Fragmentation and Coagulation in Supramolecular (Co)polymerization Kinetics

Distinct seed topologies enable comparison of elongation and secondary nucleation pathways in seeded supramolecular polymerization

The influence of seed topologies on seeded supramolecular polymerization was examined using helicoidal and toroidal supramolecular polymer seeds. The addition of these seeds to a supersaturated solution of monomers led to distinct nucleation-growth kinetics, which were attributed to the significant difference between the elongation from helicoid termini and secondary nucleation catalyzed by the toroid surface.

Theoretical and computational methodologies for understanding coordination self-assembly complexes

This perspective highlights three theoretical and computational methods to capture the coordination self-assembly processes at the molecular level: quantum chemical modeling, molecular dynamics, and reaction network analysis. These methods cover the different scales from the metal-ligand bond to a more global aspect, and approaches that are best suited to understand the coordination self-assembly from different perspectives are introduced. Theoretical and numerical researches based on these methods are not merely ways of interpreting the experimental studies but complementary to them.

Molecular communications in complex systems of dynamic supramolecular polymers

Supramolecular polymers are composed of monomers that self-assemble non-covalently, generating distributions of monodimensional fibres in continuous communication with each other and with the surrounding solution. Fibres, exchanging molecular species, and external environment constitute a sole complex system, which intrinsic dynamics is hard to elucidate. Here we report coarse-grained molecular simulations that allow studying supramolecular polymers at the thermodynamic equilibrium, explicitly showing the complex nature of these systems, which are composed of exquisitely dynamic molecular entities. Detailed studies of molecular exchange provide insights into key factors controlling how assemblies communicate with each other, defining the equilibrium dynamics of the system. Using minimalistic and finer chemically relevant molecular models, we observe that a rich concerted complexity is intrinsic in such self-assembling systems. This offers a new dynamic and probabilistic (rather than structural) picture of supramolecular polymer systems, where the travelling molecular species continuously shape the assemblies that statistically emerge at the equilibrium.

The dynamic structure of supramolecular polymers is challenging to determine both in experiments and in simulations. Here the authors use coarse-grained molecular models to provide a comprehensive analysis of the molecular communication in these complex molecular systems.

Kinetic and structural roles for the surface in guiding SAS-6 self-assembly to direct centriole architecture

Discovering mechanisms governing organelle assembly is a fundamental pursuit in biology. The centriole is an evolutionarily conserved organelle with a signature 9-fold symmetrical chiral arrangement of microtubules imparted onto the cilium it templates. The first structure in nascent centrioles is a cartwheel, which comprises stacked 9-fold symmetrical SAS-6 ring polymers emerging orthogonal to a surface surrounding each resident centriole. The mechanisms through which SAS-6 polymerization ensures centriole organelle architecture remain elusive. We deploy photothermally-actuated off-resonance tapping high-speed atomic force microscopy to decipher surface SAS-6 self-assembly mechanisms. We show that the surface shifts the reaction equilibrium by ~10⁴ compared to solution. Moreover, coarse-grained molecular dynamics and atomic force microscopy reveal that the surface converts the inherent helical propensity of SAS-6 polymers into 9-fold rings with residual asymmetry, which may guide ring stacking and impart chiral features to centrioles and cilia. Overall, our work reveals fundamental design principles governing centriole assembly.

The centriole exhibits an evolutionarily conserved 9-fold radial symmetry that stems from a cartwheel containing vertically stacked ring polymers that harbor 9 homodimers of the protein SAS-6. Here the authors show how dual properties inherent to surface-guided SAS-6 self-assembly possess spatial information that dictates correct scaffolding of centriole architecture.

Metal Ion Interactions with mAbs: Part 2. Zinc-Mediated Aggregation of IgG1 Monoclonal Antibodies

PURPOSE

To evaluate the physical and chemical degradation of monoclonal antibodies in the presence of Zn²⁺.

METHODS

A full length IgG1 monoclonal antibody (mAb1) was formulated with various amounts of Zn²⁺. The resulting mixture was incubated for several weeks at room temperature and analyzed using a variety of biochemical techniques to look for various physical (e.g. aggregation) and chemical (e.g. fragmentation) degradation pathways.

RESULTS

mAb1 of the IgG1 subclass undergoes aggregation in the presence of Zn²⁺ in a concentration dependent manner. Up to hexamers were characterized using SEC-MALS. No fragmentation was noticed in the presence of Zn²⁺ as opposed to that found in our previous report when IgG1 mAbs were incubated in the presence of Cu²⁺ ions. Site directed mutagenesis indicated the involvement of Fc histidine (His 310) in Zn²⁺ mediated aggregation.

