Water as a Solvent of Life

Water, the Solvent of Life

• Water's solvent properties shaped the evolution of living things.
• Most small intermediates of metabolism, nucleic acids, and proteins are soluble in water.
• Lipid bilayers, forerunners of biological membranes, form spontaneously in water and are stabilized by interaction with it.
• Hydrogen bonds, ionic interactions, and the hydrophobic effect, though individually weak, combine to influence the 3D shape and stability of biological molecules and structures.

Ionization Behavior of Water

• The ionization behavior of water and of weak acids and bases dissolved in water can be represented by one or more equilibrium constants.
• Most biomolecules are ionizable.
• Their structure and function depend on their ionization state, characterized by equilibrium constants.

Aqueous Solutions and Buffers

• An aqueous solution of a weak acid and its salt makes a buffer that resists changes in pH in response to added acid or base.
• Biological systems are buffered to maintain a narrow pH range.
• Macromolecules retain their functional structure (which depends on their ionization state) within this range.
• Blood pH outside the range of 7.3 to 7.5 is life-threatening in humans.

Enzymes and pH

• Enzymes catalyze cellular processes and have evolved to function optimally at near-neutral (physiological) pH.
• Enzymes in intracellular compartments of low or high pH show greatest activity and stability at those pH values.

Weak Interactions in Aqueous Systems

• Water has a higher melting point, boiling point, and heat of vaporization than most other common solvents.
• Hydrogen bond = electrostatic attraction between the oxygen atom of one water molecule and the hydrogen of another.

Strength and Nature of Hydrogen Bonds

• Hydrogen bonds are relatively weak with a bond dissociation energy of approximately $23 kJ/mol$ in liquid $H_2O$.
• Hydrogen bonds are about 10% covalent and 90% electrostatic.
• Hydrogen bonds are fleeting; the lifetime of each hydrogen bond is only 1 to 20 picoseconds in liquid.
• When one hydrogen bond breaks, another forms.

Number of Hydrogen Bonds Formed

• In liquid, each $H_2O$ molecule forms hydrogen bonds with an average of 3.4 other molecules.
• In ice, each $H_2O$ molecule forms 4 hydrogen bonds.

Hydrogen Bonds and Melting Point of Water

• During melting or evaporation, heat is taken up by the system, increasing the entropy of the aqueous system:
  • $H<em>2O(solid) \rightarrow H</em>2O(liquid)$, $\,\Delta H = +5.9 kJ/mol$
  • $H<em>2O(liquid) \rightarrow H</em>2O(gas)$, $\,\Delta H = +44.0 kJ/mol$
• At room temperature, melting and evaporation occur spontaneously.
  • Free-energy change ($\Delta G$) must be negative.
  • Because $\,\Delta H$ is positive, the increase in $\,\Delta S$ drives these changes.

Hydrogen Bonds with Polar Solutes

• Hydrogen bonds readily form between an electronegative atom (hydrogen acceptor) and a hydrogen atom covalently bonded to another electronegative atom (hydrogen donor).

Hydrogen Bonding in Biological Molecules

• Hydrogen atoms covalently bonded to carbon atoms do not hydrogen bond.
• Alcohols, aldehydes, ketones, and compounds containing N—H bonds all form hydrogen bonds with water.

Directionality of Hydrogen Bonds

• Hydrogen bonds are strongest when the acceptor atom is in line with the covalent bond between the donor atom and $H$.
• This maximizes electrostatic interaction.

Electrostatic Interactions with Charged Solutes

• Hydrophilic compounds dissolve easily in $H_2O$ and are generally charged or polar.
• Hydrophobic compounds are nonpolar molecules like lipids and waxes.
• Amphipathic compounds contain both polar (or charged) and nonpolar regions.

Water as a Solvent

• $H_2O$ dissolves salts and charged biomolecules by screening electrostatic interactions.
• The increase in entropy of the system is largely responsible for the ease of dissolving salts in water.

Dielectric Constant of Water

• Dielectric constant ($\epsilon$) = a dimensionless physical property that reflects the number of dipoles in a solvent.
  • For water at $25 ^\circ C$, $\,\epsilon = 78.5$
  • For nonpolar benzene at $25 ^\circ C$, $\,\epsilon = 4.6$

Force of Ionic Interactions

• The force ($F$) of ionic interactions in solution depends on:
  • The magnitude of the charges ($Q$).
  • The distance between the charged groups ($r$).
  • The dielectric constant of the solvent ($\epsilon$).
• Equation: $F = \frac{Q<em>1 Q</em>2}{\epsilon r^2}$
• Ionic attractions or repulsions operate over 10 to 40 nm.

