Structural Bioinformatics (C3210) - NCBRncbr.muni.cz/~martinp/C3210/StructBioinf6.pdfStructural Bioinformatics (C3210) Energy and Proteins 2 Protein Structure and Non-covalent Interactions

Structural Bioinformatics(C3210)

Energy and Proteins

2

Protein Structure and Non-covalent Interactions

The formation of a protein in its biologically active form requires the folding of the protein into a precise three-dimensional structure

The most important forces involved in protein 3D structure formation and stabilization are non-covalent interactions

3

Non-covalent Interactions in Proteins

Non-covalent interactions is the term used for all forces between atoms that are not related to covalent bonds

For practical reasons the non-covalent interactions are divided into the following groups:

● Electrostatic interactions (between atom charges and/or dipoles)

● Van der Waals interactions● Hydrogen bond interactions● Hydrophobic forces● Electrostatic interactions with solvent

Although only the first group is called electrostatic interaction, in fact all these forces are of electrostatic origin. They are related to the interaction between charged elementary particles: protons in nuclei and electrons.

In addition, some interactions, such as hydrophobic or electrostatic interactions with solvent, are result of collective behaviour of many molecules of water.

4

Electrostatic interactions

Molecules consist of positively charged nuclei and negatively charged electrons

Each nucleus with it's nearest electron neighbourhood is called atom

If number of protons in nuclei is equal to the number of electrons the total charge of the molecule is zero – the molecule is electroneutral

If number of protons differ from number of electrons within one molecule the molecule has charge and it is called ion (cation, anion)

Some molecules are charged permanently in the solution (e.g. metal ions, quaternary ammonium anions).

Other charged molecules are in equilibrium with their uncharged form (e.g. acids, bases)

5

Charged Groups

Molecules can have charged groups (amonium N+R4, carboxyl COO-), the charge of these individual groups is called formal charge (often associated with one atom of the group)

A molecule that is electrically neutral but carries formal charges on different atoms is called zwitterion (in Czech: obojetny iont)

6

Partial charges

Electrons are not evenly distributed in molecules even if they are electroneutral and do not have any formally charged groups.

The reason is that atoms with higher electronegativity attract electrons more then atoms with lower electronegativity which causes polarization of the bond.

The bond between these atoms forms a dipole and the atoms have so called partial charges.

7

Dipole and Induced Dipole Interactions

Dipoles can interact electrostatically with charged molecules or groups (dipole - monopole interaction) or with other dipoles (dipole - dipole interaction).

If charged atom or dipole approaches another atom (which can have zero charge and zero dipole moment) it induces movement of electron cloud, which results in induced dipole.

This induced dipole interacts electrostatically with that charged atom or dipole (monopole – induced-dipole interaction and dipole – induced-dipole interaction).

Fig.: An example of dipole-dipole interaction

8

Energy of Electrostatic Interactions The interaction energy between charges (monopoles) can be

derived from Coulomb's law described by the equation:

The energy between dipoles or induced-dipole interactions diminishes much faster than ~1/r (see table below)

The strength of these interactions depend on multiplication constant ɛ – permitivity (ɛ = ɛ0ɛr ,ɛr is a relative permitivity)

Permitivity depends on environment, it is lowest in vacuum (ɛr = 1). As a result, electrostatic interaction is stronger in vacuum than in other materials.

Because ɛr = 80 in water, electrostatic interaction is approx. 80 times weaker in water (at 20 °C). As a result, electrostatic interaction is significantly more short ranged in water solutions when in vacuum.

Table: Comparison of the Distace Dependence of the Interaction Energy

Monopole Dipole Induced-dipoleMonopole 1/r 1/r2 1/r4

Dipole 1/r3 1/r6

Induced-dipole 1/r6

9

Electrostatic Interactions in Proteins

Amino acid side chains in proteins can have formal charge (Asp, Glu, Lys, Arg, His) related to dissociation or association of proton

N-terminus and O-terminus of polypeptide can also be charged Some proteins can have metal ionts (Ca2+, Fe3+, etc.) in their

inferior (metalloproteins) There can also be interaction between protein atoms and mobile

ions in solution (Na+, K+, Cl-, etc.) The association of two ionic protein groups

in protein inferior is known as ion pair, ionic bond or salt bridge

Many of atoms in proteins that do not have formal charge have partial charge

They interact via dipole - dipole, dipole-monopole or dipole - induced-dipole interactions

Relative permitivity ɛr of the protein inferior is between 2 (for rigid proteins) to 4 (for proteins with flexible polar sidechains).

