arXiv subjects

Ulrich Gerland

Publications and source records attributed to Ulrich Gerland.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian Rate Inference for Sequence Motif Dynamics in Systems of Reactive Nucleic Acids

The RNA world hypothesis suggests a pathway of how life emerged on early earth. It assumes that life started with RNA based systems, capable of storing, transmitting and replicating information, envisioning that monomers and short RNA oligomers interact to form longer strands, eventually becoming catalytically active ribozymes. Key reactions in RNA pools are hybridization, dehybridization, templated ligation, and cleavage. Those reactions depend on many environmental parameters and the wide range of possible configurations among interacting strands. In order to scan such high dimensional parameter spaces, efficient descriptions are needed. Motif rate equations project complex strand reactor dynamics onto sequence motif space. Here we present a Bayesian inference framework to infer their parameters from ligation count data produced by strand reactor simulations. This provides a framework to match the simpler motif rate equations to more complex simulations. Additionally, it is a step towards inferring reaction rate constants directly from experimental data, including rigorous uncertainty estimation. This could be an essential procedure to connect theory and experiment, and deepen our understanding of the essential features necessary for life to emerge.

physics.bio-ph↗

arXiv2026

Gradient estimators for parameter inference in discrete stochastic kinetic models

Stochastic kinetic models are ubiquitous in physics, yet inferring their parameters from experimental data remains challenging. For deterministic models, parameter inference often relies on gradients, which can be obtained efficiently through automatic differentiation (AD). However, AD cannot be applied directly to the Gillespie stochastic simulation algorithm (SSA), since sampling from a discrete set of reactions introduces non-differentiable operations. In this work, we adopt three gradient estimators from machine learning for the Gillespie SSA: the Gumbel-Softmax Straight-Through (GS-ST) estimator, the Score Function estimator, and the Alternative Path estimator. We use the estimators to evaluate gradients of steady-state and time-dependent observables, and compare their performance in representative biophysical systems with relaxation dynamics (bimolecular association) and oscillatory dynamics (repressilator). We find that the GS-ST estimator generally yields well-behaved gradient estimates, but exhibits diverging variance in challenging parameter regimes, which can cause parameter inference to fail. In these cases, other estimators provide more robust, lower variance gradients. Our results demonstrate that gradient-based parameter inference can be effectively combined with the Gillespie SSA, with different estimators offering complementary advantages.

physics.comp-ph↗

arXiv2025

MoRSAIK: Sequence Motif Reactor Simulation, Analysis and Inference Kit in Python

Origins of life research investigates how life could emerge from prebiotic chemistry only. One possible explanation provides the RNA world hypothesis. It states that life could emerge from RNA strands only, storing and transferring biological information, as well as catalyzing reactions as ribozymes. Before this state could have emerged, however, the prebiotic world was probably a purely chemical pool of short RNA strands with random sequences and without biological function performing hybridization and dehybridization, as well as ligation and cleavage. In this context relevant questions are what are the conditions that allow longer RNA strands to be built and how can information carrying in RNA sequence emerge? In order to investigate such RNA reactors, efficient simulations are needed because the space of possible RNA sequences increases exponentially with the length of the strands, as well as the number of reactions between two strands. In addition, simulations have to be compared to experimental data for validation and parameter calibration. Here, we present the MoRSAIK python package for sequence motif (or k-mer) reactor simulation, analysis and inference. It enables users to simulate RNA sequence motif dynamics in the mean field approximation as well as to infer the reaction parameters from data with Bayesian methods and to analyze results by computing observables and plotting. MoRSAIK simulates an RNA reactor by following the reactions and the concentrations of all strands inside up to a certain length (of four nucleotides by default). Longer strands are followed indirectly, by tracking the concentrations of their containing sequence motifs of that maximum length.

