Deformable nanoparticles (DNPs) such as liposomes are widely used to load and deliver drugs across hydrogel-like biological barriers such as mucus and tumor interstitial matrix. The rigidity of DNPs is found to have a huge effect on their diffusivity in biological gels, while the underlying mechanism is still unclear. Here, we propose a theoretical model to describe the diffusion behavior of DNPs in biological hydrogel and elucidate the mechanism by which the stiffness of DNPs affects their diffusion properties through decoupling their deformation and transportation during diffusion. By considering three physical parameters, including the stiffness of DNPs, the mesh size of the polymer network and the adhesion property of the hydrogel, we find that both stiffness and adhesion play critical roles in the diffusion of DNPs. In addition, there is an optimal diffusivity when the stiffness and adhesion are balanced. The phase diagram of DNPs with different stiffness and optimal diffusivity in the plane of mesh size and adhesion strength is further obtained through systematic calculations. The prediction is highly consistent with recent experimental and molecular simulation findings for the diffusion of liposomes of varying stiffness in gastrointestinal mucus. By elucidating the mechanism by which stiffness affects the diffusion of DNPs in physiological gels, our model could provide a rationale for designing drug carriers with enhanced diffusion capacity in biological hydrogels.

脂质体等可变形纳米颗粒 (DNP) 广泛用于跨水凝胶样生物屏障（如粘液和肿瘤间质基质）装载和递送药物。发现 DNPs 的刚性对其在生物凝胶中的扩散性有巨大影响，但其潜在机制仍不清楚。在这里，我们提出了一个理论模型来描述 DNPs 在生物水凝胶中的扩散行为，并通过在扩散过程中解耦 DNPs 的变形和运输来阐明 DNPs 的刚度影响其扩散特性的机制。通过考虑三个物理参数，包括 DNPs 的刚度、聚合物网络的网格尺寸和水凝胶的粘附性能，我们发现刚度和粘附在 DNPs 的扩散中起着关键作用。此外，当刚度和附着力平衡时，有一个最佳的扩散率。通过系统计算，进一步得到了具有不同刚度和最佳扩散率的DNP在网格尺寸和粘附强度平面内的相图。该预测与最近关于不同硬度的脂质体在胃肠道粘液中扩散的实验和分子模拟结果高度一致。通过阐明刚度影响 DNP 在生理凝胶中扩散的机制，我们的模型可以为设计具有增强的生物水凝胶中扩散能力的药物载体提供理论基础。通过系统计算，进一步得到了具有不同刚度和最佳扩散率的DNP在网格尺寸和粘附强度平面内的相图。该预测与最近关于不同硬度的脂质体在胃肠道粘液中扩散的实验和分子模拟结果高度一致。通过阐明刚度影响 DNP 在生理凝胶中扩散的机制，我们的模型可以为设计具有增强的生物水凝胶中扩散能力的药物载体提供理论基础。通过系统计算，进一步得到了具有不同刚度和最佳扩散率的DNP在网格尺寸和粘附强度平面内的相图。该预测与最近关于不同硬度的脂质体在胃肠道粘液中扩散的实验和分子模拟结果高度一致。通过阐明刚度影响 DNP 在生理凝胶中扩散的机制，我们的模型可以为设计具有增强的生物水凝胶中扩散能力的药物载体提供理论基础。