Universality in the Dynamics of Vesicle Translocation through a Hole.

We analyze the translocation process of a spherical vesicle, made of a membrane and incompressible fluid, through a hole smaller than the vesicle size, driven by pressure difference ΔP. We show that such a vesicle shows certain universal characteristics, which are independent of the details of the membrane elasticity: (i) there is a critical pressure ΔPc below which no translocation occurs; (ii) ΔPc decreases to zero as the vesicle radius R0 approaches the hole radius a, satisfying the scaling relation ΔPc ∼ (R0 - a)3/2; and (iii) the translocation time τ diverges as ΔP decreases to ΔPc, satisfying the scaling relation τ ∼ (ΔP - ΔPc)-1/2.

Pair dynamics of active force dipoles in an odd-viscous fluid.

We discuss the lateral dynamics of two active force dipoles, which interact with each other via hydrodynamic interactions in a thin fluid layer that is active and chiral. The fluid layer is modeled as a two-dimensional (2D) compressible fluid with an odd viscosity, while the force dipole (representing an active protein or enzyme) induces a dipolar flow. Taking into account the momentum decay in the 2D fluid, we obtain analytically the mobility tensor that depends on the odd viscosity and includes nonreciprocal hydrodynamic interactions. We find that the particle pair shows spiral behavior due to the transverse flow induced by the odd viscosity. When the magnitude of the odd viscosity is large as compared with the shear viscosity, two types of oscillatory behaviors are seen. One of them can be understood as arising from closed orbits in dynamical systems, and its circular trajectories are determined by the ratio between the magnitude of the odd viscosity and the force dipole. In addition, the phase diagrams of the particle dipolar angles are obtained numerically. Our findings reveal that the nonreciprocal response leads to complex dynamics of active particles embedded in an active fluid with odd viscosity.

Time-correlation functions for odd Langevin systems.

We investigate the statistical properties of fluctuations in active systems that are governed by nonsymmetric responses. Both an underdamped Langevin system with an odd resistance tensor and an overdamped Langevin system with an odd elastic tensor are studied. For a system in thermal equilibrium, the time-correlation functions should satisfy time-reversal symmetry and the antisymmetric parts of the correlation functions should vanish. For the odd Langevin systems, however, we find that the antisymmetric parts of the time-correlation functions can exist and that they are proportional to either the odd resistance coefficient or the odd elastic constant. This means that the time-reversal invariance of the correlation functions is broken due to the presence of odd responses in active systems. Using the short-time asymptotic expressions of the time-correlation functions, one can estimate an odd elastic constant of an active material such as an enzyme or a motor protein.

Mechanochemical enzymes and protein machines as hydrodynamic force dipoles: the active dimer model.

Mechanochemically active enzymes change their shapes within every turnover cycle. Therefore, they induce circulating flows in the solvent around them and behave as oscillating hydrodynamic force dipoles. Because of non-equilibrium fluctuating flows collectively generated by the enzymes, mixing in the solution and diffusion of passive particles within it are expected to get enhanced. Here, we investigate the intensity and statistical properties of such force dipoles in the minimal active dimer model of a mechanochemical enzyme. In the framework of this model, novel estimates for hydrodynamic collective effects in solution and in lipid bilayers under rapid rotational diffusion are derived, and available experimental and computational data is examined.

Dynamics of passive and active membrane tubes.

Utilising Onsager's variational formulation, we derive dynamical equations for the relaxation of a fluid membrane tube in the limit of small deformation, allowing for a contrast of solvent viscosity across the membrane and variations in surface tension due to membrane incompressibility. We compute the relaxation rates, recovering known results in the case of purely axis-symmetric perturbations and making new predictions for higher order (azimuthal) m-modes. We analyse the long and short wavelength limits of these modes by making use of various asymptotic arguments. We incorporate stochastic terms to our dynamical equations suitable to describe both passive thermal forces and non-equilibrium active forces. We derive expressions for the fluctuation amplitudes, an effective temperature associated with active fluctuations, and the power spectral density for both the thermal and active fluctuations. We discuss an experimental assay that might enable measurement of these fluctuations to infer the properties of the active noise. Finally we discuss our results in the context of active membranes more generally and give an overview of some open questions in the field.

Kosmotropic effect leads to LCST decrease in thermoresponsive polymer solutions.

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 theory has been employed. The polymer-solvent LCST behavior in the theoretical models has 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 the addition of cosolvent. It is shown that this effect of cosolvent is weaker with an increase in polymer hydrophilicity which can explain the absence of a LCST decrease in poly(N,N-diethylacrylamide), 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.

