Albert J. Markvoort

Pathway complexity in supramolecular polymerization

Self-assembly provides an attractive route to functional organic materials, with properties and hence performance depending sensitively on the organization of the molecular building blocks. Molecular organization is a direct consequence of the pathways involved in the supramolecular assembly process, which is more amenable to detailed study when using one-dimensional systems. In the case of protein fibrils, formation and growth have been attributed to complex aggregation pathways that go beyond traditional concepts of homogeneous and secondary nucleation events. The self-assembly of synthetic supramolecular polymers has also been studied and even modulated, but our quantitative understanding of the processes involved remains limited. Here we report time-resolved observations of the formation of supramolecular polymers from π-conjugated oligomers. Our kinetic experiments show the presence of a kinetically favoured metastable assembly that forms quickly but then transforms into the thermodynamically favoured form. Quantitative insight into the kinetic experiments was obtained from kinetic model calculations, which revealed two parallel and competing pathways leading to assemblies with opposite helicity. These insights prompt us to use a chiral tartaric acid as an auxiliary to change the thermodynamic preference of the assembly process. We find that we can force aggregation completely down the kinetically favoured pathway so that, on removal of the auxiliary, we obtain only metastable assemblies.

Theoretical models of nonlinear effects in two-component cooperative supramolecular copolymerizations

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.

An equilibrium model for chiral amplification in supramolecular polymers

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.

Kinetics of the Fischer–Tropsch Reaction

Long carbon chains: Self-assembly of monomeric carbon intermediates into long-chain hydrocarbons on catalytically reactive surface was studied when full reversibility of the chain growth is included in the kinetic model. Using Brønsted-Evans-Polanyi relations, the maximum chain growth as a function of the surface reactivity is predicted.

Model-driven optimization of multicomponent self-assembly processes

Significance The molecular organization of semiconducting molecules is extremely important for the performance of functional organic materials in electronic devices. The processing of these materials often leads to multiple assembly pathways toward different types of molecular organizations. Hence, directing the assembly process toward the desired type of organization requires many trial-and-error optimization steps. In this paper, we introduce an approach to optimize these self-assembly processes. Based on experiments with a system that assembles into 1D helices in solution, we have developed models to describe the dynamics of multicomponent self-assembly processes. These models simulate the experimental data very well and allow us to understand and avoid, or alternatively attenuate, the entrapment of materials in nonequilibrium assemblies. Here, we report an engineering approach toward multicomponent self-assembly processes by developing a methodology to circumvent spurious, metastable assemblies. The formation of metastable aggregates often hampers self-assembly of molecular building blocks into the desired nanostructures. Strategies are explored to master the pathway complexity and avoid off-pathway aggregates by optimizing the rate of assembly along the correct pathway. We study as a model system the coassembly of two monomers, the R- and S-chiral enantiomers of a π-conjugated oligo(p-phenylene vinylene) derivative. Coassembly kinetics are analyzed by developing a kinetic model, which reveals the initial assembly of metastable structures buffering free monomers and thereby slows the formation of thermodynamically stable assemblies. These metastable assemblies exert greater influence on the thermodynamically favored self-assembly pathway if the ratio between both monomers approaches 1:1, in agreement with experimental results. Moreover, competition by metastable assemblies is highly temperature dependent and hampers the assembly of equilibrium nanostructures most effectively at intermediate temperatures. We demonstrate that the rate of the assembly process may be optimized by tuning the cooling rate. Finally, it is shown by simulation that increasing the driving force for assembly stepwise by changing the solvent composition may circumvent metastable pathways and thereby force the assembly process directly into the correct pathway.

Lipid acrobatics in the membrane fusion arena.

In this review, we describe the recent contribution of computer simulation approaches to unravel the molecular details of membrane fusion. Over the past decade, fusion between apposed membranes and vesicles has been studied using a large variety of simulation methods and systems. Despite the variety in techniques, some generic fusion pathways emerge that predict a more complex picture beyond the traditional stalk–pore pathway. Indeed the traditional pathway is confirmed in particle-based simulations, but in addition alternative pathways are observed in which stalks expand linearly rather than radially, leading to inverted-micellar or asymmetric hemifusion intermediates. Simulations also suggest that the first barrier to fusion is not the formation of the stalk, but rather, the formation of a lipid bridge consisting of one or two lipids only. Fusion occurring during the fission process involves other intermediates, however, and is not just fusion reversed. Finally, recent progress in simulations of peptide and protein-mediated fusion shows how fusion proceeds in a more biologically relevant scenario.