CONCLUSIONS

A novel metal ion mediated isodesmic aggregation mechanism was found in IgG1 class of monoclonal antibodies. Histidine residues in the Fc region were determined to be the binding site and implicated in Zn²⁺ mediated aggregation.

A dissipative pathway for the structural evolution of DNA fibres

Biochemical networks interconnect, grow and evolve to express new properties as different chemical pathways are selected during a continuous cycle of energy consumption and transformation. In contrast, synthetic systems that push away from equilibrium usually return to the same self-assembled state, often generating waste that limits system recyclability and prevents the formation of adaptable networks. Here we show that annealing by slow proton dissipation selects for otherwise inaccessible morphologies of fibres built from DNA and cyanuric acid. Using single-molecule fluorescence microscopy, we observe that proton dissipation influences the growth mechanism of supramolecular polymerization, healing gaps within fibres and converting highly branched, interwoven networks into nanocable superstructures. Just as the growth kinetics of natural fibres determine their structural attributes to modulate function, our system of photoacid-enabled depolymerization and repolymerization selects for healed materials to yield organized, robust fibres. Our method provides a chemical route for error-checking, distinct from thermal annealing, that improves the morphologies and properties of supramolecular materials using out-of-equilibrium systems.

Pathway Complexity in Supramolecular Porphyrin Self-Assembly at an Immiscible Liquid-Liquid Interface

Nanostructures that are inaccessible through spontaneous thermodynamic processes may be formed by supramolecular self-assembly under kinetic control. In the past decade, the dynamics of pathway complexity in self-assembly have been elucidated through kinetic models based on aggregate growth by sequential monomer association and dissociation. Immiscible liquid–liquid interfaces are an attractive platform to develop well-ordered self-assembled nanostructures, unattainable in bulk solution, due to the templating interaction of the interface with adsorbed molecules. Here, we report time-resolved in situ UV–vis spectroscopic observations of the self-assembly of zinc(II) meso-tetrakis(4-carboxyphenyl)porphyrin (ZnTPPc) at an immiscible aqueous–organic interface. We show that the kinetically favored metastable J-type nanostructures form quickly, but then transform into stable thermodynamically favored H-type nanostructures. Numerical modeling revealed two parallel and competing cooperative pathways leading to the different porphyrin nanostructures. These insights demonstrate that pathway complexity is not unique to self-assembly processes in bulk solution and is equally valid for interfacial self-assembly. Subsequently, the interfacial electrostatic environment was tuned using a kosmotropic anion (citrate) in order to influence the pathway selection. At high concentrations, interfacial nanostructure formation was forced completely down the kinetically favored pathway, and only J-type nanostructures were obtained. Furthermore, we found by atomic force microscopy and scanning electron microscopy that the J- and H-type nanostructures obtained at low and high citric acid concentrations, respectively, are morphologically distinct, which illustrates the pathway-dependent material properties.

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.

Dual self-assembly of supramolecular peptide nanotubes to provide stabilisation in water

Self-assembling peptides have the ability to spontaneously aggregate into large ordered structures. The reversibility of the peptide hydrogen bonded supramolecular assembly make them tunable to a host of different applications, although it leaves them highly dynamic and prone to disassembly at the low concentration needed for biological applications. Here we demonstrate that a secondary hydrophobic interaction, near the peptide core, can stabilise the highly dynamic peptide bonds, without losing the vital solubility of the systems in aqueous conditions. This hierarchical self-assembly process can be used to stabilise a range of different β-sheet hydrogen bonded architectures.

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.

Supramolecular Block Copolymers by Seeded Living Polymerization of Perylene Bisimides

Living covalent polymerization has been a subject of intense research for many decades and has culminated in the synthesis of a large variety of block copolymers (BCPs) with structural and functional diversity. In contrast, the research on supramolecular BCPs is still in its infancy and their generation by living processes remains a challenge. Here we report the formation of supramolecular block copolymers by two-component seeded living polymerization of properly designed perylene bisimides (PBIs) under precise kinetic control. Our detailed studies on thermodynamically and kinetically controlled supramolecular polymerization of three investigated PBIs, which contain hydrogen-bonding amide side groups in imide position and chlorine, methoxy, or methylthio substituents in 1,7 bay-positions, revealed that these PBIs form kinetically metastable H-aggregates, which can be transformed into the thermodynamically favored J-aggregates by seed-induced living polymerization. We show here that copolymerization of kinetically trapped states of one PBI with seeds of another PBI leads to the formation of supramolecular block copolymers by chain-growth process from the seed termini as confirmed by UV/vis spectroscopy and atomic force microscopy (AFM). This work demonstrates for the first time the formation of triblock supramolecular polymer architectures with A-B-A and B-A-B block pattern by alternate two-component seeded polymerization in a living manner.

