1. Lecture SS 20005

Optimization, Energy Landscapes, Protein Folding 1

OptimizationEnergy Landscapes

Protein Folding

Course will be introduce mathematical/theoretical concepts

and demonstrate their relevance to practical biological problems

Pre-requisite: knowledge of Computational Chemistry 1 lecture

Course tries to minimize overlap with Computational Chemistry 2 lecture

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Optimization, Energy Landscapes, Protein Folding 2

Content

1 IntroductionBiomolecular systems: Proteins, membranes, phenomena of protein folding,protein complexes

2 Protein folding on lattices Review of statistical thermodynamics (deltaG, deltaS) Exact enumeration of all statesFolding via Monte-Carlo algorithm, which moves? Folding funnel Roughness of the energy landscape

3 Protein folding on lattices (II) HPCC Algorithmus à la Ken Dill, work by Rolf Backofen

4 Calculation of energies in biomolecular systems (do we need this?) Molecular force fields, solvent effect

Replace by lecture on membrane protein structure and folding?

5 Off lattice protein folding simulations involving all atom simulations MD simulationscharacterization of the free energy landscape for foldingReplica exchange simulations Restraints to generate partially unfolded states

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Content (II)

6 Calculation of chemical rates

Transition state theory Kramer theoryFolding at home

7 Diffusion: Smoluchowski equation Langevin equation → Ermak-McCammon-algorithm for brownian dynamics

8 Application: Association kinetics of protein A with protein BEnergy landscape for 6 degrees of freedom (3× translation, 3× rotation) Computation of kon rates from Brownian dynamics simulationsCalculation of entropies from trajectory analysis Compare boltzmann-weighted energies for protein B on lattice with protein A

9 Protein Assemblies

10 Electron transfer (Marcus theory), proton transfer

11 Photo physics of photoactive moleculesConformational dynamics on electronic surfaces, conical intersections

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Optimization, Energy Landscapes, Protein Folding 4

Literature

lecture slides will be available 0-2 days prior to lecture

suggested reading: links will be put up on course website

http://gepard.bioinformatik.uni-saarland.de/teaching...

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Optimization, Energy Landscapes, Protein Folding 5

Schein = successful written exam

The successful participation in the lecture course („Schein“) will be certified upon

successful completion of an oral exam in February/March 2006.

Participation at the oral exam is open to those students

who have mastered the 3 - 4 assignments.

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Optimization, Energy Landscapes, Protein Folding 6

literature

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Optimization, Energy Landscapes, Protein Folding 7

My systems of interest

Proteins

- folding landscape

- membrane proteins

recent progress on folding of membrane proteins!

Protein assemblies

- molecular machines (stable complexes)

- transient complexes

Membranes

- formation

- dynamics

Protein membrane association

Partitioning of proteins in membranes

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Optimization, Energy Landscapes, Protein Folding 8

Das Rätsel der Proteinfaltung

I Was ist das Problem? „Levinthal‘sches Paradoxon“

II Lösung: Energielandschaft hat die Form eines Faltungstrichters

Studium der Energielandschaft mit Gittersimulationen

III gegenwärtiges Neuland

ungefaltete Proteinabschnitte

Proteinmissfaltung im Prion-Protein

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Optimization, Energy Landscapes, Protein Folding 9

Für ein Protein mit 100 AS und jeweils 2 Konformationen für jede Aminosäure

ergeben sich 2100 = 1.27 x 1030 mögliche Konformationen des Proteins.

Wenn das Protein 10-13 sec brauchen würde, jede einzelne Konformation

abzusuchen, zu „samplen“, dann würde es

10-13 x 1.27x1030 = 1.27 x 1017 s = 4 x 109 Jahre brauchen

bis es alle seine Konformationen abgesucht hätte und eventuell

die energetisch günstigste gefunden hätte.

Dies ist offensichtlich nicht möglich.

