Biocomputing: Molecular Modeling and Dynamics

Roland Stote IGBMC

Groupe de Modélisation Moléculaire

rstote@igbmc.fr

From structure to dynamics: An introduction to molecular

dynamics simulations Roland H. Stote

IGBMC Illkirch, France

The challenges!

Outline

•  General introduction – motivation •  Development of molecular model •  Molecular dynamics simulations – theory and practice •  Examples

Protein Structures

2012 1972

1998...Structure de l'ATP synthase F0F1

Abrahams JP, Leslie AG, Lutter R, Walker JE. * Structure at 2.8 A resolution of F1-ATPase from bovine heart mitochondria., Nature. 1994 370 p621.

* prix Nobel chimie 1997

F0/F1 ATP synthase

Noji et al (1997) Nature 386, 299-302

Modeling of Biological Macromolecules

•  Structural biology –  3D structure of proteins from biophysical methods (NMR,

XRAY …) –  Molecular mechanisms of biological function from 3D

structure

•  Bioinformatics: –  Analysis of sequence and identification of protein families

•  Molecular modelling = Structural bioinformatics = Computational structural biology –  3D structural models (uses bioinformatics) –  Molecular mechanisms of biological function beyond static

3D structure: dynamics

Modeling of Biological Macromolecules

•  Understand and predict structure-function-dynamics relationship in biomacromolecules (using molecular models).

•  Structure: how the parts of the whole complex are arranged and how this may be important for function.

•  Function: once relationships are understood, how do individual elements contribute?

Function •  Biochemical: related to

chemical reactions that occur in living organisms.

•  Reactions are intertwined with interactions.

A model: to do what? –  Gain time

•  Sequence alignment coupled with known structures => model structure for homologous sequences.

•  Search for active molecules: virtual screening

–  Overcome experimental difficulties •  Expression, solubility

–  Understand fundamental aspects of structure-function relationships => reliable predictions

•  Protein folding •  Flexibility in molecular recognition •  Energetics and kinetics of protein-protein (ligand) association

What is a molecular model?

1958, Myoglobin, Kendrew Nobel 1962

Computer representation

http://www.liv.ac.uk/Chemistry/Links/links.htm-> Mol.Modelling -> Molecular Modelling Techniques @ Geneva CH

Quantum Mechanics •  Energy as a function of structure

•  Molecular Structure (covalent and 3-dimensional)

•  ab initio

–  Resolution of the Schrödinger equation:

–  simplification : the Born-Oppenheimer approximation

–  Electronic structure for a given configuration.

•  High computational cost: –  O(N2) N: number of electrons

!! E=H

!total (nucleus,electrons) =!(electrons)!(nucleus)

Starting point: 3D Structure

•  Spatial localization of : atoms, secondary structure, domains, entire proteins, organelles, ....

•  Generally: a cartesian coordinate set

•  From visualization to calculations: mathematical description of the forces that maintain the structure together.

•  Models of structure, interactions, motions, assembly, dynamics ....

STRUCTURE, ASSEMBLY, DYNAMICS

•  The interactions underlying the folding, assembly and dynamics

of molecules are the same at all scales from very small (e.g. water, drug molecules) to very large (e.g. antibodies, virus capsids).

•  However, some important properties/effects seen in biological

macromolecules arise because of their size/complexity: allosteric communication, membrane formation.....

•  Importance of collective behaviour

What must the model do? •  Correctly estimate interaction strengths:

•  Correct estimates of interactions strength are essential to understand the stability, affinity and specificity of macromolecular assemblies

•  Strength generally refers to the free energy change associated with the interaction

•  Correctly estimate how energy varies with changes in structure •  Important for prediction & analysis of stability of structures •  Essential for studying dynamics: interconversion between

structures, assembly

Example: hydrogen bond geometry of formamide dimer

Morozov A V et al. PNAS 2004;101:6946-6951

Formamide dimer hydrogen bonding energies (kcal/mol) vs. δHA (Å), Ψ, θ, and X (°)

Development of the Potential Energy Function

MODELLING MOLECULAR INTERACTIONS

Which interactions?

Mathematical formulation

ETotal = Kl (l ! le )2 +

liens" Ka (! !!e )2 +

angles" Vn2torsions

" 1+ cos n" !#( )#$ %&+ 4!ij" ijRij

'

())

*

+,,

12

!" ijRij

'

())

*

+,,

6#

$

--

%

&

.

.+ k

qiqjRij

'

(

))

*

+

,,

i< j"

!

