CH339K
Lecture 2 and 3
Bonding
•
•
•
•
•
Covalent
Ionic
Dipole Interactions
Van der Waals Forces
Hydrogen Bonds
Covalent Bonds
• Electrons form new orbitals around multiple
atomic nuclei
• Bond energy results from electrostatic force
between redefined electron cloud and nuclei
• Strong – typically 150 – 450 kJ/mol
Common Covalent Bond Numbers For
Biochemically Significant Elements
Atom
Bond
Number*
C
4
H
1
O
2
N
3
P
3,5
S
2
*the bond numbers illustrated are typical of biological systems and should not
be considered set in stone. i.e. Don’t depend on this for your Inorganic class!
Ionic Interactions
• Energy from non-directional electrostatic force between ions
• Biomolecules frequently have large numbers of charged groups
• Charge-charge interactions stabilize intra- and intermolecular
structures
• Coulomb’s Law:
q1q 2
Fk
2
er
r
q1q 2
U   Fr dr  k
er
Fr 
• Energy drops off as function of distance between charges (i.e.
operates over long ranges)
 e is the dielectric constant of the medium
• k is the Permittivity of the Vacuum – sort of an absolute
dielectric constant to which other dielectric constants relate.
Dielectric
Some enchanted evening, you may see
a stranger; you may see a stranger
across a …
WEAK Dielectric
STRONG Dielectric
Common Dielectric Constants
Name
water
methanol
ethanol
1-propanol
1-butanol
formic acid
acetic acid
acetone
hexane
benzene
dielectric constant
80
33
24.3
20.1
17.8
58
6.15
20.7
2.02
2.28
Dipoles
• Fixed dipoles
– Molecules with asymmetric charge distributions form
dipoles
O
+
-
H3N CH2 C O
• Induced Dipoles
– One dipole can induce a charge in an adjacent molecule
O
+
H3N CH 2


