Supplementary Material Larsson Et Al. Backbone Dynamics of a Calmodulin Dimer

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Supplementary Material Larsson et al. Backbone Dynamics of a Calmodulin dimer

I. Hydrodynamic calculations.

Introduction.

The analysis of the NMR relaxation data measured at two magnetic fields (using the PINATA scripts (7), see e.g. Results/Identification of ns time scale internal motion and Fig. 3, main text) shows that the apparent tumbling time (mo)app-corr is on average 10.5 ns, and that apart from the usual ps time scale internal motion, also a ca 2.5 ns time scale internal motion is present. The ps time scale internal motion can be attributed to vibration motion of the N-HN vectors. To interpret the ns time scale internal motion is however more complex, as described by the two points below.

I) In principle, the dimeric CaM:SEF2-1mp complex allows for internal motions involving the N- and C- terminal domains as well as internal motions involving the CaM monomers as a whole. Hydrodynamic calculations can provide some indication as to the structural interpretation of the 2.5 ns internal motion.

II) The extracted apparent tumbling time (mo)app,cor of on average 10.5 ns can in principle be an average of any number of contributions on different time scales > 4 ns. These contributions can stem from the well-known modes due to anisotropic motion, but could also in part stem from slow (> 4 ns) time scale internal motions, e.g. the 7 to 9 ns internal motion of the two CaM monomers in the complex (vide infra). Hydrodynamic calculations could provide some indication as to whether one and/or the other applies.

Before, addressing these two questions, calibration of the hydrodynamic calculations is considered.

Calibration of hydrodynamic calculations.

Hydrodynamic calculations using analytical expressions are well established but their use requires simplifying the molecule to a geometric object (in this study a cylinder/ellipsoid). Here, we employed the analytical expressions for the cylinder symmetric object interpolated between the well established ones for a cylinder with length/diameter (L/D) > 3 (Broersma equation; (2,3)) and a sphere. Thus, given size (L) and axial ratio (L/D), the tumbling time of the long axis of an object, l-hydr-anal, can be predicted with high accuracy using these analytical expressions. In Figure S1 (top panel) l-hydr-anal is shown as function of L for a number of axial ratios. However, because l-hydr-anal is proportional to L3, uncertainty in the exact size of the molecule – e.g. L estimated from size in pdb file - has a strong effect on the uncertainty of the predicted tumbling time and can easily be as large as 30 %.

Bead hydrodynamics, on the other hand, takes account of the irregular shape of the molecule, but it needs overall calibration to reliably calculate the absolute values of the overall tumbling times. We employed the bead model hydrodynamics incorporated in DASHA (6,8). To calibrate the bead model hydrodynamics, the protocol of Garcia de la Torre et al. was used (5). We find that a bead size of 3.0 Å for the shell of beads surrounding the C atoms provides a good calibration estimate for the overall tumbling time of the long axis estimated from bead hydrodynamics, l-hydro-bead. Garcia de la Torre et al. find a similar value of 3.4 Å. Thus, comparing the results of both methods allows one to gauge the reliability of the hydrodynamics predictions.

In Figure S1 and Table HS1 analytical and bead model hydrodynamic estimates of the overall tumbling times (l-hydro-anal/bead) are compared with published experimentally determined overall tumbling times (l-NMR or c-NMR, for exact definition see legend of Table HS1). Also, the predicted data for some schematic models of the dimeric CaM-SEF2-1mp complex are included. As can be seen (e.g. Table HS1 and Figure S1, bottom panel), both prediction methods – analytical and bead hydrodynamics - lead to similar results and fit generally rather well with the experimental tumbling times for the calibration proteins. Given these similar results for both prediction methods, the vertical bars in Figure S1 (bottom panel) for the analytical l-hydro (l-hydro-anal) provide a semi-quantitative indication of the uncertainty in the prediction of l, which can be up to ca. 30 %.

Hydrodynamic calculations - structural interpretation of CaM domain motions

The hydrodynamic calculations on the CaM:SEF2-1mp/monomer, CaM-SMLCK/monomer and CaM N- and C-terminal domains (Table HS1) provide data on the predicted l for the free CaM monomer in the complex and the separate free N- and C-terminal domains of CaM. These predicted l values provide a means to interpret the time scales for internal motion derived from NMR relaxation data. From mode analysis of the dimeric complex both monomer and domain type internal motions are in principle possible. The observed 2.5 ns additional internal motion in the CaM:SEF2-1mp complex is most likely due to motions of the separate N- and C-terminal domains of CaM, which according to the hydrodynamic calculations have an overall correlation time of ca 3 ns.