"dEpotdr

= F = "kr

!

E(r) = k rdr = 12kr2

0

r

"

Harmonic oscillator •  Covalent bond and valence angle energies are described by a

harmonic oscillator •  A particle of mass m subjected to a force F proportional to its

displacement (from the origin)

•  This system is described by Hooke’s force law. It is a

mathematical formulation that allows only small displacements around the origin

•  Potential energy :

Force and energy for a quadratic potential

!

E(r) = k(r " r0)2

F(r) = "2k(r " r0)

E( r )

F( r )

In macromolecules, displacement is not around origin, but around an equilibrium bond length r0

Covalent bonds

!

liensE = lKliens"

2(r#r0)

0.0000

200.0000

400.0000

600.0000

800.0000

1000.0000

1200.0000

-1.500

-1.000

-0.500

0.000 0.500 1.000 1.500

Angstrom

En

erg

ie e

n K

cal

K=500

K=1000

A displacement

of 0,1Å has an

energy cost of :

10Kcal/mol

Covalent bonds

•  Different covalent bonds have different strengths –  Expl: Allinger (MM3 force field)

Valence angles

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

-30 -20 -10 0 10 20 30

K=50K=100

Ener

gy (k

cal/m

ol)

Δθ

Valence angles

!

anglesE = aKangles"

2(#$#0)

Usual Units

• Energy : 1kcal = 4.1840 kJ • Length : 1 Å = 0.1 nm = 10-10 m

Å for ångström, bond length is 1 to 2 Å

• Angles: degrees or radians

SMALL DISPLACEMENTS

Bond stretching

Angle Bending

Mathematical formulation

ETotal = Kl (l ! le )2 +

liens" Ka (! !!e )2 +

angles" Vn2torsions

" 1+ cos n" !#( )#$ %&+ 4!ij" ijRij

'

())

*

+,,

12

!" ijRij

'

())

*

+,,

6#

$

--

%

&

.

.+ k

qiqjRij

'

(

))

*

+

,,

i< j"

Dihedral angles

•  Different deformation: rotation around single bonds

•  Important element of flexibility and conformational freedom in macromolecules, for example, φ, ψ proteins

•  Larger amplitude motion

•  Periodicity in the energy (to account for symmetry) has to be introduced

DIHEDRAL

An energy function that describes rotation around single bonds correctly must be periodic: sine/cosine

Vn

!

dièdresE = nV21+ cos n" # $( )[ ] Vn barrier

n périodicity

τ (φ) dihedral angle

γ phase

Vn

n = 3; γ = 0

Improper dihedral and out of plane motion

Copyright " Molecular Modeling : Pinciples & Applications; Leach AR; Prentice Hall; ISBN 0-582-38210-6"!Reproduction ULP Strasbourg. Autorisation CFC - Paris!

Mathematical formulation

ETotal = Kl (l ! le )2 +

liens" Ka (! !!e )2 +

angles" Vn2torsions

" 1+ cos n" !#( )#$ %&+ 4!ij" ijRij

'

())

*

+,,

12

!" ijRij

'

())

*

+,,

6#

$

--

%

&

.

.+ k

qiqjRij

'

(

))

*

+

,,

i< j"

Cohesion of a molecular structure (3D): interatomic forces

•  Electrostatic Interactions

•  van der Waals Interactions

Nonbonded Interactions: electrostatics

elE = k iq jq

ijRi! j"

+1

+1

Rij

Rij Eeel Å Kcal/mol 2 166 5 66 10  33 50 7

Coulomb’s law

qi, qj charges k constant that reflects energy units and environment The energy decreases slowly (1/Rij)

Electrostatic Interactions

0 2 4 6 8 10

+1 +1 ou -1 -1

+1 -1

+1 +1

-1 -1

-1 +1

The energy decreases slowly (1/Rij)

Ener

gy (k

cal/m

ol)

Rij (Å)

Electrostatics: partial charges •  In a force field, the atoms are assigned partial (non-integral)

charges that together reflect the electronic distribution.

•  These charges depend on properties such as electronegativity, chemical bond types, etc.

•  TOTAL charge of a molecule must always be integral.

•  Partial charges can not be measured, however they must be consistent with experimental data, as the dipole moment.

OHH

+0,4

-0,8

+0,4

•  Intuitively, excess electrons should be near around the oxygen with deficient electron density around the hydrogens

•  Dipole moment (in solution) µ = 2,6 Debyes

•  The distances ri are given by the geometry, so the

charges must be coherent with µ

δ+ δ+

δ- Example: water: H2O

!