C O

-

Dipole moments
m = q·x
– Where m is the dipole moment
– q is the charge
– x is the distance between the charges
The larger the dipole moment, the more polar
the molecule.
van der Waals Interactions
• Technically, all induced dipole interactions are van
der Waals interactions
• Biochemists usually mean induced dipole-induced
dipole (London Dispersion) forces
• Any atom will have an uneven distribution of charge
at any given instant
Van der Waals (cont.)
• That temporary dipole will induce a dipole in
adjacent atoms
• This results in a net attractive force between
atoms
• Force is weak - .5 to 2 kJ/mol
• Net biochemical effect – molecules that FIT
together STICK together.
Van der Waals (cont.)
• If you live in Central Texas, you see van der
Waals forces in action every summer night:
Artificial Geckos
Climb building
Crawl through window
Find target
Detonate
Real gecko toe
hair (Courtesy of
Geico)
Synthetic gecko
toe hair
Charge Interaction Energies and Distance
Van der Waals Forces (cont.)
London Dispersion Forces cause
particles to come together…
Until they get too close.
Atomic Radii
The Lennard-Jones potential describes the interaction
between a pair of neutral atoms:
5
1 1
U α 12  6
r
r
Energy (arbitrary units)
4
3
2
1
0
0.5
1
1.5
-1
-2
-3
Electron Cloud Repulsion
London Dispersion Force
Radius (Å)
2
Multiple molecular contacts can mediate binding
hexokinase
Energy of van der Waals contacts can
subsidize conformational changes in
molecules.
Hydrogen Bonds
• Hydrogen Bonds form between
– A hydrogen covalently bound to an electronegative
atom
– Another electronegative atom
Hydrogen Bonds (cont.)
• The group to which the hydrogen is covalently
bound is the donor.
• The other group is the acceptor.
• Donors:
– -OH, -NH2, -SH (lesser donor)
• Acceptors
– -N:, =O:, -O:
H
Common H-Bonds
found in proteins
Hydrogen Bonds (cont.)
• Intermediate strength: 5 – 30 kJ/mol
• Hydrogen bonds are not just electrostatic –
partially covalent
• Therefore, they are directional
Hydrogen Bonds (cont.)
• Bond length is less than vdW contact
distances
• distance between the nuclei of the hydrogen
bond acceptor and the hydrogen itself can be
as short as 1.8-1.9 Å, well below the sum of
the atomic radii (e.g. 1.2Å for hydrogen and
~1.5Å for oxygen and nitrogen)
a-helix: An internal
protein structure
mediated by
Hydrogen Bonds
(amide hydrogens to
carbonyl oxygens)
Binding from both H-Bonds and vdW
Contacts
DNA Double Helix
EcoR1 – a DNA-cleaving Protein
Recap of Bond Energies (typical)
STRENGTH (kcal/mole)
BOND TYPE
LENGTH (nm)
IN VACUUM
IN WATER
Covalent
0.15
90
90
Noncovalent: ionic
0.25
80
3
hydrogen
0.30
4
1
van der Waals attraction (per atom)
0.35
0.1
0.1
Copyright © 2002 Bruce Alberts, Dennis Bray, Julian Lewis, Martin Raff, Keith Roberts, and
James D. Watson
Recap – bonding in biomolecules
Aka Salt Links
Water Structure
Water Forms Clusters in Solution
Dissolving nonpolar molecules
• Solvating a nonpolar molecule imposes order
on the surrounding water - (DS < 0)
Clathrate cage of ordered
water
Hydrophobic interactions
Solvating a non-polar
material in water
decreases entropy –
forces water into an
ordered structure
Minimal energy is
when water is least
ordered – the more
you can pack nonpolar materials, the
less surface area
exposed to solvent.
Hydrophobic Effect
Interaction among
leucine side chains
in insulin
Interaction among
phenylalanine and
tyrosine side chains
in prion protein
Myc protein is a transcription factor for expression
of a large number of human genes
Two myc proteins come
together – bound by a
leucine zipper – to form an
active DNA-binding dimer..
A mutant version of myc,
which causes the protein to
be permanently expressed, is
found in many cancers.
Water
•
Water
–
–
–
–
–
–
–
Has a high specific heat
Has a high heat of vaporization
Is an excellent solvent for polar materials
Is a powerful dielectric
Readily forms hydrogen bonds
Has a strong surface tension
Is less dense when it freezes (i.e. ice floats)
Acids and Bases
• Definitions
– Arrhenius
• Acids are substances which produce an excess
of H+ ions in water (HCl)
• Bases are substances which produce an
excess of OH- in water (NaOH)
– Bronsted-Lowry
• Acids are substances which can donate a
proton in a chemical reaction. (HF)
• Bases are substances which can accept a
proton in a chemical reaction (NH3)
– Lewis
• Acids are electron - pair acceptors.(BF3)
• Bases are electron - pair donors (CaO)
Conjugate Pairs
• Every acid has its conjugate base
• Every base has its conjugate acid
Conjugate Acid
Conjugate Base
H3C - COOH
H3C-COO-
NH4+
NH3
Acids and bases: pH
For our purposes :
 
pH   log H

Typical pH Values
Substance
pH
Stomach acid
1.5 - 2.5
Coca-cola
2.5
Human saliva
6.5
Human blood
7.5
Human urine
5-8
Oven cleaner
14
Acids and Bases
• Water thus acts as both a weak acid and a
weak base
• (A Strong acid is one that dissociates
completely in water; a weak acid is one that
doesn’t.)
– Hydrochloric, Hydroiodic, Hydrobromic, Nitric, Sulfuric, Perchloric
• All biochemically significant acids and bases
are weak (except for HCl – stomach acid)
Acids and Bases
• We defined an ion product for water:
Kw  H OH 

-
• Just like water, a weak acid has an ion product, the Ka
• For the weak acid HA:

-
[H ][ A ]
Keq 
[ HA][H 2O]
• Therefore

-
[H ][A ]
Ka 
[HA]
Acids and Bases
•
•
•
Ka’s for weak acids range over several
orders of magnitude
They are generally small
More convenient to define
pKa = -log Ka
•
Just like pH = -log[H+]
Typcal Ka’s and pKa’s
Acid
Ka
pKa
Acetic
1.8 x 10
Formic
1.7 x 10
Benzoic
6.5 x 10
Carbonic
4.3 x 10
Imidazole
2.8 x 10
Phenol
1.3 x 10
-5
-4
-5
-7
-7
-10
4.74
3.77
4.19
6.37
6.55
9.89
pH for Strong Acids
• Since a strong acid dissociates completely:
pH = -log([Acid])
• For a 0.1 M (100 mM) solution of HCl:
pH = -log(0.1) = 1
• Well, that was difficult…
pH for Weak Acids
• Depends on the Ka
• What’s the pH of a 100 mM solution of Acetic
Acid?
1.8  10 5
[H  ][H 3CCOO ]
[H  ]2


