2.1. Introduction

• Recent physiochemical analysis of biological solutions has yielded new understanding of H⁺ behavior and requires changes in many generally accepted concepts of H⁺ behavior.
• The new concepts can best be understood by considering progressively more complex "biological" solutions, beginning with pure water, and adding strong ions, proteins, and finally CO₂.
• The analysis shows there are independent variables in this system; these can be changed from outside the system and will result in changes in dependent variables that are internal to the system.
• Major point: changes in dependent variables are caused by changes in independent variables, but not by changes in other dependent variables (i.e., dependent variables are not causally related to each other).
• The Henderson-Hasselbalch equation accurately describes the relationship among H⁺, PCO₂, and HCO₃, but does not describe the "control" for the system.

2.2. Pure H₂O

• H₂O dissociates slightly into H⁺ and OH^- : [H₂O] ↔ [H⁺] + [OH^-].
  • the dissociation constant, K'w is essentially a constant, regardless of the degree of dissociation, but is temperature sensitive.

    Kw = [H+] [OH-]

    [H2O]

    K'w = [H⁺] [OH^-] = 1x10^-14 at 25^oC

• As in all solutions, electroneutrality must be preserved:
  • electroneutrality: sum of positive ions = sum negative ions (ie. [ H⁺] = [OH^-])
  • chemical neutrality: [H⁺] = [OH^-]
  • for pure water: [H⁺] = [OH^-] satisfies both
• One can use these relationships to calculate [H⁺] in H₂O:
  • [H⁺] = √K'w = [OH¯ ] = 1x10^-7 Eq/L (pH 7.0 at 25^oC)
    • therefore, K'w determines the [H⁺] in pure H₂O
• However, at other temperatures, [H⁺] will not= 1 x 10^-7 eq/L. For example, at 37^oC, K'w = 4.4x10^-14, and [H⁺] = 2.1x10^-7 Eq/L (pH 6.7).
  • 6.7 is the pH of chemical neutrality at body temperature-ie when [H⁺]=[OH^-]
  • i.e. body fluids are very alkaline (pH = 7.4)

2.3. Strong Ion Solutions

• Strong electrolytes dissociate essentially completely (i.e., no dissociation equlibrium) in solution.
  • strong ions in mammalian biological fluids are Na⁺, Cl¯ , K⁺, SO₄, and lactate or keto acids (when present). Ca⁺⁺ and Mg⁺⁺ are minor
• The Gamblegram is a diagram for electroneutrality in solutions with positive and negative ions; the height of the columns represents the sum of positively and negatively charged ions.
  • consider addition of 10 mM HCl or 10 mM NaOH to an NaCL solution. The diagram shows the amount of each ion present and demonstrates electroneutrality
• Consider H₂O at a constant temperature to which HCl and NaOH have been added.
  • to maiintain electroneutrality: [Na⁺] + [H⁺] = [Cl¯ ] + [OH¯ ]
  • if [Na+] = [Cl¯ ], then [H+] = [OH¯ ], but if [Na+] ≠ [Cl¯ ], then [H+] ≠ [OH¯ ]
  • in this system, the difference between [H⁺] and [OH¯ ] will exactly equal the difference between [Na⁺] and [Cl¯ ], which can be controlled by how much is added from outside the system
• Quantitative analysis of this system shows mathematically that [H⁺] depends on K'w (a constant) and [Na⁺] and [Cl¯ ], which can be controlled from outside the system.
• Strong ion difference (SID), the critical factor:
  • it is the difference [Na⁺] [Cl¯ ], or strong cations in solution not electrically balanced by strong anions that will determine [H⁺] and [OH¯ ]
  • any other strong ions present in solution (ex. K⁺) will also affect the calculation of SID, but only inorganic ions are routinely measured
  • SID = sum of all strong cation concentrations minus sum of all strong anion concentrations
  • SID will be balanced by net charge on weak ions to fulfill electroneutrality for that solution
  • in plasma, SID is normally approximately +40 mEq/L; thus [OH¯ ] > [H⁺] and the solution is alkaline: [H⁺] + SID = [OH¯ ]
  • if SID is negative, strong anions exceed strong cations; to balance, [H⁺] will be > [OH¯ ], and the solution will be acidic
• Any change in SID must change both [H⁺] and [OH¯ ]; therefore SID is an independent variable, while [H⁺] and [OH¯ ] are dependent variables.
• The [H⁺] now depends on K'w and SID, and only SID is easily changed in body fluids.

2.4. Weak Acids (Plasma Proteins)

• Weak acids dissociate partially HP ↔ H⁺ + P¯ .

