Supplementary Material
Table S1. MaxOR for the 5 regions with centers shown in Figure 8C and their pairwise
combinations. The colors refer to the color of the conformations depicted in Fig. 8C.
A (red)
B (green)
C (blue)
D (yellow)
E (magenta)
A
0.54
0.90
0.90
0.64
0.63
B
-
0.53
0.58
0.78
0.96
C
-
-
0.55
0.77
1.00
D
-
-
-
0.50
0.68
E
-
-
-
-
0.60
Table S2. MaxOR for the 4 regions with centers shown in Figure S3 and their pairwise
combinations. The colors refer to the color of the conformations depicted in Fig. S3.
A (red)
B (green)
C (blue)
D (yellow)
A
0.58
0.91
0.61
0.79
B
-
0.56
0.72
0.95
C
-
-
0.51
0.79
D
-
-
-
0.57
1
Table S3. MaxOR for the 4 regions with centers shown in Figure S4 and their pairwise
combinations. The colors refer to the color of the conformations depicted in Fig. S4.
A (red)
B (green)
C (blue)
D (yellow)
A
0.62
0.66
0.73
0.74
B
-
0.60
0.71
0.73
C
-
-
0.60
0.96
D
-
-
-
0.60
2
Table S4. Exchange between two states (extended and compact) with unequal populations:
also in this case both SES and the MaxOcc/MaxOR analysis can recover the two
conformations used to calculate the averaged data. In this simulation, the averaged
datasets were calculated from ensembles composed of two CaM conformations, one
compact and one extended, with weight of 80% or 20%. Using the SES approach, both the
major and the minor conformations could be identified in all cases (using diamagnetic or
paramagnetic data, with 80% weight for the extended or the compact conformation). The
results of the MaxOcc/MaxOR analysis are provided in table: for each simulation the spatial
and angular displacement of the centers of the ensembles of the best scoring structures
from the centers of the actually sampled distribution is reported (in all cases, the major
state was recovered with MaxOcc calculations, and the minor state required the use of the
rotation [deg]
recovered minor state
(20%)
translation
[Å]
rotation [deg]
translation
[Å]
recovered major state
(80%)
Error
Restraint
Simulation
MaxOR approach).
dRDC
1 Hz
0.0
0.0
2.45
5.2
pRDC+PCS
1 Hz/0.01
ppm
1.12
2.6
5.4
5.1
dRDC
1 Hz
0.0
0.0
3.65
10.7
pRDC+PCS
1 Hz/0.01
ppm
2.70
7.8
1.24
2.0
80% closed state
20% open state
80% open state
20% closed state
3
Fig S1. SES recovery using pRDC. Color code: green - simulated structures in the centers of
the regions, red, blue - reconstructed structures with higher and lower weight, respectively.
In all cases the correct orientations are recovered, yet the positions are inaccurate. A)
Simulation1, 3 Hz error, B) Simulation 2, 2 Hz error.
A)
B)
4
Fig S2. SES recovery using PCS. Color code: green - simulated structures in the centers of
the regions, red, blue - reconstructed structures with higher and lower weight, respectively.
A) Simulation2, 0.02 ppm error – the blue recovered structure exactly coincides with one of
the original centers , B) Simulation 3, 0.01 ppm error- one ‘average’ state recovered instead
of the two centers.
A)
B)
5
Fig S3. MaxOcc/MaxOR results for Simulation 3 with paramagnetic data (1 Hz error for
pRDC and 0.01 ppm error for PCS). Each conformation is represented by a triad of Cartesian
axes, centered at the center of mass of the C-terminal domain, A) The structures with the
highest MaxOcc, color code – according to the MaxOcc value (0.0-blue, 0.6-red) B) The
clusters formed by the structures in panel A, C) The centers of the clusters, D) The centers
of clusters chosen with MaxOR versus the centers of the simulated regions (black).
A)
B)
6
C)
D)
7
Fig S4. MaxOcc/MaxOR results for Simulation 3 with dRDC (1 Hz error). Each conformation
is represented by a triad of Cartesian axes, centered at the center of mass of the C-terminal
domain, A) The structures with the highest MaxOcc, color code – according to the MaxOcc
value (0.0-blue, 0.6-red) B) The clusters formed by the structures in panel A, C) The centers
of the clusters, D) The centers of clusters chosen with MaxOR versus the centers of the
simulated regions (black).
A)
B)
8
C)
D)
9
Fig S5. Any set of averaged RDC and PCS measurements can be seen as a point ( P ) which
can be reconstructed by a convex combination (i.e. a linear combination with weights
summing up to 1) of sets of RDC and PCS values corresponding to a number of different
protein conformations ( P1 , P2 , P3 , in the figure, panel a). The weight of each Pi is equal to
the ratio of the areas of triangles Ti and T , where T is the triangle P1 P2 P3 and Ti is the
triangle where the point Pi is replaced by P . The SES method consists in reconstructing P
using a smaller number of vertices, 2 in our example (panel b) that can still yield a solution.
In fact, we can obtain a good approximation by letting the sum of the probabilities be less
than 1: the combination of P2 and P3 reconstructing P as shown in panel b may be seen as
a combination of P2 and P3 with weights scaled down according to the linear scaling factor
between the triangles OP2 P3 and OP2 P3 (O is the origin).
P1
P1
V
(b)
(a)
M
O
T
T2
P3
P
P3
P3
P2
10
P
P2
P2
Figure S6. The number of conformations included in the ensemble determined with the SES
method is determined using the L-curve method: a smoothing spline is fitted through the points
and then the position of the maximum curvature is computed. In this example, the optimal size is
given by 2 conformations.
11