ Hydrogen ions H+ have a diameter of 10-15m, therefore cannot be pumped by membrane proteins

◦ Hydrogen ions H+ are dependent variables

◦ Mitchell’s Chemiosmotic Hypothesis (1961) cannot be correct (ATP is formed through another mechanism!) http://bcs.whfreeman.com/thelifewire/content/chp07/f07012.gif  The acidity of the bicarbonate ion

◦ The bicarbonate ion is not a buffer… it cannot

neutralize acidity in a solution

+ - + + 2 ◦ CO2(d)+ H2O  H2CO3 H + HCO3 H +H + CO3

- ◦ It’s an anion (HCO3 ), a negative charge, pKa 6.1: it’s a weak acid

◦ What increases pH is the cation (e.g. Na+, K+)

◦ Henderson-Hasselbalch equation is wrong !! Ole Siggard-Andersen Nomogram

 H-H (1916) ◦ pH = pKa + log [A-] /[HA] pH = 6.1 + log10 [HCO3− ] ◦ It’s a circular relationship: 0.03 × PaCO2  pH affects the dissociation of carbonic acid into bicarbonate  The dissociation of carbonic acid affects the concentration of bicarbonate and carbonic acid

 Anion Gap + + - - ◦ (Na + K ) - (Cl + HCO3 ) = UA –UC ◦ Value: 10-12 mEq/L  Base Excess ◦ Van Slyke equation:

◦ PaCO2 40 mmHg, pH 7.4, 37 °C, full O2 saturation) − ◦ Base excess = 0.93 × HCO3 − 24.4 + 14.8 × (pH − 7.4) - ◦ SBE = 0.9287 × (HCO3 − 24.4 + 14.83 × ([pH − 7.4])) Winter’s equation: - PCO2 = 1.54 × [HCO3 ] + 8 ± 2  The volatility of bicarbonate ions

◦ Bicarbonate ions are dependent variables, which are formed or destroyed according to the Henderson reaction:

+ - + + 2 CO2(d)+ H2O  H2CO3 H + HCO3 H +H + CO3 ◦ Carbonic Anhidrase, a really fast enzyme

- ◦ There is NO evolutionary advantage of pumping HCO3 ions from one side of a membrane to the other, because it will be change to another species of carbonate according to conditions of the medium  The volatility of bicarbonate ions (continues):

◦ There is no reabsorption of bicarbonate in the kidneys during urine production

- - ◦ NO interchange of HCO3 ions for Cl ions during gastric juice production

- ◦ NO secretion of HCO3 ions during pancreatic juice production ◦ NO use of applying bicarbonate in IV-solutions – it’s the

+ - sodium ion (Na HCO3 ) A hypothetical model of rumen epithelial ion transport (adapted from Stevens, 1988).

Lumen Cell Blood

+ + + H2O CO2 H2O CO2 H2O CO2 No c.a. c.a. c.a.

H2CO3 H2CO3 H2CO3 Cl- - - - HCO3 HCO3 HCO3 + + + H+ H+ H+ + Na - + Ac

H metabolized H++ Ac- Ac- HAc HAc

c.a. = carbonic anhidrase Strong ions (e.g. NaCl) completely dissociate in water and are hydrated by water molecules releasing + - an opposite charged water ion (H30 or OH ) to maintain electroneutrality in the aqueous solution.

Carbon dioxide (CO2) dissolved in water reacts to forms different species of carbonate according to other variables in the medium. Weak acids (HAc) dissociate into their anions (Ac-) according to their dissociation constant (Ka). + + (H30 = H ); c.a. = carbonic anhidrase.

