Introduo Modelagem Molecular

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Introdução à Modelagem Molecular

• Chemoinformatics and Medicinal Chemistry Group
• Departamento de Química UFMG
• http//www.nequim.qui.ufmg.br
• jlopes_at_netuno.lcc.ufmg.br
• jcdlopes_at_gmail.com

Julio C. D. Lopes
UFMG - Out 2007 Belo Horizonte, Brasil
2
Molecular Informatics

• Storage, retrieval and manipulation of
  information about molecules or molecular systems
• Typically deals with large numbers of molecules
  or molecular systems

Molecular Modeling
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Molecular Modeling
The compendium of methods for mimicking the
behavior of molecules or molecular systems
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Molecular Modeling
Molecular Modeling is concerned with the
description of the atomic and molecular
interactions that govern microscopic and
macroscopic behaviors of physical systems.
The essence of molecular modeling resides in the
connection between the macroscopic and the
microscopic world provided by the theory of
statistical mechanics.
Macroscopic Observable
Average of observable over selected microscopic
states
(Solvation energy, affinity between two
molecules, H-H distance, conformation, )
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Points for Consideration

• Remember
• Molecular modeling forms a model of the real
  world
• Thus we are studying the model, not the world
• A model is valid as long as it reproduces the
  real world

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Why Use Molecular Modeling?(and not deal
directly with the real world?)

• Fast, accurate and relatively cheap way to
• Study molecular properties
• Rationalize and interpret experimental results
• Make predictions for yet unstudied systems
• Study hypothetical systems
• Design new molecules

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Some Molecular Properties
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Minimal Input for Molecular Modeling

• Topological properties
• Description of the covalent connectivity of the
  molecules to be modeled
• Structural properties
• The starting conformation of the molecule,
  provided by an X-ray structure, NMR or a
  theoretical model

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Minimal Input for Molecular Modeling
Energetical properties A force field describing
the force acting on each of the
molecules Thermodynamical properties A
thermodynamical ensemble that corresponds to the
experimental conditions od the system, e.g. N,V,T
or N,P,T or ..
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Molecular Simulations

• A method to sample all 3D structures
  (conformations) of a molecule. Any molecular
  property is an average of the values of this
  property in all the different conformations.

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Force Fields

• A method to describe a molecule as a collection
  of atoms held together by forces. Based on this
  description, each of the many molecular 3D
  structures is characterized by an energy value.
  This value is then used to optimize the geometry
  of the 3D structure. The optimized structure is
  then used to calculate many molecular properties.

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Molecular Structure Saccharin
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Molecular Structure and Molecular Properties

• Property
• Activity
• Cell Permeability
• Toxicity

Structure

• Descriptors
• 1D e.g., Molecular weight
• 2D e.g., of rotatable bonds
• 3D e.g., Molecular volume

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Molecular Structure and Molecular Properties

• Property
• Activity
• Cell Permeability
• Toxicity

Structure

• Biological Targets
• 3D structures
• X-ray
• NMR
• Homology

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Which Molecule(s) Should we Test Next?

• Answer
• An (ordered) list of molecules
• Potential candidates
• Corporate database
• External databases
• Synthesis
• Information
• Biological activity
• Molecular properties

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The Drug Development Route
Lead Discovery
Lead Optimization
Design
Design
Lead
Synthesis
Synthesis
Biological Screening
Biological Screening
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Property Space

• Each axes describes a molecular property
  (descriptor).
• Each molecule is represented by a point.
• The distance between any two points represents
  the degree of similarity between the
  corresponding molecules in terms of the selected
  descriptors.

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Lead Discovery
Locating Activity Islands Through Diversity
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Activity Optimization Through Focusing
Lead Discovery
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Lead Optimization All the Rest

• Efficacy
• Oral bioavailability
• Cell permeability
• Stability (CYP P450)
• Clearance
• Toxicity
• hERG channel
• Drug-drug interactions
• Selectivity

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Predictive Models
Active

• Use all available information to build a model
  which can differentiate between active and
  inactive compounds.

• Use the model to predict the activity of yet
  unsynthesized compounds.

• Select for synthesis only compounds predicted to
  be active.

