SUPPORTING INFORMATION TO
Location, Tilt and Binding: A Molecular Dynamics Study of Voltage Sensitive Dyes in Biomembranes Marlon J. Hinner,†* Siewert-J. Marrink, Alex H. de Vries* Groningen Biomolecular Sciences and Biotechnology Institute & Zernike Institute for Advanced Materials, Department of Biophysical Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
†
Current Adress: Institute of Chemical Sciences and Engineering, Ècole Polytechnique
Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
This SUPPORTING INFORMATION contains (1) Force field parameters and topologies for atomistic simulations of Di-4-ASPBS in a POPC bilayer, page 2-15. (2) Fine-tuning of coarse grained topology for Di-4-ASPBS based on comparison with atomistic simulations, page 16-18. (3) PMF profiles and binding free energy for long chain alcohols, page 19. (4) Alternative topologies for Di-12A-ASPBS and Di-4-ASPiHA2 with PMF profiles, page 20-21. BIBLIOGRAPHY, page 22.
S1
(1) Force field parameters and topologies for atomistic simulations of Di-4ASPBS in a POPC bilayer.
Definition of topologies compatible with the GROMOS 53A6 force field In this paper, atomistic simulations were performed using the framework of the GROMOS 53A6 force field [Oostenbrink2004]. This version of the force field distinguishes itself from earlier force fields by incorporating free energy data (free energies of solvation of building blocks in water and apolar solvent) in its parameterization. The MARTINI force field used for the coarse grained simulation shares that approach. The GROMOS 53A6 force field is primarily parametrized for biomolecules, in particular peptides and proteins, sugars, and DNA as well as phospholipids. Of course, many organic molecules contain building blocks also present in biomolecules, but often additional parameters are required. In general, topologies of new molecules are constructed in close analogy to existing building blocks.
Di-4-ASPBS Parameters for bond, angle, and dihedral (torsional) potentials were assigned from the standard list of bond, angle, and torsional parameters by considering the character of the chemical bonds in Di-4-ASPBS. Assignment was in general straightforward; where standard parameters were not available, closest matching parameters were chosen to represent bond and angle parameters. The topology given in this Supporting Information contains comments on the choices made in assigning these parameters. Assignment of atom types that determine the non-bonded interactions is straightforward for Di-4-ASPBS because all atom types are available in the GROMOS 53A6 force field. For the sulphonate S we chose the standard atom type S for Sulphur, which is parameterized for thioethers and thiols. No effort was made to explicitly parameterize sulphonate ions because independent data to parameterize against are
S2
difficult to find. We expect the Coulomb interaction to be leading for this group: the S is relatively buried in the surrounding O-atoms, and therefore the non-bonded Lennard-Jones parameters are less influential on the interactions of the S-atom. Di-4-ASPBS does contain building blocks for which partial charges are unavailable. Partial charges were derived from quantum-chemical charge distributions of the entire molecule using the so-called Dipole Preserving Charge analysis. We chose to calculate the charge distribution of the entire molecule because charge shifting within the molecule through the delocalized system can be accounted for in the partial charges as compared to using standard charges for the aromatic ring-atoms for example. The DPC analysis procedure is explicated below.
Dipole Preserving Charges Charge distributions for the dye Di-4-ASPBS were calculated from the quantum chemical charge distribution of representative geometries. Hartree-Fock wave functions at the double zeta plus polarization (DZP) level were used to calculate the so-called Dipole Preserving Charges (DPCs) [Thole1983]. DPCs have proven their use in QM/MM methods. In this method, charges on atoms are calculated from the occupation numbers of overlap populations of the basis set functions used to expand the wave function in. Charges on atoms have two contributions, (i) from the charges and (ii) from the dipoles associated with the overlap distribution of two Gaussian basis functions. Contributions from charges (the so-called Mulliken charges) are partitioned using the Mulliken scheme. In the Mulliken scheme the charge associated with an overlap is positioned on a particular atom if both basis functions have their center on that atom. The charge is divided equally over two atoms for overlaps of basis functions which have their center at two different atoms. Contributions of the overlap dipoles are partitioned over all atoms of the molecule according to a fitting procedure. The fitting procedure involves finding for each overlap dipole a set of charges on all atoms that best reproduces the overlap dipole under the constraints that (i) the sum of the charges is zero, S3
(ii) the relative weight for the charge on each atom decreases exponentially with increasing distance from the center of the overlap dipole. Charges are calculated on all atoms, i.e. including all H-atoms. After calculation of DPCs, a mapping needs to be made to derive charges for the united atom model. In the compounds under study, this involves only minor changes because the standard representation for aromatic side chains uses the H-atoms attached to the ring as explicit interaction sites. For the methyl groups, we chose simply to add charges on hydrogen atoms to the charge on their bonded heavy atom. Geometries used to calculate DPCs were optimized (local) minima at the STO3-21G level using the HF wave function. All calculations were performed with the GAMESS-UK suite of programs (version 6.2) [GAMESS-UK2005]. It appears that partial charges derived in this manner are similar to the more labor intensive charges obtained from fitting to the electrostatic potential (e.g. RESP).
