Schedule for: 24w5202 - From Evolution to Bioengineering of Biological Patterning Mechanisms – Mathematical Advances and Challenges

The phenomenon of canalization is a license to develop models that are quantitative and dynamic yet do not begin from an enumeration of the relevant genes. Modern mathematics (ie post 1960), ‘dynamical systems’ so called, has many similarities to experimental embryology and allows the enumeration of categories of dynamical behaviors. Examples from stem cell differentiation, early mouse embryos, and self-organizing cell aggregates (organoids) will illustrate how systems with a few variables can model cell state transitions, Phenomenology of the sort envisioned is essential to bridge the scales from the cell, to tissue, to embryo, by breaking the system into blocks that can be separately parameterized.

Organ systems are complex, three-dimensional structures built for highly specialized tasks, yet arise from a relatively simple, uniform population of cells. Despite this initial simplicity, our knowledge of how early organ systems develop and the role that physical forces play in sculpting these complex tissue structures is extremely limited. Likewise, how dynamic physical environments influence cell fate or behaviour is unclear. We use the mouse embryo to investigate these fundamental problems in development. As mammalian embryos are highly sensitive, visualizing their development has been notoriously difficult. We have developed an advanced light-sheet microscope to gently and comprehensively image mouse embryo development at single-cell resolution over a course of days. With this system and computational tools, we can track individual cells and analyse patterns of divisions, as well as build dynamic cell fate maps and computational models. We are able to describe not only the morphogenesis of complex three-dimensional structures such as the formation of the early heart, neural tube, and developing foregut, but also follow the migration of specific cell types such as primordial germ cells. PGCs are specified far from their final destination and must travel through diverse tissue environments in the embryo. The dramatic embryo-wide structural changes that occur throughout this journey present significant challenges to studying this migration. Our high-resolution and dynamic imaging approaches provide new insights into the expansive and historically inaccessible journey of PGCs during mouse embryogenesis.

I will discuss how vertebrate skin colours and skin appendages (scales, feathers, hairs, ...) are patterned through Turing and mechanical instabilities. First, I will show that Reaction-diffusion (RD) models are particularly effective for understanding the skin colour patterning of lizards at the mesoscopic and macroscopic scales, without the need to parametrise the profusion of variables at the (sub)microscopic scales. I suggest that the efficiency of RD is due to its intrinsic ability to exploit continuous colour states and the relations among growth, skin-scale geometries, and the (Turing) pattern intrinsic length scale. Second, I will show that a three-dimensional mechanical model, integrating growth and material properties of embryonic skin layers, captures most of the dynamics and steady-state pattern of head scale patterning in crocodiles.

In vertebrates, blood vessels form early in development and continually sprout and remodel in order to quench the ever-increasing demands of metabolically active tissues and organs. This complex circulatory network is hierarchical, and remodeling is directed by oxygen gradients, mechanical and biochemical cues in the local microenvironment. Understanding, and predicting, how these cues combine to promote pro- or anti-vasculogenic behavior is imperative, as many human diseases are preceded and or confounded by vascular dysfunction. Primarily, our research group employs microfabrication, tissue engineering and imaging approaches to generate and observe complex microvascular networks in vitro. Specifically, we take advantage of the autonomous behaviour of vascular endothelial cells which coalesce, connect, sprout and remodel within our microsystems. By perturbing these in vitro systems in a controlled manner, we aim to understand how tissue-specific vessels develop and remodel in healthy and disease-like states. Our results have revealed how stromal cells, growth factors, and small changes in fluid dynamics impact the behavior of iPSC-derived, as well as specific primary, human vessels. This talk will highlight some of these findings and discuss our goals to combine our experimental work with computational approaches (fluid dynamics simulations and machine learning) to understand, and potentially direct, vascular behavior.