The time scale for a free CaM is ca 7 to 9 ns. This suggests that monomer type internal motion within the dimeric CaM:SEF2-1mp complex can potentially be mixed in with the apparent overall tumbling time of 10.5 ns. This aspect will be discussed in the next section.

Hydrodynamic calculations - structural interpretation of CaM monomer motions

The free CaM ‘monomer’ has a predicted long axis tumbling time l-hydro of 7 to 9 ns (Table HS1, Figure S1, bottom). Mode analysis suggests that in principle ‘monomer’ motion can occur within the dimeric CaM:SEF2-1mp complex. As already pointed out by Garcia de la Torre and coworkers (1,4,5), internal motion with slow ( > 4 ns) time scales reduces the apparent overall tumbling time derived from NMR. Consequently, a predicted long axis tumbling time l (l-hydro) of the whole dimeric complex that is larger than the experimental l can be indicative of such internal motions (the experimental l or l-NMR is the experimental long axis overall tumbling time and is derived from the maximum (mo)app-corr, see Table HS1 legend for exact definitions).

The data in Figure S1 show that the predicted l (l-hydro) for the CaM:SEF2-1mp complex are fully compatible with the experimental l (l-NMR) of 12 to 13 ns for molecular models with an axial ratio of 2.0 (Fig. S1, top and bottom panel), but they are larger than the experimental l for smaller axial ratios (1.6 and 1.3). Note that the axial ratio derived from the NMR relaxation data is 2.2 ± 0.4 (or 1.6±0.3) (see main text). Furthermore, for reasonable models of the CaM:SEF2-1mp complex, bead hydrodynamic calculations predict l values between 12 and 20 ns (Table HS1). This relatively large spread in the predicted l (l-hydr) is due in large part to the uncertainty in the size of the complex augmented by the third power size dependence of l.

In conclusion, the experimental l for the CaM:SEF2-1mp complex can either be equal to or smaller than l-hydr. In the former case there is no CaM monomer internal motion present in the complex. In the latter case, CaM monomer internal motion is present. It can therefore not be excluded, but also not definitely confirmed, that some degree of CaM ‘monomer’ internal motion of ca 7 ns is present in the CaM:SEF2-1mp complex. To establish the presence or absence of monomer motion requires either an independent measurement of the real overall tumbling time or a theoretical estimate from more extensive hydrodynamic calculations combined with motion modeling and normal mode analysis, which is beyond the scope of the present study.

Figure S1.Comparison of the overall tumbling time of the main axis l estimated via either analytical hydrodynamic expressions (top and bottom panel) or bead-model hydrodynamics (bottom panel).

Top panel. The overall tumbling time of the main axis, l, is plotted versus the diameter of a sphere (open circles) or the long axis for cylinder symmetric objects (lines) using well-established analytical expressions (see text). The cylinder symmetric objects have axial ratios ranging from 1.2 to 2.6 in steps of 0.1, where the axial ratio is defined as the length, L, over the diameter, D, of the cylinder. The contour for the axial ratio of 2.6 is indicated with an arrow above the panel. A temperature of 308 K is assumed and the corresponding viscosity is used in the equations.

The average (mo)app-corr for the CaM:SEF2-1mp complex together with NMR derived (mo)app for six other proteins (outlined in the figure) are overlaid in the same panel. Data of the other proteins are taken from Table 1 in (5), and are scaled to 308 K via viscosity and temperature adjustment. The length (L) of the molecules was estimated from the pdb files, and the estimated uncertainty in L (due to change/variation in side chains, etc), is indicated via the horizontal bar. The length of the CaM:SEF2-1mp dimer (~63 Å) is estimated from the final model structure (see Figures 4 and 8, main text). For CaM:SEF2-1mp the maximum and minimum (mo)app-cor are also shown (broken lines; the arrow indicates the crossing of the median length of 63 Å and maximum (mo)app).

Bottom panel. Predicted l at 308 K from either the analytical expression (l-hydr-anal, open circles, from Table HS1), or from ‘bead model’ hydrodynamics (l-hydr-bead; filled circles, from Table HS1) versus the NMR derived overall tumbling time (exp is l-NMR in Table HS1) for the CaM:SEF2-1mp complex and the same six other proteins as above. The filled circle and triangle for CaM:SEF2-1mp correspond to l-hydr-bead calculated from two models of the structure of the CaM-SEF2-1mp (see Table HS1). The vertical bars indicate uncertainty due to uncertainty in the size estimates as discussed in the legend of the top panel. For the calculation of l-hydr-anal the L and L/<D> in Table HS1 were used. For the CaM-SEF2-1mp, the solid, broken and dotted vertical bars indicate the range of l-hydr-anal obtained when the axial ratio is 2.0, 1.6, and 1.3, respectively, and taking the longest diameter equal to 63  7 Å.

