Publications

Yui Ota, Yuto Hosaka, Kento Yasuda, and *Shigeyuki Komura,
Three-disk microswimmer in a supported fluid membrane,
Physical Review E 97, 052612/1-7 (2018).

[Summary] A model of three-disk micromachine swimming in a quasi two-dimensional supported membrane is proposed. We calculate the average swimming velocity as a function of the disk size and the arm length. Due to the presence of the hydrodynamic screening length in the quasi two-dimensional fluid, the geometric factor appearing in the average velocity exhibits three different asymptotic behaviors depending on the microswimmer size and the hydrodynamic screening length. This is in sharp contrast with a microswimmer in a three-dimensional bulk fluid that shows only a single scaling behavior. We also find that the maximum velocity is obtained when the disks are equal-sized, whereas it is minimized when the average arm lengths are identical. The intrinsic drag of the disks on the substrate does not alter the scaling behaviors of the geometric factor.

Kento Yasuda, Ryuichi Okamoto, Shigeyuki Komura, and Jean-Baptiste Fournier,
Dynamics of a bilayer membrane with membrane-solvent partial slip boundary conditions,
Soft Materials 16(3), 186-191 (2018).

[Summary] We discuss the dynamics of a bilayer membrane with partial slip boundary conditions between the monolayers and the bulk fluid. Using Onsager's variational principle to account for the associated dissipations, we derive the coupled dynamic equations for the membrane height and the excess lipid density. The newly introduced friction coefficients appear in the renormalized fluid viscosities. For ordinary lipid bilayer membranes, we find that it is generally justified to ignore the effects of permeation and parallel slip at the membrane surface.

*Hailong Peng, Momoji Kubo, and *Hayato Shiba,
Molecular dynamics study of mesophase transitions upon annealing of imidazolium-based ionic liquids with long-alkyl chains,
Physical Chemistry Chemical Physics 20, 9796-9805 (2018).

[Summary] Molecular dynamics simulations are performed on a 1-dodecyl-3-methylimidazolium hexafluorophosphate ([C12mim][PF6]) ionic liquid using a united-atom model. The ionic liquid exhibits a second step relaxation at temperatures below a crossover point, where the diffusion coefficient shows Arrhenius to non-Arrhenius transition. Annealing below this crossover temperature makes isotropic-to-mesophase transition, where the smectic A (SmA) phase or crystal-like smectic B (SmB) phase forms. Hundreds of nanoseconds are required for completing these transitions. A normal diffusion process is found for anions along the layer-normal and -lateral directions in the SmA phase, but only in the lateral directions in the SmB phase. We find a preserved orientational order for the imidazolium-ring rotational and the alkyl-chain reorientational dynamics in both of the smectic phases.

*Yuta Asano, Hiroshi Watanabe, and Hiroshi Noguchi,
Polymer effects on Karman vortex: Molecular dynamics study,
The Journal of Chemical Physics 148, 144901 (2018).

[Summary] We investigated the Karman vortex behind a circular cylinder in a polymer solution by a molecular dynamics simulation. The vortex characteristics are distinctly different for short and long polymers. The solution with the long polymer exhibits a reduction in the vortex shedding frequency and broadening of the lift coefficient spectrum. On the other hand, the characteristics of the short-polymer solution are almost the same as those of the Newtonian fluid. These facts are consistent with the experiments.Because the distributions of the gyration radius and the orientational order of the long-polymer solution are highly inhomogeneous in the flow field, we conclude that the extensional property of the polymer plays an important role in changing the flow characteristics.

T. V. Sachin Krishnan, Kento Yasuda, Ryuichi Okamoto, and Shigeyuki Komura,
Thermal and active fluctuations of a compressible bilayer vesicle,
J. Phys.: Condens. Matter 30, 175101/1-9 (2018).

[Summary] We discuss thermal and active fluctuations of a compressible bilayer vesicle by using the results of hydrodynamic theory for vesicles. Coupled Langevin equations for the membrane deformation and the density fields are employed to calculate the power spectral density matrix of membrane fluctuations. Thermal contribution is obtained by means of the fluctuation dissipation theorem, whereas active contribution is calculated from exponentially decaying time correlation functions of active random forces. We obtain the total power spectral density as a sum of thermal and active contributions. An apparent response function is further calculated in order to compare with the recent microrheology experiment on red blood cells. An enhanced response is predicted in the low-frequency regime for non-thermal active fluctuations.

Swaminath Bharadwaj, P. B. Sunil Kumar, Shigeyuki Komura, and Abhijit P. Deshpande,
Kosmotropic effect leads to LCST decrease in thermoresponsive polymer solutions,
Journal of Chemical Physics 148, 084903 (2018).

[Summary] We study the phenomena of decrease in lower critical solution temperature (LCST) with addition of kosmotropic (order-making) cosolvents in thermoresponsive polymer solutions. A combination of explicit solvent coarse-grained simulations and mean-field theories has been employed. The polymer-solvent LCST behavior in the theoretical models have been incorporated through the Kolomeisky-Widom solvophobic potential. Our results illustrate how the decrease in the LCST can be achieved by the reduction in the bulk solvent energy with addition of cosolvent. It is shown that this effect of cosolvent is weaker with increase in polymer hydrophilicity which can explain the absence of LCST decrease in PDEA, water and methanol systems. The coarse-grained nature of the models indicates that a mean energetic representation of the system is sufficient to understand the phenomena of LCST decrease.