Daher muß es Faltungshilfen oder spezielle Faltungspfade geben, so dass das

Protein nicht alle theoretisch mögliche Zustände absuchen braucht.

Levinthal-Paradoxon

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FaltungspfadeEs gibt mehrere Hypothesen für die driving forces der Proteinfaltung:

• hydrophober Kollaps; die entfaltete Proteinsequenz kollabiert in einen

kompakten Klumpen. Anschließend falten sich die Sekundärstrukturelemente

und bilden sich die richtigen/optimalen dreidimensionalen Kontakte um eines

der zulässigen Faltungsmuster (folds) anzunehmen.

ODER

• die Sekundärstrukturelemente falten sich zunächst selbständig (framework

model) und lagern sich anschließend zusammen.

Für beide Faltungsszenarien gibt es experimentelle Beispiele.

Oft liegt die Wahrheit “in der Mitte”.

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Bryngelson, Wolynes, PNAS

(1987)

Gradient Rauhigkeit

beschleunigt bremst

Faltung Faltung

“Frustration”

„New view of protein folding“:Faltung entlang trichterähnlichen Energielandschaften

Brooks, Gruebele, Onuchic, Wolynes,

PNAS 95, 11037 (1998)

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Energielandschaften (H. Frauenfelder/UIUC)

Frauenfelder & Leeson, Nature Structural Biology 5, 757 - 759 (1998)

Links ein sehr einfache und rechts eine sehr komplizierte Energielandschaft

links, Energielandschaft von Ammoniak, NH3. Die konformationelle Koordinate (x-

Achse) beschreibt den Abstand des Stickstoffatoms von der Ebene der 3

Wasserstoffatome.

rechts , Eine stark vereinfachte Energielandschaft eines Proteins.

In Wirklichkeit ist die Energielandschaft eine Funktion von 3N Koordinaten, wobei N

(die Anzahl der Atome des Proteins) sehr groß ist.

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Moleculare Chaperone: Proteine, die anderen globulären Proteinen helfen,

ihre korrekte Faltung einzunehmen “molekulares Rotes Kreuz”

• Molekulare Chaperene wie hsp60 oder GroEL

(rechts gezeigt)

sind eine Klasse von Proteinen, die in der

Zelle anderen Proteinen helfen, ihre korrekte

Faltung einzunehmen

• Dazu können molekulare Chaperone sehr

effektiv an nach außen gewandte hydrophobe

Regionen von teilweise gefalteten Strukturen

binden.

• “In die Jacke helfen”.

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Fold Optimierung

• Einfache Gittermodelle (HP-Modelle)

– Zwei Sorten von Seitenketten:

hydrophob und polar

– 2-D oder 3-D Gitter

– Treibende Kräfte:

hydrophober Kollaps – es ist günstig,

Kontakte zwischen hydropoben Seitenketten

zu bilden

– Bewertung = Anzahl an HH Kontakten

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HP-Gittermodelle

Ken Dill ~ 1997

Vorteil solch einfacher Modelle:man kann den Konformationsraum systematisch absuchen.

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The importance of being unfolded?

Anscheinend sind nicht wenige Proteine der Zelle einen Großteil der Zeit teilweise

entfaltet (P.E. Wright, H.J. Dyson, J. Mol. Biol. 293, 321 (1999))

Dies klingt sehr unerwartet. Was wären mögliche biologische Vorteile davon?

(1) Entfaltete Proteine können schneller abgebaut werden

kann für Regulation eines schnellen Zellzyklus erforderlich sein.

(2) Molekulare Erkennung ist schneller, wenn Faltung und Bindung gekoppelt sind

(3) Loopstrukturen können viele biologische Targets erkennen wichtig für Kommunikation und Regulierung bzw. Bildung großer Komplexe?

(4) Entfaltete Proteine können schnell in andere Zellkompartments transportiert

werden.

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NORS regions: no regular secondary structure NORS regions are defined to have at least 70

consecutive residues with less than 12%

regular secondary structure (helix or strand).

