Protein Structure and Energetics Adam Liwo Room B325 Faculty of Chemistry, University of Gdańsk phone: 58 523 5124 (or 5124 within the University) email: adam@sun1.chem.univ.gda.pl adam.liwo@gmail.com Course language: English

Schedule and requirements Mondays, 8:15 – 10:00, room C209, Faculty of Chemistry, University of Gdańsk 2 problem sets Final exam

Scope of this course Levels of structural organization of proteins. Quantitative description of protein geometry. Secondary and supersecondary structure. Tertiary and quaternary structure. Schemes of protein-structure classification. Interactions in proteins and their interplay. Folding transition as a phase transition. Foldability and the necessary conditions for foldability. Misfolding and aggregation; formation of amyloids. Experimental methods for the investigation of protein folding. Atomistic-detailed and coarse-grained models and force fields for protein simulations.

Literature C. Branden, J. Toze, „Introduction to Proten Structure”, Garland Publishing,1999 G. E. Schultz, R.H., Schrimer, „Principles of Protein Structure”, Springer-Verlag, 1978 Ed. J. Twardowski, „Biospektroskopia”, cz. I, PWN, 1989 I. Z. Siemion, „Biostereochemia”, PWN, 1985

Proteins: history of view 1828: By syntesizing urea, Friedrich Woehler voided the vis vitalis theory, opening roads to modern organic chemistry. 1850’s: First amino acids isolated from natural products 1903-1906: By hydrolysis of natural proteins, Emil Fischer proves that they are copolymers of amino acids (strange, but none of his so fundamental papers earned more than ~60 citations!). 1930’s and 1940’s: proteins are viewed as spheroidal particles which form colloidal solution; their shape is described in terms of the long-to-short axis ratio. 1930’s: it is observed that denaturated proteins do not crystallize and change their physicochemical and spectral properties.

Proteins: history of view (continued) 1940’s: evidence from X-ray accumulates suggesting that fibrous proteins such as silk and keratin might have regular structure. 1951: Pauling, Corey, and Branson publish the theoretical model of protein helical structures. 1960: Laskowski and Scheraga discover anomalous pKa values in ribonuclease, which suggest that the acidbase groups are shielded from the solvent to different extent. 1963: First low-resolution X-ray structure of a protein (horse hemoglobin) published by the Perutz group. Today: 68840 structures of proteins, nucleic acids, and sugars in the Protein Data Bank.

Protein shapes from viscosity data b Polson, Nature, 740, 1936

Pauling’s model of helical structures

First structure: hemoglobin (X-ray)

Example of a recently solved structure: DnaK chaperone from E Example of a recently solved structure: DnaK chaperone from E.coli (2KHO)

Levels of protein structure organization

The primary structure (Emil Fischer, 1904) C-terminus N-terminus H3N+-Gly-Ile-Val-Cys-Glu-Gln-..........-Thr-Leu-His-Lys-Asn-COO- a-amino acids are protein building blocks

a-amino acids: chemical structure

Classification of amino-acids by origin Natural Synthetic Proteinic (L only) Non-Proteinic (D and L) Primary (coded) Secondary (post-translational modification) Tertiary (e.g., cystine) Endogenous Exogenous

Amino-acid names and codes Synthesized in humans Supplied with food Name Code Alanine Ala A Histidine His H Arginine Arg R Isoleucine Ile I Asparagine Asn N Leucine Leu L Aspartic acid Asp D Lysine Lys K Cysteine Cys C Methionine Met M Glutamine Gln Q Phenylalanine Phe F Glutamic acid Glu E Threonine Thr T Glycine Gly G Tryptophan Trp W Proline Pro P Valine Val V Serine Ser S Tyrosine Tyr Y

The peptide bond

Venn diagram of amino acid properties

The "Universal" Genetic Code In form of codon, Left-Top-Right (ATG is Met) Phe Ser Tyr Cys Leu Ter Trp Pro His Arg Gln Ile Thr Asn Lys Met Val Ala Asp Gly Glu

Atom symbols and numbering in amino acids

Chirality Enantiomers Phenomenological manifestation of chiraliy: optical dichroism (rotation of the plane of polarized light).

Determining chirality Highest oxidation state Chain direction

The CORN rule

Absolute configuration: R and S chirality Rotate from „heaviest” to „lightest” substituent R (D) amino acids S (L) amino acids

Representation of geometry of molecular systems Cartesian coordinates describe absolute geometry of a system, versatile with MD/minimizing energy, need a molecular graphics program to visualize. Internal coordinates describe local geometry of an atom wrt a selected reference frame, with some experience, local geometry can be imagined without a molecular graphics software, might cause problems when doing MD/minimizing energy (curvilinear space).

Cartesian coordinate system z Atom x (Å) y (Å) z (Å) C(1) 0.000000 0.000000 0.000000 O(2) 0.000000 0.000000 1.400000 H(3) 1.026719 0.000000 -0.363000 H(4) -0.513360 -0.889165 -0.363000 H(5) -0.513360 0.889165 -0.363000 H(6) 0.447834 0.775672 1.716667 zH(6) H(6) O(2) H(4) C(1) yH(6) xH(6) x H(5) y H(3)

Internal coordinate system i dij aijk bijkl j k l C(1) O(2) 1.40000 * 1 H(3) 1.08900 * 109.47100 * 1 2 H(4) 1.08900 * 109.47100 * 120.00000 * 1 2 3 H(5) 1.08900 * 109.47100 * -120.00000 * 1 2 3 H(6) 0.95000 * 109.47100 * 180.00000 * 2 1 5 H(6) O(2) H(4) C(1) H(5) H(3)

Bond length

Bond (valence) angle

Dihedral (torsional) angle The C-O-H plane is rotated counterclockwise about the C-O bond from the H-C-O plane.

Improper dihedral (torsional) angle

Bond length calculation zj zi xi yi xj xj

Bond angle calculation j aijk i k

Dihedral angle calculation bijkl k j l

The vector product of two vectors q

Some useful vector identities

i aijk 180o-aijk k j

i bijkl k j l

bijkl k j l

Calculation of Cartesian coordinates in a local reference frame from internal coordinates H(5) z H(6) d26 C(1) a426 H(3) b3426 O(2) y x H(4)

Need to bring the coordinates to the global coordinate system

Polymer chains pi-1 qi+2 qi+2 wi+1 qi+1 wi+1 i+1 i+1 di+1 di+1 i i di

For regular polymers (when there are „blocks” inside such as in the right picture, pi is a full translation vector and Ti-2Ri-1 is a full transformation matrix).

Hybrid of two canonical structures Peptide bond geometry Hybrid of two canonical structures 60% 40%

Electronic structure of peptide bond

Peptide bond: planarity The partially double character of the peptide bond results in planarity of peptide groups their relatively large dipole moment

Main chain conformation: the f, y, and w angles The cis (w=0o) and trans (w=180o) configurations of the peptide group

Peptide group: cis-trans isomerization Skan z wykresem energii

Because of peptide group planarity, main chain conformation is effectively defined by the f and y angles.

Side chain conformations: the c angles

The dihedral angles with which to describe the geometry of disulfide bridges

Some  and  pairs are not allowed due to steric overlap (e.g, ==0o)

The Ramachandran map