Ralf Metzler

The local contact potential difference measured using the Kelvin method on Pb islands is constant as a function of tip-sample distance at a distance larger than 2 nm, while it shows a logarithmic behavior above the wetting layer on silicon.

Methyl-CpG binding domain 2 (MBD2) is a critical epigenetic regulator that selectively binds methylated CpG dinucleotides, key marks controlling gene regulation and chromatin organization. Understanding the interactions and conformational dynamics underlying this high selectivity is essential to elucidate MBD2’s regulatory role. Here, using extensive classical MD simulations, we explored the formation of the MBD2–mCpG recognition complex. By initially positioning MBD2 one base pair downstream of its target, we observed its transition to the target site within microseconds. Notably, upon binding, MBD2 adopts two distinct stable conformations: a primary state closely resembling the X-ray crystal structure, and a secondary state of reduced affinity that nevertheless retains comparable selectivity for mCpG. Our results establish S189 as a key macro-switch; loss of its interaction with the methylcytosine backbone shifts the equilibrium toward the secondary state. This is corroborated by MD simulations of the S189A mutant, which preferentially adopts the secondary state-like conformation. Complementary NMR experiments confirm that S189A mutation does not alter mCpG selectivity, while fluorescence polarization measurements reveal a reduced binding affinity, consistent with our MD simulations results. Together, these findings indicate that MBD2 binding to methylated CpG involves a bistable equilibrium, providing new insights into how high affinity and adaptability are balanced in epigenetic recognition. In a broader context, our findings suggest that such alternative bound-state equilibria may represent an inherent feature of specific protein–DNA complexes.

Chirality, a systematic rotational bias in the motion of a particle, arises in a wide range of physical and biological systems, from charged colloids in magnetic fields to swimming bacteria near surfaces. While its effects in homogeneous environments are well understood, the interplay between chirality and structural disorder has remained largely unexplored. Here, we investigate the chiral random walk on two-dimensional percolation clusters above the percolation threshold, combining numerical simulations with an analytically tractable annealed-disorder approximation. We find that the long-time diffusion coefficient depends non-monotonically on both the chirality parameter and the obstacle density: for every obstacle density above the percolation threshold, there exists an optimal chirality that enhances diffusion relative to the achiral walk. We show that the optimal chirality is set by an edge-adhering mechanism: maximum diffusion is achieved when the persistence length of the wall-adhering motion matches half the typical obstacle cluster perimeter. This yields a closed-form prediction for the optimal chirality in terms of geometric properties of the medium alone, which we verify across the full range of obstacle densities studied. The enhancement extends to first-passage statistics, where chirality shortens typical search times at strong disorder while lengthening them at weak disorder, with direct implications for biological navigation in disordered environments.

In single-particle tracking experiments measuring anomalous diffusion dynamics, understanding ergodicity is crucial, as it ensures that the time average of an observable matches the ensemble average—and can thus be fitted with known ensemble-averaged observables. A commonly used criterion for assessing the ergodicity of a stochastic process is based on the comparison of the mean-squared displacement (MSD) with the time-averaged MSD (TAMSD). This approach has been widely applied and proves effective in cases of weak ergodicity breaking across various systems in both theoretical and experimental studies. However, there is relatively little discussion regarding the theoretical justification and limitations of this definition. Here, we demonstrate that this widely accepted criterion to some extent contradicts the classical definition of ergodicity as well as physical intuition, leading to spurious (non-)ergodicity results when applied to several well-known stochastic models. To address this limitation, we propose using the mean-squared increment (MSI) instead of the MSD for comparison of ensemble- and time-averaged observables. For processes with stationary increments, the results for MSI and MSD coincide. However, if the increments of the process reach stationarity at long times only, they differ, and the MSI-TAMSD comparison still provides the test for ergodicity. Several well-established examples demonstrate, through both trajectory simulations and theoretical analysis, that our MSI-TAMSD criterion provides a more accurate characterization of the genuine (non-)ergodicity of systems where the MSD-TAMSD method fails. Additionally, for systems exhibiting “ultraweak” ergodicity breaking, the MSI can reveal the asymptotic stationarity and ergodic nature of the process’s increments. Our findings emphasize the important role of the MSI observable for SPT experiments and anomalous diffusion studies.