Rost and co-workers found 4 types of proteins.

(A) Connecting loops: long loops that connect

two domains or chains (shown Formate

Dehydrogenase H, 1AA6).

(B) Loopy ends: long N- or C-terminal regions

that lack regular secondary structure (shown

Hexon from adenovirus type 2, 1DHX).

(C) Loopy wraps: long loopy regions wrapping

around globular domains (shown Class II

chitinase, 2BAA.

(D) Loopy domains: entire structures that

have almost no regular secondary structure

(shown extra-cellular domain of T beta RI,

1TBI).

Liu, Tan, Rost, J Mol Biol (2002)

332, 53-64

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Many NORS regions predicted in proteomesLiu et al. predicted many NORS regions in 31

entirely sequenced organisms. NORS proteins

appeared particularly abundant in eukaryotes.

(A) gives the percentage of proteins in respective

proteome for which at least one NORS region is

predicted. High enrichment in eukaryotic

proteomes!

(B) illustrates the percentage of all the residues

of the respective proteome for which a NORS

region is predicted.

(C) gives the percentage of all predicted NORS

regions that are between N and N+10 residues

long (note that, by definition, NORS regions are

longer than 70 residues). Surprisingly, almost

15% of all the predicted NORS regions extend

over more than 200 residues (inset of C). Liu, Tan, Rost, J Mol Biol (2002) 332, 53-64

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NORS regions use particular amino acidsThe height of the one-letter amino acid code is

proportional to the abundance of the respective

acid in each data set. The actual value is the

difference in occurrence with respect to the

frequency observed in a sequence-unique subset

of PDB:

.

Inverted letters indicate acids that are less

frequent than 'expected'. The amino acids are

sorted by 'flexibility' , with the more rigid ones

on the left. Overall, NORS regions are as

abundant in more flexible residues as loop

regions in PDB . However, we found considerably

more Serine (S), Glutamine (Q), and Glycine (G)

and considerably fewer Arginine (R), Aspartic

acid (D), Glutamic acid (E), Tryptophan (W), and

Phenylalanine (F) in NORS regions than in loop

regions, in general.

Liu, Tan, Rost, J Mol Biol (2002) 332, 53-64

21

21

PP

ppz

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Optimization, Energy Landscapes, Protein Folding 20

Das Prion-Protein PrPc:

ist ein normales zelluläres Glycoprotein- ist an die Plasmamembran über einen

GPI-Anker angehängt - hat 209 Aminosäuren

Seine genaue Funktion ist unbekannt.

Cu2+ Speicherung, Erinnerung?

Struktur aus NMR-Bestimmungen bekannt:

Die N-terminale Region 23-120 ist sehr

flexibel und meist ungeordnet.

C-terminale Region enthält 3 -Helices,

2 kurze -Stränge

PrPc wird schnell durch Proteinase K abgebaut

Prion: ein ungeklärtes Beispiel für misgefaltete Proteine

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Die mit Krankheit assoziierte Form PrPsc

PrPsc: oligomerische -reiche Struktur

teilweise Resistenz gegenüber Verdau durch Proteinase K

starke Tendenz, in unlösliche Plaques zu aggregieren

die 3D-Struktur von PrPsc ist nicht bekannt!

Nur-Protein Hypothese (Prusiner 1980s und 1990s):

der Umfaltungsprozeß PrPc PrPsc wird durch

PrP Protein autokatalysiertStanley Prusiner,Nobelpreis für Physiologieoder Medizin 1998

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Modelle für die Bildung von PrP-res aus PrPc

Caughey Trends Biochem Sci 26, 235 (2001)

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Modelle, die auf Polymerisation beruhen

Caughey Trends Biochem Sci 26, 235 (2001)

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Gegenwärtiges Verständnis von Prionen

Die molekularen Mechanismen für die Umordnung von PrPc nach PrPsc

sind immer noch unklar.

