Part I => CARBS and LIPIDS

§1.1 Thermodynamics

§1.1a General Principles

§1.1b Macromolecular Forces

§1.1c Acid-Base Equilibria

Section 1.1a:

General Principles

Synopsis 1.1a

- Thermodynamics is concerned with changes in heat and temperature as related to

energy exchange and work done by living systems—the major thermodynamic

parameters (or physical quantities) include changes in free energy (G), enthalpy

(H), entropy (S), volume (V), and heat capacity (Cp)

- The laws of thermodynamics provide general constraints that such systems must not

violate—of the four laws of thermodynamics (zeroth through third), the first and

second laws are of particular relevance to understanding living systems

- Natural processes are spontaneous (S > 0)—ie they are accompanied by an increase

in entropy (S) coupled with a decrease in free energy (G)—the energy available to do

useful work at a constant temperature, pressure, and pH

- Thermodynamic properties accompanying biochemical processes are usually quoted

under the so-called “standard state conditions” that are defined as:

Temperature (T) = 25°C (77°F / 298K)

Pressure (P) = 1 atm (105Pa)

pH = 7.0

F = (9/5)C + 32K = C + 273

Relationship Between Disorder and Entropy

Entropy is a measure of the disorder in a system—eg(a) Entrapment of gas in a chamber reduces its overall entropy(b) Release of gas from the chamber increases its entropy

Energy Flow in the Biosphere—an Open System

- Living organisms are thermodynamically open systems that tend to maintain a “steady-state” rather than reach equilibrium (G 0)—doing so would equate to death!

- “Steady-state” implies that the rates of synthesis and degradation of metabolic intermediates within a cell are more or less equal such that their concentrations change little over time—egthe mass of an organism generally remains more or less constant over time irrespective of how much food and water are consumed!

Equilibrium vs Steady-StateEquilibrium (death)

- Consider the following reaction in progress:

A + B <=> C

- Let us assume that:

-d[A]/dt = rate of decay/breakdown of A (into C)

-d[C]/dt = rate of decay/breakdown of C (into A and B)

- At equilibrium, the forward reaction is exactly balanced by reverse reaction:

-d[A]/dt = -d[C]/dt

- Concentration of C stabilizes (reaches a constant) at equilibrium—the above reaction is @ equilibrium!

Steady-State (life)

- Consider the following reactions in progress:

A + B <=> C

C + D <=> E

- Let us assume that:

d[C1]/dt = rate of formation/synthesis of C (from A and B)

-d[C2]/dt = rate of decay/breakdown of C (into E)

- At steady-state, the rate of synthesis of C equals its rate of breakdown:

d[C1]/dt = -d[C2]/dt

- Concentration of C also stabilizes (reaches a constant) but under steady-state conditions—neither of

the above reactions is @ equilibrium!

Laws of Thermodynamics

First law of Thermodynamics

Energy is neither created nor destroyed but only

conserved/exchanged —it is mathematically

expressed as:

U = q – w

U = Change in internal energy (of the system)

q = Heat exchanged/added (eg to generate steam)

w = Work done (eg piston movement)

Second law of Thermodynamics

Natural processes are spontaneous (S > 0), leading

to an increase in disorder or entropy (S)—it is

mathematically expressed as:

Suni = (Ssys + Ssur) > 0

S is the change in entropy of the universe (uni),

system (sys), and surroundings (sur)

Steam Engine

Gibb’s Free Energy (G)- Biological manifestation of the first and second laws of

thermodynamics is given by the Gibb’s equation:

G = H - TS

where G = Change in free energy (cal/mol)

H = Change in enthalpy (cal/mol)

S = Change in entropy (cal/mol/K)

T = Absolute temperature (K)

- The sign denotes standard conditions: 25C, 1 atm, and pH 7

- Gibb’s equation provides a measure of the thermodynamic potential of a biological

process to do useful work

- Biological processes are overall accompanied by a decrease in free energy—ie G < 0

- To satisfy the above thermodynamic constraint, endergonic processes (G > 0) are

coupled to exergonic reactions (G < 0)

- Similarly, endothermic processes (H > 0) are driven by an increase in entropy (TS > 0)—

ie they are under entropic control

Willard Gibbs(1839-1903)

Relationship Between H, S and G

In thermodynamic terms, thermodynamically favorable reactions (G < 0) are described as being under:

