1. Conformational Search
Potential energy surfaces
b. Systematic methods
c. Monte Carlo methods
d. Molecular Dynamics methods
e. Conformation searching examples

2. What is conformation?
• Conformation: three-dimensional
structure of a molecule •
Traditionally one defines conformations of a
molecule as those arrangements of its atoms in
space that can be interconvert purely by rotation
about single bonds.
Also, small distortions in bond angles and bond
lengths often accompany conformational changes,
and that rotations can occur about bonds in
conjugated systems that have an order between one
and two.

3. Conformation Analysis
• Conformation Analysis: The study of the conformations
of a molecule and their influence on its properties:
structural, energetic, temporal, etc.
• The physical, chemical and biological properties of a
molecule depend critically upon the three -dimensional
structures, i.e., on their conformations.
• Thus, ‘conformational analysis’ means the study of
these three dimensional structures as well as how these structures affect their properties
( physical, chemical or biological )

4. Potential energy surfaces

6. Cartesian vs. Internal coordinates

7. Cartesian coordinatesH H H H
Re-orientating the molecule leads to Cartesian coordinates that make the symmetry more obvious. This removes the bond length of from the explicit parameters. H H H H
The corresponding Z-matrix (internal coordinates), which starts from the carbon atom, could look like this: C H H H H
methane

11. N
Number of conformations = s
where N is the number of free rotation angles and s is the number of discrete values for each rotation angle. This number is given by 360/i with i being the dihedral increment of angle i.

12. Conformational Search Methods
• Conveniently, we divide conformational
search methods as:
1: Systematic Search Algorithms
2: Model – Building Methods
3: Random Approaches
4: Distance Geometry
5: Simulation Based Methods ( Metropolis
Monte Carlo & Molecular Dynamics)
6: Genetic Algorithm and Evolutionary Algorithm

13. Systematic search Procedure:
1. All rotatable bonds are identified. Bond length and angles
are fixed.
2. Each bond is rotated one by one with fixed increment.
3. A minimization follows each move
4. Finished when all possible combinations are done
Balance between resolution of grid and computer resources
• Too fine a grid and the search may take too long.
• Too coarse the grid and one might misses important
minima
• One needs to set interdependent criteria cutoffs as per the
intelligent guess so as to maintain the said balance

15. Systematic search

16. Constrained torsion angles
Ramachandran plot for peptides

17. A Ramachandran plot generated from human PCNA, a trimeric DNA clamp protein that contains both β-sheet and α-helix (PDB ID 1AXC). The red, brown, and yellow regions represent the favored, allowed, and "generously allowed" regions 

18. Model-building • Use larger building blocks/molecular fragments
• Systematic search use the conformation of fragments
• Substructure search algorithm
• Assumptions/limitations
– Each fragment is conformational independent of the other fragments
– Completeness of conformations of fragments
– Only apply to molecules where the fragments are available

20. Random search • Can move from one region of the energy surface to a
completely different unconnected region in a single step.
• Iteration:
–Starting structure generation
–Random move: rotation or moving in Cartesian space
–Minimization
–Add to list of conformation
–Determine next starting structure
–The procedure ends when desired structures generated or
predefined steps finished or all conformations sampled

21. Distance geometry:
Distance geometry uses the interatomic distances and various mathematical
procedures to generate structures of conformations for energy minimization
1. Matrix containing the maximum and minimum values permitted to each interatomic distance in the molecule is calculated.
2. Each interatomic distance is arbitrarily assigned values between the upper and lower bounds.
3. Distance Matrix is transformed into trial set of cartesian coordinates.
4. Refinement of structure and generation of conformation is the last stage.
Refinement of structure is carried out in accordance to simple trigonometric restrictions
The distance between A and C can be no greater than the sum of maximum values of distances between AB & BC.
Minimum value of AC distance can be no less than the difference between the lower bound on AB and the upper bound on BC:

22. Metropolis Monte Carlo
– The newly generated structure is accepted or
rejected based on the difference of energy between
the old and new structures.
– The probability is proportional to
– exp[-( Enew – Eold )/kT]

23. “Population” of conformations/structures
Genetic Algorithms
“Population” of conformations/structures
Each “parent” conformer comprised of “genes”
“Offspring” generated from mixtures of “genes”
“mutations” allowed
Most fit “offspring” kept for next “generation”
“Fitness” = low energy

24. Glycolaldehyde: the simplest sugar
Glycolaldehyde 1 CC (C2v) (E = 0.0 kJ/mol)
2 TT
E = kJ/mol
3 TG
E = kJ/mol
CC-W-1
CC-W-2
TS 1
TS 3
TS 2
4 CT
E = kJ/mol

25. CC-W-1
CC-W-2
TS2
TS3
TS1

28. The unfolded protein had both high entropy and high free energy
The unfolded protein had both high entropy and high free energy. The high entropy corresponds to there being a large number of possible conformational states—the molecule can take on many different three-dimensional shapes. The high free energy means that the molecule is unstable, and flops easily between the different conformational states. As the protein starts to fold, the free energy drops and the number of available conformational states (denoted by the width of the funnel) decreases. There are local minima along the way that can trap the protein in a metastable state for some time, slowing its progress towards the free energy minimum. At the bottom of the funnel, the free energy is at a minimum and there is only one conformational state available to the protein molecule. This is called its native state, and is the ground state of the system.