Membranes - Chair of Computational Biology

Optimization
Energy 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
1. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding
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Content
1 Introduction
Biomolecular systems: Proteins, membranes, phenomena of protein folding,
protein complexes
2 Protein folding on lattices
Review of statistical thermodynamics (deltaG, deltaS)
Exact enumeration of all states
Folding 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 simulations
characterization of the free energy landscape for folding
Replica exchange simulations
Restraints to generate partially unfolded states
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Content (II)
6 Calculation of chemical rates
Transition state theory
Kramer theory
Folding at home
7 Diffusion: Smoluchowski equation
Langevin equation → Ermak-McCammon-algorithm for brownian dynamics
8 Application: Association kinetics of protein A with protein B
Energy landscape for 6 degrees of freedom (3× translation, 3× rotation)
Computation of kon rates from Brownian dynamics simulations
Calculation 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 molecules
Conformational dynamics on electronic surfaces, conical intersections
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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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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.
1. Lecture SS 20005
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literature
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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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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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Levinthal-Paradoxon
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.
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Faltungspfade
Es 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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„New view of protein folding“:
Faltung entlang trichterähnlichen Energielandschaften
Bryngelson, Wolynes, PNAS
(1987)
Gradient 
beschleunigt
Faltung
Rauhigkeit
bremst
Faltung
“Frustration”
Brooks, Gruebele, Onuchic, Wolynes,
PNAS 95, 11037 (1998)
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Energielandschaften (H. Frauenfelder/UIUC)
Links ein sehr einfache und rechts eine sehr komplizierte Energielandschaft
links, Energielandschaft von Ammoniak, NH3. Die konformationelle Koordinate (xAchse) 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.
Frauenfelder & Leeson, Nature Structural Biology 5, 757 - 759 (1998)
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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 HH 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).
1. Lecture SS 20005
Liu, Tan, Rost, J Mol Biol (2002) 332,
53-64
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Many NORS regions predicted in proteomes
Liu 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).
1. Lecture SS 20005
Liu, Tan, Rost, J Mol Biol (2002) 332, 53-64
Optimization, Energy Landscapes, Protein Folding
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NORS regions use particular amino acids
The 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:
p  p2
z 1
 P P .
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.
1
2
Liu, Tan, Rost, J Mol Biol (2002) 332, 53-64
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Prion: ein ungeklärtes Beispiel für misgefaltete
Proteine
c
Das Prion-Protein PrP :
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
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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 autokatalysiert
Stanley Prusiner,
Nobelpreis für Physiologie
oder 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
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.
http://www.nature.com/horizon/livingfrontier/background/membrane.html
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Membrane bilayers
Edidin, Nature Reviews Cell Biol 4, 414 (2003)
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Membrane bilayers
Membranes are not structureless.
„Domains“ or „lipid rafts“ rich in
cholesterol and sphingo-lipids may
form transiently.
Edidin, Nature Reviews Cell Biol 4, 414 (2003)
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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
crystal structure of translocon in closed state.
White & von Heijne, Curr Opin Struct Biol 14, 397 (2004)
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Types of TM-proteins
orientation of C- and N-terminus depends on charge. Cytoplasm contains more
negatively charged lipids. By mutating the charges one can invert topology.
White & von Heijne, Curr Opin Struct Biol 14, 397 (2004)
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Folding paradigm
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.
White & von Heijne, Curr Opin Struct Biol 14, 397 (2004)
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Insertion of TM helices into bilayer
This is an ingenious experiment to
identify the code for TM helix
Two glycolization sites engineered around H.
partioning into the bilayer.
If H is inserted in membrane only G1 is
glycosilated, otherwise G1 and G2.
Hessa et al , Nature 433, 377 (2005)
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Hydrophobicity scales
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.
Hessa et al , Nature 433, 377 (2005)
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Open and closed complexes
distinguish 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 points
Focal 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
(a)
(b)
(c)
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.
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.
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.
Reddy et al. , Biophys J 74, 546 (1998)
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Virus assembly: compute energies of intermediates
(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.
Reddy et al. , Biophys J 74, 546 (1998)
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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
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