Master in Bioinformaticsmscbioinformatics.uab.cat/base/documents/bioinformatics... · 2014. 11....

Lesson 7. 3 Structural Bioinformatics

Molecular Modelling tools Jean-Didier Maréchal

The Biotechnological Computational Chemistry Team Department of Chemistry (UAB)

Course 2013-14 1

Module 2: Core Bioinformatics

MSc in Bioinformatics

MSc in Bioinformatics Module 2: Core Bioinformatics

Jean-Didier Maréchal Structural Bioinformatics Molecular Modelling tools

Jean-Didier Maréchal

General information

• JeanDi… – Email: [email protected] – Webpage: gent.uab.cat/jdidier – Room: C7/032 (chemistry building) – Research:

• Enzyme design • Drug design (novel approaches for HIV, Al, Metabolism) • Peptide development • Software development

– Past: Academia, big pharma and spin off – From computational chemistry to structural

bioinformatics

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mailto:[email protected]




While the teacher bores me…

- Get your comp to linux - Download the daily build of UCSF

Chimera - Install it

3




Introduction of Molecular Modeling

• Many atomic properties of the macromolecules can not be experimentally assessed

• Molecular Modeling tools are key elements of structural bioinformatics

• Molecular Modeling aims to provide with reproductive and hopefully predictive simulations of the molecular systems

• To do so, simulations are carried out with models that explicitly represent the atoms in the molecular system.

4




Model I. Physics

5

A physical model of a reality

Set of mathematic equations defining the model

provides

Applied on

a given system

Solved through computation

An estimated behavior

Descriptive Predictive

• Molecular modeling studies lays on the physical models used for the atomic representation of the systems

• The quality of the results is directly proportional to the exactness of the model

• By default, the results provided by modeling can not be exact




Model II. Size does matter...

6

• Algorithms and computer or time resources intrinsically limit the size of the system that can be treated

• Hence, modeling can also involves the reduction of the number of structural variables – Study of only a part of the real

system – Replacement of explicit solvent

molecules by a continuum environment

– coarse grain approaches – …




A model is ...a model

7

• The validity of a molecular modeling calculation underlays in its approximations – Size – Environment – Physico-chemical conditions – …

• Results have to be discussed in the applicative framework of the model: – Do not over criticize the results – Do not overstate the outcomes




The early XXIst Century Modeller

8

• Many models can be used to simulate the atomic behavior of molecules

• Each technique relies on its approximation which its field of applicability

• All of them are based on estimating the energy of a given spatial arrangement of atoms and reach for the stables, metastables and transition structures




The Potential Energy

9

• The potential energy, E, is a function of the coordinates (positions), R, of all the atoms in the system

• To a given geometry of the system corresponds a unique value of potential energy (if no electronic changes are involved)

• The entire map of the potential energy of a system in function of its coordinates is called the Potential Energy Surface (PES)

• Because of the high dimensionality of the entire PES, studies and analysis are generally simplified to a reduced number of variables

• The question is how to calculate the energy and how to explore the PES

-180 -135 -90 -45 0 45 90 135 1805.0

24.0

42.0

60.0

Conformational Energy

C(2)-C(4)-C(6)-C(11)(degrees)

Energ

y

(kcal

/mol)

-180 -90 0 90 180

-180

-90

0

90

1804411.38

20.31

kcal/mol

Conformational Energy

C(5)-C(6)-N(7)-C(8)(degrees)

N(7

)-C

(6)-

C(5

)-C

(4)(

degre

es

)



Jean-Didier Maréchal 10

Some key questions for Molecular Modeling

• Characterization of the most stables conformations of a system

• Atomic description of dynamical properties of the protein

• Determination in silico of the structural features of protein (i.e. Homology Modeling)

• Decode nature of interactions between biomolecules

• Determination of the catalytic processes

Some examples in this lesson




Calculation of the energy

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Molecular events

Change in chemical state Fiting/binding Pre-organization

pro

duct A

ffine c

hem

ical c

om

poud

Accurate electronic Good sampling




The three main molecular modeling families

13




A - Quantum techniques

• Generally solve Schrödinger equation… – time independent – in the Born-Oppenheimer approximation (electronic PES)

• Implies that the structure with the lowest energy is the most occupied over time

14

14

),,(),,( zyxzyx

Energy Wave function Hamiltonian

n

i

N

A iA

An

i

n

ij ij

n

ii

N

i

N

ij AB

BA

A

N

A A rZ

rRZZ

M 1 111

2

1

2

1

12

1

2

1ˆ

Tn Ven Vnn Vee Te

With the exact hamiltonian:




QM techniques

• Different levels: – ab initio

– huckel, extended huckel, semi empiric..

