Biology subjects

Endres, R. G.

Publications and source records attributed to Endres, R. G..

5 recordsLinked to original sources

bioRxiv2024

Optimal network sizes for most robust Turing patterns

Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor models and generally do not require fine-tuning of parameters as dictated by the Turing conditions. To address these issues, we employ random matrix theory to analyze the Jacobian matrices of larger networks with robust statistical properties. Our analysis reveals that Turing patterns are more likely to occur by chance than previously thought and that the most robust Turing networks have an optimal size, surprisingly consisting only of a handful of molecular species, thus significantly increasing their identifiability in biological systems. This optimal size emerges from a tradeoff between the highest stability in small networks and the greatest instability with diffusion in large networks. Furthermore, we find that with multiple immobile nodes, differential diffusion ceases to be important for Turing patterns. Our findings may inform future synthetic biology approaches and provide insights into bridging the gap to complex developmental pathways.

biophysics↗

bioRxiv2024

Effects of multistability, absorbing boundaries and growth on Turing pattern formation

Turing patterns are a fundamental concept in developmental biology, describing how homogeneous tissues develop into self-organized spatial patterns. However, the classical Turing mechanism, which relies on linear stability analysis, often fails to capture the complexities of real biological systems, such as multistability, non-linearities, growth, and boundary conditions. Here, we explore the impact of these factors on Turing pattern formation, contrasting linear stability analysis with numerical simulations based on a simple reaction-diffusion model, motivated by synthetic gene-regulatory pathways. We demonstrate how non-linearities introduce multistability, leading to unexpected pattern outcomes not predicted by the traditional Turing theory. The study also examines how growth and realistic boundary conditions influence pattern robustness, revealing that different growth regimes and boundary conditions can disrupt or stabilize pattern formation. Our findings are critical for understanding pattern formation in both natural and synthetic biological systems, providing insights into engineering robust patterns for applications in synthetic biology. Author summaryDuring development, tissues self-organize to go from a single cell to a structured organism. In this process, simple chemical reactions lead to the emergence of the intricate designs we see in nature, like the stripes on a zebra or the labyrinths on a brain cortex. Although multiple theories have been proposed to model this phenomenon, one of the most simple and popular ones was introduced in the 1950s by the mathematician Alan Turing. However, his theory oversimplifies the biological conditions and ignores properties such as non-linearities, boundary effects, or growth in the tissue. In this work, we used a combination of mathematical models and computer simulations to investigate how these real-world factors influence pattern formation. Our findings show that when we account for these realistic effects, the patterns that emerge can be very different from what Turings theory would predict. Thus, this work may help us better understand the laws behind pattern formation and could have practical applications in tissue engineering for medical or environmental applications.

biophysics↗

bioRxiv2023

A three-node Turing gene circuit forms periodic spatial patterns in bacteria

Turing patterns1 are well-known self-organising systems that can form spots, stripes, or labyrinths. They represent a major theory of patterning in tissue organisation, due to their remarkable similarity to some natural patterns, such as skin pigmentation in zebrafish2, digit spacing3,4, and many others. The involvement of Turing patterns in biology has been debated because of their stringent fine-tuning requirements, where patterns only occur within a small subset of parameters5,6. This has complicated the engineering of a synthetic gene circuit for Turing patterns from first principles, even though natural genetic Turing networks have been successfully identified4,7. Here, we engineered a synthetic genetic reaction-diffusion system where three nodes interact according to a non-classical Turing network with improved parametric robustness6. The system was optimised in E. coli and reproducibly generated stationary, periodic, concentric stripe patterns in growing colonies. The patterns were successfully reproduced with a partial differential equation model, in a parameter regime obtained by fitting to experimental data. Our synthetic Turing system can contribute to novel nanotechnologies, such as patterned biomaterial deposition8,9, and provide insights into developmental patterning programs10.

synthetic biology↗

bioRxiv2021

Thermodynamic constraints on the diversity of microbial ecosystems

Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. However, most of this interest has focused on developing coarse ecosystem-level maximisation principles, providing little insight into underlying mechanisms that lead to such emergent constraints. Microbial communities are a natural system to decipher this mechanistic basis because their interactions in the form of substrate consumption, metabolite production, and cross-feeding can be described explicitly in thermodynamic terms. Previous work has considered how thermodynamic constraints impact competition between pairs of species, but restrained from analysing how this manifests in complex dynamical systems. To address this gap, we develop a thermodynamic microbial community model with fully reversible reaction kinetics, which allows direct consideration of free-energy dissipation. This also allows species to interact via products rather than just substrates, increasing the dynamical complexity, and allowing a more nuanced classification of interaction types to emerge. Using this model, we find that community diversity increases with substrate lability, because greater free-energy availability allows for faster generation of niches. Thus, more niches are generated in the time frame of community establishment, leading to higher final species diversity. We also find that allowing species to make use of near-to-equilibrium reactions increases diversity in a low free-energy regime. In such a regime, two new thermodynamic interaction types that we identify here reach comparable strengths to the conventional (competition and facilitation) types, emphasising the key role that thermodynamics plays in community dynamics. Our results suggest that accounting for realistic thermodynamic constraints is vital for understanding the dynamics of real-world microbial communities. Author summaryThere is a growing interest in microbial communities due to their important role in biogeochemical cycling as well as plant and animal health. Although our understanding of thermodynamic constraints on individual cells is rapidly improving, the impact of these constraints on complex microbial communities remains largely unexplored theoretically and empirically. Here, we develop a new microbial community model which allows thermodynamic efficiency and entropy production to be calculated directly. We find that availability of substrates with greater free-energy allows for a faster rate of niche generation, leading to higher final species diversity. We also show that when the free-energy availability is low, species with reactions close to thermodynamic equilibrium are favoured, leading to more diverse and efficient communities. In addition to the conventional interaction types (competition and facilitation), our model reveals the existence of two novel interaction types mediated by products rather than substrates. Though the conventional interactions are generally the strongest, the novel interaction types are significant when free-energy availability is low. Our results suggest that non-equilibrium thermodynamics need to be considered when studying microbial community dynamics.

ecology↗

bioRxiv2018

Common behavioral mechanisms underlie C. elegans aggregation and swarming

In complex biological systems, simple individual-level behavioral rules can give rise to emergent group-level behavior. While such collective behavior has been well studied in cells and larger organisms, the mesoscopic scale is less understood, as it is unclear which sensory inputs and physical processes matter a priori. Here, we investigate collective feeding in the roundworm C. elegans at this intermediate scale, using quantitative phenotyping and agent-based modeling to identify behavioral rules underlying both aggregation and swarming--a dynamic phenotype only observed at longer timescales. Using fluorescent multi-worm tracking, we quantify aggregation behavior in terms of individual dynamics and population-level statistics. Based on our quantification, we use agent-based simulations and approximate Bayesian inference to identify three key behavioral rules that give rise to aggregation: cluster-edge reversals, a density-dependent switch between crawling speeds, and taxis towards neighboring worms. Our simulations suggest that swarming is simply driven by local food depletion but otherwise employs the same behavioral mechanisms as the initial aggregation. Hence, mesoscopic C. elegans uses mechanisms familiar from microscopic systems for aggregation, but implemented via more complex behaviors characteristic of macroscopic organisms.

biophysics↗