Download - I. Dynamics of living systems
I. Dynamics of living systems
• Understanding the dynamics at the molecular level. • Understanding the dynamics at the cellular level• Filling the gap between these two levels
Dynamics Dynamics Function Function
Life’s complexity pyramid
Oltvai & Barabasi, Science 2002, 298, 763-764
“The complexity pyramid might not be specific only to cells”
Different levels of structural organization:
Residues Proteins
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103 2-10
104 10-100
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microtubulesmicrotubules
Incre
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Dom
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mach
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Challenge: to understand the long-time dynamics of large systems
Model: Coarse-grained
Method: Analysis of principal modes of motion (Frame transformation: Cartesian collective coordinates)
What is the optimal (realistic, but computationally efficient) model for a given scale (length and time) of representation?
Which level of details is needed for representing global (collective) motions?
How much specificity we need for modeling large scale systems and/or motions?
What should be the minimal ingredients of a simplified (reductionist) model?
Protein dynamics
Folding/unfolding dynamics
Passage over one or more energy barriersTransitions between infinitely many conformations
Fluctuations near the folded state
Local conformational changesFluctuations near a global minimum
Gaussian Network Model
Bahar, I., Atilgan, A.R., & Erman, B. (1997) Folding & Des. 2, 173.Flory, P.J. (1976) Proc. Roy. Soc. London A. 351, 351.
FOR MORE INFO…
Can we predict fluctuations dynamics from native state topology only?
“A single parameter potential is sufficient to reproduce the slow dynamics in good detail”
Detailed specific potentials
Approximate uniform potential
Rouse chain
R1
R2
R3
R4
Rn
=
1-1
-1 2-1
-1 2
-1
.. ...-1
2-1
-1 1
Connectivity matrix
Vtot = (/2) [ (R12)2 + (R23)2 + ........ (RN-1,N)2 ]
= (/2) [ (R1 - R2)2 + (R2 - R3)2 + ........
Kirchhoff matrix of contacts
==
1 if rik < rcut
0 if rik > rcutik==
ii = = - k ik
Vtot = (/2) RT
R
Comparison with X-ray Temperature Factors
Bahar, I., Atilgan, A.R., & Erman, B. (1997) Folding & Design 2, 173-181
FOR MORE INFO...
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(b) 1omftheory
experiments
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(a) 2ccya
Debye-Waller factors:
Bk = 8 2 <Rk Rk> /3
Comparison with H/D Exchange – NMR data
Bahar, I., Wallquist, A., Covell, D.G., and Jernigan, R.L. (1998) Biochemistry 37, 1067.
Si = k ln W(Ri) = - (Ri)2/ (2T [-
1]ii)
Covariance matrix
(directly found from MD or MC trajectories)
R1 . R1> R1 . R2> R1 . R3>
R2. R1> R2 . R2>
RN . RN>
C =
Ri = instantaneous fluctuation in the position vector Ri of atom i= Ri - <Ri>
<R1 . R1> = ms fluctuation of site 1 averaged over all snapshots.
Eigenvalue decomposition of C
U is the matrix of eigenvectors, is the diagonal matrix of eigenvalues. The ith
column (eigenvector) of U is given by a linear combination of Cartesian
coordinates and represents the axis of the ith collective coordinate (principal
axis) in the conformational space.
C = U U-1
The ith eigenvalue represents the mean-square fluctuation along the ith principal axis. The motion along the ith principal axis is the ith mode.
Time-consuming
aspect of PCA
Decomposition into normal modes
Bahar, I., Atilgan, AR, Demirel MC, Erman B. (1998) Physical Review Lett. 80, 2733. Demirel MC, Atilgan AR, Jernigan RL, Erman B. & Bahar, I. (1999) Protein Science 7, 2522.
• Slowest (global) modes function• Fastest (local) modes stability
FOR MORE INFO...
Compare experimental B-factors with theoretical B-factors
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theoretical B-factorexperimental B-factor
residue number
http://www.ccbb.pitt.edu/CCBBResearchDynHemRel.htm
Comparison of the slowest modes of T and R2
0 50 100 150 200 250 300
T
R2
residue number
chain chain
b2
2
1
37-4484-94
132-141
145-146
92-100
35-40
T R transitions in Hb
Experimental T
Experimental R2
Computed (R2)Reference...
Xu & Bahar, submitted.
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-1 deoxygenated Hb
-1 CO-Hb
Ord
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par
ame
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residue index
Order parameters for CO-bound and unliganded Hb
0 50 100 150
CO-Hb ()deoxygenated ()
Ord
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par
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r
residue index
Haliloglu & Bahar, Proteins 1999, 37, 654-667
Si = 3/2 <cos2i> - 1/2
For details on theory see...
(A)
(B)
(I) (II)
(I) (II)
Fluctuations of the nevirapine-bound (A) and unliganded (B) forms of RT
• Fluctuating conformations of the nevirapine-bound (A) and unliganded (B) forms of RT. The p66 subdomains are colored cyan (fingers), yellow (palm), red (thumb), green (connection) and pink (RNase H).
• See the difference in the mechanism of global fluctuations for the liganded and unliganded RTs. This difference is significant given that the sizes or distributions of fluctuations are unaffected by ligand binding
http://www.ccbb.pitt.edu/CCBBResearchDomMot.htm
Two hinge bending sites
• (A) Two hinge-bending centers on RT forming minima in Figure 1: (I) near the NNRTI binding site, involving residues 107-110 (cyan), 161-165 (green), 180-188 (red) and 219-231 (blue), and (II) near the p66 connection and RNase H interface, comprising residues 363-366 (cyan), 394-408 (green), 410-423 (loop, magenta), 424-429 (interdomain linker, red), and 504-512 (yellow).
•(B) A closer view of region II, showing explicitly the side chains near the hinge site. Close tertiary contacts are indicated by the yellow dots.
Topology-based models• Near-native fluctuations
(springs acting on effective centroids, usually C atoms)
• Ben-Avraham (1993)• Tirion (1996)• Bahar et al. (1997)• Hinsen (1998)• Sanejouand, Tama (2000)• Wriggers, Brooks (2001)• Ma (2002)
• Folding/unfolding processes (folding loss of configurational
entropy)
• Micheletti et al, PRL (1999)• Cecconi et al. Proteins (2001)• Go & Scheraga Macromolecules (1976)• Galzitskaya & Finkelstein, PNAS (1999)• Munoz et al. PNAS (1999)• Alm & Baker, PNAS (1999)• Klimov & Thirumalai, PNAS (2000)• Clementi et al (Onuchic), JMB (2000)
“Native topology determines force-induced unfolding pathways”
Protein folding kinetics examined by a Go-like model
Koga, N. & Takada, S. J Mol. Biol. 2001, 313, 171-180
Topological and Energetic Factors: What determines the transition state ensemble, and folding intermediates?
Clementi, C. Nyemeyer, H. & Onuchic, J. N. J Mol. Biol 2000, 298, 937.
Simulations with Go-like potential
“ Topology plays a central role in determining folding mechanisms”
Can we use such simplified approaches for estimating amyloidogenic intermediates?
Applied to CI2, SH3 (2-state folders) and barnase, RNase H and CheY (have intermediates)