Predicting Rubisco-Linker Condensation from Titration in the Dilute Phase.

The condensation of Rubisco holoenzymes and linker proteins into "pyrenoids," a crucial supercharger of photosynthesis in algae, is qualitatively understood in terms of "sticker-and-spacer" theory. We derive semianalytical partition sums for small Rubisco-linker aggregates, which enable the calculation of both dilute-phase titration curves and dimerization diagrams. By fitting the titration curves to surface plasmon resonance and single-molecule fluorescence microscopy data, we extract the molecular properties needed to predict dimerization diagrams. We use these to estimate typical concentrations for condensation, and successfully compare these to microscopy observations.

Correlating fluorescence microscopy, optical and magnetic tweezers to study single chiral biopolymers such as DNA.

Biopolymer topology is critical for determining interactions inside cell environments, exemplified by DNA where its response to mechanical perturbation is as important as biochemical properties to its cellular roles. The dynamic structures of chiral biopolymers exhibit complex dependence with extension and torsion, however the physical mechanisms underpinning the emergence of structural motifs upon physiological twisting and stretching are poorly understood due to technological limitations in correlating force, torque and spatial localization information. We present COMBI-Tweez (Combined Optical and Magnetic BIomolecule TWEEZers), a transformative tool that overcomes these challenges by integrating optical trapping, time-resolved electromagnetic tweezers, and fluorescence microscopy, demonstrated on single DNA molecules, that can controllably form and visualise higher order structural motifs including plectonemes. This technology combined with cutting-edge MD simulations provides quantitative insight into complex dynamic structures relevant to DNA cellular processes and can be adapted to study a range of filamentous biopolymers.

Sticker-and-spacer model for amyloid beta condensation and fibrillation.

A major pathogenic hallmark of Alzheimer's disease is the presence of neurotoxic plaques composed of amyloid beta (Aß) peptides in patients' brains. The pathway of plaque formation remains elusive, though some clues appear to lie in the dominant presence of Aß1 - 42 in these plaques despite Aß1-40 making up approximately 90% of the Aß pool. We hypothesize that this asymmetry is driven by the hydrophobicity of the two extra amino acids that are incorporated in Aß1-42. To investigate this hypothesis at the level of single molecules, we have developed a molecular "sticker-and-spacer lattice model" of unfolded Aß. The model protein has a single sticker that may reversibly dimerise and elongate into semi-flexible linear chains. The growth is hampered by excluded-volume interactions that are encoded by the hydrophilic spacers but are rendered cooperative by the attractive interactions of hydrophobic spacers. For sufficiently strong hydrophobicity, the chains undergo liquid-liquid phase-separation (LLPS) into condensates that facilitate the nucleation of fibers. We find that a small fraction of Aß1-40 in a mixture of Aß1-40 and Aß1-42 shifts the critical concentration for LLPS to lower values. This study provides theoretical support for the hypothesis that LLPS condensates act as a precursor for aggregation and provides an explanation for the Aß1-42-enrichment of aggregates in terms of hydrophobic interactions.

Tween-20 Induces the Structural Remodeling of Single Lipid Vesicles.

The solubilization of lipid membranes by Tween-20 is crucial for a number of biotechnological applications, but the mechanistic details remain elusive. Evidence from ensemble assays supports a solubilization model that encompasses surfactant association with the membrane and the release of mixed micelles to solution, but whether this process also involves intermediate transitions between regimes is unanswered. In search of mechanistic origins, increasing focus is placed on identifying Tween-20 interactions with controllable membrane mimetics. Here, we employed ultrasensitive biosensing approaches, including single-vesicle spectroscopy based on fluorescence and energy transfer from membrane-encapsulated molecules, to interrogate interactions between Tween-20 and submicrometer-sized vesicles below the optical diffraction limit. We discovered that Tween-20, even at concentrations below the critical micellar concentration, triggers stepwise and phase-dependent structural remodeling events, including permeabilization and swelling, in both freely diffusing and surface-tethered vesicles, highlighting the substantial impact the surfactant has on vesicle conformation and stability prior to lysis.

