Equation of state for active matter.

We characterize the steady states of a suspension of two-dimensional active Brownian particles (ABPs). By approximating the first-order correction to the steady-state probability distribution to lowest order in Peclet number, we show that macroscopic quantities can be calculated in analogous way to equilibrium systems using this probability distribution. We then derive expressions for the macroscopic pressure and position-orientation correlation functions. We check our results by direct comparison with extensive numerical simulations. A key finding is the importance of many-body effective interactions even at very low densities.

Competing active and passive interactions drive amoebalike crystallites and ordered bands in active colloids.

Swimmers and self-propelled particles are physical models for the collective behavior and motility of a wide variety of living systems, such as bacteria colonies, bird flocks, and fish schools. Such artificial active materials are amenable to physical models which reveal the microscopic mechanisms underlying the collective behavior. Here we study colloids in a dc electric field. Our quasi-two-dimensional system of electrically driven particles exhibits a rich and exotic phase behavior exhibiting passive crystallites, motile crystallites, an active gas, and banding. Amongst these are two mesophases, reminiscent of systems with competing interactions. At low field strengths activity suppresses demixing, leading to motile crystallites. Meanwhile, at high field strengths, activity drives partial demixing to traveling bands. We parametrize a particulate simulation model which reproduces the experimentally observed phases.

Substrate conformational dynamics facilitate structure-specific recognition of gapped DNA by DNA polymerase.

DNA-binding proteins utilise different recognition mechanisms to locate their DNA targets; some proteins recognise specific DNA sequences, while others interact with specific DNA structures. While sequence-specific DNA binding has been studied extensively, structure-specific recognition mechanisms remain unclear. Here, we study structure-specific DNA recognition by examining the structure and dynamics of DNA polymerase I Klenow Fragment (Pol) substrates both alone and in DNA-Pol complexes. Using a docking approach based on a network of 73 distances collected using single-molecule FRET, we determined a novel solution structure of the single-nucleotide-gapped DNA-Pol binary complex. The structure resembled existing crystal structures with regards to the downstream primer-template DNA substrate, and revealed a previously unobserved sharp bend (∼120°) in the DNA substrate; this pronounced bend was present in living cells. MD simulations and single-molecule assays also revealed that 4-5 nt of downstream gap-proximal DNA are unwound in the binary complex. Further, experiments and coarse-grained modelling showed the substrate alone frequently adopts bent conformations with 1-2 nt fraying around the gap, suggesting a mechanism wherein Pol recognises a pre-bent, partially-melted conformation of gapped DNA. We propose a general mechanism for substrate recognition by structure-specific enzymes driven by protein sensing of the conformational dynamics of their DNA substrates.

Directed Assembly of Homopentameric Cholera Toxin B-Subunit Proteins into Higher-Order Structures Using Coiled-Coil Appendages.

The self-assembly of proteins into higher order structures is ubiquitous in living systems. It is also an essential process for the bottom-up creation of novel molecular architectures and devices for synthetic biology. However, the complexity of protein-protein interaction surfaces makes it challenging to mimic natural assembly processes in artificial systems. Indeed, many successful computationally designed protein assemblies are prescreened for "designability", limiting the choice of components. Here, we report a simple and pragmatic strategy to assemble chosen multisubunit proteins into more complex structures. A coiled-coil domain appended to one face of the pentameric cholera toxin B-subunit (CTB) enabled the ordered assembly of tubular supra-molecular complexes. Analysis of a tubular structure determined by X-ray crystallography has revealed a hierarchical assembly process that displays features reminiscent of the polymorphic assembly of polyomavirus proteins. The approach provides a simple and straightforward method to direct the assembly of protein building blocks which present either termini on a single face of an oligomer. This scaffolding approach can be used to generate bespoke supramolecular assemblies of functional proteins. Additionally, structural resolution of the scaffolded assemblies highlight "native-state" forced protein-protein interfaces, which may prove useful as starting conformations for future computational design.

The dynamical interplay between a megadalton peptide nanocage and solutes probed by microsecond atomistic MD; implications for design.