Theoretische Methoden konnten (leider ) noch nicht viel beitragen.

Der Übergang PrPc PrPsc ist ein kooperatives Phänomen.

Daher kann man es wohl nicht durch die Untersuchung von PrP Monomeren

verstehen.

Das „Seed“-Modell scheint plausibel.

Der Übergang nach PrPsc könnte über ein Faltungsintermediat I gehen.

Dies würde erklären, warum Mutanten anfällig für Krankheiten sind, bei

denen diese Faltungsintermediate stärker besetzt ist bzw. bei denen der

Grundzustand (F) weniger stabil gegenüber I ist als bei Gesunden.

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Fluid-Mosaic-Model of the cell membrane

http://www.nature.com/horizon/livingfrontier/background/membrane.html

Like a mosaic, the cell membrane

is a complex structure made up

of many different parts, such as

proteins, phospholipids and

cholesterol.

The relative amounts of these

components vary from membrane

to membrane, and the types of

lipids in membranes can also

vary.

The membrane structure is highly

dynamic. Its viscosity is only

about 100 times larger than that

of water.

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Membrane bilayers

Edidin, Nature Reviews Cell Biol 4, 414 (2003)

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Membrane bilayers

Edidin, Nature Reviews Cell Biol 4, 414 (2003)

Membranes are not structureless.

„Domains“ or „lipid rafts“ rich in

cholesterol and sphingo-lipids may

form transiently.

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How do helical membrane proteins fold?

White, FEBS Lett. 555, 116 (2003)

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Hydrophobicity Scales

White, FEBS Lett. 555, 116 (2003)

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Translocon-assisted folding of TM proteins?

White & von Heijne, Curr Opin Struct Biol 14, 397 (2004)

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Translocon

White & von Heijne, Curr Opin Struct Biol 14, 397 (2004)

crystal structure of translocon in closed state.

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Types of TM-proteins

White & von Heijne, Curr Opin Struct Biol 14, 397 (2004)

orientation of C- and N-terminus depends on charge. Cytoplasm contains more negatively charged lipids. By mutating the charges one can invert topology.

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Folding paradigm

White & von Heijne, Curr Opin Struct Biol 14, 397 (2004)

Back to the folding models of soluble proteins

(hydrophobic collapse vs. framework model).

Obviously, hydrophobic collapse doesn‘t apply here.

Using FRET labels (fluorescent non-natural amino acids) it could be shown that

the newly synthesized peptide assumes a compact = partially folded structure.

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Insertion of TM helices into bilayer

Hessa et al , Nature 433, 377 (2005)

This is an ingenious experiment to

identify the code for TM helix

partioning into the bilayer. Two glycolization sites engineered around H.

If H is inserted in membrane only G1 is

glycosilated, otherwise G1 and G2.

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Hydrophobicity scales

Hessa et al , Nature 433, 377 (2005)

Results from this work correlate well with partitioning

of peptides between water and octanol (Fig c)

partioning of TM helices into membrane is determined

by standard physico-chemical principles.

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Open and closed complexesdistinguish between two different types of supra-molecular complexes:

Closed complexes are relatively stable assemblies of different molecules with a

fixed stoichiometry, resulting in large molecular machines like ribosomes,

polymerases and ATPases. Although these complexes may be dynamic due to

their respective function (like capturing and releasing elongation factors for

ribosomes or transient phosphorylation for allosteric proteins), they have a well

defined structure and are degraded only as a whole (typically by proteasomes

after ubiquitylation).

In contrast, open complexes are in a constant exchange of their molecular

components with the environment. Both the total number of components and their

relative stoichiometry can vary within a certain range. A typical example are the

cytoplasmic plaques of focal adhesions, which have typical lifetimes of minutes to

hours, while the turnover time for the single proteins building up the plaque is on

the order of seconds. In contrast to closed complexes, open complexes are not

assembled and degraded as a whole, but in a gradual way.

