PHYSICAL REVIEW E 99, 042418 (2019) Effect of particles with repulsive interactions enclosed in both rigid spherical shells and flexible fluid vesicles studied by Monte Carlo simulation Hibiki Itoga, 1 , * Ryota Morikawa, 1 , † Tsuyoshi Ueta, 2 Takeshi Miyakawa, 1 Yuno Natsume, 3 and Masako Takasu 1 1 Tokyo University of Pharmacy and Life Sciences, Tokyo 192-0392, Japan 2 Jikei University, Tokyo 182-0022, Japan 3 Japan Women’s University, Tokyo 112-8681, Japan (Received 11 June 2018; revised manuscript received 7 February 2019; published 25 April 2019) Experimental observations indicate that the repulsion of particles is a factor that induces the transformation of vesicles containing multiple particles. Metropolis Monte Carlo simulations are performed with two models in which repulsive particles are enclosed inside a vesicle. The distribution of the particles and the effective bending coefficient and surface tension of the membrane are analyzed. The shape and internal structure of the vesicle containing the particles are investigated as the vesicle volume is decreased. It is revealed that the repulsive interaction between particles produces a layered structure and stiffens the membrane. When particles repulsively interact over a long range, the membrane takes on a dumbbell form. DOI: 10.1103/PhysRevE.99.042418 I. INTRODUCTION Flexible membranes and soft particles are important in molecular biology. The cell is a structure separated from an environment by a flexible lipid bilayer membrane, which contains several kinds of cytosolic molecules at a high density [1]. These molecules inside the membrane exhibit specific or nonspecific interaction with other molecules and increase the viscosity within the cell [1]. Most organelles inside the cell have membrane structures. The relationship between the membrane deformation and behavior of internal molecules has attracted attention. The physical understanding of this relationship is crucial for investigating biological phenomena, such as division and secretion. Computational studies aimed toward the complete understanding of this dynamic behavior will require a detailed understanding of the structure and prop- erties of each molecule contained in the membrane. For this reason, simple cell models were prepared in vitro, which are giant bilayer vesicles containing polystyrene latex beads [2,3] (PSLBs), polyethylene glycol (PEG), or dextran [4]. It was observed that giant vesicles containing a high concentration of PSLBs transform into a shape resembling a pearl necklace or polyhedrons when the excess area and the volume fraction of the particles increase due to increased external osmotic pressure [2,3]. The average diameters of the vesicle and the included particles are about 10 and 1 μm, respectively, and the included particles are negatively charged. In addition, it has been observed that giant vesicles in- cluding a high concentration of PEG or dextran transform into a pearl-necklace-like shape when the excess area in- creases through the fusion of vesicles caused by an electric pulse [4]. These transformation phenomena are induced by the included particles. In the reported experiments [2–4], * s096020@toyaku.ac.jp † morikawa@toyaku.ac.jp particle-particle or membrane-particle adsorption was not in- vestigated. Although the studied systems contained particles (PSLBs, PEG, or dextran) of varying surface and size prop- erties, transformations were observed in each of the three systems. Because the shape of the vesicle changes to increase the free volume of the included particles [2–4], the depletion interaction [5–9] was used to explain the transformation [4]. When a suspension contains large and small colloidal parti- cles, an effective attractive force between the large particles occurs. This is an entropic force called the depletion force. The origin of the depletion interaction is the repulsion be- tween particles. If particles are deformable, the amount of interaction strongly increases [10]. The interaction is observed not only in the famous case of a suspension containing large and small particles, but also in the case of the vesicle and in- cluded particles [8]. In this case, to maximize the free volume of the particles, the curvature of the membrane is frequently varied. When the membrane is curved, the excluded volume is reduced. Therefore, the situation is more complicated than in a hard-sphere system. The free energy of the depletion inter- action decreases proportionally to the osmotic pressure of the colloidal particles and the logarithm of the free volume of the included particles. Considering both the depletion interaction and the curvature elastic energy of the membrane, Terasawa and others showed that the free energy of the twin-shaped vesicles is lower than that of spherocylinders when the surface area and volume of the two shapes are the same [4]. The free energy for other shapes was not obtained. However, the state obtained by minimizing the steric repulsive potential between colloidal particles will be determined to increase the free volume of colloidal particles. Therefore, it is not clear whether this increase in free volume is induced by depletion interaction. To analyze the shape of a giant vesicle, the continuous membrane models are useful [11]. In these models, the fol- lowing four conditions are assumed: First, the change in the area of the lipid membrane is small in the equilibrium state. 2470-0045/2019/99(4)/042418(12) 042418-1 ©2019 American Physical Society