Transcript Centre of Excellence for Multi

From Crystallography of Biomolecules
to
More Detailed Understanding of their
Structure and Function
Bogdan Lesyng
ICM and Faculty of Physics, University of Warsaw
(http://www.icm.edu.pl/~lesyng)
and
European Centre of Excellence for
Multiscale Biomolecular Modelling,
Bioinformatics and Applications
(http://www.icm.edu.pl/mamba)
Łódź, 4/10/2004
Chapter 4.5,
page 72
W.Saenger & K.H.Sheit, J.Mol.Biol.,
50, 153-169(1970)
Crystallized from water
B.Lesyng & W.Saenger, Z.Naturforsch. C,
36, 956-960(1981)
Crystallized from butyric acid !
Towards generalization of experimentally observed
structural changes
Structures in the crystalline
state can be interpreted in
terms of packing forces,
properties of hydrogen bonds,
a kind of consensus between
the intramolecular energy and
the intermolecular interaction
energy, etc.
B.Lesyng, G.A.Jeffrey, H.A.Maluszynska,
A Model for the Hydrogen-bond-length
Probability Distributions in the Crystal
Structures of Small-molecule Components of
the Nucleic Acids, Acta Crystallog., B44,
193-8(1988)
However, this problem can also be seen in a different,
more abstract way, namely as minimization of the free
energy of a selected molecular system in its real
molecular environment – in this particular case this is the
environment formed by surrounding molecules with
imposed constraints resulting from the symmetry.
Fields are equally important as structures !
Sequences
at the protein &
nucleic acids levels
1
11
21
31
41
51
RPDFCLEPPY
TGPCKARIIR
YFYNAKAGLC
QTFVYGGCRA
KRNNFKSAED
CMRTCGGA
Metabolic
pathways &
signalling
3D & electronic
structure
Function
Dynamics,
classical and/or
quantum one in
the real
molecular
environment
10
20
30
40
50
58
Sub-cellular
structures & processes
Cell(s),
structure(s)
&
functions
Determination of biomolecular structures
Experimental and ”data-mining” approaches
X-ray and neutron
diffraction data
 x, y, z 
F h , k ,l 
F

1
V
h , k ,l
e
F e
 2i ( hx  ky  lz )
R 
,
h , k ,l
h , k ,l

i
Homology analysis
and structure prediction
NMR
h ,k ,l
”Ab intio” methods
Molecular quantum mechanics.
Minimization of the B.-O. energy
H el   E BO
E  0
R
BO
Minimization of
the MM-energy or free energy
F
R
MM
0
Towards global minimum of the free energy
(Gibbs & Boltzmann – equilibrium properties,
Kramers & Eyring - kinetics)
Homology analysis
and
structure prediction.
Making use of molecular
evolution concepts
and Darwinian-type
approach.
Optimal sequence alignment,
followed by a 3D structure
alignment, results in prediction
of a correct, 3D-hierarchical
biomolecular structure.
”Optimal” – consistent with
current evolutionary concepts.
Wrong sequence alignment
typically results in a wrong
structure.
Multiscale modelling methods, the approach to refine structures and to
understend functioning of complex biomolecular systems and
processes
•
.
Virtual titration
- J. Antosiewicz, E. Błachut-Okrasińska, T. Grycuk, J. Briggs, S. Włodek, B. Lesyng,
J.A. McCammon, Prediction of pKas of Titratable Residues in Proteins Using a
Poisson-Boltzman Model of the Solute-Solvent System, in “Computational
Molecular Dynamics: Challenges, Methods, Ideas”, Lecture Notes in Computational
Science and Engineering, vol. 4, Eds. P.Deuflhard et al, Springer-Verlag, Berlin,
Heidelberg, pp. 176-196,1999
– J.Antosiewicz, E. Błachut-Okrasińska, T. Grycuk and B. Lesyng,
A Correlation Between Protonation Equilibria in Biomolecular Systems and their
Shapes: Studies using a Poisson-Boltzmann model., in GAKUTO International
Series, ”Mathematical Science and Applications”. Kenmochi, N., editor, vol. 14, 1117, Tokyo, GAKKOTOSHO CO, pp.11-17, 2000.
- M. Wojciechowski, T. Grycuk, J. Antosiewicz, B.Lesyng, Prediction of Secondary
Ionization of the Phosphate Group in Phosphotyrosine Peptides, Biophys.J, 84,
750-756 (2003)
•
Quantum forces and dynamics in complex biomolecular systems.
– P. Bala, P. Grochowski, B. Lesyng, J.A. McCammon, Quantum Mechanical Simulation
Methods for Studying Biological System, in: ”Quantum-Classical Molecular
Dynamics. Models and Applications”, Springer-Verlag, 119-156 (1995)
– Grochowski, B. Lesyng, Extended Hellmann-Feynman Forces, Canonical
Representations, and Exponential Propagators in the Mixed Quantum-Classical
Molecular Dynamics, J.Chem.Phys, 119, 11541-11555(2003)
Protonation equilibria in proteins
14
Protonation equilibria - microstates
x   0,1,1,0,1,1,0,..
i a
x 
i a
1

Z
 x  e

i a
G xi a 

k BT
Poisson-Boltzmann (PB) method
 
 
  2 
rrqkr rk rr r
k
2
2
e
 I
2
kT
Debye-Huckel screening
parameter, I-ionic strength
r i qi
solving on a grid, or
with final elements
extr    qi ni (r)
i

  q ( r ) 

n ( r )  n0 exp  

kT 

external ionic density
in thermodynamic
equilibrium
The model group – a reference state
This difference
assumed to be
purely electrostatic
G  pH   G  pH   G
ii
i , mod
i , noH
 Gi , H