(1) Enthalpic control => H < 0 and TS < 0

(2) Entropic control => H > 0 and TS > 0

(3) Enthalpic and entropic control => H < 0 and TS > 0

When G=0 => T=H/S

Equilibrium Thermodynamics

- Consider the following reaction with an equilibrium dissociation constant (Kd) of 10M (10x10-6M):

A + B <=> C

- Change in free energy of the reaction (G) under non-equilibrium setting is given by:

G = G + RTlnKa = G - RTlnKd [1]

where G = change in free energy of all species under standard state (cal/mol)—ie @ equilibrium

R = Universal molar gas constant (2 cal/mol/K)

T = Absolute temperature (K)

Ka = Equilibrium association constant (M-1)

Kd = Equilibrium dissociation constant (M)

- Kd is defined as:

Kd = [A][B]/[C] = 1/Ka

where letters A-C in [ ] indicate corresponding concentration of each species @ equilibrium

- But, forward reaction equals reverse @ equilibrium—ie G = 0

- Thus, Eq [1] can be rewritten @ equilibrium as:

G = -RTlnKa [2]

=> G = RTlnKd [3]

=> G = (2 cal/mol/K).(298K).ln(10x10-6M) = (596 cal/mol).ln(10-5) = -(596 cal/mol).ln(105)

=> G = -6862 cal/mol = -7 kcal/mol

- Summarize the relationship between energy (U), heat (q), and work (w)

- State the first and second laws of thermodynamics

- Explain why changes in both enthalpy (ΔH) and entropy (ΔS) determine the spontaneity of a process

- What is the free energy change for a reaction at equilibrium?

- Write the equation showing the relationship between ΔG° and Kd

- Write the equation showing the relationship between ΔG, ΔG°, and the concentrations of the reactants and products

- Explain how biochemists define the standard state of a solute

Exercise 1.1a

Section 1.1b:

Macromolecular Forces

Synopsis 1.1b

- TWO major attractive forces acting on biological molecules include:(1) ionic interactions(2) van der Waals forces (eg hydrogen bonding, dipolar interactions)

- Being polar (ie electrostatically polarized), water molecules form hydrogen bonds with other molecules

- In terms of attractive forces, water can exist either in a liquid or crystalline (ice) form depending on the nature of hydrogen bonding interactions

- The exclusion of nonpolar groups from polar surroundings so as to maximize the entropy of water molecules is the basis of “hydrophobic effect”

- Atomic distances are measured in the units of Ångström (Å)

Structure of Water: van der Waals Envelope

Johannes van der Waals

(1837-1923)

- In chemical terms, water is dihydrogen monoxide (H2O)—wherein two hydrogen atoms are covalently bonded to an oxygen atom

- While essential to life, dihydrogen monoxide is a lethal chemical (!) in that it can rapidly corrode and destroy most materials!

- van der Waals envelope (or surface) is the approximate perimeter of a molecule as demarcated by the outer boundary of the surrounding cloud of electrons—the distance from the center of the molecule to the van der Waals envelope is called the “van der Waals radius”

- van der Waals radius (r) of water is 1.4Å—two water molecules cannot get closer to each other more than 2r—ie the distance from the center of one molecule to the center of the other!

Structure of Water: sp3 Orbitals

- Water is comprised of four sp3 hybridized (or mixed) orbitals—two of which are associated with H atoms, while the other two arise from the two non-bonding pairs of electrons

- The four sp3 orbitals of water adopt a tetrahedral geometry—ie each orbital occupies one of the four vertices (singular vertex) in a tetrahedral arrangement

Electronic Shell ConfigurationsH 1S1

O 1S2.2S22p4

1S

2S

2P

H OH

x y z

4 x SP3

hybridized orbitals

H2O

Tetrahedron

Triangular face (x4)

Vertex/Corner (x4)

Edge (x6)

Structure of Water: Hydrogen Bonding

+

-

+

+

-

-

-

+

- Electrons involved in mediating covalent bonds between a pair of atoms are not equally distributedbut rather become slightly polarized toward one or the other bonding partner (depending on their relative electronegativity), thereby resulting in the formation of diploes (or charge separation)

- Under such polarization in the context of a covalent bond between a pair of atoms, one atom carries a slightly negative charge (-) while the other a slightly positive charge (+)—interactions between such oppositely charged ends of dipoles are broadly termed “van der Waals” forces—an umbrella term!