physics.bio-ph↗

arXiv2024

Emergence of homochirality via template-directed ligation in an RNA reactor

RNA in extant biological systems is homochiral; it consists exclusively of D-ribonucleotides rather than L-ribonucleotides. How the homochirality of RNA emerged is not known. Here, we use stochastic simulations to quantitatively explore the conditions for RNA homochirality to emerge in the prebiotic scenario of an RNA reactor, in which RNA strands react in a non-equilibrium environment. These reactions include the hybridization, dehybridization, template-directed ligation, and cleavage of RNA strands. The RNA reactor is either closed, with a finite pool of ribonucleotide monomers of both chiralities (D and L), or the reactor is open, with a constant inflow of a racemic mixture of monomers. For the closed reactor, we also consider the interconversion between D and L monomers via a racemization reaction. We first show that template-free polymerization is unable to reach a high degree of homochirality, due to the lack of autocatalytic amplification. In contrast, in the presence of template-directed ligation, with base pairing and stacking between bases of the same chirality thermodynamically favored, a high degree of homochirality can arise and be maintained, provided the non equilibrium environment overcomes product inhibition, for instance via temperature cycling. Furthermore, if the experimentally observed kinetic stalling of ligation after chiral mismatches is also incorporated, the RNA reactor can evolve towards a fully homochiral state, in which one chirality is entirely lost. This is possible because the kinetic stalling after chiral mismatches effectively implements a chiral cross-inhibition process. Taken together, our model supports a scenario where the emergence of homochirality is assisted by template-directed ligation and polymerization in a non equilibrium RNA reactor.

physics.bio-ph↗

arXiv2024

Mechanics and wrinkling patterns of pressurized bent tubes

Take a drinking straw and bend it from its ends. After sufficient bending, the tube buckles forming a kink, where the curvature is localized in a very small area. This instability, known generally as the Brazier effect, is inherent to thin-walled cylindrical shells, which are particularly ubiquitous in living systems, such as rod-shaped bacteria. However, tubular biological structures are often pressurized, and the knowledge of the mechanical response upon bending in this scenario is limited. In this work, we use a computational model to study the mechanical response and the deformations as a result of bending pressurized tubes. In addition, we employ tension-field theory to describe the mechanical behaviour before and after the wrinkling transition. Furthermore, we investigate the development and evolution of wrinkle patterns beyond the instability, showing different wrinkled configurations. We discover the existence of a multi-wavelength mode following the purely sinusoidal wrinkles and anticipating the kinked configuration of the tube.

cond-mat.soft↗

arXiv2023

Pressure-induced Shape-shifting of Helical Bacteria

Many bacterial species are helical in form, including the widespread pathogen H. pylori. Motivated by recent experiments on H. pylori showing that cell wall synthesis is not uniform, we investigate the possible formation of helical cell shape induced by elastic heterogeneity. We show, experimentally and theoretically, that helical morphogenesis can be produced by pressurizing an elastic cylindrical vessel with helical reinforced lines. The properties of the pressurized helix are highly dependent on the initial helical angle of the reinforced region. We find that steep angles result in crooked helices with, surprisingly, reduced end-to-end distance upon pressurization. This work helps to explain the possible mechanisms for the generation of helical cell morphologies and may inspire the design of novel pressure-controlled helical actuators.

cond-mat.soft↗

arXiv2022

Robust boundary formation in a morphogen gradient via cell-cell signaling

Establishing sharp and correctly positioned boundaries in spatial gene expression patterns is a central task, both in developmental and synthetic biology. We consider situations where a global morphogen gradient provides positional information to cells, but is insufficient to ensure the required boundary precision, due to different types of noise in the system. In a conceptual model, we quantitatively compare three mechanisms, which combine the global signal with local signaling between neighboring cells, to enhance the boundary formation process. These mechanisms differ with respect to the way in which they combine the signals, by following either an AND, an OR, or a SUM rule. Within our model, we analyze the dynamics of the boundary formation process, and the fuzziness of the resulting boundary. Furthermore, we consider the tunability of the boundary position, and its scaling with system size. We nd that all three mechanisms produce less fuzzy boundaries than the purely gradient-based reference mechanism, even in the regime of high noise in the local signals relative to the noise in the global signal. Among the three mechanisms, the SUM rule produces the most accurate boundary. However, in contrast to the other two mechanisms, it requires noise to exit metastable states and rapidly reach the stable boundary pattern.

physics.bio-ph↗

arXiv2021

Emergence of colloidal patterns in AC electrical fields

Suspended microparticles subjected to AC electrical fields collectively organize into band patterns perpendicular to the field direction. The bands further develop into zigzag shaped patterns, in which the particles are observed to circulate. We demonstrate that this phenomenon can be observed quite generically by generating such patterns with a wide range of particles: silica spheres, fatty acid, oil, and coacervate droplets, bacteria, and ground coffee. We show that the phenomenon can be well understood in terms of second order electrokinetic flow, which correctly predicts the hydrodynamic interactions required for the pattern formation process.Brownian particle simulations based on these interactions accurately recapitulate all of the observed pattern formation and symmetry-breaking events, starting from a homogeneous particle suspension. The emergence of the formed patterns can be predicted quantitatively within a parameter-free theory.