µ =iq ir

i"

!

elE = +1" 2 " 0.4rNa#H+#0.8rNa#O

$

% &

'

( )

Coulomb’s Law

+0,4

Na+ -0,8

+0,4

Cl- +0,4

+0,4

-0,8

!

elE = "1# 2 # 0.4rCl"H+"0.8rCl"O

$

% &

'

( )

Absolute value of Eel is the same for Na+ et Cl- (if distance are equal)

From Coulomb’s law, the interaction energy between charges is additive (no approximation)

Ecoulomb=i< j!

qiqjRij

Electrostatic surface

Nonbonded Interactions : van der Waals interactions

•  Interactions are present even in rare gas dimers

•  Exchange-repulsion: repulsion between electrons of atoms in close proximity and the Pauli exclusion principle: atoms have a volume "hard sphere"

•  dispersion: interaction due to instantaneous dipole created by fluctuating electron clouds (1/R6) even if the charge distribution is symmetric (no electrostatic interaction)

van der Waals Interactions

!

vdwE = 4"ij12

# ijRij

$

% & &

'

( ) ) *

6

# ijRij

$

% & &

'

( ) )

+

,

- - - -

.

/

0 0 0 0

!

ij" = "ii" jj

!

ij" = ii" + jj"

2

ε

σ

Re

Units: εij kcal/mol; σij, Rij : Å

i j

Lennard-Jones potential

van der Waals potential

Les interactions

Copyright " Atoms & Molecules : An Introduction For Students of Physical Chemistry ; Karplus M, Porter RN; The Benjamin/Cumming Publishing Company » Reproduction ULP Strasbourg. Autorisation CFC - Paris

ETotal = Kl (l ! le )2 +

liens" Ka (! !!e )2 +

angles" Vn2torsions

" 1+ cos n" !#( )#$ %&+ 4!ij" ijRij

'

())

*

+,,

12

!" ijRij

'

())

*

+,,

6#

$

--

%

&

.

.+ k

qiqjRij

'

(

))

*

+

,,

i< j"

•  Energy surface: classical MM force field

•  Bonded terms maintain covalent structure

•  Non bonded terms describe interactions between atoms not directly linked by chemical bonds

!

Ebonded = Kl (l " le )2 +

bonds# Ka ($ "$e )2 +

angles# Vn2torsions

# 1+ cos n% " &( )[ ]!

ETotal (XN ) = Ebonded (X

N ) + Enonbonded (XN )

XN : atomic positions

Van der Waals

Electrostatics (H bond)

ENonbonded = 4!ij" ijRij

!

"##

$

%&&

12

'" ijRij

!

"##

$

%&&

6(

)

**

+

,

--+ k

qiqjRij

!

"

##

$

%

&&

i< j.

Approximations of the equation

Harmonic potential approximation

•  No dissociation

•  No chemical reaction

Approximations

•  No coupling between e.g. bond stretch and angle bend

•  Description of electrostatics with fixed charges

ETotal = Kl (l ! le )2 +

bonds" Ka (! !!e )2 +

angles" Vn2torsions

" 1+ cos n" !#( )#$ %&+ 4!ij" ijRij

'

())

*

+,,

12

!" ijRij

'

())

*

+,,

6#

$

--

%

&

.

.+ k

qiqjRij

'

(

))

*

+

,,

i< j"

Intermolecular: pair-wise sum

•  The total interaction energy of N atoms is the sum of the interaction energies between all atom pairs.

•  This approximation significantly reduces the computational cost.

•  However, this approximation amounts to the neglect, of electronic polarization.

EIntermolecular = 4!ij" ijRij

!

"##

$

%&&

12

'" ijRij

!

"##

$

%&&

6(

)

**

+

,

--+ k

qiqjRij

!

"

##

$

%

&&

i< j. i, j : atoms

Classical Molecular Mechanics Force Field • Characterized by the mathematical form of Epot and the

parameters used in Epot • Mathematical form: dependance on 3D structure

• Several approximations invoked

• Parameters: strength of interactions, need to be calibrated

• Determine the final quality of the predictions • Find the best compromise between accuracy and

calculation speed

Approximations: parameters

•  Covalent Interactions (bonds, angles, dihedrals): •  X-ray geometry, spectroscopy (IR) frequencies •  Quantum mechanics: geometry and frequency

•  Nonbonded Interactions •  Interactions in the gas phase •  Heat of evaporation / sublimation •  Solvation energies •  dipoles •  Quantum mechanics interaction energies

•  Which molecules?