The ability to obtain an unlimited number of organ-specific cells from pluripotent stem cells has created the possibility to regenerate an organ by replenishing the failing cells with stem cell-derived ones. However, our inability to generate a functional vasculature is one of the major bottlenecks in regenerative medicine as transplanted cells die without receiving enough oxygen and nutrients. Despite decades of work and recent progress, the complexity of inducing different (often opposing) signals over time to go from a growing immature vascular network to a quiescent and mature one has limited our ability to effectively generate blood vessels in vivo as it requires multiple cell types acting in concert to respond to local cues and to deliver signals in a spatiotemporal manner. Recently, we have demonstrated that “recycling” microvessels from fat for application in cell transplantation leads to the formation of a functional vasculature in different regenerative medicine models (cardiac ischemia, diabetes etc.). This uniquely poises us to analyze microvessel revascularization in depth to uncover the blueprint of successful vascularization. This will allow us to ‘guide’ stem cell-derived vascular cells into forming a functional vasculature, enabling us to create an isogenic cell product for organ regeneration that can regenerate both the functional units of the organ and the vasculature to support them. In this talk, I will present some preliminary data and discuss our strategy for using experimental data in combination with computational approaches to identify key pathways in revascularization to be applied enable effective vascularization.

Cells respond to and reorganize based on their mechanical and biochemical environment. However, quan;fying forces ac;ng on the ;ssue and determining its biochemical environment is challenging in vivo and in vitro. Computa;onal modeling offers a promising avenue to inves;gate ;ssue remodeling, genera;ng new knowledge from simula;ons that can inform hypothesis-driven research. In this talk, I will present our computa;onal modeling approach for vascular flow and transport simula;ons and discuss strategies to bridge scales from organ to ;ssue/cell level. I will highlight two examples of the applica;on of our models in cardiovascular disease and placental development, demonstra;ng the prac;cal implica;ons of our models.

The outer layer of the human brain, the cortex, has a highly folded structure that emerges in utero. The cortex itself has a complex structure, with six discrete layers and a consistent pattern of thick gyri (outer ridges) and thin sulci (inner valleys). Using the tools of computational mechanics to investigate the mechanisms behind these features, we have shown that the systematic cortical thickness variations seen in the brain are likely a consequence of both heterogeneous growth and the forces generated during the extensive folding of the cortex. Here, I will lay the foundation for the mechanical hypothesis of cortical thickness variations, and explore these consistent patterns during third trimester gestational development, in adult humans, and in non-human primates. Additionally, I will discuss our recent computational model that captures the contributions of distinct neuronal cohorts to the formation of the cortical layers.

Nature manages to build complex organisms from a single cell with striking precision. By forming graded concentration profiles, morphogens can instruct cells about their position in a patterned tissue, allowing them to assume location-dependent fates. Decades of research have been dedicated to understanding the foundations of this gradient-base tissue patterning mechanism known as the French Flag model, but a key question has kept puzzling the field: How can the resulting pattern be as robust and precise as it is observed to be, given that the morphogen gradients are inevitably noisy and variable between different embryos? Here I present new insight from mathematical modeling that reveals that the high patterning precision can be explained quantitatively, without requiring precision-enhancing mechanisms such as spatial averaging, cell sorting, or the simultaneous readout of multiple morphogen gradients. A reaction-diffusion model predicts the accuracy of positional information that morphogen gradients can convey, based on measured molecular noise in the morphogen production, decay and transport kinetics. I present several striking results of this new perspective on gradient-based tissue patterning, such as the role of cell size, cell shape, tissue geometry, self-enhanced morphogen degradation, and gradient dynamics. Implications on several developmental systems such as the Drosophila wing disc and the vertebrate neural tube are also discussed.

Fluid interfaces are a common motif in cell and tissue biology, from lipid bilayers to the actomyosin cortex and epithelial monolayers. These surfaces exhibit a nonlinear coupling between shape dynamics, interfacial flows, and actively generated forces, which plays a key role in biological processes like cell division, migration, and tissue morphogenesis. I will introduce a variational framework for modeling fluid surfaces from a continuum mechanics viewpoint, offering a transparent method to derive their governing equations, which involve complex couplings between chemistry, elasticity, and hydrodynamics. Additionally, I will present numerical methods to address the high-order, stiff, governing equations, which combine elliptic and hyperbolic partial differential equations and often require discretizing tensor fields on surfaces. This theoretical and computational framework will be demonstrated with examples involving lipid bilayers, the cell cortex, epithelial tissues, and cell aggregates, highlighting its relevance in understanding and simulating these biological systems.

Tissue morphogenesis is intimately linked to the changes in shape and organization of individual cells. Within curved epithelia, cells have the capacity to intercalate along their apicobasal axes, adopting a geometric configuration named as "scutoid," which minimizes energy within the tissue. The identification of the scutoidal shape underscores the utility of accurately depict the shape of epithelial cells to understand the morphogenetic processes. I will talk about our recent advances on the understanding about the several geometric and biophysical factors being linked to the appearance of scutoids. These works include CartoCell, a deep-learning-based pipeline that detects the realistic morphology of epithelial cells and their contacts in the 3D structure of the tissue. Using this new method, I will show how we have used live imaging of sea star embryos to dissect how global and local pressures drive changes in epithelial architecture. Finally, I will discuss a new idea: we know now that scutoids are a general feature in cuboidal-columnar epithelia, but... it is possible to have animals without scutoids?