cond-mat.soft↗

arXiv2020

Cross-diffusion induced patterns for a single-step enzymatic reaction

Several different enzymes display an apparent diffusion coefficient that increases with the concentration of their substrate. Moreover, their motion becomes directed in substrate gradients. Currently, there are several competing models for these transport dynamics. Here, we analyze whether the enzymatic reactions can generate a significant feedback from enzyme transport onto the substrate profile. We find that this feedback can generate spatial patterns in the enzyme distribution, with just a single-step catalytic reaction. However, patterns are formed only for a subclass of transport models. For such models, nonspecific repulsive interactions between the enzyme and the substrate cause the enzyme to accumulate in regions of low substrate concentration. Reactions then amplify local substrate fluctuations, causing enzymes to further accumulate where substrate is low. Experimental analysis of this pattern formation process could discriminate between different transport models.

physics.bio-ph↗

arXiv2016

Beyond the French Flag Model: Exploiting Spatial and Gene Regulatory Interactions for Positional Information

A crucial step in the early development of multicellular organisms involves the establishment of spatial patterns of gene expression which later direct proliferating cells to take on different cell fates. These patterns enable the cells to infer their global position within a tissue or an organism by reading out local gene expression levels. The patterning system is thus said to encode positional information, a concept that was formalized recently in the framework of information theory. Here we introduce a toy model of patterning in one spatial dimension, which can be seen as an extension of Wolpert's paradigmatic "French Flag" model, to patterning by several interacting, spatially coupled genes subject to intrinsic and extrinsic noise. Our model, a variant of an Ising spin system, allows us to systematically explore expression patterns that optimally encode positional information. We find that optimal patterning systems use positional cues, as in the French Flag model, together with gene-gene interactions to generate combinatorial codes for position which we call "Counter" patterns. Counter patterns can also be stabilized against noise and variations in system size or morphogen dosage by longer-range spatial interactions of the type invoked in the Turing model. The simple setup proposed here qualitatively captures many of the experimentally observed properties of biological patterning systems and allows them to be studied in a single, theoretically consistent framework.

q-bio.MN↗

arXiv2013

Optimization of collective enzyme activity via spatial localization

The spatial organization of enzymes often plays a crucial role in the functionality and efficiency of enzymatic pathways. To fully understand the design and operation of enzymatic pathways, it is therefore crucial to understand how the relative arrangement of enzymes affects pathway function. Here we investigate the effect of enzyme localization on the flux of a minimal two-enzyme pathway within a reaction-diffusion model. We consider different reaction kinetics, spatial dimensions, and loss mechanisms for intermediate substrate molecules. Our systematic analysis of the different regimes of this model reveals both universal features and distinct characteristics in the phenomenology of these different systems. In particular, the distribution of the second pathway enzyme that maximizes the reaction flux undergoes a generic transition from co-localization with the first enzyme when the catalytic efficiency of the second enzyme is low, to an extended profile when the catalytic efficiency is high. However, the critical transition point and the shape of the extended optimal profile is significantly affected by specific features of the model. We explain the behavior of these different systems in terms of the underlying stochastic reaction and diffusion processes of single substrate molecules.

q-bio.SC↗

arXiv2013

Clustering and optimal arrangement of enzymes in reaction-diffusion systems

Enzymes within biochemical pathways are often colocalized, yet the consequences of specific spatial enzyme arrangements remain poorly understood. We study the impact of enzyme arrangement on reaction efficiency within a reaction-diffusion model. The optimal arrangement transitions from a cluster to a distributed profile as a single parameter, which controls the probability of reaction versus diffusive loss of pathway intermediates, is varied. We introduce the concept of enzyme exposure to explain how this transition arises from the stochastic nature of molecular reactions and diffusion.

q-bio.MN↗

arXiv2013

Simulation of stochastic network dynamics via entropic matching

The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space renders full-fledged stochastic simulations impractical, motivating approximation schemes. Here we propose an approximation scheme which improves upon the standard linear noise approximation while retaining similar computational complexity. The underlying idea is to minimize, at each time step, the Kullback-Leibler divergence between the true time evolved probability distribution and a Gaussian approximation (entropic matching). This condition leads to ordinary differential equations for the mean and the covariance matrix of the Gaussian. For cases of weak nonlinearity, the method is more accurate than the linear method when both are compared to stochastic simulations.

q-bio.QM↗

arXiv2011

Physical limits on cooperative protein-DNA binding and the kinetics of combinatorial transcription regulation

