Systematic calculation and characterization of local motions in allosteric proteins
Michael D.
Introduction
novel effector
substrate
PDB 1
G proteins
1HUR
1E0S
1AN0
1TUI
1OIV
1VG1
1HH4(A)
NA*
1KAO
4Q21
1XTQ
1FTN
1G16
1KY3
1SVI
1GDD
1TAG
protein kinases 1ERK
1P4O
1IRK
1GZK
response
3CHY
regulators
1L5Z
1DBW
1H4Y
PDB 2
NA*
1HFV
1NF3(A)
1EFT
1OIW
1VG8
1MH1
1IBR(A)
2RAP
6Q21
1XTS
1A2B
1G17
1KY2
1SVW
1GIA
1TND
2ERK
1K3A
1IR3
1O6K
1FQW
1L5Y
1D5W
1H4X
protein
anthranilate synthase
ATCase
ATP sulfurylase
ATP-PRT
caspase
chorismate mutase
DAHP synthase
FBPase-1
glcN-6-P deaminase
glycogen phosphorylase
GTP cyclohydrolase I
hemoglobin
lactate DH
NAD-malic enzyme
phosphofructokinase
phosphoglycerate DH
PTP1B
uracil PRT
• Major mechanism of control and regulation
in biology
PDB 1
1I7S
1RAC
1M8P
1NH8
1SHJ
2CSM
1KFL
1EYJ
1CD5
1GPB
1WPL
4HHB
1LTH(T)
1QR6
6PFK
1PSD
1T48
1XTU
PDB 2
1I7Q
1D09
1I2D
1NH7
1F1J
1CSM
1N8F
1EYI
1HOT
7GPB
1IS7
1HHO
1LTH(R)
1PJ2
4PFK
1YBA
1PTY
1XTT
Precise, diverse motion calculations
X
− understanding / treating diseases caused by
malfunctioning allosteric proteins
ΔCα
max(|Δφ|, |Δψ|)
− Designing novel allosteric proteins as biological
control devices
displacements
PDB 2
2ARC
1XXA
1HXD
1EFA
1CMA
1I6A
1WET
1QPI
Design allosteric response into a nonallosteric protein
Δφ
θαβ
L
L
L
backbone position
relative to protein core
side-chain orientation
ΔSC
max(fI, fA)
max(|Δχ1|, |Δχ2|)
T (inactive) state
L
L
L
L
atomic interactions with other
residues
local side-chain conformation
Choe et al. (2000), fig. 1
Manually compare I and A states →
qualitative mechanistic models
Low-resolution structural models
Discriminating true motions from crystallographic noise
Goals and new contributions
measure
X
statistic
|Δφ| (°)a
max(|Δφ|, |Δψ|) |Δψ| (°)a
ΔCα
ΔCα (Å)
θαβ (°)a,b
θαβ
max(|Δχ1|, |Δχ2|) |Δχ1| (°)a,c
ΔSC
ΔSC (Å)d
fI
max(fI, fA)
fA
X
X
X
X
X
X
X
X
A
X
X
X
X
X
X
X
X
X
X
X
Motion value histograms for five non-allosteric protein pairs
(control 1, black), nine allosteric protein pairs in same state
(control 2), and allosteric benchmark. Threshold.
Dataset of 51 Allosteric Proteins
Three functional classes
threshold
30°
1.2 Å
28°
46°
2.0 Å
0.20
• Smaller motions may be functionally
significant in some allosteric proteins
Allosteric motions in protein space
Sequence space
DNA-binding proteins
Enzymes
G protein ran (1IBR.pdb)
phosphofructokinase (4PFK.pdb)
PurR (1WET.pdb)
Control signaling
pathways
average
29.9
30.4
1.20
27.8
46.1
3.91
0.202
0.195
• Thresholds are intuitively reasonable
cutoffs for large motions
C
Statistically investigate amount and
structural distribution of motions
99th percentile
control 1 control 2
27.1
32.7
30.5
30.3
1.38
1.01
23.9
31.8
42.8
49.5
4.12
3.69
0.213
0.190
0.200
0.190
• Set thresholds to exclude ~99% of
background motion in controls
X
X
Precisely identify local motions in
known allosteric protein structures
• Contact changes, backbone motions cluster strongly in space
Statistics of allosteric transitions
MWC “pre-existing equilibrium” model
Control transcription by
binding DNA
Regulate reactions and
biochemical pathways
Δφ,ψ
ΔCα
Θαβ
Δχ1,2
ΔSC
fI,A
10
20
30
40
50
60
MTEYKLVVVGAGGVGKSALTIQLIQNHFVDEYDPTIEDSYRKQVVIDGETCLLDILDTAG
---------XX-------------XX---XX--XXXX----------------------X
----------------------------------XXX---------------------XX
---------.-..-.-------------------XXXX---------.----------X.
