On the role of membrane embedding, protein rigidity and transmembrane length in lipid membrane fusion.

The fusion of biological membranes is ubiquitous in natural processes like exo- and endocytosis, intracellular trafficking and viral entry. Membrane fusion is also utilized in artificial biomimetic fusion systems, e.g. for drug delivery. Both the natural and the biomimetic fusion systems rely on a wide range of (artificial) proteins mediating the fusion process. Although the exact mechanisms of these proteins differ, clear analogies in their general behavior can be observed in bringing the membranes in close proximity and mediating the fusion reaction. In our study, we use molecular dynamics simulations with coarse grained models, mimicking the general behavior of fusion proteins (spikes), to systematically examine the effects of specific characteristics of these proteins on the fusion process. The protein characteristics considered are (i) the type of membrane embedding, i.e., either transmembrane or not, (ii) the rigidity, and (iii) the transmembrane domain (TMD) length. The results show essential differences in fusion pathway between monotopic and transmembrane spikes, in which transmembrane spikes seem to inhibit the formation of hemifusion diaphragms, leading to a faster fusion development. Furthermore, we observed that an increased rigidity and a decreased TMD length both proved to contribute to a faster fusion development. Finally, we show that a single spike may suffice to successfully induce a fusion reaction, provided that the spike is sufficiently rigid and attractive. Not only does this shed light on biological fusion of membranes, it also provides clear design rules for artificial membrane fusion systems.

Unequal Perylene Diimide Twins in a Quadruple Assembly.

Natural light-harvesting (LH) systems can divide identical dyes into unequal aggregate states, thereby achieving intelligent "allocation of labor". From a synthetic point of view, the construction of such kinds of unequal and integrated systems without the help of proteinaceous scaffolding is challenging. Here, we show that four octatetrayne-bridged ortho-perylene diimide (PDI) dyads (POPs) self-assemble into a quadruple assembly (POP)4 both in solution and in the solid state. The two identical PDI units in each POP are compartmentalized into weakly coupled PDIs (P520) and closely stacked PDIs (P550) in (POP)4 . The two extreme pools of PDI chromophores were unambiguously confirmed by single-crystal X-ray crystallography and NMR spectroscopy. To interpret the formation of the discrete quadruple assembly, we also developed a two-step cooperative model. Quantum-chemical calculations indicate the existence of multiple couplings within and across P520 and P550, which can satisfactorily describe the photophysical properties of the unequal quadruple assembly. This finding is expected to help advance the rational design of dye stacks to emulate functions of natural LH systems.

Photodynamic Control of the Chain Length in Supramolecular Polymers: Switching an Intercalator into a Chain Capper.

Supramolecular systems are intrinsically dynamic and sensitive to changes in molecular structure and external conditions. Because of these unique properties, strategies to control polymer length, composition, comonomer sequence, and morphology have to be developed for sufficient control over supramolecular copolymerizations. We designed photoresponsive, mono acyl hydrazone functionalized benzene-1,3,5-tricarboxamide (m-BTA) monomers that play a dual role in the coassembly with achiral alkyl BTAs (a-BTA). In the E isomer form, the chiral m-BTA monomers intercalate into stacks of a-BTA and dictate the chirality of the helices. Photoisomerization to the Z isomer transforms the intercalator into a chain capper, allowing dynamic shortening of chain length in the supramolecular aggregates. We combine optical spectroscopy and light-scattering experiments with theoretical modeling to show the reversible decrease in length when switching from the E to Z isomer of m-BTA in the copolymer with inert a-BTA. With a mass-balance thermodynamic model, we gain additional insights into the composition of copolymers and length distributions of the species over a broad range of concentrations and mixing ratios of a-BTA/m-BTA. Moreover, the model was used to predict the impact of an additive (chain capper and intercalator) on the chain length over a range of concentrations, showing a remarkable amplification of efficiency at high concentrations. By employing a stimuli-responsive comonomer in a mostly inert polymer, we can cooperatively amplify the effect of the switching and obtain photocontrol of polymer length. Moreover, this dynamic decrease in chain length causes a macroscopic gel-to-sol phase transformation of the copolymer gel, although 99.4% of the organogel is inert to the light stimulus.

