An introduction into “Docking” and “Molecular Dynamics ... · Department for Biosimulation and Bioinformatics Medical University of Vienna / AKH (General Hospital) [email protected]

23.02.2012 Bernhard Knapp 1

An introduction into

“Docking”

and

“Molecular Dynamics simulations”

Univ. Ass. Dipl.-Ing. (FH) Dr. scient. med. Bernhard Knapp

Center for Medical Statistics, Informatics and Intelligent Systems

Department for Biosimulation and Bioinformatics

Medical University of Vienna / AKH (General Hospital)

[email protected]


TOC

1. Basic biology knowledge

2. Docking

• Docking in general

• Example AutoDock

3. Molecular Dynamics

• Introduction

• Limitations

• Example Gromacs

3. Tutorial on PDB / jmol


Basic biology knowledge

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4

Amino acids

Build up proteins (german “Eiweiß”)

all have the same basic structure (“backbone” consisting of an amine group, a carboxylic acid group and a C-alpha atom) but differ in their side-chain => residue (the side chain defines which AA it is)

20 different canonical amino acids (AAs) are existing (that means 20 different side-chains)

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Wikimedia


Several amino acids are connected via „peptide bonds“

Wikimedia


peptide: > 1 AAoligopeptide: < 10 (other sources state 30)polypeptide: > 10 AAsprotein: > 50 AAsmacropeptide: > 100 AAs

monopeptide: 1 AAdipeptide: 2 AAtripeptide: 3 AAtetrapeptide: 4 AApentapeptide: 5 AAhexapeptide: 6 AAheptapentide: 7 AAoctapeptide: 8 AAnonapeptide: 9 AAdecapeptide: 10 AAundecapeptide: 11 AAs...icosapeptide: 20 AAstricontapeptide: 30 AAstetracontapeptide: 40 AAs

Then they are called:

… however the exact definitions differ (and you do not need to learn them for the examination of this lecture!)


Structure levels

Primary structure: the pure sequence of the AAs

Secondary structure: e.g. beta-sheet, alpha-helix, or turns

Tertiary structure: 3D arrangement of secondary structure elements

Quaternary structure: several proteins together

Wikimedia

23.02.2012 9

How we can illustrate them(also see the tutorial at the end)

And whatabout thesize ofproteinsand AAs?

[Janeway]

~13x6x5 nm~20x20x20 nm

1 Nanometer == 10-9m == 0.0000000001m


2 more definitions:

Ligand: also known as (small) peptide, epitope, guest, antigenic determinant

Receptor: also known as (big) protein, host, macro molecule


Docking in general


What does docking mean?

trying to find the „best matching“ between 2 molecules

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(„induced fit“)

Let us try with this one …

Who could fit to me?



[Kitchen et al., 2004]


Why is docking useful?

Docking (~Virtual Screening) is of paramount interest for drug discovery

For one target millions of different possible drugs can be tested

The best n matches will be tried in experiments

Will save time, resources and money


Usually 3 steps

1) Decide how to search through the spatial space

2) Decide how flexible ligand and receptor can be

3) Decide how to score various parameter sets

23.02.2012 Bernhard Knapp 20 B h d K

Where is the difficulty?

1) 6 degrees of freedom in 3d space (3 translational, 3 rotational)

2) 100+ degrees of freedom if we consider full flexibility of all bounds

3) nearly each atom interacts witch every other one


Ad 1) Search Algorithms used (for spatial space)Systematic docking

- Brute Force

- Fragmentation

- Database

Heuristic docking

- Monte Carlo

- Genetic algorithms

- Tabu search

Simulations Docking

- Molecular Dynamics

- Gradient (Energy) Methods


Ad 2) Deciding about the flexibility“rigid body” docking

- receptor and ligand are considered as 100% rigid

- very fast (6dfs only), but inaccurate

“induced fit” docking

- moveable [backbone| side] chains

“flexible ligand”

- only the ligand is considered als flexible, the receptor remains rigid

“full flexibility”

- computational very expensive


Ad 3) Scoring functions (1/2)

Force Field based scoring function

- energy of the interaction and internal energy of the ligand

- combination of : Van der Waales, Lennard Jones, electrostatic energy, …

- e.g. D-Score, GoldScore, AutoDock, CHARMM, …

empirical scoring functions

- Trying to reproduce experimental observed docking behaviors by means of formulas

- usually the sum of uncorrelated terms

- e.g. LUDI, F-Score, SCORE, X-SCORE, …


Scoring Funktionen (2/2)

Knowledge based scoring function

- trying the deduce rules form experiments

- e.g. DrugScore, PMF, …

Geometrical scoring function

- based on shape complementarity

- e.g. Connely Surface, Soft Belt Scoring

Consensus scoring function

- hybrid versions

- e.g. various Review Papers: [Trost, 2005]

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Difference between position score and rank score

„The pose score is often a rough measure of the fit of a ligand into the active site. The rank score is generally more complex and might attempt to estimate binding energies.“

"relatively small chemical modifications can lead to significant changes in binding."

