THE MOLECULAR MODELLING IS THE MOST IMPORTANT TOPIC FOR CHEMISTRY STUDENTS , HENCE THE THEORY OF MOLECULAR MODELLING IS COVER IN THIS PRESNTATION . HOPE THIS MATTER SAISFY ALL AS WE HAVE TRIED TO ATTEMPT ALL TH TOPICS OF IT.

2. Target
Identification
&Validation
Hit Lead Lead
Identification Identification Optimisa-
tion
CD
Prenomi-
nation
Concept
Testing
Development
for launch
Launch
Phase
FDA Submission
Launch
Finding Potential
Drug Targets
Validating Therapeutic Targets
Finding Potential Drugs
Drug<>Target<>Therapeutic
Effect Association Finalized
Testing in Man
(toxicity and efficacy)
Drug Discovery is a goal of research. Methods and approaches from different science areas
can be applied to achieve the goal.
2

3. Hugo Kubinyi , www.kubinyi.de
3

4.  R&D cost per new drug is $500 to $700 millions
 To sustain growth, each of top 20 pharma company
should produce more new drugs
 Currently, total industry produces only 32 new drugs
per year.
 Current rate of NDAs far below than required for
sustained growth. 4

5. U
n
k
n
o
w
n
K
n
o
w
n
Unknown Known
Molecular
Docking
Drug receptor
interaction
De NOVO Design ,
Virtual screening
Build or find the key
that fits the lock
Receptor based drug design
Rational drug designIndirect drug design
2D/3D QSAR and
Pharmacophore
Infer the lock by
expecting key
Homology modelling
Generate 3D
structures,
HTS, Comb. Chem
Build the lock and then
find the key
7

6. • Molecular modelling allow scientists to use computers
to visualize molecules means representing molecular
structures numerically and simulating their behavior
with the equations of quantum and classical physics , to
discover new lead compounds for drugs or to refine
existing drugs in silico.
• Goal
: To
system
developasufficient accurate model of the
so that physical experiment may not be
necessary .
8

7. • The term “ Molecular modeling “expanded over the last
decades from a tool to visualize three-dimensional
structures and to simulate , predict and analyze the
properties and the behavior of the molecules on an
atomic level to data mining and platform to organize
many compounds and their properties into database and
to perform virtual drug screening via 3D database
screening for novel drug compounds .
9

8. Molecular modeling starts from structure determination
Selection of calculation methods in computationalchemistry
Starting geometry from
standard geometry, x-ray, etc.
Molecule
Molecular
mechanics
Quantum
mechanics
Molecular
dynamics or
Monte Carlo
Is bond formation or
breaking important?
Are many force field
parameters missing ?
Is it smaller than
100 atoms?
Are charges
of interest?
Are there many closely
spaced conformers?
Is plenty of computer
time available?
Is the free energy
Needed ?
Is solvation
Important ?
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9. 11

10. • Molecular modelling or more generally computational chemistry
is the scientific field of simulation of molecular systems.
• Basically in the computational chemistry , the free energy of the
system can be used to assess many interesting aspects of the
system.
• In the drug design , the free energy may be used to assess
whether a modification to a drug increase or decrease target
binding.
• The energy of the system is a function of the type and number of
atoms and their positions.
• Molecular modelling softwares are designed to calculate this
efficiently.
12

11. • The energy of the molecules play important role in the
computational chemistry. If an algorithm can estimate
the energy of the system, then many important
properties may be derived from it.
• On today's computer , however energy calculation takes
days or months even for simple system. So inpractice,
various approximations must be introduced that
reduce the calculations time while adding acceptably
small effect on the result.
13

12. • Example :
• Familiar conformation of the Butane
7
6
5
4
3
2
1
0
0.3
0.25
0.2
0.15
0.10
0.1
0.05
0
C
B
E
F
Potentialenergy
D
0 60 120 180 240 300 360
Dihedral angle
Probability
14