Mass-Balance Models for Scrutinizing Supramolecular (Co)polymerizations in Thermodynamic Equilibrium.

Recent years have witnessed increasing attention on supramolecular polymerization, i.e., the formation of one-dimensional aggregates in which the monomeric units bind together via reversible and usually highly directional non-covalent interactions. Because of the presence of these reversible interactions, such as hydrogen bonding, π-π interactions, or metal coordination, supramolecular polymers exhibit numerous desirable properties ranging from high thermoresponsiveness to self-healing and great capacity for processability and recycling. These properties relate to intriguing experimentally observed nonlinear effects such as the monomer-dependent presence of a critical temperature for aggregation and a solvent- and temperature-tunable aggregate morphology. For coassemblies this is complemented with monomer-ratio- and monomer-compatibility-dependent internal order as well as majority-rules-type chiral amplification. However, the dynamic nature of the (co)polymers and the intricate interplay of many interactions make these effects difficult to rationalize without theoretical models. This Account presents recent advances in the development and use of equilibrium models for supramolecular copolymerization based on mass balances, mainly developed by our group. The basic idea of these models is that we describe a supramolecular (co)polymerization by a set of independent equilibrium reactions, like monomer associations and dissociations, and that in thermodynamic equilibrium the concentrations of the reactants and products in each reaction are coupled via the equilibrium constant of that reaction. Recursion then allows the concentration of each possible aggregate to be written as a function of the free monomer concentrations. Because a monomer should be present either as a free monomer or in one of the aggregates, a set of n equations can be formed with the n free monomer concentrations as the only unknowns. This set of mass-balance equations can then be solved numerically, yielding the free monomer concentrations, from which the complete system can be reconstituted. By a step-by-step extension of the model for the aggregation of a single monomer type to include the formation of multiple aggregate types and the coassembly of multiple monomer types, we can capture increasingly complex supramolecular (co)polymerizations. In each step we illustrate how the extended model explains in detail another of the experimentally observed nonlinear effects, with the common denominator that small differences in association energies are intricately amplified at the supramolecular level. We finally arrive at our latest and most general approach to modeling (cooperative) supramolecular (co)polymerization, which encompasses all of our earlier models and shows great promise to help rationalize also future systems featuring ever-increasing complexity.

Designed Asymmetric Protein Assembly on a Symmetric Scaffold.

Cellular signaling is regulated by the assembly of proteins into higher-order complexes. Bottom-up creation of synthetic protein assemblies, especially asymmetric complexes, is highly challenging. Presented here is the design and implementation of asymmetric assembly of a ternary protein complex facilitated by Rosetta modeling and thermodynamic analysis. The wild-type symmetric CT32-CT32 interface of the 14-3-3-CT32 complex was targeted, ultimately favoring asymmetric assembly on the 14-3-3 scaffold. Biochemical studies, supported by mass-balance models, allowed characterization of the parameters driving asymmetric assembly. Importantly, our work reveals that both the individual binding affinities and cooperativity between the assembling components are crucial when designing higher-order protein complexes. Enzyme complementation on the 14-3-3 scaffold highlighted that interface engineering of a symmetric ternary complex generates asymmetric protein complexes with new functions.

Unexpectedly Strong Chiral Amplification of Chiral/Achiral and Chiral/Chiral Copolymers of Biphenylylacetylenes and Further Enhancement/Inversion and Memory of the Macromolecular Helicity.