Membraneless organelles formed by liquid-liquid phase separation increase bacterial fitness.

Liquid-liquid phase separation is emerging as a crucial phenomenon in several fundamental cell processes. A range of eukaryotic systems exhibit liquid condensates. However, their function in bacteria, which, in general, lack membrane-bound compartments, remains less clear. Here, we used high-resolution optical microscopy to observe single bacterial aggresomes, nanostructured intracellular assemblies of proteins, to undercover their role in cell stress. We find that proteins inside aggresomes are mobile and undergo dynamic turnover, consistent with a liquid state. Our observations are in quantitative agreement with phase-separated liquid droplet formation driven by interacting proteins under thermal equilibrium that nucleate following diffusive collisions in the cytoplasm. We have found aggresomes in multiple species of bacteria and show that these emergent, metastable liquid-structured protein assemblies increase bacterial fitness by enabling cells to tolerate environmental stresses.

Stretching of Bombyx mori Silk Protein in Flow.

The flow-induced self-assembly of entangled Bombyx mori silk proteins is hypothesised to be aided by the 'registration' of aligned protein chains using intermolecularly interacting 'sticky' patches. This suggests that upon chain alignment, a hierarchical network forms that collectively stretches and induces nucleation in a precisely controlled way. Through the lens of polymer physics, we argue that if all chains would stretch to a similar extent, a clear correlation length of the stickers in the direction of the flow emerges, which may indeed favour such a registration effect. Through simulations in both extensional flow and shear, we show that there is, on the other hand, a very broad distribution of protein-chain stretch, which suggests the registration of proteins is not directly coupled to the applied strain, but may be a slow statistical process. This qualitative prediction seems to be consistent with the large strains (i.e., at long time scales) required to induce gelation in our rheological measurements under constant shear. We discuss our perspective of how the flow-induced self-assembly of silk may be addressed by new experiments and model development.

Power Law Stretching of Associating Polymers in Steady-State Extensional Flow.

We present a tube model for the Brownian dynamics of associating polymers in extensional flow. In linear response, the model confirms the analytical predictions for the sticky diffusivity by Leibler-Rubinstein-Colby theory. Although a single-mode Doi-Edwards-Marrucci-Grizzuti approximation accurately describes the transient stretching of the polymers above a "sticky" Weissenberg number (product of the strain rate with the sticky-Rouse time), the preaveraged model fails to capture a remarkable development of a power law distribution of stretch in steady-state extensional flow: while the mean stretch is finite, the fluctuations in stretch may diverge. We present an analytical model that shows how strong stochastic forcing drives the long tail of the distribution, gives rise to rare events of reaching a threshold stretch, and constitutes a framework within which nucleation rates of flow-induced crystallization may be understood in systems of associating polymers under flow. The model also exemplifies a wide class of driven systems possessing strong, and scaling, fluctuations.

Silk Protein Solution: A Natural Example of Sticky Reptation.

Silk is one of the most intriguing examples of biomolecular self-assembly, yet little is understood of molecular mechanisms behind the flow behavior generating these complex high-performance fibers. This work applies the polymer physics of entangled solution rheology to present a first microphysical understanding of silk in the linear viscoelastic regime. We show that silk solutions can be approximated as reptating polymers with "sticky" calcium bridges whose strength can be controlled through the potassium concentration. This approach provides a new window into critical microstructural parameters, in particular identifying the mechanism by which potassium and calcium ions are recruited as a powerful viscosity control in silk. Our model constitutes a viable starting point to understand not only the "flow-induced self-assembly" of silk fibers but also a broader range of phenomena in the emergent field of material-focused synthetic biology.

Morphology formation in binary mixtures upon gradual destabilisation.

Spontaneous liquid-liquid phase separation is commonly understood in terms of phenomenological mean-field theories. These theories correctly predict the structural features of the fluid at sufficiently long time scales and wavelengths. However, these conditions are not met in various examples in biology and materials science where the mixture is slowly destabilised, and phase separation is strongly affected by critical thermal fluctuations. We propose a mechanism of pretransitional structuring of a mixture that approaches the miscibility gap and predict scaling relations that describe how the characteristic feature size of the emerging morphology decreases with an increasing quench rate. These predictions quantitatively agree with our kinetic Monte Carlo and molecular dynamics simulations of a phase-separating binary mixture, as well as with previously reported experimental observations. We discuss how these predictions are affected by non-conserved order parameters (e.g., due to chemical reactions or alignment of liquid-crystalline molecules), hydrodynamics and active transport.