Solubility of Nonpolar Gases

• Biologically important gases such as $CO<em>2, O</em>2$, and $N_2$ are nonpolar.
• Their movement into aqueous solution decreases entropy by constraining their motion.

Effect of Nonpolar Compounds on Water Structure

• Nonpolar compounds interfere with hydrogen bonding among $H_2O$ molecules, increasing enthalpy ($\Delta H$) and decreasing entropy ($\Delta S$).
• The free-energy change ($\Delta G = \Delta H - T\Delta S$) for dissolving a nonpolar solute in water is unfavorable.
  • $\,\Delta H$ has a positive value.
  • $\,\Delta S$ has a negative value.
  • $\,\Delta G$ has a positive value.

Ordering of Water Molecules around Nonpolar Solutes

• $H_2O$ molecules form a highly ordered, cagelike shell around each solute molecule to maximize solvent-solvent hydrogen bonding.
• $H_2O$ molecules are not as highly oriented as those in clathrates (crystalline compounds of nonpolar solutes and water).

Amphipathic Compounds in Aqueous Solutions

• Polar, hydrophilic regions interact favorably with $H_2O$ and tend to dissolve.
• Nonpolar, hydrophobic regions tend to avoid contact with $H_2O$ and cluster together.

The Hydrophobic Effect

• Hydrophobic effect = nonpolar regions cluster together, and polar regions arrange to maximize interactions with each other and with the solvent.
• Micelles = thermodynamically stable structures of amphipathic compounds in water.

Role of Water in Enzyme-Substrate Complex Formation

• Release of ordered water favors formation of an enzyme-substrate complex.
• Enzyme-substrate interaction is stabilized by hydrogen bonding, ionic interactions, and the hydrophobic effect.

Van der Waals Interactions

• Van der Waals interactions (London dispersion forces) = distance-dependent weak attractions and repulsions between transient dipoles.
• Van der Waals radius = measure of how close an atom will allow another to approach

Weak Interactions and Macromolecular Structure

• Noncovalent interactions are much weaker than covalent bonds.
• They are continually forming and breaking.
• For macromolecules, the most stable structure usually maximizes weak interactions.
• $H_2O$ molecules are often bound so tightly to biomolecules that they are part of the crystal structure.

Water and Protein Function

• Cytochrome f has a chain of five bound $H_2O$ molecules.
• This may provide a path for protons to move through the membrane.

Colligative Properties and Osmotic Pressure

• Solutes alter the colligative properties of the solvent:
  • Vapor pressure
  • Boiling point
  • Melting point (freezing point)
  • Osmotic pressure
• The effect depends on the number of solute particles (molecules or ions) in a given amount of water.

Osmotic Pressure

• Osmotic pressure, Π = the force necessary to resist water movement.
• Approximated by the van’t Hoff equation: $\,\Pi = icRT$

Calculating Osmotic Pressure

• The osmotic pressure, Π, depends on:
  • The van’t Hoff factor, a measure of the extent to which the solution dissociates into 2+ ionic species ($i$).
    • For nonionizing solutes, $i=1$.
    • For solutes that dissociate into two ions, $i=2$.
  • The solute’s molar concentration ($c$).
• $\Pi = icRT$ where R is the gas constant and T is the absolute temperature.

Osmolarity and Osmosis

• Osmolarity = the product of the van’t Hoff factor $i$ and the solute’s molar concentration, $c$.
• Osmosis = water movement across a semipermeable membrane driven by differences in osmotic pressure.

Effects of Extracellular Osmolarity on Water Movement

• Isotonic solution = osmolarity equal to that of a cell’s cytosol.
• Hypertonic solution = higher osmolarity than that of the cytosol.
• Hypotonic solution = lower osmolarity than that of the cytosol.

Ionization of Water

• $H<em>2O$ molecules have a slight tendency to undergo reversible ionization to yield a hydrogen ion (a proton) and a hydroxide ion: $H</em>2O \rightleftharpoons H^+ + OH^-$
• Hydrogen ions are immediately hydrated to form hydronium ions ($H_3O^+$).