We report an unexpectedly strong amplification of the macromolecular helicity in dynamic helical copolymers of chiral/achiral and chiral/chiral ( R/ S) biphenylylacetylenes in which the chiral residues are remote from the biphenyl pendants and further from the main chains. The copolymers consisting of 20 mol % chiral monomers and chiral monomers of 20% enantiomeric excess (ee) showed a full induced circular dichroism as intense as that of the chiral homopolymer. In contrast, an analogous poly(phenylacetylene) bearing the identical chiral residue (100% ee) showed no circular dichroism in the polymer backbone, indicating the critical role of the biphenyl moieties in the observed high chiral amplification. As anticipated, the helix-sense excesses of the copolymer backbones composed of a small amount of chiral units (<20 mol %) and chiral units of low ee (<20%) were reduced. Interestingly, however, the macromolecular helicity of the copolymers was further drastically enhanced as a greater excess of a one-handed helix or inverted upon noncovalent interaction with nonracemic alcohols and subsequently retained (memorized) after complete removal of the chiral alcohol. Even in a polymer consisting of completely racemic repeating units, one-handed right- and left-handed helices could almost be induced and memorized. These unique hierarchical amplifications and memory of the macromolecular helicity in the copolymers by the covalent and further noncovalent chiral interactions are quantitatively explained on the basis of a linear Ising model.

Tuning the Length of Cooperative Supramolecular Polymers under Thermodynamic Control.

In the field of supramolecular (co)polymerizations, the ability to predict and control the composition and length of the supramolecular (co)polymers is a topic of great interest. In this work, we elucidate the mechanism that controls the polymer length in a two-component cooperative supramolecular polymerization and unveil the role of the second component in the system. We focus on the supramolecular copolymerization between two derivatives of benzene-1,3,5-tricarboxamide (BTA) monomers: a-BTA and Nle-BTA. As a single component, a-BTA cooperatively polymerizes into long supramolecular polymers, whereas Nle-BTA only forms dimers. By mixing a-BTA and Nle-BTA in different ratios, two-component systems are obtained, which are analyzed in-depth by combining spectroscopy and light-scattering techniques with theoretical modeling. The results show that the length of the supramolecular polymers formed by a-BTA is controlled by competitive sequestration of a-BTA monomers by Nle-BTA, while the obvious alternative Nle-BTA acts as a chain-capper is not operative. This sequestration of a-BTA leads to short, stable species coexisting with long cooperative aggregates. The analysis of the experimental data by theoretical modeling elucidates the thermodynamic parameters of the copolymerization, the distributions of the various species, and the composition and length of the supramolecular polymers at various mixing ratios of a-BTA and Nle-BTA. Moreover, the model was used to generalize our results and to predict the impact of adding a chain-capper or a competitor on the length of the cooperative supramolecular polymers under thermodynamic control. Overall, this work unveils comprehensive guidelines to master the nature of supramolecular (co)polymers and brings the field one step closer to applications.

Competing Interactions in Hierarchical Porphyrin Self-Assembly Introduce Robustness in Pathway Complexity.

Pathway complexity in supramolecular polymerization has recently sparked interest as a method to generate complex material behavior. The response of these systems relies on the existence of a metastable, kinetically trapped state. In this work, we show that strong switch-like behavior in supramolecular polymers can also be achieved through the introduction of competing aggregation pathways. This behavior is illustrated with the supramolecular polymerization of a porphyrin-based monomer at various concentrations, solvent compositions, and temperatures. It is found that the monomers aggregate via an isodesmic mechanism in weakly coupled J-type aggregates at intermediate solvent quality and temperature, followed by nucleated H-aggregates at lower solvent qualities and temperatures. At further increased thermodynamic driving forces, such as high concentration and low temperature, the H-aggregates can form hierarchical superhelices. Our mathematical models show that, contrary to a single-pathway polymerization, the existence of the isodesmic aggregation pathway buffers the free monomer pool and renders the nucleation of the H-aggregates insensitive to concentration changes in the limit of high concentrations. We also show that, at a given temperature or solvent quality, the thermodynamically stable aggregate morphology can be selected by controlling the remaining free external parameter. As a result, the judicious application of pathway complexity allows us to synthesize a diverse set of materials from only a single monomer. We envision that the engineering of competing pathways can increase the robustness in a wide variety of supramolecular polymer materials and lead to increasingly versatile applications.

Supramolecular Block Copolymers under Thermodynamic Control.

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.

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.