- If such dipole-dipole interactions occur between an electropositive H atom bonded to another highly electronegative atom (such as O or N), the resulting van der Waals forces are called “hydrogen bonding”—ie hydrogen bonding (or H-bonding) is a special case of van der Waals forces due to its rather strong nature coupled with its ubiquity in biological systems

- Hydrogen bonding—represented by a dotted or dashed line—is the supreme attractive force that renders water a liquid at room temperature

- Changes in H-bonding pattern impart upon water the ability to exist in a liquid or crystalline (ice) form

- Because of charge separation or polarization of electronic clouds of H and O atoms, water is described as being a highly “polar” molecule—such polarity of water enables it to act both as H-bond donor as well as an H-bond acceptor in biochemical processes

- Ice is a crystal of an highly ordered network of hydrogen-bonded water molecules

- In ice, each water molecule interacts tetrahedrally with four other neighboring (or surrounding) water molecules

- In ice, H-bonds are highly stable (static)

- Because of a regular “open” ordered network of hydrogen bonding, water expands on freezing—ie ice (0.92 g/ml) has a lower density than liquid water (1.00 g/ml)

- What is the difference between 1, 1.0, and 1.00?!

1 => 0.5-1.41.0 => 0.95-1.041.00 => 0.995-1.004

----- H-bond

Oxygen atom

Hydrogen atom

Structure of Water: Ice crystals

Structure of Water: Liquid

- Liquid water consists of a rather “loose” network of hydrogen-bonded water molecules—iewater molecules rapidly fluctuate and tumble on a picosecond (ps) timescale (1ps = 10-12s)

- Unlike ice, liquid water thus harbors an highly disordered and irregular structure

- In liquid water, H-bonds are highly unstable (dynamic)

- Nevertheless, water molecules transiently engage in rings of three (3-mer), four (4-mer), or five (5-mer) molecules in liquid

- Because of their irregularity in liquid, water molecules can pack together much more tightly than in ice, thereby rendering water (1.00 g/ml) more dense than ice (0.92 g/ml)—cf highly-ordered rows of people (ice) versus a random crowd (water)

3-mer 4-mer 5-mer

Typical Bond Energies in Biomolecules

- Non-covalent forces underlying intermolecular interactions between biological molecules (or biomolecules) can be divided into TWO major categories:

(1) Ionic interactions —eg between oppositely charged ions such as Na+ and Cl-

(2) van der Waals forces —interactions due to dipoles

- Hydrogen bonding is a type of van der Waals interaction—albeit of a major significance

- The term “electrostatic interactions” is ambiguous and must be avoided at all costs

Van der Waals Forces: Dipole-Dipole Interactions

Van der Waals forces are dipole-dipole interactions that can be divided into three major categories:

(a) Dipole-dipole interactions—interactions between permanent dipoles such as a -C=O group (H-bonding is a special case of such dipolar interactions)

(b) Dipole-induced-dipole interactions—permanent dipoles in groups such as –C=O can also induce a dipole moment in a neighboring group (eg -CH3) by virtue of their ability to distort the distribution of its electronic cloud

(c) London dispersion forces—these arise from the fact that the electronic cloud of nonpolar groups such as –CH3 is not “static” but rather experiences rapidly fluctuating motions and, in so doing, generates a small transient dipole

polarpolar

polar nonpolar

nonpolar nonpolar

Hydration: Solvation of Ionic Substances

Cations are shielded by electronegative O atoms

Anions are shielded by electropositive H atoms

- Water is often described as a “universal solvent” due to the fact that its polar character renders it an excellent solvent for hydrophilic substances—eg those with polar or ionic character

- The ability of water to dissolve polar substances—such as NaCl—arises from the fact that its dipolar character enables it to weaken attractive forces between oppositely charged Na+ and Cl- ions

- Multiple water molecules can surround each ion and neutralize its charge in a phenomenon referred to as “hydration”—or solvation in generic terms

Hydroxyl Keto

Carboxylate Amino

Hydration: Solvation of Polar Substances

- Water is also an excellent solvent for polar substances for the same reason that it is for ionic substances

- The dipolar character of water enables it to engage in H-bonding with other polar groups such as hydroxyl (OH), carboxylate (O=CO-), keto (C=O) and amino (NH3+)

Hydrophobic Effect: An Entropic Phenomenon

- Apolar (or nonpolar) molecules such as oils and lipids aggregate when in contact with water—ie they tend to “stick” together rather than dissolve in water—why?!

- Such ability of apolar molecules to minimize contact with water or vice versa is termed the “hydrophobic effect”—what thermodynamic force drives the hydrophobic effect? Enthalpic (H) or entropic (TS)?

