Large-Scale Field-Theoretic Simulation of Soft Polymer Assemblies

Researchers:

• Glenn H. Fredrickson, UCSB
• Kim O. Rasmussen, T-11
• Paul M. Welch, T-17
• Sriram Swaminaraya, CCS-2

Project  Objectives:

The overarching objective is to enable field-theoretic simulations on Cell architecture computers, and thereby significantly expand the range of problems and scope of material systems that can be effectively addressed with this simulation methodology. In the process of accomplishing this we will tackle a challenging problem in soft material self assembly that relates to energy security—proteorhodopsin artificial membranes.

Project Description:

In the emerging areas of nanotechnology and energy security many practical applications of polymers and other soft condensed matter systems involve mixtures that through equilibrium self-assembly or nonequilibrium processing steps develop complex, multiphase morphologies. The desirable properties of such materials depend critically on the ability to control and manipulate morphology by adjusting a combination of molecular and macroscopic variables. Unfortunately, theoretical and computational techniques for anticipating the structure and equilibrium phase behavior of complex polymeric fluids are still in their infancy. A significant reason for the lack of progress in this area is that traditional atomistic simulation methods employing Monte Carlo or molecular dynamics techniques cannot address the range of temporal and spatial scales that are manifest in soft condensed matter systems. Specifically, it is very difficult or impossible to equilibrate sufficiently large systems of polymers at realistic densities in order to extract meaningful information about structure and thermodynamics. This limitation is particularly acute for multiphase, inhomogeneous systems, which are often those of primary interest. An alternative approach for classical fluid systems at equilibrium is to integrate out the particle coordinates in the partition function, replacing them with functional integrals over one or more fluctuating auxiliary potential fields that are confined to a simulation domain. This particle-to-field transformation can be done exactly for any classical fluid (simple or complex) and substitutes a statistical field theory for the original many-body problem. The field theory can be tackled numerically using a variety of stochastic techniques. Such “field-theoretic simulation” methods are rapidly taking center stage as the most powerful suite of tools for exploring the equilibrium properties of a wide range of important soft materials systems and are also beginning to enable access to nonequilibrium properties. The general field-theoretic strategy for calculating equilibrium properties involves four steps: (1) development of a suitable particle-based model, (2) conversion of the particle-based model into a field theory, (3) discretization of the simulation domain, and (4) stochastic sampling of the discretized field theory. With regard to step (3), there are many ways in which a continuum field theory can be discretized for the purpose of numerical simulation. However a well-suited approach in this context is a collocation method based on Fourier modes. The advantage of this “pseudospectral” approach stems from the flexibility of evaluating terms in the field equations in either real or reciprocal space, and because it leads to discrete Fourier transform pairs, which are efficiently evaluated by applying fast Fourier transform (FFT) algorithms. Within this numerical methodology, ~95% of the computational expense of a field theoretic simulation is spent on performing FFTs. Given that Cell processors can perform FFTs at speeds greatly exceeding that of conventional CPUs, we expect that field-theoretic simulations could greatly benefit from the new Roadrunner Cell processor cluster.

Although the described simulation tool development and implementations are of general applicability this project will focus on a challenging problem in soft material self assembly that relates to energy security--proteorhodopsin artificial membranes:  Such membrane proteins, which serve as the gatekeepers of the cell, play an important role in many biological functions and processes and consequently serve as the target for approximately 70% of all drugs in the marketplace.  Proteorhodopsin (PR) is a  particularly fascinating membrane protein that was discovered in marine bacterioplankton only in the past decade. PR serves as a light-driven proton pump used by marine planktons to transport protons across their cell membranes.  Because it can be readily engineeered and expressed in Escherichia coli in large quantities and has unusual stability, PR is being actively investigated for a variety of applications including security inks, biomimetic ATP production, optical data storage, artificial retinas, and photovoltaic devices.  It has recently been discovered that PR can be assembled with cationic lipids into artificial membranes with a wide variety of liquid crystalline structural configurations.  This process effectively positions the PR molecules into two-dimensional lattices within lipid bilayer sheets.  Remarkably, by tuning pH and other solution parameters it is possible to electrostatically assemble the sheets into lamellar and cubic lyotropic phases, thereby achieving three-dimensional long-range order for the PR assemblies.

Figure 1 A. Schematic of a lyotropic lamellar phase produced by co-assembling a cationic lipid (green) with proteorhodopsin (PR, in blue). By tuning pH and other solution parameters, it is possible to achieve a variety of in plane ordered configurations of the PR. B, Square in-plane packings of PR. C, A hexagonal in-plane PR lattice. Reproduced from H. Liang, G. Whited, C. Nguyen, and G. D. Stucky, Proc. Nat. Acad. Sci. (USA) 104, 8212 (2007)

It has been demonstrated as shown in Figure 1 that two different forms of in-plane packing within a lyotropic lamellar phase of PR and cationic lipid exists. This remarkable discovery opens many possibilities for engineered materials that address applications in energy and storage devices. This project will included a theoretical investigation of the physico-chemical factors that control PR artificial membrane structure and thermodynamics. The size and complexity of the PR/cationic lipid assemblies rules out atomistic computer simulation approaches. Instead, we will develop field theory models based on coarse grained models for PR, the cationic lipid, and the solvent medium. Specifically, PR will be described as a multiblock copolymer with hydrophobic blocks that assemble into the membrane interior and pH sensitive hydrophilic blocks that can be anionic or cationic depending on solution conditions. Previous work using similar models has demonstrated that lyotropic assembly of lipid/water mixtures, as well as charge complexation of oppositely charged polyelectrolytes, can be captured within field theoretic simulation approaches. However, because the relevant structures are fully three-dimensional and have large unit cells, even field-theoretic simulations will be extremely computationally demanding.