Wrapping of a vesicle nanoparticle with variable bending stiffness by membrane

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Cellular uptake of nanoparticle (NP) is an important biological process involving mechanically and structurally heterogeneous environments, such as biophysical heterogeneity of single extracellular vesicles and biomechanical heterogeneity of small viral capsids. Despite of these heterogeneous environments, poor understanding of membrane interacting with vesicle NP of non-uniform mechanical properties still exists. To address this issue, combining the continuum Canham–Helfrich theory of membrane and the stochastic Markov method on state transition, we establish a theoretical model of the wrapping of a NP with any variable bending stiffness. As NPs are hypothesized with two typical types of non-uniform bending stiffness distributions (Gaussian-like and piecewise), through both minimum energy and stochastic dynamic approaches, it is identified that the membrane tends to encapsulate the NP with a sealing near soft region of NP. Because complete wrapping of NP with a sealing near its stiff region requires large elastic deformation of membrane. In addition, during cellular uptake, rotation phenomenon of the NP with variable bending stiffness is found, which is reminiscent of previous observations on homogeneous NP as reported in literature. These predictions are verified by relevant Monte Carlo simulations. Our findings are of interest to not only the fundamental understanding of cellular uptake but also the applications in the design of nanocarriers for drug delivery.