Chapter 22, Macromolecules and aggregates Ideality and reality Simplicity of small systems and complexity of real systems Entropy and order Dealing with large systems

Proteins

DNA

Amyloids and Cellucoses

Liposome

Artificially Synthetic macromolecules

Common synthetic polymers

Contents Structure and dynamics 22.1 different levels of structure 22.2 Random coils 22.3 The structure of proteins 22.4 The structure of nucleic acids 22.5 The stability of biological polymers Determination of shape and size 22.6 Mean molar mass 22.7 Mass spectroscopy 22.8 Laser light scattering 22.9 Ultracentrifugation Electrophoresis Size exclusion chromatography Viscosity Self-assembly Colloids Micelles and biological membranes Surface films

Assignment for chapter (b) 22.5(a)

Structure and dynamics Configuration Structural features elated to a given arrangement of chemical bonds Spatial arrangement of the different parts of a chain. Conformation It can be changed only by breaking Chemical bonds and forming new ones. It can be changed into another by Rotating one part of a chain around a bond.

Different levels of structure Primary structure (sequence) Secondary structure (helix, sheet etc.) Tertiary structure (overall 3D structure) Quaternary structure (formed by different 3D structures)

Random coils All bond angles are arbitrary. Free rotation.

Random coils (a more realistic model) Bond angle is fixed. Free rotation. Freely jointed chain model

Measure of size Contour length: l

Measure of size 1D chain, N units, each with length l, The probability that the ends are nl apart:

Proof Number of chains pointing to the right: N R Number of chains pointing to the left: N L Effective length: (N R -N L )l=nlN=N R +N L The number of ways forming a chain with end-to-end distance nl: With Stirling’s approximation: The probability that the ends are nl apart:

3D case l nl P(R  R+dR)=fdR

Measure of size Root mean square separation: (classroom exercise)

Measure of size Radius of gyration: R ij : separation of atoms i and j

Exercise Calculate the mean separation of the ends of a freely jointed chain of N bonds pf length l.

Conformational entropy The most probable conformation is the one with n=0:

Constrained chains For tetrahedral bonds, For polyethylene with M=56 kg/mol, N=4000, l=154 pm (C-C bond),

The structure of proteins Corey-Pauling rules Classroom question: How many standard amino acids are most commonly found in living things?

α helix

Conformational energy Bond stretching: Bond bending: Bond torsion: Coulomb forces between partial charges: Dispersion and repulsive forces: Hydrogen bonding:

Potential Energies

K b :bond force constants b : bond length vibration b

K θ : angle force constant Θ: bond angle bending Θ

K X :dihedral angle force constant X: dihedral angle torsion

K imp : improper dihedral angle Φ: improper torsion angle (e.g., angle between ab and acd) Improper torsion a b c d

ε i j : Lennards-Jones well depth σ ij : Distance at the Lennards-Jones minimum between atoms i and j. q i : Partial atomic charge ε 0 : Dielectric constant r ij : The distance between atoms i and j Intermolecular forces (van der Walls forces)

Lower energy means more stable

Typical distribution of torsion angles (Ramachandran plot)

Glycyl residue

Alanyl residue

βsheet Parallel and anti-parallel sheets

Higher-order structure Four-helix bundle

Higher-order structure β-barrel

The structure of nucleic acids

Secondary structure of DNA

Higher-order structure of DNA

The stability of biological polymers Denaturation and renaturation

Determination of shape and size 22.6 Mean molar mass 22.7 Mass spectroscopy 22.8 Laser light scattering 22.9 Ultracentrifugation Electrophoresis Size exclusion chromatography Viscosity

Mean molar masses Number-average molar mass: Weight-average molar mass: Z-average (mean cubic) molar mass: Viscosity-average molar mass

MALDI principle

A typical MALDI mass spectrum

Laser light scattering

Determining molecular size with light scattering

Ultracentrifugation

Electrophoresis

Isoelectric point of a protein

Size-exclusion chromatography

Viscosity

Molar mass from viscosity

Self-assembly Colloids Micelles and biological membranes Surface films