From where do the parameters come?

Parameters for bond, angles from vibrational frequencies

•  Basic equation for bond (angle) elongation:

!

E(r) = k(x " x0)2

F(r) = "2k(x " x0)

!

E(r) = k2(x " x0)

2

F(r) = "k(x " x0)

or

Harmonic oscillator •  From Newton second law :

•  Thus :

•  This is a differential equation for a particle that has a

trajectory x=x(t) :

kxdtxd

mF !== 22

mkx

dtxd !=2

2

!!"

#

$$%

&'(

)*+

,+!!"

#

$$%

&'(

)*+

,= tmk

Btmk

Atx2/12/1

cossin)(

Harmonic oscillator •  If x=0 when t=0 we have :

•  The particle oscillate in a sinusoidal fashion between –A and +A : !

x(t) = Asin km"

# $

%

& ' 1/ 2

t(

) *

+

, -

x

t

A

!

T = 1"

-xo

xo

0

Harmonic oscillator •  If x=0 when t=0 we have :

•  The particle oscillate in a sinusoidal fashion between –A and +A :

!

x(t) = Asin km"

# $

%

& ' 1/ 2

t(

) *

+

, -

x

t

A

!

T = 1"

-xo

xo

0

Harmonic oscillator •  The characteristics of the motion are :

!

mred =m1m2m1 + m2!

T = 2" mk

#

$ %

&

' ( 1/ 2

!

v = 12"

kmred

!

" =1#

="c

Period(s) Frequency (s-1) Wave number (cm1)

Reduced mass, m1, m2 oscillating masses

c = 3 x1010 cm/s (speed of light)

λ wavelength

k force constant

Harmonic oscillator •  The characteristics of the motions are :

!

A = 2Ek

A amplitude

E total energy

Experimental spectroscopy

Absorption of light will happen if there is a match between the intrinsic frequencies of the system and the frequency of incident light.

*If the frequency of the IR light matches the frequency of the molecular vibration, light will be absorbed by the molecule and the amplitute of the vibration will increase.

IR spectrum of 1-butanol, CH3CH2CH2CH2OH

Wavenumber, ν, cm-1

%T

O-H stretch C-H stretch C-H bend C-O stretch

4000 500

IR absorption corresponds to frequency of bond vibration, ie stretching

Examples of frequencies

!

~

" =12#c

km$

% &

'

( ) 1/ 2

Copyright " Atoms & Molecules : An Introduction For Students of Physical Chemistry ; Karplus M, Porter RN; The Benjamin/Cumming Publishing Company"

Reproduction ULP Strasbourg. Autorisation CFC - Paris

Basic units •  Energy : 1kcal = 4.1840 kJ •  Length : 1 Å = 0.1 nm = 10-10 m

–  Å for ångström, bond length 1-2 Å •  Mass : 1Da = 1 u = 1.66053.10-27 kg

–  1 Da : 1 Dalton –  1 u : unified mass atomic unit –  1 u = 1/12 of C12 mass

•  Time : –  1 fs = 10-15 s; femto 1 ps = 10-12 s; pico –  1 ns = 10-9 s; nano 1 µs = 10-6 s; micro

Potential Energy Function

•  Etotal = E(x1, y1,z1,………………….xN, yN, zN)

•  The energy is composed of both internal (bonded) terms and external (nonbonded) terms

•  The energy is a function of 3N variables •  N: total number of atom in the system

•  Describes a potential energy hypersurface

Energy Surface

Exploration of this hypersurface, can identify the biologically relevant structures/pathways

Certain structures are more interesting than others :

Minimum : stable structures Saddle Point : transition states

Dynamics of Macromolecules

•  Local Motions –  (0.01 to 5 Å, 10-15 to 10-1 s)

–  Atomic Fluctuations –  Side chain motions –  Rigid body motions

–  (1 to 10 Å, 10-9 to 1 s) –  Helix motions –  Domain motions –  Sub-unit motions

•  Large-scale motions •  helix-coil Transitions –  Dissociation/Association –  Folding/Unfolding

•  Biological function requires flexibility

Molecular Dynamics simulations •  One of the principle tools for modeling proteins, nucleic acids and

their complexes. •  Stability of protéines •  Protein Folding •  Molecular recognition: Proteins, DNA, RNA, lipids, hormones, ATP,

etc. •  Enzymatic reactions •  Rational drug design •  Conformational searching and study of large-scale conformational

changes •  Determination et construction of 3D structures (homology, X-tal,

NMR) •  Ion transport in biological systems.