Much of the complexity observed in gene regulation originates from cooperative protein-DNA binding. While studies of the target search of proteins for their specific binding sites on the DNA have revealed design principles for the quantitative characteristics of protein-DNA interactions, no such principles are known for the cooperative interactions between DNA-binding proteins. We consider a simple theoretical model for two interacting transcription factor (TF) species, searching for and binding to two adjacent target sites hidden in the genomic background. We study the kinetic competition of a dimer search pathway and a monomer search pathway, as well as the steady-state regulation function mediated by the two TFs over a broad range of TF-TF interaction strengths. Using a transcriptional AND-logic as exemplary functional context, we identify the functionally desirable regime for the interaction. We find that both weak and very strong TF-TF interactions are favorable, albeit with different characteristics. However, there is also an unfavorable regime of intermediate interactions where the genetic response is prohibitively slow.

q-bio.BM↗

arXiv2011

Target search on a dynamic DNA molecule

We study a protein-DNA target search model with explicit DNA dynamics applicable to in vitro experiments. We show that the DNA dynamics plays a crucial role for the effectiveness of protein "jumps" between sites distant along the DNA contour but close in 3D space. A strongly binding protein that searches by 1D sliding and jumping alone, explores the search space less redundantly when the DNA dynamics is fast on the timescale of protein jumps than in the opposite "frozen DNA" limit. We characterize the crossover between these limits using simulations and scaling theory. We also rationalize the slow exploration in the frozen limit as a subtle interplay between long jumps and long trapping times of the protein in "islands" within random DNA configurations in solution.

q-bio.BM↗

arXiv2010

Designing sequential transcription logic: a simple genetic circuit for conditional memory

The ability to learn and respond to recurrent events depends on the capacity to remember transient biological signals received in the past. Moreover, it may be desirable to remember or ignore these transient signals conditioned upon other signals that are active at specific points in time or in unique environments. Here, we propose a simple genetic circuit in bacteria that is capable of conditionally memorizing a signal in the form of a transcription factor concentration. The circuit behaves similarly to a "data latch" in an electronic circuit, i.e. it reads and stores an input signal only when conditioned to do so by a "read command". Our circuit is of the same size as the well-known genetic toggle switch (an unconditional latch) which consists of two mutually repressing genes, but is complemented with a "regulatory front end" involving protein heterodimerization as a simple way to implement conditional control. Deterministic and stochastic analysis of the circuit dynamics indicate that an experimental implementation is feasible based on well-characterized genes and proteins. It is not known, to which extent molecular networks are able to conditionally store information in natural contexts for bacteria. However, our results suggest that such sequential logic elements may be readily implemented by cells through the combination of existing protein-protein interactions and simple transcriptional regulation.

q-bio.MN↗

arXiv2010

Induction kinetics of a conditional pH stress response system in Escherichia coli

The analysis of stress response systems in microorganisms can reveal molecular strategies for regulatory control and adaptation. Here, we focus on the Cad module, a subsystem of E. coli's response to acidic stress, which is conditionally activated at low pH only when lysine is available. When expressed, the Cad system counteracts the elevated H+ concentration by converting lysine to cadaverine under the consumption of H+, and exporting cadaverine in exchange for external lysine. Surprisingly, the cad operon displays a transient response, even when the conditions for its induction persist. To quantitatively characterize the regulation of the Cad module, we have experimentally recorded and theoretically modeled the dynamics of important system variables. We establish a quantitative model that adequately describes and predicts the transient expression behavior for various initial conditions. Our quantitative analysis of the Cad system supports a negative feedback by external cadaverine as the origin of the transient response. Furthermore, the analysis puts causal constraints on the precise mechanism of signal transduction via the regulatory protein CadC.

q-bio.MN↗

arXiv2010

Timing and dynamics of single cell gene expression in the arabinose utilization system

The arabinose utilization system of E. coli displays a stochastic "all or nothing" response at intermediate levels of arabinose, where the population divides into a fraction catabolizing the sugar at a high rate (ON state) and a fraction not utilizing arabinose (OFF state). Here we study this decision process in individual cells, focusing on the dynamics of the transition from the OFF to the ON state. Using quantitative time-lapse microscopy, we determine the time delay between inducer addition and fluorescence onset of a GFP reporter. Through independent characterization of the GFP maturation process, we can separate the lag time caused by the reporter from the intrinsic activation time of the arabinose system. The resulting distribution of intrinsic time delays scales inversely with the external arabinose concentration, and is compatible with a simple stochastic model for arabinose uptake. Our findings support the idea that the heterogeneous timing of gene induction is causally related to a broad distribution of uptake proteins at the time of sugar addition.

q-bio.MN↗