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The Physics of proteins

Protein folding, magic numbers and hinge forces. The Physics of proteins. Dymanics of proteins, solitons. Per-Anker Lindgård Risoe National Laboratory, Roskilde, DTU, Denmark. Proteins very interesting. We need ~100.000 different for life (why so many?) Are the nano-machines of life

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The Physics of proteins

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  1. Protein folding, magic numbers and hinge forces The Physics of proteins Dymanics of proteins, solitons Per-Anker Lindgård Risoe National Laboratory, Roskilde, DTU, Denmark

  2. Proteinsvery interesting We need ~100.000 different for life (why so many?) Are the nano-machines of life Globular (free floating) Membrane bound • Structure: Rather dense, but not like a crystal, frac. dim. = 2.5 • Function: Act on light pulse or chem. binding: HOW? • Folding: Spontanous, rather fast: HOW? • Aggregation: (avoid) HOW?

  3. Water channel (no H+)very important 1.000.000.000 w./sec.

  4. Protein structureglobular – membraneprimary, secondary, tertiary structure • Primary structure: The sequence~100 long (20 letters – amino acids)IAMWRITINGTOINFORMYOUTHATWEHAVEANEWPROGRAMOFCROSSDISCIPLINARYFELLOWSHIPSFORYOUNGSCIENTISTSQUALIFIEDINTHEPHYSICALSCIENCESWHOARELOOKINGFORPOSTDOCTORALTRAININGABROADINBIOLOGY.(208 characters) HFSP see DPL home page: http://DPL.Risoe.DK • How can it fold on an information like this • We can now identify ’words’ > 80% sure:α-helix, -sheet, turns… Iam writing to inform you that we have a new program of Cross-Disciplinary Fellowships for young scientists qualified in the physical sciences who are looking for postdoctoral training abroad in biology.

  5. Secondary structuretypicalfolding times α-helix (~ 0.1 µsec) -sheet (~ 6 µsec) Turns (maybe faster) Tertiary 1 msec – few sec

  6. Protein folding Proteins come as a piece of rope First they must fold a b c d e f g h . . . r s t u v y Two real cases:1qpu: Cytochrome b562, chain A, oxygen transport (106 aminoacids) ADLEDNMETLNDNLKVIEKADNAAQVKDALTKMRAAALDAQKATPPKLEDKSPDSPEMKDFRHGFDILVGQIDDALKLANEGKVKEAQAAAEQLKTTRNAYHQKYR 2hmq: Hemerythrin, chain A, electron transport(114 aminoacids) GFPIPDPDPYCWDDISFRTFYTIVIDDEHKTLFNGILLLSQADNADHLNELRRCTGKHFLNEQQLMQASQYAGYAEHKKAHDDFIIHKLDTWDGDVTYAKNWLVNHIKTIDFKYRGKI

  7. Various representations of the structure1qpu: Cytochrome b562, chain A, oxygen transport (106 aminoacids) i r i l i Rectified structure: on a cubic lattice all lengths the same Hinge forces H-H model Hydrophobic-Hinge model

  8. Structure must be known in the unfolded stateFirst come – first served principle • To be predictable from the sequence • To prevent non-native contacts (like +…-) • To screen interactions • Non-equilibrium problem (in general) • Secondary/turns/loops form first – at least partially • Hinge-guide towards the native structureis the any evidence for this?

  9. Highly controversial:Schools are forming • spin glass– funnel model - ‘concerted’ motion, folding nucleus equilib., second and tertiary simultaneous(Fersht, Wolynes …….) 2) Hierarchical, diffusion-collision model, turns & secondary first (partially)(Balwin, Rose, Karplus) Studies of small proteins point towards case 1 Recent studies accumulate evidence in favor of case 2 Support basis for the H-H-model

  10. Is the spin glass scenario correct? • Spin glass: multitude of energy minima no definite structure • what is a ‘funnel’upside down • More like a ‘single crystal’just one form, produced by ‘seeds’

  11. Solid state structures • 230 symmetry groupsor different structures: bcc, fcc, hcp etc. • Can we do the same for protein structures? • How many fold classes? • Simplify: simple metals always have liquid -> bcc‘parent’ bcc -> closed packed ‘variants’ • Can we do the same for protein structures?