*Hayato Shiba, Peter Keim, and Takeshi Kawasaki,
Isolating long-wavelength fluctuation from structural relaxation in two-dimensional glass: cage-relative displacement,
Journal of Physics: Condensed Matter 30, 094004/1-9 (2018).

[Summary] arate the long-wavelength fluctuation from the original MSD. For increasing system size the amplitude of acoustic long wavelength fluctuations not only increases but shifts to later times causing a crossover with structural relaxation of caging particles. We further analyse the dynamic correlation length using the cage-relative quantities. It grows as the structural relaxation becomes slower with decreasing temperature, uncovering an overestimation by the four-point correlation function due to the long-wavelength fluctuation. These findings motivate the usage of cage-relative MSD as a starting point for analysis of 2D glassy dynamics.

Koh M. Nakagawa and *Hiroshi Noguchi,
Bilayer sheet protrusions and budding from bilayer membranes induced by hydrolysis and condensation reactions,
Soft Matter 14, 1397-1407 (2018).

[Summary] Shape transformations of flat bilayer membranes and vesicles induced by hydrolysis and condensation reactionsof amphiphilic molecules are studied using coarse-grained molecular dynamics simulations. The hydrolysis and condensation reactions result in the formation and dissociation of amphiphilic molecules, respectively. Asymmetric reactions between the inner and outer leaflets of a vesicle can transport amphiphilic molecules between the leaflets. It is found that the resulting area difference between the two leaflets induces bilayer sheet protrusion (BP) and budding at low reduced volumes of the vesicles, whereas BP only occurs at high reduced volumes. The probabilities of these two types of transformations depend on the shear viscosity of the surrounding fluids compared to the membrane as well as the reaction rates. A higher surrounding fluid viscosity leads to more BP formation. The inhomogeneous spatial distribution of the hydrophobic reaction products forms the nuclei of BP formation, and faster diffusion of the products enhances BP formation. Our results suggest that adjustment of the viscosity is important to control membrane shape transformations in experiments.

Takuma Hoshino, *Shigeyuki Komura, and David Andelman,
Permeation through a lamellar stack of lipid mixtures,
EPL 120, 18004 (4pp) (2017).

[Summary] We study material transport and permeation through a lamellar stack of multi-component lipid membranes by performing Monte Carlo simulations of a stacked two-dimensional Ising model in presence of permeants. In the model, permeants are transported through the stack via in-plane lipid clusters, which are inter-connected in the vertical direction. These clusters are formed transiently by concentration fluctuations of the lipid mixture, and the permeation process is affected especially close to the critical temperature of the binary mixture. We show that the permeation rate decays exponentially as function of temperature and permeant lateral size, whereas the dependency on the characteristic waiting time obeys a stretched exponential function. The material transport through such lipid clusters can be significantly affected around physiological temperatures.

Yuto Hosaka, Kento Yasuda, Isamu Sou, Ryuichi Okamoto, and *Shigeyuki Komura,
Thermally driven elastic micromachines,
Journal of the Physical Sciety of Japan 86, 113801/1-4 (2017).

[Summary] We discuss the directional motion of an elastic three-sphere micromachine in which the spheres are in equilibrium with independent heat baths having different temperatures.Even in the absence of prescribed motion of springs, such a micromachine can gain net motion purely because of thermal fluctuations. A relation connecting the average velocity and the temperatures of the spheres is analytically obtained. This velocity can also be expressed in terms of the average heat flows in the steady state. Our model suggests a new mechanism for the locomotion of micromachines in nonequilibrium biological systems.

Isamu Sou, Ryuichi Okamoto, *Shigeyuki Komura, and Jean Wolff,
Coexistences of lamellar phases in ternary surfactant solutions,
Soft Materials 15, 272-281 (2017).

[Summary] We theoretically investigate the coexistences of lamellar phases both in binary and ternary surfactant solutions. The previous free energy of a lamellar stack is extended to take into account the translational entropy of membrane segments. The obtained phase diagram for binary surfactant solutions (surfactant/water mixtures) shows a phase separation between two lamellar phases and also exhibits a critical point. For lamellar phases in ternary surfactant solutions (surfactant/surfactant/water mixtures), we explore possible phase behaviors and show that the phase diagrams exhibit various three-phase regions as well as two-phase regions in which different lamellar phases coexist. We also find that finite surface tension suppresses undulation fluctuations of membranes and leads to a wider three-phase and two-phase coexistence regions.

*Hiroshi Noguchi,
Acceleration and suppression of banana-shapedprotein-induced tubulation by addition of small membrane inclusions of isotropic spontaneous curvatures,
Soft Matter 13, 7771-7779 (2017).

[Summary] Membrane tubulation induced by banana-shaped protein rods is investigated by using coarse-grained meshless membrane simulations. It is found that tubulation is promoted by laterally isotropic membrane inclusions that generate the same sign of spontaneous curvature as the adsorbed protein rods. The inclusions are concentrated in the tubules and reduce the bending energy of the tip of the tubules. On the other hand, inclusions with an opposite curvature suppress tubulation by percolated-networkformation at a high protein-rod density while they induce the formation of a spherical membrane bud at a low rod density. When equal amounts of the two types of inclusions (with positive and negative curvatures) are added, their effects cancel each other for the first short period but later the tubulation is slowly accelerated. Positive surface tension suppresses tubulation. Our results suggest that the cooperation of scaffolding of BAR (Bin/Amphiphysin/Rvs) domains and isotropic membrane inclusions is important for tubulation.

Kento Yasuda, Yuto Hosaka, Mizuki Kuroda, Ryuichi Okamoto, and *Shigeyuki Komura,
Elastic three-sphere microswimmer in a viscous fluid,
Journal of the Physical Sciety of Japan 86, 093801/1-4 (2017).