Classical first-passage theory based on Brownian motion predicts that the mean fastest-arrival time decreases only logarithmically with the number of searchers, however this is an artifact of the unphysical infinite-speed assumption of Brownian dynamics.

We propose a noninteger-dimensional spatial model for anisotropic solids incorporating a q -deformed derivative operator inspired by the Tsallis nonadditive entropy framework. This generalization provides a unified and flexible analytical formalism for exploring anisotropic thermal properties. We derive explicit expressions for the electronic and phonon densities of states and for the phonon specific heat, showing how the Hausdorff dimension α and the deformation parameter q affect the spectral and thermodynamic response. The model is applied to several solid-state materials and provides a close description of their measured specific-heat behavior over broad temperature ranges. The fitted results illustrate the ability of the regularized entropic formulation to describe departures from the standard Debye response. Finally, we relate the q -deformation qualitatively to disorder-controlled conformable kinetics, suggesting a possible connection to microscopic heterogeneity and effective memory signatures without assuming a universal quantitative relation between q and the kinetic exponent μ .

Continuous-time random walks (CTRWs) are highly appreciated as a model of anomalous diffusion (AD) in complex media such as structured and heterogeneous environments. These walks are used to describe AD phenomena characterized by a nonlinear functional dependence of the mean-squared displacement (MSD) of particles with time. The introduction of asymmetric waiting-time distributions (WTDs) depending on the diffusion directions leads to biased CTRWs and to AD phenomena. Here, we examine the general formulation of such CTRWs with asymmetric WTDs in continuous space. From the balance equations, we derive the corresponding generalized Montroll-Weiss equation in Fourier-Laplace space as well as the generalized master equations with asymmetric waiting times. For random jump lengths obeying an asymmetric modified Gaussian distribution (AMGD), we analytically obtain the probability-density function of the particles as well as the first two moments in Laplace space. We unveil that CTRWs with exponential WTDs and jump lengths following the AMGD exhibit a ballistic diffusion, whereas in a symmetric case for the jump lengths both the MSD and variance at long time have a linear scaling with time. The AD properties of the MSD and of the variance at long times depend on a exponent of the power-law WTDs, while the AMGD-distributed jump lengths the AD scaling exponents for such CTRWs. In this continuous-space model, the possibility of length-distributed jumps—in contrast to the case of only neighboring-site jumps allowed in the discrete version of a similar model we proposed recently [G. Li , ]—leads to different resulting scaling properties of the MSD. The analytical results are in close agreement with the results of computer simulations, both for the case of asymmetric exponential and of power-law WTDs. The current theoretical results are extendable to more elaborate CTRW models. The latter are applicable for the description of more complicated AD-related phenomena taking place in the presence of external fields.

Mathematical models of diffusion based on stochastic processes of the type of continuous-time random walks (CTRWs) are widely used for the description of various transport characteristics in complex media. An external or internal bias in a given CTRW model is often attributed to an asymmetric distribution of jump lengths, while the waiting times are assumed to possess identical distributions in all directions. However, for a number of real-world transport phenomena the latter assumption is violated. To account for such situations, we examine the properties of such biased CTRWs in one dimension. We propose a CTRW-based model of diffusion with the waiting-time distributions (WTDs) of the tracers chosen for right- and left-directed jumps. Below we name CTRWs with such asymmetric WTDs (AWTDs) as A t -CTRWs. We derive the corresponding generalized Montroll-Weiss and master equations in Laplace and Z space. We consider both exponential and power-law WTDs as the standard and most useful functional choices for the purposes of data analysis. For these two WTD classes, we analyze the average displacement (generally nonzero) and the mean-squared displacement of the diffusing particles and analytically compute the variance as effective statistical measures. Our analytical predictions favorably agree with the results of the performed computer simulations. Specifically, for a CTRW with power-law WTDs we find that at long times the emerging anomalous diffusion depends not only on the smallest exponent of the left- and right-directed WTDs. Such diffusion models can, e.g., be used to describe the anomalous diffusion in various anisotropic media in the presence of a drift. One hydrological example is a gravity-affected spreading of contaminants in porous rocks, a system where the CTRW-based models are widely known to be applicable. A biological example of a biased-CTRW-based transport is a regulated driven bidirectional transport of cargoes between the center of a living biological cell and its periphery taking place along the microtubule filaments.