Biology subjects

Veerman, F.

Publications and source records attributed to Veerman, F..

6 recordsLinked to original sources

bioRxiv2025

Curvature induced patterns: A geometric, analytical approach to understanding a mechanochemical model

The exact mechanisms behind many morphogenic processes are still a mystery. Mechanical cues, such as curvature, play an important role when tissue or cell shape is formed. In this work, we derive and analyze a mechanochemical model. This particular spatially one-dimensional model describes the deformation of a tissue- or cell surface over time, which is driven by a morphogen that locally induces curvature. The model consists of two PDEs with periodic boundary conditions; one reaction-diffusion equation for the morphogen and one PDE that describes the dynamics of the curve, derived by taking the L2-gradient flow of the Helfrich energy. We analyze the possible steady states of this model using geometric singular perturbation theory. It turns out that the strength of interaction between the morphogen and the curvature plays a key role in the type of possible steady state solutions. In the case of weak interaction, the geometry of the slow manifolds allows only for (in space) slowly changing periodic orbits that lay completely on one slow manifold. In the case of strong interaction, there exist multiple front solutions: periodic orbits that jump between different slow manifolds. The singular skeletons of the steady state solutions do not meet the required consistency conditions for the curvature, a priori indicating that the solutions might not be observable. The observability and stability are investigated further using numerical simulation.

developmental biology↗

bioRxiv2023

Travelling waves due to negative plant-soil feedbacks in a model including tree life-stages

The emergence and maintenance of tree species diversity in tropical forests is commonly attributed to the Janzen-Connell (JC) hypothesis, which states that growth of seedlings is suppressed in the proximity of conspecific adult trees. As a result, a JC distribution due to a density-dependent negative feedback emerges in the form of a (transient) pattern where conspecific seedling density is highest at intermediate distances away from parent trees. Several studies suggest that the required density-dependent feedbacks behind this pattern could result from interactions between trees and soil-borne pathogens. However, negative plant-soil feedback may involve additional mechanisms, including the accumulation of autotoxic compounds generated through tree litter decomposition. An essential task therefore consists in constructing mathematical models incorporating both effects showing the ability to support the emergence of JC distributions. In this work, we develop and analyse a novel reaction-diffusion-ODE model, describing the interactions within tropical tree species across different life stages (seeds, seedlings, and adults) as driven by negative plant-soil feedback. In particular, we show that under strong negative plant-soil feedback travelling wave solutions exist, creating transient distributions of adult trees and seedlings that are in agreement with the Janzen-Connell hypothesis. Moreover, we show that these travelling wave solutions are pulled fronts and a robust feature as they occur over a broad parameter range. Finally, we calculate their linear spreading speed and show its (in)dependence on relevant nondimensional parameters. 2020 MSC35C07, 34C60, 34D05, 35K57, 37C25, 65M06, 92D40.

ecology↗

bioRxiv2021

Beyond Turing: Far-from-equilibrium patterns and mechano-chemical feedback

Turing patterns are commonly understood as specific instabilities of a spatially homogeneous steady state, resulting from activator-inhibitor interaction destabilised by diffusion. We argue that this view is restrictive and its agreement with biological observations is problematic. We present two alternative to the classical Turing analysis of patterns. First, we employ the abstract framework of evolution equations to enable the study of far-from-equilibrium patterns. Second, we introduce a mechano-chemical model, with the surface on which the pattern forms being dynamic and playing an active role in the pattern formation, effectively replacing the inhibitor. We highlight the advantages of these two alternatives vis-a-vis the classical Turing analysis, and give an overview of recent results and future challenges for both approaches.

systems biology↗

bioRxiv2020

The influence of autotoxicity on the dynamics of vegetation spots

Plant autotoxicity has proved to play an essential role in the behaviour of local vegetation. We analyse a reaction-diffusion-ODE model describing the interactions between vegetation, water, and autotoxicity. The presence of autotoxicity is seen to induce movement and deformation of spot patterns in some parameter regimes, a phe-nomenon which does not occur in classical biomass-water models. We aim to analytically quantify this novel feature, by studying travelling wave solutions in one spatial dimension. We use geometric singular perturbation theory to prove the existence of symmetric, stationary and non-symmetric, travelling pulse solutions, by constructing appropriate homoclinic orbits in the associated 5-dimensional dynamical system. In the singularly perturbed context, we perform an extensive scaling analysis of the dynamical system, identifying multiple asymptotic scaling regimes where (travelling) pulses may or may not be constructed. We show that, while the analytically constructed stationary pulse corresponds to its numerical counterpart, there is a discrepancy between the numerically observed travelling pulse and its analytical counterpart. Our findings indicate how the inclusion of an additional ODE may significantly influence the properties of classical biomass-water models of Klausmeier/Gray-Scott type.

ecology↗

bioRxiv2019

Robust Stability of Multicomponent Membranes: theRole of Glycolipids

We present the multicomponent functionalized free energies that characterize the low-energy packings of amphiphilic molecules within a membrane through a correspondence to connecting orbits within a reduced dynamical system. To each connecting orbits we associate a manifold of low energy membrane-type configurations parameterized by a large class of admissible interfaces. The normal coercivity of the manifolds is established through criteria depending solely on the structure of the associated connecting orbit. We present a class of examples that arise naturally from geometric singular perturbation techniques, focusing on a model that characterizes the stabilizing role of cholesterol-like glycolipids within phospholipid membranes.

biochemistry↗

bioRxiv2018

Parameter inference with analytical propagators for stochastic models of autoregulated gene expression

Stochastic gene expression in regulatory networks is conventionally modelled via the Chemical Master Equation (CME). As explicit solutions to the CME, in the form of so-called propagators, are oftentimes not readily available, various approximations have been proposed. A recently developed analytical method is based on a separation of scales that assumes significant differences in the lifetimes of mRNA and protein in the network, allowing for the efficient approximation of propagators from asymptotic expansions for the corresponding generating functions. Here, we showcase the applicability of that method to simulated data from a telegraph model for gene expression that is extended with an autoregulatory mechanism. We demonstrate that the resulting approximate propagators can be applied successfully for Bayesian parameter inference in the non-regulated model; moreover, we show that, in the extended autoregulated model, autoactivation or autorepression may be refuted under certain assumptions on the model parameters. Our results indicate that the method showcased here may allow for successful parameter inference and model identification from longitudinal single cell data.

cell biology↗