  • Ka = [H+] [P¯ ]

    [HP]

  • the dissociation constant Ka will be part of the quantitative analysis
• The total amount of "P" per liter is a constant determined by the amount originally present (conservation of mass), regardless of the degree of dissociation:
  • [P_tot] = [HP] + [P¯ ]
• [P_tot] is a new independent variable, and [H⁺] and [P¯ ] are dependent variables that change when [P_tot] changes.
• To satisfy electroneutrality: [H⁺] + SID = [P¯ ] + [OH¯ ].
• [H⁺] now depends on K'w, SID, and [P_tot]; of these, only SID and [P_tot] change in body fluids.

2.5. Addition of CO₂

• Addition of CO₂ adds dissolved CO₂ and H₂CO₃ (both negligible), and bicarbonate (HCO₃ ) and carbonate (CO₃⁼) anions.
  • H₂O + CO₂↔ H₂CO₃↔ H+ + HCO₃-- ↔ H+ + CO₃⁼
    • for quantitative analysis, there are new dissociation constants

• Electroneutrality statement: [H⁺] + SID = [P¯ ] + [OH¯ ] + [ HCO₃--] + [CO₃⁼].
• The new independent variable is PCO₂, not [ HCO₃^- ] !.
• [H⁺] quantitatively now depends on K'w, SID, [P_tot], and PCO₂.
  • [H⁺] does not depend on [ HCO₃-- ], rather [ HCO₃-- ] is another dependent variable, like [OH¯], that will change when independent variables are manipulated

2.6. Summary and Conclusions

• We can now identify the mechanisms by which changes in [H⁺] are brought about.
• In biological fluids, we have three independent variables: SID, [P_tot] and PCO₂.
  • [H⁺], [OH¯ ], [HP], [P¯ ], and [ HCO₃-- ] are dependent variables that all change when one or more independent variables are changed
  • acid base derangements arise from abnormalities of SID, proteins, and PCO₂
  • evaluation of acid base status requires evaluation of SID (serum electrolytes), serum proteins, and PCO₂
  • therapeutic efforts to correct acid base derangements will be directed toward correction of SID and PCO₂

3.1. Changes in the Independent Variables

• PCO₂ depends on respiration, and changes occur rapidly (within minutes) and will affect acid base status of plasma and other fluids.
  • increased PCO₂ = respiratory acidosis
  • decreased PCO₂ = respiratory alkalosis
• The concentration of strong ions depends on GI absorption and GI and renal loss, both normal and pathological; SID changes occur slowly (over hours).
  • normal SID in plasma is 42 mEq/L
  • increased SID causes metabolic alkalosis (hypochloremic alkalosis)
  • decreased SID causes metabolic acidosis
  • if [H⁺] PCO₂, [P_tot] and inorganic SID are known, the difference between measured inorganic SID and the point on the graph represents the SID component due to any unmeasured strong ions present (ex. keto-acids or lactate)
• Proteins are the major weak acids in plasma, and their concentration is determined by hepatic synthesis or pathologic losses; changes occur slowly (over days).
  • hyperproteinemia causes metabolic acidosis
  • The [ HCO₃-- ] is of minor interest, since it is a dependent variable and does not determine [H⁺]

3.2. Body Fluid Interactions

• Interactions across semipermeable membranes depend on changes in independent variables.
  • i.e., to change [H⁺] in a fluid, one must change SID, [P_tot], or PCO₃
  • [H⁺] is a dependent variable, and moving H⁺ from one compartment to another cannot explain changes in [H⁺] of either fluid (the same is true for HCO₃^-)
• CO₂ is very soluble and most biological membranes are permeable to it; it diffuses rapidly between fluids on the basis of partial pressure gradient.
  • thus, PCO₂ changes are a potential mechanism for overall short term changes in acid base status of all body fluids, but not for interactions between fluids in different compartments
• Most membranes are highly impermeable to protein, and protein movement between fluids is thus not a mechanism of interaction.
• Biological membranes are selectively permeable to strong ions, and membrane pumps allow movements between compartments.
  • therefore, SID changes are the major mechanism of body fluid interactions among compartments (for example, renal control of Na⁺, Cl¯ and K⁺ excretion

3.3. Metabolic Acid Base Control Revisited

• The kidney does not act to remove H⁺, it lowers [H⁺] of plasma by excreting more Cl¯ than Na⁺, and thus raising the plasma SID.
• Movement of HCO₃-- in or out of plasma or renal tubules does not alter [H⁺], because both are dependent variables.
• Thus, renal control of acid base status is via control of SID through selective strong ion excretion, and not through retention or removal of HCO₃^-.
  • ex. Excretion of CL- in excess of Na⁺ or K⁺ will influence plasma SID and [H⁺]
• GI absorption and loss of strong ions also contributes to acid base equlibrium through effects on SID
  • for example, gastric pH is lowered by creating a high negative SID (Cl¯ secretion or Na⁺ absorption), not by pumping H⁺