Cristian Micheletti SISSA (Trieste)
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1 Cristian Micheletti SISSA (Trieste) Mar 2009
2
3 5pal - parvalbumin Calcium-binding protein HEADER CALCIUM-BINDING PROTEIN 25-SEP-91 5PAL 5PAL 2 COMPND PARVALBUMIN (ALPHA LINEAGE) 5PAL 3 SOURCE LEOPARD SHARK (TRIAKIS SEMIFASCIATA) 5PAL 4 SEQRES PRO MET THR LYS VAL LEU LYS ALA ASP ASP ILE ASN LYS 5PAL 50 SEQRES ALA ILE SER ALA PHE LYS ASP PRO GLY THR PHE ASP TYR 5PAL 51 SEQRES LYS ARG PHE PHE HIS LEU VAL GLY LEU LYS GLY LYS THR 5PAL 52 SEQRES ASP ALA GLN VAL LYS GLU VAL PHE GLU ILE LEU ASP LYS 5PAL 53 SEQRES ASP GLN SER GLY PHE ILE GLU GLU GLU GLU LEU LYS GLY 5PAL 54 SEQRES VAL LEU LYS GLY PHE SER ALA HIS GLY ARG ASP LEU ASN 5PAL 55 SEQRES ASP THR GLU THR LYS ALA LEU LEU ALA ALA GLY ASP SER 5PAL 56 SEQRES ASP HIS ASP GLY LYS ILE GLY ALA ASP GLU PHE ALA LYS 5PAL 57 SEQRES MET VAL ALA GLN ALA 5PAL 58 O C H C R C N R H H
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5 HEADER CALCIUM-BINDING PROTEIN 25-SEP-91 5PAL 5PAL 2 COMPND PARVALBUMIN (ALPHA LINEAGE) 5PAL 3 SOURCE LEOPARD SHARK (TRIAKIS SEMIFASCIATA) 5PAL 4 SEQRES PRO MET THR LYS VAL LEU LYS ALA ASP ASP ILE ASN LYS 5PAL 50 SEQRES ALA ILE SER ALA PHE LYS ASP PRO GLY THR PHE ASP TYR 5PAL 51 SEQRES LYS ARG PHE PHE HIS LEU VAL GLY LEU LYS GLY LYS THR 5PAL 52 SEQRES ASP ALA GLN VAL LYS GLU VAL PHE GLU ILE LEU ASP LYS 5PAL 53 SEQRES ASP GLN SER GLY PHE ILE GLU GLU GLU GLU LEU LYS GLY 5PAL 54 SEQRES VAL LEU LYS GLY PHE SER ALA HIS GLY ARG ASP LEU ASN 5PAL 55 SEQRES ASP THR GLU THR LYS ALA LEU LEU ALA ALA GLY ASP SER 5PAL 56 SEQRES ASP HIS ASP GLY LYS ILE GLY ALA ASP GLU PHE ALA LYS 5PAL 57 SEQRES MET VAL ALA GLN ALA 5PAL 58 HEADER CALCIUM-BINDING PROTEIN 27-AUG-92 1RRO 1RRO 2 COMPND RAT ONCOMODULIN 1RRO 3 SEQRES SER ILE THR ASP ILE LEU SER ALA GLU ASP ILE ALA ALA 1RRO 55 SEQRES ALA LEU GLN GLU CYS GLN ASP PRO ASP THR PHE GLU PRO 1RRO 56 SEQRES GLN LYS PHE PHE GLN THR SER GLY LEU SER LYS MET SER 1RRO 57 SEQRES ALA SER GLN VAL LYS ASP ILE PHE ARG PHE ILE ASP ASN 1RRO 58 SEQRES ASP GLN SER GLY TYR LEU ASP GLY ASP GLU LEU LYS TYR 1RRO 59 SEQRES PHE LEU GLN LYS PHE GLN SER ASP ALA ARG GLU LEU THR 1RRO 60 SEQRES GLU SER GLU THR LYS SER LEU MET ASP ALA ALA ASP ASN 1RRO 61 SEQRES ASP GLY ASP GLY LYS ILE GLY ALA ASP GLU PHE GLN GLU 1RRO 62 SEQRES MET VAL HIS SER 1RRO 63 5pal Sequence identity: 45% 1rro
6 Lock-and-key mechanism (Fisher 1894) Function and structural changes (Perutz, 1950 s 1960 s) Induced fit mechanism (Kadosh 1958)
7 WolfWatz et al. Nature 2004 ; JACS 2007 Hanson et al. PNAS 2007; Kern et al ) Substrates shift prexisting equilibrium states towards catalytically active states. 2) Preferred directionalities for large scale conformational changes encoded in fold. See also Lange et al. Science 2008; Beach JACS 2005, Pontiggia et al. Biophys. J. 2008; Phys. Rev. Lett. 2007
8 Why?
9 HIV-1 Protease Mutations causing resistance to inhibiting drugs are located at a few sites: 36, 46, 63, 71, 84. Elastic properties of HIV-1 PR: Jacobs et al. Proteins (2001); Kurt et al., Proteins (2003), Piana et al. J Mol Biol (2002), Micheletti et al. Proteins (2004)
10 Piana et al., JMB, 2002
11 Point-wise perspective: how much do single amino acids fluctuate?
12 Mobility profile obtainable by X-ray or NMR
13 Time series of y-axis displacements of a.a. 200 and 146
14 r = 0.4
15 r = 0.1
16 r = -0.35
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18 X(t) X(0) Brownian motion (applet from Virtual Physics Laboratory)
19 time position
20 Two roles of the surrounding environment: friction + thermal noise
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27 for t >> m/!
