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The bioactivity of nanoparticles crucially depends on their ability to cross biomembranes. Recent simulations indicate the cooperative wrapping and internalization of spherical nanoparticles in tubular membrane structures. In this article, we systematically investigate the energy gain of this cooperative wrapping by minimizing the energies of the rotationally symmetric shapes of the membrane tubes and of membrane segments wrapping single particles. We find that the energy gain for the cooperative wrapping of nanoparticles in membrane tubes relative to their individual wrapping as single particles strongly depends on the ratio ρ/R of the particle radius R and the range ρ of the particle-membrane adhesion potential. For a potential range of the order of one nanometer, the cooperative wrapping in tubes is highly favorable for particles with a radius of tens of nanometers and intermediate adhesion energies, but not for particles that are significantly larger.

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Global change threatens the maintenance of ecosystem functions that are shaped by the persistence and dynamics of populations. It has been shown that the persistence of species increases if they possess larger trait adaptability. Here, we investigate whether trait adaptability also affects the robustness of population dynamics of interacting species and thereby shapes the reliability of ecosystem functions that are driven by these dynamics. We model co‐adaptation in a predator–prey system as changes to predator offense and prey defense due to evolution or phenotypic plasticity. We investigate how trait adaptation affects the robustness of population dynamics against press perturbations to environmental parameters and against pulse perturbations targeting species abundances and their trait values. Robustness of population dynamics is characterized by resilience, elasticity, and resistance. In addition to employing established measures for resilience and elasticity against pulse perturbations (extinction probability and return time), we propose the warping distance as a new measure for resistance against press perturbations, which compares the shapes and amplitudes of pre‐ and post‐perturbation population dynamics. As expected, we find that the robustness of population dynamics depends on the speed of adaptation, but in nontrivial ways. Elasticity increases with speed of adaptation as the system returns more rapidly to the pre‐perturbation state. Resilience, in turn, is enhanced by intermediate speeds of adaptation, as here trait adaptation dampens biomass oscillations. The resistance of population dynamics strongly depends on the target of the press perturbation, preventing a simple relationship with the adaptation speed. In general, we find that low robustness often coincides with high amplitudes of population dynamics. Hence, amplitudes may indicate the robustness against perturbations also in other natural systems with similar dynamics. Our findings show that besides counteracting extinctions, trait adaptation indeed strongly affects the robustness of population dynamics against press and pulse perturbations.

Theory predicts that resource variability hinders consumer performance. How this effect depends on the temporal structure of resource fluctuations encountered by individuals remains poorly understood. Combining modelling and growth experiments with Daphnia magna, we decompose the complexity of resource fluctuations and test the effect of resource variance, supply peak timing (i.e. phase) and co‐limiting resource covariance along a gradient from high to low frequencies reflecting fine‐ to coarse‐grained environments. Our results show that resource storage can buffer growth at high frequencies, but yields a sensitivity of growth to resource peak timing at lower ones. When two resources covary, negative covariance causes stronger growth depression at low frequencies. However, negative covariance might be beneficial at intermediate frequencies, an effect that can be explained by digestive acclimation. Our study provides a mechanistic basis for understanding how alterations of the environmental grain size affect consumers experiencing variable nutritional quality in nature.