Supporting Information

Size: px

Start display at page:

Download "Supporting Information"

Gavin Clarke
5 years ago
Views:

1 pk a values of titrable amino acids at the water/membrane interface Vitor H. Teixeira, Diogo Vila-Viçosa, Pedro B. P. S. Reis, and Miguel Machuqueiro Centro de Química e Bioquímica, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade de Lisboa, 9- Lisboa, Portugal machuque@ciencias.ulisboa.pt Phone: +--. Fax: Supporting Information

2 Methods Constant-pH MD Our constant-ph MD methodology follows a series of small steps in a repeating cycle, starting with a Poisson Boltzmann / Monte Carlo (PB/MC) calculation to determine the protonation states of the titrable groups for a specific conformation and at a given ph value. Representative protonation states are assigned to the solute and, in the second step, a short (τ rlx ) molecular mechanics / molecular dynamics (MM/MD) simulation in the NVT ensemble is performed with the solute frozen to allow the local water molecules to relax to the new charge distribution. The third step consists of a production run of MM/MD simulation of the unfrozen system (τ prt ). These steps are repeated until the desired simulation time. The τ prt was ps for the simulations in water and ps for the simulations in bilayer membranes. A τ prt value of ps has been successfully used with peptides and proteins in aqueous solution,, while in a membrane environment our method has been shown to work better with larger values, like ps or even ps. Conformations were saved every ps. MM/MD settings All simulations were done using the v-rescale thermostat at K with separate couplings for solute and solvent and a relaxation time of. ps. The pressure was kept at bar using the Berendsen barostat (isotropic in water and semi-isotropic in the bilayer membrane) with an isothermal compressibility of bar and a relaxation time of. ps (water) and. ps (bilayer membrane). Solutes bond-lengths were constrained using P-LINCS algorithm, while for water the SETTLE algorithm was used. 8 Nonbonded interactions were treated with a twin-range method 8/ Å whose neighbor list was updated every steps ( ps). Long-range electrostatics were treated with a generalized reaction field 9 with a relative dielectric constant of and an ionic strength of. M. The time equations of motion were integrated with a time step of fs.

3 In the aqueous systems, the pentapeptides were solvated in a dodecahedron box with periodic boundary conditions and filled with SPC water molecules. The lipid membrane systems started from an equilibrated lipid bilayer of 8 DMPC molecules and was solvated in a tetragonal box with SPC water molecules, with the membrane surface oriented parallel to the xy plane. Energy minimization was performed in steps that consisted of an initial steps of steepest-descent unconstrained calculation, followed by a steps low-memory Broyden-Fletcher-Goldfarb-Shanno algorithm also without constraints and the final step was a steps of steepest-descent with all bonds constrained. The aqueous systems were initialized in steps of, and ns of MD simulation. Initial velocities were taken from a Maxwell distribution at K. Position restraints were applied to all peptide atoms, all heavy atoms and all CA atoms in the initiation steps, respectively, with a force constant of kj mol nm ). The membrane systems were initialized in four steps of,,, and ns of MD simulation. Position restraints were applied sequentially in all steps to all solute atoms, all heavy atoms, all P atoms ( kj mol nm ), and to all P atoms with a lower position restraint force constant ( kj mol nm ). PB/MC settings The program DelPhi Version., was used for the PB calculations using the partial charges referred in the previous section and radii derived from the GROMOS A force field, Lennard-Jones parameters. The molecular surface was defined with a probe of radius. Å, the ion exclusion layer was. Å and the ionic strength was. M. In the calculations of the membrane systems, we added % of the box vector dimension in the x and y direction, to ensure continuity in the membrane surface definition (see Ref ). Periodic boundary conditions were explicitly applied in both x and y directions for the potential calculation in the coarser grid. In water systems, the maximum number of linear iterations was set to, while in membrane the coarser grid relaxation parameters were

4 changed to. and. for linear and nonlinear PB equations, respectively. A dielectric constant of was used for peptide and membrane and 8 for water. In the lipid membrane systems, we used a cutoff of Å to calculate the background contributions and pairwise interaction. The convergence threshold value based on maximum change of potential was set to. k B T/e. Calculations were done in a cubic grid of grid points and a two step focusing 8 with the focus grid being one fourth of the coarser grid size. These settings result in grid spacings of Å and.å for the coarser and focus grids, respectively. The MC sampling was performed with the PETIT program 9 version.. All runs were performed at an absolute temperature of K using MC cycles. Each cycle consists of sequential state changes over all individual sites and pairs of sites with an interaction larger than pk units. pk a calculation procedure The pk a values in the membrane systems cannot be calculated similarly to those in water. To capture the average effects of the lipid interactions with the titrating groups, we propose a fractioning of our system in the membrane normal direction. This was achieved by defining a distance in the z-vector to the closest lipid (measured to its phosphor atom) and partitioning it in small slabs (. Å). The pentapeptides reference atoms chosen for distance measurements were the C atoms in the carboxylic groups, N in amines, O in Tyr, S in Cys and Nɛ in His. The closest lipid was chosen instead of the most commonly used phosphor atom average z-positions (from the closest lipid monolayer), in order to avoid erroneous averaging out of the membrane deformation induced by the pentapeptides. Each fraction of our system is associated with a degree of insertion and the pentapeptide conformation/protonation states are separated accordingly. The pk a values for each slab can be calculated using a Henderson Hasselbalch fit to the weighted average protonation states from the three ph values simulations. The fact that we are splitting the available conformations can generate limited sampling in some less populated slabs, which we circumvented by simulating five

5 replicas at longer times ( ns), per ph value. On the other hand, with this approach, we can avoid sampling problems for those cases where the pentapeptide is trapped deep in the membrane. Here, due to the lack of protonation changes (only the neutral form is stable), the resulting conformations are ignored by the pk a calculation procedure. We also implemented three rules in order to avoid calculating pk a values in slabs with insufficient sampling, namely: () the site needs to be titrating (with protonation different from. or.) in at least different ph values; () at least a number of conformations per ph value is required in the averaging before the Henderson Hasselbalch fit; and () the slice region has to be sampled in more than one replicate. The errors of pk a values were computed using the jackknife method, which is a leave-one-out resampling strategy. Results and discussion Calibration of model compound pk a values in water Table S: Model Compound pk a values in Water. Residue Exp DelPhi (Mead) a b pk a Shift c pk modd CTr Asp Glu His NTr Cys Tyr Lys a Values from Refs.,. b Obtained from the CpHMD simulations in water. pk mod c Calculated as Exp pk a. d Calculated as pk mod (Mead) + shift.