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Focal adhesion pointsFocal adhesions are the most prominent sites

of adhesion when cell-matrix adhesion is studied

on rigid surfaces (glass or plastic).

In a physiological (soft) environment, similar sites of

adhesion exists, although they tend to be smaller and

of somehow different molecular composition.

Focal adhesions consist of four layers

(see Fig. from bottom to top): - an external layer of ECM ligand,- a layer of transmembrane receptors from

the integrin family, - a cytoplasmic plaque consisting of more than

50 different proteins, and - a layer of actin connecting the focal adhesion to the cytoskeleton.

Focal adhesions strongly signal to the cytoskeleton, mainly through the small GTPases from the Rho family.

They also trigger other signalling pathways like the MAP kinase pathway, thus influencing gene expression and

cell fate.

Focal adhesions are also the main sites for force transmission between the extracellular environment and the

cell. They seem to function as mechanosensors which convert both internal and external force into protein

aggregation and signalling. In particular, cells might sense the mechanical properties of their environment by

actively pulling on it through actomyosin contractility and focal adhesions.

How can one model all this?

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Virus assembly: idealized examples of closed complexes

Reddy et al. , Biophys J 74, 546 (1998)

(a) Schematic representation of a T = 3 quasiequivalent lattice,

corresponding to a rhombic triacontahedron, the geometrical

architecture of black beetle virus (BBV). Each of the trapezoids

represents a single subunit with the same amino acid sequence.

The T = 3 particle is formed of 180 subunits that lie in three

structurally unique positions (labeled A, B, and C). Subunits labeled

with same letter are related by icosahedral symmetry axes

corresponding to twofold, threefold, and fivefold rotations identified

by white ovals, triangles, and pentagons, respectively. Subunits

marked with different letters are related to one another by

quasisymmetry axes corresponding to twofold and threefold local

rotation axes identified, respectively, by yellow ovals and triangles.

The subunits labeled A, B, and C are related by quasi-threefold

symmetry; they form an icosahedral asymmetrical unit (protomer) of

the T = 3 particle.

(b) pseudo T = 3 surface lattice. In this lattice there are three types of

trapezoids (VP1, VP2, and VP3) representing subunits with different

amino acid sequences. The subunits identified by the same label

are related by icosahedral symmetry elements, twofold, threefold,

and fivefold, identified by white ovals, triangles, and pentagons.

(c) black beetle virus (BBV). blue, red, green = A, B, and C subunits.

The average diameter of the particle is 312 Å. Icosahedral and

quasisymmetry elements are identified by white and yellow labels.

(d) icosahedral

asymmetrical unit

(protomer) of BBV

made up of the A, B,

and C subunits and a

strand of partially

ordered RNA of

10 bases.

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Virus assembly: compute energies of intermediates

Reddy et al. , Biophys J 74, 546 (1998)

(a) A table showing the top three preferred configurations

for each association of subunits in the computed

assembly pathway for BBV, with the monomer as the

assembling unit. The first column shows the number of

associating monomers. Columns 2, 4, and 6 show a

schematic of the three best structures for each

association. G12 and G23 refer to the negative

differences of the association energies of the first and

second and second and third configurations.

(b) The preferred structures, with the trimer as the

assembling unit. It is important to note that the best

configurations for both assembly pathways are nearly

always the same; in some cases even the second best is

the same, emphasizing that the trimer is the likely

assembling unit. An exception is the best structure of the

15mer association. In this case the most stable monomer

assembly is not made up of a multiple of protomers, but

its preference, compared to the second and third most

stable structures, which are made of protomers, is

marginal.

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Summary

- Protein folding problem is well-isolated problem, almost „classical“

- some aspects are reasonably well understood

- interest currently widens towards studying multi-protein assemblies, superstructural units

- few concepts available, learn from protein folding field?

- many interesting phenomena involve membranes