The Physics of proteins

Per-Anker Lindgård Risoe National Laboratory, Roskilde,

DTU, Denmark

Protein folding, magic numbers and hinge forces

Dymanics of proteins, solitons

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?

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

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…

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Secondary structuretypical folding times

α-helix (~ 0.1 µsec)-sheet (~ 6 µsec)Turns (maybe faster)

Tertiary 1 msec – few sec

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

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

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?

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

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’

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?

My scenarioProtein

Unfolded

Molten globule

Parent structure

Final ‘native’ str.

Solid state

Gas

Liquid

bcc

Closed packed

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)

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

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

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

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

Configurational entropy

Phase diagram as for a martensitic transformation

Magic numbers and abundance

Representative data base of foldsRost & Sander J. Mol. Biol.232, 584 (92)

Prediction from the H-H model

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)

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

Free-electron Laser: FELIX

As good as a grand piano

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)

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

H-bonds in an -helix

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)

Solitons on 3-H-chainsboth for Toda and LJ

time

Position Molecular Dynamics simulations

Propagation of a energy pulse in a helix

Molecular Dynamics simulation

Time (ps)

site

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