Relaxation dynamics of two-component fluid bilayer membranes.

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. Mutual diffusion is the collective irreversible process that leads to homogenization of the density difference between the two lipid species. 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. Because of the symmetry, only one of the two diffusive modes is coupled to the bending mode. The two diffusive modes are much slower than the bending and compression modes in the entire realistic wave number range. This means that the long time relaxation behavior is dominated by the mutual diffusion in binary membranes. The two diffusive modes become even slower in the vicinity of the unstable region towards phase separation, while the other modes are almost unchanged. In short time scales, on the other hand, the lipid composition heterogeneity induces in-plane compression and bending of the bilayer.

Correlated lateral phase separations in stacks of lipid membranes.

Motivated by the experimental study of Tayebi et al. [Nat. 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 a function of the increased inter-layer interaction.

Structural rheology of focal conic domains: a stress-quench experiment.

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.

Charge-induced phase separation in lipid membranes.

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.

Odd Response-Induced Phase Separation of Active Spinners.

Due to the breaking of time-reversal and parity symmetries and the presence of non-conservative microscopic interactions, active spinner fluids and solids respectively exhibit nondissipative odd viscosity and nonstorage odd elasticity, engendering phenomena unattainable in traditional passive or active systems. Here, we study the effects of odd viscosity and elasticity on phase behaviors of active spinner systems. We find the spinner fluid under a simple shear experiences an anisotropic gas-liquid phase separation driven by the odd-viscosity stress. This phase separation exhibits equilibrium-like behavior, with both binodal-like and spinodal curves and critical point. However, the formed dense liquid phase is unstable, since the odd elasticity instantly takes over the odd viscosity to condense the liquid into a solid-like phase. The unusual phase behavior essentially arises from the competition between thermal fluctuations and the odd response-induced effective attraction. Our results demonstrate that the cooperation of odd viscosity and elasticity can lead to exotic phase behavior, revealing their fundamental roles in phase transition.

Nonreciprocality of a micromachine driven by a catalytic chemical reaction.

We propose a model that describes cyclic state transitions of a micromachine driven by a catalytic chemical reaction. We consider a mechanochemical coupling of variables representing the degree of a chemical reaction and the internal state of a micromachine. The total free energy consists of a tilted periodic potential and a mechanochemical coupling energy. We assume that the reaction variable obeys a deterministic stepwise dynamics characterized by two typical timescales, i.e., the mean first passage time and the mean first transition path time. To estimate the functionality of a micromachine, we focus on the quantity called "nonreciprocality" and further discuss its dependence on the properties of catalytic reaction. For example, we show that the nonreciprocality is proportional to the square of the mean first transition path time. The explicit calculation of the two timescales within the decoupling approximation model reveals that the nonreciprocality is inversely proportional to the square of the energy barrier of catalytic reaction.

Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity.

We discuss hydrodynamic forces acting on a two-dimensional liquid domain that moves laterally within a supported fluid membrane in the presence of odd viscosity. Since active rotating proteins can accumulate inside the domain, we focus on the difference in odd viscosity between the inside and outside of the domain. Taking into account the momentum leakage from a two-dimensional incompressible fluid to the underlying substrate, we analytically obtain the fluid flow induced by the lateral domain motion and calculate the drag and lift forces acting on the moving liquid domain. In contrast to the passive case without odd viscosity, the lateral lift arises in the active case only when the in and out odd viscosities are different. The in-out contrast in the odd viscosity leads to nonreciprocal hydrodynamic responses of an active liquid domain.

Brownian motion of a charged colloid in restricted confinement.

We study the Brownian motion of a charged colloid, confined between two charged walls, for small separation between the colloid and the walls. The system is embedded in an ionic solution. The combined effect of electrostatic repulsion and reduced diffusion due to hydrodynamic forces results in a specific motion in the direction perpendicular to the confining walls. The apparent diffusion coefficient at short times as well as the diffusion characteristic time are shown to follow a sigmoid curve as a function of a dimensionless parameter. This parameter depends on the electrostatic properties and can be controlled by tuning the solution ionic strength. At low ionic strength, the colloid moves faster and is localized, while at high ionic strength it moves slower and explores a wider region between the walls, resulting in a larger diffusion characteristic time.

Nonreciprocal response of a two-dimensional fluid with odd viscosity.

