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Aim: Multifunctional polymer-based biomaterials, which combine degradability with a shape-memory capability and in this way enable the design of actively moving implants such as self-anchoring implants or controlled release systems, have been recently introduced. Of particular interest are approved degradable polymers such as poly(L-lactide) (PLLA), which can be easily functionalized with a shape-memory effect. In the case of semicrystalline PLLA, the glass transition can be utilized as shape-memory switching domain.
Methods: In this work we applied a fully atomistic molecular dynamics simulation to study the shape-memory behavior of PLLA. A heating-deformation-cooling programming procedure was applied to atomistic PLLA packing models followed by a recovery module under stress-free conditions allowing the shape recovery. The recovery was simulated by heating the samples from T-low = 250 K to T-high = 500 K with different heating rates beta of 125, 40 and 4 K.ns(-1).
Results: We could demonstrate that the obtained strain recovery rate (R-r) was strongly influenced by the applied simulation time and heating rate, whereby R-r values in the range from 46% to 63% were achieved. On its own the application of a heating rate of 4 K.ns(-1) enabled us to determine a characteristic switching temperature of T-sw = 473 K for the modeled samples.
Conclusions: We anticipate that the atomistic modeling approach presented should be capable of enabling further study of T-sw with respect to the molecular structure of the investigated SMP and therefore could be applied in the context of design and development of new shape-memory (bio) materials.

The polymer-controlled and bioinspired precipitation of inorganic minerals from aqueous solution at near-ambient or physiological conditions avoiding high temperatures or organic solvents is a key research area in materials science. Polymer-controlled mineralization has been studied as a model for biomineralization and for the synthesis of (bioinspired and biocompatible) hybrid materials for a virtually unlimited number of applications. Calcium phosphate mineralization is of particular interest for bone and dental repair. Numerous studies have therefore addressed the mineralization of calcium phosphate using a wide variety of low- and high-molecular-weight additives. In spite of the growing interest and increasing number of experimental and theoretical data, the mechanisms of polymer-controlled calcium phosphate mineralization are not entirely clear to date, although the field has made significant progress in the last years. A set of elegant experiments and calculations has shed light on some details of mineral formation, but it is currently not possible to preprogram a mineralization reaction to yield a desired product for a specific application. The current article therefore summarizes and discusses the influence of (macro)molecular entities such as polymers, peptides, proteins and gels on biomimetic calcium phosphate mineralization from aqueous solution. It focuses on strategies to tune the kinetics, morphologies, final dimensions and crystal phases of calcium phosphate, as well as on mechanistic considerations.

We study buckling instabilities of filaments in biological systems. Filaments in a cell are the building blocks of the cytoskeleton. They are responsible for the mechanical stability of cells and play an important role in intracellular transport by molecular motors, which transport cargo such as organelles along cytoskeletal filaments. Filaments of the cytoskeleton are semiflexible polymers, i.e., their bending energy is comparable to the thermal energy such that they can be viewed as elastic rods on the nanometer scale, which exhibit pronounced thermal fluctuations. Like macroscopic elastic rods, filaments can undergo a mechanical buckling instability under a compressive load. In the first part of the thesis, we study how this buckling instability is affected by the pronounced thermal fluctuations of the filaments. In cells, compressive loads on filaments can be generated by molecular motors. This happens, for example, during cell division in the mitotic spindle. In the second part of the thesis, we investigate how the stochastic nature of such motor-generated forces influences the buckling behavior of filaments. In chapter 2 we review briefly the buckling instability problem of rods on the macroscopic scale and introduce an analytical model for buckling of filaments or elastic rods in two spatial dimensions in the presence of thermal fluctuations. We present an analytical treatment of the buckling instability in the presence of thermal fluctuations based on a renormalization-like procedure in terms of the non-linear sigma model where we integrate out short-wavelength fluctuations in order to obtain an effective theory for the mode of the longest wavelength governing the buckling instability. We calculate the resulting shift of the critical force by fluctuation effects and find that, in two spatial dimensions, thermal fluctuations increase this force. Furthermore, in the buckled state, thermal fluctuations lead to an increase in the mean projected length of the filament in the force direction. As a function of the contour length, the mean projected length exhibits a cusp at the buckling instability, which becomes rounded by thermal fluctuations. Our main result is the observation that a buckled filament is stretched by thermal fluctuations, i.e., its mean projected length in the direction of the applied force increases by thermal fluctuations. Our analytical results are confirmed by Monte Carlo simulations for buckling of semiflexible filaments in two spatial dimensions. We also perform Monte Carlo simulations in higher spatial dimensions and show that the increase in projected length by thermal fluctuations is less pronounced than in two dimensions and strongly depends on the choice of the boundary conditions. In the second part of this work, we present a model for buckling of semiflexible filaments under the action of molecular motors. We investigate a system in which a group of motors moves along a clamped filament carrying a second filament as a cargo. The cargo-filament is pushed against the wall and eventually buckles. The force-generating motors can stochastically unbind and rebind to the filament during the buckling process. We formulate a stochastic model of this system and calculate the mean first passage time for the unbinding of all linking motors which corresponds to the transition back to the unbuckled state of the cargo filament in a mean-field model. Our results show that for sufficiently short microtubules the movement of kinesin-I-motors is affected by the load force generated by the cargo filament. Our predictions could be tested in future experiments.