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Types of Models

• CSAR Classification Structure Activity
  Relationship
• Qualitative data
• HTS data
• QSAR Quantitative Structure Activity
  Relationship
• Quantitative data

Property f(structure) Property f(desc1,
desc2, , descN)
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Docking and Scoring
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Docking and Scoring
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Introdução à Mecânica Molecular

• Chemoinformatics and Medicinal Chemistry Group
• Departamento de Química UFMG
• http//www.nequim.qui.ufmg.br
• jlopes_at_netuno.lcc.ufmg.br
• jcdlopes_at_gmail.com

Julio C. D. Lopes
UFMG - Out 2007 Belo Horizonte, Brasil
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Introduction
Energy minimization Single minimum Conformationa
l search Multiple minima Simulation methods A
complete quantification of the energy
surface Minima populated according to their free
energy
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Potential energy functions
QM ab initio distribution of electrons over the
system, given The position of the atom
cores. Gaussian94, Gamess, ... Semi-empirical
methods pre-calculated values or neglect of some
parts of the ab-initio calculation. MOPAC
(mopac6, -7, -93, -2000, -2002) Empirical
methods observed/fitted values for
interactions between atoms. Amber, MM3, CHARMM,
Gromos, ...
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Basic Concepts
Energy Energy as a function of a coordinate
X. Energy penalty for distorting X from its
equilibrium position. Steric Energy a
k(X-X0)2 (Hook's law). Parameterization Matchi
ng a function to a set of data points by varying
its parameters (a and k).
Minimization Finding the minimum of a potential
function. First Derivative force dE/dX
2k(X-X0) 0.
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Force Field
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Potential energy vs. bond length
Similar equation for valence angles
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Potential energy vs. dihedral angle
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Potential energy vs. dihedral angle
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Potential energy vs. dihedral angle
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van der Waals energy vs. distance
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The CHARMM Force Field
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The CHARMM Force Field
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CHARMM Parameter Set
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Other Interactions

• Hydrogen Bond
• Interaction of type D-H --- A
• The origin of this interaction is a dipole-dipole
  attraction

• Hydrophobic Effect
• The origin of this interaction is a unfavorable
  surface of contact between the water and an
  apolar medium (entropic driving)
• The apolar medium reorganizes to minimize the
  water exposed surface

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Treatment of long range interactions
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Effect of cutoff on energy calculations
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Existing Force Fields

• AMBER (Assisted Model Building with Energy
  Refinement)
• Parameterized specifically for proteins and
  nucleic acids.
• Uses only 5 bonding and non-bonding terms along
  with a sophisticated electrostatic treatment.
• No cross terms are included.
• Results can be very good for proteins and nucleic
  acids, less so for other systems.
• CHARMM (Chemistry at Harvard Macromolecular
  Mechanics)
• Originally devised for proteins and nucleic
  acids.
• Now used for a range of macromolecules, molecular
  dynamics, solvation, crystal packing, vibrational
  analysis and QM/MM studies.
• Uses 5 valence terms, one of which is
  electrostatic term.
• Basis for other force fields (e.g., MOIL).

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Existing Force Fields

• GROMOS (Gronigen molecular simulation)
• Popular for predicting the dynamical motion of
  molecules and bulk liquids.
• Also used for modeling biomolecules.
• Uses 5 valence terms, one of which is an
  electrostatic term.
• MM1, 2, 3, 4
• General purpose force fields for
  (mono-functional) organic molecules.
• MM2 was parameterized for a lot of functional
  groups.
• MM3 is probably one of the most accurate ways of
  modeling hydrocarbons.
• MM4 is very new and little is known about its
  performance.

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Existing Force Fields

• MMFF (Merck Molecular Force Field)
• General purpose force fields mainly for organic
  molecules.
• MMFF94 was originally designed for molecular
  dynamics simulations but is also widely used for
  geometry optimization.
• Uses 5 valence terms, one of which is an
  electrostatic term and one cross term.
• MMFF was parameterized based on high level ab
  initio calculations.
• OPLS (Optimized Potential for Liquid Simulations)
• Designed for modeling bulk liquids.
• Has been extensively used for modeling the
  molecular dynamics of biomolecules.
• Uses 5 valence terms, one of which is an
  electrostatic term but no cross terms.