[H 3CCOOH]
(0.1M - [H  ])
[H  ]2  K a [H  ]  (0.1)[K a ]  0
 K a  K a  4(0.1)K a
2
[H  ] 
2
[H+] = 0.00134 M
Quadratic Formula :
 b  b 2  4ac
x
2a
Shortcut
• The quadratic solution is a pain, but we can
approximate:
[H  ]  K a  [HAc]  K a (0.1)
[H+] = 0.00134 M
• Accurate as long as acid < 5% dissociated
Titrating a Strong Acid
10 ml of an HCl sln.
Titrate with 0.5 M NaOH
OH- + H+ → H2O
Takes 8.5 ml NaOH to
bring solution to neutrality
14
12
10
8
pH
•
•
•
•
Titration of Strong Acid
6
4
V1C1  V2 C 2 or C1 
C1 
V2 C 2
V1
0.0085 L  0.5 M
 0.425 M
0.010 L
2
0
0
5
10
NaOH added (m l)
15
20
Titrating a Weak Acid
Titration of Weak Acid
8
7
6
5
pH
• Titrating .1 M HAc
• Initial pH is 2.88 instead
of 1
• Little change until large
amounts of NaOH have
been added
• Buffering effect
• Caused by equilibrium
that exists between a
weak acid and conjugate
base.
4
3
2
1
0
0
5
10
15
NaOH added (m l)
20
25
Henderson-Hasselbach Equation

[H  ][A ]
 Ka
[HA]


[H ][A ]
 log
 pK a
[HA]