[Kitchen et al., 2004]

23.02.2012 Bernhard Knapp 26 [Sousa, 2006]

23.02.2012 Bernhard Knapp 27 [Sousa, 2006]

23.02.2012 Bernhard Knapp 28 23232322222232232222222 .02.2012 Bernhard

Correct result vs incorrect result


… and what about the correctness and reliability?

Currently correct results are more or less restricted to the area where the tools have been calibrated

e.g. for pMHC the area under the ROC is between 0.5 and 0.75 using different substitution and scoring tools [Knapp, 2008]

But

"We have long known that there is nothing in biology which is fundamentally inconsistent or incommensurable with mathematics, chemistry, and physics. Biology long ago rejected vitalism. The only information needed for life is provided by an organism's chemical constituents. It is unlikely in the extreme that living systems cannot be understood in terms of chemistry and physics.“ [Wan, 2008]


Example Autodock


What is Autodock

“AutoDock is a suite of automated docking tools. It is designed to predict how small molecules, such as substrates or drug candidates, bind to a receptor of known 3D structure. AutoDock actually consists of two main programs: AutoDock performs the docking of the ligand to a set of grids describing the target protein; AutoGrid pre-calculates these grids. In addition to using them for docking, the atomic affinity grids can be visualised. This can help, for example, to guide organic synthetic chemists design better binders.”

url: http://autodock.scripps.edu/


search algorithms used for spatial spaceSystematic docking

- Brute Force

- Fragmentation

- Database

Heuristic docking

- Monte Carlo

- Genetic algorithms

- Tabu search

Simulations Docking

- Molecular Dynamics

- Gradient (Energy) Methods


Deciding about the flexibility“rigid body” docking

- receptor and ligand are considered as 100% rigid

- very fast (6dfs only), but inaccurate

“induced fit” docking

- moveable [backbone| side] chains

“flexible ligand”

- only the ligand is considered als flexible, the receptor remains rigid

“full flexibility”

- computational very expensive


Scoring functions (1/2)

Force Field based scoring function

- energy of the interaction and internal energy of the ligand

- combination of : Van der Waales, Lennard Jones, electrostatic energy, …

- e.g. D-Score, GoldScore, AutoDock, CHARMM, …

empirical scoring functions

- Trying to reproduce experimental observed docking behaviors by means of formulas

- ususlly the sum of uncorrelated terms

- e.g. LUDI, F-Score, SCORE, X-SCORE, …


Scoring Funktionen (2/2)

Knowledge based scoring function

- trying the deduce rules form experiments

- e.g. DrugScore, PMF, …

Geometrical scoring function

- based on shape complementarity

- e.g. Connely Surface, Soft Belt Scoring

Consensus scoring function

- hybrid versions

- e.g. various Review Papers: [Trost, 2005]


Autodock: sampling of spatial space (1/4)

Simulated Annealing

Different solutions

Qua

lity

of s

olut

ion

Global min

Random start up position, e.g. here

Stack in local min


Autodock: sampling of spatial space (2/4)simulated annealing (german “abkühlen”) procedure:

Idea: local neighborhood search but „sometimes“ accepting worse solutions (certain probability)

Similar to annealing of crystals in physics

1. Melt a solid body in a heating pot

2. Atoms are almost randomly distributed

3. Slowly anneal

4. At each temperature a thermical balance is found

5. Atoms will arrange in an energetically advantageous position

TkEE

B

ij

ep


Autodock: sampling of spatial space (3/4)Genetic Algorithms

- A set a values is used to define the ligand, receptor and their current states

- Doing it as nature:

1. Creating random population of solutions

2. Evaluation of fitness

3. Selection of the fittest n solutions

4. cross over, mutation, …

5. goto 2 again

244678904339965

2366849092127844

244678909212544

×

P1 P2 C1


Autodock: Flexibility (1/1)

receptor hold rigid

ligands bounds have full flexibility according to a rotamer library

state of ligands bounds are represented as genes in the GA


Autodock: Scoring in 1998 (1/1)

12, 6 Lennard Jones potential

Hydrogen bounds, weighted by angle t

Electrostatic forces

Torsion angles

Solvation effects


Autodock2007: in general zero!