POPC Parameters for phospholipids are incorporated in the GROMOS 53A6 force field, following work by Chandrasekhar et al. on parameterization of the parent lipid DPPC [Chandrasekhar2003, Chandrasekhar2004] However, in order to obtain the experimentally observed liquid crystalline (as opposed to gel) phase structure at 323 K, a surface tension needs to be applied to the system. A development of parameters that do not require a surface tension to obtain the experimentally observed phase was started by one of the authors (AHV) in collaboration with the developers of the GROMOS force field. An important reason for starting this development pertains to the type of simulation that is performed here. Whereas appropriate surface tensions under which to simulate pure lipid bilayers may be obtained from experiment, for mixed systems obtaining the appropriate surface tension is problematic. The development of a new parameter set is ongoing and the present parameter set for POPC represents only a stage. The main differences between the current development version of S4
phospholipids and standard phospholipids are: (i) the introduction of a new atom type (OE) to represent ether and phosphoester linkages; (ii) partial charges on the atoms; in the development version DPC charges are used; (iii) bond lengths and bond angles in the head group region; (iv) specific non-bonded interactions between some head group atoms and water. All changes have been made with the eye to reproduce (relative) free energies of solvation of appropriate building blocks (small ethers and esters, choline head group), quantum-chemical data (bond lengths and bond angles), and phase transition behavior (in particular lamellar gel to liquid crystalline transitions). Full details of the parameterization strategy will be given in a forthcoming publication. Meanwhile, the topology of POPC is given in this Supporting Material and full bonded and nonbonded force field files for use with GROMACS (ffG53a6.itp, ffG53a6bon.itp, ffG53a6nb.itp) are available upon request from the authors.
TOPOLOGY FILE FOR DI-4-ASPBS TOPOLOGY FILE FOR POPC
S5
; Di-4-ASPBS topology ;; to be used with ffG53a6.itp [ moleculetype ] ; Name nrexcl DYE4 3 [ atoms ] ; nr 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
type resnr CH3 CH2 CH2 CH2 NR CH2 CH2 CH2 CH3 C C HC C HC C HC C HC C C HC C HC C C HC C HC C HC C HC NR CH2 CH2 CH2 CH2 S OM OM OM
[ bonds ] ; ai aj fu 1 2 2 3 3 4 4 5 5 6 5 10 6 7 7 8 8 9 10 11 10 15
2 2 2 2 2 2 2 2 2 2 2
resid atom cgnr 1 DYE4 C4A 1 DYE4 C3A 1 DYE4 C2A 1 DYE4 C1A 1 DYE4 NAN 1 DYE4 C1B 1 DYE4 C2B 1 DYE4 C3B 1 DYE4 C4B 1 DYE4 R1A 1 DYE4 R1B 1 DYE4 H1B 1 DYE4 R1C 1 DYE4 H1C 1 DYE4 R1D 1 DYE4 H1D 1 DYE4 R1E 1 DYE4 H1A 1 DYE4 R1F 1 DYE4 DBA 1 DYE4 HDA 1 DYE4 DBB 1 DYE4 HDB 1 DYE4 R2A 1 DYE4 R2B 1 DYE4 H2A 1 DYE4 R2C 1 DYE4 H2B 1 DYE4 R2D 1 DYE4 H2C 1 DYE4 R2E 1 DYE4 H2D 1 DYE4 NAR 1 DYE4 CC1 1 DYE4 CC2 1 DYE4 CC3 1 DYE4 CC4 1 DYE4 SAD 1 DYE4 SO1 1 DYE4 SO2 1 DYE4 SO3