Proton Hopping

• Proton hopping results in high ionic mobility.

Equilibrium Constant

• Equilibrium constant, $K_{eq}$ = gives the position of equilibrium.
• For the generalized reaction $A + B \rightleftharpoons C + D$, $K<em>{eq}$ is defined in terms of the concentrations of reactants ($A$ and $B$) and products ($C$ and $D$) at equilibrium: $K</em>{eq} = \frac{[C][D]}{[A][B]}$

Ionization of Water and Equilibrium Constant

• The equilibrium constant for the reversible ionization of $H<em>2O$ is $K</em>{eq} = \frac{[H^+][OH^-]}{[H_2O]}$
• In pure $H<em>2O$ at $25^\circ C$, the concentration of $H</em>2O$ is:
  $\frac{1000\frac{g}{l}}{18.015 \frac{g}{mol}} \approx 55.5 M$

Ion Product of Water

• Substituting $55.5 M$ in the equilibrium constant expression yields: $K_{eq} = \frac{[H^+][OH^-]}{55.5 M}$
• $(55.5 M)K<em>{eq} = [H^+][OH^-] = K</em>w$
• Where $K_w$ is the ion product of water at $25^\circ C$.

Calculating the Ion Product of Water

• In pure water at $25^\circ C$, $K_{eq} = 1.8 \times 10^{-16} M$
• Substituting this value in:
  • $K_w = [H^+][OH^-] = (55.5 M)(1.8 \times 10^{-16} M) = 1.0 \times 10^{-14} M^2$

Neutral pH

• Neutral pH = exactly equal concentrations of $H^+$ and $OH^−$, as in pure water.
• At neutral pH: $[H^+] = [OH^-] = 10^{-7}M$ and $K_w = 1.0 \times 10^{-14} M^2$

The pH Scale

• The pH scale is based on the ion product of water, $K_w$.
• The term pH is defined by the expression $pH = -\log[H^+]$.
• For a precisely neutral solution at $25 ^\circ C$, $pH = 7.0$.

pH of Aqueous Fluids

• pH values > 7 are alkaline or basic, and the concentration of $OH^−$ is greater than that of $H^+$.
• pH values < 7 are acidic, and the concentration of $H^+$ is greater than that of $OH^−$.

pH and Medical Diagnoses

• Acidosis = pH of blood plasma below the normal value of 7.4; common in people with severe, uncontrolled diabetes.
• Alkalosis = pH of blood plasma above the normal value of 7.4.
• Extreme acidosis or alkalosis can be life-threatening.

Weak Acids and Bases

• Conjugate acid-base pair = a proton donor and its corresponding proton acceptor.
• The stronger the acid, the greater its tendency to lose its proton.

Ionization Constants

• The tendency for any acid (HA) to lose a proton and form its conjugate base ($A^−$) is defined by the equilibrium constant ($K_{eq}$) for the reversible reaction $HA \rightleftharpoons H^+ + A^−$
• $K<em>{eq} = \frac{[H^+][A^-]}{[HA]} = K</em>a$

pKa

• $pK<em>a = -\log K</em>a$
• The stronger the tendency to dissociate a proton, the stronger the acid and the lower its $pK_a$.
• $pK_a$ can be determined experimentally.

Titration Curves

• Titration curve = a plot of pH against the amount of $NaOH$ added.

Acetic Acid Equilibrium Constants

• Two reversible equilibria are involved in the process:
  • $H<em>2O \rightleftharpoons H^+ + OH^−$ with $K</em>w = [H^+][OH^-] = 1 \times 10^{-14} M^2$
  • $HAc \rightleftharpoons H^+ + Ac^−$ with $K_a = \frac{[H^+][Ac^-]}{[HAc]} = 1.74 \times 10^{-5} M$

Titration Curve of Acetic Acid

• At the midpoint, the pH of the equimolar solution = the $pK_a$ of acetic acid.

Buffers

• Buffers = aqueous systems that tend to resist changes in pH when small amounts of acid ($H^+$) or base ($OH^−$) are added.
• Components: a weak acid (proton donor) and its conjugate base (proton acceptor)

The Buffering Region

• Buffering region = the flat zone of a titration curve

Henderson-Hasselbalch Equation

• $pH = pK_a + \log\frac{[A^-]}{[HA]}$

Buffering in Biological Systems

• Proteins containing histidine (side chain $pK_a$ of 6.0) residues buffer effectively near neutral pH.