Insights into the Kinetics of Supramolecular Comonomer Incorporation in Water

Multicomponent supramolecular polymers are a versatile platform to prepare functional architectures, but a few studies have been devoted to investigate their noncovalent synthesis. Here, we study supramolecular copolymerizations by examining the mechanism and time scales associated with the incorporation of new monomers in benzene-1,3,5-tricarboxamide (BTA)-based supramolecular polymers. The BTA molecules in this study all contain three tetra(ethylene glycol) chains at the periphery for water solubility but differ in their alkyl chains that feature either 10, 12 or 13 methylene units. C₁₀BTA does not form ordered supramolecular assemblies, whereas C₁₂BTA and C₁₃BTA both form high aspect ratio supramolecular polymers. First, we illustrate that C₁₀BTA can mix into the supramolecular polymers based on either C₁₂BTA or C₁₃BTA by comparing the temperature response of the equilibrated mixtures to the temperature response of the individual components in water. Subsequently, we mix C₁₀BTA with the polymers and follow the copolymerization over time with UV spectroscopy and hydrogen/deuterium exchange mass spectrometry experiments. Interestingly, the time scales obtained in both experiments reveal significant differences in the rates of copolymerization. Coarse-grained simulations are used to study the incorporation pathway and kinetics of the C₁₀BTA monomers into the different polymers. The results demonstrate that the kinetic stability of the host supramolecular polymer controls the rate at which new monomers can enter the existing supramolecular polymers.

Hetero-association models of non-covalent molecular complexation

The present review discusses the current state-of-the-art in building models enabling the description of non-covalent equilibrium complexation of different types of molecules in solution, which results in the formation of supramolecular structures different in length and composition (hetero-association or supramolecular multicomponent co-polymerisation). The description is focused on standard physical and chemical quantities such as experimental observables and equilibrium parameters of interaction (equilibrium constants and concentrations). The major partial cases of the hetero-association models, such as finite and indefinite isodesmic and cooperative complexations, and Benesi-Hildebrand and Langmuir adsorption models are considered. Future challenges in the development of the hetero-association models are provided.

Regression Analysis for Nucleation-Elongation Model of Supramolecular Assembly: How To Determine Nucleus Size

Nucleation-elongation is known to give satisfactory descriptions of many supramolecular polymerization systems in thermal equilibrium. Its key feature is the necessity to form a "nucleus" consisting of a certain number of monomer units before being able to grow into a longer polymer chain. The size of the nucleus has significant implications for the understanding of the supramolecular polymerization mechanism. Here we investigate how experiments can give information on the nucleus size by regression analysis of various types of measurements. The measurements of free monomer concentrations, diffusion coefficients, and calorimetric response as functions of concentration or temperature are considered. The nucleation-elongation model with a general value for the nucleus size is used to provide mathematical expressions for these experimental observables. Numerical experiments are performed where experimental errors are simulated by computer-generated random numbers, and it is investigated whether least-squares fitting analyses can give the correct values of the nucleus size in the presence of experimental errors. It is recommended that the calorimetric measurements such as differential scanning calorimetry (DSC) or isothermal titration calorimetry (ITC) be performed under various conditions to correctly determine the nucleus size experimentally.

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.

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.

Directed assembly of functionalized nanoparticles with amphiphilic diblock copolymers

We theoretically propose a simple approach to achieve soft nanoparticles with a self-patchiness nature, which are further directed to assemble into a rich variety of highly ordered superstructures.

Modeling the Kinetics of Open Self-Assembly

In this work, we explore theoretically the kinetics of molecular self-assembly in the presence of constant monomer flux as an input, and a maximal size. The proposed model is supposed to reproduce the dynamics of viral self-assembly for enveloped virus. It turns out that the kinetics of open self-assembly is rather quantitatively different from the kinetics of similar closed assembly. In particular, our results show that the convergence toward the stationary state is reached through assembly waves. Interestingly, we show that the production of complete clusters is much more efficient in the presence of a constant input flux, rather than providing all monomers at the beginning of the self-assembly.