arXiv subjects

Hiroshi Noguchi

Publications and source records attributed to Hiroshi Noguchi.

At least 19 recordsLinked to original sources

arXiv2026

Blinking membrane patterns induced by protein binding/unbinding

Nonequilibrium membrane pattern formation is studied using meshless membrane simulation. Bound proteins are considered to have two states that generate different membrane spontaneous curvatures. Protein binding and unbinding occur cyclically owing to chemical potential differences, as an off-lattice active Potts model. It is found that this cyclic binding/unbinding can induce blinking domains, with oscillating size: convex domains of the proteins with a higher spontaneous curvature grow, and subsequently, the proteins change to the other state with a lower spontaneous curvature, resulting in domain shrinkage. These processes repeat. In thermal equilibrium, hexagonal convex domains are formed by the competition between bending and surface tension energies, so that they are stably formed only under positive surface tension. However, blinking domains can form even in tensionless membranes.

cond-mat.soft↗

arXiv2026

Spiral, target, stripe, and disordered waves in active six-state Potts models

Wave propagation can be observed in various nonequilibrium systems. In this study, we investigated the properties of several wave modes in active six-state Potts models using Monte Carlo simulations of square and hexagonal lattices. Disordered and spiral (SP) waves of six states are formed under weak and strong repulsions at nonflip contacts, respectively. The target (TG) and stripe (ST) waves were found to emerge under stronger repulsion. These three wave modes (SP, TG, and ST) can temporally coexist in small systems near the transition points but they do not switch in large systems or far from these transition points. During coarsening from randomly mixed states to ST waves, SP waves appear at an intermediate stage. The SP wave modes of three even- or odd-numbered states (states $s=0,2,4$ or $s=1,3,5$) emerge under two conditions: repulsion at the diagonal contact and attraction at nonflip contacts. Previously thought to be identical for both conditions, the wave types were found to differ, comprising forward and backward waves ($s=1\to 3\to 5\to 1$ or $s=1\to 5\to 3\to 1$), whose domain boundaries move by the two-step and four-step forward flips, respectively. The transition between the waves of the even- and odd-numbered states is first-order for both the forward and backward waves.

cond-mat.stat-mech↗

arXiv2026

Coarsening dynamics for spiral and disordered waves in active Potts models

This study examines the domain-growth dynamics of $q$-state active Potts models ($q=3$--$8$) under the cyclically symmetric conditions using Monte Carlo simulations on square and hexagonal lattices. By imposing active cyclic flipping of states, finite-length waves emerge in the long-term limit. This study focuses on coarsening dynamics from an initially random mixture of states to these moving-domain states. The correlation length and mean cluster size grow, following the Lifshitz--Allen--Cahn (LAC) law ($\propto t^{1/2}$) in the intermediate time range, and in the late range, saturation is observed at the characteristic wavelengths. It is found that the growth rate is raised prior to saturation, leading to a transient increase in the coarsening exponent. The coarsening dynamics to disordered waves exhibit greater transient increases than those to spiral waves. Moreover, the transient increase is greater at higher $q$. In factorized symmetry modes at $q=6$, domains composed of two or three states similarly follow the LAC law. Finally, this study confirms that the choice of lattice type (square or hexagonal) and update scheme (Metropolis or Glauber) does not alter the dynamic behavior.

cond-mat.stat-mech↗

arXiv2026

Dynamics due to competitive flip cycles in active Potts models

Nonequilibrium spatiotemporal patterns have been extensively studied. However, a single oscillator or cyclic loop of states is typically employed at each site in theories and simulations. Here, we investigate how competition among multiple identical cyclic loops at each site alters patterns. We simulate active Potts models with standard Potts interactions between neighboring sites in two-dimensional square lattices. When multiple three-state cycles exist in state flips, such as in octahedral and square-antiprism networks, all types of spiral waves comprising the three states are formed simultaneously at high flip energies. However, at lower energies, only one or a few types emerge and switch stochastically into different types. At even lower energies, cyclic changes in single-state dominant homogeneous phases emerge [homogeneous cycling (HC) mode]. At intermediate flip energies, the spiral wave and HC modes temporally coexist in small systems but do not switch between each other in large systems. Conversely, when multiple four-state cycles exist in six-state and cubic networks, one state remains dominant for the entire range of flip energies, whereas the other states occasionally form domains at intermediate flip energies. Therefore, the number of spatially coexisting states can be controlled using flip networks and energies.