- H accompanying the transfer of apolar substances from water to an apolar solvent is unfavorable (H >= 0), while TS is consistently favorable (TS > 0)

- Thus, the hydrophobic effect is largely driven by an entropic force in that the ability of apolar substances to aggregate confers upon surrounding water molecules an entropic advantage—ie exclusion of water molecules enables them to move and tumble freely in lieu of being “locked” or “entrapped” in an ordered manner with apolar neighbors

Hydrophobic Effect: Orientation of Water Molecules

- Maintenance of intramolecular H-bonding network is critical to the random motion of water molecules

- Intrusion of apolar solute into water disrupts such extensive network due to its inability to engage in H-bonding interactions

- Accordingly, water molecules orient away from the surface of the apolarsolute to engage in H-bonding network with bulk water molecules—the surrounding water molecules that are not in direct contact with the solute

- Such orientation constitutes an ordering of the water structure (as their degree of freedom or the number of ways in which they can hydrogen bond becomes restricted)

- In order to minimize such ordering of water molecules, apolar molecules aggregate so as to minimize their surface area in contact with water and thereby maximize the overall entropy of the system

Individual hydration of apolar substances increases their surface

area in contact with water—thereby resulting in greater loss of entropy

Aggregation of apolar substances minimizes their surface area in contact with water—thereby

resulting in lesser loss of entropy

Hydrophobic Effect: Aggregation of Apolar Substances

Hydrophobic effect is central to many (bio)physicochemical phenomena:- Separation of oil and water- Membrane bilayer integrity- Folding of proteins in water and lipid bilayer

- Sketch a diagram of a water molecule and indicate the ends that bear partial positive and negative charges

- Compare the structures of ice and water with respect to the number and geometry of hydrogen bonds

- Describe the nature and relative strength of covalent bonds, ionic interactions, and van der Waals forces

- Explain why polar substances dissolve in water while nonpolar substances do not

- What is the role of entropy in the hydrophobic effect?

Exercise 1.1b

Section 1.1c:

Acid-Base Equilibria

- The acidity of a solution is expressed in terms of a pH value

- An acid is a compound that can donate a proton

- A base is a compound that can accept a proton

- Biological molecules that harbor ionizable groups are sensitive to changes in pH

- The relationship between the extent of ionization of a weak acid and the pH of a solution is embodied in the so-called “Henderson-Hasselbalch equation”

Synopsis 1.1c

- Water is a neutral molecule with a hightendency to ionize into correspondinghydrogen (H+) and hydroxide (OH-) ions:

HOH <=> H+ + OH-

- The hydrogen (H+) ion is more commonly referred toas a “proton”

- In essence, the proton (H+) largely existsas an hydronium ion (H3O+) in solution—ie theH+ is associated with another H2O molecule ratherthan roaming around as a free agent!

- The H+ of H3O+ ion is not static but highly dynamic in thatit can jump from one H2O molecule to another and soon virtually in an infinite (or endless) manner in aphenomenon referred to as “proton jumping”

- Owing to proton jumping, H+ and OH- ions exhibit much higher mobilities in bulk watercompared to other ions—accordingly, acid-base reactions (involving exchange of H+) rankamong the fastest processes occurring in water

- For simplicity, the H+ is often considered as one of the two dissociative products of ionization ofwater in lieu of the more complex H3O+ ion

Proton Jumping Occurs Rapidly

pH Values: Measure of the acidity of a solution- Consider the ionization of water:

HOH <=> H+ + OH-

- In pure water @ 25C, the concentration of H+ is close to 10-7M (100nM):

[H+] = [OH-] = 10-7M = 100nM

[H+] + [OH-] = 2x10-7M = 200nM

- A solution is described as:

Neutral => if [H+] = 10-7M => 1M = 1mol/L

Acidic => if [H+] > 10-7M

Alkaline/Basic => if [H+] < 10-7M

- The measure of acidity (or alkalinity/basicity) of an aqueous solution is defined by the concentration of

H+ ions expressed in terms of a quantity known as “pH”

- First introduced by Sorensen in 1909, the pH of a solution is defined as:

pH = -log[H+]

where [H+] must be in the units of molar (M)—ie moles per liter (or litre in Imperial English)

- Thus, the pH is the negative log (to base 10) of the concentration of H+ ions in solution

- The pH of pure water is:

pH = -log[10-7M] = 7

Soren Sorensen(1868-1939)

pH Values: Relationship of pH, [H+], and [OH-]

pH Values: pH of Common Substances

pKa Values: Measure of the strength of an acid

- Consider the dissociation of an acid HA into its constituent components in hydrogen ion

(H+) and the conjugate base (A-):

HA <=> H+ + A-

- The equilibrium dissociation constant of the acid (Ka) is defined as:

Ka = [H+][A-]/[HA] [1]

- The strength an acid in aqueous solution is expressed in terms of a quantity called the

“pKa“, which is analogous to pH!