Understanding the assembly and dynamics of protein-based supramolecular capsids and cages is of fundamental importance and could lead to applications in synthetic biology and biotechnology. Here we present long and large atomistic molecular dynamics simulations of de novo designed self-assembling protein nanocages (SAGEs) in aqueous media. Microsecond simulations, comprised of ≈42 million atoms for three pre-formed SAGEs of different charges, in the presence of solutes and solvent have been completed. Here, the dynamics, stability and porosity of the peptide networks are explored along with their interactions with ions, small molecules and macromolecular solutes. All assemblies are stable over the µs timescale, and the solutes show a mixture of transport behaviour across or adherence to the fabric of the SAGE particles. Solute proteins largely retained native-like conformation on contact with SAGE. Certain residues of the SAGE peptides are identified as "repeat offenders" for contacting many different solutes, which suggest modifications to reduce non-specific binding. These studies highlight how molecular dynamics can aid the design process of SAGE and similar assemblies for potential applications as diverse as platforms for drug and vaccine delivery and nanoreactors to encapsulate enzyme pathways.

Bioinspired Silicification Reveals Structural Detail in Self-Assembled Peptide Cages.

Understanding how molecules in self-assembled soft-matter nanostructures are organized is essential for improving the design of next-generation nanomaterials. Imaging these assemblies can be challenging and usually requires processing, e.g., staining or embedding, which can damage or obscure features. An alternative is to use bioinspired mineralization, mimicking how certain organisms use biomolecules to template mineral formation. Previously, we have reported the design and characterization of Self-Assembled peptide caGEs (SAGEs) formed from de novo peptide building blocks. In SAGEs, two complementary, 3-fold symmetric, peptide hubs combine to form a hexagonal lattice, which curves and closes to form SAGE nanoparticles. As hexagons alone cannot tile onto spheres, the network must also incorporate nonhexagonal shapes. While the hexagonal ultrastructure of the SAGEs has been imaged, these defects have not been observed. Here, we show that positively charged SAGEs biotemplate a thin, protective silica coating. Electron microscopy shows that these SiO2-SAGEs do not collapse, but maintain their 3D shape when dried. Atomic force microscopy reveals a network of hexagonal and irregular features on the SiO2-SAGE surface. The dimensions of these (7.2 nm ± 1.4 nm across, internal angles 119.8° ± 26.1°) are in accord with the designed SAGE network and with coarse-grained modeling of the SAGE assembly. The SiO2-SAGEs are permeable to small molecules (<2 nm), but not to larger biomolecules (>6 nm). Thus, bioinspired silicification offers a mild technique that preserves soft-matter nanoparticles for imaging, revealing structural details <10 nm in size, while also maintaining desirable properties, such as permeability to small molecules.

Beyond icosahedral symmetry in packings of proteins in spherical shells.

The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral cage. In turn, this has inspired synthetic biologists to design de novo protein cages. We use simple models, on multiple scales, to investigate the self-assembly of a spherical cage, focusing on the regularity of the packing of protein-like objects on the surface. Using building blocks, which are able to pack with icosahedral symmetry, we examine how stable these highly symmetric structures are to perturbations that may arise from the interplay between flexibility of the interacting blocks and entropic effects. We find that, in the presence of those perturbations, icosahedral packing is not the most stable arrangement for a wide range of parameters; rather disordered structures are found to be the most stable. Our results suggest that (i) many designed, or even natural, protein cages may not be regular in the presence of those perturbations and (ii) optimizing those flexibilities can be a possible design strategy to obtain regular synthetic cages with full control over their surface properties.

Force-Induced Rupture of a DNA Duplex: From Fundamentals to Force Sensors.

The rupture of double-stranded DNA under stress is a key process in biophysics and nanotechnology. In this article, we consider the shear-induced rupture of short DNA duplexes, a system that has been given new importance by recently designed force sensors and nanotechnological devices. We argue that rupture must be understood as an activated process, where the duplex state is metastable and the strands will separate in a finite time that depends on the duplex length and the force applied. Thus, the critical shearing force required to rupture a duplex depends strongly on the time scale of observation. We use simple models of DNA to show that this approach naturally captures the observed dependence of the force required to rupture a duplex within a given time on duplex length. In particular, this critical force is zero for the shortest duplexes, before rising sharply and then plateauing in the long length limit. The prevailing approach, based on identifying when the presence of each additional base pair within the duplex is thermodynamically unfavorable rather than allowing for metastability, does not predict a time-scale-dependent critical force and does not naturally incorporate a critical force of zero for the shortest duplexes. We demonstrate that our findings have important consequences for the behavior of a new force-sensing nanodevice, which operates in a mixed mode that interpolates between shearing and unzipping. At a fixed time scale and duplex length, the critical force exhibits a sigmoidal dependence on the fraction of the duplex that is subject to shearing.

