membrane structure prediction 1 cb1 tmh1 - rostlab · • makeup: oct 13, 2015 - morning/noon 2...
TRANSCRIPT
/00© Burkhard Rost
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title: Computational Biology 1 - Protein structure: Membrane structure prediction 1short title: cb1_tmh1
lecture: Protein Prediction 1 - Protein structure Computational Biology 1 - TUM Summer 2015
/00© Burkhard Rost
Videos: YouTube / www.rostlab.org THANKS : Tim Karl + Carlo Di Domenico Special lectures:
• TBA No lecture:
• 05/12 Student assembly (SVV) • 05/14 Ascension day • 05/26 Whitsun holiday • 06/04 Corpus Christi LAST lecture: Jul 7 Examen: Jul 9
• Makeup: Oct 13, 2015 - morning/noon
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CONTACT: Inga Weise [email protected]
Tim Karl
Tatyana Goldberg
Edda Kloppmann
Andrea Schaffer-
hans
Jonas Reeb
Carlo Di [email protected]
/00© Burkhard Rost
1D: TM
transmembrane helix
prediction3
/00© Burkhard Rost
What to put around a cell?
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Roshni Nelson: Cell Membranes
© Roshni Nelson UT Southwestern Dallas http://www.roshninelson.com
http://utsouthwestern.edu/STARS - vimeo.com/31412291
/00© Burkhard Rost
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Roshni Nelson: Phospholipids
© Roshni Nelson UT Southwestern Dallas http://www.roshninelson.com
http://utsouthwestern.edu/STARS - vimeo.com/31412291
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Prokaryotic Cell Eukaryotic Cell (bacillus type)
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Cellular compartments
© Tatyana Goldberg (TUM Munich)
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Localization for drug targets
TM Bakheet and AJ Doig (2008) Bioinforma)cs
Membrane 57%
Cytoplasm 13%
Extra-cellular 13%
ER 7%
Nucleus 3%
Mito 2%
Other 2%
Microsome 2%
Pero 1%
Drug targets tend to be found in membranes, cytoplasm or are
extra-cellular!© Tatyana Goldberg (TUM Munich)
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TMH (Transmembrane
helix) background
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1JB0Cyanobacterial Photosystem I
Jordan P, Krauss N
1E7PFumarate ReductaseLancaster CD, Michel
H
periplasm
cytoplasmCytoplasm (stromal side)
?
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1KFYQuinol Fumarate Reductase
Iverson TM, Rees DC1MSL
Mechanosensitive Ion ChannelMscL Homolog
Chang G, Rees DC
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2BCC Cytochrome bc1 Zhang Z, Kim S
1QCR Cytochrome bc1 complex from Bovine Heart Mitochondria Xia D, Diesenhofer J
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Transmembrane vs. membrane anchored/associated
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Membrane prediction
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HTM prediction wait for db growth ...
1993
1999
1996
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Topology for membrane helical proteins.
exex tratra -cy-cy toto pp ll aa smsm ii cc
ii nn tt rr aa -- cc yy tt oo pp ll aa ss mm ii ccin
protein Aprotein C
C-term
out
in
protein B
C-term
C-term
lipid membranebilayer
inside cytoplasm
outside cytoplasm
/00© Burkhard Rost
TMH prediction
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PHDsec “success” on Poly-Valine
HEADER LIPOPROTEIN(SURFACE FILM)COMPND PULMONARY SURFACTANT-ASSOCIATED POLYPEPTIDE C(SP-C)SOURCE PIG (SUS SCROFA)AUTHOR J.JOHANSSON,T.SZYPERSKI,T.CURSTEDT,K.WUTHRICH
AA LRIPCCPVNLKRLLVVVVVVVLVVVVTVGALLMGLOBS sec HHHHHHHHHHHHHHHHHHHHHHHHHPHD sec EEEEEEEEEEEEEEEEEEEEEEE
/00© Burkhard Rost
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How 2 separate outside/inside?