charge 1 0.000 2 0.000 3 0.000 4 0.170 5 -0.370 6 0.170 7 0.000 8 0.000 9 0.000 10 0.540 11 -0.270 11 0.110 13 -0.170 13 0.160 15 -0.270 15 0.110 17 -0.170 17 0.160 19 0.008 20 -0.005 20 0.100 22 -0.200 22 0.100 24 0.300 25 -0.220 25 0.130 27 0.170 27 0.120 29 -0.220 29 0.130 31 0.170 31 0.120 33 -0.200 34 0.200 35 0.040 36 0.060 37 -0.120 37 1.580 37 -0.820 37 -0.820 37 -0.820
mass 15.0350 14.0270 14.0270 14.0270 14.0067 14.0270 14.0270 14.0270 15.0350 12.0110 12.0110 1.0080 12.0110 1.0080 12.0110 1.0080 12.0110 1.0080 12.0110 12.0110 1.0080 12.0110 1.0080 12.0110 12.0110 1.0080 12.0110 1.0080 12.0110 1.0080 12.0110 1.0080 14.0067 14.0270 14.0270 14.0270 14.0270 32.0600 15.9994 15.9994 15.9994
c0, c1, ... gb_27 ; C4A C3A gb_27 ; C3A C2A gb_27 ; C2A C1A gb_21 ; C - NH2 as in Lysine, closest match available gb_21 ; C - NH2 as in Lysine, closest match available gb_10; gb_27 ; C1B C2B gb_27 ; C2B C3B gb_27 ; C3B C4B gb_16; aromatic C=C Bond as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine
S6
11 11 13 13 15 15 17 17 19 20 20 22 22 24 24 25 25 27 27 29 29 31 31 33 34 35 36 37 38 38 38
12 13 14 19 16 17 18 19 20 21 22 23 24 25 29 26 27 28 33 30 31 32 33 34 35 36 37 38 39 40 41
[ pairs ] ; ai aj fu 1 4 2 5 3 6 3 10 4 7 5 8 6 9 6 11 6 15 7 10 31 35 33 36 34 37 35 38 36 39 36 40 36 41
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
gb_3; C-H as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_3; C-H as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_3; C-H as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_3; C-H as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_3; C-H as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_3; C-H as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_3; C-H as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_3; C-H as in Phenylalanine gb_17; from NADP IV-155 aromatic C=N gb_3; C-H as in Phenylalanine gb_16; aromatic C=C Bond as in Phenylalanine gb_3; C-H as in Phenylalanine gb_17; from NADP IV-155 aromatic C=N gb_23; CAC SAD from NADP IV-155 gb_27 ; CC1 CC2 gb_27 ; CC2 CC3 gb_27 ; CC3 CC4 gb_32; CH2-S as in Methionine, closest match available gb_25; SAD OAG corresponds to S-O bond in SO42. gb_25; SAD OAF gb_25; SAD OAE
c0, c1, ... 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[ angles ] ; ai aj ak fu 1 2 3 2 3 4 3 4 5 4 5 6 4 5 10 6 5 10 5 6 7 6 7 8 7 8 9
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
2 2 2 2 2 2 2 2 2
c0, c1, ... ga_15; normal CHn-CHn-C, ga_15; normal CHn-CHn-C, ga_15; normal CHn-CHn-C, ga_21; CH2-N-CH1 ga_31; CH1, CH2- N -C ga_31; CH1, CH2- N -C ga_15; normal CHn-CHn-C, ga_15; normal CHn-CHn-C, ga_15; normal CHn-CHn-C,
CAZ CAY CAX CAX CAW NAV CBA CBA CBA CBB CAH NAJ CAA CAA CAB CAB CAB
CAW NAV CBA CAS CBB CBC CBD CAU CAR CAS CAB CAC SAD SAD OAG OAF OAE
CHn...; CHn... CHn...;
CHn... CHn... CHn...