Introducing improved structural properties and salt dependence into a coarse-grained model of DNA.

We introduce an extended version of oxDNA, a coarse-grained model of deoxyribonucleic acid (DNA) designed to capture the thermodynamic, structural, and mechanical properties of single- and double-stranded DNA. By including explicit major and minor grooves and by slightly modifying the coaxial stacking and backbone-backbone interactions, we improve the ability of the model to treat large (kilobase-pair) structures, such as DNA origami, which are sensitive to these geometric features. Further, we extend the model, which was previously parameterised to just one salt concentration ([Na(+)] = 0.5M), so that it can be used for a range of salt concentrations including those corresponding to physiological conditions. Finally, we use new experimental data to parameterise the oxDNA potential so that consecutive adenine bases stack with a different strength to consecutive thymine bases, a feature which allows a more accurate treatment of systems where the flexibility of single-stranded regions is important. We illustrate the new possibilities opened up by the updated model, oxDNA2, by presenting results from simulations of the structure of large DNA objects and by using the model to investigate some salt-dependent properties of DNA.

The role of loop stacking in the dynamics of DNA hairpin formation.

We study the dynamics of DNA hairpin formation using oxDNA, a nucleotide-level coarse-grained model of DNA. In particular, we explore the effects of the loop stacking interactions and non-native base pairing on the hairpin closing times. We find a nonmonotonic variation of the hairpin closing time with temperature, in agreement with the experimental work of Wallace et al. (Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 5584-5589). The hairpin closing process involves the formation of an initial nucleus of one or two bonds in the stem followed by a rapid zippering of the stem. At high temperatures, typically above the hairpin melting temperature, an effective negative activation enthalpy is observed because the nucleus has a lower enthalpy than the open state. By contrast, at low temperatures, the activation enthalpy becomes positive mainly due to the increasing energetic cost of bending a loop that becomes increasingly highly stacked as the temperature decreases. We show that stacking must be very strong to induce this experimentally observed behavior, and that the existence of just a few weak stacking points along the loop can substantially suppress it. Non-native base pairs are observed to have only a small effect, slightly accelerating hairpin formation.

Soft modes and nonaffine rearrangements in the inherent structures of supercooled liquids.

We find that the hierarchical organization of the potential energy landscape in a model supercooled liquid can be related to a change in the spatial distribution of soft normal modes. For groups of nearby minima, between which fast relaxation processes typically occur, the localization of the soft modes is very similar. The spatial distribution of soft regions changes, instead, for minima between which transitions relevant to structural relaxation occur. This may be the reason why the soft modes are able to predict spatial heterogeneities in the dynamics. Nevertheless, the very softest modes are only weakly correlated with dynamical heterogeneities and instead show higher statistical overlap with regions in the local minima that would undergo nonaffine rearrangements if subjected to a shear deformation. This feature of the supercooled liquid is reminiscent of the behavior of nonaffine deformations in amorphous solids, where the very softest modes identify the loci of plastic instabilities.

Deformation of inherent structures to detect long-range correlations in supercooled liquids.

We propose deformations of inherent structures as a suitable tool for detecting structural changes underlying the onset of cooperativity in supercooled liquids. The non-affine displacement (NAD) field resulting from the applied deformation shows characteristic differences between the high temperature liquid and supercooled state, which are typically observed in dynamic quantities. The average magnitude of the NAD is very sensitive to temperature changes in the supercooled regime and is found to be strongly correlated with the inherent structure energy. In addition, the NAD field is characterized by a correlation length that increases upon lowering the temperature towards the supercooled regime.

Probing a critical length scale at the glass transition.

We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size, which is typical of critical phenomena. Our approach is to introduce an external, static perturbation to extract the structural information from the system's response. In particular, we consider the transformation behavior of the local minima of the underlying potential energy landscape (inherent structures), under a static deformation. The finite-size scaling analysis of our numerical results indicate that the correlation length diverges at a temperature Tc, below the temperatures where the system can be equilibrated. Our numerical results are consistent with random first order theory, which predicts such a divergence with a critical exponent ν=2/3 at the Kauzmann temperature, where the extrapolated configurational entropy vanishes.