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• Proteins are dynamic systems
Concerted motions of the p53binding domain of MDM2
• protein dynamics:– Timescale: from s to fs.
– Inhomogeneity within same structure.
– Conformational substates
– Temperature dependence.
Motions of tyrosine kinase
Observation of protein dynamics
– Mössbauer spectroscopy: based on the interaction between x-ray (e. g. synchrotron radiation) and atomic nucleus in solids or some liquids (nuclear resonance scattering).
Lamb-Mössbauer factor f:
22
0 xkef
– Incoherent neutron scattering:
j
xkj
jeII22
0 j jj xIx 2
02
Experimental observation
• Linear up to about Tc=180K.
• T>Tc: a dramatic increase of the slope new modes of motion contribute to MSD, even in dry Mb.
• This phenomenon has been found in a large number of proteins.
Data from incoherent neutron scattering (open symbols), and Mössbauer absorption (full symbols) with different Mb-crystals.
Experimental observation
How fast are these new modes of motion?– Consider the relation of
energy and time resolution:
The new protein specific motions (T>Tc) occur on a
timesacle < 4ps!
meVE 1 st 12104/1
Symbols: data from several Mössbauer experiments"—": calculated data from phonon density.
Example: photosystem II of spinach
Average mean square displacements of iron in photosystem II of spinach (•) and efficiency of the electron transfer from quinone A to quinone B as a function of temperature.
Proteins and glasses
• Glasses are better studied and much simpler than proteins, so they can serve as guides to formulate concepts and theories for proteins.
Attributes Glass Protein
Structurally disordered Many mimina in the
energy landscape -, -relaxation
Glass transition• Unlike crystalline solids,
glasses do not have a certain melting temperature.
• The viscosity changes gradually with increasing temperature.
• Glass transition temperature Tg: At which the viscosity of a material reaches 10^13p = poise (=0.1kg/ms).
SiO2 crystal
SiO2 glass
Glass transition
• T<Tg: „Frozen“ in one of many local minima, very little mobility.
• T>Tg: The energy barriers can be overcome and other local minima explored.
Energy landscape
Glass-like transition in proteins
• Proteins also possess a glass transition temperature Tg:– Near Tg: Dynamical transition to a glass-like solid,
– T<Tg: Quenched anharmonic motions and long-range correlated motion. (functionally relevant motions)
• From computer simulations: Glassy behaviour of solvent drives the transition of protein.
Atomic-Detail Computer Simulation
Model System
Molecular Mechanics Potential
ji ij
ji
ji ij
ij
ij
ijij
impropersdihedrals
N
n
n
anglesbondsb
Dr
rr
KnK
kbbkV
,,
612
20
1
20
20
4
cos1
Energy Surface Exploration by Simulation..
Mountain Landscape
Energy Landscapes
More realistic pictures of energy landscapes
kTVV
j
i jieN
N /)(
Dynamical Transition
Mean-Square Displacement Nonlinear in T
The Protein Glass Transition
d
d
nn
Onset of Protein Function
Harmonic
Liquid
Glass
Dynamics & Activity of Glutamate Dehydrogenasein a Cryosolvent
[70% MeOD; 30%; D2O]
VALERIE REATRACHEL DUNNROY DANIELJOHN FINNEY
.
Principal Component Analysis of the Myoglobin Glass Transition
ALEXTOURNIER
7500
jjiiij rtrrtrA )()(
ALEX TOURNIER
Anharmonicity Factor= N/ P
Normal Mode Frequency, N
Principal Mode Frequency, P
N
P
Good Fit
Bad Fit
Error in Gaussian Fit
P(r)
P(r)
Free Energy Profiles of Dominant Principal Components
Mode Incipient at Myoglobin Glass Transition
Low temperature onset of anharmonic dynamics
Simulation details :Simulation details :
• Hydrated Myoglobin crystalHydrated Myoglobin crystal
• 10 ns MD trajectory (NPT)10 ns MD trajectory (NPT)
• Methyl dynamics at 150 KMethyl dynamics at 150 K
Mean Square DisplacementMean Square Displacement
• Protein dynamical transition~220KProtein dynamical transition~220K
• Onset of anharmonic dynamics~150KOnset of anharmonic dynamics~150K
Methyl dynamic heterogeneityMethyl dynamic heterogeneity
Site-specific spectral analysisSite-specific spectral analysis
• Low frequency methyl dynamics Low frequency methyl dynamics is sensitive to local packing is sensitive to local packing
Role of Xenon cavitiesRole of Xenon cavities
• Mobile CH3 groups Mobile CH3 groups are populated near are populated near xenon cavitiesxenon cavities
Dynamical Transition in an Isolated ProteinIsolated Protein:MD Simulation of Myoglobin.