S7
5 10 11 2 outside 5 10 15 2 outside 11 10 15 2 10 11 12 2 Phenylalanine (PA) 10 11 13 2 12 11 13 2 11 13 14 2 11 13 19 2 14 13 19 2 10 15 16 2 10 15 17 2 16 15 17 2 15 17 18 2 15 17 19 2 18 17 19 2 13 19 17 2 13 19 20 2 17 19 20 2 19 20 21 2 19 20 22 2 21 20 22 2 20 22 23 2 20 22 24 2 23 22 24 2 22 24 25 2 22 24 29 2 25 24 29 2 24 25 26 2 24 25 27 2 26 25 27 2 25 27 28 2 25 27 33 2 28 27 33 2 24 29 30 2 24 29 31 2 30 29 31 2 29 31 32 2 29 31 33 2 32 31 33 2 27 33 31 2 27 33 34 2 outside 31 33 34 2 33 34 35 2 34 35 36 2 35 36 37 2 36 37 38 2 for sulfonate 37 38 39 2 37 38 40 2 approp 37 38 41 2 approp 39 38 40 2 39 38 41 2 40 38 41 2 [ dihedrals ] ; ai aj ak al fu 5 4 6 10
ga_27; aromatic 6 ring, N, C, CR1... but to the ga_27; aromatic 6 ring, N, C, CR1... but to the ga_27; aromatic 6 ring, N, C, CR1... ga_25; C-H bond in aromatic 6 ring as in ga_27; ga_25; ga_25; ga_27; ga_25; ga_25; ga_27; ga_25; ga_25; ga_27; ga_25; ga_27; ga_27; ga_27; ga_25; ga_27; ga_25; ga_25; ga_27; ga_25; ga_27; ga_27; ga_27; ga_25; ga_27; ga_25; ga_25; ga_27; ga_25; ga_25; ga_27; ga_25; ga_25; ga_27; ga_25; ga_27; ga_27;
aromatic C-H bond C-H bond aromatic C-H bond C-H bond aromatic C-H bond C-H bond aromatic C-H bond aromatic aromatic aromatic C-H bond aromatic C-H bond C-H bond aromatic C-H bond aromatic aromatic aromatic C-H bond aromatic C-H bond C-H bond aromatic C-H bond C-H bond aromatic C-H bond C-H bond aromatic C-H bond aromatic aromatic
6 ring, N, C, in aromatic 6 in aromatic 6 6 ring, N, C, in aromatic 6 in aromatic 6 6 ring, N, C, in aromatic 6 in aromatic 6 6 ring, N, C, in aromatic 6 6 ring, N, C, 6 ring, N, C, 6 ring, N, C, in aromatic 6 6 ring, N, C, in aromatic 6 in aromatic 6 6 ring, N, C, in aromatic 6 6 ring, N, C, 6 ring, N, C, 6 ring, N, C, in aromatic 6 6 ring, N, C, in aromatic 6 in aromatic 6 6 ring, N, C, in aromatic 6 in aromatic 6 6 ring, N, C, in aromatic 6 in aromatic 6 6 ring, N, C, in aromatic 6 6 ring, N, C, 6 ring, N, C,
CR1... ring as in ring as in CR1... ring as in ring as in CR1... ring as in ring as in CR1... ring as in CR1... CR1... CR1... ring as in CR1... ring as in ring as in CR1... ring as in CR1... CR1... CR1... ring as in CR1... ring as in ring as in CR1... ring as in ring as in CR1... ring as in ring as in CR1... ring as in CR1... CR1... but
ga_27; ga_15; ga_15; ga_15; ga_16;
aromatic 6 ring, N, C, CR1... normal CHn-CHn-C, CHn... normal CHn-CHn-C, CHn... normal CHn-CHn-C, CHn... C-C-S as in sulphide, not strictly applicable
PA PA PA PA PA PA PA
PA PA PA PA
PA PA PA PA PA PA PA PA to the
ga_6; not well defined ga_25; angle of around 106 degrees would be more ga_25; angle of around 106 degrees would be more ga_25; ga_16 might be more appropriate ga_25; ga_16 might be more appropriate ga_25; ga_16 might be more appropriate
2
c0, c1, m, ... gi_1; keeping the chromophore flat H
S8
10 11 13 15 17 19 20 22 24 25 27 29 31 33 38 10 11 13 19 17 15 24 25 27 33 31 29 4 5 3
5 10 11 10 15 20 19 20 29 24 25 24 29 27 37 11 13 19 17 15 10 25 27 33 31 29 24 3 4 4
15 13 19 17 19 17 22 24 25 27 33 31 33 31 40 13 19 17 15 10 11 27 33 31 29 24 25 2 3 5
11 12 14 16 18 13 21 23 22 26 28 30 32 34 39 19 17 15 10 11 13 33 31 29 24 25 27 1 2 10
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1
gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat H gi_2; keeping the sulfonate tetrahedral gi_1; keeping the chromophore flat C gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat gi_1; keeping the chromophore flat C gd_34; normal lipid tail dihedral gd_34; normal lipid tail dihedral gd_40; dihedral as in phenylalanine close to
7
6
5
4
1
gd_40; dihedral as in phenylalanine close to
1
gd_14; as db in retinol: keeping aniline
1 1 1
gd_34; normal lipid tail dihedral gd_34; normal lipid tail dihedral gd_14; as db in retinol: keeps rings flat
1
gd_14; as db in retinol: keeping the trans
1
gd_14; as db in retinol: rings flat resp. to
1
gd_40; dihedral as in phenylalanine close to
1 1 1 1
gd_34; gd_34; gd_27; gd_19;
1
gd_22; as in O-P bond for phosphoester, second
ring ring 4 5 10 15 Nitrogen flat to ring 8 7 6 5 9 8 7 6 17 19 20 22 resp. to double bond 19 20 22 23 bond 20 22 24 25 double bond 27 33 34 35 ring 36 35 34 33 37 36 35 34 38 37 36 35 41 38 37 36 part 41 38 37 36 part
normal lipid tail dihedral normal lipid tail dihedral as in C-O bond for a phospoester as in O-P bond for phosphoester, first
[ exclusions ] ;Standard exclusion of 1-4 interaction in aromatic rings 6 15 11 4 15 11 5 12 16 13 17 10 14 18 19 11 16 17 20 15 12 13 20 12 14 19 16 18 11 19
S9
13 17 14 18 19 20 21 22 23 24 25 29 26 30 27 31 28 32
18 21 17 20 23 25 23 26 25 28 30 26 29 32 32 28 34 34
21 22 22 20 24 29 24 30 29 32 31 27 28 33
27 31 33 34 34 33
S10
; TOPOLOGY FOR POPC ; Development version April 2007 ; Use with ffG53a6.itp [ moleculetype ] ; Name nrexcl POPC 3 [ atoms ] ; nr type resnr residu 1 CH2 1 POPC 2 OE 1 POPC 3 P 1 POPC 4 OM 1 POPC 5 OM 1 POPC 6 OE 1 POPC 7 CH2 1 POPC 8 CH1 1 POPC 9 OE 1 POPC 10 C 1 POPC 11 CH2 1 POPC 12 CH2 1 POPC 13 CH2 1 POPC 14 CH2 1 POPC 15 CH2 1 POPC 16 CH2 1 POPC 17 CH2 1 POPC 18 CH2 1 POPC 19 CH2 1 POPC 20 CH2 1 POPC 21 CH2 1 POPC 22 CH2 1 POPC 23 CH2 1 POPC 24 CH2 1 POPC 25 CH3 1 POPC 26 CH2 1 POPC 27 OE 1 POPC 28 C 1 POPC 29 CH2 1 POPC 30 CH2 1 POPC 31 CH2 1 POPC 32 CH2 1 POPC 33 CH2 1 POPC 34 CH2 1 POPC 35 CH2 1 POPC 36 CH2 1 POPC 37 CH2 1 POPC 38 CH2 1 POPC 39 CH2 1 POPC 40 CH2 1 POPC 41 CH2 1 POPC 42 CH2 1 POPC 43 CH3 1 POPC 44 CH2 1 POPC 45 NL 1 POPC 46 CH3 1 POPC 47 CH3 1 POPC 48 CH3 1 POPC 49 O 1 POPC 50 O 1 POPC 51 C 1 POPC 52 C 1 POPC 53 HC 1 POPC 54 HC 1 POPC
atom CB OA P OB OC OD CC CD OE C1A C1B C1C C1D C1E C1F C1G C1H C1I C1J C1K C1L C1M C1N C1O C1P CE OG C2A C2B C2C C2D C2E C2F C2G C2H C2I C2J C2K C2L C2M C2N C2O C2P CA NTM CN1 CN2 CN3 OH OF CI1 CJ1 HI1 HJ1
cgnr 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
charge mass 0.3000 14.0270 -0.610 15.9994 1.480 30.9738 -0.880 15.9994 -0.880 15.9994 -0.610 15.9994 0.280 14.0270 0.160 13.0190 -0.360 15.9994 0.6600 12.0010 -0.00 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 15.0350 0.24 14.0270 -0.36 15.9994 0.660 12.0010 -0.00 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 14.0270 0 15.0350 0.1750 14.0270 0.3000 14.0670 0.1750 15.0350 0.1750 15.0350 0.1750 15.0350 -0.540 15.9994 -0.540 15.9994 -0.100 12.0010 -0.100 12.0010 0.100 1.0080 0.100 1.0080
S11
[ bonds ] ; ai 1 1 2 3 3 3 6 7 8 8 9 10 10 11 12 13 14 15 16 17 51 51 52 52 18 19 20 21 22 23 24 26 27 28 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 44 45 45 45