[Summary] We discuss the dynamics of a generalized three-sphere microswimmer in which the spheres are connected by two elastic springs. The natural length of each spring is assumed to undergo a prescribed cyclic change. We analytically obtain the average swimming velocity as a function of the frequency of cyclic change in the natural length. In the low- frequency region, the swimming velocity increases with frequency, and its expression reduces to that of the original three-sphere model by Najafi and Golestanian. Conversely, in the high-frequency region, the average velocity decreases with increasing frequency. Such behavior originates from the intrinsic spring relaxation dynamics of an elastic swimmer moving in a viscous fluid.

*Ryuichi Okamoto, Shigeyuki Komura, and Jean-Baptiste Fournier,
Dynamics of a bilayer membrane coupled to a two-dimensional cytoskeleton: Scale transfers of membrane deformations,
Physical Review E 96, 012416/1-10 (2017).

[Summary] We theoretically investigate the dynamics of a floating lipid bilayer membrane coupled with a two-dimensional cytoskeleton network, taking into account explicitly the intermonolayer friction, the discrete lattice structure of the cytoskeleton, and its prestress. The lattice structure breaks lateral continuous translational symmetry and couples Fourier modes with different wave vectors. It is shown that within a short time interval a long-wavelength deforma- tion excites a collection of modes with wavelengths shorter than the lattice spacing. These modes relax slowly with a common renormalized rate originating from the long-wavelength mode. As a result, and because of the prestress, the slowest relaxation is governed by the intermonolayer friction. Conversely, and most interestingly, forces applied at the scale of the cytoskeleton for a sufficiently long time can cooperatively excite large-scale modes.

Hideo Shindou, Hideto Koso, Junko Sasak, Hiroki Nakanishi, Hiroshi Sagara,h Koh M. Nakagawa, Yoshikazu Takahashi, Daisuke Hishikawa, Yoshiko Iizuka-Hishikawa, Fuyuki Tokumasu, Hiroshi Noguchi, Sumiko Watanabe, Takehiko Sasaki, and Takao Shimizu,
Docosahexaenoic acid preserves visual function by maintaining correct disc morphology in retinal photoreceptor cells,
Journal of Biological Chemistry 292, 12054-12064 (2017).

[Summary] Docosahexaenoic acid (DHA) has essential roles in photoreceptor cells in the retina and is therefore crucial to healthy vision. Although the influence of dietaryDHAon visual acuity is well known and the retina has an abundance of DHA-containing phospholipids (PL-DHA), the mechanisms associated with DHA’s effects on visual function are unknown. We previously identified lysophosphatidic acid acyltransferase 3 (LPAAT3) as a PL-DHA biosynthetic enzyme. Here, using comprehensive phospholipid analyses and imaging mass spectroscopy, we found that LPAAT3 is expressed in the inner segment of photoreceptor cells and that PL-DHA disappears from the outer segment in the LPAAT3-knock-out mice. Dynamic light-scattering analysis of liposomes and molecular dynamics simulations revealed that the physical characteristics ofDHAreduced membrane-bending rigidity. Following loss of PL-DHA, LPAAT3-knock-out mice exhibited abnormalities in the retinal layers,such as incomplete elongation of the outer segment and decreased thickness of the outer nuclear layers and impaired visual function, as well as disordered disc morphology in photoreceptor cells. Our results indicate that PL-DHA contributes to visual function by maintaining the disc shape in photoreceptor cells and that this is a function of DHA in the retina. This study thus provides the reason why DHA is required for visual acuity and may help inform approaches for overcoming retinal disorders associated with DHA deficiency or dysfunction.

Yuto Hosaka, Kento Yasuda, Ryuichi Okamoto, *Shigeyuki Komura,
Lateral diffusion induced by active proteins in a biomembrane,
Physical Review E 95, 052407/1-10 (2017).

[Summary] We discuss the hydrodynamic collective effects due to active protein molecules that are immersed in lipid bilayer membranes and modeled as stochastic force dipoles. We specifically take into account the presence of the bulk solvent which surrounds the two-dimensional fluid membrane. Using the generalized membrane mobility tensors, we estimate the active diffusion coefficient and the drift velocity as a function of the size of a diffusing object.

Hiroshi Noguchi and Jean-Baptiste Fournier,
Membrane structure formation induced by two types of banana-shaped proteins,
Soft Matter 13, 4099-4111 (2017).

[Summary] The assembly of banana-shaped rodlike proteins on membranes and the associated membrane shape transformations are investigated by analytical theory and coarse-grained simulations. The membranemediatedinteractions between two banana-shaped inclusions are derived theoretically using a point-like formalism based on fixed anisotropic curvatures, both for zero surface tension and for finite surface tension. On a larger scale, the interactions between the assemblies of such rodlike inclusions are determined analytically. Meshless membrane simulations are performed in the presence of a largenumber of inclusions of two types, corresponding to the curved rods of opposite curvatures, both for flat membranes and vesicles. Rods of the same type aggregate into linear assemblies perpendicular to the rod axis, leading to membrane tubulation. However, rods of the other type, those of opposite curvature, are attracted to the lateral sides of these assemblies, and stabilize a straight bump structure that prevents tubulation. When the two types of rods have almost opposite curvatures, the bumps attract one another, forming a striped structure. Positive surface tension is found to stabilize stripe formation. The simulation results agree well with the theoretical predictions provided the point-like curvatures of the model are scaled-down to account for the effective flexibility of the simulated rods.

