Manifestations of projection-induced memory: General theory and the tilted single file.

Over the years the field of non-Markovian stochastic processes and anomalous diffusion evolved from a specialized topic to mainstream theory, which transgressed the realms of physics to chemistry, biology and ecology. Numerous phenomenological approaches emerged, which can more or less successfully reproduce or account for experimental observations in condensed matter, biological and/or single-particle systems. However, as far as their predictions are concerned these approaches are not unique, often build on conceptually orthogonal ideas, and are typically employed on an ad hoc basis. It therefore seems timely and desirable to establish a systematic, mathematically unifying and clean approach starting from more fine-grained principles. Here we analyze projection-induced ergodic non-Markovian dynamics, both reversible as well as irreversible, using spectral theory. We investigate dynamical correlations between histories of projected and latent observables that give rise to memory in projected dynamics, and rigorously establish conditions under which projected dynamics is Markovian or renewal. A systematic metric is proposed for quantifying the degree of non-Markovianity. As a simple, illustrative but non-trivial example we study single file diffusion in a tilted box, which, for the first time, we solve exactly using the coordinate Bethe ansatz. Our results provide a solid foundation for a deeper and more systematic analysis of projection-induced non-Markovian dynamics and anomalous diffusion

Toolbox for quantifying memory in dynamics along reaction coordinates

Memory effects in time series of experimental observables are ubiquitous, have important consequences for the interpretation of kinetic data, and may even affect the function of biomolecular nanomachines such as enzymes. Here we propose a set of complementary methods for quantifying conclusively the magnitude and duration of memory in a time series of a reaction coordinate. The toolbox is general, robust, easy to use, and does not rely on any underlying microscopic model. As a proof of concept we apply it to the analysis of memory in the dynamics of the end-to-end distance of the analytically solvable Rouse-polymer model, an experimental time series of extensions of a single DNA hairpin measured by optical tweezers, and the fraction of native contacts in a small protein probed by atomistic molecular dynamics simulations

BetheSF V2: 3-point propagator and additional external potentials

In a recent paper (Comput. Phys. Commun. 258 (2021) 107569) we obtained exactly the tagged-particle propagator in a single-file with N particels diffusing in a generic confining potential via the coordinate Bethe-Ansatz. A naïve implementation of this solution requires a non-polynomial algorithm. To speed-up the computation we implemented a more efficient algorithm that exploits the particle exchange-symmetry. In this new version we expand the code-base to allow for the computation of the three point Green's function. The latter is required e.g. in the analysis of the breaking of time-translational invariance. In addition we include the support for two canonical potentials of general interest: one presenting an energy barrier and one featuring an asymmetric potential landscape

Time- and ensemble-average statistical mechanics of the Gaussian network model

We present analytical results for a set of time- and ensemble-averaged physical observables in the non-Hookean Gaussian network model (GNM)—a generalization of the Rouse model to elastic networks with links that display a certain degree of extensional and rotational stiffness. We focus on a set of coarse-grained observables that may be of interest in the analysis of GNM in the context of internal motions in proteins and mechanical frames in contact with a heat bath. A C++ computer code is made available that implements all analytical results

Advanced Glycation End Products are Increased in the Skin and Blood of Patients with Severe Psoriasis

Psoriasis is frequently associated with metabolic comorbidities. Advanced glycation end products (AGEs) are highly oxidant, biologically active compounds that accumulate in tissues in association with hyperglycaemia, hyperlipidaemia and oxidative stress. This is a cross-sectional case-control study involving 80 patients with mild/severe psoriasis and 80 controls matched for age, sex and body mass index (40 with severe eczema, 40 healthy individuals). Patients and healthy individuals with a smoking habit, diabetes, dyslipidaemia, hypercholesterolaemia, hypertension or who were under systemic treatment were excluded from the study. Skin AGEs were measured in normal-appearing skin by a standard fluorescence technique, and blood AGEs (total AGEs, pentosidine and AGEs receptor) by enzyme-linked immunosorbent assay. Levels of cutaneous AGEs (p < 0.04), serum AGEs (p < 0.03) and pentosidine (p < 0.05) were higher in patients with severe psoriasis. Cutaneous AGEs correlated well with serum AGEs (r = 0.93, p < 0.0001) and with Psoriasis Area and Severity Index score (r = 0.91, p < 0.0001). Receptor levels were lower (p < 0.001) in severe psoriasis, and inversely correlated with disease severity (r = –0.71, p < 0.0002). Patients with severe psoriasis have accumulation of skin and serum AGEs, independent of associated metabolic disorders