Fluorescence microscopy is one of the most common technique for quantifying biological systems, from the subcellular scale to the tissue scale. Yet, extracting meaningful physical information from fluorescent images, especially in 3D, remains a challenging task. At the same time, physical and computer models of tissues are becoming more and more realistic, but their direct comparison, calibration or initialization from biological images remains generally out of reach. Here I will present our recent efforts to bridge the gap between images and mechanical models of tissues. I will start with the presentation of a novel segmentation and 3D tension inference method that can generate 3D atlases of the mechanics of embryos or tissues comprising up to a thousand cells from microscopy images. Then I will present our cell-resolved computational model of 3D tissues based on tensional forces, which explicitly accounts for viscous dissipation at cell interfaces, can handle cell divisions or other topological events (T1, T2) and can be coupled to biochemical signaling networks to model multicellular mechanochemical feedbacks. Finally, I will show how we can close the loop between mechanical models and microscopy images with a generic and differentiable pipeline to create realistic fluorescence microscopy images from simulation meshes for devising, training or benchmarking novel image analysis methods and for seamlessly solving inverse mechanical problems.

The insect respiratory system is a network of air-filled tubes permeating the animal body, supplying oxygen for metabolic activity and removing waste carbon dioxide. The majority of gas exchange occurs in the finest regions of the tracheal system, the terminal cells. These cells have a unique and highly specialized tree-like structure with long thin branches, reminiscent of neuronal arbors. While many aspects of the terminal cell are understood on a molecular level, including the mechanisms that guide branch extension and lumen formation, the macroscopic network features that allow for proper oxygen distribution remain mysterious. We use the Drosophila terminal cell as a model system for fundamental developmental problems of net- work structure and functions, utilizing an imaging data set that fully maps the structure of over one hundred individual cells. First, we find that scaling relations succinctly encapsulate the dynamics of growing networks, and use the empirical scalings observed in the terminal cells to construct a minimal model of network growth that de- scribes the system. Second, to understand the interplay between structure and function in the trees, we developed a model of oxygen distribution by a network embedded in a two-dimensional absorbing tissue, driven purely by diffusion along oxygen partial pressure gradients. Our method works well on complex geometries, including curved and branched networks that approximate the geometry of the terminal cells. These investigations offer insights into mammalian capillary networks, which have different structural fea- tures and delivery mechanisms from terminal cells but are guided by similar developmental principles. Understanding the salient features that govern the structure of these biological networks is essential to designing synthetic vasculature, a major step in the manufacture of artificial organs.

Many natural phenomena involve individual agents coming together to create group dynamics, whether the agents are cells in a developing tissue or locusts in a swarm. Here I will focus on two examples of emergent behavior in biology: cell interactions during pattern formation in fish skin and gametophyte development in ferns. Different modeling approaches provide complementary insights into these systems and face different challenges. For example, vertex-based models describe cell shape, while more efficient agent-based models treat cells as particles. Continuum models, which track cell densities, are more amenable to analysis, but in some cases it can be more difficult to relate their few parameters to specific cell interactions. In this talk, I will overview our models of cell behavior and discuss our ongoing work on quantitatively relating different types of models using topological data analysis and data-driven techniques.

Skin, like most living tissue, adapts to mechanical cues, for example after wound healing, reconstructive surgery, or in tissue expansion. We have created computational models that combine mechanics and mechanobiology to describe the deformation, growth, and remodeling of skin, and applied these models to clinically relevant scenarios. Together with experiments on a porcine model, and leveraging ML tools such as multi-fidelity Gaussian processes, we have performed Bayesian inference to learn mechanistically how skin grows in response to stretch and heals after being wounded. One central aspect in creating these multi-scale computational models is the consideration cell-signaling networks and their dynamics. In this talk we discuss the mechnobiological and biomechanical feedback loops at play in wound healing, building models from the cell scale to the tissue level. We also show the application of these models to better understand lumpectomy wound healing. Suggested readings: Harbin Z, Sohutskay D, Vanderlaan E, Fontaine M, Mendenhall C, Fisher C, Voytik-Harbin S, Tepole AB. Computational mechanobiology model evaluating healing of postoperative cavities following breast-conserving surgery. Computers in Biology and Medicine. 2023 Oct 1;165:107342. Pensalfini M, Tepole AB. Mechano-biological and bio-mechanical pathways in cutaneous wound healing. PLoS computational biology. 2023 Mar 9;19(3):e1010902.. Sohutskay DO, Tepole AB, Voytik-Harbin SL. Mechanobiological wound model for improved design and evaluation of collagen dermal replacement scaffolds. Acta Biomaterialia. 2021;135:368-82.