We discuss the linear hydrodynamic response of a two-dimensional active chiral compressible fluid with odd viscosity. The viscosity coefficient represents broken time-reversal and parity symmetries in the 2D fluid and characterizes the deviation of the system from a passive fluid. Taking into account the hydrodynamic coupling to the underlying bulk fluid, we obtain the odd viscosity-dependent mobility tensor, which is responsible for the nonreciprocal hydrodynamic response to a point force. Furthermore, we consider a finite-size disk moving laterally in the 2D fluid and demonstrate that the disk experiences a nondissipative lift force in addition to the dissipative drag one.

Shear viscosity of two-state enzyme solutions.

We discuss the shear viscosity of a Newtonian solution of catalytic enzymes and substrate molecules. The enzyme is modeled as a two-state dimer consisting of two spherical domains connected with an elastic spring. The enzymatic conformational dynamics is induced by the substrate binding and such a process is represented by an additional elastic spring. Employing the Boltzmann distribution weighted by the waiting times of enzymatic species in each catalytic cycle, we obtain the shear viscosity of dilute enzyme solutions as a function of substrate concentration and its physical properties. The substrate affinity distinguishes between fast and slow enzymes, and the corresponding viscosity expressions are obtained. Furthermore, we connect the obtained viscosity with the diffusion coefficient of a tracer particle in enzyme solutions.

Dynamics of a membrane coupled to an active fluid.

The dynamics of a membrane coupled to an active fluid on top of a substrate is considered theoretically. It is assumed that the director field of the active fluid has rotational symmetry in the membrane plane. This situation is likely to be relevant for in vitro reconstructed actomyosin-membrane system. Different from a membrane coupled to a polar active fluid, this model predicts that only when the viscosity of the fluid above the membrane is sufficiently large, a contractile active fluid is able to slow down the relaxation of the membrane for perturbations with wavelength comparable to the thickness of the active fluid. Hence, our model predicts a finite-wavelength instability in the limit of strong contractility, which is different from a membrane coupled to a polar active fluid. However, a membrane coupled to an extensile active fluid is always unstable against long-wavelength perturbations due to active extensile stress enhanced membrane undulation.

Coupled modulated bilayers: a phenomenological model.

We propose a model addressing the coupling mechanism between two spatially modulated monolayers. We obtain the mean-field phase diagrams of coupled bilayers when the two monolayers have the same preferred modulation wavelength. Various combinations of the monolayer modulated phases are obtained and their relative stability is calculated. Due to the coupling, a spatial modulation in one of the monolayers induces a similar periodic structure in the second one. We have also performed numerical simulations for the case when the two monolayers have different modulation wavelengths. Complex patterns may arise from the frustration between the two incommensurate but annealed structures.

Nonequilibrium probability flux of a thermally driven micromachine.

We discuss the nonequilibrium statistical mechanics of a thermally driven micromachine consisting of three spheres and two harmonic springs [Y. Hosaka et al., J. Phys. Soc. Jpn. 86, 113801 (2017)JUPSAU0031-901510.7566/JPSJ.86.113801]. We obtain the nonequilibrium steady state probability distribution function of such a micromachine and calculate its probability flux in the corresponding configuration space. The resulting probability flux can be expressed in terms of a frequency matrix that is used to distinguish between a nonequilibrium steady state and a thermal equilibrium state satisfying detailed balance. The frequency matrix is shown to be proportional to the temperature difference between the spheres. We obtain a linear relation between the eigenvalue of the frequency matrix and the average velocity of a thermally driven micromachine that can undergo a directed motion in a viscous fluid. This relation is consistent with the scallop theorem for a deterministic three-sphere microswimmer.

Pattern formation of skin cancers: Effects of cancer proliferation and hydrodynamic interactions.

We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional model H for macrophase separations by considering a logistic growth of cancer cells and also a mechanical friction between dermis and epidermis. Importantly, our model exhibits a microphase separation due to the proliferation of cancer cells. By numerically solving the time evolution equations of the cancer composition and its velocity, we show that the phase separation kinetics strongly depends on the cell proliferation rate as well as on the strength of hydrodynamic interactions. A steady-state diagram of cancer patterns is established in terms of these two dynamical parameters and some of the patterns correspond to clinically observed cancer patterns. Furthermore, we examine in detail the time evolution of the average composition of cancer cells and the characteristic length of the microstructures. Our results demonstrate that different sequence of cancer patterns can be obtained by changing the proliferation rate and/or hydrodynamic interactions.