Table HS1: .Comparison of NMR-derived experimental and hydrodynamic estimates
of the overall tumbling times 
L(Lz)
(Å) / Lx
(Å) / Ly
(Å) / L/<D> / 2Dzz/(Dxx+Dyy) / c-NMR (l-NMR)
(ns) / trace-hydr-bead
(ns) / l-hydro-bead
(ns) / l-hydro-analyt
(L/<D>) (ns)
Calibration Proteins used
Calbindin / 32 / 24 / 27 / 1.3 / 0.9 / 3.2 (3.3) / 2.9 / 3.0 / 2.5
Ubiquitin / 32 / 27 / 27 / 1.2 / 1.4 / 3.3 (3.6) / 3.3 / 3.8 / 2.3
Lys / 40 / 26 / 26 / 1.6 / 1.4 / 5.1 (5.6) / 5.0 / 5.6 / 4.4
Savinase / 45 / 37 / 42 / 1.1 / 0.9 / 7.7 (7.7) / 8.4 / 8.6 / 7.4
HIV / 51 / 33 / 24 / 1.7 / 1.5 / 8.2 (9.2) / 7.2 / 8.4 / 8.7
Trp / 72 / 47 / 30 / 2.0 / 1.4 / 14.3 (15.7) / 14.7 / 16.6 / 19
CaM:SEF2-1mp models
CaM-SEF2-1mp / 63 / 20 / 45 / 2.0 / 1.3 / 10.5 (12.5) / 17.3 / 18.9 / 14
CaM-SEF2
Dimer/Narrow / 1.4 / - / 13
CaM- monomer and N- and C-domains
CaM-SEF2
Monomer / 1.5 / - / 8.1 / 9.2
CaM-SMLCK
Monomer / 1.4 / - / 6.5 / 7.3
CaM-N-tern / 1.3 / - / 3.1 / 3.5
CaM-C-term / 1.5 / - / 3.4 / 3.8

The hydrodynamic estimates of the overall tumbling time are obtained from either analytical expressions or bead-models (see text). Protein dimensions are estimated from pdb files as described below. To gauge reliability of the estimates used in the analytical expression, the axial ratios are compared with the anisotropy of the diffusion tensor derived from bead-model hydrodynamic calculations. For the ‘bead model’ hydrodynamics the optimal shell ‘bead size’ was found to have the calibration value of 3 Å. Temperature is taken to be 308 K and the solvent viscosity is set to the corresponding value.

c-NMR: average (mo)app-cor; l-NMR: maximum (mo)app; l-hydr-anal: longest axis tumbling time predicted via analytical expressions (see text); l-hydr-bead: longest axis tumbling time predicted using ‘bead model’ hydrodynamics with calibration shell size of 3 Å; trace-hydr-bead: tumbling time predicted using ‘bead model’ hydrodynamics with consensus shell size of 3 Å calculated from trace of the diffusion tensor, (6Tr(D/3))-1. The l-hydr-anal, l-hydr-bead are plotted versus l-NMR in Figure S1 (bottom panel). L (Lz) > Ly > Lx are diameters of each molecule as measured from the pdb file (the estimated uncertainty in L - due to change/variation in side chains, etc. - is indicated in Figure S1, top panel, via the horizontal bar). <D> is the average value of Lx and Ly. L and L/<D> are the length and axial ratio used to calculate l-hydr-anal. Dxx, Dyy, and Dzz are the x, y, and z components of the diffusion tensor derived via DASHA from the structure coordinates (pdb file). For the published structures, l-NMR was calculated from the published c-NMR based on the anisotropy, 2Dzz/(Dxx+Dyy).

CaM-SEF2-1mp: Calculations using one molecular model for the CaM-SEF2-1mp complex compatible with all experimental NMR data including the global structure information derived from the NMR relaxation data. In this structure (to be presented elsewhere) the N- and C-domains are opened slightly (by ca. 30) compared to the ‘wraparound’ structure (see Figure 4, main text). Cam_SEF2-1mp, Dimer/Narrow: CaM-SEF2-1mp complex where the open eight form of the complex is more closed (by ca. 20).

References:

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3. de la Torre,J.G. 1981. Rotational diffusion coefficients. In Molecular Electro-Optics. Electro-optical Properties of Macromolecules and Colloids in Solution. S.Krause, editor. Plenum Press, New York. 75-103.

4. de la Torre,J.G., M.L.Huertas, and B.Carrasco. 2000. Calculation of hydrodynamic properties of globular proteins from their atomic-level structure. Biophys. J. 78:719-730.

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