– Functional Density Theory

• Techniques used when aiming to high quality results

• Necessary for processes with changes in electronic nature of the system: – Catalysis

– Changes in covalent bonds

– Changes in coordination bonds

• QM method still have a substantially high ratio Time/natom




B - Molecular Mechanics techniques

• Nuclei and electrons behaviors incorporated in a potential

• Parametrization of the different kind of atomic forces

• Will be necessary to treat conformational changes large molecular system

• Can not treat changes in chemical natures

)]cos(1[ nAVtorsió

d- d+

i ij ij

ji

ticElectrostar

qqV

])/()/[(4 612

ijijijijijVDW rrV

l

2

0 )( llkV bEnllaç 2

0)( bPlegament kV




QM .vs. MM

• At same number of atoms, the conformational explorations are a lot faster for MM than QM approaches

• This velocity of calculation allows to treat easily the system time dependently with MM

• Some techniques allow to explore large conformational motions

• MM can not treat changes in the chemical state of the system




C – QM/MM methods

• Enzymes performs catalysis at their active site

• The proteic environment has some impact on the active centre: – Steric

– Electrostatic

– …

• When modeling the entire system QM and MM approximations are required

• Hybrid QM/MM – Part of the protein is treated with MM

techniques

– Where the key region is located, QM is used (example catalytic center)




Docking

Molecular Dynamics

Normal Mode Analysis

Recognition

Sampling

Catalysis

Motions

Folding

Homology Modeling

Transition metal

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Fine Electronics = Quantum Based

QM and QM/MM

Simplicity of calculation of E

Wide space = Approx. Energy




Exploration of the PES

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The number of local minima typically increases exponentially with the number of variables (degrees of freedom).

• Combinatorial Explosion Problem

A multidimensional problem

21

Possible Conformations (3n) for linear alkanes CH3(CH2)n+1CH3

n = 1 3

n = 2 9

n = 5 243

n = 10 59,049

n = 15 14,348,907

n = 100 ?



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Minimization

E

r

Transition

state

Global

Minimum

Local

Minimum

?

?

?




Minimization: General Scheme 1. start at an initial point and

calculate E

2. determine according to a fixed rule a direction of movement

3. move in that direction to a (hopefully) lowest energy structure.

4. At the new point, a new direction is determined and the same process is repeated.

The primary difference between algorithms is the rule by which successive directions of movement are selected.

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Energy

Gradient Hessian

Search Algorithm

Coordinates {x}0

New coordinates {x}1

Converged?

Optimized

YES

NO




Optimizers main families

• Don’t have any derivatives (hard to know which way to move to reduce function value) – Simplex method – Sequential Univariant Method

• Do have derivatives (use them to move toward minimum ) – Line optimization

• Golden Mean Method • Parabolic Optimization

– First derivate methods • Steepest Descent • Conjugate Gradient

– Second derivative methods • Newton-Raphson

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d

d

d

d

d

d

)()(

)()(

)()(

3

2

1

3

2

1

)(xfexf

xfexf

xfexf

e

f

e

f

e

f

xf

Not efficient




Steepest Descent

25

nRx 0

0)( ixf

)( ii xfh

)(minarg0

iii hxf

iiii hxx 1

Data:

Step 0: set i=0

Step 1: if stop

else, compute search direction

Step 2: compute the step-size

Step 3: set go to step 1




Conjugate Gradient

• The basic idea: decompose the n-dimensional quadratic problem into n problems of 1-dimension

• This is done by exploring the function in “conjugate directions”

• CG will find minimum of an N-dimensional quadratic function in at most N steps! Non-quadratic functions take longer – but all functions become quadratic near their minimum so CG is efficient




Practical aspects

• SD are generally applied at the beginning of the optimization and the CG at the end.

• Other methodologies are even more eficient when one want to reach accuracy in the determination of the minimium (Newton-Raphson)

• In many cases, it could be interesting to start with different structures.

• And to verify (frequency) that we are indeed with a minimum.

• For macromolecules: • Minimization is used to relax the structure but not to catch the exact absolute minimum • The minimization generally ends in a local minimum




Exercise 1.