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Lipid bilayer
Wikipedia © http://en.wikipedia.org/wiki/Lipid_bilayer
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Example 1: GPCR*: signaling
* G-Protein Coupled Receptor
Wikipedia © http://en.wikipedia.org/wiki/Lipid_bilayer
40% of all drugs target GPCRs
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Example 2: pumps and channels
Wikipedia © http://en.wikipedia.org/wiki/Potassium_channel
Shaker: voltage gated potassium channel
SB Long, EB Campbell & R Mackinnon (2005) Science 309: 897–903
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Example 3: cell fusion
J Rizo & TC Südhof (2002) Snares and munc18 in synaptic vesicle fusion. Nature Reviews Neuroscience 3, 641-653
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Lipid bilayer: hydrophobic in inside
Wikipedia © http://en.wikipedia.org/wiki/Lipid_bilayer
/00© Burkhard Rost
-+-
+ +++
-
-
--
----
- ++
++
+
+
HHHHH
H HH
HHH H H
H-
+
solvent
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Hydrophobic core of a protein
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Topology for membrane helical proteins.
exex tratra -cy-cy toto pp ll aa smsm ii cc
ii nn tt rr aa -- cc yy tt oo pp ll aa ss mm ii ccin
protein Aprotein C
C-term
out
in
protein B
C-term
C-term
lipid membranebilayer
inside cytoplasm
outside cytoplasm
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Hydrophobic side chains
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Eisenberg hydrophobicity indexAA-3 AA-1 Eisenberg
Ile I 1.38Phe F 1.19Val V 1.08Leu L 1.06Trp W 0.81Met M 0.64Ala A 0.62Gly G 0.48Cys C 0.29Tyr Y 0.26Pro P 0.12Thr T -0.05Ser S -0.18His H -0.4Glu E -0.74Asn N -0.78Gln Q -0.85Asp D -0.9Lys K -1.5Arg R -2.53
David Eisenberg, UCLA © https://www.uclaaccess.ucla.edu/
uploads/image/faculty/134.jpg
D Eisenberg et al. (1984) J Mol Biol 179:125-42
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Pure hydrophobicity scaleshydrophobicity scales
-6.75
-4.50
-2.25
0.00
2.25
4.50
6.75
9.00
A R N D C Q E G H I L K M F P S T W Y VGES EISEN KYDO
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5 Hydrophobicity/tm/occupancy scaleshydrophobicity scales
0.00
0.25
0.50
0.75
1.00
A R N D C Q E G H I L K M F P S T W Y VGES EISEN KYDO OOI HEIJNE
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Many indices exist
K Tomii and M Kanehisa (1996) Analysis of amino acid indices and mutation matrices for sequence comparison and structure prediction of proteins. Protein Eng 9:27-36: Fig. 2 (402 indices)
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PHDsec success on Poly-Valine
HEADER LIPOPROTEIN(SURFACE FILM)COMPND PULMONARY SURFACTANT-ASSOCIATED POLYPEPTIDE C(SP-C)SOURCE PIG (SUS SCROFA)AUTHOR J.JOHANSSON,T.SZYPERSKI,T.CURSTEDT,K.WUTHRICH
AA LRIPCCPVNLKRLLVVVVVVVLVVVVTVGALLMGLOBS sec HHHHHHHHHHHHHHHHHHHHHHHHHPHD sec EEEEEEEEEEEEEEEEEEEEEEE
NLKRLLVVVVVVVLVVVVTVGALL h hhhhhhhhhhhhhh h hhhh: hydrophobic
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Gunnar von Heijne • G von Heijne (1981) On the hydrophobic nature of signal sequences. Eur J
Biochem 116: 419-22. • G von Heijne (1981) Membrane proteins: the amino acid composition of
membrane-penetrating segments. Eur J Biochem 120: 275-8. • G von Heijne (1992) Membrane protein structure prediction. Hydrophobicity
analysis and the positive-inside rule. J Mol Biol 225: 487-94.
• I Nilsson & G von Heijne (1990) Fine-tuning the topology of a polytopic membrane protein: role of positively and negatively charged amino acids. Cell 62: 1135-41.
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Membrane protein prediction
Gunnar von HeijneStockholm Univ
Royal Swedish Academy of Sciences
©http://www.abo.fi/public/fi/media/6765/
heijne_von_gunnar_2.jpg
/00© Burkhard Rost
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Identify hydrophobic regions
G von Heijne (1992) Membrane protein structure prediction. Hydrophobicity analysis and the positive-inside rule. J Mol Biol 225: 487-94: Fig. 4
/00© Burkhard Rost
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Identify hydrophobic regions
G von Heijne (1992) Membrane protein structure prediction. Hydrophobicity analysis and the positive-inside rule. J Mol Biol 225: 487-94: Fig. 1
/00© Burkhard Rost
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Identify hydrophobic regions
G von Heijne (1992) Membrane protein structure prediction. Hydrophobicity analysis and the positive-inside rule. J Mol Biol 225: 487-94: Fig. 4
/00© Burkhard Rost
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Topology for membrane helical proteins.