----XX--X....-.--.--X--XXXX-XX--X.XXXXX-----X--.---XX-X--X..
----XX--X....-.--.--X---XXX-X-XX-.--XXX-X---X--.---XX----X..
----X----XXXX---X-------------XXXXXXXX-----------------X-XXX
Δφ,ψ
ΔCα
Θαβ
Δχ1,2
ΔSC
fI,A
70
80
90
100
110
120
QEEYSAMRDQYMRTGEGFLCVFAINNTKSFEDIHQYREQIKRVKDSDDVPMVLVGNKCDL
XXXXXXXXXXXXX-------------------------------XXXXX----------XXXXXXXXXXXX--------------------------------X--X-----------XXXXX-XX-X-XX-.-.-----------------------------XX------.----XXXXX.XX-XXXX-.-.-----.----X--X---X-X-X--XXX-XXXX.-XXX.--X-X
XXXXX.-X-XXXX-.-.-----.-----------X---X--XX--XXXX.-XXX.----X
X-XXXXXXXXX--X------------------------X---X-----------------
Δφ,ψ
ΔCα
Θαβ
Δχ1,2
ΔSC
fI,A
130
140
150
160
AARTVESRQAQDLARSYGIPYIETSAKTRQGVEDAFYTLVREIRQHKL
XX-------------------------------------------------------------------------------------------------------------.----------X-.----------------..---X-XX.XXX.XXX.-.-X---.--XX.---.-X--X----X--X
..---X-XX.X-X.XX-.-.-----.---X.---.X---X---XX--X
X------X----------------------------------------
Motions for ras G protein (4Q21.pdb vs. 6Q21.pdb)
Cartesian correlation function Cm(r)
• Switch I and II
previously identified by
Milburn et al.
• Most of protein is rigid
• Motions tend to occur
in contiguous
segments (especially
backbone and
contacts)
• Strong consensus
between measures in
most flexible regions
Allosteric transitions comprise 10-20% of protein residues
max(|Δφ|,
|Δψ|)
ΔCα
θαβ
max(|Δχ1|,
|Δχ2|)
control 1
0.03 ± 0.03
0.02 ± 0.03
0.01 ± 0.02
0.13 ± 0.09
0.11 ± 0.08 0.03 ± 0.02
control 2
0.03 ± 0.02
0.01 ± 0.01
0.01 ± 0.01
0.16 ± 0.08
0.10 ± 0.05 0.02 ± 0.02
signaling
0.16 ± 0.06
0.22 ± 0.09
0.13 ± 0.05
0.33 ± 0.07
0.26 ± 0.06 0.24 ± 0.09
transcription
0.20 ± 0.08
0.12 ± 0.08
0.07 ± 0.03
0.35 ± 0.12
0.24 ± 0.09 0.18 ± 0.07
enzymes
0.12 ± 0.07
0.21 ± 0.11
0.06 ± 0.03
0.30 ± 0.09
0.21 ± 0.07 0.16 ± 0.06
ΔSC
• Backbone and contact motions strongly correlated at short separations (< 20 res.
or < 20Å) → local clustering of motions
• Apparent long-range correlations for backbone and side-chain motions present
only in a small minority of allosteric proteins (data not shown)
• Summary: distinctly non-random organization of backbone and contact motions in
allosteric proteins
• PFK: motions localize between catalytic and allosteric sites (esp. contact changes)
→ possible allosteric pathway
R (active) state
Signaling proteins
max(fI, fA)
≥ 0.2 0.3 0.4 0.5
• Backbone displacements, dihedral changes, and contact motions localize to similar
regions of structures
L
L
max(|Δχ1|,|Δχ2|) ≥ 46°
max(|Δφ|,|Δψ°|) ≥ 30°
max(|Δφ|,|Δψ°|) ≥ 65°
• Most of protein is structurally conserved
local backbone conformation
Sequence correlation function Cm(Δi)
• Correlation functions statistically measure strength and significance of local
cooperative effects and distance ranges over which they occur
Δψ
KNF “sequential transition” model
L
contact changes
Correlations are normalized against reference correlation (correlation expected if moving residues are distributed randomly)
ΔSC ≥ 2.0 Å
ΔCα ≥ 1.2 Å
ΔCα ≥ 3.0 Å
Previous work in allostery
L
dihedral changes
Enzymes
*obtained directly from authors; not in PDB
• Improved high-resolution understanding of
allostery will aid in
PDB 1
2ARA
1XXC
1BIA
1TLF
1CMB
1I69
1DBQ
2TRT
ras G protein
Protein
AraC
arg repressor
biotin repressor
lac repressor
met repressor
OxyR
PurR
tet repressor
Coupling among local allosteric motions
purine repressor
protein
arf1
arf6
cdc42
EF-Tu
rab11
rab7
rac1
ran
rap2a
ras
rheb
rhoA
sec4
ypt7p
YsxC
Giα1
Gtα
ERK2
IGF-1R
IRK
PKB
CheY
DctD
fixJ
SpoIIAA
Three-dimensional space
DNA-binding proteins
Signaling proteins
We have exploited the large number of known allosteric crystal structures to
systematically characterize local conformational changes in allosteric proteins toward the goal of
increasing the theoretical understanding of the structural basis of protein allostery on the atomic
scale. We have compiled a set of 51 pairs of known inactive and active allosteric protein