Kento Yasuda, Ryuichi Okamoto, and *Shigeyuki Komura,
Swimmer-microrheology,
Journal of the Physical Society of Japan 86, 043801/1-4 (2017).

[Summary] We discuss the locomotion of a three-sphere microswimmer in a viscoelastic medium and propose a new type of active microrheology. We derive a relation that connects the average swimming velocity and the frequency-dependent viscosity of the surrounding medium. In this relation, the viscous contribution can exist only when the time-reversal symmetry is broken, whereas the elastic contribution is present only when the structural symmetry of the swimmer is broken. Purcell’s scallop theorem breaks down for a three-sphere swimmer in a viscoelastic medium.

Kento Yasuda, Ryuichi Okamoto, and *Shigeyuki Komura,
Anomalous diffusion in viscoelastic media with active force dipoles,
Physical Review E 95, 032417/1-14 (2017).

[Summary] With the use of the ``two-fluid model", we discuss anomalous diffusion induced by active force dipoles in viscoelastic media. Active force dipoles, such as proteins and bacteria, generate non-thermal fluctuating flows that lead to a substantial increment of the diffusion. Using the partial Green's function of the two-fluid model, we first obtain passive (thermal) two-point correlation functions such as the displacement cross-correlation function between the two point particles separated by a finite distance. We then calculate active (non-thermal) one-point and two-point correlation functions due to active force dipoles.The time correlation of a force dipole is assumed to decay exponentially with a characteristic time scale. We show that the active component of the displacement cross-correlation function exhibits various crossovers from super-diffusive to sub-diffusive behaviors depending on the characteristic timescales and the particle separation. Our theoretical results are intimately related to the microrheology technique to detect fluctuations in non-equilibrium environment.

Swaminath Bharadwaj, *Palakurissi B. Sunil Kumar, Shigeyuki Komura, Abhijit P. Deshpande,
Spherically symmetric solvent is sufficient to explain lower critical solution temperature in polymer solutions,
Macromolecular Theory and Simulations 26, 1600073/1-11 (2017).

[Summary] The mechanism of the lower critical solution temperature (LCST) in thermoresponsive polymer solutions has been studied. The simulation model includes solvent explicitly and thus accounts for solvent interactions and entropy directly. The theoretical model consists of a single chain polymer in an implicit solvent where the effect of solvent is included through the intrapolymer solvophobic potential proposed by Kolomeisky and Widom. The results of this study indicate that the LCST behavior is determined by the competition between the mean energy difference between the bulk and bound solvent, and the entropy loss due to the bound solvent.

Kento Yasuda, Ryuichi Okamoto, *Shigeyuki Komura, and Alexander S. Mikhailov,
Localization and diffusion of tracer particles in viscoelastic media with active force dipoles,
EPL 117, 38001/1-7 (2017).

[Summary] The two-fluid model of a gel is considered where active macromolecules, described as force dipoles, cyclically operate both in the elastic and the fluid components. Through coarse-graining, effective equations of motions for idealized tracer particles displaying local deformations and local fluid flows are derived. The equation for deformation tracers coincides with the earlier phenomenological model and thus confirms it. For flow tracers, diffusion enhancement caused by active force dipoles in the fluid component, and thus due to metabolic activity, is found.

T. V. Sachin Krishnan, Ryuichi Okamoto, and *Shigeyuki Komura,
Relaxation dynamics of a compressible bilayer vesicle containing highly viscous fluid,
Physical Review E 94, 062414/1-14 (2016).

[Summary] We study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium. A higher fluid viscosity inside the vesicle shifts the crossover mode between the bending and the slipping to a larger value. As the vesicle parameters approach the unstable regions, the relaxation dynamics is dramatically slowed down, and the corresponding mode structure changes significantly.

*Hayato Shiba, Yasunori Yamada, Takeshi Kawasaki, and Kang Kim,
Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation,
Physical Review Letters 117, 245701/1-6 (2016).

[Summary] By using large-scale molecular dynamics simulations, the dynamics of two-dimensional (2D) supercooled liquids turns out to be dependent on the system size, while the size dependence is not pronounced in three-dimensional (3D) systems. It is demonstrated that the strong system-size effect in 2D amorphous systems originates from the enhanced fluctuations at long wavelengths , which are similar to those of 2D crystal phonons. This observation is further supported by the frequency dependence of the vibrational density of states, consisting of the Debye approximation in the low-wave-number limit. However, the system-size effect in the intermediate scattering function becomes negligible when the length scale is larger than the vibrational amplitude. This suggests that the finite-size effect in a 2D system is transient and also that the structural relaxation itself is not fundamentally different from that in a 3D system. In fact, the dynamic correlation lengths estimated from the bond-breakage function, which do not suffer from those enhanced fluctuations, are not size dependent in either 2D and or 3D systems.

Koh M. Nakagawa and *Hiroshi Noguchi,
Nonuniqueness of local stress of three-body potentials in molecular simulations,
Physical Review E 94, 053304/1-11 (2016).

[Summary] Microscopic stress fields arewidely used in molecular simulations to understand mechanical behavior.Recently,decomposition methods of multibody forces to central force pairs between the interacting particles have beenproposed. Here, we introduce a force center of a three-body potential and propose different force decompositionsthat also satisfy the conservation of translational and angular momentum. We compare the force decompositionsby stress-distribution magnitude and discuss their difference in the stress profile of a bilayer membrane by usingcoarse-grained and atomistic molecular dynamics simulations.