exex tratra -cy-cy toto pp ll aa smsm ii cc
ii nn tt rr aa -- cc yy tt oo pp ll aa ss mm ii ccin
protein Aprotein C
C-term
out
in
protein B
C-term
C-term
lipid membranebilayer
/00© Burkhard Rost
G von Heijne (1986) The distribution of positively charged residues in bacterial inner membrane proteins correlates with the trans-membrane topology. EMBO J 5:3021-7Fig. 2
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Positive-inside rule
cytosolic loops
periplasmic loops
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Topology for membrane helical proteins.
exex tratra -cy-cy toto pp ll aa smsm ii cc
ii nn tt rr aa -- cc yy tt oo pp ll aa ss mm ii ccin
protein Aprotein C
C-term
out
in
protein B
C-term
C-term
lipid membranebilayer
/00© Burkhard Rost
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Heijne rule: positive inside out
0.920.95
0.93
0.91 0.900.92
0.870.89
N-term C-term
5 30 6 5
outout
Eight bestHTM's
µ=0: 0 HTM
µ=2: 2 HTMµ=3: 3 HTM
µ=1: 1 HTM
Loop lengths
Charge:Number of R+Kin loops 1-4
final prediction:∆ =(5+1) - (2+3)>0=> first loop out lipid membrane bilayer
extra-cytoplasmic
intra-cytoplasmic
R+KΣ=2
R+KΣ =5
R+KΣ =3
R+KΣ=1
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1. predict <H> 2. assign positive inside-out 3. choose threshold to optimize inside-out difference
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G von Heijne (1992) Membrane protein structure prediction. Hydrophobicity analysis and the positive-inside rule. J Mol Biol 225: 487-94: Fig. 4
Identify hydrophobic regions
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S Jayasinghe, K Hristova, SH White (2001) Energetics, stability, and prediction of transmembrane helices. J Mol Biol 12:927-34idea: optimize hydrophobicity scale for prediction
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Hydrophobicity-based
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PHDsec success on Poly-Valine
HEADER LIPOPROTEIN(SURFACE FILM)COMPND PULMONARY SURFACTANT-ASSOCIATED POLYPEPTIDE C(SP-C)SOURCE PIG (SUS SCROFA)AUTHOR J.JOHANSSON,T.SZYPERSKI,T.CURSTEDT,K.WUTHRICH
AA LRIPCCPVNLKRLLVVVVVVVLVVVVTVGALLMGLOBS sec HHHHHHHHHHHHHHHHHHHHHHHHHPHD sec EEEEEEEEEEEEEEEEEEEEEEE
/00© Burkhard Rost
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HTM
nonHTM
outputlayer
inputlayer
hiddenlayer
20444
21+3""""""
percentage of each amino acid in proteinlength of protein (≤60, ≤120, ≤240, >240)distance: centre, N-term (≤40,≤30,≤20,≤10)distance: centre, C-term (≤40,≤30,≤20,≤10)
input global in sequence
input local in sequence
localalign-ment13
adjacentresidues
:::
AAA
AA.