Ligand-regulated oligomerisation of allosterically interacting proteins.

The binding of ligands to distinct sites at proteins or at protein clusters is often cooperative or anti-cooperative due to allosteric signalling between those sites. The allostery is usually attributed to a configurational change of the proteins from a relaxed to a configurationally different tense state. Alternatively, as originally proposed by Cooper and Dryden, a tense state may be achieved by merely restricting the thermal vibrations of the protein around its mean configuration. In this work, we provide theoretical tools to investigate fluctuation allostery using cooling and titration experiments in which ligands regulate dimerisation, or ring or chain formation. We discuss in detail how ligands may regulate the supramolecular (co)polymerisation of liganded and unliganded proteins.

Polymer Solar Cells: Solubility Controls Fiber Network Formation.

The photoactive layer of polymer solar cells is commonly processed from a four-component solution, containing a semiconducting polymer and a fullerene derivative dissolved in a solvent-cosolvent mixture. The nanoscale dimensions of the polymer-fullerene morphology that is formed upon drying determines the solar cell performance, but the fundamental processes that govern the size of the phase-separated polymer and fullerene domains are poorly understood. Here, we investigate morphology formation of an alternating copolymer of diketopyrrolopyrrole and a thiophene-phenyl-thiophene oligomer (PDPPTPT) with relatively long 2-decyltetradecyl (DT) side chains blended with [6,6]-phenyl-C71-butyric acid methyl ester. During solvent evaporation the polymer crystallizes into a fibrous network. The typical width of these fibers is analyzed by quantification of transmission electron microscopic images, and is mainly determined by the solubility of the polymer in the cosolvent and the molecular weight of the polymer. A higher molecular weight corresponds to a lower solubility and film processing results in a smaller fiber width. Surprisingly, the fiber width is not related to the drying rate or the amount of cosolvent. We have made solar cells with fiber widths ranging from 28 to 68 nm and found an inverse relation between fiber width and photocurrent. Finally, by mixing two cosolvents, we develop a ternary solvent system to tune the fiber width. We propose a model based on nucleation-and-growth which can explain these measurements. Our results show that the width of the semicrystalline polymer fibers is not the result of a frozen dynamical state, but determined by the nucleation induced by the polymer solubility.

Controlling chemical self-assembly by solvent-dependent dynamics.

The influence of the ratio between poor and good solvent on the stability and dynamics of supramolecular polymers is studied via a combination of experiments and simulations. Step-wise addition of good solvent to supramolecular polymers assembled via a cooperative (nucleated) growth mechanism results in complete disassembly at a critical good/poor solvent ratio. In contrast, gradual disassembly profiles upon addition of good solvent are observed for isodesmic (non-nucleated) systems. Due to the weak association of good solvent molecules to monomers, the solvent-dependent aggregate stability can be described by a linear free-energy relationship. With respect to dynamics, the depolymerization of π-conjugated oligo(p-phenylene vinylene) (OPV) assemblies in methylcyclohexane (MCH) upon addition of chloroform as a good solvent is shown to proceed with a minimum rate around a critical chloroform/MCH solvent ratio. This minimum disassembly rate bears an intriguing resemblance to phenomena observed in protein unfolding, where minimum rates are observed at the thermodynamic midpoint of a protein denaturation experiment. A kinetic nucleation-elongation model in which the rate constants explicitly depend on the good solvent fraction is developed to rationalize the kinetic traces and further extend the insights by simulation. It is shown that cooperativity, i.e., the nucleation of new aggregates, plays a key role in the minimum polymerization and depolymerization rate at the critical solvent composition. Importantly, this shows that the mixing protocol by which one-dimensional aggregates are prepared via solution-based processing using good/poor solvent mixtures is of major influence on self-assembly dynamics.