The Phosphate Buffer System

• The phosphate buffer system acts in the cytoplasm of all cells: $H<em>2PO</em>4^- \rightleftharpoons H^+ + HPO_4^{2-}$
• $H<em>2PO</em>4^-$ acts as a proton donor, and $HPO_4^{2-}$ acts as a proton acceptor.
• The buffer system is maximally effective at a pH close to its $pK_a$ of 6.86; works best between 5.9 and 7.9.

The Bicarbonate Buffer System

• The bicarbonate buffer system acts in the blood plasma: $H<em>2CO</em>3 \rightleftharpoons H^+ + HCO_3^−$
• $H<em>2CO</em>3$ acts as a proton donor, and $HCO_3^−$ acts as a proton acceptor.
• Buffer system is effective near pH 7.4

Additional Equilibrium Constants

• Carbonic acid ($H<em>2CO</em>3$) is formed from dissolved carbon dioxide and water in a reversible reaction:
  • $CO<em>2(aq) + H</em>2O \rightleftharpoons H<em>2CO</em>3$
  • $K<em>2 = \frac{[H</em>2CO<em>3]}{[CO</em>2(aq)][H_2O]}$
• $CO<em>2$ dissolved in an aqueous solution is in equilibrium with $CO</em>2$ in the gas phase:
  • $CO<em>2(g) \rightleftharpoons CO</em>2(aq)$
  • $K<em>a = \frac{[CO</em>2(aq)]}{[CO_2(g)]}$

Bicarbonate Buffer System and pH

• The pH of a bicarbonate buffer system exposed to a gas phase depends on:
  • The concentration of $HCO_3^−$.
  • The partial pressure of $CO<em>2$ ($pCO</em>2$) = the concentration of $CO_2$ in the gas phase.

Equilibria in Bicarbonate Buffer System

• The rate of respiration (controlled by the brain stem) can quickly adjust these equilibria to keep the blood pH nearly constant.
• Hyperventilation raises blood pH.

Equilibrium of Hydration of CO2

• The rapid equilibrium of aqueous $CO<em>2$ dissolved in blood forms additional $H</em>2CO<em>3$ for buffering: $CO</em>2(aq) + H<em>2O \rightleftharpoons H</em>2CO_3$
• $K<em>h$ = the equilibrium constant for the hydration of $CO</em>2$ to form $H<em>2CO</em>3$: $K<em>h = \frac{[H</em>2CO<em>3]}{[CO</em>2(aq)]}$

Overall Equilibrium for Dissociation of H2CO3

• $K<em>h = \frac{[H</em>2CO<em>3]}{[CO</em>2(aq)]}$
• $K<em>a = \frac{[H^+][HCO</em>3^-]}{[H<em>2CO</em>3]}$
• $K<em>{combined} = K</em>h K<em>a = \frac{[H^+][HCO</em>3^-]}{[CO_2(aq)]}$

Calculating Kcombined and pKcombined

• Experimentally determined values at $37^\circ C$:
  • $K_h = 3.0 \times 10^{-3} M$
  • $K_a = 2.7 \times 10^{-4} M$
• From $K<em>h$ and $K</em>a$: $K_{combined} = (3.0 \times 10^{-3} M)(2.7 \times 10^{-4} M) = 8.1 \times 10^{-7} M^2$
• $pK<em>{combined} = -\log K</em>a = -\log (8.1 \times 10^{-7} M^2) = 6.1$

Calculating Blood pH

• Typical values:
  • $[H<em>2CO</em>3] \approx 1.2 mM$
  • Plasma $[HCO_3^-] \approx 24 mM$
• From these typical values: $pH = pK_a + \log\frac{[A^-]}{[HA]} = 6.1 + \log\frac{[24 mM]}{[1.2 mM]} \approx 7.4$

Diabetes and Acidosis

• Untreated Diabetes Mellitus results in acidosis, the accumulation of high concentrations of two carboxylic acids, β- hydroxybutyric acid and acetoacetic acid
• Dissociation of these acids lowers the pH of blood plasma to less than 7.35
• severe acidosis causes enzymes to not function properly

Physiological pH

• Optimum pH = the characteristic pH at which enzymes typically show maximum catalytic activity.