arXiv subjects

Robert G. Endres

Publications and source records attributed to Robert G. Endres.

At least 19 recordsLinked to original sources

arXiv2026

How nature discovers rare Turing islands: exploration by common limit cycles

Turing patterns are a cornerstone of biological self-organization, yet their emergence typically requires finely tuned parameters occupying narrow regions of high-dimensional space. This poses a fundamental challenge: how can evolving biological systems reliably find and exploit such rare conditions? In this work, we propose that common biochemical limit cycles, such as those arising from genetic feedback loops, can act as natural explorers of Turing space. By coupling a reaction-diffusion system to an orbit that modulates some of its parameters, we show that the system can dynamically sweep through Turing-permissive regimes and generate transient spatial patterns. We use an entropy-based measure in Fourier space to quantify pattern formation and demonstrate how cycles enhance the detectability and robustness of Turing islands. We further explore how coupling to positional gradients increases reproducibility, suggesting a route from oscillatory dynamics to stable developmental programs. Our results highlight a powerful mechanism by which nature might bootstrap complex spatial structure from simple temporal motifs.

q-bio.CB↗

arXiv2026

Robust chemotaxis beyond sensing limits: signal, noise, and strategy

Bacterial chemotaxis has long been viewed as operating near the physical limits of sensing, as originally articulated by Berg and Purcell. Recent information-theoretic analyses challenge this view, suggesting that Escherichia coli uses only a small fraction of the information available in ligand arrival statistics to bias its motion. How should such low information efficiency be interpreted at the level of behavior? Here, I argue that chemotactic performance is shaped not only by information transmission and noise, but by the strategy of movement itself. Using simple scaling arguments and minimal models, I show how run-and-tumble chemotaxis can remain robust to noise through symmetry and temporal averaging, even when internal information processing is inefficient. Comparing bacterial and eukaryotic chemotaxis highlights how different sensing strategies convert physical limits into observable behavior. These considerations suggest that low information efficiency need not imply poor performance, but may instead reflect an evolved balance between robustness, simplicity, and function.

q-bio.CB↗

arXiv2026

Is E. coli good at chemotaxis?

Bacteria seem masters of chemotaxis, yet recent work suggests otherwise. Henry Mattingly and colleagues (Nature Physics, 2026) argue that Escherichia coli uses only a small fraction of the sensory information available at its surface, challenging the long-held view that bacterial chemotaxis operates near physical sensing limits. This article offers a brief conceptual discussion of their findings, placing them in the context of classical chemotaxis models, robustness to noise, and broader perspectives drawn from physics, biology, and Greek mythology.

q-bio.CB↗

arXiv2025

The unreasonable likelihood of being: origin of life, terraforming, and AI

The origin of life on Earth via the spontaneous emergence of a protocell prior to Darwinian evolution remains a fundamental open question in physics and chemistry. Here, we develop a conceptual framework based on information theory and algorithmic complexity. Using estimates grounded in modern computational models, we evaluate the difficulty of assembling structured biological information under plausible prebiotic conditions. Our results highlight the formidable entropic and informational barriers to forming a viable protocell within the available window of Earth's early history. While the idea of Earth being terraformed by advanced extraterrestrials might violate Occam's razor from within mainstream science, directed panspermia -- originally proposed by Francis Crick and Leslie Orgel -- remains a speculative but logically open alternative. Ultimately, uncovering physical principles for life's spontaneous emergence remains a grand challenge for biological physics.

q-bio.PE↗

arXiv2025

From Toggle to Tuning: Controlling Turing Patterns in Gene Circuits

Controlling spatial patterns in synthetic biological systems remains challenging due to poor parameter robustness and limited experimental tunability. We introduce two complementary mechanisms-the pattern switch and the pattern dial-to systematically control Turing pattern formation in gene circuits. The switch toggles pattern onset via a single parameter, while the dial enables transitions between distinct pattern types using weakly nonlinear amplitude equations. Analyzing network size reveals a key trade-off: small networks are easier to control but less robust, while larger networks gain robustness at the cost of tunability-suggesting a sweet spot for both evolvability and designability. Our results offer practical design rules for engineering programmable patterns in living systems.

physics.bio-ph↗

arXiv2025

Local Clustering and Global Spreading of Receptors for Optimal Spatial Gradient Sensing

Spatial information from cell-surface receptors is crucial for processes that require signal processing and sensing of the environment. Here, we investigate the optimal placement of such receptors through a theoretical model that minimizes uncertainty in gradient estimation. Without requiring a priori knowledge of the physical limits of sensing or biochemical processes, we reproduce the emergence of clusters that closely resemble those observed in real cells. On perfect spherical surfaces, optimally placed receptors spread uniformly. When perturbations break their symmetry, receptors cluster in regions of high curvature, massively reducing estimation uncertainty. This agrees with mechanistic models that minimize elastic preference discrepancies between receptors and cell membranes. We further extend our model to motile receptors responding to cell-shape changes and external fluid flow, demonstrating the relevance of our model in realistic scenarios. Our findings provide a simple and utilitarian explanation for receptor clustering at high-curvature regions when high sensing accuracy is paramount.

