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We use the bond fluctuation model to study the contraction process of two polymer loops with $N$ segments that are connected each to the bottom and top parts of a Feringa engine. The change in the size of the molecules as well as the folding of the two strands follows approximately scaling predictions that are derived by assuming that the strands are confined inside an effective tube. Conformation data can be overlapped when plotting it as a function of ${W}_{\text{n}}{N}^{\ensuremath{-}1/4}$, where ${W}_{\text{n}}$ is the winding number of the two strands that is proportional to the number of blobs inside the ``knotted'' region of the molecule and $N$ is the degree of polymerization of the strands. Our data support a weak localization of the knots along the contour of flexible cyclic athermal polymers with a localization exponent $t\ensuremath{\approx}0.78$. more...

Cell-instructive characteristics of extracellular matrices (ECM) resulting from a subtle balance of biomolecular and biophysical signals must be recapitulated in engineered biomaterials to facilitate regenerative therapies. However, no material explored so far allows the independent tuning of the involved molecular and physical cues due to the inherent correlation between biopolymer concentration and material properties. Addressing the resulting challenge, a rational design strategy for ECM-inspired biohybrid hydrogels based on multi-armed poly(ethylene glycol) and heparin, adapting a mean field approach to identify conditions at which the balance of elastic, electrostatic, and excluded volume forces results in constant heparin concentrations within swollen polymer networks with gradually varied physical properties is introduced. Applying heparin-based biofunctionalization schemes, multiple distinct combinations of matrix parameters could be identified to effectively stimulate the pro-angiogenic state of human endothelial cells and the differentiation of human mesenchymal stem cells. The study demonstrates the power of joint theoretical and experimental efforts in creating bioactive materials with specifically and independently controllable characteristics. more...

We study the segregation of two long chains from parallel but randomly twisted start conformations under good solvent conditions using Monte Carlo simulations to mimic chromatin segregation after replication in eukaryotic cells in the end of prophase. To measure the segregation process, we consider the center-of-mass separation between the two chains and the average square distance between the monomers which were connected before segregation starts. We argue that segregation is dominated by free diffusion of the chains, assuming that untwisting can be achieved by Rouse-like fluctuations on the length scale of a twisted loop. Using scaling analysis, we find that chain dynamics is in very good agreement with the free diffusion hypothesis, and segregation dynamics follows this scaling nearly. Long chains, however, show retardation effects that can be described by a new (to us) dynamical exponent, which is slightly larger than the dynamical exponent for Rouse-like diffusion. Our results indicate that nearly free diffusion of chains during a timescale of a few Rouse-times can lead to segregation of chains. A main obstacle during segregation by free diffusion is random twists between daughter strands. We have calculated the number of twists formed by the daughter strands in the start conformations, which turns out to be rather low and increases only with the square-root of the chain length. more...

We study the changes in the conformations of brushes upon the addition of crosslinks between the chains using the bond fluctuation model. The Flory-Rehner model applied to uni-axially swollen networks predicts a collapse for large degrees of crosslinking $q$ proportional to $q^{-1/3}$ in disagreement with our simulation data. We show that the height reduction of the brushes is driven by monomer fluctuations in direction perpendicular to the grafting plane and not due to network elasticity. We observe that the impact of crosslinking is different for reactions between monomers of the same or on different chains. If the length reduction of the effective chain length due to both types of reactions is accounted for in a function $\beta(q)$, the height of the brush can be derived from a Flory approach for the equilibrium brush height leading to $H(q)\approx H_{b}\beta(q)^{1/3}$, whereby $H_{b}$ denotes the height of the non-crosslinked brush. more...