Straightforward model construction and analysis of multicomponent biomolecular systems in equilibrium.

Mathematical modelling of molecular systems can be extremely helpful in elucidating complex phenomena in (bio)chemistry. However, equilibrium conditions in systems consisting of more than two components, such as for molecular glues bound to two proteins, can typically not be analytically determined without assumptions and (semi-)numerical models are not trivial to derive by the non-expert. Here we present a framework for equilibrium models, geared towards molecular glues and other contemporary multicomponent chemical biology challenges. The framework utilizes a general derivation method capable of generating custom mass-balance models for equilibrium conditions of complex molecular systems, based on the simple, reversible biomolecular reactions describing these systems. Several chemical biology concepts are revisited via the framework to demonstrate the simplicity, generality and validity of the approach. The ease of use of the framework and the ability to both analyze systems and gain additional insights in the underlying parameters driving equilibria formation strongly aids the analysis and understanding of biomolecular systems. New directions for research and analysis are brought forward based on the model formation and system and parameter analysis. This conceptual framework severely reduces the time and expertise requirements which currently impede the broad integration of such valuable equilibrium models into molecular glue development and chemical biology research.

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.

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.

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.

Proximity-induced caspase-9 activation on a DNA origami-based synthetic apoptosome.

Living cells regulate key cellular processes by spatial organisation of catalytically active proteins in higher-order signalling complexes. These act as organising centres to facilitate proximity-induced activation and inhibition of multiple intrinsically weakly associating signalling components, which makes elucidation of the underlying protein-protein interactions challenging. Here we show that DNA origami nanostructures provide a programmable molecular platform for the systematic analysis of signalling proteins by engineering a synthetic DNA origami-based version of the apoptosome, a multi-protein complex that regulates apoptosis by co-localizing multiple caspase-9 monomers. Tethering of both wildtype and inactive caspase-9 variants to a DNA origami platform demonstrates that enzymatic activity is induced by proximity-driven dimerization with half-of-sites reactivity, and additionally, reveals a multivalent activity enhancement in oligomers of three and four enzymes. Our results offer fundamental insights in caspase-9 activity regulation and demonstrate that DNA origami-based protein assembly platforms have the potential to inform the function of other multi-enzyme complexes involved in inflammation, innate immunity and cell death.

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.

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.

Detailed Approach to Investigate Thermodynamically Controlled Supramolecular Copolymerizations.

Elucidating the microstructure of supramolecular copolymers remains challenging, despite the progress in the field of supramolecular polymers. In this work, we present a detailed approach to investigate supramolecular copolymerizations under thermodynamic control. Our approach provides insight into the interactions of different types of monomers and hereby allows elucidating the microstructure of copolymers. We select two monomers that undergo cooperative supramolecular polymerization by way of threefold intermolecular hydrogen bonding in a helical manner, namely, benzene-1,3,5-tricarboxamide (BTA) and benzene-1,3,5-tris(carbothioamide) (thioBTA). Two enantiomeric forms and an achiral analogue of BTA and thioBTA are synthesized and their homo- and copolymerizations are studied using light scattering techniques, infrared, ultraviolet, and circular dichroism spectroscopy. After quantifying the thermodynamic parameters describing the homopolymerizations, we outline a method to follow the self-assembly of thioBTA derivatives in the copolymerization with BTA, which involves monitoring a characteristic spectroscopic signature as a function of temperature and relative concentration. Using modified types of sergeants-and-soldiers and majority-rules experiments, we obtain insights into the degree of aggregation and the net helicity. In addition, we apply a theoretical model of supramolecular copolymerization to substantiate the experimental results. We find that the model describes the two-component system well and allows deriving the hetero-interaction energies. The interactions between the same kinds of monomers (BTA-BTA and thioBTA-thioBTA) are slightly more favorable than those between different monomers (BTA-thioBTA), corresponding to a nearly random copolymerization. Finally, to study the interactions of the monomers at the molecular level, we perform density functional theory-based computations. The results corroborate that the two-component system exhibits a random distribution of the two monomer units along the copolymer chain.

Counterion-Dependent Mechanisms of DNA Origami Nanostructure Stabilization Revealed by Atomistic Molecular Simulation.

The DNA origami technique has proven to have tremendous potential for therapeutic and diagnostic applications like drug delivery, but the relatively low concentrations of cations in physiological fluids cause destabilization and degradation of DNA origami constructs preventing in vivo applications. To reveal the mechanisms behind DNA origami stabilization by cations, we performed atomistic molecular dynamics simulations of a DNA origami rectangle in aqueous solvent with varying concentrations of magnesium and sodium as well as polyamines like oligolysine and spermine. We explored the binding of these ions to DNA origami in detail and found that the mechanism of stabilization differs between ion types considerably. While sodium binds weakly and quickly exchanges with the solvent, magnesium and spermine bind close to the origami with spermine also located in between helices, stabilizing the crossovers characteristic for DNA origami and reducing repulsion of parallel helices. In contrast, oligolysine of length ten prevents helix repulsion by binding to adjacent helices with its flexible side chains, spanning the gap between the helices. Shorter oligolysine molecules with four subunits are weak stabilizers as they lack both the ability to connect helices and to prevent helix repulsion. This work thus shows how the binding modes of ions influence the stabilization of DNA origami nanostructures on a molecular level.

