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Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein–protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work, here, we focus on the role of explicit aggregation of proteins on the surface of the membrane in the presence of membrane bending and diffusion. We develop a comprehensive framework that includes lipid flow, membrane bending, the entropy of protein distribution, along with an explicit aggregation potential and derive the governing equations for the coupled system. We compare this framework to the Cahn–Hillard formalism to predict the regimes in which the proteins form patterns on the membrane. We demonstrate the utility of this model using numerical simulations to predict how aggregation and diffusion, when coupled with curvature generation, can alter the landscape of membrane–protein interactions.
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This content will become publicly available on October 7, 2026
Renormalization of Mechanical Properties in Fluctuating Active Membranes
We develop a theoretical framework to quantify how active forces renormalize the effective bending rigidity, Gaussian modulus, and surface tension of thermally fluctuating membranes. Building on classical statistical mechanics, we extend the analysis to include nonequilibrium active forces, both direct forces and those coupled to membrane curvature, within a nonlinear continuum formulation. Our model also incorporates hydrodynamic interactions mediated by the surrounding viscous fluid, which significantly alter the fluctuation spectrum. We find that direct active forces enhance long-wavelength undulations, leading to a substantial reduction in both the effective bending rigidity and surface tension, with the extent of softening strongly modulated by fluid viscosity. In contrast, curvature-coupled active forces primarily influence intermediate and short-wavelength fluctuations and show minimal sensitivity to viscosity. Together, these findings provide key insights into the nonequilibrium mechanics of active membranes and yield testable predictions for interpreting fluctuation spectra in both biological contexts and engineered membrane systems.
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- PAR ID:
- 10643588
- Publisher / Repository:
- American Society of Mechanical Engineers (ASME)
- Date Published:
- Journal Name:
- Journal of Applied Mechanics
- Volume:
- 92
- Issue:
- 12
- ISSN:
- 0021-8936
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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