Supporting Information for Origin of 1/f noise in hydration dynamics on lipid membrane surfaces

Transcription

1 Supporting Informati for Origin of /f noise in hydrati dynamics lipid membrane surfaces Eiji Yamamoto, Takuma kimoto, Masato Yasui, 2 and Kenji Yasuoka Department of Mechanical Engineering, Keio University, Yokohama, Japan 2 Department of Pharmacology, School of Medicine, Keio University, Shinjuku-ku, Tokyo, Japan dditial molecular dynamics simulatis Molecular dynamics (MD) simulatis of pure palmitoyl-oleoyl-phosphatidylethanolamine (POPE) and POP/palmitoyl-oleoyl phosphatidylserine (POPS) bilayers were performed to clarify the universality of the hydrati dynamics the lipid membrane surfaces. The HRMM36 [] force field was used for the lipids. The lipid bilayer systems of pure POPE lipids csisted of 28 lipids (64 for each leaflet) and 7,680 TIP3P water molecules. The POP/POPS (4:) lipid system of 0 POP lipids and 28 POPS lipids was solvated with 7552 TIP3P water molecules, and Nal is at 50 mm ccentrati were added to neutralize the system. The simulati cditis were the same as that in the main text. To cfirm the universality of results, we changed water models, force fields, thermostat, and barostat. We performed a.4 µs MD simulati of the membrane system which has 28 POP molecules and 7823 SP water molecules [2] using GROMS software [3]. The GROMOS96 53a6 force field [4], which is a united-atom model, was used for the POP lipid. The pressure of bar and a temperature of 3 K were ctrolled using the Parrinello-Rahman barostat [5] and velocity rescaling method [6] with a coupling time of ps and 0. ps, respectively. The lengths of bds involving the hydrogen atoms were cstrained to equilibrium lengths using the LINS method [7]. The time step was set at 2 fs. The particle-mesh Ewald method was used for lg-range electrostatic interactis. cut- distance of nm was used for the van der Waals interactis. [] Klauda, J.. et al. Update of the charmm all-atom additive force field for lipids: validati six lipid types. J. Phys. hem. 4, (20). [2] erendsen, H. J.., Postma, J. P. M., Van Gunsteren, W. F. & Hermans, J. Interacti models for water in relati to protein hydrati. In Intermolecular forces, (Springer, 98). [3] Hess,., Kutzner,., Van Der Spoel, D. & Lindahl, E. Gromacs 4: lgorithms for highly efficient, load-balanced, and scalable molecular simulati. J. hem. Theory omput. 4, (2008). [4] Oostenbrink,., Villa,., Mark,. E. & Van Gunsteren, W. F. biomolecular force field based the free enthalpy of hydrati and solvati: The gromos force-field parameter sets 53a5 and 53a6. J. omput. hem. 25, (2004). [5] Parrinello, M. & Rahman,. Polymorphic transitis in single crystals: new molecular dynamics method. J. ppl. Phys. 52, (98). [6] ussi, G., Dadio, D. & Parrinello, M. anical sampling through velocity rescaling. J. hem. Phys. 26, 04 (2007). [7] Hess,., ekker, H., erendsen, H. J.. & Fraaije, J. G. E. M. Lincs: a linear cstraint solver for molecular simulatis. J. omput. hem. 8, (997).

2 ~ f -.5 Z 0 = 2.5 nm Z 0 = 4.0 nm -4 4 Z 0 = 2.5 nm ~ f Z 0 = 4.0 nm Fig. S : Ensemble-averaged PSD of number of water molecules in regis near the POP membrane surface. () ox (size is l x l y l z = nm 3 ) and () sphere (radius is r = 0.35 nm 3 ). The centers of the box and sphere are located at a perpendicular diastase Z 0 from the center of mass of the membrane. Z 0 = 2.5 nm is around the surface of the membrane. The fluctuatis at Z 0 = 4.0 nm are white Gaussian noise ~ f Fig. S 2: Ensemble-averaged PSD of temporal fluctuatis of perpendicular positi of lipid molecules in the POP membrane. The positi of a lipid molecule is defined by the perpendicular distance between center of mass of the membrane and a phosphorus atom in the phosphate group of the lipid molecule. We use 28 time series (28 lipid molecules) to obtain the ensemble-averaged PSD. The PSD exhibits /f noise.

3 ~ f ns 32.8 ns 8.9 ns 2.05 ns D ~ f ns 32.8 ns 8.9 ns 2.05 ns SDP Renewal process E ~ f ~ f ~ f f Fig. S 3: /f noise in the hydrati dynamics the POP membrane with using different hydrogen bd distance 0.3 nm. () Ensemble-averaged PSD of number of water molecules POP lipid head group. We use 28 time series to obtain the ensemble-averaged PSD. The different colored lines represent different measurement times. The solid line is shown as a reference. () Ensemble-averaged PSD of the time series of the two states. The dichotomous process was generated in the same way as the POP membrane in the main text. () PDFs of residence times of and states POP. Solid lines are fitted curves for power-law distributis with expential cuts: P (τ) = τ α exp( τ/τ c) (α =.4, : τ c = 35 ps, : α =.45, τ c = 350 ps). (D) Ensemble-averaged PSD of shuffled dichotomous processes (SDP) (black line). Numerical simulati of alternating renewal process; residence times are given by power-law distributi with expential cut, where : α =.4, τ c = 35 ps, : α =.45, τ c = 350 ps (green line). (E) Ensemble-averaged PSD of residence times of two states. There are no significant qualitative differences in observati of β and the origin of the /f noise compared to the definiti of the hydrogen bd distance 0.35 nm.

