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Active Matter

Thermophoresis
Macromolecules assume compact conformations in certain situations. Examples include DNA in living cells, proteins in native states, and other polymers in poor solvent conditions or under a compression field. Once released from the condition, these polymers expand to swollen coiled state, which is characterized by developed fluctuations. This expansion process is of interest in two different contexts. First, this process is relevant to coil-globule transitions, thus, regarded as a fundamental topic in polymer science. Unfortunately, there are comparatively fewer past studies on this expansion process than on the folding (coil to globule) process. The second case of interest is encountered in the field of confined polymers. A recent advance in nanoscale fabrications and singlechain experiments allows one to manipulate and observe individual polymers, thereby facilitating a number of potential applications in biological as well as nanoscale sciences.

Physics inspired by Biology

Physics of stress fibers
Stress fibers are contractile actomyosin bundles commonly observed in the cytoskeleton of metazoan cells. The spatial profile of the polarity of actin filaments inside contractile actomyosin bundles is either monotonic (graded) or periodic (alternating). In the framework of linear irreversible thermodynamics, we write the constitutive equations for a polar, active, elastic one-dimensional medium. An analysis of the resulting equations for the dynamics of polarity shows that the transition from graded to alternating polarity patterns is a nonequilibrium Lifshitz point. Active contractility is a necessary condition for the emergence of sarcomeric, alternating polarity patterns.

Polymer Translocation
Macromolecules assume compact conformations in certain situations. Examples include DNA in living cells, proteins in native states, and other polymers in poor solvent conditions or under a compression field. Once released from the condition, these polymers expand to swollen coiled state, which is characterized by developed fluctuations. This expansion process is of interest in two different contexts. First, this process is relevant to coil-globule transitions, thus, regarded as a fundamental topic in polymer science. Unfortunately, there are comparatively fewer past studies on this expansion process than on the folding (coil to globule) process. The second case of interest is encountered in the field of confined polymers. A recent advance in nanoscale fabrications and singlechain experiments allows one to manipulate and observe individual polymers, thereby facilitating a number of potential applications in biological as well as nanoscale sciences.

Transition Kinetics of a single semiflexible polymer
We investigate theoretically the kinetics of the folding transition of a single semiflexible polymer. In the folding process, long-axis length of a chain decreases linearly in time. In the unfolding process, dynamic scaling exponents, 1/8 and 1/4, were determined for disentanglement and relaxation processes, respectively.

Polymer stretching
Kinetics of conformational change of a semiflexible polymer under mechanical external Field were investigated with Langevin dynamics simulations. It is found that a semiflexible polymer exhibits large hysteresis in mechanical folding/unfolding cycle even with a slow operation, whereas in a °exible polymer, the hysteresis almost disappears at a sufficiently slow operation. This suggests that the essential features of the structural transition of a semiflexible polymer should be interpreted at least on a two-dimensional phase space. The appearance of such large hysteresis is discussed in relation to different pathways in the loading and unloading processes. By using a minimal two-variable model, the hysteresis loop is described in terms of different pathways on the transition between two stable states.

The movie shows kinetics of comformational change during stretching a semiflexible polymer.

movie: mechanical unfolding of a semiflexible polymer

Rod-coil copolymer
We investigate the folding transition of a single diblock copolymer consisting of a semiflexible and a flexible blocks. We obtain the saturn shaped core-shell conformation in the folded state, where the flexible block form a core and the semiflexible block wrap around them. We find two distinctive features in the core-shell structures. (i) The kinetics of the folding transition in the copolymer are more efficient than that in a semiflexible homopolymer. (ii) The core-shell structure does not depend on pathways of the transition.

Two-state polymer
Monte Carlo simulation of annealed copolymers of solvophobic/solvophilic monomers show collapsed globular states having a dynamic core-shell structures. In these, the core is mostly solvophobic while the core boundary contains an excess of solvophilic monomers. This two state model, where each monomer undergoes interconversion between solvophobic and solvophilic state, is a minimal version of models of neutral water soluble polymers such as PEO. The reduced surface tension of such core-shell structures suggests an explanation of the stability of PNIPAM globules as observed in the experiments of X.Wang, X.Qiu, C.Wu, Macromolecules, 1998, 31, 2972. The statitistics of the monomeric states along the chain vary with the degree of chain swelling. They are differ from those of quenched copolymers designed to create water soluble globules though both systems involve a core-shell structures.

movie of a two-state polymer

phase transition in DNA
Semiflexible polymers started to be paid attention after conformation of DNA molecules were observed. It is surprising 2m length DNA are packed into a cell with the size of several um. The conformations are not disorderd, but ordered like a toroidal shape. For example, bacteria phase has DNA with the toroidal conformation inside a capsule in head. Naive questions arised not only from biologists but also from physicists: How such a long molecule packs in a small capsid?; How does it have ordered conformations? Biopolymers, in general, have bending elsticity, which plays a important role for conformations of polymers. For example, a DNA molecule has the persistence length of approximately 50 nm. 2 This value is much larger than the width of a DNA molecule (approximately 2 nm in diameter), and smaller than the contour length. T4 phage DNA, for example, has approximately 57 um contour length. It behaves therefore as a rigid rod in a small length scale,

Kyoto University

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Active Matter

Physics inspired by Biology