13. Quantum mechanics Molecular mechanics
Ab initio methods DFT method Semiimpirical methods
Molecular Modelling
15

14. • Quantum mechanics is basically the molecular orbital calculation
and offers the most detailed description of a molecule’s chemical
behavior.
• HOMO – highest energy occupied molecular orbital
• LUMO – lowest energy unoccupied molecular orbital
• Quantum methods utilize the principles of particle physics to
examine structure as a function of electron distribution.
• Geometries and properties for transition state and excited state can only be
calculated with Quantum mechanics.
• Their use can be extended to the analysis of molecules as yet
unsynthesized and chemical species which are difficult (or
impossible) to isolate.
16

15. • Quantum mechanics is based on Schrödinger equation
HΨ = EΨ = (U + K ) Ψ
E = energy of the system relative to one in which allatomic
particles are separated to infinite distances
H = Hamiltonian for the system.
It is an “operator” ,a mathematical construct that operates
on the molecular orbital , Ψ ,to determine the energy.
U = potentialenergy
K = kineticenergy
Ψ = wave function describes the electron distribution around the
molecule.
17

16. The Hamiltonian operator H is, in general,
18
Where Vi2 is the Laplacian operator acting on particle i. Particles
are both electrons and nuclei. The symbols mi and qi are the mass
and charge of particle I, and rij is the distance between particles.
The first term gives the kinetic energy of the particle within a wave
formulation.
The second term is the energy due to Coulombic attraction or
repulsion of particles.

17. • In currently available software, the Hamiltonian above is nearly
never used.
• The problem can be simplified by separating the nuclear and
electron motions.
kinetic energy
of electrons
Attraction of
electrons to
nuclei
Repulsion
between
electrons
Born-Oppenheimerapproximation
19

18. • Thus, each electronic structure calculation is performed for a
fixed nuclear configuration, and therefore the positions of all
atoms must be specified in an input file.
• The ab initio program like MOLPRO then computes the
electronic energy by solving the electronic Schrödinger equation
for this fixed nuclear configuration.
• The electronic energy as function of the 3N-6 internal nuclear
degrees of freedom defines the potential energy surface (PES)
which is in general very complicated and can have many minima
and saddle points.
• The minima correspond to equilibrium structures of different
isomers or molecules, and saddle points to transition states
between them.
20

19. • The term ab initio is Latin for “from the beginning” premises of
quantum theory.
• This is an approximate quantum mechanical calculation for a
function or finding an approximate solution to a differential
equation.
• In its purest form, quantum theory uses well known physical
constants such as the velocity of light , values for the masses and
charges of nuclear particles and differential equations to directly
calculate molecular properties and geometries. This formalism is
referred to as ab initio (from first principles) quantum
mechanics.
21

20. 22

21. • The Process of finding the minimum of an empirical potential
energy function is called as the Molecular mechanics. (MM)
• The process produce a molecule of idealized geometry.
• Molecular mechanics is a mathematical formalism which attempts
to reproduce molecular geometries, energies and other features by
adjusting bond lengths, bond angles and torsion angles to
equilibrium values that are dependent on the hybridization of an
atom and its bonding scheme.
23

22. • Molecular mechanics breaks down pair wise interaction into
√ Bonded interaction ( internal coordination )
- Atoms that are connected via one to three bonds
√ Non bonded interaction .
- Electrostatic and Van der waals component
The general form of the force field equation is
E P (X) = E bonded + E nonbonded
24

23. • Bondedinteractions
• Used to better approximate the interaction of the adjacent
atoms.
• Calculations in the molecular mechanics is similar to the
Newtonians law of classical mechanics and it will calculate
geometry as a function of steric energy
• Hooke’slawisappliedhere
• f = kx
• f = force on the spring needed to stretch an ideal spring is
proportional to its elongation x ,and where k is the force
constant or spring constant of the spring.
25

24. • Ebonded = Ebond + Eangle + Edihedral
26
• Bond term
Ebond = ½ kb (b – bo) 2
• Angle term
EAngle = ½ kθ (θ – θ0)
• Energy of the dihedral angles
Edihedral = ½ kΦ(1 – cos (nΦ + δ)

25. H
CC
H
H
Graphical representation of the bonded and non bonded interaction and the
corresponding energy terms.
27
E coulomb
Electrostatic attraction
E vdw
Van der waals
Yij
θ0
K θ
Kb
KФ
Ф 0
b0
b
E b
Bond stretching
E Ф
Dihedral rotation
E θ
Angle bending