  12. My scenario Protein Unfolded Molten globule Parent structure Final ‘native’ str. Solid state Gas Liquid bcc Closed packed

  13. Computer simulation of (un) folding α-helix (en-HD) -sheet (FBP28 WW) Fersht et al Nature 421, 843 (2003) Fersht et al PNAS 98, 13008 (2001)

  14. i ~J l ~K Hydrophobic-hinge model • Problem reduced from ~2100 random contact tests (Levinthals paradox) to • Pack ~20 sticks as closely as possible! • How many ways can that be done? (count) • How to select just one of those? (hinge) • The name (irili)~ Hamiltonian: Int. b. spins H = - J ΣSn • Sm - K ΣSnxSm • First how many

  15. Total number of dense folds 2 x 2 x 2 box, coordination number z = 4 and z = 5. Number of configurations as a function of elements. #elements #dense(z=4) #total(z=4) #dense(z=5) 1 1 1 1 2 1 1 1 3 1 4 1 4 6 15 8 5 9 53 12 6 8 161 8 7 6 444 6 8 24 1100 36 9 76 2590 164 10 84 5560 192 11 48 11412 146 12 120 20384 584 13 722 35280 3984 14 988 52078 6488 15 424 76116 3264 16 396 90936 5464 17 172 106728 4220 18 160 97362 8440 19 2908 87696 115084 20 6366 57460 313360 21 1752 36684 86115 22 3300 15088 496650 23 656 5812 242210 24 848 924 865544 25 0 0 780625 26 0 0 206692 27-mer (z/e)N 36-mer

  16. How many fold classes? • We know all the names:‘PROTEINFALTUNG’ • 3  2  2=2 times1  2  2+1 • < 4000 fold classes, if all used (up to 17 elements) • ~ 1000 fold classes suggested by Chothia "firilifarufilifil" "filirifabufarufar" 17 elements ~ 100 amino acids

  17. Hinge forces? • Native structure must know in extend. state • Lift conf. degeneracy as H= - Σ J Sn• Sm – h ΣSnz (small h lift inf. deg.) 6 folds: N- and C C N N C Hinge: to place the rest on the right side Structures need not be perfect We need to learn how to identify the hinges α-helix length - -turns are candidates

  18. Configurational entropy

  19. Phase diagram as for a martensitic transformation

  20. Magic numbers and abundance Prediction from the H-H model Representative data base of folds Rost & Sander J. Mol. Biol. 232, 584 (92)

  21. Conclusion • Alternative, simplistic (but ambitious) view • Consider 2nd & loops/turns on same footing • Hydrophobic packing ->~ 4000 fold classes-> domains (~100 a.acid)-> abundance, magic numb. • Hinge force: a method to reach corr. fold ’native’ known in the extend. state predict tertiary str. from sequence • Problem: ‘native’ may be distorted-> difficult to find 2nd & loops and hingesPer-Anker LindgårdJ. Phys. Cond. Matter 15, S1779 (2003)Per-Anker Lindgård&Henrik Bohr PRL 77, 779 (96), PRE 56, 4497 (97)

  22. Dynamics of proteins • Now they are folded, interesting to test the properties. • Pump-probe experiments with LASER -like a piano tuner • Soliton theory for αn α–helix -the exact Toda solitons

  23. Free-electron Laser: FELIX As good as a grand piano

  24. Interpretation? • Bacteriorhodopsin (85% -helix) • Line at 115 cm-1 specially long-living • Strange if onlarge scale • We have suggested a new interpretation:F. D’Ovido, PA Lindgård & H.Bohr, PRE 71, 026606 (2005) • H-bond excitations alongthe -helixas in poly-amidesO.Fauerskov Moritsugu et al, PRL 85, 3970 (2000)

  25. Opticalspectrum of a soliton • Moving pulse (Tsunami) - is not an oscillation • Difficult to measure • Gives no resonance peak • Gives a 1/ω 2 ‘background’ peak around ω =0 • More fancy effects: • Frequencies inside bump are different (local different struc. self-trapped) • Non-perfect soliton emits slowly phonons(i.e. can seemingly sustain phononsand give long life-time) • Possible energy channel

  26. H-bonds in an-helix

  27. LJ- & Toda potentials Analytic tools for solitons and periodic waves in helical proteins Phys. Rev. E 71, 026606 (2005) LJ: k = 1.4 104 dyn/cm m = 1.7 10-22 g hν= 100 cm-1 118 cm-1 (full)

  28. Solitons on 3-H-chainsboth for Toda and LJ time Position Molecular Dynamics simulations

  29. Propagationof aenergy pulse in a helix site Time (ps) Molecular Dynamics simulation

  30. Conclusion • Proteins are important and interesting • Folding: a very major problem in Science • Dynamics: interesting non-linear excitationsSolitons • Lots of interesting work for physicists, mathematicians and computer people Thank you for your attention

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