Single Chain Mean Field Technique for
Simulation of Complex Molecular Systems
Sergey Pogodin† ([email protected]) and Vladimir Baulin†,‡ ([email protected])
†
‡
Universitat Rovira i Virgili, Departament d’Enginyeria Química, Tarragona, Spain
Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain
Our Mission:
- Why SCMF?
- What is the SCMF?
Single Chain Mean Field (SCMF) theory is a powerful tool for investigation of equilibrium behavior of complex molecular systems.
It provides detailed microscopic information and gives direct
access to the free energy of soft matter systems which is hard to
obtain with others theoretical methods, such as Molecular Dynamics or Monte-Carlo simulation. However, the limiting factor
preventing the SCMF theory from a wide use is the technical complexity in realization of reliable and eﬃcient SCMF simulation
code and a lack of standard simulation packages. In order to overcome these problems, we are developing fast and flexible SCMF
program, which can be directly applied for the investigation of
broad spectrum of complex molecular systems.
Our 5 reasons to develop SCMF
+
+
+
+
+
1. Develop fast and flexible SCMF simulation code suitable for a broad scientific use
2. Apply it for the investigation of relevant molecular systems’ behavior
It gives direct access to the free energy and other equilibrium properties of soft matter systems
It is extremely flexible, thus allowing for numerous applications to wide range of molecular systems
It can be coupled with other simulations methods, proviing them with equilibrium initial states of the system
Unlike the Monte-Carlo simulation method, it allows for
direct parallelization of calculations
It is challenging to develop the new method wich is not
widely used due to technical complexity of realization
SCMF theory uses mean-field approach which finds directly the
minimums of the free energy for the system.
We use the following three approximations
Conformational states of diﬀerent molecules are assumed to be
Intermolecular interactions
uncorrelated
are approximated via interaction of single molecules with
the mean-field concentrations The solvent is treated implicitly
of others molecules
and the incompressibility condition is applied in each point of
the system
This allows to separate the free-energy on entropy, intra- and intermolecular parts
- How does the SCMF work?
The current version of our SCMF simulation code is written in C++
with the use of OpenMP parallelization protocol. It is already suitable for performing real calculations, although it still have numerous restrictions and simplifications. So, we continue our work towards creation of complete SCMF package with flexible modular
structure, easy to use, modificate and expand.
Scheme of the SCMF program work flow
Particular coarse-grained
model for the molecules in
the system
Input of simulation parameters
Properties of the simulation box (size, geometry, boundary conditions, ets.)
Parameters, controlling
the actual flow of the
simulation process
Potentials for intra- and
inter- molecular interactions
and derive a set of equations which determine the equilibrium distributions of the system’s compounds by minimizing the freeenergy.
The average concentrations and the volumes occupied by the
molecule’s units in each point are the averages of corresponding
single-molecule quantities over the single-molecule probability
functions ρ. The single-molecule probability functions ρ, in its
turn, are the known combinations of average concentrations and
the occupied volume distributions and others single-molecule
properties, which could be calculated. Thus, generating suﬃcient
sampling of single-molecule conformational spaces and solving the
SCMF equations we are able to obtain with a reasonable accuracy
data concerning the equilibrium behavior of multimolecular
system.
Generation of representative
single-molecule conformational
sampling for every kind of molecules presented in the system
Potentials created by
the molecules in diﬀerent points of the simulation box
Solving the SCMF equations
Equilibrium distributions of the sistem
compounds
Data concerning bias of
the generated sampling
Calculation of auxiliary properties related to conformations in
the samplings
Distribution of the
molecules’ beads inside
the simulation box
Solving the equations for
diﬀerent numbers of the
molecules in the simulation box
Coordinates of the
beads for every conformation in the sampling
Tracing multiple solutions, corresponding to
the equilibrium and
meta-stable states of the
system
Sorting and posttreatment of computed
data
Data output
Free-energy values
for the found solutions
Mean field snapshots
revealing the system
behavior in the most
representable way
- What are we using the SCMF for?
Simulation of Phospholipid Membrane 1
Piercing of the Membrane with a Nanotube 2
Micellization of Pluronic® surfactants
Three models of dimyristoylphosphatidylcholine (DMPC) phospholipid molecule at diﬀerent coarse-grained levels (44-, 10- and 3beads) were developed. Their parameters were fitted to reproduce
the real properties of DMPC membranes:
– Density profile of the membrane bilayer;
– Average interfacial area per lipid (60 Å2);
– Compressibility modulus (260 dyn/cm).