+ + - Na + H2O Na + OH NaCl - - + + Cl +H2O Cl H

H2O H2O Pool Lumen Cell Blood Pool

+ + H O H2O CO + H O CO H O 2 2 H2O CO2 2 2 2 No c.a. c.a. c.a. + - H2CO3 H CO H2CO3 H + OH 2 3 - OH - - + + - + + + H + HCO3 HCO + H H H HCO3 + H 3

+ + 2- 2- + + + CO 2- + CO + H H H 3 metabolized 3 H CO3 + H

Fermentation Ka + - Ka H + Ac Ka - Ac- HAc HAc HAc Ac + + + H H H+ H

+ - OH- OH- Na+ Na + OH - + H+ H+ Cl- Cl + H  Definition:

◦ The administration of fluids and electrolytes with the objective of maintaing or restablishing corporal homeostasis

 Priorities:

◦ To conserve the volume of blood ◦ To conserve osmotic pressure and equilibrate ion composition in each body compartment ◦ To conserve normal concentration of hydrogen ions (pH) in each compartment Author(s), year Research Solution used Observations

Denys, 1667 First blood transfusion From a dog to a human RIP O’Shaughnessy, 1831 Loss of water, alcali and Pérdida de agua, álcali Not known if it was 0.9 salts in blood in cases of libre, urea en orina, bajo % NaCl cholera en carbonato de sodio Latta, 1832 Loss of soidum volume Use of glass tube into “Rapid recovery but in an elderly woman basilic vein, 3.4 L died because treatment was not followed”

Stadelman, 1883 Acidosis in diabetic Alcaline Sol.: Na2CO3: 2 % = 208 mM coma 2-3 % 3 % = 312.5 mM Ringer, 1882 Frog’s heart can survive 1 Litre contains: NaCl: 111.2 mEq/L in a balanced solution Sodium chlorine (6.5 g), NaHCO3: 3.125 mEq/L Sodium bicarbonate (0.2 KCl: 5.63 mEq/L g) Calcium chlorine CaCl2: 2.25 mEq/L (0.25 g) y Potassium chlorine (0.42 g) Hamburger, 1882 Establishes the 0.9 % NaCl Mistake: 154 mEq/L ! physiological saline NaCl is only 0.6 % solution Other salts of Na+ 0.3%

Cantani, 1892 Comatose patients Subcutaneous 0.4 % NaCl = 68.44 mM

solutions: 0.3 % Na2CO3 = 31.25 Typhic reactions – RIP! mM Author(s), Year Research Solutions used Observations

Perros: estudio sobre Gran pérdida de líquidos por SSF puede provocar más muerte de perros con Hartwell & Houget, 1912 vómito excesivo, vómito, por sobrecarga de obstrucción intestinal no administración SC con SSF cloruro estrangulada Produce intoxicación por Descripción del trastorno en Dilución de iones puede Rowntree, 1922 agua experimentalmente el ser humano llevar a la muerte Mayor velocidad de infusión, Goteo IV, en vez de goteo Mata, 1924 Cánula de vidrio pero no da tiempo a que el rectal y epidermoclisis organismo regule Na+ : 131 mmol/L Requieren más sodio que Cl- : 111 mmol/L cloruro Hartmann, 1935 Lactantes con diarrea severa Lac-: 29 mmol/L Ringer con Lactato K+ : 5 mmol/L Incluye Calcio, potasio Ca2+: 2 mmol/L Movimiento de liquido entre Darrow & Yannet, 1935 compartimentos, sin Diagrama Darrow- Yannet radioisotopos Movimiento de liquido entre Gamble, 1942 Gamblegrama Diagrama muy útil compartimentos Na+ .: 121 mmol/L 35 mEq/L de KCl Cl- : 103 mmol/L Se recomienda en casos de Pediatría, Lac-: 53 mmol/L Darrow, 1949 acidosis por pérdida de Diarrea severa K+ : 35 mmol/L potasio, pero contiene alto cloruro y lactato

Perros, hombres Pérdida de liq. Extracelular, Fogelman & Wilson, 1960 Traumatismo severo reposición con sal. Solutions Na+ K+ Ca2+ Cl- Precursors SID pH*

