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1. Avidity and surface mobility in multivalent ligand–receptor binding

   https://doi.org/10.1039/D1NR02083H  

   Merminod, Simon; Edison, John R.; Fang, Huang; Hagan, Michael F.; Rogers, W. Benjamin (July 2021, Nanoscale)

   null (Ed.)

   Targeted drug delivery relies on two physical processes: the selective binding of a therapeutic particle to receptors on a specific cell membrane, followed by transport of the particle across the membrane. In this article, we address some of the challenges in controlling the thermodynamics and dynamics of these two processes by combining a simple experimental system with a statistical mechanical model. Specifically, we characterize and model multivalent ligand–receptor binding between colloidal particles and fluid lipid bilayers, as well as the surface mobility of membrane-bound particles. We show that the mobility of the receptors within the fluid membrane is key to both the thermodynamics and dynamics of binding. First, we find that the particle-membrane binding free energy—or avidity—is a strongly nonlinear function of the ligand–receptor affinity. We attribute the nonlinearity to a combination of multivalency and recruitment of fluid receptors to the binding site. Our results also suggest that partial wrapping of the bound particles by the membrane enhances avidity further. Second, we demonstrate that the lateral mobility of membrane-bound particles is also strongly influenced by the recruitment of receptors. Specifically, we find that the lateral diffusion coefficient of a membrane-bound particle is dominated by the hydrodynamic drag against the aggregate of receptors within the membrane. These results provide one of the first direct validations of the working theoretical framework for multivalent interactions. They also highlight that the fluidity and elasticity of the membrane are as important as the ligand–receptor affinity in determining the binding and transport of small particles attached to membranes. 

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2. Lateral Migration of Cancer Cells in a Microchannel

   https://doi.org/10.1115/dmd2024-1096  

   Akerkouch, Lahcen; Le, Trung B; Haage, Amanda (April 2024, American Society of Mechanical Engineers)

   Abstract This work presents the development of a novel approach to model cancer cell dynamics in microcirculation. The proposed numerical model is based on a hybrid continuum-particle approach. The cancer cell model includes the cell membrane, nucleus, cytoplasm and the cytoskeleton. The Dissipative Particle Dynamics method was employed to simulate the mechanical components. The blood plasma is modeled as a Newtonian incompressible fluid. A Fluid-Structure Interaction coupling, leveraging the Immersed Boundary Method is developed to simulate the cell's response to flow dynamics. The model is applied to resolve the transport of cancer cells with realistic morphologies in microcirculatory flows. Our results suggest that the controlling of oscillatory flows can be utilized to induce specific morphological shapes and the surrounding fluid patterns, allowing full manipulation and control of the cell. Furthermore, the intracellular and extracellular dynamics response of the cancer cell is intrinsically linked to their shape, in which certain morphologies displayed strong resistance to the fluid-induced forces and the ability to migrate in various directions. Our computational framework provides new capabilities for designing bioengineering devices for cell manipulation and separation. 

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3. A Hybrid Continuum-Particle Approach for Fluid-Structure Interaction Simulation of Red Blood Cells in Fluid Flows

   https://doi.org/10.3390/fluids6040139  

   Akerkouch, Lahcen; Le, Trung Bao (April 2021, Fluids)

   Transport of cells in fluid flow plays a critical role in many physiological processes of the human body. Recent developments of in vitro techniques have enabled the understanding of cellular dynamics in laboratory conditions. However, it is challenging to obtain precise characteristics of cellular dynamics using experimental method alone, especially under in vivo conditions. This challenge motivates new developments of computational methods to provide complementary data that experimental techniques are not able to provide. Since there exists a large disparity in spatial and temporal scales in this problem, which requires a large number of cells to be simulated, it is highly desirable to develop an efficient numerical method for the interaction of cells and fluid flows. In this work, a new Fluid-Structure Interaction formulation is proposed based on the use of hybrid continuum-particle approach, which can resolve local dynamics of cells while providing large-scale flow patterns in the vascular vessel. Here, the Dissipative Particle Dynamics (DPD) model for the cellular membrane is used in conjunction with the Immersed Boundary Method (IBM) for the fluid plasma. Our results show that the new formulation is highly efficient in computing the deformation of cells within fluid flow while satisfying the incompressibility constraints of the fluid. We demonstrate that it is possible to couple the DPD with the IBM to simulate the complex dynamics of Red Blood Cells (RBC) such as parachuting. Our key observation is that the proposed coupling enables the simulation of RBC dynamics in realistic arterioles while ensuring the incompressibility constraint for fluid plasma. Therefore, the proposed method allows an accurate estimation of fluid shear stresses on the surface of simulated RBC. Our results suggest that this hybrid methodology can be extended for a variety of cells in physiological conditions. 

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4. Entropic Pressure Between Fluctuating Membranes With Surface Tension

   https://doi.org/10.1115/1.4068468  

   Hassan, Rubayet; Farokhirad, Samaneh; Ahmadpoor, Fatemeh (September 2025, Journal of Applied Mechanics)

   Entropic pressure, a longstanding topic of interest in biophysics and biomechanics, has been studied for over four decades. Similar to an ideal gas, fluctuating surfaces can generate entropic pressure through thermally driven motions. These thermal fluctuations impact a wide range of biological activities, including but not limited to vesicle fusion, cell adhesion, exocytocis, and endocytocis among many others. It has been proposed (and validated) by many researchers that the entropic pressure near a fluctuating confined fluid membrane without surface tension scales as p∝1/d3, where d is the confining distance, and this power law is size independent. In this article, we show that entropic pressure near a fluctuating fluid membrane could be strongly affected by the membrane’s size and surface tension. We show that while for membranes of size L=1μm and larger, the pressure is size independent, for smaller membranes, the pressure does indeed depend on the membrane’s size. Our findings also shows that the surface tension changes this scaling law and at larger distance makes the pressure decay exponentially. Our work provides insights into how surface tension enhances biological vesicles fusion by suppressing membrane fluctuations, and consequently, the repulsive entropic force, and impacts biomembranes interactions with external objects at the early stage of approaching. 

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5. Tension Pistons: Amplifying Piston Force Using Fluid-Induced Tension in Flexible Materials

   Shuguang Li, Daniel M. (June 2019, Advanced functional materials)

   Pistons are ubiquitous devices used for fluid-mechanical energy conversion. However, despite this ubiquity and centuries of development, the forces and motions produced by conventional rigid pistons are limited by their design. The use of flexible materials and structures opens a door to the design of a piston with unconventional features. In this study, an architecture for pistons that utilizes a combination of flexible membrane materials and compressible rigid structures is proposed. In contrast to conventional pistons, the fluid- pressure-induced tension forces in the flexible membrane play a primary role in the system, rather than compressive forces on the internal surfaces of the piston. The compressive skeletal structures offer the opportunity for the production of tunable forces and motions in the “tension piston” system. The experimental results indicate that the tension piston concept is able to produce substantially greater force (more than three times), higher power, and higher energy efficiency (more than 40% improvement at low pressures) compared to a conventional piston, and these features enable myriad potential applications for the tension piston as a drop-in replacement for existing pistons. 

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