Alder (1957): First Molecular Dynamics (MD) simulation of a liquid (hard spheres) Rahman (1964): First MD simulation with Lennard-Jones potential McCammon & Karplus (1977) First MD simulation of proteins Karplus (1983): The CHARMM general purpose FF & MD program Kollman(1984): The AMBER general purpose FF & MD program Car-Parrinello(1985): First full QM simulations Kollmann(1986): First QM-MM simulations

Incomplete historical perspective

Classical Molecular Dynamics

•  Newton’s Equations of Motion

•  Position, velocity and acceleration as a function of time ri(t); vi(t); ai(t)

•  The force coupled acceleration to the potential energy.

•  Integration the equations of motion => Initial structure: ri(t=0); initial velocity distribution: vi(t=0)

Fi =mi !ai =mi !dvidt

=m ! d2ridt2

Fi = !"iE

v(t) = dx(t)dt

x(t) = v ! t + x0 = a !t2

2+ v0t + x0

Simple Case study : a particule in one dimension

•  Acceleration:

•  If a is constant a≠f(t)

•  Velocity: •  Position:

•  The trajectory x(t) is obtained by integration taking into account the positions and the initial velocities (x0 et v0)

a = dvdt

v(t) = at + v0

Numerical Integration •  Development of Taylor series

•  If we are at x at time t, after a Δt we find ourselves at x(t+Δt)

•  We restart from the coordinates x(t+Δt) •  To go from x(t) to x(t+Δt) corresponds to having done one step of dynamics •  The change in velocity from v(t) to v(t+Δt) can be calculated in the same way •  The acceleration is recalculated at each step from the gradient of the energy,

E(r)

x(t) = x0 + v0t + a0t2

2+ 0

'a t3

3!+O(t4 )

x(t + !t) = x(t) + v(t)!t + F(t)m

!t2

2+F' (t)m

!t3

3!+O(!t4)

Principle of a trajectory

t0

t0+Δt

t0+2Δt

t0+4 Δt

t0+7Δt

Principle of a trajectory

t0

t0+Δt

t0+2Δt

t0+4 Δt

t0+7Δt

Principe de la trajectoire

t0

t0+Δt

t0+2Δt

t0+4 Δt

t0+7Δt

Principle of a trajectory

t0

t0+Δt

t0+2Δt

t0+4 Δt

t0+7Δt

Integration algorithms

Verlet, Velocity Verlet LeapFrog, Beeman • Choice of algorithm :

– Conservation of energy of the system – Minimal computational cost – Largest integration time step possible

To be able to integrate Newton’s equations as described one NEEDS" initial structure: xi(t=0);! Initial velocities for all atoms: vi(t=0) "

Initial position xi(t=0)"Xray"NMR"Model"

Initial velocities vi(t=0) : linked to temperature"""

Acceleration"Calculated from the forces, i.e. derivatives of potential energy """

Trajectory of a macromolecule!

32NkT = mivi

2

2i!

a = ! 1mdEdr

Modeling of Biological Macromolecules

•  Understand and predict the relationship between structure, dynamics and function in macromolecules using computational models.

•  Calculate and predict molecular properties

Molecular dynamics trajectory!

Calculate forces Integrate for t=Δt

New coordinates and velocities

Some time averaged properties that can be calculated from molecular dynamics

•  Average energy

•  RMS between 2 structures (ex : initial and final structures)

•  Atomic Fluctuations

•  Temperature Factors

•  Radius of gyration

Molecular dynamics simulation programs

AMBER

CHARMM

NAMD

POLY-MD

etc

http://www.pharmacy.umaryland.edu/faculty/amackere/research.html

Practical Aspects •  Choice of integration time step Δt

>  Take the longest time step that is compatible with a correct numerical integration

>  1 à 2 fs (10-15 s) for an all-atom force field

•  Nonbonded Interactions: the most time consuming to calculate >  The cost is proportional to N2 (N number of atoms) >  Truncation

4! ij" ijrij

#

$ % %

&

' ( (

12

)" ijrij

#

$ % %

&

' ( (

6*

+

, ,

-

.