nlin.PS↗

arXiv2025

Dynamic modes of active Potts models with factorizable numbers of states

We studied the long-term nonequilibrium dynamics of $q$-state Potts models with $q=4$, $5$, $6$, and $8$ using Monte Carlo simulations on a two-dimensional square lattice. When the contact energies between the nearest neighbors for the standard Potts models are used, cyclic changes in the $q$ homogeneous phases and $q$-state coexisting wave mode appear at low and high flipping energies, respectively, for all values of $q$. However, for a factorizable $q$ value, dynamic modes with skipping states emerge, depending on the contact energies. For $q=6$, a spiral wave mode with three domain types (one state dominant or two states mixed) and cyclic changes in three homogeneous phases are found. Although three states can coexist spatially under thermal equilibrium, the scaling exponents of the transitions to the wave modes are modified from the equilibrium values.

cond-mat.stat-mech↗

arXiv2025

Curvature-sensing and generation by membrane proteins: a review

Membrane proteins are crucial in regulating biomembrane shapes and controlling the dynamic changes in membrane morphology during essential cellular processes. These proteins can localize to regions with their preferred curvatures (curvature sensing) and induce localized membrane curvature. Thus, this review describes the recent theoretical development in membrane remodeling performed by membrane proteins. The mean-field theories of protein binding and the resulting membrane deformations are reviewed. The effects of hydrophobic insertions on the area-difference elasticity energy and that of intrinsically disordered protein domains on the membrane bending energy are discussed. For the crescent-shaped proteins, such as Bin/Amphiphysin/Rvs superfamily proteins, anisotropic protein bending energy and orientation-dependent excluded volume significantly contribute to curvature sensing and generation. Moreover, simulation studies of membrane deformations caused by protein binding are reviewed, including domain formation, budding, and tubulation.

cond-mat.soft↗

arXiv2025

Spatiotemporal pattern formation of membranes induced by surface molecular binding/unbinding

Nonequilibrium membrane pattern formation is studied using meshless membrane simulation. We consider that molecules bind to either surface of a bilayer membrane and move to the opposite leaflet by flip--flop. When binding does not modify the membrane properties and the transfer rates among the three states are cyclically symmetric, the membrane exhibits spiral-wave and homogeneous-cycling modes at high and low binding rates, respectively, as in an off-lattice cyclic Potts model. When binding changes the membrane spontaneous curvature, these spatiotemporal dynamics are coupled with microphase separation. When two symmetric membrane surfaces are in thermal equilibrium, the membrane domains form 4.8.8 tiling patterns in addition to stripe and spot patterns. In nonequilibrium conditions, moving biphasic domains and time-irreversible fluctuating patterns appear. The domains move ballistically or diffusively depending on the conditions.

cond-mat.soft↗

arXiv2024

Spatiotemporal Patterns in Active Four-State Potts Models

Many types of spatiotemporal patterns have been observed under nonequilibrium conditions. Cycling through four or more states can provide specific dynamics, such as the spatial coexistence of multiple phases. However, transient dynamics have only been studied by previous theoretical models, since absorbing transition into a uniform phase covered by a single state occurs in the long-time limit. Here, we reported steady long-term dynamics using cyclic Potts models, wherein nucleation and growth play essential roles. Under the cyclic symmetry of the four states, the cyclic changes in the dominant phases and the spatial coexistence of the four phases are obtained at low and high flipping energies, respectively. Under asymmetric conditions, the spatial coexistence of two diagonal phases appears in addition to non-cyclic one-phase modes. The circular domains of the diagonal state are formed by the nucleation of other states, and they slowly shrink to reduce the domain boundary. When three-state cycling is added, competition between the two cycling modes changes the spatiotemporal patterns.

cond-mat.stat-mech↗

arXiv2024

Growth and shrinkage of tissue sheets on substrates: buds, buckles, and pores

Many tissues take the form of thin sheets, being only a single cell thick, but millions of cells wide. These tissue sheets can bend and buckle in the third dimension. In this work, we investigated the growth and shrinkage of suspended and supported tissue sheets using particle-based simulations. We construct a minimum model, combining particle-based tissue growth and meshless membrane models, to simulate the growth of tissue sheets with mechanical feedback. Free suspended growing tissues exhibit wrinkling when growth is sufficiently fast. Conversely, tissues on a substrate form buds when the adhesion to the substrate is weak and/or when the friction with the substrate is strong. These buds undergo a membrane-mediated attraction and subsequently fuse. The complete detachment of tissues from the substrate and straight buckled bump formation are also obtained at very weak adhesion and/or fast growth rates. In the tissue shrinkage, tissue pores grow via Ostwald ripening and coalescence. The reported dynamics can also be applied in research on the detachment dynamics of different tissues with weakened adhesion.