26. • Nearly applied to allpairs of atoms
• The nonbonded interaction terms usually include electrostatic
interactions and van der waals interaction , which are expressed
as coloumbic interaction as well as
Lennard-Jones type potentials, respectively.
• All of them are a function of the distance between atom pairs , rij
.
Nonbondedinteraction
28

27. • E Nonbonded = E van der waals + E electrostatic
• E van der waals
Lennard Jones potential
• E electrostatic
Coulomb's Law
29

28. Force Fields
 A force field refers to the functional form and
parameter sets used to describe the potential energy of
a system of particles (typically but not necessarily
atoms

29. • The molecular mechanics energy expression consists of a simple
algebraic equation for the energy of the compound.
• Aset of the equations with their associated constants which are
the energy expression is called a force field.
• Such equations describes the various aspects of the equation like
stretching, bending, torsions, electronic interactions van der
waals forces and hydrogen bonding.
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30.  Functions that associate an energy with a given nuclear
configuration
 Key issues we will consider:
• QM
• Semi-empirical
• Force fields Computational
expense
• Calculations on small model
systems
• Geometry optimization on
small/intermediate model systems
• Extensive sampling of
macromolecular systems
Importance of Force field:
 Energy expression is the equation that describes the
potential energy surface of a particular model as a
function of its atomic coordinates
 Analysis of the energy contributions at the level of
individual or classes of interactions
Force Field

31. • Valance term. Terms in the energy expression which describes a
single aspects of the molecular shape. Eg., such as bond stretching
, angle bending , ring inversion or torsional motions.
• Cross term. Terms in the energy expression which describes how
one motion of the molecule affect the motion of the another. Eg.,
Stretch-bend term which describes how equilibrium bond length
tend to shift as bond angles are changed.
• Electrostatic term. force field may or may not include this term.
Eg., Coulomb’s law.
33

32. • Some force fields simplify the complexity of the calculations by
omitting most of the hydrogen atoms.
• The parameters describing the each backbone atom are then
modified to describe the behavior of the atoms with the attached
hydrogens.
• Thus the calculations uses a CH2 group rather than a Sp3
carbon bonded to two hydrogens.
• These are called united atom force field or intrinsichydrogen
methods.
• Some popular force fields are
 AMBER
 CHARMM
 CFF 59

33. 35
Force Field

34. • Assisted model building with energy refinement is the name of
both a force field and a molecular mechanics program.
• It was parameterized specifically for the protein and nucleic
acids.
• It uses only five bonding and nonbonding terms and no any
cross term.
60

35. (HarvardUniversity)
• Chemistry at Harvard macromolecular mechanics is the name of
both a force field and program incorporating the force field.
• It was originally devised for the proteins and nucleic acids. But
now it is applied to the range of the bimolecules , molecular
dynamics, solvation , crystal packing , vibrational analysis and
QM/MM studies.
• It uses the five valance terms and one of them is an electrostatic
term.
61

36. • The consistent force field .
• It was developed to yield consistent accuracy of results for
conformations , vibrational spectras , strain energy and
vibrational enthalpy of proteins.
• There are several variations on this
 CVFF – consistent valence forcefield
 UBCFF – Urefi Bradley consistent forcefield
 LCFF – Lynghy consistent forcefield
• These forcefields use five to six valance terms . One of which is
electrostatic and four to six others are Cross terms.38

37. Parameters in Force Field

38.  Energy term has no absolute meaning only sum of energy terms
could be used
 Force fields are best used within the class of compounds for which
 Parameters in force field are not transferable to others
 Properties related to electronic structure
(electrical conductivity, optical, magnetic) are not accessible
Limitation of Force fields

39. 41 41
• Energy minimization
• Methods
 First-order minimization: Steepest descent, Conjugate
gradient minimization
 Second derivative methods: Newton-Raphson method
 Quasi-Newton methods: L-BFGS
Energy Minimization
Local
minimum