KRZYSZTOF KUCZERAMARTIN KARPLUS
100 150 200 250 3000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
6 8 10 12 14 16 18 20 22
0.001
0.002
0.003
0.004
0.005
0 - 8Å 8 - 12Å 12 - 16Å 16 - 20Å 20 - 26Å
u2 si
de-c
hain
s [Å
2]
Temperature [K]
slo
pe [Å
2 K-1]
D [Å]
5 4 32 1
Radial Dependence of Dynamical TransitionJIANCONG XUALEX TOURNIER
Hydrated Myoglobin
54
3
2
1
System
Heatbaths
Prot Solv.
kTQ
pp
pQ
PdNkT
mp
kQ
p
Q
P
m
N
i i
i
kk
iii
i
ii
k
1
21
121
2
1
2
2
1
1
2,1
p
pFp
pr
t thermostaof Mass :
Momentum Thermostat:
variableThermostat:
Q
p
aim eTemperatur :T
particles ofNumber : N
constant sBoltzmann' :k
Nose-Hoover-Chain Multiple Heatbath Simulation Algorithm
System
1st Heatbath
2nd Heatbath
Prot Solv.
Canonical Distribution ofTemperatures
KEEP COLD
VARY T
T1
T2
DUAL HEAT-BATH SIMULATIONS
e.g.
ALEX TOURNIER
100 150 200 250 3000.0
0.5
1.0
1.5
2.0
(b)
(a) Protein 300K Control Protein fixed
D [
10
5 Å2 s-
1 ]
150 200 250 30010
1
102
103
104
105
106
107
108
109
Protein fixed Control Protein 300K
Dip
ole
co
rre
latio
n t
ime
[p
s]
Tem perature [K ]
Translation
Rotation
Water Diffusionon a Protein Surface
TranslationALEXTOURNIER
160 180 200 220 240 260 280 300101
102
103
104
105
Fig. 3
Control
Dip
ole
co
rre
latio
n tim
e (
ps)
Temperature (K)
Water Diffusion and the Glass Transition
ALEXTOURNIER
Protein
Water Translational Diffusion
Protein Fluctuations
160 180 200 220 240 260 280 300101
102
103
104
105
Fig. 3
Control
Dip
ole
co
rre
latio
n tim
e (
ps)
Temperature (K)
Rotation
Effect of Approximations in Experimental Neutron Scattering Data Analysis
u2 1 ns
Low-q, 20 eV resolution
‘High’-q, (0q2 23Å-2),20 eV resolution
‘Low’-q (0q2 1.44Å-2) perfect resolution
Harmonic
JENNIFERHAYWARD
22
3
1
0,Luq
L
incLinc ebqS
GERALD KNELLER
FIT RIGID REFERENCE STRUCTURES TO EACH FRAME OF FULLY-FLEXIBLE TRAJECTORY
TRAJECTORY OF RIGID BODIES
6 5 4 36 2 1Atomic Dynamicsas a function of
Distance from Protein Centre
Concentric Shells
SERGE DELLERUE,ANDREI PETRESCU,MARIE-CLAIRE BELLISSENT-FUNEL
10-1 100 101 102 103
t (ps)
0.0
0.2
0.4
0.6
0.8
1.0A
I(q,t)
B
0.0
0.2
0.4
0.6
0.8
1.0
I(q,t)
10-1 100 101 102 103
t (ps)
Derivation of
Simplified Dynamical Description from
Molecular Dynamics Simulation Data:
Fit of a Stretched Exponential Model
to the
Intermediate Scattering Function.
Radially-Softening Dynamical Model
Rav= radius of sphere in which atom diffuses. = dynamical correlation time = stretch factor (range of timescales spanned)
)q(A)t,q()q(A1)t,q(Iinc
t
etq,
Atom in Sphere
Some “Predictions” for the Spallation Neutron Source….