28

Lets get minimized

Minimization cyclosporin A




From wells to wells

29

T

R




More than a structure

• Minimization only provides one structure: the closest minimum of a given starting point

• As the degrees of freedom of system increase, the number of minima increase

• Exploring the PES is not as trivial

• Numerous methodologies aim at exploring the conformational space: – To locate the best minimum

– To extract statistical data with thermodynamical means

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Some common conformational exploration schemes

• Monte Carlo: Allows random changes of the structure and evaluate their energetical cost. Low energy structures are kept (can form ensembles that are statistically relevant)

• Genetic Algorithms: Structural displacements mix randoms and evolutionary guided changes. Only low energy structures are kept based on survival criteria

• Simulated Annealing: Overheat the system to allow barrier jump then cool down to encounter lowest energy structures

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Molecular Dynamics

• Calculate the motion of the atoms using Newtonian dynamics

• determine the net force and acceleration experienced by each atom.

• Several algorithms are used to calculate displacements of the atom over time (verlet, leapfrog…)

• Like MC allow statistical analysis

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Time steps

33

• Knowledge of the atomic forces and masses can be used to solve the position of each atom along a series of extremely small time steps (on the order of femtoseconds = 10-15 seconds).

• The resulting series of snapshots of structural changes over time is called a trajectory.




Time scale

34

Biological molecules exhibit a wide range of time scales

over which specific processes occur;

for example

Local Motions (0.01 to 5 Å, 10-15 to 10-1 s) Atomic fluctuations

Sidechain Motions

Loop Motions

Rigid Body Motions (1 to 10Å, 10-9 to 1s) Helix Motions

Domain Motions (hinge bending)

Subunit motions

Large-Scale Motions (> 5Å, 10-7 to 104 s) Helix coil transitions

Dissociation/Association

Folding and Unfolding




The meaning of trajectories

Vibrations in proteins vary widely in energy

Low frequencies vibration correspond to collective motion of the proteins

High frequencies vibration to localized motions

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Relationship accuracy / time scale

• Computing numerous structures (energy, gradient, forces, etc.) is increasingly ressource demanding in function of the quality of the energetic model

• Force field approaches are simplified enough so that calculations can be performed on a very wild conformational and chemical space

• Simulations can be performed nowadays on solvated systems and for long runs

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Exercise 2

Molecular Dynamics of Cyclosporin A

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Homology Modeling

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The problem

• Most biochemical projects (drug design, enzyme design, etc.) require the physical three dimensional structure of the physiological target

• Experimental resolution (NMR or X-ray) is not always accessible.

• Computational tools have been set up to produce models of proteins to further study – Ab initio – Comparative/homology

modeling

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The grounds of comparative modeling

• From the mid 80s, studies showed that: – Proteins with SeqID upper 80% mainly have

differences in fold in the range of experimental error

– Up to 30-20%, protein share a strong structural similarity

– Below this threshold protein might be or not structurally related.

• With a good engouh SeqID and alignment modeling could find out its way to produce accurate models.

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The general methodology

Required material:

The structure of a “close” parent

The sequence of the target protein

A sequence alignment program (e.g. ClustalW, T-Coffee)‏

A homology modeling program (e.g. modeller)‏

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A framework like modeller

1. template recognition 2. alignment 3. alignment correction 4. backbone generation 5. generation of canonical loops (data based) 6. side chain generation plus optimisation 7. ab initio loop building (energy based) 8. overall model optimisation (energy minimisation) 9. model verification with optional repeat of previous steps.

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Step 1 and 2: research of templates

and sequence alignements Step 3 – Generation of

main chain model

Step 4 and 5 – Optimization of side chains and flexible parts

step 6 – Full relaxation




The success and the limitations

• When SeqID high, the method is generally highly efficient.

• In dark regions or difficult structural assignment, homology modeling could be helped by secondary structure prediction programs

• Moreover, multiple alignment can be particularly useful

• HM methods are generally updated tools that improve the evaluation of the quality of the model and better explore the conformational space of flexible regions (i.e. loops)

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Post Modeling

• The accuracy of the model has to be checked.

• Generally the same than those of experimental structure • Procheck(http://biotech.embl-ebi.ac.uk:8400/)

• Check for protein stereochemistry

– MolProbity (http://molprobity.biochem.duke.edu/)

• Ramachandran plot, bond length etc

– Verify3D (http://www.doe-mbi.ucla.edu/Services/Verify_3D/)

• Check sequence vs structure

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Exercise 3

Not quite!

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Docking

Molecular Dynamics

Normal Mode Analysis

Recognition

Sampling

Catalysis

Motions

Folding

Homology Modeling

Transition metal

46

Fine Electronics = Quantum Based

QM and QM/MM

Simplicity of calculation of E

Wide space = Approx. Energy

Master in Bioinformaticsmscbioinformatics.uab.cat/base/documents/bioinformatics... · 2014. 11....

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Transcript of Master in Bioinformaticsmscbioinformatics.uab.cat/base/documents/bioinformatics... · 2014. 11....