Coarse grained simulations of Lipid Bilayer Membranes

Transcription

1 Coarse grained simulations of Lipid Bilayer Membranes P. B. Sunil Kumar Department of Physics IIT Madras, Chennai

2 Atomistic MD: time scales ~ 10 ns length scales ~100 nm 2 To study phenomena like fusion, fission, domain formation, elasticity etc, atomistic models are not useful. How to explore length and time scales much larger than that is achievable through atomistic MD? Continuum models, that treat bilayer as a single elastic sheet are are unable to answer many questions where self assembly and bilayer fluid structure are important. A course grained model, that treat a group of atoms as effective interaction centers, will be useful to bridge this gap Some general features Reduction in the number of degrees of freedom Use of short range interaction potentials - finite cut off for LJ and electrostatic interactions Smooth potentials and energy to enable large integration time steps.

3 Goetz-Lipowsky Model Journal of Chemical Physics 108, 7397 (1998) Spherical particles are linked together to make a surfactant molecule Only three types of particles: (a) water, (b) hydrophobic and ( c) hydrophilic Interaction between (b) and (c ) are soft repulsive with All other particles interact with LJ of the form All interactions are cut off at. To avoid discontinuities due to cut off all potentials are shifted by

4 The particles within a chain are connected by harmonic springs Stiffness of the chain is maintained by a three body potential; If there is a preferred angle for the bonds this potential Modified to Characteristic time scale Characteristic energy scale Here m is the mass of the particles, and are length and energy scales that enters the LJ interaction

5 Different models for lipids ht 4 - flexible chain with one head and four tail particles HT 4 - Semiflexible chain with one head and four tail particle H 3 (T 4 ) 2 - semilflexible double chain with 3 head particles. Comparing the length of these chains with that of an actual lipid molecule like DOPC we get a length scale to be of the order of.35 nm. This length scale selection implies that each particle represent two or three CH 2 groups. The mass of the particle is thus between that of water and that of three CH 2 groups - 16 g/mol <m N a < 56 g/mol Similarly one can choose the value of to be that between two water molecules or that of a CH 2 group giving. 42 KJ/mol < N av < 1.20 KJ/mol With these the characteristic time scale in the simulation is t sc = 1.5 ps. The actual time step used is however t sc /2000 ~.75 fs

6 Starting from a random configuration of lipids, Monte Carlo simulations were used to obtain a bilayer structure. This structure was then equilibrated using MD simulations using a leap frog integrator.

7 A semi-quantitative coarse grained model for membranes S. J, Marrink et.al J. Phys. Chem B 108,750 ( 2004) As before many molecules are clubbed together in to few interaction centers The idea here was to parameterize the interactions such as to get a realistic lipid to make quantitative predictions Interactions are tuned by comparing with MD simulations for a variety of phases and components Model Interaction sites are of four different types (P) polar - Hydrophilic groups (N) non - polar - mixed polar and apolar groups ( C) apolar - Hydrophobic groups (Q) charged N and Q can be of four types (0) No- hydrogen bonding (a) Acceptor (b) Donor (c) Both acceptor and donor

8 Interactions All non-bonded particles interact via Five different values of are used (I) 5 KJ/mol (II) 4.2 KJ/mol (III) 3.4 KJ/mol (IV) 2.6 KJ/mol and (V) 1.8 KJ/mol

9 For electrostatic interactions an =20 was used The effect of hydration shell was taken into account by using a smaller effective charge for small ions. In all cases of LJ interaction All interactions are cut off at nm nm As before a shift function is used to make the potential and forces go to zero smoothly at Bonded interactions are represented by linear springs with spring constant k bond =1250 KJ/mol-nm 2 allowing for 15% variation in bond length Bond angles are fixed by with k rad =25KJ/mol-rad 2 allowing for 30% variation in angle With these parameters the time scale per step is fs

10 Example: Alkane +Water 4 H 2 O in one P Link up C particles to form Butane, Hexane etc. 4 CH 2 in one C Mass of the C particle is adjusted whenever the number of CH 2 is not a multiple of 4 The average C-C-C bond angle is kept at o The bonds connecting CM of 4 carbon atoms in MD makes an angle of 136 o Temperature = 300 K. Salt is represented by hydrated ions with 6 H 2 O surrounding an ion. The Mass is calculated accordingly and an effective charge of.7 is used Hydration implies hydrogen bonding, hence dissolved charges have an additional da interaction. MARTINI force field -- Marrink et. al J. Phys. Chem. B 2007, 111,

11 QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture.

12 Vesicle simulated with periodic boundary conditions was fused with its periodic image Starting from preformed stalk, hemifused state was formed within 2 ns In one out of six simulations, a transient pore formed close to the stalk, resulting in the mixing of DPPC lipids between the outer and the inner leaflets. PH induced fusion mechanisms of DPPC/palmitic acid at 1:2 ratio. T= K

13 Solvent free models Common feature: Attractive potential between lipids It turns out that simple LJ pair wise attractive potential will not be sufficient to get self-assembly Brownian dynamics and Monte Carlo using hard core and soft core potentials have been tried. Advantage: Since all the time is spend in updating the membrane configuration alone, larger length and time scales can be achieved. Disadvantage: Cannot be used to study dynamics. Absence of solvent leads to wrong conservation laws Mapping of interactions with real systems is hard. The model can be used to study broad physical features of the membrane at equilibrium. Since internal degrees of freedom are included, effect of gel-fluid transition can be studied

14 A modified LJ, in which the attractive basin is widened to make it longer ranged, was used by Cook and Deserno: JCP 123, (2005) The Lipids are represented by one head bead and two tail beads All beads interact via a shifted LJ of the form The bonds are represented by FENE springs The lipids are straightened by an harmonic spring connecting the head and the second tail particle. an attractive interaction between the tail beads mimic hydrophobic interaction induced attraction between lipids,

15 Cooke and Deserno introduces two different forms for the attractive interaction V cos ( r ) and V flat LJ ( r )

16 Solvent free models with soft core interaction Joel D. Revalee, Mohamed Laradji and Sunil Kumar : JCP (2007) lipid molecules are modeled as semi-flexible amphiphilic linear chains composedof soft beads: one hydrophilic bead, mimicking the lipid head group, and three hydrophobic particles, mimicking the lipid tail group. BD using a Langevin thermostat with interaction potentials given by soft pairwise interaction between neighboring particles, U (0), is given by

17 The equations of motion, The integration time step value set by fluctuation dissipation. are integrated using the velocity- Verlet algorithm with ensures average temperature to the The value of the area per lipid of the molecule in the fluid phase Comparing this with the exp. Value of a l for DPPE bilayers we get Diffusion coefficient is found to be experimental values we get, comparing with

18 The phase behavior of the lipid bilayer can be characterized by the diffusivity of the lipids, the chainorientational order parameter, the bond-orientational order parameter, and translational and bondorientational correlation functions Solid circles correspond to a micellar phase, pluses correspond to stable bilayers, and open circles correspond to defective bilayers or an isotropic solution of lipids The lateral lipid diffusivity of lipids center of mass

19 The lipid sixfold bond-orientational order parameter The positional and bond-orientational correlation functions k B T=2.70 and k B T=2.74