Jean Wolff, *Shigeyuki Komura, and David Andelman,
Budding transition of asymmetric two-component lipid domains,
Physical Review E 94, 032406/1-8 (2016).

[Summary] We propose a model that accounts for the budding transition of asymmetric two-component lipid domains, where the two monolayers (leaflets) have different average compositions controlled by independent chemical potentials. Within a mean-field treatment, we obtain various phase diagrams containing fully budded, dimpled, and flat states as a function of the two leaflet compositions. The global phase behavior is analyzed, and depending on system parameters, the phase diagrams include one-phase, two-phase, and three-phase regions.

*Hiroshi Noguchi,
Construction of nuclear envelope shape by a high-genus vesicle with pore-size constraint,
Biophysical Journal 111, 824-831 (2016).

[Summary] Nuclear pores have an approximately uniform distribution in the nuclear envelope of most living cells. Hence, the morphology of the nuclear envelope is a spherical stomatocyte with a high genus. We have investigated the morphology of high-genus vesicles under pore-size constraint using dynamically triangulated membrane simulations. Bending-energy minimization without volume or other constraints produces a circular-cage stomatocyte, where the pores are aligned in a circular line on an oblate bud. As the pore radius is reduced, the circular-pore alignment is more stabilized than a random pore distribution on a spherical bud. However, we have clarified the conditions for the formation of a spherical stomatocyte: a small perinuclear volume, osmotic pressure within nucleoplasm, and repulsion between the pores. When area-difference elasticity is taken into account, the formation of cylindrical or budded tubules from the stomatocyte and discoidal stomatocyte is found.

Kento Yasuda, *Shigeyuki Komura, and Ryuichi Okamoto,
Dynamics of a membrane interacting with an active wall,
Physical Review E 93, 052407/1-12 (2016).

[Summary] We discuss the dynamics of a membrane interacting hydrodynamically with an active wall that exerts random velocities on the ambient fluid. In the case of an active wall, the MSD grows linearly in time in the early stage, which is unusual for a membrane segment. This linear-growth region of the MSD is further extended when the active wall has a finite intrinsic time scale.

*Ryuichi Okamoto, Naofumi Shimokawa, and Shigeyuki Komura,
Nano-domain formation in charged membranes: Beyond the Debye-Huckel approximation,
EPL 114, 28002/1-6 (2016).

[Summary] We investigate the microphase separation in a membrane composed of charged lipids, by taking into account explicitly the electrostatic potential and the ion densities in the　surrounding solvent. The static structure factor in the homogeneous state is analytically obtained without using the Debye-Huckel approximation and is found to have a peak at an intermediate wave number. For a binary membrane composed of anionic and neutral lipids, the characteristic wave number corresponds to a scale from several to tens of nanometers.

*Hiroshi Noguchi,
Shape deformation of lipid membranes by banana-shaped protein rods: Comparison with isotropic inclusions and membrane rupture,
Physical Review E 93, 052404/1-10 (2016).

[Summary] The assembly of curved protein rods on fluid membranes is studied using implicit-solvent meshless membranesimulations. As the rod curvature increases, the rods on a membrane tube assemble along the azimuthal directionfirst and subsequently along the longitudinal direction. Here, we showthat both transition curvatures decreasewithincreasing rod stiffness. For comparison, curvature-inducing isotropic inclusions are also simulated. When theisotropic inclusions have the same bending rigidity as the other membrane regions, the inclusions are uniformlydistributed on the membrane tubes and vesicles even for large spontaneous curvature of the inclusions. However,the isotropic inclusions with much larger bending rigidity induce shape deformation and are concentrated on theregion of a preferred curvature. For high rod density, high rod stiffness, and/or low line tension of the membraneedge, the rod assembly induces vesicle rupture, resulting in the formation of a high-genus vesicle. A gradualchange in the curvature suppresses this rupture. Hence, large stress, compared to the edge tension, induced bythe rod assembly is the key factor determining rupture. For rod curvature with the opposite sign to the vesiclecurvature, membrane rupture induces inversion of the membrane, leading to division into multiple vesicles aswell as formation of a high-genus vesicle.

*Ryuichi Okamoto, Yuichi Kanemori, Shigeyuki Komura, and Jean-Baptiste Fournier,
Relaxation dynamics of two-component fluid bilayer membranes,
The European Physical Journal E 39, 52/1-21 (2016).

[Summary] We theoretically investigate the relaxation dynamics of a nearly flat binary lipid bilayer membrane by taking into account the membrane tension, hydrodynamics of the surrounding fluid, inter-monolayer friction and mutual diffusion. We find that two relaxation modes associated with the mutual diffusion appear in addition to the three previously discussed relaxation modes reflecting the bending and compression of the membrane.

*Naofumi Shimokawa, Hiroki Himeno, Tsutomu Hamada, Masahiro Takagi, Shigeyuki Komura, and David Andelman,
Phase diagrams and ordering in charged membranes: Binary mixtures of charged and neutral lipids,
The Journal of Physical Chemistry B 120, 6358-6367 (2016).

[Summary] We propose a model describing the phase behavior of two-component membranes consisting of binary mixtures of electrically charged and neutral lipids. We distinguish between two types of charged membranes: mixtures of charged saturated lipid/neutral unsaturated lipid and a second case of mixtures of neutral saturated lipid/charged unsaturated lipid. The corresponding phase behavior is calculated and shown to be very different.

*Hiroshi Noguchi,
Membrane tubule formation by banana-shaped proteins with or without transient network structure,
Scientific Reports 6, 20935 (2016).

