Kasson et al. 10.1073/pnas.0601597103.

Supporting Information

Files in this Data Supplement:

Supporting Figure 6
Supporting Figure 7
Supporting Table 1
Supporting Figure 8
Supporting Table 2
Supporting Figure 9
Supporting Figure 10
Supporting Figure 11
Supporting Figure 12
Supporting Figure 13





Supporting Figure 6

Fig. 6.

 K-means clustering of trajectory snapshots into macrostates. The assignment of trajectory snapshots into macrostates via k-means clustering is plotted by using a 2D projection of the lipid and contents mixing space. Dots represent structural snapshots and are colored according to macrostate assignment. Representative clusters are labeled for the unfused, stalk-like, hemifused, and fused states. Hemifused snapshots are densely clustered along the horizontal axis. Outer and inner leaflet mixing are measured by number of lipid mixed between vesicle leaflets as specified in Methods.





Supporting Figure 7

Fig. 7.

 Failure of rmsd metric to capture reaction coordinates for fusion. rmsd between structures is a commonly used means of comparing protein structures. Because of the large size of the fusing vesicles relative to the fusion interface, fluctuations in lipid position far from the fusion interface overwhelm the contribution of fusion-related changes to overall rmsd. The failure of the rmsd metric is demonstrated by this rendering, which depicts cutaway views of 10 randomly selected snapshots from a 10-state k-means clustering of 1,000 randomly-selected fusion snapshots. Pairwise rmsd between phosphate groups after rotational and translational alignment was used as the distance metric for clustering. As demonstrated, a single cluster contains some structures that are unfused, some that are hemifused, and some that are fully fused.





Supporting Figure 8

Fig. 8.

 Tests for Markovian characteristics. (a) Eigenvalues for sampled transition probability matrices are plotted. The observed exponential scaling of the eigenvalues with sampling interval is indicative of Markovian characteristics (see Methods for details). The average rmsd of linear fits to the eigenvalue logarithms is 0.122, and these fits well describe all eigenvalues except the smallest (black circles). Error bars represent 95% confidence intervals for eigenvalues. (b) MFPTs are plotted. The MFPTs for formation of the fused state are invariant of sampling interval to within error, again indicating Markovian characteristics. Variance of sampled values increases at long sampling time intervals because of smaller data sets.





Supporting Figure 9

Fig. 9.

 Contents and mixing values for a single trajectory. Extents of lipid and contents mixing between vesicles are plotted as a function of time. Mixing occurs sequentially, first outer leaflets, then inner leaflets shortly followed by vesicle contents. Mixing thresholds for outer leaflets, inner leaflets, and contents are 10, 1, and 10 molecules, respectively.





Supporting Figure 10

Fig. 10.

 Inner leaflet and vesicle contents mixing are independent of tether length. Cumulative distribution functions as a function of time (Dt from the previous mixing event) are plotted for inner leaflet mixing (a) and contents mixing (b). Cumulative distribution functions are defined as fraction of simulations having exceeded the given mixing threshold, and error bars represent one standard deviation of the mean. Rates of inner leaflet and contents mixing are statistically indistinguishable based on tether length.





Supporting Figure 11

Fig. 11.

 Kinetics of fusion using a crosslinker length and starting distance corresponding to the folded SNARE complex. To match the starting configuration more closely to experiment, vesicles were placed 2 nm away from each other and connected by a 2-nm crosslinker. This separation distance is consistent with membrane-membrane separation distance estimates for the folded SNARE fusion protein complex (1). Fractional abundance of fusion intermediates is plotted as a function of time. Reaction trajectories for these simulations were clustered and used to create an MSM. The unfused state decays to form a stalk-like intermediate with a t½ of 460 ns. The MFPT for formation of the fused state from the unfused state is 14 ms. MSM transitions beyond the stalk-like intermediate were created by using both the 2-nm separation data and 1-nm separation data to increase available sample size and thus simulation accuracy.

1. Sutton, R. B., Fasshauer, D., Jahn, R. & Brunger, A. T. (1998) Nature 395, 347-353.





Supporting Figure 12

Fig. 12.

 Lipid diffusion in the coarse-grained model. Lateral mean squared displacement is plotted as a function of time for palmitoyl-oleyl-phosphatidylcholine (POPC) phospholipids in a periodic bilayer. A linear fit to the data are also shown. The simulation box contained 512 POPC molecules by using periodic boundary conditions and an NPT ensemble and the simulation was run under conditions identical to the vesicle fusion simulations except that the Marrink-Mark POPC forcefield was used instead of the POPE forcefield (1). Time-scale normalization was not applied to this simulation. The simulation of multilamellar POPC bilayers allows comparison of lipid diffusion rates with those determined by NMR on multilamellar POPC vesicles (2). Previous validation studies on the Marrink-Mark model noted 4-fold faster diffusion of water in coarse-grained simulations, and a 4-fold time normalization factor was applied to all subsequent simulations using the model (1, 3, 4). We calculate a 2D diffusion constant of 5.2 ± 2.4 ´ 10-11 m2/s without applying any time-correction factor to the coarse-grained simulations, compared with 1.9 ± 0.1 ´ 10-11 m2/s from experiment. This is within error of the previous 4-fold correction, thus suggesting that a 4-fold time-scale normalization is a valid approximation for lipid simulations using the Marrink-Mark model.