Autodock2007: unbound?

3 approches for the unbound state

Extended

Compact

Bound


Autodock2007


Autodock2007: the formula

the weighting factors W have been calibrated on a set of 188 recptor/ligand complexes with known experimental binding affinities

Coordinates from the protein data bank (www.pdb.org)

Binding data from ligand-protein database (http://lpdb.scripps.edu/)


Autodock2007: AD3 vs AD4


Autodock2007: successrate against exp data

75 cases: found but other scored better

67 cases: found and scored best

28 cases: not found

=> 84% of all ligands found


Video Autodock

[published on Autodock Homepage]

23.02.2012 48

Biologists have often concerns about the success of computational techniques. [Jorgensen, 2004] nicely summarizes such a situation:

“’Is there really a case where a drug that’s on the market was designed by acomputer?’ When asked this, I invoke the professorial mantra (’All questions are good questions.’), while sensing that the desired answer is ’no’. Then, the inquisitor could go back to the lab with the reassurance that his or her

choice to avoid learning about computational chemistry remains wise.”

So what is the role of computers in drug discovery?


Take home messages for the first part

Computational methods can be used to identify potential drugs

They can help to reduce the number of candidates to test or predict a set of possible candidates. However, they can not predict the one and only working substance in one step

The methods are diverse

Nowadays there is still much space for improvement of the methods

"The day is coming when theory and computation will guide biology, as it does physics now.“ [Wan, 2008]


Molecular Dynamics (MD)


Introduction

MD is a type of computer simulation

Atoms interact under given laws of physics for a specified time

MD can be seen as an interface between “wet”-lab experiments and theoretical models

Used to analyze the spatial and energetic dynamics of e.g. bio-molecules, materials, …

Usually very computational power and memory consuming

Calculate forces between all atoms of the system …

… but what does forces mean?

A combination of bonded and non-bonded interactions …

n=6, usually n>1000

Bonded interactions

bond length

bond angle

torision

= = 12 = =

= arc cos × ×× ×= 12 1 +

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What does the „bond length“ term really mean?

[Shaw et al.]

perfect

too faraway

tooclose

23.02.2012 55

What does the „bond angle“ term really mean?

[Shaw et al.]

perfect

too big

toosmall

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What does the „torsion“ term really mean?

[Shaw et al.]

perfect

tilted

Non bonded interactions

Coulomb

Lennard-Jones

= 12 +

= 4

=

23.02.2012 58

What does the „coulomb“ term really mean?

[Shaw et al.]

23.02.2012 59

What does the „Lennard-Jones“ term really mean?

[Shaw et al.]

perfect

too faraway

tooclose

This all together is called a „force field“

… and of course the real implementations are waymore complicated. There are several softwarepackages available (e.g. GROMACS, AMBER, CHARMM, Schroedinger, …)

We divide time into discrete time steps of e.g. 1 fs (= 10-15 s)

…

t -> 10 000 000 fs (=10 ns)0 fs

What can we do with this force field?

… and calculate the forces for each time step while adjusting the postions

Iterate …and iterate …and iterate …and iterate …and iterate …

[from wikipedia]

Finally we get something like this:

In reality however more like this:


„The equations are solved simultaneously in small time steps. The system isfollowed for some time, taking care that the temperature and pressure remain atthe required values, and the coordinates are written to an output file at regularintervals. The coordinates as a function of time represent a trajectory of thesystem.“ [Gromacs Manual]


Define initial atoms positions

Calculate forces

Move atoms

Increment time

Stop criterionreached?