physics.bio-ph↗

arXiv2024

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.

q-bio.MN↗

arXiv2024

Persistent pseudopod splitting is an effective chemotaxis strategy in shallow gradients

Single-cell organisms and various cell types use a range of motility modes when following a chemical gradient, but it is unclear which mode is best suited for different gradients. Here, we model directional decision-making in chemotactic amoeboid cells as a stimulus-dependent actin recruitment contest. Pseudopods extending from the cell body compete for a finite actin pool to push the cell in their direction until one pseudopod wins and determines the direction of movement. Our minimal model provides a quantitative understanding of the strategies cells use to reach the physical limit of accurate chemotaxis, aligning with data without explicit gradient sensing or cellular memory for persistence. To generalize our model, we employ reinforcement learning optimization to study the effect of pseudopod suppression, a simple but effective cellular algorithm by which cells can suppress possible directions of movement. Different pseudopod-based chemotaxis strategies emerge naturally depending on the environment and its dynamics. For instance, in static gradients, cells can react faster at the cost of pseudopod accuracy, which is particularly useful in noisy, shallow gradients where it paradoxically increases chemotactic accuracy. In contrast, in dynamics gradients, cells form de novo pseudopods. Overall, our work demonstrates mechanical intelligence for high chemotaxis performance with minimal cellular regulation.

q-bio.CB↗

arXiv2023

Unraveling biochemical spatial patterns: machine learning approaches to the inverse problem of Turing patterns

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is challenging. To address this, we aim to solve the inverse problem in artificial and experimental Turing patterns. This task is challenging since high levels of noise corrupt the patterns and slight changes in initial conditions can lead to different patterns. We used both least squares to explore the problem and physics-informed neural networks to build a noise-robust method. We elucidate the functionality of our network in scenarios mimicking biological noise levels and showcase its application through a prototype involving an experimentally obtained chemical pattern. The findings reveal the significant promise of machine learning in steering the creation of synthetic patterns in bioengineering, thereby advancing our grasp of morphological intricacies within biological systems while acknowledging existing limitations.

physics.bio-ph↗

arXiv2023

Upper limits on the robustness of Turing models and other multiparametric dynamical systems

Traditional linear stability analysis based on matrix diagonalization is a computationally intensive $O(n^3)$ process for $n$-dimensional systems of differential equations, posing substantial limitations for the exploration of Turing systems of pattern formation where an additional wave-number parameter needs to be investigated. In this study, we introduce an efficient $O(n)$ technique that leverages Gershgorin's theorem to determine upper limits on regions of parameter space and the wave number beyond which Turing instabilities cannot occur. This method offers a streamlined avenue for exploring the phase diagrams of other complex multiparametric models, such as those found in systems biology.

q-bio.QM↗

arXiv2022

T cell morphodynamics reveal periodic shape oscillations in 3D migration

T cells use sophisticated shape dynamics (morphodynamics) to migrate towards and neutralise infected and cancerous cells. However, there is limited quantitative understanding of the migration process in 3D extracellular matrices (ECMs) and across timescales. Here, we leveraged recent advances in lattice light-sheet microscopy to quantitatively explore the 3D morphodynamics of migrating T cells at high spatiotemporal resolution. We first developed a new shape descriptor based on spherical harmonics, incorporating key polarisation information of the uropod. We found that the shape space of T cells is low-dimensional. At the behavioural level, run-and-stop migration modes emerge at ~150 s, and we mapped the morphodynamic composition of each mode using multiscale wavelet analysis, finding 'stereotyped' motifs. Focusing on the run mode, we found morphodynamics oscillating periodically (every ~100 s) that can be broken down into a biphasic process: front-widening with retraction of the uropod, followed by a rearward surface motion and forward extension, where intercalation with the ECM in both of these steps likely facilitates forward motion. Further application of these methods may enable the comparison of T cell migration across different conditions (e.g. differentiation, activation, tissues, and drug treatments), and improve the precision of immunotherapeutic development.

physics.bio-ph↗

arXiv2021

Thermodynamic constraints on the assembly and diversity of microbial ecosystems are different near to and far from equilibrium

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. 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.

q-bio.PE↗

arXiv2021

Physics-Informed Deep Learning Characterizes Morphodynamics of Asian Soybean Rust Disease