Figure: The salt bridge between Glu and Arg

10

Van der Waals Interactions

Small attraction force is observed between atoms that do not have formal nor partial charge (e.g. atoms of noble gases).

This forces are called London dispersion forces (shortly dispersion forces or London forces)

Classical description of these forces says that electron clouds fluctuate with respect to nuclei, which results in small temporary dipole moment. This moment induces dipole moments in neighbouring atoms. This results in attractive force between primary and induced dipoles.

Quantum mechanics provide more exact explanation for dispersion forces

11

Van der Waals Interactions

Dispersion forces also act between atoms with formal or partial charge, but they are only a small part of the total interaction force

Dispersion forces diminish rapidly with distance, approximately with 1/r6

Dispersion forces are negligible at atom-atom distances > 8 Å In computational chemistry the term van Der Waals forces

(abbreviated vdW) is used for dispersion forces. Nevertheless, this term can sometimes include dispersion forces plus dipole and induced dipole interactions (this is especially used in general chemistry).

12

Lennard-Jones Potential

If distance between atoms is very small, the repulsion between positively charged nuclei dominates (and also repulsion between electrons from Pauli exclusion principle applies) which results in rapid increase in interaction energy. The energy grows approx. with 1/109 to 1/1014. This is sometimes denoted steric repulsion.

Steric repulsions and van Der Waals forces are sometimes treated together (and sometimes the term van Der Waals forces is used for the sum of these both)

Different functions were designed to desrcribe development of these forces with energy, the Lennard-Jones potential is the most popular: V(r) = A/r12 - B/r6

VdW forces (including steric repulsions) are strongest at distance about 4Å although there are some deviations from this value among atoms of different elements (and possibly different hybridization state etc.)

Figure: Lennard-Jones potential for argon dimer

13

Stacking Interactions

Dispersion interaction between planar aromatic rings in parallel configuration is especially strong. This interaction is called stacking or π-π stacking or π-π interaction

This interaction is important in stabilisation of DNA/RNA structure and it can also occur within protein structure between aromatic residues (Phe, Tyr, His, Trp), and can play role in protein-DNA/RNA and protein-ligand interactions

14

Hydrogen Bond

Hydrogen atom that is covalently bonded to highly electronegative atom can create week bond with lone electron pair of other electronegative atom. This bond is called hydrogen bond.

Hydrogen bonds are denoted as D‒H····A where hydrogen atom H is covalently bonded to donor atom D and interacts with acceptor atom A

In biological systems, donors (D) and acceptors (A) are typically highly electronegative atoms N and O and occasionally S

Hydrogen bond is approx. 10 times weaker than covalent bond, it has dissociation energy from about 12 to 40 kJ/mol (3 – 10 kcal/mol).

15

Nature of Hydrogen Bond

The nature of hydrogen bond is predominantly electrostatic: D‒H bond forms a dipole with positively charged H atom and negatively charged D atom. Acceptor atom A and its lone electron pair also form dipole.