Pressure Transition in Protein Dynamics
LARS MEINHOLD
WATER
THE FREQUENCIES AFFECTED
PROTEINCrystalline
Staphylococcal Nuclease
solvent
Pressure-induced transition in protein dynamics
Meinhold, Smith. PRE 72:061908 (2005)
DoS: i ig )(
mode 1 mode 5 mode 30 mode 100
PMF:m
pTkG Bm lnprotein
22 )()()( tt kk rrrMSD:
t
r()
r(+t)
Protein:Protein Interactions.Vibrations at 150K
VANDANAKURKAL-SIEBERT
GERALD KNELLER
FIT RIGID REFERENCE STRUCTURES TO EACH FRAME OF FULLY-FLEXIBLE TRAJECTORY
TRAJECTORY OF RIGID BODIES
Scattering of X-Rays by Protein Crystals
Real Crystal =
IdealCrystal
+ Perturbations
STÉPHANIE HÉRYDANIEL GENESTSVEN LAMMERS
PROTEINFUNCTION
CollectiveMotions
Dynamics
Structure
NMR (13%) X-ray (87%)X-ray
beam
detector Bragg el(r)
phaseproblem
disorderstatic - dynamic
DIFFUSEScattering
'1)',( '
kk
quuq Tkk
T
ekkf
Diff. Scatt.(B factors)
CORRELATION
Rigid-Body Decomposition
Rigid-Body Fit(R-factor re: Full Trajectory = 5.3%)
Molecular Dynamics of Lysozyme Unit Cell
Experimental Full Trajectory
STÉPHANIE HÉRYDANIEL GENEST
X-Ray Diffuse Scattering
LARS MEINHOLD
Staphylococcal Nuclease
Staph nuclease S Gruner et al
still exposure diffuse scattering after removalof Bragg peaks
Staph nuclease S Gruner et al
h
l
k
Interpreting the experimental data …
datareduction3D – 2D – 1D
MD simulations
• unit cell: 15993 atoms 4 proteins 2115 TIP3P + 48
Cl-
• CHARMM (param:22)• PME• Nose-Hoover (300K,1bar)• 4 X10ns, t =1fs
Unit cell of Staphylococcal nuclease
Space group P41 (4 proteins)
Water box with unit cell dimensions (1972 molecules)
36 chloride ions
Total number of atoms 15540
S.LAMMERS
Intensity in hk0 plane Experimental intensity
distribution
Theoretical intensitydistribution
Scattering vector in hk0 plane
Intensity in hk0 plane
25 frames250 frames 2500 frames 12000 frames
R-factor for hk0 plane
LARS MEINHOLD
X-Ray Diffuse Scattering
1D
decomposition
unit cell scattering
protein scattering ''
'
eee
e
)(
)('
'
kkkk
kk
iii
ik
kkk ffI
uququuq
rrq
diff
Meinhold, Smith. PRL 95:218103 (2005)
2D
'' 1e)',(kk
Tkk
T
kkfIquuq
diff
variance-covariance matrix<ukuk’
T>
Which parts of the protein and which types ofmotion cause the intense scattering features?
pairs (k,k’) PCA
decomposition
decomposition
Protein Scattering
Solvent Scattering
LARS MEINHOLD
SolventRing ?
decomposition
Protein Scattering?
Solvent Scattering?
LARS MEINHOLD
PROTEIN
SOLVENT
Helix Repeat
Interstrand Distance
Water O…O
2D
Meinhold, Smith. PRL 95:218103 (2005)
'' 1e)',(kk
Tkk
T
kkfIquuq
diff
Specific Motions in Diffuse Scattering Pattern
Feature F2
LARS MEINHOLD
20vv
v
N. Calimet, CMB
Characterisation of PCA modes:
m
pTkG
M
Bm
mT
m
ln
vu2/1
3D
q
q
qq1q Exp
MDExp
I
IINR
without
hydrogensincluding
Agreement factor: EXP - MDMD scattering not converged
μs1log * ttR t
Meinhold, Smith. BiophysJ 88:2554 (2005)
TkE
T Bt exp
Convergence properties of collective variables
protein topology
Meinhold, Smith. BiophysJ 88:2554 (2005)
2'
2
'
''kk
kTk
uu
uu
kkTkk Cuu
an-isotropic isotropiclinear correlation
PROTEINFUNCTION
CollectiveMotions
??
temperaturepressure
Tournier, Smith. PRL 91:208106 (2003)
MD Simulation
s a m p l i n gp r o b l e m
brute force
replica exchange
conformational flooding
(T2,p2)(T1,p1)
Bragg & DiffuseX-ray Scattering
r e f i n e m e n t
PROTEINFUNCTION
DynamicsStructure
ComputerSimulation
NeutronScattering
4th generationX-ray sources
CollectiveMotions
- new concepts -
SystemsBiology- networks -
ab-initioFolding