 log[H ]  log[A ]  log[HA]  pK a
pH  pK a  log[A  ]  log[HA]
[A  ]
pH  pK a  log
[HA]
Predicting pH
• Let’s make 1 liter of a solution that is 0.1 M in
acetic acid ( pKa = 4.74 ) and 0.3 M in
sodium acetate.
[A  ]
pH  pK a  log
[HA]
0.3
pH  4.76  log
0.1
pH  5.24
Buffering Effect
• Addition of significant amounts of acid or
base changes the ratio of conjugate base to
conjugate acid
• pH changes as the log of that ratio
• Result is resistance to pH change in a
buffered solution
Factors impacting pKa: Ionic Strength
The ionic strength of a system is the sum of
contributions from all ions present:
J   Ci Z
2
i
i
where
Ci is the concentration of ion I,
Zi is the charge on ion I
Factors impacting pKa: Ionic Strength
Example: Phosphoric Acid has 3 pKa’s
H3PO4 ⇄ H+ + H2PO4- ⇄ 2H+ + HPO4-2 ⇄ 3H+ + PO4-3
pKa1
pKa2
pKa3
pKa2 = 7.2 at ionic strength J = 0
pKa2 = 6.86 at physiological ionic strengths
(Physiological saline is 0.91% NaCl. Calculation of J
is left as an exercise for the student)
Factors impacting pKa: Temperature
pKa can (i.e. does) vary with temperature
Example: one of the most common biochemical
buffers is Tris (tris(hydroxymethyl)aminomethane)
Tris is a good buffer at near- physiological
pHs, is biologically pretty inert, and is
(relatively) inexpensive.
BUT Tris has a large thermal coefficient: 0.031 units/oC
At 25o C,
At 0o C
pKa = 8.30
pKa = 7.77
A Physiological Example: Blood pH
• Blood pH is maintained at ~7.4
– pH below 7.35 is acidosis
– pH above 7.45 is alkalosis
• pH < 7.0 or > 7.8 is generally fatal
Blood pH Control
Blood pH is regulated by four buffer systems:
•
•
•
•
Carbonate
H2CO3 ⇄ H+ + HCO3Phosphate
H2PO4- ⇄ H+ + HPO4-2
Plasma Proteins
Hemoglobin
pKa = 6.1
pKa = 7.2
The primary system, carbonate, has 3 interlocking
equilibria:
CO2(g) ⇄ CO2(aq) + H2O ⇄ H2CO3 ⇄ H+ + HCO3Excess H+ or HCO3- drives the equilibrium to the left
Excess H2CO3 drives the equilibrium to the right
Blood pH Control
• Diseases that effect the level of [HCO3-] are
metabolic effects, due to changes in cellular
metabolism.
• Diseases that change [H2CO3] are
respiratory effects; the lungs control the
exchange of CO2, and therefore the
concentration of H2CO3 .
Blood pH Control
Metabolic Acidosis:
• Diseases such as diabetes or diarrhea result
in an excess of H+ in the tissues.
• [HCO3-] goes DOWN (equilibrium pushed to
left)
• Blood pH goes DOWN. (equilibrium to left;
higher carbonic acid, lower bicarbonate)
Blood pH Control
Metabolic Alkalosis:
• Vomiting (intoxication, gastrointestinal
illnesses) causes loss of H+.
• [HCO3-] goes UP (equilibrium pulled to right)
• Blood pH goes UP. (equilibrium to right;
lowerer carbonic acid, higher bicarbonate)
Blood pH Control
Respiratory Acidosis:
• In conditions like emphysema, pneumonia,
your lungs do not work effectively to clear
CO2.
• [H2CO3] goes UP (driven by carbon dioxide
build-up.)
• Blood pH goes DOWN (as carbonic acid
accumulates.)
Blood pH Control
Respiratory Alkalosis:
• When you hyperventilate or become
hysterical, you blow off lots of CO2.
• [H2CO3] goes DOWN (since its being
withdrawn as CO2.)
• Blood pH goes UP (less carbonic acid.)
A Practical Buffer Problem
Benzoic acid is a weak carboxylic acid that is
reasonably soluble in water (3.4 g/l).
– Molecular Weight:
– pKa
122.12 g/mol
4.21
HO
O
I wish to make 4 liters of 10 mM
Sodium Benzoate buffer, pH 5.0.
I have solid benzoic acid in a jar, a stock solution of 5 M
Sodium Hydroxide (NaOH), a 4 liter graduated cylinder
and all the deionized, distilled water I can use.
How do I make the buffer?
Practical Buffer Problem (cont.)
• Step 1: Okay, how much benzoic acid do I
need? Since benzoate will be the buffering
ion, I want my solution to be 10 mM in total
benzoate. Solid benzoic acid is my only
source of benzoate, so I need to add 10 mM
worth:
10mM = 0.01 mol/l
0.01mol/l × 4 l × 122.12 g/mol = 4.88 g
Practical Buffer Problem (cont.)
Step 2: How do I get it to the right pH?
• The conjugate base of benzoic acid is
benzoate anion.
• Addition of a strong base (like NaOH) to
benzoic acid converts it to benzoate.
• The pH of the solution depends on the ratio of
conjugate base to conjugate acid as
determined by the Henderson-Hasselbach
equation.
• How much benzoic acid to I have to convert
to benzoate base to give me the desired ratio
of conjugate base to conjugate acid
Practical Buffer Problem (cont.)
• Step 1: Okay, how much benzoic acid do I
need? Since benzoate will be the buffering
ion, I want my solution to be 10 mM in total
benzoate. Solid benzoic acid is my only
source of benzoate, so I need to add 10 mM
worth:
10mM = 0.01 mol/l
0.01mol/l × 4 l × 122.12 g/mol = 4.88 g
Practical Buffer Problem (cont.)
 [conjugate base] 
pH = pKa + log 

 [conjugate acid] 
 [benzoate] 
5.0 = 4.21 + log 

 [benzoic acid] 
 [benzoate] 
0.79 = log 

 [benzoic acid] 
6.17 =
[benzoate]
[benzoic acid]
6.17  [benzoic acid] = [benzoate]
Rats! 1 equation with 2 unknowns…
But wait! That’s not all!
We also know that total benzoate is 10 mM
[benzoate] + [benzoic acid] = 10 mM
6.17  [benzoic acid] + [benzoic acid] = 10 mM
7.17 [benzoic acid] = 10 mM
[benzoic acid] = 1.39 mM
[benzoate] = 10 mM - 1.39 mM = 8.61 mM
We need to convert 8.61 mM benzoic acid to the
conjugate base, benzoate.
To convert 8.61 mM benzoic acid to 8.61 mM benzoate,
we need to add 8.61 mM (.00861 M) NaOH
0.00861 mol/l desired
 4 l total volume = 0.00689 l
5 mol/l stock
So: add 4.88 g of Benzoic Acid, 6.89 ml of 5M
NaOH, and enough H2O to make 4 liters.