However, hydrogen bond also has some features of covalent bonding: it is directional, strong, produces interatomic distances shorter than typical vdW distances

Hydrogen bonds are much more directional than vdW forces but less then covalent bonds

Sometimes a single hydrogen atom participates in two hydrogen bonds, rather than one. This is called bifurcated hydrogen bond

16

Geometry of Hydrogen Bond

Typical length of hydrogen bond is 1.6 – 2.0 Å. Hydrogen bonds tend to be approximately linear, with the D‒H

bond pointing along the acceptor's lone pair orbital (angle between 140° to 180°)

Large deviations from this ideal geometry are not unusual For example, in α-helices and antiparallel β-sheets the N‒H

bonds point approximately along the C=O bonds rather than along an O lone pair orbital

Many hydrogen bonds in proteins are bifurcated (e.g. many N‒H groups in α-helices are bonded via bifurcated hydrogen bond to form both n→n-4 and n→n-3 hydrogen bonds)

17

Hydrogen Bonds in Proteins

In the 3D structure of folded protein almost all hydrogen bond donors and acceptors form hydrogen bonds

However, an unfolded protein makes hydrogen bonds with water molecules

As a result, energy of internal hydrogen bonds in folded protein is similar to the energy of hydrogen bonds of unfolded protein => contribution of hydrogen bonds to stabilisation energy of folded protein is usually very small

Figure 1:Unfolded protein makes hydrogen bonds with molecules of solvent (water)

Figure 2:Folded protein makes intramolecular hydrogen bonds. Water molecules forms hydrogen bond with each other

18

Hydrogen Bonds in Proteins

Despite of this fact, the internal hydrogen bonds are important for formation of native folding pattern, because all improper folds are energetically disfavoured as hydrogen bond acceptors or donors cannot form hydrogen bonds with protein atoms nor solvent (for example, they are in contact with carbon atoms)

Formation of α-helices and β-sheets efficiently satisfies the polypeptide backbone's hydrogen bonding requirements

Figure 1:In proper fold necessary hydrogend bonds can form

Figure 2:In improper fold some hydrogen bond donors or acceptors cannot form h-bonds (within protein or with solvent)

19

Hydrogen Bonds in Proteins

Most of the hydrogen bonds in a proteins are local (mainly in α-helices, turns) – they involve donors and acceptors that are close together in sequence => they can readily find their hydrogen bonding partners during folding

Approximately 68% of the hydrogen bonds are between backbone atoms

Hydrogen bonds are also formed between side chains

20

Hydrophobic Forces

Non-polar molecules, such as hydrocarbons, are poorly dissolved in water – they are called hydrophobic molecules or non-polar molecules

Hydrophobic molecules aggregate in water to minimize their contacts with water molecules

9 from 20 amino acid residues in proteins are hydrophobic Hydrophobic residues enforce the polypeptide chain to fold into

a compact structure with hydrophobic residues inside The hydrophobic effect derives from the special properties of

water as a solvent

21

Water Molecule

Molecule of water can make two hydrogen bonds by donating two hydrogens and it can also be acceptor of two other hydrogen bonds because it has two lone electron pairs

Thus, water molecule can form four hydrogen bonds with neighbouring water molecules - these four hydrogen bonds form near-tetrahedral structure

Water has a permanent dipole moment due to partial negative charge on O atom and positive charge on H atom

22

The Structure of Liquid Water and Ice

In ice, the water molecules have ordered tetrahedral structure where each molecule is hydrogen bonded with 4 neighbours

In liquid state the tetrahedral structure is partially disrupted – the density is higher than in the ice and hydrogen bond angles differes from optimal value which leads to weakening of the bonds

Figure:The structure of ice (left) and liquid water (right)

23

Origin of Hydrophobic Forces

Non-polar molecules cannot accept nor donate hydrogen bonds Water molecules at the surface of the non-polar molecules

orient in a specific way to maximize the hydrogen bonding of the water molecules around a hydrophobic surface

These surface water molecules are constrained in their rotational motions because orientations of D‒H bond or lone pairs oriented toward polar molecule surface are energetically disfavoured (because one hydrogen bond would be "lost")

This results in arrangement of water molecules similar to the structure of ice

24

Convex and Concave Surfaces

The previous applies to small molecules with approximately spherical surface

Surfaces of large molecules includes convex and concave area

Figure:Molecular surface. Red corresponds to convex areas, blue to concave areas, and white to almost flat areas.