SSF 154 0 0 154 0 0 7.30 0.9% NaCl Ketone-R 131 5 3 111 +28 ßOH- +25.5 7.38 Butirate Ringer 131 5 3 111 +28DL-Lactate +25.5 7.38 DL-Lactate Ringer 131 5 3 111 +28 L-Lactate +25.5 7.38 L-Lactate Glucosa 5% 154 0 0 154 + 5 % Glucose 0 7.30 + 0.9% NaCl (560 mOsm) - Plasma 143 4 3 107 +25.1 HCO3 +42 7.42 Stewart + 1 McSherry 138 12 3 100 +50 Acetate +54.5 7.45 +41 7.42 PlasmaLyte 140 5 0 98 + 27 Acetate +40 7.40** A Mg2+ 3 + 23 Gluconate *pH: calculated as the result of adding 1 L solution to a patient with 5 L of blood:

pH 7.41 , PaCO2 40mmHg, Albumin 19mEq/L. ** published values 200

180

160

140

120

100

80

60

Ion concnetration (mMol/L) concnetration Ion 40

20

0 Plasma Plasma Intersticial Intersticial Intracelular Intracelular cationes aniones cationes aniones cationes aniones Proteínas citoesqueleto 0 0 50 Proteínas solubles 16 0 55 Ácidos orgánicos 3 4 3 SO42- 0.5 0.5 10 PO43- 1 1 57 HCO3- 26 30 8 Cl- 102 114 2 Mg2+ 1 0.5 13 Ca2+ 2.5 2.5 1.5 K+ 4 4 160 Na+ 142 144 10 Plasma Urine Plasma Urine Diff. Reabs. % (g/dL) (g/dL) (mmol/L) (mmol/L) Conc. Water 90-93 95 52M 53M - 99.1 Protein 7.0-8.5 - 1.3 - Urea 0.03 2 5 333 X 60 41.4 Uric acid 0.002 0.03 X 15

Glucose 0.1 - 5.5 - 100 Creatinine 0.001 0.1 X 100 Sodium 0.32 0.6 140 188 X 2 99.1 Potasium 0.02 0.15 5 38 X 7 Calcium 0.01 0.015 2.5 3.8 X 1.5 98.8 Magnesium 0.0025 0.01 1 4 X 4 Chlorine 0.37 0.6 105 171 X 2 98.5 Phosphates 0.003 0.12 0.32 12.6 X 40 Sulfates 0.003 0.18 0.31 18.75 X 60 76.5 Ammonia 0.0001 0.05 0.06 29.4 X 500 20.5 + Plasma Urine Urine+NH4 (mmol/L) (mmol/L) (mmol/L) Sodium 140 188 188 Potasium 5 38 38 Calcium 2.5 3.8 3.8 Magnesium 1 4 4 Chlorine 105 171 171 Phosphatos 1.4 12.6 12.6 Sulfates 0.31 18.75 18.75 Cations +148.5 +234 +234 Anions -106.7 -203 -203 SID’ +41.8 -31 -31 + Other Cations 0.06 - 38 (29 NH4 ) SID” +42 -31 +7 pH-calc 7.4 1.4 5.6 - + 2- Variables Normal ↑Anion ↓Na SO4 ↑PaCO2 ↑PaCO2 ↓ ATOT Na+ 140 140 131 140 140 131 131 K+ 4 4 4 4 4 4 4 Ca2+ 4 4 4 4 4 4 4 Cl- 104 104 110 104 104 104 104 Otros- 6 16 6 6 6 6 6 2- SO4 0.6 0.6 0.6 7.0 7.0 7.0 7.0 SID 38 32 23 31 31 22 31

PaCO2 40 40 40 40 50 50 50 Alb- 4.2 4.2 4.2 4.2 4.2 4.2 2.1 Pi- 1.4 1.4 1.4 1.4 1.4 1.4 1.4

HCO3- 24.0 18.5 10.8 17.6 18.1 10.5 23

CO2tot 25.3 19.8 12.0 18.9 19.6 12.0 24.5 BE -0.65 -6.65 -15.65 -7.65 -7.65 -16.65 -1.96 AG 12.0 11.6 10.2 18.4 17.9 16.5 13.0 pH 7.39 7.28 7.04 7.25 7.17 6.93 7.27 Traditional theories of acids Stewart’s theory (1981)

