Protein Structure and Energetics

Adam Liwo

Room B325Faculty 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

1. Levels of structural organization of proteins.

2. Quantitative description of protein geometry.

3. Secondary and supersecondary structure.

4. Tertiary and quaternary structure.

5. Schemes of protein-structure classification.

6. Interactions in proteins and their interplay.

7. Folding transition as a phase transition.

8. Foldability and the necessary conditions for foldability.

9. Misfolding and aggregation; formation of amyloids.

10. Experimental methods for the investigation of protein folding.

11. 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

ba

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.coli (2KHO)

Levels of protein structure organization

The primary structure (Emil Fischer, 1904)

H3N+-Gly-Ile-Val-Cys-Glu-Gln-..........-Thr-Leu-His-Lys-Asn-COO-

N-terminusC-terminus

-amino acids are protein building blocks

-amino acids: chemical structure

Classification of amino-acids by origin

Amino acids

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 codesSynthesized in humans Supplied with food

Name Code 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

T C A G

T

Phe

Ser

Tyr Cys TC

Leu TerTer A

Trp G

C Leu ProHis

ArgTC

Gln AG

AIle

ThrAsn Ser T

C

Lys ArgA

Met G

G Val AlaAsp

GlyTC

Glu AG

The "Universal" Genetic CodeIn form of codon, Left-Top-Right (ATG is Met)

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).

z

x yxH(6)

yH(6)

Cartesian coordinate system

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)

C(1)

O(2)

H(3)

H(4)

H(5)

H(6)

Internal coordinate system

i dij ijk ijkl j k lC(1) O(2) 1.40000 * 1H(3) 1.08900 * 109.47100 * 1 2H(4) 1.08900 * 109.47100 * 120.00000 * 1 2 3H(5) 1.08900 * 109.47100 * -120.00000 * 1 2 3H(6) 0.95000 * 109.47100 * 180.00000 * 2 1 5

C(1)

O(2)

H(3)

H(4)

H(5)

H(6)

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

jizzyyxxd ijijijij 222

xi yi

zi

xj

zj

xj

jkji

jkij

jkjijkjijkjiijk

jk

jk

ji

ji

jkji

jkji

dd

zzzzyyyyxxxx

uu ˆˆ

cos

ijk

i

j

k

Bond angle calculation

i

j

k

l

ijkl

a

b

jk

jkijklijkl

ba

ba

ba

ba

sincos

ba

Dihedral angle calculation

The vector product of two vectors

ba

a

b

ab

xyyxz

xzzxy

yzzyx

baba

baba

baba

ba

ba

ba

baab

baba

sin

xyyxxzzxyzzy

zyx

zyx

babababababa

bbb

aaa

kji

kji

ba

Some useful vector identities

cbabaccabcba

0aa

abba

i

j

k

'a

a

ijk ijk

ijkjiijkji

ijkjk

ji

ijkjk

jiijk

dd

jkd

dji

jkd

dji

jk

jk

ji

sincos1

cos

cos180cos'

'

22

aaa

a

a

aa

i

j

k

l

ijkl

a

b

ba

ijkklijkjk

kl

ijkjiijkjk

ji

dkjd

dkl

djkd

dji

sincos

sincos

bb

aa

jklijk

jklijkklij

ijkl

ddklji

sinsin

coscos

cos

ba

ba

jklijkkljkij

ijkl

jklijk

jklijkklij

ijkl

ddd

jkklji

ddklji

sinsinsin

sinsin

coscos

cos

ba

ba

j

k

l

ijkl

a

b

ba

yx

z

342642626H(6)

342642626H(6)

42626H(6)

sinsin

cossin

cos

dz

dy

dx

3426

426

d26

C(1)

H(3)

O(2)

H(4)

H(5)

H(6)

Calculation of Cartesian coordinates in a local reference frame from internal coordinates

Need to bring the coordinates to the global coordinate system

localTglobal

locali

locali

locali

iii

iii

iii

globali

globali

globali

z

y

x

eee

eee

eee

z

y

x

RER

332313

322212

312111

i-2

i-1

i

i+1

di-1

di

di+1

i-1

i

i+1

i+2

i

Polymer chains

i-2

i-1

i

i+1

di-1

di+1

i-1

i+2

i-1

i+1

i-1

i+1

pi-1

1112134231

111213423

331214

2213

112

01

nnnnnnn

iiiiiii

rpTTRTRTRr

rpTTRTRTRr

rpTTRr

rpTr

rpr

pr

ii

iiiii

ii

i

i

i

d

cossin0

sincos0

001

100

0cossin

0sincos

0

0 RTp

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).

60% 40%

Hybrid of two canonical structures

Peptide bond geometry

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 , , and angles

The cis (=0o) and trans (=180o) configurations of the peptide group

Skan z wykresem energii

Peptide group: cis-trans isomerization

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

Side chain conformations: the 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