LLL
LII
AAG
CCS
GVV
:::
globalstatist.wholeprotein
%AALength∆ N-term∆ C-term
A C L I G S V ins del cons
100 0 0 0 0 0 0 0 0 1.17
100 0 0 0 0 0 0 33 0 0.42
0 0 100 0 0 0 0 0 33 0.92
0 0 33 66 0 0 0 0 0 0.74
66 0 0 0 33 0 0 0 0 1.17
0 66 0 0 0 33 0 0 0 0.74
0 0 0 33 0 0 66 0 0 0.48
HTM
nonHTM
3+1""""""
20444
first levelsequence-to- structure
second levelstructure-to- structure
P H D ht m
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Dynamic programming on NN ‘energy’
1
01
0residue number
T
N
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PHDhtm
refine
0.920.95
0.93
0.91 0.900.92
0.870.89
N-term C-term
5 30 6 5
outout
Eight bestHTM's
µ=0: 0 HTM
µ=2: 2 HTMµ=3: 3 HTM
µ=1: 1 HTM
Loop lengths
Charge:Number of R+Kin loops 1-4
final prediction:∆ =(5+1) - (2+3)>0=> first loop out lipid membrane bilayer
extra-cytoplasmic
intra-cytoplasmic
R+KΣ=2
R+KΣ =5
R+KΣ =3
R+KΣ=1
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PHDhtm on Poly-Valine
HEADER LIPOPROTEIN(SURFACE FILM)COMPND PULMONARY SURFACTANT-ASSOCIATED POLYPEPTIDE C(SP-C)SOURCE PIG (SUS SCROFA)AUTHOR J.JOHANSSON,T.SZYPERSKI,T.CURSTEDT,K.WUTHRICH
AA LRIPCCPVNLKRLLVVVVVVVLVVVVTVGALLMGLOBS htm TTTTTTTTTTTTTTTTTTTTTTTTTPHD htm TTTTTTTTTTTTTTTTTTTTTTTT
/00© Burkhard Rost
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Membrane helix prediction: TMHMM
TMHMM: sketch
details: inside/outside loop
details: TM core
A Krogh, B Larsson, G von Heijne, EL Sonnhammer (2001) 305:567-80, Fig. 1
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Gabor E Tusnady & Istvan Simon (2001) The HMMTOP transmembrane topology prediction server. Bioinformatics 17:849-850.
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Membrane helix prediction: HMMTOP
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Prediction of membrane helicesQo
k: %
of p
rote
in w
ith al
l TM
H rig
ht
J Reeb & E Kloppmann unpublished
/00© Burkhard Rost
Other problems unravelled by recent
structures
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Inventory of life: membrane proteins
0 5 10 15 20 25 30
A pernixA fulgidus
M jannaschiiM thermoautotrophicu
P abyssiP horikoshii
A aeolicusB subtilis
B burgdorferiC jejuni
C pneumoniaeC trachomatisD radiodurans
E coliH influenzae
H pyloriM genitalium
M pneumoniaeM tuberculosisN meningitidis
R prowazekiiS PCC6803T maritimaT pallidum
U urealyticum
S cerevisiaeC elegans
D melanogasterH sapiens (SP/TrEmbl
H sapiens(chr 22)
%mem
eukaryotes
bacteria
archaea
J Liu. & B Rost (2001) Prot. Sci. 10, 1970-1979.
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Kingdoms similar in length
J Liu. & B Rost (2001) Prot. Sci. 10, 1970-1979.B Rost (2002) Curr Op Struct Biol, 12, 409-416
eukaryotesbacteriaarchaea
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Kingdoms similar in amino acids usage
J Liu. & B Rost (2001) Prot Sci 10, 1970-1979.B Rost (2002) Curr Op Struct Biol, 12, 409-416
eukaryotes
bacteria
archaea
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010203040506070
0 20 40 60 80 100
yeastcaeeldromehumanhs22
01020304050607080
0 20 40 60 80 100
aerpearcfumetjamettmpyrabpyrho
0 20 40 60 80 100
Number of proteins in familyJ Liu & B Rost 2001 Prot Science 10, 1970-79 55
Family sizes similar
01020304050607080
0 20 40 60 80 100
aquaebacsuborbucamjechlpnchltrdeiraecolihaeinhelpymycgemycpnmyctuneimericprsyny3thematrepaureur
0 20 40 60 80 100
eukaryotes
Cum
ulat
ive
perc
enta
ge o
f pro
tein
s
bacteria
archaea
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Inventory of life: membrane proteins
0 5 10 15 20 25 30
A pernixA fulgidus
M jannaschiiM thermoautotrophicu
P abyssiP horikoshii
A aeolicusB subtilis
B burgdorferiC jejuni
C pneumoniaeC trachomatisD radiodurans
E coliH influenzae
H pyloriM genitalium
M pneumoniaeM tuberculosisN meningitidis
R prowazekiiS PCC6803T maritimaT pallidum
U urealyticum
S cerevisiaeC elegans
D melanogasterH sapiens (SP/TrEmbl
H sapiens(chr 22)
%mem
eukaryotes
bacteria
archaea
J Liu. & B Rost (2001) Prot. Sci. 10, 1970-1979.
