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Structural Bioinformatics
(C3210)
Energy and Proteins
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

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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.

3
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)

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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)

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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.

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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
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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-dipole
Monopole
1/r
Dipole
1/r2
1/r3
Induced-dipole
1/r4
1/r6
1/r6
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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 (Ca 2+, 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, dipolemonopole 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
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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

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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).

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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
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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

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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).

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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

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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)

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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
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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 hbonds (within protein or with solvent)
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Hydrogen Bonds in Proteins
Most of the hydrogen bonds in a proteins are local (mainly in αhelices, 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

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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

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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

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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)
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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

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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.
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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)
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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
Cys
Thr
Pro
Asp
4.5
2.5
-0.7
-1.6
-3.5
Val
Met
Ser
His
Asn
4.2
1.9
-0.8
-3.2
-3.5
Leu
Ala
Trp
Glu
Lys
3.8
1.8
-0.9
-3.5
-3.9
Phe
Gly
Tyr
Gln
Arg
2.8
-0.4
-1.3
-3.5
-4.5
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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
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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

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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 electroneutral, 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.
29
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)

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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

31
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

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