aj 2 44 3 4 5 6 7 8 9 26 10 11 50 12 13 14 15 16 17 51 52 53 54 18 19 20 21 22 23 24 25 27 28 29 49 30 31 32 33 34 35 36 37 38 39 40 41 42 43 45 46 47 48
funct 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
pars alternative gb_18 gb_27 0.164 4.72e+06 ; gb_28 gb_24 gb_24 0.164 4.72e+06 ; gb_28 gb_18 gb_27 gb_18 gb_27 gb_13 gb_27 gb_5 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_15 gb_10 gb_3 gb_3 gb_15 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_18 gb_18 gb_27 gb_5 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 gb_27 0.151 5.43e+06 ; gb_21 0.151 5.43e+06 ; gb_21 0.151 5.43e+06 ; gb_21 0.151 5.43e+06 ; gb_21
[ pairs ] ; ai aj funct 1 4 1 1 5 1 1 6 1 1 46 1
S12
1 1 2 2 3 3 4 5 6 6 7 7 8 8 8 9 9 10 10 11 12 12 13 14 15 16 16 17 17 51 53 52 54 18 19 20 21 22 26 26 27 28 29 30 30 31 32 33 34 35 36 37 38 39 40
47 48 7 45 8 44 7 7 9 26 10 27 11 28 50 12 27 13 26 14 15 50 16 17 51 52 53 18 54 19 18 20 19 21 22 23 24 25 29 49 30 31 32 33 49 34 35 36 37 38 39 40 41 42 43
[ angles ] ; ai 1 1 2 2 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
aj 2 44 1 3 3
ak 3 45 44 4 5
funct 2 2 2 2 2
pars (possible alternative(s)) ga_12 ; ga_26 ga_13 ; ga_15 ga_13 ; ga_15 ga_14 ga_14
S13
2 3 4 4 5 6 7 7 8 8 9 9 9 11 10 11 12 13 14 15 16 17 17 52 51 51 18 52 18 19 20 21 22 23 26 27 27 29 28 29 30 31 32 33 34 35 36 37 38 39 40 41 44 44 44 46 46 47 [ dihedrals ] ; ai aj 1 2 1 2
3 6 3 3 3 7 8 8 9 26 8 10 10 10 11 12 13 14 15 16 17 51 51 51 52 52 52 18 19 20 21 22 23 24 27 28 28 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 45 45 45 45 45 45
ak 3 3
6 7 5 6 6 8 9 26 10 27 26 11 50 50 12 13 14 15 16 17 51 52 53 53 18 54 54 19 20 21 22 23 24 25 28 29 49 49 30 31 32 33 34 35 36 37 38 39 40 41 42 43 46 47 48 47 48 48
al funct 6 1 6 1
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
ga_1 ; ga_5 ga_12 ; ga_26 ga_29 ga_14 ga_14 ga_13 ; ga_15 ga_13 ; ga_15 ga_13 ; ga_15 ga_12 ga_13 ; ga_15 ga_13 ; ga_15 ga_19 ga_33 ga_30 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_27 ga_27 ga_27 ga_27 ga_27 ga_27 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_13 ; ga_12 ga_19 ga_33 ga_30 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_15 ga_8 ; ga_11 ga_8 ; ga_11 ga_8 ; ga_11 ga_8 ; ga_11 ga_8 ; ga_11 ga_8 ; ga_11
phi0 gd_19 gd_22
cp
mult
S14
1 2 2 2 2 3 3 6 7 7 8 8 9 10 11 12 13 14 15 16 17 51 52 18 19 20 21 22 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
44 1 1 3 3 2 6 7 8 8 26 9 10 11 12 13 14 15 16 17 51 52 18 19 20 21 22 23 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
45 44 44 6 6 1 7 8 26 9 27 10 11 12 13 14 15 16 17 51 52 18 19 20 21 22 23 24 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
[ dihedrals ] ; ai aj ak 8 9 10 9 28 27 51 53 52 54
46 45 45 7 7 44 8 9 27 10 28 11 12 13 14 15 16 17 51 52 18 19 20 21 22 23 24 25 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
al funct 26 11 29 17 51
gd_41 gd_4 gd_36 gd_19 gd_22 gd_23 gd_23 gd_18 gd_34 gd_23 gd_23 gd_13 gd_40 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 180.0 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 gd_13 gd_40 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34 gd_34
7 50 49 52 18
41.8
2 2 2 2 2
1
gi_2 gi_1 gi_1 gi_1 gi_1
S15
(2) Fine-tuning of coarse grained topology for Di-4-ASPBS based on comparison with atomistic simulations.