2013 note: some issues with data (incomplete sequences?)e.g. human has more than 18%
/00© Burkhard Rost
Number of transmembrane helices
Cum
ulat
ive
perc
enta
ge o
f mem
bran
e pr
otei
ns
0
20
40
60
80
100
0 5 10 15 20
ArchaeaProkaryoteEukaryote
57
More TM -> more complexity?
J Liu. & B Rost (2001) Prot. Sci. 10, 1970-1979.
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Membraneproteins:
0
10
20
30
40 aerpe bacsu yeast
0
10
20
30
40 arcfu camje caeel
0
10
20
30
40 metja ecoli drome
0
10
20
30
40
1 3 5 7 9 11 13 15 17
pyrho haein human
inout
1 3 5 7 9 11 13 15 17 1 3 5 7 9 11 13 15 17
J Liu. & B Rost (2001) Prot. Sci. 10, 1970-1979.
/00© Burkhard Rost
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Membrane LEGO
J Liu. & B Rost (2001) Prot. Sci. 10, 1970-1979.
/00© Burkhard Rost
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Length of globular regions in membrane proteins
IntracellularExtracellular
Length of globular regions in membrane proteins
Perc
enta
ge o
f glo
bula
r reg
ions
10
20
30
40
50
10
20
30
40
50
0
10
20
30
40
50
100 200 300 400 500 600 100 200 300 400 500 600 700
Aeropyrum pernix K1
Caenorhabditiselegans
Bacillussubtilis
Drosophilamelangoster
Archaeoglobus fulgidus
Escherichiacoli
J Liu. & B Rost (2001) Prot. Sci. 10, 1970-1979.
/00© Burkhard Rost
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Inventory of life: coiled-coil proteins
0 5 10 15 20 25 30
A pernixA fulgidus
M jannaschiiM thermoautotrophicu
P abyssiP horikoshii
A aeolicusB subtilis
B burgdorferiC jejuni
C pneumoniaeC trachomatisD radiodurans
E coliH influenzae
H pyloriM genitalium
M pneumoniaeM tuberculosisN meningitidis
R prowazekiiS PCC6803T maritimaT pallidum
U urealyticumS cerevisiae
C elegansD melanogaster
H sapiens (SP/TrEmblH sapiens(chr 22)
%mem
0 2 4 6 8 10 12
%coils
J Liu. & B Rost (2001) Prot. Sci. 10, 1970-1979.
eukaryotes
bacteria
archaea
/00© Burkhard Rost
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Inventory of life: compartments
5 10 15 20 25
% extra-cellular
0 5 10 15 20 25 30
A pernixA fulgidus
M jannaschiiM thermoautotrophicu
P abyssiP horikoshii
A aeolicusB subtilis
B burgdorferiC jejuni
C pneumoniaeC trachomatisD radiodurans
E coliH influenzae
H pyloriM genitalium
M pneumoniaeM tuberculosisN meningitidis
R prowazekiiS PCC6803T maritimaT pallidum
U urealyticumS cerevisiae
C elegansD melanogaster
H sapiens (SP/TrEmblH sapiens(chr 22)
% membrane
5 10 15 20
% nuclear
J Liu. & B Rost (2001) Prot. Sci. 10, 1970-1979.B Rost (2002) Curr Op Struct Biol, 12, 409-416
euka
ry
otes
bact
eria
arch
aea
/00© Burkhard Rost
statistics for PDB in June 2010:67,086 structures in PDB (June 2010) 1,197 transmembrane 1,014 alpha helical 179 beta barrel
-> < 2% BUT: >20% of all proteins!
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TMH proteins: reminders
GE Tusnady, ZS Dosztanyi & I Simon (2005) Bioinformatics 21:1276-7
/00© Burkhard Rost
statistics for PDB in June 2010:67,086 structures in PDB (June 2010) 246 unique* transmembrane
-> < way less than 2% BUT: >20% of all proteins!
• * unique=non-identical sequence (can have PIDE>99.5%!)
