We review a class of new computer simulation methods for polymeric fluids and other soft condensed matter systems that are based on an underlying field-theoretic description. These methods, while still in an early stage of development, show considerable promise for studying the equilibrium properties of many-component systems capable of intricate self-assembly, such as solutions and blends containing block and graft copolymers. Field-theoretic simulation methods also provide a great deal of flexibility in model building and coarse graining, and appear to be particularly well suited to treat systems with soft, long-range interactions, such as polyelectrolytes. We attempt to connect various related theoretical approaches, such as self-consistent field theory and dynamic density functional theory, within a common framework.

Field-Theoretic Computer Simulation Methods for Polymers and Complex Fluids

As a result of important advances over the last decade, block copolymer melts have become an excellent model system for studying fundamental phenomena associated with molecular self-assembly. During this time, good quantitative agreement has been achieved between theory and experiment in regards to equilibrium phase behaviour, and with it has emerged a thorough understanding in terms of simple intuitive explanations. The theoretical contributions to this effort are largely attributed to mean-field calculations on a standard Gaussian model. Here, we review this present understanding of block copolymer phase behaviour, the model and its underlying assumptions, the mean-field approximation and its limitations, and the attempts to incorporate fluctuation corrections. Rather than following the traditional rigorous derivations, we present slightly more intuitive and transparent ones in such a way to stress the close connection between the related calculations. In this way, we hope to provide a valuable introduction to block copolymer theory.

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The standard Gaussian model for block copolymer melts

One of the most unique physical features of cell adhesion to external surfaces is the active generation of mechanical force at the cell-material interface. This includes pulling forces generated by contractile polymer bundles and networks, and pushing forces generated by the polymerization of polymer networks. These forces are transmitted to the substrate mainly by focal adhesions, which are large, yet highly dynamic adhesion clusters. Tissue cells use these forces to sense the physical properties of their environment and to communicate with each other. The effect of forces is intricately linked to the material properties of cells and their physical environment. Here a review is given of recent progress in our understanding of the role of forces in cell adhesion from the viewpoint of theoretical soft matter physics and in close relation to the relevant experiments.

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Physics of adherent cells

Microtubules are hollow cylindrical structures that constitute one of the three major classes of cytoskeletal filaments. On the mesoscopic length scale of a cell, their material properties are characterized by a single stiffness parameter, the persistence length l(p). Its value, in general, depends on the microscopic interactions between the constituent tubulin dimers and the architecture of the microtubule. Here, we use single-particle tracking methods combined with a fluctuation analysis to systematically study the dependence of l(p) on the total filament length L. Microtubules are grafted to a substrate with one end free to fluctuate in three dimensions. A fluorescent bead is attached proximally to the free tip and is used to record the thermal fluctuations of the microtubule's end. The position distribution functions obtained with this assay allow the precise measurement of l(p) for microtubules of different contour length L. Upon varying L between 2.6 and 47.5 mum, we find a systematic increase of l(p) from 110 to 5,035 mum. At the same time we verify that, for a given filament length, the persistence length is constant over the filament within the experimental accuracy. We interpret this length dependence as a consequence of a nonnegligible shear deflection determined by subnanometer relative displacement of adjacent protofilaments. Our results may shine new light on the function of microtubules as sophisticated nanometer-sized molecular machines and give a unified explanation of seemingly uncorrelated spreading of microtubules' stiffness previously reported in literature.

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Thermal fluctuations of grafted microtubules provide evidence of a length-dependent persistence length

Single-molecule experiments on single- and double-stranded DNA have sparked a renewed interest in the force versus extension of polymers. The extensible freely jointed chain (FJC) model is frequently invoked to explain the observed behavior of single-stranded DNA, but this model does not satisfactorily describe recent high-force stretching data. We instead propose a model (the discrete persistent chain) that borrows features from both the FJC and the wormlike chain, and show that it resembles the data more closely. We find that most of the high-force behavior previously attributed to stretch elasticity is really a feature of the corrected entropic elasticity; the true stretch compliance of single-stranded DNA is several times smaller than that found by previous authors. Next we elaborate our model to allow coexistence of two conformational states of DNA, each with its own stretch and bend elastic constants. Our model is computationally simple and gives an excellent fit through the entire overstretching transition of nicked, double-stranded DNA. The fit gives the first value for the bend stiffness of the overstretched state. In particular, we find the effective bend stiffness for DNA in this state to be about 12 nm k(B)T, a value quite different from either the B-form or single-stranded DNA.

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Theory of High-Force DNA Stretching and Overstretching

The statistical mechanical theory of stiff chains which can be represented by differentiable space curves is developed by the analogy of the path integral formulation in quantum mechanics. The second and fourth moments of end-to-end distance of the chain are calculated. The stretching and contraction of the chain are also taken into account. The Brownian motion of the stiff chain is discussed, and some statistical properties, especially the correlation function of random forces, are determined.

Yasuo Yunoki

Papers

The Statistical Mechanical Theory of Stiff Chains