Medicines and agricultural biocides are often discovered using large phenotypic screens across hundreds of compounds, where visible effects of whole organisms are compared to gauge efficacy and possible modes of action. However, such analysis is often limited to human-defined and static features. Here, we introduce a novel framework that can characterize shape changes (morphodynamics) for cell-drug interactions directly from images, and use it to interpret perturbed development of Phakopsora pachyrhizi, the Asian soybean rust crop pathogen. We describe population development over a 2D space of shapes (morphospace) using two models with condition-dependent parameters: a top-down Fokker-Planck model of diffusive development over Waddington-type landscapes, and a bottom-up model of tip growth. We discover a variety of landscapes, describing phenotype transitions during growth, and identify possible perturbations in the tip growth machinery that cause this variation. This demonstrates a widely-applicable integration of unsupervised learning and biophysical modeling.

physics.bio-ph↗

arXiv2020

Thermodynamics of switching in multistable non-equilibrium systems

Multistable non-equilibrium systems are abundant outcomes of nonlinear dynamics with feedback but still relatively little is known about what determines the stability of the steady states and their switching rates in terms of entropy and entropy production. Here, we will link fluctuation theorems for the entropy production along trajectories with the action obtainable from the Freidlin--Wentzell theorem to elucidate the thermodynamics of switching between states in the large volume limit of multistable systems. We find that the entropy production at steady state plays no role, but the entropy production during switching is key. Steady-state entropy and diffusive noise strength can be neglected in this limit. The relevance to biology, ecological, and climate models is apparent.

physics.bio-ph↗

arXiv2019

Maximal information transmission is compatible with ultrasensitive biological pathways

Cells are often considered input-output devices that maximize the transmission of information by converting extracellular stimuli (input) via signaling pathways (communication channel) to cell behavior (output). However, in biological systems outputs might feed back into inputs due to cell motility, and the biological channel can change by mutations during evolution. Here, we show that the conventional channel capacity obtained by optimizing the input distribution for a fixed channel may not reflect the global optimum. In a new approach we analytically identify both input distributions and input-output curves that optimally transmit information, given constraints from noise and the dynamic range of the channel. We find a universal optimal input distribution only depending on the input noise, and we generalize our formalism to multiple outputs (or inputs). Applying our formalism to Escherichia coli chemotaxis, we find that its pathway is compatible with optimal information transmission despite the ultrasensitive rotary motors.

q-bio.CB↗

arXiv2019

Screening by changes in stereotypical behavior during cell motility

Stereotyped behaviors are series of postures that show very little variability between repeats. They have been used to classify the dynamics of individuals, groups and species without reference to the lower-level mechanisms that drive them. Stereotypes are easily identified in animals due to strong constraints on the number, shape, and relative positions of anatomical features, such as limbs, that may be used as landmarks for posture identification. In contrast, the identification of stereotypes in single cells poses a significant challenge as the cell lacks these landmark features, and finding constraints on cell shape is a non-trivial task. Here, we use the maximum caliber variational method to build a minimal model of cell behavior during migration. Without reference to biochemical details, we are able to make behavioral predictions over timescales of minutes using only changes in cell shape over timescales of seconds. We use drug treatment and genetics to demonstrate that maximum caliber descriptors can discriminate between healthy and aberrant migration, thereby showing potential applications for maximum caliber methods in automated disease screening, for example in the identification of behaviors associated with cancer metastasis.

q-bio.CB↗

arXiv2018

A Critical-like Collective State Leads to Long-range Cell Communication in Dictyostelium discoideum Aggregation

The transition from single-cell to multicellular behavior is important in early development but rarely studied. The starvation-induced aggregation of the social amoeba Dictyostelium discoideum into a multicellular slug is known to result from single-cell chemotaxis towards emitted pulses of cyclic adenosine monophosphate (cAMP). However, how exactly do transient short-range chemical gradients lead to coherent collective movement at a macroscopic scale? Here, we use a multiscale model verified by quantitative microscopy to describe wide-ranging behaviors from chemotaxis and excitability of individual cells to aggregation of thousands of cells. To better understand the mechanism of long-range cell-cell communication and hence aggregation, we analyze cell-cell correlations, showing evidence for self-organization at the onset of aggregation (as opposed to following a leader cell). Surprisingly, cell collectives, despite their finite size, show features of criticality known from phase transitions in physical systems. Application of external cAMP perturbations in our simulations near the sensitive critical point allows steering cells into early aggregation and towards certain locations but not once an aggregation center has been chosen.

q-bio.CB↗

arXiv2017

Drift and behavior of E. coli cells

Chemotaxis of the bacterium Escherichia coli is well understood in shallow chemical gradients, but its swimming behavior remains difficult to interpret in steep gradients. By focusing on single-cell trajectories from simulations, we investigated the dependence of the chemotactic drift velocity on attractant concentration in an exponential gradient. While maxima of the average drift velocity can be interpreted within analytical linear-response theory of chemotaxis in shallow gradients, limits in drift due to steep gradients and finite number of receptor-methylation sites for adaptation go beyond perturbation theory. For instance, we found a surprising pinning of the cells to the concentration in the gradient at which cells run out of methylation sites. To validate the positions of maximal drift, we recorded single-cell trajectories in carefully designed chemical gradients using microfluidics.

q-bio.CB↗