the physics of proteins per-anker lindgård risoe national laboratory, roskilde, dtu, denmark...
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![Page 1: The Physics of proteins Per-Anker Lindgård Risoe National Laboratory, Roskilde, DTU, Denmark Protein folding, magic numbers and hinge forces Dymanics of](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e4f5503460f94b4746a/html5/thumbnails/1.jpg)
The Physics of proteins
Per-Anker Lindgård Risoe National Laboratory, Roskilde,
DTU, Denmark
Protein folding, magic numbers and hinge forces
Dymanics of proteins, solitons
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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?
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Water channel (no H+) very important 1.000.000.000 w./sec.
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Protein structureglobular – membrane
primary, secondary, tertiary structure
• Primary structure: The sequence~100 long (20 letters – amino acids)
IAMWRITINGTOINFORMYOUTHATWEHAVEANEWPROGRAMOFCROSSDISCIPLINARYFELLOWSHIPSFORYOUNGSCIENTISTSQUALIFIEDINTHEPHYSICALSCIENCESW
HOARELOOKINGFORPOSTDOCTORALTRAININGABROADINBIOLOGY.(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…
I am 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
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Secondary structuretypical folding times
α-helix (~ 0.1 µsec)-sheet (~ 6 µsec)Turns (maybe faster)
Tertiary 1 msec – few sec
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Protein folding
Proteins come as a piece of rope
First they must fold
Two real cases:1qpu: Cytochrome b562, chain A, oxygen transport (106 aminoacids)ADLEDNMETLNDNLKVIEKADNAAQVKDALTKMRAAALDAQKATPPKLEDKSPDSPEMKDFRHGFDILVGQIDDALKLANEGKVKEAQAAAEQLKTTRNAYHQKYR
2hmq: Hemerythrin, chain A, electron transport (114 aminoacids)GFPIPDPDPYCWDDISFRTFYTIVIDDEHKTLFNGILLLSQADNADHLNELRRCTGKHFLNEQQLMQASQYAGYAEHKKAHDDFIIHKLDTWDGDVTYAKNWLVNHIKTIDFKYRGKI
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Rectified structure:on a cubic latticeall lengths the sameHinge forces
H-H modelHydrophobic-Hinge model
Various representations of the structure1qpu: Cytochrome b562, chain A, oxygen transport (106 aminoacids)
i r i l i
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Structure must be known in the unfolded state
First 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 structure is the any evidence for this?
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Studies of small proteins point towards case 1
Recent studies accumulate evidence in favor of case 2
1) 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)
Support basis for the H-H-model
Highly controversial:Schools are forming
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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’
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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?
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My scenarioProtein
Unfolded
Molten globule
Parent structure
Final ‘native’ str.
Solid state
Gas
Liquid
bcc
Closed packed
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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)
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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 Σ Sn • Sm - K Σ Sn x Sm
• First how manyi ~J l ~K
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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 12 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
(z/e)N
27-mer
36-mer
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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
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Hinge forces?
• Native structure must know in extend. state• Lift conf. degeneracy as H= - Σ J Sn• Sm – h Σ Sn
z
(small h lift inf. deg.)
6 folds: N- and C CN
NC
Hinge: to place the rest on the right sideStructures need not be perfect
We need to learn how to identify the hingesαhelix length - turns are candidates
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Configurational entropy
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Phase diagram as for a martensitic transformation
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Magic numbers and abundance
Representative data base of foldsRost & Sander J. Mol. Biol.232, 584 (92)
Prediction from the H-H model
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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. statepredict tertiary str. from sequence
• Problem: ‘native’ may be distorted difficult to find 2nd & loops and hinges
Per-Anker Lindgård J. Phys. Cond. Matter 15, S1779 (2003)Per-Anker Lindgård&Henrik Bohr PRL 77, 779 (96), PRE 56, 4497 (97)
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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
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Free-electron Laser: FELIX
As good as a grand piano
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Interpretation?• Bacteriorhodopsin
(85% -helix)• Line at 115 cm-1
specially long-living • Strange if on large
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)
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Optical spectrum 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
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H-bonds in an -helix
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LJ- & Toda potentials
Analytic tools for solitons and periodic waves in helical proteinsPhys. Rev. E 71, 026606 (2005)
LJ: k = 1.4 104 dyn/cmm = 1.7 10-22 ghν= 100 cm-1
118 cm-1 (full)
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Solitons on 3-H-chainsboth for Toda and LJ
time
Position Molecular Dynamics simulations
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Propagation of a energy pulse in a helix
Molecular Dynamics simulation
Time (ps)
site
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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