structures from the Protein Data Bank. We have measured changes in dihedral angles and
Cartesian displacements for backbones and side chains and rearrangements in residue-residue
contacts for each protein. Several examples show that these automated calculations reveal
functionally interesting pictures of local motions which corroborate many features previously
observed manually by crystallographers. In addition, statistical analysis of the calculated
motions shows that on average, 20 percent of residues differ significantly between the two
crystal structures of an allosteric protein in addition to possible changes in dynamics. Allosteric
motion is more probable in weakly constrained local structural environments like loops and
solvent-exposed regions than in strongly constrained environments like helices, strands, and
buried regions. Backbone and contact motions are correlated at separations of up to 20
residues in sequence space and up to 20 Å in Cartesian space. Together, these observations
suggest structural rules for designing allosteric protein systems.
Importance and applications
in Molecular & Computational Biophysics and 2Chemical & Biomolecular Engineering, Johns Hopkins University
A wide variety of targets
Abstract
and Jeffrey J.
1,2
Gray
phosphofructokinase
1Program
1
Daily
max(fI, fA)
0.20 ± 0.10
0.09 ± 0.05
0.32 ± 0.09 0.24 ± 0.07 0.20 ± 0.09
all allosteric 0.15 ± 0.07
Average fraction of residues moving (mean ± s.d) by six measures in six sets of proteins: two control
datasets, three classes of allosteric proteins, and all allosteric proteins.
• 10-20% of an allosteric protein changes backbone conformation, moves relative to
the core, or changes interactions with other residues
• Side-chain motion is significant in controls (10-15%) but more common in allosteric
proteins (25-30%)
• Extents of motion have high σ → significant variability in allosteric mechanisms
• Proteins in three classes change conformation to similar extents
Local structural environment influences allosteric motion
Theoretical implications
• Calculate motions in three types of degrees of freedom important to
protein structure
• Calculated motions do not in themselves constitute comprehensive
mechanistic models
• Statistical analyses reveal basic insights into structural basis of protein
allostery:
− Significant changes in average structure (~20%) are common in allosteric
proteins → not just a dynamic phenomenon
− Protein structures use constraints to control location of motion, possibly to
direct signal propagation between allosteric and functional sites
− Local motions are correlated up to 20Å distance, enough to bridge two spatially
distinct sites over several residues
− Mechanical communication is an important, general phenomenon in protein
allostery
• Possible test resource for flexibility prediction algorithms such as
COREX (Hilser & Freire 1996), elastic network models (Bahar et al. 1997), FIRST (Jacobs et
al. 2001), and statistical coupling analysis (Suel et al. 2003)
Future Directions
Domain and subunit motion
Allosteric mechanisms
effector
• Polar residues (especially side-chains)
more likely to move than apolar
residues
loop 1
Tetramer interface
7° rotation
• Secondary structure (backbone Hbonds) constrains backbone but not
side-chain
substrate
loop 1
• Burial constrains all motions (contact
constraints)
• Polar vs. apolar effect is a proxy for
exposed vs. buried (data not shown)
• Summary: Motion most likely in
weakly constrained environments
apolar: A, C, F, I, L, M, P, V, W, Y;
polar: D, E, G, H, K, N, Q, R, S, T
secondary structure (helix, strand, loop) assigned by
DSSP
buried, exposed – all-atom ASA ≤ 30% or > 30%,
respectively (naccess)
loop 2
substrate
loop 2
effector
An important part of allostery in
many oligomers
Quantify organization of moving
parts, connectivity between sites
Funding/ Acknowledgements
ARCS fellowship (M. Daily)
JHU Program in Molecular and
Computational Biophysics NIH
training grant (M. Daily)
NIH award K01-HG02316
(J. Gray)
Pymol and R (figures and
calculations)