[Summary] In living cells, membrane morphology is regulated by various proteins. Many membrane reshaping proteins contain a Bin/Amphiphysin/Rvs (BAR) domain, which consists of a banana-shaped rod. The BAR domain bends the biomembrane along the rod axis and the features of this anisotropic bending have recently been studied. Here, we report on the role of the BAR protein rods in inducing membrane tubulation, using large-scale coarse-grained simulations. We reveal that a small spontaneous sidecurvature perpendicular to the rod can drastically alter the tubulation dynamics at high protein density, whereas no significant difference is obtained at low density. A percolated network is intermediately formed depending on the side curvature. This network suppresses tubule protrusion, leading to the slow formation of fewer tubules. Thus, the side curvature, which is generated by protein–protein andmembrane–protein interactions, plays a significant role in tubulation dynamics. We also find that positive surface tensions and the vesicle membrane curvature can stabilize this network structure by suppressing the tubulation.

Hayato Shiba, Hiroshi Noguchi, and *Jean-Baptiste Fournier,
Monte Carlo study of the frame, fluctuation and internal tensions of fluctuating membranes with fixed area,
Soft Matter 12, 2373-2380 (2016).

[Summary] Three types of surface tensions can be defined for lipid membranes: the internal tension, σ, conjugated to the real membrane area in the Hamiltonian, the mechanical frame tension, τ, con- jugated to the projected area, and the “fluctuation tension”, r, obtained from the fluctuation spec- trum of the membrane height. We investigate these surface tensions by means of a Monge gauge lattice Monte Carlo simulation involving the exact, nonlinear, Helfrich Hamiltonian and a measure correction for excess entropy of the Monge gauge. Our results for the relation between σ and τ agrees well with the theoretical prediction of [J.-B. Fournier and C. Barbetta, Phys. Rev. Lett., 2008, 100, 078103] based on a Gaussian approximation. This provides a valuable knowledge of τ in the standard Gaussian models where the tension is controlled by σ. However, contrary to the conjecture in the above paper, we find that r exhibits no significant difference from τ over more than five decades of tension. Our results appear to be valid in the thermodynamic limit and are robust to changing the ensemble in which the membrane area is controlled.

*Hiroshi Noguchi,
Shape transitions of high-genus fluid vesicles,
EPL 112, 58004/1-6 (2015).

[Summary] The morphologies of genus-2 to -8 fluid vesicles are studied by using dynamically triangulated membrane simulations with area-difference elasticity. It is revealed that the alignments of the membrane pores alter the vesicle shapes and the types of shape transitions for the genus-3 or higher genus. At a high reduced volume, a stomatocyte with a circular alignment of g + 1 pores continuously transforms into a discocyte with a line of g pores with increasing intrinsic area difference. In contrast, at a low volume, a stomatocyte transforms into a (g+1)-hedral shape and subsequently exhibits a discrete phase transition to a discocyte.

Takuma Hoshino, Shigeyuki Komura, and David Andelman,
Correlated lateral phase separations in stacks of lipid membranes,
Journal of Chemical Physics 143, 243124/1-9 (2015).

[Summary] Motivated by the experimental study of Tayebi et al. [Nature Mater. 11, 1074 (2012)] on phase separation of stacked multi-component lipid bilayers, we propose a model composed of stacked two-dimensional Ising spins. We study both its static and dynamical features using Monte Carlo simulations with Kawasaki spin exchange dynamics that conserves the order parameter. We show that at thermodynamical equilibrium, due to strong inter-layer correlations, the system forms a continuous columnar structure for any finite interaction across adjacent layers. Furthermore, the phase separation shows a faster dynamics as the inter-layer interaction is increased. This temporal behavior is mainly due to an effective deeper temperature quench because of the larger value of the critical temperature, Tc, for larger inter-layer interaction. When the temperature ratio, T/Tc, is kept fixed, the temporal growth exponent does not increase and even slightly decreases as function of the increased inter-layer interaction.

*Shigeyuki Komura, Kento Yasuda, and Ryuichi Okamoto,
Dynamics of two-component membranes surrounded by viscoelastic media,
Journal of Physics: Condensed Matter 27, 432001/1-7 (2015).

[Summary] We discuss the dynamics of two-component fluid membranes which are surrounded by viscoelastic media. We assume that membrane-embedded proteins can diffuse laterally and induce a local membrane curvature. The mean squared displacement of a tagged membrane segment is obtained as a generalized Einstein relation. When the elasticity of the surrounding media obeys a power-law behavior in frequency, an anomalous diffusion of the membrane segment is predicted. We also consider the situation where the proteins generate active non-equilibrium forces. The generalized Einstein relation is further modified by an effective temperature that depends on the force dipole energy. The obtained generalized Einstein relations are useful for membrane microrheology experiments.

*Hiroshi Noguchi,
Formation of polyhedral vesicles and polygonal membrane tubes induced by banana-shaped proteins,
Journal of Chemical Physics 143, 243109/1-7 (2015).

[Summary] The shape transformations of fluid membranes induced by curved protein rods are studied using meshless membrane simulations. The rod assembly at low rod density induces a flat membrane tube and oblate vesicle. It is found that the polyhedral shapes are stabilized at high rod densities.The discrete shape transition between triangular and buckled discoidal tubes is obtained and their curvature energies are analyzed by a simple geometric model. For vesicles, triangular hosohedron and elliptic-disk shapes are formed in equilibrium, whereas tetrahedral and triangular prism shapes are obtained as metastable states.