Proton donors Generalized solvent definitions

Brønsted-Lowry (1923) (Germann, 1925)

Henderson-Hasselbalch equations (1916) A system of simultaneous equations with 6 only one variable variables

Nomogramas Electroneutral equilibrium of water

Confussion of dependent and independent Independent variables: variables: H+, HCO - 3 SID, PCO2, ATOT Dependent variables:

+ - - 2- - H , OH , HCO3 CO3 , A , HA

Anion gap: 10-12 mEq/L Anion gap: 6-8 mEq/L

+ + 2+ 2+ + Applications: Only for small ranges of pH Cations: Na , K , Ca , Mg , NH4 e.g. Blood pH (7.0-7.8) - 2- 3- - Anions: Cl , SO4 , PO4 , R-COO Boston School Stewart’s theory pH PaCO2 (Henderson- Hasselbalch) - Respiratory Normal or     HCO3  PaCO2 Acidosis (compensated) (dysnea) - Respiratory Normal or    HCO3 PaCO2 Alcalosis (small) (hypervent.) - + - Metabolic Normal or    HCO3 H + HCO3 Acidosis They do not Anion gap - affect! - loss HCO3 -Normal:  Excr. H+  Prod. HCl Cations -Augmented:  Anions (LacElectrochemical-) acidosis  Anions - Metabolic Normal or     HCO3 Anions Alcalosis (small)  Cations Analysis of clinical cases in ICU

Cálculo de pH y otros iones según Stewart

80 7.9 SIDcambio PCO2 70 7.8 Atot 7.7 60 pH

7.6 H+ 50 OH- 7.5 HCO3 40 7.4 CO32-

30 A- 7.3 Concentración(mmol/L) HA 20 PO4 7.2 Acidez H+ nanoEq/L 10 7.1 pHcalc pHpaciente - 7.0 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 Tiempo (8am a 7am) Pacient with Hyponatremia

Tiempo pH Na+ K+ Ca2+ Mg2+ Cl- SO42-Lactato-PO43- SID pCO2 ATOT pHcalc 1 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 2 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 3 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 4 7.2 131 4 2 1 105 3 1 2 29 40 19 7.209 5 7 124 4 2 1 105 3 1 2 22 40 19 7.009 6 7 124 4 2 1 105 3 1 2 22 40 19 7.009 7 7.05 126 4 2 1 105 3 1 2 24 40 19 7.074 8 7.1 127 4 2 1 105 3 1 2 25 40 19 7.104 9 7.2 131 4 2 1 105 3 1 2 29 40 19 7.209 10 7.3 135 4 2 1 105 3 1 2 33 40 19 7.297 11 7.35 138 4 2 1 105 3 1 2 36 40 19 7.354 12 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 13 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 14 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 15 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389

160 7.8 7.7 Na+ 140 K+ 7.6 120 Ca2+ 7.5 Mg2+ 100 7.4 Cl- SO42- 80 7.3 Lactato- 7.2 60 PO43- 7.1 SID 40 pCO2 7 ATOT 20 6.9 pH 0 6.8 pHcalc 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Pacient with lactic acidosis

Tiempo pH3 Na+ K+ Ca2+ Mg2+ Cl- SO42-Lactato-PO43- SID pCO2 ATOT pHcalc 1 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 2 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 3 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 4 7.2 140 4 2 1 105 3 11 2 28 40 19 7.209 5 7 140 4 2 1 105 3 20 2 19 40 19 7.04 6 7 140 4 2 1 105 3 20 2 19 40 19 7.04 7 7.05 140 4 2 1 105 3 19 2 20 40 19 7.07 8 7.1 140 4 2 1 105 3 18 2 21 40 19 7.103 9 7.2 140 4 2 1 105 3 14 2 25 40 19 7.209 10 7.3 140 4 2 1 105 3 10 2 29 40 19 7.297 11 7.35 140 4 2 1 105 3 7 2 32 40 19 7.354 12 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406 13 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406 14 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406 15 7.4 140 4 2 1 105 3 4 2 35 40 19 7.406