physics.bio-ph↗

arXiv2024

Spatiotemporal patterns in the active cyclic Potts model

The nonequilibrium dynamics of a cycling three-state Potts model is studied on a square lattice using Monte Carlo simulations and continuum theory. This model is relevant to chemical reactions on a catalytic surface and to molecular transport across a membrane. Several characteristic modes are formed depending on the flipping energies between successive states and the contact energies between neighboring sites. Under cyclic symmetry conditions, cycling homogeneous phases and spiral waves form at low and high flipping energies, respectively. In the intermediate flipping energy regime, these two modes coexist temporally in small systems and/or at low contact energies. Under asymmetric conditions, we observed small biphasic domains exhibiting amoeba-like locomotion and temporal coexistence of spiral waves and a dominant non-cyclic one-state phase. An increase in the flipping energy between two successive states, say state 0 and state 1, while keeping the other flipping energies constant, induces the formation of the third phase (state 2), owing to the suppression of the nucleation of state 0 domains. Under asymmetric conditions regarding the contact energies, two different modes can appear depending on the initial state, due to a hysteresis phenomenon.

cond-mat.stat-mech↗

arXiv2024

Nonequilibrium Membrane Dynamics Induced by Active Protein Interactions and Chemical Reactions: A Review

Biomembranes wrapping cells and organelles are not only the partitions that separate the insides but also dynamic fields for biological functions accompanied by membrane shape changes. In this review, we discuss the spatiotemporal patterns and fluctuations of membranes under nonequilibrium conditions. In particular, we focus on theoretical analyses and simulations. Protein active forces enhance or suppress the membrane fluctuations; the membrane height spectra are deviated from the thermal spectra. Protein binding or unbinding to the membrane is activated or inhibited by other proteins and chemical reactions, such as ATP hydrolysis. Such active binding processes can induce traveling waves, Turing patterns, and membrane morphological changes. They can be represented by the continuum reaction-diffusion equations and discrete lattice/particle models with state flips. The effects of structural changes in amphiphilic molecules on the molecular-assembly structures are also discussed.

cond-mat.soft↗

arXiv2024

Cycling and spiral-wave modes in an active cyclic Potts model

We studied the nonequilibrium dynamics of a cycling three-state Potts model using simulations and theory. This model can be tuned from thermal-equilibrium to far-from-equilibrium conditions. At low cycling energy, the homogeneous dominant state cycles via nucleation and growth, while spiral waves are formed at high energy. For large systems, a discontinuous transition occurs from these cyclic homogeneous phases to spiral waves, while the opposite transition is absent. Conversely, these two modes can coexist for small systems. The waves can be reproduced by a continuum theory, and the transition can be understood from the competition between nucleation and growth.

cond-mat.stat-mech↗

arXiv2024

Curvature sensing of curvature-inducing proteins with internal structure

Many types of peripheral and transmembrane proteins can sense and generate membrane curvature. Laterally isotropic proteins and crescent proteins with twofold rotational symmetry, such as Bin/Amphiphysin/Rvs superfamily proteins, have been studied theoretically. However, proteins often have an asymmetric structure or a higher rotational symmetry. We theoretically studied the curvature sensing of proteins with asymmetric structures and structural deformations. First, we examined proteins consisting of two rod-like segments. When proteins have mirror symmetry, their sensing ability is similar to that of single-rod proteins; hence, with increasing protein density on a cylindrical membrane tube, a second- or first-order transition occurs at a middle or small tube radius, respectively. As asymmetry is introduced, this transition becomes a continuous change, and metastable states appear at high protein densities. Protein with threefold, fivefold, or higher rotational symmetry has laterally isotropic bending energy. However, when a structural deformation is allowed, the protein can have a preferred orientation and stronger curvature sensing.

cond-mat.soft↗

arXiv2023

Estimation of anisotropic bending rigidities and spontaneous curvatures of crescent curvature-inducing proteins from tethered-vesicle experimental data

