First-passage-time distribution for diffusion through a planar wedge

A mean-field theory for characterizing the closing rates of DNA origami hinges

The evolution of dynamic DNA nanostructures has propelled DNA nanotechnology into a robust and versatile field, offering groundbreaking applications in nanoscale communication, drug delivery, and molecular computing. Yet, the full potential of this technology awaits further enhancement through optimization of kinetic properties governing conformational changes. In this work, we introduce a mean-field theory to characterize the kinetic behavior of a dynamic DNA origami hinge where each arm bears complementary single-stranded DNA overhangs of different lengths, which can latch the hinge at a closed conformation. This device is currently being investigated for multiple applications, being of particular interest the development of DNA-based rapid diagnostic tests for coronavirus. Drawing from classical statistical mechanics theories, we derive analytical expressions for the mean binding time of these overhangs within a constant hinge. This analysis is then extended to flexible hinges, where the angle diffuses within a predetermined energy landscape. We validate our model by comparing it with experimental measurements of the closing rates of DNA nanocalipers with different energy landscapes and overhang lengths, demonstrating excellent agreement and suggesting fast angular relaxation relative to binding. These findings offer insights that can guide the optimization of devices for specific state lifetimes. Moreover, the framework introduced here lays the groundwork for further advancements in modeling the kinetics of dynamic DNA nanostructures.

Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics

Characterization of composite materials, whose properties vary in space over microscopic scales, has become a problem of broad interdisciplinary interest. In particular, estimation of the inhomogeneous transport coefficients, e.g., the diffusion coefficient or the heat conductivity, which shape important processes in biology and engineering, is a challenging task. The analysis of such systems is further complicated because two alternative formulations of the inhomogeneous transport equations exist in the literature-the Smoluchowski and Fokker-Planck equations, which are also related to the so-called Ito-Stratonovich dilemma. Using the theory of statistical physics, we show that the two formulations, usually regarded as distinct models, are physically equivalent. From this result we develop efficient estimates for the transverse space-dependent diffusion coefficient in fluids near a phase boundary. Our method requires only measurements of escape probabilities and mean exit times of molecules leaving a narrow spatial region. We test our estimates in three case studies: (i) a Langevin model of a Büttikker-Landauer ratchet; atomistic molecular-dynamics simulations of liquid-water molecules in contact with (ii) vapor, and (iii) soap (surfactant) film which has promising applications in physical chemistry. Our analysis reveals that near the surfactant monolayer the mobility of water molecules is slowed down almost twice with respect to the bulk liquid. Moreover, the diffusion coefficient of water correlates with the transition from hydrophilic to hydrophobic parts of the film.

First-encounter time of two diffusing particles in confinement

We investigate how confinement may drastically change both the probability density of the first-encounter time and the associated survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we focus on two one-dimensional settings: a half-line and an interval. We first consider the case with equal particle diffusivities, for which exact results can be obtained for the survival probability and the associated first-encounter time density valid over the full time domain. We also evaluate the moments of the first-encounter time when they exist. We then turn to the case with unequal diffusivities and focus on the long-time behavior of the survival probability. Our results highlight the great impact of boundary effects in diffusion-controlled kinetics even for simple one-dimensional settings, as well as the difficulty of obtaining analytic results as soon as the translational invariance of such systems is broken.

Theory for controlling individual self-propelled micro-swimmers by photon nudging I: directed transport

Photon nudging is a new experimental method which enables the force-free manipulation and localization of individual self-propelled artificial micro-swimmers in fluidic environments.

Survival probability of a Brownian motion in a planar wedge of arbitrary angle

We study the survival probability and the first-passage time distribution for a Brownian motion in a planar wedge with infinite absorbing edges. We generalize existing results obtained for wedge angles of the form π/n with n a positive integer to arbitrary angles, which in particular cover the case of obtuse angles. We give explicit and simple expressions of the survival probability and the first-passage time distribution in which the difference between an arbitrary angle and a submultiple of π is contained in three additional terms. As an application, we obtain the short-time development of the survival probability in a wedge of arbitrary angle.

First-passage characteristics of biased diffusion in a planar wedge

We obtain compact, exact, analytical expressions for the first-passage-time distribution for a particle undergoing biased diffusion in a planar wedge for wedge angles π/p, where p is a positive integer. We then provide the long-time limit of the first-passage time and found it to be dependent on the drift direction and wedge angle. We finally provide exact expressions for the mean first-passage time for specific cases.

Fokker-Planck equation in a wedge domain: anomalous diffusion and survival probability

We obtain exact solutions and the survival probability for a Fokker-Planck equation subjected to the two-dimensional wedge domain. We consider a spatial dependence in the diffusion coefficient and the presence of external forces. The results show an anomalous spreading of the solution and, consequently, a nonusual behavior of the survival probability which can be connected to anomalous diffusion.