1. Introduction-2 Important molecular interactions in Biomolecules
Homework 2 (due Fr, Feb. 1):
Van Holde 3.1 (Coulomb potential)
Van Holde 3.2 (Dipole-diople interaction)
Van Holde 3.3 (Lennard-Jones potential)
Van Holde 3.4 (force is gradient of potential)
Van Holde 3.6 (Manning theory of counterion condensation)
Van Holde 3.9 (Hydrogen-bond potential)
Reading:
Van Holde, Chapter 1
Van Holde Chapter 3.1 to 3.3
Van Holde Chapter 2
(we’ll go through Chapters 1 and 3 first.
Paper list (for presentations) is posted on web site

2. Introduction-2 Important molecular interactions in Biomolecules

3. The notion of potential energy
The force, with which molecules attract or repel each other is:
Force is negative of (gradient) slope of potential well
Molecules get “pushed” to the lowest point of potential
Molecules sit in minimum of potential function V
(We are ignoring entropy for the time being ( Gibbs free energy) x
Molecular potentials:

4. Bonding potential (covalent bonds)
( kJ/mole)
The bond potentials are often approximated by harmonic potentials (good for small deflection):
Vbonding is big, but DVbonding between conformations is not so big  Vnonbonding is what counts most for folding

5. Charge-charge interaction
(~ 60 kJ/mole, long-range)
A lot of biological molecules are charged. Amino acids: Asp-, Glu-, Lys+ Arg+, His+; DNA: phosphates- in backbone, salt ions, etc.
Like charges repel, opposite charges attract.
Z1,2… amount of charge
e … charge of electron e = 1.6*10-19C
r … separation of charges
D … Dielectric constant; D =kere0
e0 … permittivity constant e0 = 8.85*10-12 C2/Nm2
…4p in SI units
er… relative permittivity (depends on material)
The tricky part 1: D not constant)
Dwater = 78.5·ke0 (easy).
D inside a protein varies (1·ke0 to 20· ke0, average ~3.5 ke0) and depends on the local environment
Various approx. to deal with this
Tricky part 2: (counterion screening)
Really also related to D not being constant)
Counterions (salt) condense/surround fixed charges on protein/DNA

6. Counterion shielding (screening)
Solution ions form a “cloud’ around the fixed charges on protein surfaces or DNA.  The electric potential of these fixed charges is weakened (damped). This damping is called Screening.
N fixed charges in vacuum have the following potential:
The ions in solution are then forming a “cloud” around those charges, which effectively screens the fixed charges from each other:
Debye-Hückel screening parameter k:
(“decay length of charge strength)
D … dielectric constant
kB … Boltzmann constant
T … absolute temperature
I … ionic strength;
e … electron charge
NA … Avogadro’s number
c … ion concentration
Z… valency

7. Counterion condensation
Charges also condense (bind longer) onto fixed protein/DNA charges, and partly neutralize them.
For condensation of counterions onto DNA: If a charge is actually “condensed”, depends on the parameter x
b … distance between charges.
For DNA: b = h/Z = 0.34/2 = 0.17
For x > 1, condensation occurs.
For an electrolyte in water, x = 0.71/b, with b in nm. At 25°C, x = 4.2 for B DNA.  So, counterions do condense on DNA.
How large is the net charge of the phosphates then?
Amount of charge neutralized:
Thus, for B-DNA, 76% is compensated in aqueous Na+ environment and 24% is not compensated.

8. Dipole-dipole Interactions
(~ -2 to 2 kJ/mole, shorter range, can act in series) + -
Dipole moment (note: vectors)
General dipole-dipole interaction:
If m1 and m2 are side by side:
If m1 and m2 are parallel:

9. Induced dipole-induced dipole interactions (van der Waals interactions)
(~ kJ/mole, very short range)
I … ionization energy of atoms
a1, a2 polarizabilities of atoms
Attractive London Dispersion potential:
Repulsive potential from electron cloud:
Strong force when r is small, m = 5 to 12
Combining them we get the van der Waals potential:
And for m = 12 the Lennard-Jones potential:
A, B are constants that depend on the type of interacting atoms in table 3.4

10. Hydrogen-bonds m1 m2 Important for protein/DNA stability
(0-48 kJ/mole, very short range, directional  provide specificity)
Important for protein/DNA stability
Easy make-easy break, directional  requires very accurate alignment. m1
H-bonds – it is still debated how to treat H-bond potential.
Treat like dipole-dipole interaction (4-48 kJ/mole). Best alignment (diagram) gives: m2
D-H ………….A
However, some aspects of H-bond are similar to covalent bonds – e.g. the optimal distance between donor and acceptor is very short (see next page)! So, model that by a van der Waals potential:
C, D depend on the particular donor and acceptor
This potential is added to the dipole-dipole interaction and only contributes ~ 2 KJ/mole of energy.
In real life, we need to consider H-bonding to water too!! So unless solvent is accounted for, H-bonding affect is overestimated.
Hydrogen bond are important in the inside of proteins and DNA (obviously).

11. Watson-Crick base-pairing
H-bond examples
Watson-Crick base-pairing

12. Non-Watson-Crick base-pairing
a-helix
(© by Irvine Geis)
Biochemistry Voet & Voet
Watson-Crick base-pairing
Non-Watson-Crick base-pairing
Red – oxygen
Black – carbon
Blue – nitrogen
Purple – R-group
White – Ca
Hydrogen-bonds between C-O of nth and N-H group of n+4th residue.