4 ~ f ns 32.8 ns 8.9 ns 2.05 ns Fig. S 4: /f noise in the hydrati dynamics the POPE membrane. () Ensemble-averaged PSD of number of water molecules a lipid head group. We use 28 time series to obtain the ensemble-averaged PSD. The solid lines represent powerlaw behavior for reference. Total measurement time was 3 ns. () Ensemble-averaged PSD for four different measurement times: 2.05, 8.9, 32.8, and 3 ns. There is no aging.

5 ~ f ns 32.8 ns 8.9 ns 2.05 ns D SDP Renewal process ~ f Fig. S 5: /f noise in the dichotomous process the POPE membrane. The dichotomous process was generated in the same way as the POP membrane in the main text. () Ensemble-averaged PSD of the time series of the two states. We use 28 time series to obtain the ensemble-averaged PSD. The solid lines are shown as reference for higher and lower frequencies. () Ensemble-averaged PSD of the time series of the two states for four different measurement times: 2.05, 8.9, 32.8, and 3 ns. There is no aging. () PDFs of residence times of and states. Solid lines are fitted curves for power-law distributis with expential cuts: P (τ) = τ α exp( τ/τ c) (: α =., τ c = 240 ps, : α =.2, τ c = 3000 ps). (D) Ensemble-averaged PSD of shuffled dichotomous processes (SDP) (black line). Numerical simulati of alternating renewal process; residence times are given by power-law distributi with expential cut, where : α =., τ c = 240 ps, : α =.2, τ c = 3000 ps (green line). The solid line is shown for reference.

6 6 0 <τ i+ >τ i G( ) τ i ~ f ~ f ~ f DP SDP MDP Fig. S 6: orrelati of residence times the POPE membrane. () ditial averages of the residence times. Different color lines distinguish the pairs used for the analysis. () Degree of n-markovianity for dichotomous processes (DP), shuffled dichotomous processes (SDP), and Markovian dichotomous processes (MDP). () Ensemble-averaged PSD of residence times. The solid lines are shown for reference. f

7 ~ f -.35 POP POPS Fig. S 7: /f noise in the hydrati dynamics the POP/POPS membrane. Ensemble-averaged PSD of number of water molecules a lipid head groups. We use 0 and 28 time series to obtain the ensemble-averaged PSDs POP (red) and POPS (blue) lipids, respectively. The solid lines represent power-law behavior for reference. Total measurement time was 3 ns. We cfirmed that there is no aging.

8 ~ f -.35 POP POPS 3 2 ~ f -0.8 POP POPS D E <τ i+ >τ i F <τ i+ >τ i τ i τ i G ~ f ~ f ~ f H ~ f ~ f f f Fig. S 8: /f noise in the dichotomous process the POP/POPS membrane. The dichotomous process was generated in the same way as the POP membrane in the main text. () Ensemble-averaged PSD of dichotomous processes. We use 0 and 28 time series to obtain the ensemble-averaged PSD POP and POPS lipids, respectively. The solid lines are shown as reference for higher and lower frequencies. We cfirmed that there is no aging (results are not shown). () Ensemble-averaged PSD of shuffled dichotomous processes. () PDFs of residence times of and states POP. Solid lines are fitted curves for power-law distributis with expential cuts: P (τ) = τ α exp( τ/τ c) (α =.2, : τ c = 68 ps, : τ c = 00 ps). (D) PDFs of residence times of and states POPS. Solid lines are fitted curves for power-law distributis with expential cuts: P (τ) = τ α exp( τ/τ c) (α =.2, : τ c = 53 ps, : τ c = 3420 ps). (E) ditial averages of the residence times POP and (F) POPS lipids. (G) Ensemble-averaged PSD of residence times POP and (H) POPS lipids. The solid lines are shown for reference.

9 D E -2 - Fig. S 9: /f noise in the hydrati dynamics the POP membrane with using GROMOS force filed, SP water model, Parrinello-Rahman barostat and velocity rescaling method for temperature ctrolling. () Ensemble-averaged PSD of number of water molecules POP lipid head group. We use 28 time series to obtain the ensemble-averaged PSD. The different colored lines represent different measurement times. The solid line is shown as a reference. () Ensemble-averaged PSD of the time series of the two states. The dichotomous process was generated in the same way as the POP membrane in the main text. () PDFs of residence times of and off states POP. Solid lines are fitted curves for power-law distributis with expential cutoffs: P (τ ) = τ α exp( τ /τc ) (α =.3, : τc = 96 ps, off: α =.4, τc = 0000 ps). (D) Ensemble-averaged PSD of shuffled dichotomous processes (SDP) (black line). Numerical simulati of alternating renewal process; residence times are given by power-law distributi with expential cutoff, where : α =.3, τc = 200 ps, off: α =.4, τc = 0000 ps (green line). (E) Ensemble-averaged PSD of residence times of two states.