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Existing Force Fields

• Tripos (SYBYL force field)
• Designed for modeling organic and biomolecules.
• Often used for CoMFA analysis (QSAR method).
• Uses 5 valence terms, one of which is an
  electrostatic term.

• CVFF (Consistent Valence Force Field)
• Parameterized for small organic (amides,
  carboxylic acids, etc.) crystals and gas phase
  structures.
• Handles peptides, proteins, and a wide range of
  organic systems.
• Primarily intended for studies of structures and
  binding energies, although it predicts
  vibrational frequencies and conformational
  energies reasonably well.

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Minimização da Energia Otimização da Geometria

• Chemoinformatics and Medicinal Chemistry Group
• Departamento de Química UFMG
• http//www.nequim.qui.ufmg.br
• jlopes_at_netuno.lcc.ufmg.br
• jcdlopes_at_gmail.com

Julio C. D. Lopes
UFMG - Out 2007 Belo Horizonte, Brasil
46
Potential Energy Surface
A system of N atoms is defined by 3N Cartesian
coordinates or 3N-6 internal coordinates. These
define a multi-dimensional potential energy
surface (PES).
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Potential Energy Surface
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Minimization Definitions
Given a function Find values for the variables
for which f is a minimum
Functions Quantum mechanics energy Molecular
mechanics energy Variables Cartesian (molecular
mechanics) Internal (quantum mechanics) Minimizat
ion algorithms Derivatives-based Non
derivatives-based
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A Schematic Representation
Starting geometry
Easy to implement useful for well defined
structures Depends strongly on starting geometry
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Population of Minima
Active Structure
Most populated minimum
Global minimum
Most minimization method can only go downhill and
so locate the closest (downhill sense)
minimum. No minimization method can guarantee
the location of the global energy minimum. No
method has proven the best for all problems.
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Common minimization protocols

• First order algorithms
• Steepest descent
• Conjugated gradient
• Second order algorithms
• Newton-Raphson
• Adopted basis Newton Raphson (ABNR)

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Steepest Descent

• This is the simplest minimization method
• The first directional derivative (gradient) of
  the potential is calculated and displacement is
  added to every coordinate in the opposite
  direction (the direction of the force).
• Advantages Simple and fast.
• Disadvantages Inaccurate, usually does not
  converge.

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Steepest Descent
SD is forced to make 90º turns between subsequent
steps and so is slow to converge.
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Conjugated gradient

• Uses first derivative information information
  from previous steps the weighted average of the
  current gradient and the previous step direction.
• The weight factor is calculated from the ratio of
  the previous and current steps.
• This method converges much better than SD.

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Newton-Raphson algorithm

• Uses both first derivative (slope) and second
  (curvature) information.
• In the one-dimensional case
• Advantage Accurate and converges well.
• Disadvantage Computationally expensive, for
  convergence, should start near a minimum.

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Adopted basis Newton Raphson (ABNR)

• An adaptation of the NR method that is especially
  suitable for large systems.
• Instead of using a full matrix, it uses a basis
  that represents the subspace in which the system
  made the most progress in the past.
• Advantage Second derivative information,
  convergence, faster than the regular NR method.
• Disadvantages Still quite expensive, less
  accurate than NR.

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Busca Conformacional

• Chemoinformatics and Medicinal Chemistry Group
• Departamento de Química UFMG
• http//www.nequim.qui.ufmg.br
• jlopes_at_netuno.lcc.ufmg.br
• jcdlopes_at_gmail.com

Julio C. D. Lopes
UFMG - Out 2007 Belo Horizonte, Brasil
58
Conformational Analysis

• Conformers
• Structures differing only by rotation around one
  or more bonds.
• Constitute stationary points on the PES.

• Conformation
• Any point on the PES.

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Butane
CH3CH2
CH2CH3
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Cyclohexane

• Chair
• Global minimum
• 6 axial and 6 equatorial bonds

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Ring Inversion
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Population of Minima
Active Structure
Most populated minimum
Global minimum
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Sampling the PES

• Energy minimization
• Single minimum
• Conformational search
• Multiple minima
• Both methods produce results which only reflect
  the enthalpic contribution to the free energy.