The Bin/amphiphysin/Rvs (BAR) superfamily proteins have a crescent binding domain and bend biomembranes along the domain axis. However, their anisotropic bending rigidities and spontaneous curvatures have not been experimentally determined. Here, we estimated these values from the bound protein densities on tethered vesicles using a mean-field theory of anisotropic bending energy and orientation-dependent excluded volume. The dependence curves of the protein density on the membrane curvature are fitted to the experimental data for the I-BAR and N-BAR domains reported by C. Prevost et al. Nat. Commun. 6, 8529 (2015) and F.-C. Tsai et al. Soft Matter 17, 4254 (2021), respectively. For the I-BAR domain, all three density curves of different chemical potentials exhibit excellent fits with a single parameter set of anisotropic bending energy. When the classical isotropic bending energy is used instead, one of the curves can be fitted well, but the others exhibit large deviations. In contrast, for the N-BAR domain, two curves are not well-fitted simultaneously using the anisotropic model, although it is significantly improved compared to the isotropic model. This deviation likely suggests a cluster formation of the N-BAR domains.

cond-mat.soft↗

arXiv2023

Binding of Curvature-Inducing Proteins onto Biomembranes

We review the theoretical analyses and simulations of the interactions between curvature-inducing proteins and biomembranes. Laterally isotropic proteins induce spherical budding, whereas anisotropic proteins, such as Bin/Amphiphysin/Rvs (BAR) superfamily proteins, induce tabulation. Both types of proteins can sense the membrane curvature. We describe the theoretical analyses of various transitions of protein binding accompanied by a change in various properties, such as the number of buds, the radius of membrane tubes, and the nematic order of anisotropic proteins. Moreover, we explain the membrane-mediated interactions and protein assembly. Many types of membrane shape transformations (spontaneous tubulation, formation of polyhedral vesicles, polygonal tubes, periodic bumps, and network structures, etc.) have been demonstrated by coarse-grained simulations. Furthermore, traveling waves and Turing patterns under the coupling of reaction-diffusion dynamics and membrane deformation are described.

cond-mat.soft↗

arXiv2022

Membrane domain formation induced by binding/unbinding of curvature-inducing molecules onto both membrane surfaces

The domain formation of curvature-inducing molecules, such as peripheral or transmembrane proteins and conical surfactants, is studied in thermal equilibrium and nonequilibrium steady states using meshless membrane simulations. These molecules can bind onto both surfaces of a bilayer membrane and also move to the opposite leaflet by a flip-flop. In symmetric conditions for the two leaflets, the membrane domains form checkerboard patterns in addition to stripe and spot patterns. The unbound membrane stabilizes the vertices of the checkerboard. In asymmetric conditions, the domains form kagome-lattice and thread-like domains. In the nonequilibrium steady states, a flow of the binding molecules between the upper and lower solutions can occur via the flip-flop.

cond-mat.soft↗

arXiv2022

Conformation of ultra-long-chain fatty acid in lipid bilayer: Molecular dynamics study

Ultra-long-chain fatty acids (ULCFAs) are biosynthesized in the restricted tissues such as retina, testis, and skin. The conformation of a single ULCFA, in which the sn-1 unsaturated chain has 32 carbons, in three types of tensionless phospholipid bilayers is studied by molecular dynamics simulations. It is found that the ultra-long tail of the ULCFA flips between two leaflets and fluctuates among an elongation into the opposite leaflet, lying between two leaflets, and turning back. As the number ratio of lipids in the opposite leaflet increases, the ratio of the elongated shape linearly decreases in all three cases. Thus, ULCFAs can sense the density differences between the two leaflets and respond to these changes.

physics.bio-ph↗

arXiv2022

Excitable reaction-diffusion waves of curvature-inducing proteins on deformable membrane tubes

Living cells employ excitable reaction-diffusion waves for internal cellular functions, in which curvature-inducing proteins are often involved. However, the role of their mechanochemical coupling is not well understood. Here, we report the membrane deformation induced by the excitable reaction-diffusion waves of curvature-inducing proteins and the alternation in the waves due to the deformation, using a coarse-grained simulation of tubular membranes with a modified FitzHugh--Nagumo model. Protein-propagating waves deform tubular membranes, and large deformations induce budding and erase waves. The wave speed and shape are determined by a combination of membrane deformation and spatial distribution of the curvature-inducing protein. Waves are also undulated in the azimuthal direction depending on the condition. Rotationally symmetric waves locally deform the tubes into a symmetric shape but maintain a straight shape on average. Our simulation method can be applied to other chemical reaction models and used to investigate various biomembrane phenomena.

cond-mat.soft↗