As described in the main text, after initially assigning standard parameter values to bonds and angles, distributions were compared to mapped atomistic distributions, and the CG values were iteratively refined to give better agreement with mapped atomistic distributions. Selected comparisons of the distributions are shown here in Supporting Tables 1-3, which contains the results of fitting the equilibrium value and effective force constants for angles (Supporting Table 1), dihedrals reflecting the chromophore stiffness (Supporting Table 2), and dihedrals reflecting the out-of-plane movement for beads attached to the chromophore, and the rotation of the alkylamine moiety (Supporting Table 3). The distribution p(θ) of angles and selected dihedrals θ was evaluated by fitting the distribution to an exponential of the form
p (θ ) = exp(−V / RT ) , with gas constant
R = 8.31 JK-1mol-1, temperature T = 323 K, and V the harmonic angle potential or improper dihedral
Vangle (θ ) =
potential
used
in
the
MARTINI
forcefield:
Here,
1 K angle {cos(θ ) − cos(θ 0 )}2 and Vi.dihedral = K id (θ − θ 0 ) 2 , respectively. In the case 2
of the out-of-plane movements of the beads 2 and 9 of Di-4-ASPBS with respect to the chromophore plane, the simulations lead to a bimodal distribution of the dihedrals which is symmetrical around θ = 0. It was fitted as the sum of two exponentials with p (θ ) = exp( − K eff (θ − θ 0 ) 2 / RT ) + exp( − K eff (θ + θ 0 ) 2 / RT ) .
A comparison with the angle and dihedral distribution of the "naive" coarse grained model showed the following results: (1) The stiffness of the angles within the aromatic rings is well captured by the model. (2) The fitted average angles are in good accord with the values defined in the topologies.
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(3) The stiffness of the angle between the aniline nitrogen and the chromophore was much too low and only 10 % in the CG model as compared to the atomistic model. (4) The stiffness of the angles with the aniline nitrogen as the central atom was too low by more than 50%. (5) The stiffness of the angles within the chromophore was also too low by about 50%. (6) The effective force constant of the dihedrals reflecting the stiffness of the chromophore with regard to a twisting movement is three- to sevenfold too high in the coarse grained model. (7) Both the angles and fitted force constants of the out-of-plane movements of the atoms do not agree with the atomistic simulation. (8) The barrier to rotation in the dialkylamine moiety that leads to a distinct bimodal angle distribution in the atomistic simulation is not present in the coarse grained simulation: Consequently, the angle distribution for the coarse grained model is nearly flat.
The overestimated stiffness of the chromophore is a result of the extra bonds introduced between atoms 5 and 7 and 4 and 6, respectively. However, this construction is a prerequisite for compatibility with large timesteps and was therefore not changed. As described above, introducing dihedral potentials in order to take care of the problems (7) and (8) was also precluded by incompatibility with large timesteps. A new topology of the dye was constructed with reduced bond and dihedral force constants in the chromophore, and angle force constants were increased ("Final" CG model). A simulation of the dye in water was performed, and the trajectory was evaluated as described above for the other simulations. The results of the fitted force constants are shown in Supporting Tables 1 and 2. As can be seen, the fitted force constants now more closely resemble the distribution in the atomistic model; as a side effect, also the out of plane movements of the beads 2 and 9 are now in very good accord with the atomistic simulation. However, as an unwanted side effect the stiffness of the chromophore with regard to the twisting movement is now even more exaggerated.
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Supporting Table 1. Fitted values of equilibrium angle θ0 and force constant Kangle (in kJmol-1) for molecular dynamics simulation of Di-4-ASPBS in water. Shown are three models, corresponding to (i) an atomistic simulation of Di-4-ASPBS mapped to the coarse grained topology shown in Figure 3, (ii) a “naïve” coarse grained model that was constructed using mostly standard values, and the final coarse grained model that was optimized to match the values obtained by the mapped atomistic model. The numbering of the beads is the same as in Figure 3. Atomistic Model naive CG-Model final CG-model Angle θ0 (fit) Kangle (fit) θ0 (fit) Kangle (fit) θ0 (fit) Kangle (fit) θ0 123 234 345 356 456 567 789 8 9 10 8 9 11
180 150 60 135 75 75 150 120 120
138 140 60 134 76 75 147 121 117
26 150 9800 930 710 840 1670 137 114
135 139 60 134 75 75 140 115 114
76 113 9200 520 300 300 125 50 48
135 133 60 132 74 75 145 115 116
59 47 9200 680 434 407 491 88 113
Supporting Table 2. Comparison of the chromophore stiffness for CG and mapped atomistic models. Shown are the fitted values for the force constant Ki,dihedral (in kJmol-1rad-2) around an equilibrium angle of θ = 0° (cf. text). The numbering of the beads is the same as in Figure 3. Dihedral Atomistic model Naive CG model Final CG model 3586 4576 6534
2.1 5.7 12.1
16.6 27.4 29.8
61.3 49.0 67.8
Supporting Table 3. Comparison of effective force constants describing the rotational barrier for the bond between the aromatic ring and the aniline nitrogen and for the out of plane movements of beads attached to the chromophore for the CG and mapped atomistic models. Shown are the fitted values for the force constant Keff (in kJmol-1rad-2) and the equilibrium angles θ0 (cf. text). The numbering of the beads is the same as in Figure 3. Dihedral Atomistic model CG model 1 CG model 2 θ0 (fit) Keff θ0 (fit) Keff θ0 (fit) Keff Amine rotation 6 8 9 10 27.4 16.8 nearly even dist. even distribution Amine out of plane 6 7 8 9 27.7 19.2 78.7 2.5 30 7.3 Head out of plane 5423 41.7 13 60 3.5 36.6 8.1
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(3) PMF profiles and binding free energy for long chain alcohols.