Motivated by experiments of H. Togashi and M. Sato’s lab on tissue growth and early development in drosophila brain, we hypothesize an individual based model based on attractive and repulsive effects. We explore a mathematical model based on these principles that can be obtained by coarse graining to a population model for densities of cells. It is capable of reproducing and predicting mixing/segregation of populations. We show that Steinberg’s hypothesis of differential adhesion from the 60s/70s can be understood in terms of the differential strength of attraction between different cells in the experiments due to cadherin and nectins knock out/knock down. Differential adhesion is proposed as alternative mechanism to Turing for explaining pattern formation in related experiments in zebra-fish skin patterns. We discuss microscopic and continuum cell-cell adhesion models and their derivation based on the underlying microscopic assumptions. We will derive these macroscopic limits via mean-field assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type populations. The model is based on basic principles of localized repulsion and nonlocal attraction due to adhesion forces at the microscopic level. Asymptotic models are obtained via Cahn-Hilliard approximations. The new models are able to capture both qualitatively and quantitatively experiments. We also review some of the applications of these models in other areas of tissue growth in developmental biology.

We shall report on our recent investigations of transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions, considerable attention has also been directed towards understanding spatio-temporal behaviours, particularly the propagation of patterning from localised disturbances. We analyse these waves of patterning using both the well-established marginal stability criterion and weakly nonlinear analysis with envelope equations. Both methods provide estimates for the wave speed but the latter method, in addition, approximates the wave profile and amplitude. We then compare these two approaches analytically near a bifurcation point and reveal that the marginal stability criterion yields exactly the same estimate for the wave speed as the weakly nonlinear analysis. Furthermore, we evaluate these estimates against numerical results for CDIMA and Schnakenberg kinetics. In particular, our study emphasises the importance of the characteristic speed of pattern propagation, determined by diffusion dynamics and a complex relation with the reaction kinetics in Turing systems. This speed serves as a vital parameter for comparison with experimental observations, akin to observed pattern length scales. Furthermore, more generally our findings provide systematic methodologies for analysing transient wave properties in Turing systems, generating insight into the dynamic evolution of pattern formation. (In R1, minor revision, in Physica D)

Turing established that diNusion of morphogens can drive periodic patterning in tissues. Herein we explore the role of diNusion in creating salt-and-pepper patterns where adjacent cells achieve distinct cell fates. By mimicking quantitatively the pattern of rhizoid precursors in the gemmae of the plant Marchantia polymorpha, we establish a new mechanism for diNusion-driven patterning. In this mechanism, diNusion drives a switch to patterning while it does not unstabilize the homogeneous state. Consequences of these mechanism are to enable random salt-and-pepper patterning and inhomogeneous lateral inhibition, two features that we quantify in wild-type gemmae.

Most evolutionary models either do not consider development or consider it indirectly through abstract models of the genotype-phenotype map (GPM) that are uninformed by development. This limits their applicability to morphological evolution. We present a general model of evolution combining development and population genetics (i.e. selection, mutation, drift, etc.) and results arising from it. In the model, each individual’s morphology arises from its genotype through a development model, EmbryoMaker, and is selected based on that morphology. EmbryoMaker can implement any network of gene and cell interactions, cell behaviors (contraction, adhesion, etc.), cell signaling and the 3D morphologies developing from them. Our model, thus, does not assume a GPM, the GPM arises and evolves from it. We simulate how both morphology and development evolve under different selection criteria. We simulate whole morphologies and, thus, the number and nature of traits can evolve (novelty). We found that, for most selection criteria, periods of rapid evolution alternated with long stagnation periods, i.e. a ziggurat evolution. Any developmental network produces morphological variation within specific directions and specific ranges in those. Further changes beyond these ranges and directions irremediably require changes in the topology of developmental networks (e.g. mutations changing which genes regulate which). Stagnation occurs because these mutations are rare and then take some time to occur. When they finally occur, rapid evolution ensues while populations explore the new ranges and directions of morphologies produced by the new development. We contrast these findings with classical views on developmental constraints, selection and artificial selection experiments.