40. Energy Minimization
Conformational Analysis (Equilibrium Conformer)
A conformational analysis is global geometry optimization
which yields multiple structurally stable conformational
geometries (i.e. equilibrium geometries)
Equilibrium Geometry
An equilibrium geometry may be a local geometry optimization
which finds the closest minimum for a given structure (conformer)
or an equilibrium conformer
BOTH are geometry optimizations (i.e. finding where
the potential gradient is zero)
E local greater than or equal to E global

41.  A first-order method
 Direction of net force is followed with:
 An arbitrary step size
 Line search
 Two strategies
 Iteratively select points between two
lower-energy points (lots of function
evaluations necessary
 Fit a curve to the three points and use
its minima as the next point selected
nx
nn
x
f
fu
uxx






1
Steepest descent

42. Limitations of Steepest Descent
 Can’t differentiate between maxima, minima and saddle points
 Very slow at low gradient values (near minima)
 Very inefficient for long, narrow energy wells
Saddle point: Saddle Point is a point in the domain of a function that
is stationary point but not a local extremum.
44
Steepest descent

43.  A first-order method (will have same problem as steepest descent
with maxima/minima/saddle points)
 Uses gradients from two successive points to determine direction
after first step – behaves in a less oscillatory fashion
Conjugate Gradient

44. In each step of conjugate gradient methods, a search vector pk is
defined by a recursive formula:
The corresponding new position is found by line minimization along
pk:
the CG methods differ in their definition of b:
- Fletcher-Reeves:
- Polak-Ribiere
- Hestenes-Stiefel
  kkkk pxfp 11   
kkkk pxx 1
)()(
)()( 11
1
kk
kkFR
k
xfxf
xfxf


 

 
)()(
)()()( 11
1
kk
kkkPR
k
xfxf
xfxfxf


 

 
 )()(
)()()(
1
11
1
kkk
kkkHS
k
xfxfp
xfxfxf






Conjugate gradients (CG)

45.  Suitable for relatively small systems (~100 atoms)
due the way the derivatives are handled
 Truncated Newton
 Solves for the second derivative iteratively
(truncated after some number of iterations)
 Method of choice except for highly strained
systems
47
Newton-Raphson Method

46. Newton’s method is a popular iterative method for finding the 0 of a
one-dimensional function:
 
 k
k
kk
xg
xg
xx
'
1 
x0x1x2x3
The equivalent iterative scheme for multivariate functions is based on:
   kkkkk xfxHxx  

1
1
Several implementations of Newton’s method exist, that avoid
computing the full Hessian matrix: quasi-Newton, truncated
Newton, “adopted-basis Newton-Raphson” (ABNR),…
It can be adapted to the minimization of a one –dimensional function,
in which case the
iteration formula is:
 
 k
k
kk
xg
xg
xx
''
'
1 
Newton-Raphson Method

47. Z score
 Z-Score is a statistical measurement of a
score's relationship to the mean in a group of scores.
A Z-score of 0 means the score is the same as the mean.
A Z-score can also be positive or negative, indicating
whether it is above or below the mean and by how
many standard deviations
 The Z-score of a protein is defined as the energy
separation between the native fold and the average of
an ensemble of misfolds in the units of the standard
deviation of the ensemble..

48. • Geometry optimization is an iterative procedure of computing
the energy of a structure and then making incremental increase
changes to reduce the energy.
• Minimization involves two steps
1– an equation describes the energy of the system as a function of
its coordinates must be defined and evaluated for a given
conformation
2– the conformation is adjusted to lower the value of the
potential function .
50

49. V
L
X
L
X
X (1) X (2) X (min)
L = Local minimum
G = Global minimum
G
Local and global minima for a function of one variable and
solution.
Algorithm for decent series minimization.
an example of a sequenceof
67

50. 52

51. • So molecular dynamics and molecular mechanics are often used
together to achieve the target conformer with lowest energy
configuration
• Visualise the 3D shape of a molecule
• Carry out a complete analysis of allpossible conformations and
their relative energies
• Obtain a detailed electronic structure and the polarisibility with
take account of solvent molecules.
• Predict the binding energy for docking a small molecule i.e. a drug
candidate, with a receptor or enzyme target.
• Producing Block busting drug
• Nevertheless, molecular modelling, if used with caution, can provide
very useful information to the chemist and biologist
medicinal research.
involved in
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