Non-equilibrium supramolecular polymerization.

Supramolecular polymerization has been traditionally focused on the thermodynamic equilibrium state, where one-dimensional assemblies reside at the global minimum of the Gibbs free energy. The pathway and rate to reach the equilibrium state are irrelevant, and the resulting assemblies remain unchanged over time. In the past decade, the focus has shifted to kinetically trapped (non-dissipative non-equilibrium) structures that heavily depend on the method of preparation (i.e., pathway complexity), and where the assembly rates are of key importance. Kinetic models have greatly improved our understanding of competing pathways, and shown how to steer supramolecular polymerization in the desired direction (i.e., pathway selection). The most recent innovation in the field relies on energy or mass input that is dissipated to keep the system away from the thermodynamic equilibrium (or from other non-dissipative states). This tutorial review aims to provide the reader with a set of tools to identify different types of self-assembled states that have been explored so far. In particular, we aim to clarify the often unclear use of the term "non-equilibrium self-assembly" by subdividing systems into dissipative, and non-dissipative non-equilibrium states. Examples are given for each of the states, with a focus on non-dissipative non-equilibrium states found in one-dimensional supramolecular polymerization.

Supramolecular Copolymers: Structure and Composition Revealed by Theoretical Modeling.

Supramolecular copolymers, non-covalent analogues of synthetic copolymers, constitute a new and promising class of polymers. In contrast to their covalent counterparts, the details of their mechanism of formation, as well as the factors determining their composition and length, are still poorly understood. Here, the supramolecular copolymerization between two slightly structurally different benzene-1,3,5-tricarboxamide (BTA) monomers functionalized with either oligodimethylsiloxane (oDMSi) or alkyl side chains is unraveled by combining experimental and theoretical approaches. By applying the "sergeant-and-soldiers" approach using circular dichroism (CD) experiments, we are able to obtain detailed insights into the structure and composition of these supramolecular copolymers. Moreover, we observe an unexpected chiral induction upon mixing two independently CD-silent solutions of the achiral (soldier) and chiral (sergeant) monomers. We find that the subtle differences in the chemical structure of the two monomers impact their homopolymerization mechanism: whereas alkyl-BTAs cooperatively self-assemble, oDMSi-BTAs self-assemble in an isodesmic manner. The effect of these mechanistic differences in the supramolecular copolymerization process is investigated as a function of the composition of the two monomers and explicitly rationalized by mathematical modeling. The results show that, at low fractions of oDMSi-BTA sergeants (<10 mol%), the polymerization process is cooperative and the supramolecular helicity is biased toward the helical preference of the sergeant. However, at higher fractions of oDMSi-BTA sergeant (>25 mol%), the isodesmic assembly of the increasing amounts of sergeant becomes more dominant, and different species start to coexist in the copolymerization process. The analysis of the experimental data with a newly developed theoretical model allows us to quantify the thermodynamic parameters, the distribution of different species, and the compositions and stack lengths of the formed supramolecular copolymers existing at various feed ratios of the two monomers.

Model-driven optimization of multicomponent self-assembly processes.

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.

Programmable chemical reaction networks: emulating regulatory functions in living cells using a bottom-up approach.

Living cells are able to produce a wide variety of biological responses when subjected to biochemical stimuli. It has become apparent that these biological responses are regulated by complex chemical reaction networks (CRNs). Unravelling the function of these circuits is a key topic of both systems biology and synthetic biology. Recent progress at the interface of chemistry and biology together with the realisation that current experimental tools are insufficient to quantitatively understand the molecular logic of pathways inside living cells has triggered renewed interest in the bottom-up development of CRNs. This builds upon earlier work of physical chemists who extensively studied inorganic CRNs and showed how a system of chemical reactions can give rise to complex spatiotemporal responses such as oscillations and pattern formation. Using purified biochemical components, in vitro synthetic biologists have started to engineer simplified model systems with the goal of mimicking biological responses of intracellular circuits. Emulation and reconstruction of system-level properties of intracellular networks using simplified circuits are able to reveal key design principles and molecular programs that underlie the biological function of interest. In this Tutorial Review, we present an accessible overview of this emerging field starting with key studies on inorganic CRNs followed by a discussion of recent work involving purified biochemical components. Finally, we review recent work showing the versatility of programmable biochemical reaction networks (BRNs) in analytical and diagnostic applications.

