research has revealed that, together with the provision of morphogens and the presentation of adhesion ligands, [ 2 ] the mechanical characteristics of extracellular matrices have a decisive infl uence on cell fate, provoking the development of materials with effective physical properties. [ 3 ] This interplay of biomolecular and biophysical signals thus defi nes an obvious, but until now unmet, need for a new generation of biomaterials that can be selectively and independently tuned for biomolecular properties and physical material parameters. A conceptual basis to address this need is currently missing. As such, we have developed a rational design approach relying on mean fi eld concepts to guide the design of biofunctional matrices. Considering the decisive role of electrostatic interactions in functional assemblies of living matter we selected a system that allows for a far-reaching modulation of structure-determining forces: crosslinking a hydrophilic and fl exible, multi-armed polymer (with four-armed, amino-terminated poly(ethylene glycol) (starPEG) as an example system known for its anti-adhesive characteristics towards proteins, [ 4 ] with a multifunctional, highly charged crosslinker (such as heparin (HEP) or a similarly charged glycosaminoglycan), which can function as a multivalent binding site capable of complexing a plethora of important bioactive molecules. [ 5 ] We explored whether and how the combination of the particular gel components permits varying the physical and biomolecular characteristics of the swollen materials independently.Based on the successful experimental verifi cation of the theoretical predictions and the functionalization of starPEG-heparin gels with adhesive ligand peptides (such as the integrinbinding arginine-glycine-aspartic acid sequence (RGD))) and morphogens (vascular endothelial growth factor (VEGF), bone morphogenetic protein-2 (BMP-2)) through covalent and noncovalent conjugation schemes we were able to illustrate the resulting options for two selected example systems: studying the interplay of matrix elasticity and growth factor presentation in inducing the pro-angiogenic state of human endothelial cells and promoting osteogenic differentiation of human mesenchymal stem cells we identifi ed effective combinations of matrix parameters and demonstrated exciting options for the fully matrix controlled direction of the cells, i.e., removed the Using Mean Field Theory to Guide Biofunctional Materials DesignCell-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 he...

Recently developed chain walking (CW) catalysis is an elegant approach to produce materials with controllable structure and properties. However, there is still a lack in understanding of how the reaction mechanism influences the macromolecular structures. In this study, a series of dendritic polyethylenes (PE) synthesized by Pd-α-diimine-complex through CW catalysis (CWPE) is investigated by means of theory and experiment. Thereby, the exceptional ability of in situ tailoring polymer structure by varying synthesis parameters was exploited to tune the branching architecture, which allowed us to establish a precise relationship between synthesis, structure, and solution properties. The systematically produced polymers were characterized by state-of-the-art multidetector separation and neutron scattering experiments as well as atomic force microscopy to access molecular properties of CWPE. On a global scale, the CWPE appear in a worm-like conformation independently on the synthesis conditions. However, severe differences in their contraction factors suggested that CWPE differ substantially in topology. These observations were verified by NMR studies that showed that CWPE possess a constant total number of branches but varying branching distribution. Small angle neutron scattering experiments gave access to structural characteristics from global to segmental scale and revealed the unique heterogeneity of CWPE, which is predominantly based on differences in their dendritic side chains. The experimental data were compared to theoretical CW structures modeled with different reaction-to-walking probabilities. Simple theoretical arguments predict a crossover from dendritic to linear topologies yielding a structural range from purely linear to dendritic chain growth. Yet, comparison of theoretical and empirical scattering curves gave the first evidence that a transition state to worm-like topologies is actually experimentally accessible. This crossover regime is characterized by linear global features and dendritic local substructures contrary to randomly hyperbranched systems. Instead, the obtained CWPE systems have characteristics of disordered dendritic bottle brushes and can be adjusted by the walking rate/reaction probability of the catalyst.

We grow AB2 random hyperbranched polymer structures in different ways and using different simulation methods. In particular we use a method of ad hoc construction of the connectivity matrix and the bond fluctuation model on a 3D lattice. We show that hyperbranched polymers split into two universality classes depending on the growth process. For a "slow growth" (SG) process where monomers are added sequentially to an existing molecule which strictly avoids cluster-cluster aggregation the resulting structures share all characteristic features with regular dendrimers. For a "quick growth" (QG) process which allows for cluster-cluster aggregation we obtain structures which can be identified as random fractals. Without excluded volume interactions the SG model displays a logarithmic growth of the radius of gyration with respect to the degree of polymerization while the QG model displays a power law behavior with an exponent of 1/4. By analyzing the spectral properties of the connectivity matrix we confirm the behavior of dendritic structures for the SG model and the corresponding fractal properties in the QG case. A mean field model is developed which explains the extension of the hyperbranched polymers in an athermal solvent for both cases. While the radius of gyration of the QG model shows a power-law behavior with the exponent value close to 4/5, the corresponding result for the SG model is a mixed logarithmic-power-law behavior. These different behaviors are confirmed by simulations using the bond fluctuation model. Our studies indicate that random sequential growth according to our SG model can be an alternative to the synthesis of perfect dendrimers.

Sulfation patterns of glycosaminoglycans (GAG) govern the electrostatic complexation of biomolecules and thus allow for modulating the release profiles of growth factors from GAG-based hydrogels. To explore options related to this, selectively desulfated heparin derivatives were prepared, thoroughly characterized, and covalently converted with star-shaped poly(ethylene glycol) into binary polymer networks. The impact of the GAG sulfation pattern on the network characteristics of the obtained hydrogels was theoretically evaluated by mean field methods and experimentally analyzed by rheometry and swelling measurements. Sulfation-dependent differences of reactivity and miscibility of the heparin derivatives were shown to determine network formation. A theory-based design concept for customizing growth factor affinity and physical characteristics was introduced and validated by quantifying the release of fibroblast growth factor 2 from a set of biohybrid gels. The resulting new class of cell-instructive polymer matrices with tunable GAG sulfation will be instrumental for multiple applications in biotechnology and medicine.