25

Hydrophobic Forces vs. Surface Shape

Ordering of water molecules on convex areas is similar to ordering on surface of small spherical molecules

Water molecules on concave surfaces can not satisfy hydrogen bonding requirements => they form less hydrogen bonds in comparison with bulk water molecules or molecules on convex surfaces which is energetically disfavouring

Figure:Water molecules ordering on concave surface (left) and convex surface (right)

26

Hydropathy Index of Amino Acids

The hydropathy index of an amino acid is a number representing the hydrophobic or hydrophilic properties of its side-chain

It combines hydrophobic and hydrophilic tendencies The larger the number is, the more hydrophobic the amino acid The most hydrophobic amino acids are isoleucine (4.5) and

valine (4.2). The most hydrophilic ones are arginine (-4.5) and lysine (-3.9).

Hydrophobic amino acids are more abundant inside a protein while hydrophilic amino acids are more common outside, in contact with the aqueous solvent

Hydropathy Scale for Amino Acid Side Chain

Ile 4.5 Val 4.2 Leu 3.8 Phe 2.8Cys 2.5 Met 1.9 Ala 1.8 Gly -0.4Thr -0.7 Ser -0.8 Trp -0.9 Tyr -1.3Pro -1.6 His -3.2 Glu -3.5 Gln -3.5Asp -3.5 Asn -3.5 Lys -3.9 Arg -4.5

27

Hydrophobic amino acids are more abundant inside a protein

Hydrophobic amino acids are more abundant inside a protein while hydrophilic amino acids are more common outside, in contact with the aqueous solvent

28

Electrostatic Interactions with Solvents

If charged molecule is inserted into water, water molecules (which have dipole moment) orient in direction of electrostatic field

Oxygen atom of water, which has negative partial charge, is attracted to positive charges while hydrogen atoms are attracted to negative charges

Not all water molecules are oriented in direction of the electric field because thermal motions partially disrupt this ordering

Because electrostatic forces are long ranged, they influence orientation of molecules at relatively long distances

This electrostatic interaction is responsible for dissolution of charged molecules in water

29

Ion Dissociation in Water

Two ions with opposite charge are attracted together - this attraction is strongest at short distances

At short anion-cation distances, the electrostatic interaction with water molecules is weak because the electrostatic field generated by one ion is almost cancelled by the second ion

At long distances, the interaction between ions is negligible but the interaction of each ion with water solvents is highly favourable

Whether the ions will be dissociated or not depends on difference between energy of these two interactions (ion-ion and ion-water)

Figure 1:Attraction between two ions of oposite charge is strong at short distance, but interaction with water molecules is weak (because ion pair as a whole is electro- neutral, it only has some dipole moment)

Figure 2:Attraction between two ions of oposite charge is weak at long distance, but interaction of each ion with water molecules is strong.

30

Ion Dissociation in Proteins

Interaction with water is also responsible for dissociation of acids including some amino acid side chains (Asp, Glu, Lys, Arg, His)

Amino acids Asp, Glu, Lys, Arg (His) have charged side chains if they are in contact with solvent

But they are usually uncharged if buried into protein, because they are not in contact with water molecules (they can only interact with distant water molecules which gives only very weak interaction)

31

Forces Driving Protein Folding

Although interaction between ionized (formally charged) groups can be strong they do not contribute significantly to stabilization of protein structure (with exception of some salt bridges or metal coordination sites)

Dipole-dipole and VdW interactions are weak and contribute moderately to stabilization of protein structure

Hydrogen bonds only weakly stabilize protein structure but they provide structural basis for native folding pattern (they disfavour non-native folding patterns)

Hydrophobic interaction is a major force responsible for folding proteins into their native conformation

32

Disulfide Bonds

A disulfide bond is a covalent bond derived by the coupling of two thiol groups. It is also called an SS-bond or disulfide bridge.

In proteins, it is formed from the oxidation of thiol (-SH) groups of cysteine residues

Disulfide bonds form as a protein folds to its native conformation The relatively reducing chemical character of the cytoplasm

decreases the stability of intracellular disulfide bonds Almost all proteins with disulfide bonds are secreted to more

oxidized extracellular destinations, where their disulfide bonds stabilize their 3D structure