Download - From Crystallography of Biomolecules to
From Crystallography of Biomoleculesto
More Detailed Understanding of their Structure and Function
Bogdan LesyngICM and Faculty of Physics, University of Warsaw
(http://www.icm.edu.pl/~lesyng)and
European Centre of Excellence forMultiscale 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)
B.Lesyng & W.Saenger, Z.Naturforsch. C,36, 956-960(1981)
Crystallized from water
Crystallized from butyric acid !
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.
Towards generalization of experimentally observedstructural changes
Fields are equally important as structures !
Dynamics, classical and/or quantum one in
the real molecular environment
Sequences at the protein & nucleic acids levels
3D & electronicstructure
Function
Metabolic pathways & signalling
Sub-cellular
structures & processes
Cell(s), structure(s) & functions
1 RPDFCLEPPY 10 11 TGPCKARIIR 20 21 YFYNAKAGLC 30 31 QTFVYGGCRA 40 41 KRNNFKSAED 50
51 CMRTCGGA 58
Determination of biomolecular structures
X-ray and neutrondiffraction data
NMR
Molecular quantum mechanics.Minimization of the B.-O.
energy
Homology analysisand structure prediction
”Ab intio” methods
Minimization of the MM-energy or free energy
Experimental and ”data-mining” approaches
0
RE
EHBO
BOel
0
RF MM
eFF
eFzyx
lkhi
lkhlkh
lkh
lzkyhxi
lkhV
,,
,,,,
,,
)(2
,,
1,,
R ,
Towards global minimum of the free energy(Gibbs & Boltzmann – equilibrium properties,
Kramers & Eyring - kinetics)
Homology analysisand
structure prediction.
Making use of molecular evolution conceptsand Darwinian-type
approach.
Optimal sequence alignment, followed by a 3D structure alignment, results in predictionof a correct, 3D-hierarchical biomolecular structure.
”Optimal” – consistent withcurrent evolutionary concepts.
Wrong sequence alignmenttypically 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, 11-17, 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)
14
Protonation equilibria in proteins
Protonation equilibria - microstates
,..0,1,1,0,1,1,0aix
Tk
aiaiB
aixGe
Z xx1
)( rnqri
iiext
kT
rqnrn
)(exp)( 0
kTIe
rrrrrqrrk
kk
22
2
2
P o i s s o n - B o l t z m a n n ( P B ) m e t h o d
i n t h e r m o d y n a m i c e q u i l i b r i u m
s o l v i n g o n a g r i d , o rw i t h fi n a l e l e m e n t s
e x t e r n a l i o n i c d e n s i t y
r i q i
D e b y e - H u c k e l s c r e e n i n g p a r a m e t e r , I - i o n i c s t r e n g t h
The model group – a reference state
GGGG HinoHiiiipHpH
,,mod,
This differenceassumed to bepurely electrostatic
Ensamble -role of a reference state (”model group”)
Z
ZGH
noHRT ln GGGG HnoHpHpH
mod
The microstate energy
GGxGxG ijjiji
ii
iiioaixxpH
,2
1
Phosphotyrosine in phospholipase C-
SH2 domain of phospholipase C-1
(pdb: 2PLE)
S.M.Pascal,A.U.Singer,G.Gish,T.YamazkiS.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
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
Phosphoserine in phosphoglucomutase
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-1 3.71 4.0
phosphoserine
tetrapeptide 2 5.7 6.1
phosphoglucomutase <4
phosphothreonine
tetrapeptide 3 6.1 6.1
Active site(quantum subsystem)
Classical molecular scaffold (real molecular environment)
Solvent (real thermal bath)
Interacting quantum and classical subsytsems.Enzymes, special case of much more general
problem.
Quantum-classical dynamics in simulations of enzymatic processes (phospholipase A2 – a case study)
Conclusions• I n general, experimental structures
should be refi ned, which in particular, requires application of virtual titrationprocedures.
• Knowledge of intra- and intermolecular fi elds (electrostatic, hydrophobic, etc.) are required f or better understanding ofmolecular and f unctional properties. I nfl uence of the real molecular environment can be modelled by such fi elds.
• Development and applications of multiscalemolecular modelling methods (f romquantum to mezoscopic ones) allow to much better describe biomolecular mechanisms and logic of their f unctioning(a f ew 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 HallayJarek KalinowskiPiotr KmiećMagda GruzielMichał WojciechowskiŁukasz WalewskiFranek RakowskiJanek Iwaszkiewicz
Coworkers:Prof. J.AntosiewiczProf. P.BałaDr. P.Grochowski
Collaboration:Prof. J.A.McCammonProf. W.SaengerProf. 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 – (quantum)• AVB/GROMOS - (quantum-classical)
• SCC-DFTB - (quantum)• SCC-DFTB/GROMOS - (quantum-classical)• SCC-DFTB/CHARMM - (quantum -classical)• ....
Dynamics
• MD (classical)• QD (quantum)• QCMD (quantum-classical)• ....
Mesoscopic potential energy functions
•Poisson-Boltzmann (PB)•Generalized Born (GB)•....
G e n e r a l i z e d B o r n ( G B )
G e lG B = G e l
0 + G e ls o l
ji ijin
jioel r
qqG
21
ji ij
ji
ex
f
in
solel f
qqeG
i j
,
121
G e l – T o t a l e l e c t r o s t a t i c e n e r g y
C o u l o m b i c i n t e r a c t i o n e n e r g yb e t w e e n a t o m s
E l e c t r o s t a t i c i n t e r a c t i o n e n e r g y ( s o l v a t i o n e n e r g y ) o f t h e m o l e c u l a r s y s t e mw i t h d i e l e c t r i c e n v i r o n m e n t ( e g . w a t e r ) .
r i j – d i s t a n c e b e t w e e n a t o m s
– D e b y e - H u c k e l p a r a m e t e r
R i – B o r n r a d i u s i – V a n d e r W a a l s r a d i u s
ji
ijjiijij RR
rRRrf
4exp
22
w h e r e :
The same atoms are characterized by diff erent Bornradii. Their values depend on geometry of themolecular system, and on localization of the atoms inthe system (geometrical property). The Born radii are large inside, and are close to VdW radii on the surface.
Born radiiand
Van der Waals radii
Molecular area
E x p r e s s i o n s f o r B o r n r a d i i
rdrR solventi
34
1
4
11
3
1
36
1
4
31
rd
rR solventi
3
1
314
31
n
solventn
i
rdr
nR
3.0
033
32.4
solv
solute
n
A . O n u f r i e v , D . B a s h f o r d , D . C a s e , J . P h y s . C h e m . B , 1 0 4 , 3 7 1 2 - 3 7 2 0 ( 2 0 0 0 )
T . G r y c u k , J . C h e m . P h y s , 1 1 9 , 4 8 1 7 - 4 8 2 6 ( 2 0 0 3 )
M . W o j c i e c h o w s k i , B . L e s y n g , J . P h y s C h e m , i n p r e s s
1
233
1
714
ex
inex
exo
i
ED
ACAC
R
4
1
3747
141
41
rd
rRA
inVdW
M.Feig, W.Im, C.L.Brooks, J.Chem.Phys.,120,903-911(2004)
(I)
(II)
(III)
(IV)
Coulomb Field appr.
Kirkwood Model