Turing gene regulatory networks are prominent models to study multi-cellular self-organization, but it is still unclear how they can drive different self-organizing behaviors. Here we use an automated algebraic method to derive a topological atlas of self-organizing Turing networks that can generate periodic patterns, traveling waves or noisy amplifying patterns. The atlas reveals that different self- organizing behaviors are organized into distinct topological clusters that are characterized by specific network feedbacks. These clusters are connected together by multi-functional networks that can undergo different self-organizing behaviors upon feedback modulations. Our analysis also reveals that feedbacks on immobile nodes play a central role in canalizing the noise of the system by controlling the speed and precision of pattern formation. Taken together, our results show that changes in network topology and feedback modulations can drive continuous transitions between Turing behaviors, providing a novel framework to study evolution and development of multi-cellular self-organization.

The social dinner will take place at Carmen de la Victoria, a university residence managed by the University of Granada.

Topological data analysis (TDA) comprises a set of techniques of computational topology that has had enormous growth in the last decade, with applications to a wide variety of fields, such as image analysis, biological data, meteorology, materials science, time-dependent data, economics, etc. In this talk, we will first have a walk through a typical pipeline in TDA, to move later to its adaptation to specific problems regarding biological data, such as self-organization of cells in a packed tissue or spatial distribution of different cell types from biological images.

Modeling a natural phenomenon has a dual objective: on one hand, to abstractly (and by simplification of reality) describe the set of relationships within the phenomenon under study. On the other hand, it aims to anticipate future dynamics. The global attractor accounts for all observable dynamics, both future and transient. Sometimes, we can provide an accurate description of the structure of these attractors (then defined as informational structures), generating an informational landscape that explains all system dynamics, not just the attracting ones. The relationship between the complex network serving as the substrate for the phenomenon and the structure of the attractor is an important subject of study. However, it is this informational structure that can explain certain key qualities of the phenomena which are not observable from their description as complex graphs. In this talk, we introduce these concepts of informational structures and fields and, in a non-autonomous framework (i.e., when, for instance, parameters depend on time), we will show their potential utility for some problems in Ecology.

Development plays a crucial role in determining complex phenotypes by integrating genetic, epigenetic, and environmental factors. Classical examples of how developmental processes influence complex traits include butterfly wing patterns or Arabidopsis thaliana’s floral organs, to name a few. But these examples and the broader study of the developmental underpinnings of complex phenotypes typically confront two challenges. On the one hand, the characterization of complex phenotypes is usually problematic. Although some classes of these phenotypes, like morphological or behavioural phenotypes, are now benefiting of modern large-scale microscopic and tracking techniques, we are still far from a full large- scale characterization of the phenome. A second challenges is that of quantitatively describing development. This task has usually been approached by considering a number of discrete and sequential stages associated with the onset of particular developmental phenomena. In this talk, I address this problem using two novel resources for studying phenotypes and development on a large scale in Caenorhabditis elegans. I will propose a simple null model for the association between development and complex phenotypes, discuss its limitations, and explore how pleiotropy and the level of cell organization can also be examined within this framework.

During the development of an organism, cells specialize by transitioning between a limited set of discrete cell fates, defined by distinct gene expression profiles. These transitions occur in a characteristic sequence and are controlled by cues in the environment, such as morphogens. While quantitative models that describe signaling pathways and gene regulatory networks are commonly used to investigate cell differentiation, these sometimes suffer from having too many parameters to constrain with available data, and their complexity hinders a high-level understanding. A popular and intuitive metaphor for the process of cell differentiation is the Waddington landscape, in which a differentiating cell is represented as a marble rolling down a landscape of hills and valleys, encountering decision points between different lineages, eventually settling in a valley that defines its cell fate. In this talk, we will show that this metaphor can be mathematically formalized using Catastrophe Theory, where the landscape is defined by a potential function, and the different cell states correspond to attractors in the landscape. Moreover, we will present some preliminary data where we aim to study the two complementary mathematical approaches, gene regulatory network and landscape models, in parallel.

