Biased diffusion in periodic potentials: Three types of force dependence of effective diffusivity and generalized Lifson-Jackson formula

RNA polymerase drives ribonucleotide excision DNA repair in E. coli

Ribonuclease HII (RNaseHII) is the principal enzyme that removes misincorporated ribonucleoside monophosphates (rNMPs) from genomic DNA. Here, we present structural, biochemical, and genetic evidence demonstrating that ribonucleotide excision repair (RER) is directly coupled to transcription. Affinity pull-downs and mass-spectrometry-assisted mapping of in cellulo inter-protein cross-linking reveal the majority of RNaseHII molecules interacting with RNA polymerase (RNAP) in E. coli. Cryoelectron microscopy structures of RNaseHII bound to RNAP during elongation, with and without the target rNMP substrate, show specific protein-protein interactions that define the transcription-coupled RER (TC-RER) complex in engaged and unengaged states. The weakening of RNAP-RNaseHII interactions compromises RER in vivo. The structure-functional data support a model where RNaseHII scans DNA in one dimension in search for rNMPs while "riding" the RNAP. We further demonstrate that TC-RER accounts for a significant fraction of repair events, thereby establishing RNAP as a surveillance "vehicle" for detecting the most frequently occurring replication errors.

Periodic potential can enormously boost free-particle transport induced by active fluctuations

Active fluctuations are detected in a growing number of systems due to self-propulsion mechanisms or collisions with an active environment. They drive the system far from equilibrium and can induce phenomena that are forbidden at equilibrium states by, e.g., fluctuation-dissipation relations and detailed balance symmetry. Understanding their role in living matter is emerging as a challenge for physics. Here we demonstrate a paradoxical effect in which a free-particle transport induced by active fluctuations can be boosted by many orders of magnitude when the particle is additionally subjected to a periodic potential. In contrast, within the realm of only thermal fluctuations, the velocity of a free particle exposed to a bias is reduced when the periodic potential is switched on. The presented mechanism is significant for understanding nonequilibrium environments such as living cells, where it can explain from a fundamental point of view why spatially periodic structures known as microtubules are necessary to generate impressively effective intracellular transport. Our findings can be readily corroborated experimentally, e.g., in a setup comprising a colloidal particle in an optically generated periodic potential.

Parallel computing for mobilities in periodic geometries

We examine methods for calculating the effective mobilities of molecules driven through periodic geometries in the context of particle-based simulation. The standard formulation of the mobility, based on the long-time limit of the mean drift velocity, is compared to a formulation based on the mean first-passage time of molecules crossing a single period of the system geometry. The equivalence of the two definitions is derived under weaker assumptions than similar conclusions obtained previously, requiring only that the state of the system at subsequent period crossings satisfy the Markov property. Approximate theoretical analyses of the computational costs of estimating these two mobility formulations via particle simulations suggest that the definition based on first-passage times may be substantially better suited to exploiting parallel computation hardware. This claim is investigated numerically on an example system modeling the passage of nanoparticles through the slit-well device. In this case, the traditional mobility formulation is found to perform best when the Péclet number is small, whereas the mean first-passage time formulation is found to converge much more quickly when the Péclet number is moderate or large. The results suggest that, given relatively modest access to modern GPU hardware, this alternative mobility formulation may be an order of magnitude faster than the standard technique for computing effective mobilities of biomolecules through periodic geometries.

Enhanced diffusion and the eigenvalue band structure of Brownian motion in tilted periodic potentials

We consider enhanced diffusion for Brownian motion on a tilted periodic potential. Expressing the effective diffusion in terms of the eigenvalue band structure, we establish a connection between band gaps in the eigenspectrum and enhanced diffusion. We explain this connection for a simple cosine potential with a linear force and then generalize to more complicated potentials including one-dimensional potentials with multiple frequency components and nonseparable multidimensional potentials. We find that potentials with multiple band gaps in the eigenspectrum can lead to multiple maxima or broadening of the force-diffusion curve. These features are likely to be observable in experiments.