1. Marrink, S. J., de Vries, A. H. & Mark, A. E. (2004) J. Phys. Chem. B 108, 750-760.

2. Gaede, H. C. & Gawrisch, K. (2003) Biophys. J. 85, 1734-1740.

3. Marrink, S. J. & Mark, A. E. (2003) J. Am. Chem. Soc. 125, 11144-11145.

4. Marrink, S. J. & Mark, A. E. (2003) J. Am. Chem. Soc. 125, 15233-15242.





Supporting Figure 13

Fig. 13.

 Intravesicle lipid mixing. Some models for fusion present transient pore formation in a single vesicle as a means by which lipids can migrate between inner and outer leaflets in the stalk state and thus relieve energetic strain (1-3). We have assessed such intravesicle mixing between inner and outer leaflets of each vesicle to determine the extent to which this occurs in our simulations. (a) Intravesicle lipid mixing has occurred in <2% of trajectory snapshots. (b and c) Initial mixing events occur with similar frequency in the unfused and stalk-like states and along the early portion of the hemifused pathway (b), and cumulative mixing events increase monotonically with simulation time (c). The odds ratio for rapid fusion versus formation of a metastable hemifusion intermediate was 17% for vesicles that mixed inner and outer leaflets, slightly lower than that for all vesicles simulated (24%, 95% confidence interval of 22–26%). This suggests that although intravesicle lipid mixing is a rare event in our simulations, it slightly increases the probability of forming a hemifused state instead of rapid fusion.

1. Marrink, S. J. & Mark, A. E. (2003) J. Am. Chem. Soc. 125, 11144-11145.

2. Katsov, K., Muller, M. & Schick, M. (2006) Biophys. J. 90, 915-925.

3. Muller, M., Katsov, K. & Schick, M. (2003) J. Polym. Sci. 41, 1441-1450.





Table 1. Mixing measurements for clustered states

Classification

Outer leaflet

Inner leaflet

Contents

Unfused

10

0

0

Stalk-like

36

0

6

Intermediate 1

55

0

2

Intermediate 2

75

0

3

Hemifused 1

98

0

5

Hemifused 2

130

0

7

Fused 1

53

23

312

Fused 2

103

43

343

Shown are the numbers of inner leaflet lipids, outer leaflet lipids, and contents water molecules mixed for the centroids of each macrostate cluster. These measurements reflect the structural state of the clusters and show increasing outer leaflet mixing from unfused vesicles through the formation of stalk-like and hemifused intermediates. Fused vesicles are characterized by mixing of inner leaflet lipids and contents. Contents mixing measurements also reflect minor leakage of vesicle contents.





Table 2. Estimation of sampling error for rate calculations

Forward rates

Calculated, s-1

90% confidence bounds, s-1

Unfused > stalk-like

4.3E + 07

4.0E + 07

to

4.5E + 07

Stalk-like > hemifused 1

4.8E + 07

4.7E + 07

to

5.0E + 07

Hemifused 1 > hemifused 2

3.4E + 07

3.5E + 07

to

3.3E + 07

Hemifused 2 > hemifused 3

1.9E + 07

1.9E + 07

to

2.0E + 07

Hemifused 3 > hemifused 4

1.0E + 07

9.8E + 06

to

1.1E + 07

Hemifused 4 > fused 2

1.3E + 05

7.2E + 04

to

2.0E + 05

Stalk-like > fused 1

4.5E + 06

4.2E + 06

to

4.8E + 06

Fused 1 > fused 2

9.4E + 06

8.7E + 06

to

1.0E + 07

Reverse rates

 

 

 

 

Stalk-like > unfused

1.2E + 05

6.9E + 04

to

1.8E + 05

Hemifused 1 > stalk-like

2.4E + 06

2.2E + 06

to

2.6E + 06

Hemifused 2 > hemifused 1

5.7E + 06

5.3E + 06

to

6.0E + 06

Hemifused 3 > hemifused 2

8.1E + 06

7.6E + 06

to

8.6E + 06

Hemifused 4 > hemifused 3

7.5E + 06

6.9E + 06

to

8.1E + 06

Fused 2 > hemifused 4

ND

--

 

--

Fused 1 > stalk-like

2.5E + 04

1.0E + 03

to

6.4E + 04

Fused 2 > fused 1

1.4E + 06

1.1E + 06

to

1.6E + 06

Sampling error for rate calculations is estimated by resampling transition matrices by using the Dirichlet distribution as described . No reverse transitions were observed from the fused state to the hemifused state. ND, not determined.

1. Singhal, N. & Pande, V. S. (2005) J. Chem. Phys. 123, 204909.