Koh M. Nakagawa and *Hiroshi Noguchi,
Morphological changes of amphiphilic molecular assemblies induced by chemical reactions,
Soft Matter 11, 1403-1411 (2015).

[Summary] Shape transformations of amphiphilic molecular assemblies induced by chemical reactions are studied using coarse-grained molecular simulations. A binding reaction between hydrophilic and hydrophobic molecules is considered. It is found that the reaction induces transformation of an oil droplet to a tubular vesicle via bicelles and vesicles with discoidal arms. The discoidal arms close into vesicles, which are subsequently fused into the tubular vesicle. Under the chemical reaction, the bicelle-to-vesicle transition occurs at smaller sizes than in the absence of the hydrophobic molecules. It is revealed that the enhancement of this transition is due to embedded hydrophobic particles that reduce the membrane bending rigidity.

Jean Wolff, *Shigeyuki Komura, and David Andelman,
Budding of domains in mixed bilayer membranes,
Physical Review E 91, 012708/1-10 (2015).

[Summary] We propose a model that accounts for the budding behavior of domains in lipid bilayers, where each of the bilayer leaflets has a coupling between its local curvature and the local lipid composition. The compositional asymmetry between the two monolayers leads to an overall spontaneous curvature. The membrane free energy contains three contributions: the bending energy, the line tension, and a Landau free energy for a lateral phase separation.Within amean-field treatment, we obtain various phase diagrams which contain fully budded, dimpled, and flat states. In particular, for some range of membrane parameters, the phase diagrams exhibit a tricritical behavior as well as a three-phase coexistence region. The global phase diagrams can be divided into three types and are analyzed in terms of the curvature-composition coupling parameter and domain size.

*Hiroshi Noguchi, Ai Sakashita, and Masayuki Imai,
Shape transformations of toroidal vesicles,
Soft Matter 11, 193-201 (2015).

[Summary] Morphologies of genus-1 and 2 toroidal vesicles are studied numerically by dynamically triangulated membrane models and experimentally by confocal laser microscopy. Our simulation results reproduce shape transformations observed in our experiments well. At large reduced volumes of the genus-1vesicles, obtained vesicle shapes agree with the previous theoretical prediction, in which axisymmetric shapes are assumed: double-necked stomatocyte, discoidal toroid, and circular toroid. However, for small reduced volumes, it is revealed that a non-axisymmetric discoidal toroid and handled discocyte exist in thermal equilibrium in the parameter range, in which the previous theory predicts axisymmetric discoidal shapes. Polygonal toroidal vesicles and subsequent budding transitions are also found. The entropy caused by shape fluctuations slightly modifies the stability of the vesicle shapes.

*Hiroshi Noguchi,
Two- or three-step assembly of banana-shaped proteins coupled with shape transformation of lipid membranes,
EPL 108, 48001/1-6 (2014).

[Summary] BAR superfamily proteins have a banana-shaped domain that causes the local bending of lipid membranes. We study as to how such a local anisotropic curvature induces effectiveinteraction between proteins and changes the global shape of vesicles and membrane tubes using meshless membrane simulations. Our study reveals that the rods assemble via two continuous directional phase separations unlike a conventional two-dimensional phase separation. As the rod curvature increases, in the membrane tube the rods assemble along the azimuthal direction and subsequently along the longitudinal direction accompanied by shape transformation of the tube. In the vesicle, in addition to these two assembly processes, further increase in the rod curvature induces tubular scaffold formation.

Hiroki Himeno, Naofumi Shimokawa, Shigeyuki Komura, David Andelman, *Tsutomu Hamada, and Masahiro Takagi,
Charge-induced phase separation in lipid membranes,
Soft Matter 10, 7959-7967 (2014).

[Summary] Phase separation in lipid bilayers that include negatively charged lipids is examined experimentally. We observed phase-separated structures and determined the membrane miscibility temperatures in several binary and ternary lipid mixtures of unsaturated neutral lipid, dioleoylphosphatidylcholine (DOPC), saturated neutral lipid, dipalmitoylphosphatidylcholine (DPPC), unsaturated charged lipid, dioleoylphosphatidylglycerol (DOPG(−)), saturated charged lipid, dipalmitoylphosphatidylglycerol (DPPG(−)), and cholesterol. In binary mixtures of saturated and unsaturated charged lipids, the combination of the charged head with the saturation of the hydrocarbon tail is a dominant factor in the stability of membrane phase separation. DPPG(−) enhances phase separation, while DOPG(−) suppresses it. Furthermore, the addition of DPPG(−) to a binary mixture of DPPC/cholesterol induces phase separation between DPPG(−)-rich and cholesterol-rich phases. This indicates that cholesterol localization depends strongly on the electric charge on the hydrophilic head group rather than on the ordering of the hydrocarbon tails. Finally, when DPPG(−) was added to a neutral ternary system of DOPC/DPPC/cholesterol (a conventional model of membrane rafts), a three-phase coexistence was produced. We conclude by discussing some qualitative features of the phase behaviour in charged membranes using a free energy approach.

*Shuji Fujii, Shigeyuki Komura, and Chun-Yi David Lu,
Structural rheology of the smectic phase,
Materials 7, 5146-5168 (2014).

[Summary] In this review article, we discuss the rheological properties of the thermotropic smectic liquid crystal 8CB with focal conic domains (FCDs) from the viewpoint of structural rheology. It is known that the unbinding of the dislocation loops in the smectic phase drives the smectic-nematic transition. Here we discuss how the unbinding of the dislocation loops affects the evolution of the FCD size, linear and nonlinear rheological behaviors of the smectic phase. By studying the FCD formation from the perpendicularly oriented smectic layers, we also argue that dislocations play a key role in the structural development in layered systems. Furthermore, similarities in the rheological behavior between the FCDs in the smectic phase and the onion structures in the lyotropic lamellar phase suggest that these systems share a common physical origin for the elasticity.