64
TMH proteins: reminders
S Jayasinghe, K Hristova, SH White (2001) Protein Sci 10:455-8
/00© Burkhard Rost
Edda Kloppmann & Marco Punta: 1,035 PDB unique TM structures (Jan 2012)-> 107 Pfam families
65
TMH proteins: reminders
E Kloppmann, M Punta & B Rost (2012) Curr Op Struct Biol 22:326-32
/00© Burkhard Rost
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Thanks to Arne Elofsson
Following slides taken from Arne Elofsson, Stockholm Univ
/00© Burkhard Rost
78 interface helices ~50% of chains contain interface helix Average length ~ 9 aa Longest is 19 aa Most frequent in photosynthetic reaction center
E Granseth, G von Heijne & A Elofsson (2005) J Mol Biol 346:377-85
© Arne Elofsson (Stockholm Univ) 67
Interface helices (Granseth, JMB 2005)
/00© Burkhard Rost
36 reentrant helices • 20 in new classification 24% contain reentry 72% on the outside Length 3-32 residues Loops 11-117 residues
68
Reentry regions
H Viklund, E Granseth & A Elofsson (2006) J Mol Biol 361:591-603
© Arne Elofsson (Stockholm Univ)
/00© Burkhard Rost
69
36 reentry regions in 3 classes
Helix-coil/Coil-helix
Helix-coil-helix Coil
H Viklund, E Granseth & A Elofsson (2006) J Mol Biol 361:591-603© Arne Elofsson (Stockholm Univ)
/00© Burkhard Rost
70
Predict re-entry regions
H Viklund, E Granseth & A Elofsson (2006) J Mol Biol 361:591-603: Fig. 5
/00© Burkhard Rost
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Rentry predicted in entire genomes
H Viklund, E Granseth & A Elofsson (2006) J Mol Biol 361:591-603
© Arne Elofsson (Stockholm Univ)
0.280.720.24079Observed in dataset
0.520.480.167773E. coli0.400.600.10757S. cerevisiae
0.540.460.154181H. sapiens
Reentrants in
Reentrants out
Reentrant fraction
ProteinsGenome
0.310.220.110.07FractionChannels
Active transporters
Electron transporters
Signal receptors
/00© Burkhard Rost
Membrane protein structures are complex • TM-helices ends at different locations • Different angles • Neighboring helices often interact • Interface helices • reentrant regions No sheets close to the membrane
72
The not so simple TM proteins
H Viklund, E Granseth & A Elofsson (2006) J Mol Biol 361:591-603
© Arne Elofsson (Stockholm Univ)
/00© Burkhard Rost
73
More complex structures need new prediction methods
Nout
Cin
C
N
cytoplasm
periplasm
Membrane
H Viklund, E Granseth & A Elofsson (2006) J Mol Biol 361:591-603
© Arne Elofsson (Stockholm Univ)
/00© Burkhard Rost
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The Z-coordinate
Z-coordinate: distance residue 2 membrane center
Z
0
15
-15
Periplasm
Cytoplasm
H Viklund, E Granseth & A Elofsson (2006) J Mol Biol 361:591-603 © Arne Elofsson (Stockholm Univ)
/00© Burkhard Rost
01: 04/14 Tue: no lecture 02: 04/16 Thu: no lecture 03: 04/21 Tue: Organization of lecture: intro into cells & biology 04: 04/23 Thu: Intro I - acids/structure 05: 04/28 Tue: Intro 2 - domains/3D comparisons 06: 04/30 Thu: Alignment 1 07: 05/05 Tue: Alignment 2 08: 05/07 Thu: Comparative modeling 1 09: 05/12 Tue: SKIP: student assembly (SVV) 10: 05/14 Thu: SKIP: Ascension Day 11: 05/19 Tue: Experimental structure determination/Secondary structure assignment 12: 05/21 Thu: 1D: Secondary structure prediction 1 13: 05/26 Tue: SKIP: Whitsun holiday (05/23-26) 14: 05/28 Thu: 1D: Secondary structure prediction 2 15: 06/02 Tue: 1D: Secondary structure prediction 3 / Transmembrane structure prediction 1 16: 06/04 Thu: SKIP: Corpus Christi 17: 06/09 Tue: 1D: Transmembrane structure prediction 2 18: 06/11 Thu: 1D: Transmembrane structure prediction 3 - Jonas 19: 06/16 Tue: 1D: Solvent accessibility prediction 20: 06/18 Thu: 1D: Disorder prediction 21: 06/23 Tue: 2D prediction 1 22: 06/25 Thu: 2D prediction 2 23: 06/30 Tue: 3D prediction 1 24: 07/02 Thu: Nobel prize symposium 25: 07/07 Tue: wrap up 26: 07/09 Thu: examen, no lecture 27: 07/14 Tue: examen, no lecture 28: 07/16 Thu: examen alternative, no lecture
75
Lecture plan (CB1 structure)