Download Interatomic forces Covalent bonds Ionic bonds

Interatomic forces
Protein physics, Lecture 6
What are the forces that hold protein atoms together, and hold the protein
in a particular configuration?
Covalent bonds
• Hold individual atoms in amino acids together
• Hold amino acids residues together in protein chain
• Caused by sharing of electrons between atoms
• Very strong interaction – takes a lot of energy to break apart
• The propensity for an atom to gain or lose electrons measured by the
atoms electronegativity
Ionic bonds
• Arises when two atoms have very
different electronegativity
• One atom ‘steals’ an electron from
another atom and they both end up
having a net charge
• They will then stay close to one
another due to electrostatic
interactions
• Less important in biological
situations as ions are readily
dissolved in water
Van der Waals interactions
What happens when 2 neutral atoms are brought together?
Do they feel an attractive force, repulsive force, or nothing?
Van der Waals interactions
Van der Waals interactions
There is an attractive interaction between any two atoms
– even apolar ones (van der Waals 1873)
Interaction arises because of induced dipole moment on each atom
+
+
-
-
r
Each atom helps to polarise the other
Atoms behave as linear harmonic oscillators, the –ve electron clouds
oscillating about the +ve nucleus
By considering the atoms as coupled harmonic quantum oscillators,
London showed that the energy of the two atom system is given by:
U (r ) = −
A
r6
where A is a constant
Van der Waals interactions
Lennard-Jones (6-12) potential
Repulsive interaction
As two atoms approach each other their charge distributions (electron
clouds) start to overlap, thus changing the electrostatic energy of the
system.
The total potential energy for two neutral atoms at separation r can be
written as
B A
U (r ) =
r 12
−
r6
⎡⎛ σ ⎞12 ⎛ σ ⎞ 6 ⎤
= 4ε ⎢⎜ ⎟ − ⎜ ⎟ ⎥
⎝ r ⎠ ⎥⎦
⎣⎢⎝ r ⎠
⎡ ⎛ r ⎞12 ⎛ r ⎞ 6 ⎤
= E0 ⎢− ⎜ 0 ⎟ + 2⎜ 0 ⎟ ⎥
⎝ r ⎠ ⎦⎥
⎣⎢ ⎝ r ⎠
At small enough separations the interaction is repulsive, mainly
because of the Pauli exclusion principle
To occupy the same space, one of the electrons must occupy a higher
energy orbital, thus raising the energy of the system
r0
Experimental data from inert gases show that the repulsion interaction
energy has the form
U (r ) = +
B
r 12
Lennard-Jones (6-12) potential
B is a +ve constant
E0
Van der Waals radius of atoms
4εσ 6 ≡ A
4εσ 12 ≡ B
E0 = −
B2
= −ε
4A
1/ 6
⎛ 2A ⎞
r0 = ⎜
⎟
⎝ B ⎠
How important are induced dipole interactions?
The boiling points of the noble gases are
Helium -269 oC
Neon
-246 oC
Argon -186 oC
Krypton -152 oC
Xenon -108 oC
Radon -62 oC
Lower on list
Electrostatic interactions
Unless two atoms that are covalently bonded share there electrons
equally (ie if they don’t have the same electronegativity) then the
electron ends up spending more time near one nucleus than another
Asymmetric charge distribution
Partial charges on atoms
More electrons
Larger radius
Greater possible movement of electrons
Larger induced dipoles
Polar groups are just those that contain atoms bonded together of
very different electronegativity, and thus have atoms with large
partial charges
Bigger dispersion force
Greater temperature required to break atoms apart
Higher boiling point
Partial charges of amino acid backbone and some sidechains
Electrostatic interactions
The electrostatic interaction between to charged atoms is defined by Coulomb’s
law that includes that charge on the two atoms (q) and the dielectric constant of
the medium (ε).
U (r ) =
q1q2
4πε 0ε r
Coulomb’s law
Dielectric constant is difficult to define for microscopic systems
Discussed values range from 1 < ε < 10
(Water has ε ~ 80)
Examples:
1. “Salt bridge” between Lys and Asp assuming ε = 4
-COO- …… H3N+
U(r0) = -5 kcal / mol
1 kcal/mol = 6.95x10-21J
Attractive interaction
How do you define the partial charge?
What is the charge of an atom in a molecule?
2. Two carbonyl groups at contact distance
C+ = O- …... O- = C+
U(r0) = +0.3 kcal / mol
repulsive interaction
Electrostatic interactions
In principle electrostatic forces are long range (1/r2)
Hydrogen bonds
Generally the contact distance between two non-covalently bonded atoms is
the sum of their Van-der Waals radii
However, in a protein there are few monopoles, most charges pair up
to form dipoles or multipoles
This rule is grossly violated by a number of contacts involving hydrogen
Interaction between dipoles is shorter range (1/r3)
When a hydrogen atom is bonded to a strongly electronegative atom, it
becomes almost a bare proton H+
Calculation of electrostatic interactions can be somewhat simplified by
ignoring the interactions between atoms that are a long way apart
Thus electron shell Pauli repulsion is minimal
The bare proton can act as a bond between electronegative atoms
H+ ……. O- = C+
O-
Hydrogen bond energies
intermediate between energies
of van der Waals and covalent
bonds
H+
O-
O-
~3 kcal / mol
Hydrogen bonds
N-
H+
……. O- = C+
This hydrogen bond is particularly
important in stabilising α - helices
1 kcal/mol = 6.95x10-21J
Thermal energy (body temp)
1.5kT ~ 0.6 kcal/mol
Another important H-bond