We establish the complete phase diagram of self-propelled hard disks in two spatial dimensions from the analysis of the equation of state and the statistics of local order parameters. The equilibrium melting scenario is maintained at small activities, with coexistence between active liquid and hexatic order, followed by a proper hexatic phase, and a further transition to an active solid. As activity increases, the emergence of hexatic and solid order is shifted towards higher densities. Above a critical activity and for a certain range of packing fractions, the system undergoes motility-induced phase separation and demixes into low and high density phases; the latter can be either disordered (liquid) or ordered (hexatic or solid) depending on the activity.

Active systems, or active matter, are self-driven systems that live, or function, far from equilibrium – a paradigmatic example that we focus on here is provided by a suspension of self-motile particles. Active systems are far from equilibrium because their microscopic constituents constantly consume energy from the environment in order to do work, for instance to propel themselves. The non-equilibrium nature of active matter leads to a variety of non-trivial intriguing phenomena. An important one, which has recently been the subject of intense interest among biological and soft matter physicists, is that of the so-called “motility-induced phase separation”, whereby self-propelled particles accumulate into clusters in the absence of any explicit attractive interactions between them. Here we review the physics of motility-induced phase separation, and discuss this phenomenon within the framework of the classic physics of phase separation and coarsening. We also discuss theories for bacterial colonies where coarsening may be arrested. Most of this work will focus on the case of run-and-tumble and active Brownian particles in the absence of solvent-mediated hydrodynamic interactions – we will briefly discuss at the end their role, which is not currently fully understood in this context.

DNA polymerase θ (Polθ) is a unique polymerase-helicase fusion protein that promotes microhomology-mediated end-joining (MMEJ) of DNA double-strand breaks (DSBs). How full-length human Polθ performs MMEJ at the molecular level remains unknown. Using a biochemical approach, we find that the helicase is essential for Polθ MMEJ of long ssDNA overhangs which model resected DSBs. Remarkably, Polθ MMEJ of ssDNA overhangs requires polymerase-helicase attachment, but not the disordered central domain, and occurs independently of helicase ATPase activity. Using single-particle microscopy and biophysical methods, we find that polymerase-helicase attachment promotes multimeric gel-like Polθ complexes that facilitate DNA accumulation, DNA synapsis, and MMEJ. We further find that the central domain regulates Polθ multimerization and governs its DNA substrate requirements for MMEJ. These studies identify unexpected functions for the helicase and central domain and demonstrate the importance of polymerase-helicase tethering in MMEJ and the structural organization of Polθ.

DNA origami technology allows for the precise nanoscale assembly of chemical entities that give rise to sophisticated functional materials. We have created a versatile DNA origami nanofork antenna (DONA) by assembling Au or Ag nanoparticle dimers with different gap sizes down to 1.17 nm, enabling signal enhancements in surface-enhanced Raman scattering (SERS) of up to 10¹¹. This allows for single-molecule SERS measurements, which can even be performed with larger gap sizes to accommodate differently sized molecules, at various excitation wavelengths. A general scheme is presented to place single analyte molecules into the SERS hot spots using the DNA origami structure exploiting covalent and noncovalent coupling schemes. By using Au and Ag dimers, single-molecule SERS measurements of three dyes and cytochrome c and horseradish peroxidase proteins are demonstrated even under nonresonant excitation conditions, thus providing long photostability during time-series measurement and enabling optical monitoring of single molecules.

Significance: Pore translocation, the driven passage of molecules through narrow channels, has become an important tool for probing DNA properties. In a recent breakthrough experiment, this technique was used to detect knots that form spontaneously in DNA filaments and can hence impact their in vivo functionality. Here, by using an accurate model, we simulate the translocation of knotted DNA, expose its unexpectedly rich phenomenology, and clarify the implications for experiments. We show that knot translocation occurs in two possible modes, depending on the knot initial position and size. These properties also account for the typically late occurrence of the knot passage event. Finally, the passage duration is found to depend more on the translocation velocity of the knot than its size.