Transcript ElLilkova_slides

Application of
metadynamics for
investigation of human
interferon gamma mutants
Peicho Petkov, Elena Lilkova, Petko Petkov,
Nevena Ilieva, Leandar Litov
2nd Regional Conference
“Supercomputing Applications in Science and Industry”
Sunny Beach, 21.09.2011
Introduction

Newton’s equations:
d
d2
V x t 
v t   x t 
F  2 x t   
dt

dt
Potential energy (forcefield):
x
V   Vs   Va   Vt   Vvdw   Ve  ...
Bond strength
Sum over all
bonds

Bond angle
Sum over
all angles
Torsion
Van der Waals
interactions
Free energy: F  T ln dx e
1
 V x 
T
Coulomb
interaction
Metadynamics
Metadynamics influences the
evolution of the system by
addition of a time-dependent
external potential,
constructed as a sum of
gaussians, centered along the
trajectory of a set of collective
variables.



 
V' ri , S(ri ), t  VG S(ri ), t  V ri
Metadynamics external potential


 S(r )  s(t' ) 2 
i
VG S(ri ), t  ω  exp

2
2δs
t'  τ G ,2 τ G ,..




t'  t


ω  height of the gaussians;
τ G  frequency at which the gaussians are added;
δs  width of the gaussians;

S ri  CV as explicit function of ri ;
st   value of the CV at the moment t
Basic assumption:
lim VG s, t  ~ Fs 
t 
Laio A, and Gervasio FL,
Metadynamics: a method
to simulate rare events and
reconstruct the free energy
in biophysics, chemistry and
material science.
2008, Rep. Prog. Phys. 71,
126601 (22pp).
Collective variables



The CVs are explicit functions of the
coordinates of the particles (or a group of
particles) of the investigated systems.
The set of CVs should be able to clearly
distinguish between the initial and the
final state and preferably the intermediates.
Ideally, the CVs should describe all the
slow events that are relevant to the
investigated process, but in the same time
their number should be small.
Human Interferon Gamma (hIFN)
PDB ID: 1fg9
Amino acids forming H-bonds with
receptor residues
Task
Aberrant IFNγ expression is associated with many
autoinflammatory and autoimmune diseases. The
task is to find a possible way to inhibit its activity by:
 Blocking the binding sites of hIFNγ
• Find a ligand binding hIFNγ and blocking its
activity
 Blocking the binding receptors (hIFNγRα) on the
cell surface
• With mutated hIFNγ proteins, lacking
biological activity
• With some other ligand
Mutation site - 87Lys-88Lys-89Lys
IFNγ accomplishes its multiple
biological effects by activating
STAT transcription factors,
which are translocated to the
nucleus through a specific
nuclear localization
sequence (NLS) in the IFNγ
molecule. Two putative NLS
have been pointed out in the
hIFNg, one of which is located
in helix E (residues 83-89).
100 random mutations
These residues do not take part in the interaction between
hIFNγ and its cell-surface receptor, but participate in
inducing biological effect in the cell.
Metadynamics model


Colective variables – the backbone torsional angles φ
and ψ of the amino acid which is on position 87;
The reconstructed free energy profiles in the space,
defiend by φ and ψ were assessed by:
• Similarity with respect to the FES profile of the
native hIFNγ:
S
•
1
n
n
 E , ψ   E  , ψ 
i1
2
i
i
ref
i
i
Height of the free energy barrier G, separating the
α-helical and extended conformation regions
Free energy surface of hIFNγ
ΔG  16.3 kCal/mol
Mutant 120 – Gln Ala Gly
Mutant 61 – His Pro Leu
Selected stable mutants (S<0.155
kCal/mol and ΔG > 13.0 kCal/mol)
ID
5-4
14
22
61
62
87
108
116
133
135
153
149-1
Amino
acid 87
Pro
Leu
Ser
His
Phe
Arg
Phe
Val
Pro
Val
Ser
His
Amino
acid 88
Leu
Pro
Ser
Pro
Thr
Pro
Leu
Leu
Pro
Ser
Phe
Gln
Amino
acid 89
Ser
Phe
Leu
Leu
Arg
Ser
Val
Leu
Ser
Pro
Cys
Arg
ΔG
S
[kCal/mol] [kCal/mol]
13.0
0.13350
24.4
0.12005
20.1
0.15407
24.3
0.10548
21.1
0.13945
18.1
0.15533
23.7
0.13894
>20
0.12167
17.6
0.15584
14.8
0.14989
>20
0.14239
>20
0.13683
Conclusions
Biomolecular processes having long characteristic times and
involving large-scale special rearrangement of many atoms
are still challenging to simulate.
 Advanced sampling techniques as metadynamics now allow
such phenomena to be studied more efficiently.
Metadynamics is a very powerful and effective method for
accelerating rare events and reconstructing free energy
surfaces of complex systems.
 We used metadynamics to investigate the effect of 100
random mutations of three aminoacids in the molecule of
human interferon gamma on the stability of the local
secondary structure.
 As a result 12 mutants were selected for further
experimental investigations, which are assessed to maintain
the local secondary structure of helix E and show similar or
better stability than the native protein.

Thank You for Your Attention!
Back-up slides
Backbone torsional angles
hIFNγ Ramachandran plot
Ramachandran plot
Accuracy of the reconstructed FES
The error in the reconstructed free energy is independent
on the underlying FES;
 The accuracy and the efficiency of the reconstructed FES
depend on the width of the Gaussians δs and on the ratio
ω/τG;
 The accuracy also depends on parameters, characterizing the
investigated physical system and the chosen CVs;


S 2T s
  Cd
D G S
2

The most important parameter that controls the efficiency
and the error of FES reconstruction is the filling speed δs/S.

S F
 c
t sim 
2
Advanced Metadynamics Techniques

Multiple walkers metadynamcis
The same metadynamics simulation is run simultaneously on
multiple replicas of the system, called walkers. The walkers interact
with each other by sharing and contributing to the construction of
the same metadynamics bias.

Parallel tempering metadynamcis
Multiple replicas of the system are simulated at different
temperatures. At time intervals τx an exchange of the coordinates
of two replicas at adjacent temperatures is attempted and
accepted according to a Metropolis criterion

Bias exchange metadynamcis
Several replicas are simulated in parallel at the same temperature,
but each replica is biased with a history-dependent potential,
acting on just one or two CVs. At fixed time intervals, swaps of the
history dependent potentials between pairs of replicas are
attempted and accepted according to a Metropolis criterion.