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 BondNumber*

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:

• Energy drops off as function of distance between charges (i.e. operates over long ranges)

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.

r

qqk F U 21

r

r

rF

dr221

r

qqk F

Dielectric

Some enchanted evening, you may see a stranger; you may see a stranger across a …

WEAK Dielectric

STRONG Dielectric

Common Dielectric Constants

Name dielectric constantwater 80

methanol 33ethanol 24.3

1-propanol 20.11-butanol 17.8

formic acid 58

acetic acid 6.15

acetone 20.7

hexane 2.02

benzene 2.28

Dipoles• Fixed dipoles

– Molecules with asymmetric charge distributions form dipoles

• Induced Dipoles– One dipole can induce a charge in an adjacent molecule

NH3+

CH2 C O-

O

NH3+

CH2 C O-

O

Dipole moments

= q·x– Where 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 GeckosClimb buildingCrawl through windowFind targetDetonate

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 RadiiThe Lennard-Jones potential describes the interaction

between a pair of neutral atoms:

612 r

1

r

1 α U

-3

-2

-1

0

1

2

3

4

5

0.5 1 1.5 2

Radius (Å)

Ener

gy (a

rbitra

ry u

nits)

London Dispersion ForceElectron Cloud Repulsion

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)

-helix: An internal protein structure mediated by Hydrogen Bonds

(amide hydrogens to carbonyl oxygens)

Binding from both H-Bonds and vdW Contacts

EcoR1 – a DNA-cleaving Protein

DNA Double Helix

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 - S < 0)

Clathrate cage of ordered water

Hydrophobic interactionsSolvating 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 non-polar 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

A mutant version of myc, which causes the protein to be permanently expressed, is found in many cancers.

Two myc proteins come together – bound by a leucine zipper – to form an active DNA-binding dimer..

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

HpH

purposesourFor

log

:

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

• Just like water, a weak acid has an ion product, the Ka• For the weak acid HA:

• Therefore

[HA]

]][A[H Ka

-

O]HA][H[

]A][[H Keq

2

-

-OH HKw

• We defined an ion product for water:

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 10-5 4.74

Formic 1.7 x 10-4 3.77

Benzoic 6.5 x 10-5 4.19

Carbonic 4.3 x 10-7 6.37

Imidazole 2.8 x 10-7 6.55

Phenol 1.3 x 10-10 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?

])[H- (0.1M

][H

CCOOH][H

]CCOO][H[H101.8

2

3

35

0](0.1)[K][HK][H aa2

2

4(0.1)KKK][H a

2aa

[H+] = 0.00134 M 2a

4acbbx

:Formula Quadratic

2

Shortcut

• The quadratic solution is a pain, but we can approximate:

• Accurate as long as acid < 5% dissociated

(0.1)K[HAc]K][H aa

[H+] = 0.00134 M

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

Titration of Strong Acid

0

2

4

6

8

10

12

14

0 5 10 15 20

NaOH added (ml)

pH

1

2212211 V

CV Cor CVCV

M 0.425L 0.010

M 0.5 L 0.0085C1

Titrating a Weak Acid• 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.

Titration of Weak Acid

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25

NaOH added (ml)

pH

Henderson-Hasselbach Equation

[HA]

][AlogpKpH

log[HA]]log[ApKpH

pKlog[HA]]log[A]log[H

pK[HA]

]][A[Hlog

K[HA]

]][A[H

a

a

a

a

a

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.

[HA]

][AlogpKpH a

0.1

0.3log4.76pH

5.24pH

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:

 

where Ci is the concentration of ion I,

Zi is the charge on ion I

i

iiZCJ 2

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, pKa = 8.30At 0o C 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+ + HCO3- pKa = 6.1

• Phosphate H2PO4- ⇄ H+ + HPO4

-2 pKa = 7.2

• Plasma Proteins

• Hemoglobin

The primary system, carbonate, has 3 interlocking equilibria:

CO2(g) ⇄ CO2(aq) + H2O ⇄ H2CO3 ⇄ H+ + HCO3-

Excess 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: 122.12 g/mol

– pKa 4.21

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?

OH O

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]

[benzoate]6.17 =

[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.