Na+ 160 7.8 K+ 140 7.7 Ca2+ 7.6 120 Mg2+ 7.5 Cl- 100 7.4 SO42- 80 7.3 Lactato- 7.2 60 PO43- 7.1 40 SID 7 pCO2 20 6.9 ATOT

0 6.8 pH3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 pHcalc Pacient with respiratory acidosis

Lactat Tiempo pH Na+ K+ Ca2+ Mg2+ Cl- SO42- o- PO43- SID pCO2 ATOT pHcalc 1 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 2 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 3 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 4 7.2 140 4 2 1 105 3 1 2 38 64 19 7.201 5 7 140 4 2 1 105 3 1 2 38 106 19 7.001 6 7 140 4 2 1 105 3 1 2 38 106 19 7.001 7 7.05 140 4 2 1 105 3 1 2 38 93 19 7.053 8 7.1 140 4 2 1 105 3 1 2 38 82 19 7.102 9 7.2 140 4 2 1 105 3 1 2 38 64 19 7.201 10 7.3 140 4 2 1 105 3 1 2 38 50 19 7.299 11 7.35 140 4 2 1 105 3 1 2 38 44 19 7.351 12 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 13 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 14 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 15 7.4 140 4 2 1 105 3 1 2 38 40 19 7.389 160 7.8 Na+ 140 7.7 K+ 7.6 Ca2+ 120 7.5 Mg2+ Cl- 100 7.4 SO42- 80 7.3 Lactato- 60 7.2 PO43- 7.1 SID 40 7 pCO2 ATOT 20 6.9 pH 0 6.8 pHcalc 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Stewart, P.A. (1981). How to Understand Acid-Base. A Quantitative Acid-Base

Primer for Biology and Medicine, Elsevier Nordholland, New York.

Stewart, P.A. (1983). Modern quantitative acid-base chemistry. Can J Physiol Pharmacol. 61: 1444-1461.

Häubi Segura, C.U. (2004). Use of the Rumen Simulation Technique (RUSITEC) to model clinical and subclinical rumen acidosis in dairy cattle. PhD Thesis,

Department of Agriculture, The University of Reading, Reading, UK.

From the above we know that

+ - [H ] * [OH ] = KW' To determine the hydrogen ion concentration it is necessary

to know KW', and the other variable, the hydroxyl ion concentration. In pure water the only ions present are hydrogen ion and hydroxyl ion, so if the water is to be electrically neutral, then: [H+] - [OH-] = 0 The dissociation of water into hydrogen ions responds to the chemical laws to maintain electro-neutrality. An excess of other positively charged ions will decrease the dissociation of water into H+ ions, conversely, an excess of negatively charged ions increase the dissociation of H+ ions. With the addition of strong electrolytes to water, such as NaOH and HCl, which will almost completely dissociate, there is a mix of water, Na+, Cl-, H+ and OH- ions.

[H+] - [OH-] + [Na+] - [Cl-] = 0 .. Equation #1

If the amount of sodium and chloride ion (or any other strong ions) in solution is known, it is possible to determine the hydrogen ion concentration. Only the difference in ionic concentrations (SID) is of importance, therefore the above equation can be abbreviated to:

[SID] + [H+] - [OH-] = 0 A weak acid, HA (such as albumin or VFAs) dissociates to form H+ and A-, as follows: HA <=> H+ + A- Previous equations (dissociation of water and the requirement for electrical neutrality ) are slightly modified to include the dissociated anion A-, derived from the acid:

+ - [H ] * [OH ] = KW' Equation #0 [H+] + [OH-] + [SID] + [A-] = 0 Equation #1A

The following two equations are based on the dissociation of the acid, and the necessity for conservation of the total

amount of acid, which is abbreviated to ATOT : + - [H ] * [A ] = KA * [HA] Equation #4 - [HA] + [A ] = [ATOT] Equation #5 The effect of carbon dioxide on aqueous solutions is generally expressed by the Henderson-Hasselbalch equation, but this only represents part of the truth.

