arXiv subjects

Stephan W. Grill

Publications and source records attributed to Stephan W. Grill.

6 recordsLinked to original sources

arXiv2026

In vitro binding energies capture Klf4 occupancy across the human genome

Transcription factors (TFs) regulate gene expression by binding to specific genomic loci determined by DNA sequence. Their sequence specificity is commonly summarized by a consensus binding motif. However, eukaryotic genomes contain billions of low-affinity DNA sequences to which TFs associate with a sequence-dependent binding energy. We currently lack insight into how the genomic sequence defines this spectrum of binding energies and the resulting pattern of TF localization. Here, we set out to obtain a quantitative understanding of sequence-dependent TF binding to both motif and non-motif sequences. We achieve this by first pursuing accurate measurements of physical binding energies of the human TF Klf4 to a library of short DNA sequences in a fluorescence-anisotropy-based bulk competitive binding assay. Second, we show that the highly non-linear sequence dependence of Klf4 binding energies can be captured by combining a linear model of binding energies with an Ising model of the coupled recognition of nucleotides by a TF. We find that this statistical mechanics model parametrized by our in vitro measurements captures Klf4 binding patterns on individual long DNA molecules stretched in the optical tweezer, and is predictive for Klf4 occupancy across the entire human genome without additional fit parameters.

physics.bio-ph↗

arXiv2025

Non Equilibrium Transitions in a Polymer Replication Ensemble

The fuel-driven process of replication in living systems generates distributions of copied entities with varying degrees of copying accuracy. Here we introduce a thermodynamically consistent ensemble for investigating universal population features of replicating systems. In the context of copolymer copying, coarse-graining over molecular details, we establish a phase diagram of copying accuracy. We discover sharp non-equilibrium transitions between populations of random and accurate copies. Maintaining a population of accurate copies requires a minimum energy expenditure that depends on the configurational entropy of copolymer sequences.

cond-mat.stat-mech↗

arXiv2018

Multiplex decomposition of non-Markovian dynamics and the hidden layer reconstruction problem

Elements composing complex systems usually interact in several different ways and as such the interaction architecture is well modelled by a multiplex network. However often this architecture is hidden, as one usually only has experimental access to an aggregated projection. A fundamental challenge is thus to determine whether the hidden underlying architecture of complex systems is better modelled as a single interaction layer or results from the aggregation and interplay of multiple layers. Here we show that using local information provided by a random walker navigating the aggregated network one can decide in a robust way if the underlying structure is a multiplex or not and, in the former case, to determine the most probable number of hidden layers. As a byproduct, we show that the mathematical formalism also provides a principled solution for the optimal decomposition and projection of complex, non-Markovian dynamics into a Markov switching combination of diffusive modes. We validate the proposed methodology with numerical simulations of both (i) random walks navigating hidden multiplex networks (thereby reconstructing the true hidden architecture) and (ii) Markovian and non-Markovian continuous stochastic processes (thereby reconstructing an effective multiplex decomposition where each layer accounts for a different diffusive mode). We also state and prove two existence theorems guaranteeing that an exact reconstruction of the dynamics in terms of these hidden jump-Markov models is always possible for arbitrary finite-order Markovian and fully non-Markovian processes. Finally, we showcase the applicability of the method to experimental recordings from (i) the mobility dynamics of human players in an online multiplayer game and (ii) the dynamics of RNA polymerases at the single-molecule level.

physics.soc-ph↗

arXiv2016

Stochastic resetting in backtrack recovery by RNA polymerases

Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally-inactive backtracked state is determined by a kinetic competition between 1D diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-passage time of a random walker to reach an absorbing state. We represent RNA cleavage as a stochastic resetting process, and derive exact expressions for the recovery time distributions and mean recovery times from a given initial backtrack depth for both continuous and discrete-lattice descriptions of the random walk. We show that recovery time statistics do not depend on the discreteness of the DNA lattice when the rate of 1D diffusion is large compared to the rate of cleavage.

physics.bio-ph↗

arXiv2012

Thin Films of Chiral Motors

Hydrodynamic flows in biological systems are often generated by active chiral processes near or on surfaces. Important examples are beating cilia, force generation in actomyosin networks, and motile bacteria interacting with surfaces. Here we develop a coarse grained description of active chiral films that captures generic features of flow and rotation patterns driven by chiral motors. We discuss force and torque balances within the film and on the surface and highlight the role of the intrinsic rotation field. We arrive at a two dimensional effective theory and discuss our results in the context of ciliary carpets and thin films of bacterial suspensions.

physics.bio-ph↗

arXiv2009

The first passage problem for diffusion through a cylindrical pore with sticky walls

We calculate the first passage time distribution for diffusion through a cylindrical pore with sticky walls. A particle diffusively explores the interior of the pore through a series of binding and unbinding events with the cylinder wall. Through a diagrammatic expansion we obtain first passage time statistics for the particle's exit from the pore. Connections between the model and nucleocytoplasmic transport in cells are discussed.

cond-mat.soft↗