Ensamble -role of a reference state (”model group”)
G  pH   G mod  pH   G noH  G H 
G
 Z noH 

  RT ln


 ZH 
The microstate energy
1








pH

 x x G
G x G  x G
2
i a
o
i
i
ii
i , j i
i
j
ij
Phosphotyrosine in phospholipase C-g
SH2 domain of
phospholipase C-g1
(pdb: 2PLE)
S.M.Pascal,A.U.Singer,G.Gish,T.Yamazki
S.E.Shoelson,
T.Pawson,
L.E.Kay,
J.D.Forman-Kay,
Nuclear
Magnetic
Resonance Structure Of An Sh2 2ple
Domain Of Phospholipase C-Gamma1
Complexed With A High Affinity Binding
Peptide, Cell, 77,461-472(1994)
phosphotyrosine
Phosphoserine in phosphoglucomutase
phosphoglucomutase
(pdb: 3PMG)
W.J.Ray, Junior, Y.Liu,
S.Baranidharan,
Structure of Rabbit Muscle
Phosphoglucomutase at 2.4
Angstroms Resolution. Use of
Freezing Point Depressant and
Reduced Temperature to Enhance
Diffractivity, to be published
phosphoserine
Open and close forms of PKA
Typical results for phosphorylated proteins
molecule
prediction
experimental
phopsphotyrosine
tetrapeptide 1
5.36
5.9
dodecapeptide
5.66
6.1
phospholipase C-g1
3.71
4.0
phosphoserine
tetrapeptide 2
5.7
phosphoglucomutase
6.1
<4
phosphothreonine
tetrapeptide 3
6.1
6.1
Interacting quantum and classical subsytsems.
Enzymes, special case of much more general problem.
Active site
(quantum subsystem)
Classical molecular scaffold
(real molecular environment)
Solvent (real thermal bath)
Quantum-classical dynamics in simulations of enzymatic processes
(phospholipase A2 – a case study)
Conclusions
•
In general, experimental structures
should be refined, which in particular,
requires application of virtual titration
procedures.
•
Knowledge of intra- and intermolecular
fields (electrostatic, hydrophobic, etc.)
are required for better understanding of
molecular and functional properties.
Influence of the real molecular
environment can be modelled by such
fields.
•
Development and applications of multiscale
molecular modelling methods (from
quantum to mezoscopic ones) allow to
much better describe biomolecular
mechanisms and logic of their functioning
(a few ongoing projects in my group).
•
Development and applications of a variety
of mathematical models and theories
makes such studies to be not boaring !
Acknowledgements
PhD students:
Marta Hallay
Jarek Kalinowski
Piotr Kmieć
Magda Gruziel
Michał Wojciechowski
Łukasz Walewski
Franek Rakowski
Janek Iwaszkiewicz
Coworkers:
Prof. J.Antosiewicz
Prof. P.Bała
Dr. P.Grochowski
Collaboration:
Prof. J.A.McCammon
Prof. W.Saenger
Prof. D.Truhlar
Studies are supported by
”European CoE for Multiscale Biomolecular
Modelling, Bioinformatics and Applications”
and
Polish State Committee for Scientific Research.
Microscopic generators of the potential
energy function
• AVB
• AVB/GROMOS
•
•
•
•
SCC-DFTB
- (quantum)
SCC-DFTB/GROMOS - (quantum-classical)
SCC-DFTB/CHARMM - (quantum -classical)
....
Dynamics
•
•
•
•
– (quantum)
- (quantum-classical)
MD (classical)
QD (quantum)
QCMD (quantum-classical)
....
Mesoscopic potential energy functions
•Poisson-Boltzmann (PB)
•Generalized Born (GB)
•....
Generalized Born (GB)
GelGB = Gel0 + Gelsol
Gel – Total electrostatic energy
qi q j
1
G  
2 i  j  in rij
o
el
Coulombic interaction energy
between atoms
 f
sol
el
G
1  1 e ij
  
2   in  ex
 qi q j

 i, j f
ij

Electrostatic interaction energy
(solvation energy) of the molecular system
with dielectric environment (eg. water).
where:
2



r
ij
2


f ij  rij  Ri R j exp
 4R R 
 i j
rij – distance between atoms
 – Debye-Huckel parameter
Ri– Born radius
i– Van der Waals radius
Born radii
and
Van der Waals radii
Molecular area
The same atoms are characterized by different Born
radii. Their values depend on geometry of the
molecular system, and on localization of the atoms in
the system (geometrical property). The Born radii
are large inside, and are close to VdW radii on the
surface.
Expressions for Born radii
1
1

Ri 4
1 3
d r
4

r
so lven t
Coulomb Field appr. (I)
A.Onufriev, D.Bashford,D.Case, J.Phys.Chem.B, 104,3712-3720(2000)
1  3
 
Ri  4
1 3
d r 
6

r
solvent

1
3
Kirkwood Model (II)
T.Grycuk, J.Chem.Phys, 119, 4817-4826(2003)
Ri  
1
 3 ex 
 A7
Co A4  C1 
 3 ex  2 in 
D
E
 ex  1
(III)
 1
1
A7   4 
 4RVdW 4
1 3
in r 7 d r 
1
4
M.Feig, W.Im, C.L.Brooks, J.Chem.Phys.,120,903-911(2004)
1  n3
1 3


d r 
n

Ri  4 so lven t r

1
n 3
n
4.32
  so lu te
 033


so lv


M.Wojciechowski, B.Lesyng, J.Phys Chem, in press
0. 3
(IV)