6 Energy landscapes of gyration radius vs membrane insertion Figure S: Energy landscapes of R g for Glutamate distributed along the membrane normal (z-axis). The black line refers to the R g histogram of this pentapeptide in water simulations.

7 Figure S: Energy landscapes of R g for the N-terminus distributed along the membrane normal (z-axis). The black line refers to the R g histogram of this pentapeptide in water simulations.

8 C Terminus (CTr) ph =. ph = ph = RT z/å Figure S: Energy landscapes of R g for the C-terminus distributed along the membrane normal (z-axis). The black line refers to the R g histogram of this pentapeptide in water simulations. Aspartate (Asp) ph =. ph = ph = RT z/å Figure S: Energy landscapes of R g for Aspartate distributed along the membrane normal (z-axis). The black line refers to the R g histogram of this pentapeptide in water simulations. 8

9 Histidine (His) ph = ph =. ph =. RT z/å Figure S: Energy landscapes of R g for Histidine distributed along the membrane normal (z-axis). The black line refers to the R g histogram of this pentapeptide in water simulations. Lysine (Lys) ph = 9. ph =. ph =. RT z/å Figure S: Energy landscapes of R g for Lysine distributed along the membrane normal (z-axis). The black line refers to the R g histogram of this pentapeptide in water simulations. 9

10 Cysteine (Cys) ph = 8. ph = 9. ph = 9. RT z/å Figure S: Energy landscapes of R g for Cysteine distributed along the membrane normal (z-axis). The black line refers to the R g histogram of this pentapeptide in water simulations. Tyrosine (Tyr) ph = 9. ph =. ph =. RT z/å Figure S8 Energy landscapes of R g for Tyrosine distributed along the membrane normal (z-axis). The black line refers to the R g histogram of this pentapeptide in water simulations.

11 References () Baptista, A. M.; Teixeira, V. H.; Soares, C. M. J. Chem. Phys.,, 8. () Machuqueiro, M.; Baptista, A. M. J. Phys. Chem. B,, 9 9. () Vila-Viçosa, D.; Teixeira, V. H.; Baptista, A. M.; Machuqueiro, M. J. Chem. Theory Comput.,,. () Magalhães, P. R.; Machuqueiro, M.; Baptista, A. M. Biophys. J., 8, 8 9. () Bussi, G.; Donadio, D.; Parrinello, M. J. Chem. Phys.,,. () Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. J. Chem. Phys. 98, 8, 8 9. () Hess, B. J. Chem. Theory Comput. 8,,. (8) Miyamoto, S.; Kollman, P. J. Comput. Chem. 99,, 9 9. (9) Tironi, I. G.; Sperb, R.; Smith, P. E.; van Gunsteren, W. F. J. Chem. Phys. 99,, 9. () Smith, P.; van Gunsteren, W. J. Chem. Phys. 99,, 9. () Hermans, J.; Berendsen, H. J. C.; van Gunsteren, W. F.; Postma, J. P. M. Biopolymers 98,, 8. () Rocchia, W.; Sridharan, S.; Nicholls, A.; Alexov, E.; Chiabrera, A.; Honig, B. J. Comput. Chem.,, 8. () Li, L.; Li, C.; Sarkar, S.; Zhang, J.; Witham, S.; Zhang, Z.; Wang, L.; Smith, N.; Petukh, M.; Alexov, E. BMC Biophys.,, 9. () Teixeira, V. H.; Cunha, C. C.; Machuqueiro, M.; Oliveira, A. S. F.; Victor, B. L.; Soares, C. M.; Baptista, A. M. J. Phys. Chem. B, 9, 9.

12 () Schmid, N.; Eichenberger, A.; Choutko, A.; Riniker, S.; Winger, M.; Mark, A.; Van Gunsteren, W. Eur. Biophys. J.,, 8 8. () Huang, W.; Lin, Z.; van Gunsteren, W. F. J. Chem. Theory Comput.,,. () Teixeira, V. H.; Vila-Viçosa, D.; Baptista, A. M.; Machuqueiro, M. J. Chem. Theory Comput.,, 8. (8) Gilson, M.; Sharp, K.; Honig, B. J. Comput. Chem. 98, 9,. (9) Baptista, A. M.; Soares, C. M. J. Phys. Chem. B,, 9 9. () Efron, B.; Tibshirani, R. J. An introduction to the bootstrap (chapman & hall/crc monographs on statistics & applied probability); Chapman and Hall/CRC, 99. () Carvalheda, C. A.; Campos, S. R. R.; Machuqueiro, M.; Baptista, A. M. J. Chem. Inf. Model.,, () Carvalheda, C. A.; Campos, S. R. R.; Baptista, A. M. J. Chem. Inf. Model.,,.

MARTINI simulation details

S1 Appendix MARTINI simulation details MARTINI simulation initialization and equilibration In this section, we describe the initialization of simulations from Main Text section Residue-based coarsegrained