Flow diagram of a MD:


Example for MD simulation using Gromacs [Hess et al., 2008]

1. Obtain atom coordinates for the system to be simulated (e.g. pdbformat from www.pdb.org) (takes minutes to days, mostly depended on the human)

2. Validate the pdb file (takes seconds)

3. Create a virtual simulation box around the system (takes seconds)

4. Fill the box with artificial water (takes seconds)

5. Minimize the energy of the system (takes minutes to hours)

6. Warm the system up to room temperature (takes hours to days)

7. Start the real MD simulation (takes days to months)

8. Evaluate Results (takes minutes to years(!) depended on the human)


Example for MD simulation

0 ns 20 ns


Video MD-Simulation shown via VMD


Example for MD simulation


Limitations of MD simulations (1 of 2) (on the basis of Gromacs)

Newton’s equations of motion describe classical mechanics, not quantum mechanics (=> sometimes problems with e.g. hydrogen atoms)

Electrons are in ground state: they are supposed to adjust their dynamics when the atomic positions changes (Born-Oppenheimer approximation)

Force fields are approximate: balance between computational load and accuracy, their parameters can be user-modified

Force fields are pair additive: omission of polarization


Limitations of MD simulations (2 of 2) (on the basis of Gromacs)

Long range interactions are cutoff: only one image of each particle in the periodic boundary conditions is considered => cutoff can not exceed half the box size

Boundary conditions are unnatural: a lot of particles have vacuum as neighbor to avoid that periodic boundary conditions are used. => Sometimes the system is influencing itself

Computational costs and runtime (3 months for 20 ns!)

Cumulative errors in numerical integration and limitation in floating point representation


Evaluations of MD-trajectories

Now we have something like that:

… a huge set of individual configurations over time. But what does this agglomeration of single structures tell us?


RMSD

First idea: difference of the single frames (transparent) from starting structure (solid). Calculate the root mean square deviation:

N

i

Yi

Xi rr

NRMSD

1

21

Where N is the number of atoms, i is the current atom, rX is the target structure and rY is the reference structure.

Be careful if you compare structures with different positions and rotations in space. You will properly need to superimpose (fit) them first.


RMSD cont

The RMSD over time (in this case rY is the first frame)

All frames:

Frame with highest RMSD:



Radius of Gyration

A similar measurement is the radius of gyration. It measures the distance of the regions’ parts from its center of gravity. Or in other words how packed a certain region is.

E.g.

The radius of gyration is an interesting property since it can be determined experimentally using “static light scattering” as well as with “small angle neutron-” or “x-ray scattering”. This allows theoretical scientists to check their models against reality.


RMSF

Next idea: fluctuation of a particular amino acid over time. Calculate the “root mean square fluctuation”:

M

kikii rtr

MRMSF

1

2~)(1

Where M is the number of frames taken into account, ri(tk) is particle i of complex r at time k and r with tilde is the reference. This reference can for example be the average over a given time window.


RMSF cont



SASA

How much of a certain area is exposed to the solvent (e.g. a amino acid or a region)? Calculate the solvent accessible surface area

solvent

protein

(possible) target


SASA

Methodology to calculate the SASA:




Take home messages for the second part

MD is a computer simulation of “real” atom-atom interactions

MD is very time and resource consuming

The output trajectories are huge and various ways to analyze them are existing

There are still certain limitations


Tutorial on PDB / jmol

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Introduction TCRpMHC interaction on white board


www.pdb.org => 1mi5


right click => „console“select *cartoon offselect *:Cwireframe 100


Opinions, comments und suggestions?


Further literatureDocking:

Sousa SF, Fernades P, Ramos MJ. Protein-Ligand Docking Current Status and Future Challanges, Proteins 2006; 65:15-26.A semiempirical free energy force field with charge-based desolvation. Huey,R., Morris,G.M., Olson,A.J., and Goodsell,D.S. (2007). J Comput Chem. 28, 1145-1152.Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function. Morris, G. M., Goodsell, D. S., Halliday, R. S., Huey, R., Hart, W. E., Belew, R. K., and Olson, A. J. J.ComputationalChemistry 19, 1639-1662. 1998. Kitchen DB, Decornez H, Furr JR, Bajorath J. Docking and scoring in virtual screening for drug discovery: methods and applications, Nat. Rev. Drug Discov. 2004; 3:935-949.

Molecular Dynamics simulations:

Dodson GG, Lane DP, Verma CS (2008) Molecular simulations of protein dynamics: new windows onmechanisms in biology. EMBO Rep 9: 144-150.Karplus M, Kuriyan J (2005) Molecular dynamics and protein function. Proc Natl Acad Sci U S A 102: 6679-6685.Hess B, Kutzner C, vanderSpoel D, Lindahl E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J Chem Theory Comput 2008.

Documents

An introduction into “Docking” and “Molecular Dynamics ... · Department for Biosimulation and Bioinformatics Medical University of Vienna / AKH (General Hospital) [email protected]