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Boltzmann Averaging and Conformational Search

• Approximations come about from the set of
  conformers (or conformations), i.e., which is
  considered.
• If we choose to go with conformational searching,
  we should at least look for a set of
  energetically accessible minima.

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Boltzmann Averaged Properties

• Fraction of conformation i in an equilibrium
  mixture

• Equilibrium molecular properties are obtained by
  Boltzmann averaging the properties of the
  individual conformations

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Conformational Search Outline

• Randomly or systematically generated starting
  geometries

• Energy minimization

• Duplicates elimination

• Representative structures for each potential
  minimum

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Systematic Methods

• Systematically vary each of the (N) rotatable
  bonds in the molecule.
• Number of conformations
• Limitations
• Number of processed structure rapidly increases
  with N.
• Problematic structures may be removed prior to
  minimization.
• Poor coverage of conformational space at the
  beginning of the run.

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Systematic Methods Example
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Genetic Algorithm (GA)

• A method for global optimization.
• Uses ideas taken from evolution processes.
• Assumes that good parents have better chance to
  produce good offspring.

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Genetic Algorithm (GA)

• Create an initial population of m conformations
• Each conformation is represented by a chromosome.

• In this chromosome, each torsion can be
  represented by one of 2532 values.

• Calculate a fitness function (e.g., energy) for
  each chromosome.

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Genetic Algorithm (GA)

• Select a number of chromosome pairs (e.g., m/2)
• Selection biased towards fitter (e.g., lower
  energy) chromosomes
• Object Fitness Roulette fraction
• A 3 1/4
• B 6 1/2
• C 2 1/6
• D 1 1/12
• Subject the new population to genetic operators
• Propagate highest-ranking individuals.
• Crossover (80)
• Point mutation (1)
• Replace least fit chromosomes by new chromosomes
  and repeat the procedure on new population.

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Other Methods
Distance geometry Refinement of NMR
structures Monte Carlo Simulated
annealing Molecular dynamics High
temperature Simulated annealing
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MD or MC
Molecular dynamics Advantages Average
properties reflect free energies. Good
converge of local energy minima. Disadvantages
Requires energy derivatives. Slow crosses
of energy barriers of 2-3 kcal/mol. Monte
Carlo Advantages Average properties reflect
free energies. Can cross high energy
barriers. Disadvantages Do not require energy
derivatives. Slow convergence for large
molecules and ring systems.
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Simulated Annealing (SA) and simulated quenching
(SQ)
In these techniques, the temperature of the
system is raised and cooled several times during
a standard MD or MC simulation
Two different types of cooling can be
achieved - A slow protocol annealing - A
fast protocol quenching
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Solvent Treatment
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Monte Carlo Integration
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Thermodynamic Properties (NVT Ensemble) via Monte
Carlo Integration

• Average potential energy

• The probability of obtaining the configuration rN

• Z is the configuration integral (related to Q)

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Thermodynamic Properties via Monte Carlo
Integration

• Obtain a configuration of the system by
  generating 3N Cartesian coordinates which are
  assigned to the particles.
• Calculate the potential energy of the
  configuration.
• Calculate the Boltzmann factor.
• Add the Boltzmann factor to the accumulated sum
  of Boltzmann factors and the potential energy
  contribution to its accumulated sum.
• After Ntrial steps evaluate the mean potential
  energy by

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Metropolis Monte Carlo

• Only a small part of the phase space (low energy
  region) contribute to physical observables.
• The above procedure is hampered by the presence
  of many configurations with a negligible
  contribution to the integral due to their high
  energies.
• Solution
• Bias the generation of configurations towards
  those which make the most significant
  contribution to the integral.
• Metropolis Monte Carlo generates state with a
  probability of exp(-V(rN)/kt) and counts them
  equally (Simple MC generates states with equal
  probability and then assign them a weight of
  exp(-V(rN)/kt)). By doing so , sampling from the
  NVT (canonical) ensemble is guaranteed.

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Energy Minimization (Geometry Optimization) and
Conformational Search

• A method to find a set of the most stable (lowest
  in energy) 3D structures (conformers) of a
  molecule. Any molecular property is a (weighted)
  average of the values of this property in the
  different conformers.