*Shigeyuki Komura and David Andelman,
Physical aspects of heterogeneities in multi-component lipid membranes,
Advances in Colloid and Interface Science 208, 34-46 (2014).

[Summary] Ever since the raft model for biomembranes has been proposed, the traditional view of biomembranes based on the fluid-mosaic model has been altered. In the raft model, dynamical heterogeneities in multi-component lipid bilayers play an essential role. Focusing on the lateral phase separation of biomembranes and vesicles, we review some of the most relevant research conducted over the last decade. We mainly refer to those experimental works that are based on physical chemistry approach, and to theoretical explanations given in terms of soft matter physics. In the first part, we describe the phase behavior and the conformation of multi-component lipid bilayers. After formulating the hydrodynamics of fluid membranes in the presence of the surrounding solvent, we discuss the domain growth-law and decay rate of concentration fluctuations. Finally, we review several attempts to describe membrane rafts as two-dimensional microemulsion.

*Shuji Fujii, Shigeyuki Komura, and C.-Y. David Lu,
Structural rheology of focal conic domains: a stress-quench experiment,
Soft Matter 10, 5289-5295 (2014).

[Summary] We study the dynamics of focal conic domain (FCD) formation in a thermotropic smectic phase under shear stress. It is known that increasing the shear stress induces a non-equilibrium phase transition from a smectic phase with FCDs (SmAI) to another smectic phase (SmAII) in which the layers are oriented. By quenching the shear stress from the SmAII phase to the SmAI phase, we find three characteristic modes in the FCD formation process. The first mode is attributed to the edge dislocation dynamics induced by climb motions. The second mode results from FCD formation. The first and second modes show slowing down close to the smectic–nematic transition temperature, implying that the dynamics are dominated by dislocation unbinding. The third mode originates from the alignment of FCDs which form oily streaks. Such an alignment occurs when the shear stress balances the line tension of the oily streaks.

Ai Sakashita, Masayuki Imai, and *Hiroshi Noguchi,
Morphological variation of lipid vesicle confined in spherical vesicle,
Physical Review E 89, 040701(R)/1-4 (2014).

[Summary] Morphologies of a double-bilayer vesicle were explored experimentally by fast confocal laser microscopy and numerically by a dynamically triangulated membrane model with area-difference elasticity. The confinement was found to induce several shapes of the inner vesicles that had not been observed in unilamellar vesicles: double and quadruple stomatocytes, slit vesicle, and vesicles of two or three compartments with various shapes. The simulations reproduced the experimental results very well and some of the shape transitions can be understood by a simple theoretical model for axisymmetric shapes.

*Kazuhiko Seki, Saurabh Mogre, and Shigeyuki Komura,
Diffusion coefficients in leaflets of bilayer membranes,
Physical Review E 89, 022713/1-12 (2014).

[Summary] We study diffusion coefficients of liquid domains by explicitly taking into account the two-layered structure called leaflets of the bilayer membrane. In general, the velocity fields associated with each leaflet are different and the layers sliding past each other cause frictional coupling. We obtain analytical results of diffusion coefficients for a circular liquid domain in a leaflet, and quantitatively study their dependence on the inter-leaflet friction. We also show that the diffusion coefficients diverge in the absence of coupling between the bilayer and solvents, even when the inter-leaflet friction is taken into account. In order to corroborate our theory, the effect of the inter-leaflet friction on the correlated diffusion is examined.

*Hayato Shiba and Takeshi Kawasaki,
Spatiotemporal heterogeneity of local free volumes in highly supercooled liquid,
The Journal of Chemical Physics 139, 184502/1-8 (2013).

[Summary] We discussed the spatiotemporal behavior of local density and its relation to dynamical heterogeneity in a highly supercooled liquid by using molecular dynamics simulations of a binary mixture with different particle sizes in two dimensions. To trace voids heterogeneously existing with lower local densities, which move along with the structural relaxation, we employ the minimum local density for each particle in a time window whose width is set along with the structural relaxation time. Particles subject to free volumes correspond well to the configuration rearranging region of dynamical heterogeneity. While the correlation length for dynamical heterogeneity grows with temperature decrease, no growth in the correlation length of heterogeneity in the minimum local density distribution takes place. A comparison of these results with those of normal mode analysis reveals that superpositions of lower-frequency soft modes extending over the free volumes exhibit sp!atial correlation with the broken bonds. This observation suggests a possibility that long-ranged vibration modes facilitate the interactions between fragile regions represented by free volumes, to induce dynamical correlations at a large scale.

*Ryuichi Okamoto, Youhei Fujitani, and Shigeyuki Komura,
Drag coefficient of a rigid spherical particle in a near-critical binary fluid mixture,
Journal of the Physical Society of Japan 82, 084003/1-10 (2013).

[Summary] We calculate the drag coefficient of a rigid spherical particle in an incompressible binary fluid mixture. A weakpreferential attraction is assumed between the particle surface and one of the fluid components, and the difference in the viscosity between the two components is neglected. Using the Gaussian free-energy functional and solving the hydrodynamic equation explicitly, we can show that the preferential attraction makes the drag coefficient larger as the bulk correlation length becomes longer. The dependence of the deviation from the Stokes law on the correlation length, when it is short, turns out to be much steeper than the previous estimates.