Allosterically controlled threading of polymers through macrocyclic dimers.

As part of an ongoing study to construct a molecular Turing machine in which a polymer chain is encoded via allosteric information transfer between macrocyclic complexes, we describe the thermodynamic and kinetic characterization of a multicomponent self-assembled system based on a zinc porphyrin macrocyclic compound, a bidentate ligand (1,4-diazabicyclo[2.2.2]octane, DABCO), and a viologen-substituted polymer guest. Initial addition of DABCO to the porphyrin macrocycle in chloroform solution leads to the formation of a stable 2:1 (porphyrin:DABCO) dimeric complex, even under dilute conditions, by means of strong cooperative interactions involving hydrogen and metal-ligand bonds. Further titration of the porphyrin-DABCO mixtures with the polymer gives rise to a complex array of species in the solution. The system is analyzed in detail by a combination of spectroscopic measurements and computational modeling. Each association constant in the binding scheme and the fraction of each individual complex that is formed in solution are determined precisely using a mass-balance model. Kinetic studies revealed that the rates of the polymer threading and dethreading in and out of the dimeric system are remarkably slow, indicating that the polymer is locked inside the cavity of the stable 2:1 dimeric complex as a result of strong allosteric interactions.

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.

Computer simulations of cellular group selection reveal mechanism for sustaining cooperation.

We present a computer simulation of group selection that is inspired by proto-cell division. Two types of replicating molecules, cooperators and defectors, reside inside membrane bound compartments. Cooperators pay a cost for other replicators in the cell to receive a benefit. Defectors pay no cost and distribute no benefits. The total population size fluctuates as a consequence of births and deaths of individual replicators. Replication requires activated substrates that are generated at a constant rate. Our model includes mutation between cooperators and defectors and selection on two levels: within proto-cells and between proto-cells. We find surprising similarities and differences between models with and without cell death. In both cases, a necessary requirement for group selection to favor some level of cooperation is the continuous formation of a minimum fraction of pure cooperator groups. Subsequently these groups become undermined by defectors, because of mutation and selection within cells. Cell division mechanisms which generate pure cooperator groups more efficiently are stronger promoters of cooperation. For example, division of a proto-cell into many daughter cells is more powerful in enhancing cooperation than division into two daughter cells. Our model differs from previous studies of group selection in that we explore a variety of different features and relax several restrictive assumptions that would be needed for analytic calculations.

Threshold sensing through a synthetic enzymatic reaction-diffusion network.

A wet stamping method to precisely control concentrations of enzymes and inhibitors in place and time inside layered gels is reported. By combining enzymatic reactions such as autocatalysis and inhibition with spatial delivery of components through soft lithographic techniques, a biochemical reaction network capable of recognizing the spatial distribution of an enzyme was constructed. The experimental method can be used to assess fundamental principles of spatiotemporal order formation in chemical reaction networks.

Ultrasensitivity by molecular titration in spatially propagating enzymatic reactions.

Delineating design principles of biological systems by reconstitution of purified components offers a platform to gauge the influence of critical physicochemical parameters on minimal biological systems of reduced complexity. Here we unravel the effect of strong reversible inhibitors on the spatiotemporal propagation of enzymatic reactions in a confined environment in vitro. We use micropatterned, enzyme-laden agarose gels which are stamped on polyacrylamide films containing immobilized substrates and reversible inhibitors. Quantitative fluorescence imaging combined with detailed numerical simulations of the reaction-diffusion process reveal that a shallow gradient of enzyme is converted into a steep product gradient by addition of strong inhibitors, consistent with a mathematical model of molecular titration. The results confirm that ultrasensitive and threshold effects at the molecular level can convert a graded input signal to a steep spatial response at macroscopic length scales.