Supplementary Figure 1. Potentials of mean force and binding free energies for linear
alcohols with varying hydrophobic tail length in a POPC membrane. (A) PMF profiles. Plotted are curves for butanol represented with the beads P3-C1 (solid line), octanol (P3-C1C1, dashed line) and dodecanol (P3-C1-C1-C1, dotted line). The model building strategy corresponds to the alternative strategy for hydroxyl groups as described in the main text. The profiles correspond to 80 ns umbrella sampling simulations. The variability as judged from PMF profiles corresponding to the first and second half of the simulation was below 1 kJmol-1 for all profiles. (B) Free energy and hydrophobic tail chain length. Plotted is the free energy of binding ∆GPMF for the alkanols obtained by the PMF calculations (triangles), and experimental data ∆GEXP for alkanols with chain length 6 to 9 (squares). The free energy ∆GEXP was computed from partitioning constants based on titration calorimetry obtained by
Rowe ES et al. (see main text) after conversion from mole fraction units to volume fraction units (which corrrespond to CMem /Wat , cf. Materials and Methods). Conversion was performed by multiplication with the quotient of the molar volumes of lipid and water VW/VL, which were taken as VL = 0.7Lmol-1 and VW = 0.018Lmol-1. A linear fit through the respective data
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sets yielded an increment per methylene group of 3.8 kJmol-1 (experimental data, solid line) and 3.5 kJmol-1 (simulation, dashed line), respectively.
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(4) Alternative topologies for Di-12A-ASPBS and Di-4-ASPiHA2 and PMF profiles.
Supplementary Figure 2. Alternative coarse-grained representation of the voltage-sensitive
dyes Di-12A-ASPBS and Di-4-ASPiHA2, where the hydroxyl group is introduced as a separate P2 or P3 bead. The models are based on the model of Di-4-ASPBS 1 (Figure 3 in the main text); All additional bonds and angles are represented by standard values except for the bond length between the hydroxyl groups and the adjacent C1 beads which is reduced to 0.37 nm.
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Supplementary Figure 3. Potentials of mean force for the alternative representations of the
dyes Di-12A-ASPBS 5 and Di-4-ASPiHA2 3 in a POPC membrane. The PMFs corresponds to 80 ns umbrella sampling simulations except in the region which corresponds to the membrane/water interface which was further simulated to a total of 480 ns. Shown are the PMF profiles corresponding to the full simulation time (solid line) and to the respective first and second halves of the simulation time (grey lines).
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BIBLIOGRAPHY
[Chandrasekhar2003] Chandrasekhar, I., Kastenholz, M.A., Lins, R.D., Oostenbrink, C., Schuler, L.D., Tieleman, D.P., van Gunsteren, W.F. 2003. Eur. Biophys. J. 32, 67. [Chandrasekhar2004] Chandrasekhar, I., Oostenbrink, C., van Gunsteren, W.F. 2004. Simulating the Physiological Phase of Hydrated DPPC Bilayers: The Ester Moiety, SOFT MATERIALS 2, 27–45. [GAMESS-UK2005]
GAMESS-UK
is
a
package
of
ab
initio
programs.
See:
"http://www.cfs.dl.ac.uk/gamess-uk/index.shtml", M.F. Guest, I.J. Bush, H.J.J. van Dam, P. Sherwood, J.M.H. Thomas, J.H. van Lenthe, R.W.A Havenith, J. Kendrick, "The GAMESSUK electronic structure package: algorithms, developments and applications", Molecular Physics, Vol. 103, No. 6-8, 20 March-20 April 2005, 719-747. [Oostenbrink2004] Oostenbrink, C., Villa, A., Mark, A. E., van Gunsteren, W. F. 2004. A biomolecular force field based on the free enthalpy of hydration and solvation: The GROMOS force-field parameter sets 53A5 and 53A6. J. Comput. Chem. 25, 1656-1676. [Thole1983]: Thole, B.T., van Duijnen, P. Th. 1983. Theor. Chim. Acta 63, 209-211.
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