Epithelial tissues can be dramatically remodelled during embryogenesis or in adult organs undergoing fast turnover. These events are often associated with high rates of dying cell elimination which requires well-orchestrated remodelling steps to maintain tissue sealing. This process, named cell extrusion, has been mostly analysed in regards of actomosin dynamics leading apical constriction. Yet, the mechanistic relationship between caspase activation and cell extrusion is still poorly understood. Here I will present how we found that the initiation of cell extrusion and apical constriction are surprisingly not associated with the modulation of actomyosin concentration and dynamics. Instead, cell apical constriction is initiated by the disassembly of a microtubules mesh by effector caspases. I will highlight how their disassembly by caspases is a key rate-limiting step of extrusion, and outline a more general function of microtubules in epithelial cell shape stabilisation. Accurately counting and localising cellular events from movies is an important bottleneck of tissue live imaging. I will described how we developped DeXtrusion : a new methodology based on recurrent neural networks allowing automatic detection of cellular events in live fluorescent imaging movies without segmentation. This pipeline is easily trainable, provides fast and accurate predictions in a large range of imaging conditions. Our methodology also performs well on other epithelial tissues labelled for cell contour with reasonable re-training and can easily be applied for other cellular events (cell division or cell differentiation).

This talk explores the mathematical modeling of biological patterning across diverse organisms— the filamentous cyanobacterium Anabaena, Arabidopsis thaliana plants, and Drosophila melanogaster flies. We delve into how genetic and environmental factors influence the quasi-regular patterning of nitrogen-fixing specialized cells, called heterocysts, in Anabaena. The model highlights key genes and cellular processes that govern pattern appearance and maintenance, illustrating the impact of physical boundary conditions in biological systems. For Arabidopsis, we examine how light and temperature cues affect the growth of the hypocotyl through interactions between photoreceptors and thermal sensors, shedding light on plant morphogenesis. Lastly, in Drosophila, we focus on how BMP2/4 signaling regulates cell proliferation and apoptosis to ensure precise organ size during development. This studies collectively underscore the utility of mathematical models in providing insights into the complex phenomena of patterning and growth across different biological kingdoms.

All biological systems, all the way down to individual cells, act as agents in their environment. Rather than being passively directed by local conditions, they instead drive an asymmetry with their environment: they perform actions on their own behalf and in accordance with their own goals. We are interested in the question of how minimal agency emerged at the origins of life; namely, of how dividing and evolving populations of protocells could have first started developing regulatory mechanisms that enabled them to survive under changeful environmental conditions. In my talk, I will describe an abstract 'artificial life' computational model that we are using to better frame this conceptual problem. The model abstractly represents a continuous flow chamber in a hydrothermal vent and spans three levels of scale: metabolism, ecology and evolution. I will present first results, showing that we can achieve complex cross-feeding ecologies of protocell species which evolve over time. I will also present how protocells can develop regulatory networks to deal with changing levels of environment nutrients. Our overall aim is to explore research questions such as if- and how fast regulatory networks develop in response to environmental challenges, and how they may grant a protocell ecology higher robustness, or other advantages, compared to when they are absent.

Plants, unlike animals, keep forming new organs throughout their life. The root system of plants grows and ramifies through the iterated, hierarchical formation of new side branches from older branches. These new so-called lateral roots are formed deep inside the root from which they originate, and as they develop have to carve through overlaying tissue in order to reach the soil. Interestingly, priming, the prepatterning of internal cells to endow them with the competence of future lateral root formation entails a temporally periodic signalling process involving the plant hormone auxin in the root tip that through growth becomes translated into a spatially periodic prepattern. I will discuss the cell-based models of single roots we developed to discern whether this prepatterning process involves a true oscillator, Turing patterning mechanism combined with growth or yet another mechanism, highlighting the important role of cell geometry and growth as well as stem cell division dynamics in potentially explaining lateral root priming. I will also discuss recent developments in building models for simulating overall root system architecture development as well as models incorporating tissue mechanics.

Turing patterns and positional information are two of the canonical examples of biological patterning mechanisms. The were proposed in isolation and, arguably, sometimes in antagonism to one another. Here we build on recent mathematical developments that allow us to compare different models and to quantify their differences. We will show that through this lense we can discern shared characteristics of models that were previously proposed to present the Turing or the positional information formalism. In important aspects the models show equivalences that suggest that the same molecular machinery may be repurposed for the generation of patterns under either mechanism.