/ / +

qiqj!rij

0 1 2

3 2

4 5 2

6 2 i, j7

Truncation

•  SWITCH Bring the potential to zero between ron and roff. The potential is not modified r < ron is zero r > roff

•  SHIFT Modify the potential over the entire range of distances such that the potential is zero r > rcut

Treatment of solvent •  Implicit: intramolecular

interactions( between atoms of the macromolecule) only and with scaled electrostatic interactions in order to take into account solvent effects.

•  All the solvent effects are in the dielectric constant ε

Vaccum ε =1 protein ε = 2-20 Water ε = 80

Eelec r( ) = Aqiqj!r

Treatment of solvant •  Explicit Representation

The macromolecule is surrounded by solvent molecules (water, ions) with which it interactions via expliocit nonbonded interactions

•  One must use ε =1 in this case •  More correct, but more expensive.

4! ij" ijrij

#

$ % %

&

' ( (

12

)" ijrij

#

$ % %

&

' ( (

6*

+

, ,

-

.

/ / +

qiqjrij

0 1 2

3 2

4 5 2

6 2 i, j7

Periodic Boundary Conditions •  Explicit representation of

solvent •  One must define the

borders of the system

•  Periodic system Permits one to model a very large (infinite) system through the introduction of periodicity

Other boundary conditions Solvation sphere : finite system

Around an entire macromolecule Around just an active site

Simulation Protocol Initial Coordinates

Coordinates X-tal or NMR from the Protein Data Bank (Coordinates constructed by homology modeling)

Treatment of nonbonded interactions Choice of truncation

Treatment of solvent implicit: choice of dielectric constant explicit: protocol of solvation

If using explicit solvent, need to choose boundary conditions periodic conditions Solvation sphere Active site solvation

Integration time step

Steps of a molecular dynamics simulation

www.pdb.org

Energy Minimization

• Steepest decsent: slowly converging

• Conjugate gradient: more efficient, use for larger systems

• Newton-Raphson: calculates both the slope of energy and the rate of change

Change conformation to decrease energy of the molecule

The initial velocities are calculated from a Gaussian distribution or from a Maxwell Boltzman distribution at a given temperature.

Assignment of intial velocities

!

P(v) = F v( )dv =v 2 exp "mv 2 /2kT( )dv

v 2 exp "mv 2 /2kT( )dv0

#

$

Velocity(m/s)

P(v)

300K

….

100K 50K

time

Temperture in K

Heating and Equilibration Production

Equilibration of the system

Molecular Dynamics Simulation

Example of Molecular Dynamics: Spontaneous folding of Staphylococ Protein G, Segment B1 (56 AA, Four stranded beta-sheet and an alpha helix) One can see the spontaneous formation of -hydrophobic core -H-bonds REAL duration 10 ns (10-8 s) From: http://xray.bmc.uu.se/~michiel/research.php

Real Case Example

An application of Molecular Dynamics Simulations!

The acetylcholinesterase story!(From the McCammon Group, U. San Diego, USA)!

Neuromuscular junction: motor neurons : muscle cells

Acetylcholinesterase!

•  Acetylcholinesterase (AChE) is an enzyme that hydrolyzes ACh to acetate and choline to inactivate the neurotransmitter"

•  A very fast enzyme, approaching diffusion controlled."

•  Inhibitors are utilized in the treatment of various neurological diseases, including Alzheimerʼs disease."

•  Organophosphorus compounds serve as potent insecticides by selectively inhibiting insect AChE."

1EA5

Title Native Acetylcholinesterase (E.C. 3.1.1.7) From Torpedo Californica At 1.8A Resolution Classification Cholinesterase Compound Mol_Id: 1; Molecule: Acetylcholinesterase; Chain: A; Ec: 3.1.1.7 Exp. Method X-ray Diffraction

Access of ligands to the active site is blocked --> requires fluctuations

Molecular Dynamics Simulation of Acetylcholinesterase

•  10 ns simulations •  Protein obtained from the Protein Data Bank (PDB) •  Structure solved by x-ray crystallography •  Solvated in a cubic box of water •  Ions added to neutralize the system •  Periodic Boundary Conditions •  Treatment of Long-Range electrostatic interactions •  Total of 8289 solute atoms and 75615 solvent atoms

•  Biophysical Journal Volume 81 715-724 (2001)

Molecular Dynamics Simulation of

Acetylcholinesterase

Molecular Dynamics Simulation of Acetylcholinesterase

•  Time dependence of the root mean square deviation (RMSD)

Molecular Dynamics Simulation of Acetylcholinesterase