Four reactions can happen to CO2 gas when exposed to water: 1) Dissolution in water, 2) Reaction with water to from carbonic acid, 3) Dissociation to form bicarbonate ion, 4) Second dissociation to form carbonate ions:

+ CO2(d) + H2O K1 H2CO3 K2 H +

- + + 2- HCO3 K3 H + H + CO3 The two most significant reactions are the formation of carbonate and bicarbonate, as each has its own equilibrium constant. These reactions with their equilibrium constants will have a profound influence on the whole system, but it is only in the context of the whole system that is possible to understand the role of carbon dioxide:

1. CO2 can dissolve in water, as expressed by the equation:

CO2(gas) <=> CO2 (dissolved)

The forward reaction depends on partial pressure of CO2,, = with a rate

Kf * PCO2 The reverse reaction depends on the concentration of dissolved

CO2 with the rate

Kr * [CO2 (dissolved)] According to Henry´s Law, the dissolution of molecular

carbon dioxide [ CO2(dissolved) ] into the rumen fluid medium is related to the solubility coefficient for carbon

dioxide (SCO2) and the partial pressure of carbon dioxide

(PCO2) via the formula:

[CO2(dissolved)] = SCO2 * PCO2 Equation #7A

The solubility of CO2 (SCO2) has substituted Kf/Kr .

SCO2 is dependent on temperature, and at 37 °C it is about 3.0 * 10-5 Eq/litre/mmHg. 2. CO2 can react with water to form carbonic acid:

CO2 + H2O  H2CO3 Equilibrium is represented by:

[CO2(dissolved)] * [H20] = K * [H2CO3] .. Equation #7B

If [H20] is treated as a constant, it can be rearranged:

[H2CO3] = KH * PCO2 -8 The value of KH at 37 °C is 9 * 10 Eq/litre - therefore, the

H2CO3 concentration is far smaller than the amount of

dissolved CO2.

The reaction of CO2 with water is very slow , with a half time of about 30 seconds, speeded up to microseconds by the carbonic anhydrase abundantly present in most tissues but not in the rumen. 3. H2CO3 thus formed can dissociate into bicarbonate and hydrogen ions:

+ - H2CO3  H + HCO3 Equilibrium is represented by:

+ - [H ] * [HCO3 ] = K * [H2CO3] It follows that:

+ - [H ] * [HCO3 ] = KC * PCO2 Equation #8

A physiological value for KC is 2.6 * 10-11 (Eq/l)2/mmHg - 4. Once formed, HCO3 can rapidly dissociate:

- + 2- HCO3  H + CO3

Equilibrium is represented by:

+ 2- - [H ] * [CO3 ] = K3 * [HCO3 ] Equation #9

-11 A typical value for K3 is 6 * 10 Eq/litre.

+ - CO2(d) + H2O K1 H2CO3 Kc H + HCO3

+ + 2- K3 H + H + CO3 Stewart’s original theory combined strong ions, carbon dioxide and a weak acid to model blood plasma and intracellular fluids. Blood plasma is rich in weak acids, specially proteins (albumin) and for the purposes of analysis and simplicity

he regarded them as being all one acid with a single ATOT

and single KA. Nevertheless it is possible to expand the model with

multiple KA (Figge et al., 1991). Fencl Model: pH = f(pH){SID, PCO2, [PiTOT ], [Albumin], [CitrateTOT ]} The knowledge of the independent variables ( [SID], PCO2,

and ATOT) and the equilibrium constants KW', KA, KC and

K3. allow to calculate any one of eight dependent variables:

- ◦ HCO3 ◦ A- ◦ HA

◦ CO2 (dissolved) 2- ◦ CO3

◦ H2CO3 ◦ OH- ◦ H+

Note that dissolved CO2 and H2CO3 are easily determined from Equations #7A and #7B.