Kinetic Analysis as a Tool to Distinguish Pathway Complexity in Molecular Assembly: An Unexpected Outcome of Structures in Competition

While the sensitive dependence of the functional characteristics of self-assembled nanofibers on the molecular structure of their building blocks is well-known, the crucial influence of the dynamics of the assembly process is often overlooked. For natural protein-based fibrils, various aggregation mechanisms have been demonstrated, from simple primary nucleation to secondary nucleation and off-pathway aggregation. Similar pathway complexity has recently been described in synthetic supramolecular polymers and has been shown to be intimately linked to their morphology. We outline a general method to investigate the consequences of the presence of multiple assembly pathways, and show how kinetic analysis can be used to distinguish different assembly mechanisms. We illustrate our combined experimental and theoretical approach by studying the aggregation of chiral bipyridine-extended 1,3,5-benzenetricarboxamides (BiPy-1) in n-butanol as a model system. Our workflow consists of nonlinear least-squares analysis of steady-state spectroscopic measurements, which cannot provide conclusive mechanistic information but yields the equilibrium constants of the self-assembly process as constraints for subsequent kinetic analysis. Furthermore, kinetic nucleation-elongation models based on one and two competing pathways are used to interpret time-dependent spectroscopic measurements acquired using stop-flow and temperature-jump methods. Thus, we reveal that the sharp transition observed in the aggregation process of BiPy-1 cannot be explained by a single cooperative pathway, but can be described by a competitive two-pathway mechanism. This work provides a general tool for analyzing supramolecular polymerizations and establishing energetic landscapes, leading to mechanistic insights that at first sight may seem unexpected and counterintuitive.

Self-Reproduction of Fatty Acid Vesicles: A Combined Experimental and Simulation Study

Dilution of a fatty acid micellar solution at basic pH toward neutrality results in spontaneous formation of vesicles with a broad size distribution. However, when vesicles of a defined size are present before dilution, the size distribution of the newly formed vesicles is strongly biased toward that of the seed vesicles. This so-called matrix effect is believed to be a key feature of early life. Here we reproduced this effect for oleate micelles and seed vesicles of either oleate or dioleoylphosphatidylcholine. Fluorescence measurements showed that the vesicle contents do not leak out during the replication process. We hypothesized that the matrix effect results from vesicle fission induced by an imbalance of material across both leaflets of the vesicle upon initial insertion of fatty acids into the outer leaflet of the seed vesicle. This was supported by experiments that showed a significant increase in vesicle size when the equilibration of oleate over both leaflets was enhanced by either slowing down the rate of fatty acid addition or increasing the rate of fatty acid transbilayer movement. Coarse-grained molecular-dynamics simulations showed excellent agreement with the experimental results and provided further mechanistic details of the replication process.

Vesicle deformation by draining : geometrical and topological shape changes

A variety of factors, including changes in temperature or osmotic pressure, can trigger morphological transitions of vesicles. Upon osmotic upshift, water diffuses across the membrane in response to the osmotic difference, resulting in a decreased vesicle volume to membrane area ratio and, consequently, a different shape. In this paper, we study the vesicle deformations on osmotic deflation using coarse grained molecular dynamics simulations. Simple deflation of a spontaneously formed spherical vesicle results in oblate ellipsoid and discous vesicles. However, when the hydration of the lipids in the outer membrane leaflet is increased, which can be the result of a changed pH or ion concentration, prolate ellipsoid, pear-shaped and budded vesicles are formed. Under certain conditions the deflation even results in vesicle fission. The simulations also show that vesicles formed by a bilayer to vesicle transition are, although spontaneously formed, not immediately stress-free. Instead, the membrane is stretched during the final stage of the transition and only reaches equilibrium once the excess interior water has diffused across the membrane. This suggests the presence of residual membrane stress immediately after vesicle closure in experimental vesicle formation and is especially important for MD simulations of vesicles where the time scale to reach equilibrium is out of reach.

Consequences of Cooperativity in Racemizing Supramolecular Systems

Saluting the sergeant: Phg-BTA (see scheme) cooperatively self-assembles into helical aggregates and shows unprecedented racemization behavior in the presence of base. In thermodynamically controlled conditions, the addition of a small amount of chiral auxiliary to this mixture results in a deracemization reaction and a final enantiomeric excess of 32 %. A theoretical model is presented to understand in detail the results obtained.