28 26 th March 2009 Cristian Micheletti SISSA (Trieste)
29 m/! time
30 We started with: and found that for T>> m/! : but we could have got this directly by solving:
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32 Diffusion coefficient
33 Consider the ordinary differential equation: Simple Euler integration scheme gives: Is it safe to use the above formula replacing with? Let us experiment with the provided numerical code!!!
34 X(t) t
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36 But if we are interested in behaviour over time scales >> m/!: Formally analogous to the Langevin equation that we solved before:
37 Recall the solution of the velocity of the freely diffusing particle: Using the previous analogy we have:
38 Spring constant from equilibrium properties Friction coefficient from decay of autocorrelation function
39 Source:
40 Consider an oscillator without friction: The instantaneous potential and kinetic energies are: The average energy is:
41 We can look at the trajectory of our stochastic oscillator as a superposition of pure oscillatory modes. Let us compute the Fourier transform of :
42 From what we saw for the simple oscillator, the average energy stored in the mode with angular frequency w is so that the corresponding power is: From the previously calculated Fourier transform we have:
43 Use the provided numerical code to: 1) Generate a trajectory for the stochastic oscillator 2) Fourier transform the data and compute the power spectrum 3) Fit the power spectrum with the functional derived before
44 Source:
45 31 st March 2009
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48 Compare with a stochastic oscillator subject to white thermal noise Hands-on: experiment with provided code for oscillator coupled to a heat bath
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52 April 2, 2009
53 HIV-1 Protease Mutations causing resistance to inhibiting drugs are located at a few sites: 36, 46, 63, 71, 84. Elastic properties of HIV-1 PR: Jacobs et al. Proteins (2001); Kurt et al., Proteins (2003), Piana et al. J Mol Biol (2002), Micheletti et al. Proteins (2004)
54 Auto-correlation: with
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56 reference distance Assume small fluctuations around reference positions and expand:
57 See e.g. Atilgan et al. Biophys. J. (2001); Delarue and Sanejouand, JMB (2002); CM, Banavar and Maritan. Phys. Rev. Lett. (2001). CM, Carloni and Maritan Proteins (2004) - BetaGM code available upon request
58 Langevin dynamics: Characterize with eigenvectors, u, and eigenvalues,!, of matrix M. Limiting cases: Normal modes view: Overdamped dynamics view: Brooks et al. PNAS 82; McCammon et al. Nature, 262; Levitt et al. JMB 181; Case Curr. Biol. 4; Hinsen, Proteins, 33; Hinsen et al. Chem. Phys. 261; Micheletti et al. JMB 321 (2002); Micheletti et al. PRL (2006) and Biophys. J. (2006)
59 Mobility profile obtainable by X-ray or NMR
60 Measure of residue mobility: Chymotrypsin inhibitor Haliloglu et al., Phys. Rev. Lett. 1997; Atilgan et al., Biophys. J. 2001;Micheletti et al. Proteins 2003;
61 Time series of y-axis displacements of a.a. 200 and 146
62 r = 0.4
63 r = 0.1
64 r = -0.35
65 Normalised covariance matrix: CM, Carloni and Maritan, Proteins 2004
66 Positive correlation: 25, 47, 84 Negative correlation: 15, 37, 59, 63 Mutations: 36, 46, 63, 71, 84
67 Front view Top view
68 Aspartic proteases Serine proteases Cysteine proteases Metallo proteases
69 Beta-secretase and HIV-1 protease: evolutionarily related? -!Conserved residues in the loops containing ASP dyad -!Similar large scale movements in visually-matching regions Rawlings et. al. Methods Enzymol. (1995), Blundell et al. PNAS (1996), Cascella et. al. JACS (2005)
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71 A B N N A B amino acids amino acids
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73 Reward correspondences of regions having -! similar intra-molecular distances and similar movements Dynamical consistency: Spatial consistency: Hybrid dynamical/structural score: 4 A
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78 Zen, Carnevale, Lesk and CM, Protein Science 2008
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82 Significant Alignments 1yb7 hydroxynitrile lyase L: 256 EC: 4 CATH: had haloalkane dehalogenase L: 310 EC: 3 CATH: aligned residues
83 Significant Alignments 1dy4 cellobiohydrolase I L: 436 EC: 3 CATH: ayh endo-1,3-1,4-beta-d-glucan 4-glucanohydrolase L: 214 EC: 3 CATH: aligned residues
84 Significant Alignments 1ako exonuclease III L:268 EC: 3 CATH: avp human adenovirus proteinase L:199 EC: 3 CATH: aligned residues
85 Significant Alignments 1ako exonuclease III L: 268 EC: 3 CATH: d7o enoyl reductase L: 297 EC: 1 CATH: aligned residues
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