Simulation of the DMPC membrane piercing by a carbon nanotube
was carried out. Three diameters of the nanotube (1.00, 2.43, 4.86
nm.) corresponds to tipical sizes of the single-walled nanotubes.
The membrane was simulated within the 3-beads model of lipid
molecule and the level of the nanotube-membrane aﬃnity was
varied in vast region, changing the tube’s behavior from hydrophilic to strongly hydrophobic.
Our measurements of the energy barriers created by the membrane of the nanotube penetration allowed us to conclude that the
nanotubes are not able to spontaneously cross the membrane just
by thermal motion without application of additional external
force.
The mean field snapshots (a set of most probable conformations)
show the molecular details of piercing of the nanotube into lipid
layer and the details of the bilayer rearrangements around the
nanotube with the variation of the nanotube hydrophobicity.
This work is devoted to creation of the unified coarse-grained
models for Pluronic surfactants, (water soluble tri-block copolymers PEO-PPO-PEO). Due to the fact that diﬀerent Pluronics
diﬀer only in their blocks length, the unified coarse-grained model
of their chemical structure could be formulated. Interactions between the beads and the solvent, assumed to be the same for diﬀerent Pluronics, are to be fitted to represent experimentally measured values of the surfactants’ critical micellization concentrations.
Chemical structure of the DMPC phospholipid (a),
shown against its 44-, 10- and 3- beads representations,
(b), (c) and (d). Red and blue beads are hydrophobic
and hydrophilic, correspondingly. Orange beads for the
model (b) have completely the same properties as the
red ones.
Free energy plot for the 3-beads DMPC model. Red and
green curves correspond to solution with one and two
bilayers formed in the simulation box. In the last case
both of the layers are slightly compressed, which
results in the energy diﬀerence. The inset shows
zoomed area of the red curve minimum.
Coarse-grained representation of L64, P65, P84 and P85 Pluronic
molecules.
Micelle comprising of 100 L64 molecules.
Summary
Working prototype of the SCMF simulation package was developed
and used for calculations of real systems.
Mean field snapshot showing partial insertion of 2.43 nm.
diameter hydrophobic nanotube inside the DMPC bilayer
(part of the layer is not shown in order to simplify the picture).
Energy barriers for perpendicular penetration of
the nanotube with diameter 2.43 nm. inside the
DMPC membrane. Diﬀerent curves corresponds to
diﬀerent levels of the nanotube’s hydrophobicity.
It was proved the ability of the method to simulate phospholipid
membranes at various levels of coarse graining and reproduce the
experimentaly relevant membrane properties.
The method can be used for precise calculations of equilibrium
free energy of insertion of nano-objects into lipid layers. This was
used to study the process of the carbon nanotube translocation
through the lipid membrane in order to show that spontaneous
translocation of carbon nanotubes through the membranes is not
possible.
Perspectives
Further developing of the SCMF software up to its public release.
Design of hydrophobic/hydrophilic patterns on the nanotube surface, indicating the ways to lower the energy barrier for their translocation through the phospholipid membrane.
Comparison of equilibrium DMPC membrane structure, obtained with three diﬀerent levels of coarse-graining (a),
and the membrane's density profiles (b), (c), (d) for 44-, 10- and 3- beads models, correspondingly. Red and blue
lines on the profiles represents density of the hydrophobic and hydrophilic beads, while the black curves shows
overall distribution of the lipids.
References:
[1]. Sergey Pogodin and Vladimir Baulin, Soft Matter, 2010, DOI: 10.1039/b927437e
[2]. Sergey Pogodin and Vladimir Baulin, to be published
Rearrangement of the DMPC bilayer around the nanotube with diameter 2.43 nm. during its perpendicular insertion. Snapshots represent the densities of the hydrophobic (red) and hydrophilic (blue) beads in the cross-section
of the simulation box, taken through the symmetry axis of the nanotube. The tube’s hydrophobicity is increasing
from the left to right, while the insertion depth is increasing from top to bottom.
Study of insertion of peptides and proteins into phospholipid
layers