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

Proteins very interesting We need ~ 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 w./sec.

Protein structure globular – membrane primary, secondary, tertiary structure Primary structure: The sequence ~100 long (20 letters – amino acids) IAMWRITINGTOINFORMYOUTHATWEHAVEANEWPROGRAMOFCROSSDISCIPLI NARYFELLOWSHIPSFORYOUNGSCIENTISTSQUALIFIEDINTHEPHYSICALSCIE NCESWHOARELOOKINGFORPOSTDOCTORALTRAININGABROADINBIOLOGY. (208 characters) HFSP see DPL home page: 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 training abroad in biology.

Secondary structure typical folding times α -helix (~ 0.1 µ sec)  -sheet(~ 6 µ sec) 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) ADLEDNMETLNDNLKVIEKADNAAQVKDALTKMRAAALDAQKATPPKLEDK SPDSPEMKDFRHGFDILVGQIDDALKLANEGKVKEAQAAAEQLKTTRNAYH QKYR 2hmq:Hemerythrin, chain A, electron transport (114 aminoacids) GFPIPDPDPYCWDDISFRTFYTIVIDDEHKTLFNGILLLSQADNADHLNELRR CTGKHFLNEQQLMQASQYAGYAEHKKAHDDFIIHKLDTWDGDVTYAKNWL VNHIKTIDFKYRGKI

Rectified structure: on a cubic lattice all lengths the same Hinge forces H-H model Hydrophobic-Hinge model Various representations of the structure 1qpu: 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 groups or 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 scenario Protein 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, (2001)

Hydrophobic-hinge model Problem reduced from  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 S n S m - K Σ S n x S m First how many i ~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) (z/e) N 27-mer 36-mer

How many fold classes? We know all the names: ‘PROTEINFALTUNG’ 3  2  2= 2 times 1  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 S n  S m – h Σ S n z (small h lift inf. deg.) 6 folds: N- and C C 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

Configurational entropy

Phase diagram as for a martensitic transformation

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

Conclusion Alternative, simplistic (but ambitious) view Consider 2 nd & 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 2 nd & 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, (2005) H-bond excitations along the  -helix as in poly-amides O.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 phonons and give long life-time) Possible energy channel

H-bonds in an  -helix

LJ- & Toda potentials Analytic tools for solitons and periodic waves in helical proteins Phys. Rev. E 71, (2005) LJ : k = dyn/cm m = g h ν = 100 cm cm -1 (full)

Solitons on 3-H-chains both 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 excitations Solitons Lots of interesting work for physicists, mathematicians and computer people Thank you for your attention