Principal Component Analysis (PCA)

Transcription

1 Principal Component Analysis (PCA) Projection onto 2-dim subspace: v 2 v 1 Trajectory x(t) in 3N-dim configuration space

2 A 100-dimensional data set viewed at random orientation

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9 Example: Conformational Flooding of BPTI

10 Fluctuation spectrum of BPTI 95% of atomic motion C i relevant...irrelevant

11 Quasi-harmonic approximation v 2 v 1

12 Reversible Folding Dynamics of a β-peptide X. Daura, B. Jaun, D. Seebach, W.F. van Gunsteren, A.E. Mark, J. Mol. Biol. 280 (1998) 925

13 Reversible Folding Dynamics of a β-peptide Color: Conformational space density B. de Groot, X. Daura, A. Mark, H. Grubmüller, JMB 309 (2001) 299

14 Clustering Markov Process No memory > 100 ps! B. de Groot, X. Daura, A. Mark, H. Grubmüller, JMB 309 (2001) 299

15 Concept 1: Relevant vs. irrelevant degrees of freedom; Separation of time scales Water molecules: fast Brownian particle: slow 3 + noise

16 Concept 2: Collective degrees of freedom (quasi particles) m 1 m 2 x 2 c 2 x 1 x 2 c 1 x 1 M R c 1

17 Concept 2: Collective degrees of freedom (quasi particles)

18 Principal Component Analysis (PCA) Projection onto 2-dim subspace: v 2 v 1 Trajectory x(t) in 3N-dim configuration space

19 Idea: Combine two concepts: Concept 1: Relevant vs. irrelevant degrees of freedom Concept 2: Collective degrees of freedom PCA 95% of atomic motion Water molecules: fast Brownian particle: slow 3 + noise C i relevant...irrelevant

20 Fluctuation spectrum of BPTI Consider many-body system: M conformational coordinates c 95% of atomic motion Treat c M+1...c 3N as heat bath; then the c s form a canonical ensemble in the free energy landscape with: C i relevant...irrelevant H. Grubmüller, et al., Proceedings Nonlin. Excitations in Biomol., Les Houches (1994)

21 Quasi-harmonic approximation v 2 v 1

22 Quasi-harmonic approximation v 2 v 1

23 STEP 1: compute quasi harmonic free energy approximation from a conventional simulation STEP 2: compute flooding potential V fl STEP 3: carry out flooding simulations by including V fl into the molecular force field H. Grubmüller, Phys.Rev.E 52 (1995) 2893 B.G. Schulze, H. Grubmüller, J.D. Evanseck, JACS 122 (2000) 8700

24 Example: Conformational Flooding of BPTI

25 Example: Conformational Flooding of BPTI

26 Example: Conformational Flooding of BPTI

27 Example: Conformational Flooding of BPTI

28 Example: Conformational Flooding of BPTI

29 Example: Conformational Flooding of BPTI

30 Example: Conformational Flooding of BPTI

31 Example: Conformational Flooding of BPTI

32 Example: Conformational Flooding of BPTI

33 The Prion-only Hypothesis: (Prusiner 1982) TSEs are caused by autocathalytic conformational conversion of PrP (C) into PrP (Sc) Prion domain PrP( ) Riek et al., Nature 382 (1996) 180 benign - protease resistant - high β-sheet content infectious

34 (1) Initial exposure of helix 3:

35 (2) Subsequent extension of β-sheet:

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37 Hot spots of predicted PrP( ) transitions:

38 Conformational dynamics and flexibility of nuclear transport proteins

39 Spontaneous Closing and Flexibility of Exportin Cse1p Exportin Cse1p Nuclear Pore Complex (Beck et al., Science, 2004) U. Zachariae, H. Grubmüller. Structure (2006)

40 Nuclear Transport Cycle Cytoplasm Nucleus

41 Nuclear Transport Cycle NLS Cytoplasm Nucleus

42 Nuclear Transport Cycle NLS Cytoplasm α Nucleus

43 Nuclear Transport Cycle NLS Cytoplasm α β Nucleus

44 Nuclear Transport Cycle NLS Cytoplasm α β Nucleus NPC

45 Nuclear Transport Cycle Cytoplasm Nucleus NLS α β NPC

46 Nuclear Transport Cycle Cytoplasm Nucleus Ran GTP β NPC NLS α

47 Nuclear Transport Cycle Cytoplasm Nucleus NPC α CAS Ran GTP

48 Nuclear Transport Cycle α CAS Cytoplasm Ran GTP Nucleus NPC

49 Nuclear Transport Cycle α CAS Cytoplasm Ran GDP Nucleus NPC

50 Nuclear Transport Cycle α CAS Cytoplasm Ran GDP Nucleus NPC

51 Open Questions GTP hydrolysis sufficient to rapidly dissociate complexes? - Large surface, high interaction energy high affinity - Does distortion of NTRs serve as energy storage? Spring loaded molecules? (Matsuura and Stewart, Nature, 2004) CAS Discrete regions of flexibility or continuum of conformations? (Chook and Blobel, Curr. Opin. Struct. Biol., 2001) - Two independent arches?

52 Simulation of CAS/Cse1 Fast Spontaneous ring closure 20 Å change. Four independent simulations 10 ns simulation time Control: cargo present -> no changes

53 Exportin conformational dynamics Domino-like closure 3 Å Final RMSD to closed conformation: (not used as input) U. Zachariae, H. Grubmüller. Structure (2006)

54 Importin-β: A Huge Conformational Change RanGTP ~9 nm Importin-β unbound RanGTP complex ~ 24 ns Importin-β (free) ~15 nm Rapid, biphasic transition into extended S-like state, RG ~ 4.4 nm Zachariae and Grubmüller, Structure (in press).

55 Comparison with Experimental Data SAXS measurement: RG 4.3±0.1 nm (Fukuhara et al., JBC 2004) Importin β: agreement with SAXS Open state: Very flexible, hinges at HEAT repeat 5 & 14/15 three dynamic regions, (D. Svergun, private communication) similar to CAS. Zachariae and Grubmüller, Structure (in press).

56 Role of Energy Storage in NTRs Conformation of Imp-β in RanGTP complex highly unstable energy storage If affinity of Impβ:RanGTP larger than ~65 kj/mol: Reconstitution of Impβ:RanGTP from RanGDP+P i Cycle blocked Zachariae and Grubmüller, Structure (in press).

57 MHC peptide dynamics

58 HLA-B*2705 Resolution: 2.10 Å Structure: Hülsmeyer et al., JBC (2002), 277, 47844

59 HLA-B*2709 Resolution: 1.09 Å Structure: Hülsmeyer et al., JBC (2002), 277, 47844

60 HLA-B*2705 C N

61 HLA-B*2709 C N

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64 HLA-B*2705 HLA-B*2709 Pöhlmann et al., JBC. (2004)