The understanding of multi-component mixtures of self-assembling molecules under thermodynamic equilibrium can only be advanced by a combined experimental and theoretical approach. In such systems, small differences in association energy between the various components can be significantly amplified at the supramolecular level via intricate nonlinear effects. Here we report a theoretical investigation of two-component, self-assembling systems in order to rationalize chiral amplification in cooperative supramolecular copolymerizations. Unlike previous models based on theories developed for covalent polymers, the models presented here take into account the equilibrium between the monomer pool and supramolecular polymers, and the cooperative growth of the latter. Using two distinct methodologies, that is, solving mass-balance equations and stochastic simulation, we show that monomer exchange accounts for numerous unexplained observations in chiral amplification in supramolecular copolymerization. In analogy with asymmetric catalysis, amplification of chirality in supramolecular polymers results in an asymmetric depletion of the enantiomerically related monomer pool.

We describe a model that rationalizes amplification of chirality in cooperative supramolecular copolymerization. The model extends nucleation-elongation based equilibrium models for growth of supramolecular homopolymers to the case of two monomer and aggregate types. Using the principle of mass-balance for the two monomer types, we derive a set of two nonlinear equations, describing the thermodynamic equilibrium state of the system. These equations can be solved by numerical methods, but also analytical approximations are derived. The equilibrium model allows two-sided growth of the aggregates and can be applied to symmetric supramolecular copolymerizations, corresponding to the situation in which the monomers are enantiomerically related, as well as to the more general case of nonsymmetric supramolecular copolymerizations. In detail, so-called majority-rules phenomena in supramolecular systems with isodesmic as well as cooperative growth are analyzed. Comparison of model predictions with experimental data shows that the model gives a very good description of both titration and melting curves. When the system shows cooperative growth, the model leads to a phase diagram in which the presence of the various aggregate types is given as a function of composition and temperature.

Supramolecular block copolymers are becoming attractive materials in nascent optoelectronic and catalytic technologies. However, their dynamic nature precludes the straightforward tuning and analysis of the polymer’s structure. Here we report the elucidation on the microstructure of triarylamine triamide-based supramolecular block copolymers through a comprehensive battery of spectroscopic, theoretical, and super-resolution microscopic techniques. Via spectroscopic analysis we demonstrate that the direct mixing of preassembled homopolymers and the copolymerization induced by slow cooling of monomers lead to the formation of the same copolymer’s architecture. The small but pronounced deviation of the experimental spectra from the linear combination of the homopolymers’ spectra hints at the formation of block copolymers. A mass balance model is introduced to further unravel the microstructure of the copolymers formed, and it confirms that stable multiblock supramolecular copolymers can be accessed from different routes. The multiblock structure of the supramolecular copolymers originates from the fine balance between favorable hydrogen-bonding interactions and a small mismatch penalty between two different monomers. Finally, we visualized the formation of the supramolecular block copolymers by adapting a recently developed super-resolution microscopy technique, interface point accumulation for imaging in nanoscale topography (iPAINT), for visualizing the architectures formed in organic media. Combining multiple techniques was crucial to unveil the microstructure of these complex dynamic supramolecular systems.

In the vertebrate retina, horizontal cells generate the inhibitory surround of bipolar cells, an essential step in contrast enhancement. For the last decades, the mechanism involved in this inhibitory synaptic pathway has been a major controversy in retinal research. One hypothesis suggests that connexin hemichannels mediate this negative feedback signal; another suggests that feedback is mediated by protons. Mutant zebrafish were generated that lack connexin 55.5 hemichannels in horizontal cells. Whole cell voltage clamp recordings were made from isolated horizontal cells and cones in flat mount retinas. Light-induced feedback from horizontal cells to cones was reduced in mutants. A reduction of feedback was also found when horizontal cells were pharmacologically hyperpolarized but was absent when they were pharmacologically depolarized. Hemichannel currents in isolated horizontal cells showed a similar behavior. The hyperpolarization-induced hemichannel current was strongly reduced in the mutants while the depolarization-induced hemichannel current was not. Intracellular recordings were made from horizontal cells. Consistent with impaired feedback in the mutant, spectral opponent responses in horizontal cells were diminished in these animals. A behavioral assay revealed a lower contrast-sensitivity, illustrating the role of the horizontal cell to cone feedback pathway in contrast enhancement. Model simulations showed that the observed modifications of feedback can be accounted for by an ephaptic mechanism. A model for feedback, in which the number of connexin hemichannels is reduced to about 40%, fully predicts the specific asymmetric modification of feedback. To our knowledge, this is the first successful genetic interference in the feedback pathway from horizontal cells to cones. It provides direct evidence for an unconventional role of connexin hemichannels in the inhibitory synapse between horizontal cells and cones. This is an important step in resolving a long-standing debate about the unusual form of (ephaptic) synaptic transmission between horizontal cells and cones in the vertebrate retina.

Atrial fibrillation, a common cardiac arrhythmia, is promoted by atrial dilatation. Acute atrial dilatation may play a role in atrial arrhythmogenesis through mechanoelectric feedback. In experimental studies, conduction slowing and block have been observed in acutely dilated atria. In the present study, the influence of the stretch-activated current (I(sac)) on impulse propagation is investigated by means of computer simulations. Homogeneous and inhomogeneous atrial tissues are modeled by cardiac fibers composed of segments that are electrically and mechanically coupled. Active force is related to free Ca(2+) concentration and sarcomere length. Simulations of homogeneous and inhomogeneous cardiac fibers have been performed to quantify the relation between conduction velocity and I(sac) under stretch. In our model, conduction slowing and block are related to the amount of stretch and are enhanced by contraction of early-activated segments. Conduction block can be unidirectional in an inhomogeneous fiber and is promoted by a shorter stimulation interval. Slowing of conduction is explained by inactivation of Na(+) channels and a lower maximum upstroke velocity due to a depolarized resting membrane potential. Conduction block at shorter stimulation intervals is explained by a longer effective refractory period under stretch. Our observations are in agreement with experimental results and explain the large differences in intra-atrial conduction, as well as the increased inducibility of atrial fibrillation in acutely dilated atria.