- pKa is defined as the negative log (to the base 10) of Ka:

pKa = -logKa [2]

where Ka must be in the units of molar (M)

- The relationship between the pH of a solution and pKa of an acid can be derived as follows:

(1) Rearrange Eq [1] for [H+]: [H+] = Ka[HA]/[A-]

(2) Take negative logarithm of each term: -log[H+] = -logKa - log{[HA]/[A-]}

(3) Substitute the quantities and rearrange: pH = pKa + log{[A-]/[HA]} [3]

- Eq[3] has come to be known as the “Henderson-Hasselbalch equation”

pKa Values: Ka and pKa of Common Acids @ 25C

Ka pKa

pKa Values: Henderson-Hasselbalch Equation

pH = pKa + log{[A-]/[HA]}

- When [HA] = [A-], log{[A-]/[HA]} = 0 => pH = pKa

- In other words, the pH of a solution is equivalent to pKa of an acid @

50% dissociation

- Note that the Henderson-Hasselbalch equation does not take into

account the ionization of water

- Thus, it is only useful for rationalizing the ionization of weak

acids/bases such as buffers and amino acid sidechain groups in proteins

- A buffer with a pKa value of 8 would be most effective @ pH 8! Why?

What is a buffer?!

- Since buffers resist changes in pH, they are most effective when the

concentration of its hydrogen ion (H+) and conjugate base (A-) are

equal—and when they are so, pH = pKa

Lawrence Henderson(1878-1942)

Karl Hasselbalch(1874-1962)

pKa Values: Titration Curves of Weak Acids

- A buffer is a mixture of a weak acid (HA) and its conjugate base (A-):

HA <=> H+ + A-

- Thus, a buffer helps to maintain constant pH. How?

- Addition of small amounts of OH- or H+ are quickly mopped up with little changes in solution pH:

OH- + HA <=> HOH + A-

H+ + A- <=> HA

- A buffer ONLY resists small changes in pH in the region close to its pKa value:

pH = pKa 1

Consider acetate buffer (pKa ~ 5):(1) When pH < 4, acetate largely exists as HA

(undissociated acid form) => thus no good as a buffer!

(2) When pH > 6, acetate largely exists as A-

(dissociated base form) => again no good as a buffer!

pK1

pK3

pK2

pKa Values: Titration of a Polyprotic Acid

- Acids such as phosphoric acid (H3PO4) are called “polyprotic acids” due to the fact that they can lose more than one proton upon successive ionizations

- Thus, a polyprotic acid has multiple pKa values—eg H3PO4 has three pKa values:pK1 = 2.2 pK2 = 6.8 pK3 = 12.2

- Thus, phosphate buffer can be used to resist small changes in pH around pH 2.2, 6.8 and 12.2

- What are the products of ionization of water? How are their concentrations related?

- Describe how to calculate pH from the concentration of H+ or OH-

- Define acid and base

- What is the relationship between the strength of an acid and its pKa value?

- What must a buffer solution include in order to resist changes in pH on addition of acid or base?

- Why is it important to maintain biological molecules in a buffered solution?

Exercise 1.1c

Debunking Alkaline Diet—an Alternative Fact

Rather Than Alternative Medicine!

- Alkaline diet postulates that the consumption of certain fruits and vegetables helps to alkalinize the body fluids to a pH of around 7.4—a pH that cellular homeostasis achieves regardless of alkaline diet!

- Thus, alkaline diet is believed to offset acidosis resulting from a typical Western diet, thereby keeping diseases such as cancer at bay—indeed, many cancers cells thrive under acidic conditions!

- But, the enigma is that the proponents of alkaline diet cannot explain how it helps to alkalinize the body fluids—do all foods not go through the stomach?!

- If so, then all foods are churned in the stomach @ a pH of around 2! Does it really matter what the acidity/alkalinity of the intake food is? It represents a small drop in a big ocean—does it not?

- What about thousands who swear to have benefited from having been on the super-scampensive alkaline diet?—nothing but a coincidence and a placebo effect—correlation does not imply causation!