Equilibrium Model for Supramolecular Copolymerizations.

The coassembly of different building blocks into supramolecular copolymers provides a promising avenue to control their properties and to thereby expand the potential of supramolecular polymers in applications. However, contrary to covalent copolymerization which nowadays can be well controlled, the control over sequence, polymer length, and morphology in supramolecular copolymers is to date less developed, and their structures are more determined by the delicate balance in binding free energies between the distinct building blocks than by kinetics. Consequently, to rationalize the structures of supramolecular copolymers, a thorough understanding of their thermodynamic behavior is needed. Though this is well established for single-component assemblies and over the past years several models have been proposed for specific copolymerization cases, a generally applicable model for supramolecular cooperative copolymers is still lacking. Here, we provide a generalization of our earlier mass-balance models for supramolecular copolymerizations that encompasses all our earlier models. In this model, the binding free energies of each pair of monomer types in each aggregate type can be set independently. We provide scripts to solve the model numerically for any (co)polymerization of one or two types of monomer into an arbitrary number of distinct aggregate types. We illustrate the applicability of the model on data from literature as well as on new experimental data of triarylamine triamide-based copolymers in three distinct solvents. We show that apart from common properties such as the degree of polymerization and length distributions, our approach also allows us to investigate properties such as the copolymer microstructure, that is, the internal ordering of monomers within the copolymers. Moreover, we show that in some cases, also intriguing analytical approximations can be derived from the mass balances.

Multivalency in a Dendritic Host-Guest System.

Multivalency is an important instrument in the supramolecular chemistry toolkit for the creation of strong specific interactions. In this paper we investigate the multivalency effect in a dendritic host-guest system using molecular dynamics simulations. Specifically, we consider urea-adamantyl decorated poly(propyleneimine) dendrimers that together with compatible mono-, bi-, and tetravalent ureidoacetic acid guests can form dynamic patchy nanoparticles. First, we simulate the self-assembly of these particles into macromolecular nanostructures, showing guest-controlled reduction of dendrimer aggregation. Subsequently, we systematically study guest concentration dependent multivalent binding. At low guest concentrations multivalency of the guests clearly increases relative binding as tethered headgroups bind more often than free guests' headgroups. We find that despite an abundance of binding sites, most of the tethered headgroups bind in close proximity, irrespective of the spacer length; nevertheless, longer spacers do increase binding. At high guest concentrations the dendrimer becomes saturated with bound headgroups, independent of guest valency. However, in direct competition the tetravalent guests prevail over the monovalent ones. This demonstrates the benefit of multivalency at high as well as low concentrations.

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.

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.

Elucidation of the origin of chiral amplification in discrete molecular polyhedra.

Chiral amplification in molecular self-assembly has profound impact on the recognition and separation of chiroptical materials, biomolecules, and pharmaceuticals. An understanding of how to control this phenomenon is nonetheless restricted by the structural complexity in multicomponent self-assembling systems. Here, we create chiral octahedra incorporating a combination of chiral and achiral vertices and show that their discrete nature makes these octahedra an ideal platform for in-depth investigation of chiral transfer. Through the construction of dynamic combinatorial libraries, the unique possibility to separate and characterise each individual assembly type, density functional theory calculations, and a theoretical equilibrium model, we elucidate that a single chiral unit suffices to control all other units in an octahedron and how this local amplification combined with the distribution of distinct assembly types culminates in the observed overall chiral amplification in the system. Our combined experimental and theoretical strategy can be applied generally to quantify discrete multi-component self-assembling systems.

Photoisomerization induced scission of rod-like micelles unravelled with multiscale modeling.

HYPOTHESIS: In photorheological fluids, subtle molecular changes caused by light lead to abrupt macroscopic alterations. Upon UV irradiation of an aqueous cetyltrimethylammonium bromide (CTAB) and trans-ortho-methoxycinnamic acid (trans-OMCA) solution, for instance, the viscosity drops over orders of magnitude. Multiscale modeling allows to elucidate the mechanisms behind these photorheological effects. EXPERIMENTS: We use time-dependent DFT calculations to study the photoisomerization, and a combination of atomistic molecular dynamics (MD) and DFT to probe the influence of both OMCA isomers on the micellar solutions. FINDINGS: The time-dependent DFT calculations show that the isomerization pathway occurs in the first triplet excited state with a minimum energy conformation closest to the after photoisomerization predominant cis configuration. In the MD simulations, with sub-microsecond timescales much shorter than the experimental morphological transition, already a clear difference is observed in the packing of the two OMCA isomers: contrary to trans-OMCA, cis-OMCA exposes notable part of its hydrophobic aromatic rings at the micelle surface. This can explain why trans-OMCA adopts rod-like micellar packing (high viscosity) while cis-OMCA spherical micellar packing (low viscosity). Moreover, lowering of the OMCA co-solute concentration allowed us to perform full simulation of the breakup process of the rod-like micelles which are stable prior to isomerization.

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.

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.