Interdisciplinary Center for Quantitative Modeling in Biology

Robustness strategies in growth and morphogenesis during cell polarity and tissue development

Weitao Chen, Department of Mathematics, University of California Irvine
 

Patterns of tissues are usually specified by the spatial information recognized by cells with a precise control of shapes and sizes. Current studies focus on pattern formation or growth independently, but new experimental data points to the importance of the interplay between patterning and growth. However, the mechanisms underlying the crosstalk between growth and morphogenesis remain unknown. In this talk, I will present our recent works on robustness strategies in growth control and developmental patterning with an emphasis on the role of coordination between growth and patterning in morphogenesis. We used stochastic PDE models consisting of moving boundaries of tissues that contain stem cells and their progenitors. Biological systems we studied include wing imaginal discs of drosophila and taste bud patterning of mouse tongue. I will also introduce a novel computational framework on a study of how individual cells maintain robust polarization and direct its morphological change in a noisy environment with multiple cells.

 

Ripping yourself a new one: In vivo biomechanics lessons from Hydra

Eva-Maria Schoetz Collins, Department of Physics and Section of Cell and Developmental Biology of the Division of Biological Sciences, University of California San Diego
 

The establishment of patterns in an initially near-uniform system is at the core of developmental biology. Because of its anatomic simplicity and remarkable regenerative capabilities Hydra is a well-suited system to quantitatively study pattern formation and large-scale morphological changes in vivo. I will give two examples of our current work in the Hydra system illustrating how cells can coordinate large-scale morphological changes in the organism. Firstly, I will describe the biomechanics of mouth opening. In contrast to most other animals Hydra’s mouth is sealed when not in use and thus it needs to rip a hole every time it wants to eat. Secondly, I will talk about the use of physics concepts to explain cell sorting of epithelial cells during regeneration of Hydra from cellular aggregates. Because cell sorting is a basic mechanism to generate tissue boundaries during animal development, our results in Hydra may provide insights into tissue organization in general.

 

Functional-Structural Modelling of Fruit Trees Using L-Systems

Ted DeJong, Department of Plant Sciences, UC Davis
 

Dynamic simulation of the growth and physiology of trees is a complex problem that requires modelling the assimilation and distribution resources to individual organs of a tree while simultaneously growing the architecture of trees in three-dimensional space in response to the availability of those resources, under specific environmental conditions and over multiple years. The L-PEACH model uses L-systems to approach this problem. It simultaneously simulates the architectural development and carbohydrate dynamics (assimilation, transport, distribution, storage and remobilization) and water use of growing peach trees. L-PEACH combines the supply/demand concepts of carbon allocation with an L-systems model of tree architecture to create a distributed supply/demand system of carbon allocation in a three dimensional, growing, virtual tree. The L-PEACH model was expressed in terms of modules that represent plant organs. Organs were represented as a set of elementary sources and sinks for carbohydrates and the whole plant was modeled as a branching network of modules (i.e. organs) connected by conductive elements. This work resulted in realistic simulations of peach tree growth and development over multiple years. Recently, this work has been extended to simulate the growth and development of almond trees however the L-ALMOND model has pointed out substantial limitations of our L-systems for simulating the growth of large unpruned trees. Converting the L-PEACH model to an L-ALMOND model initially required merely substituting the peach parameters for each of the different organ types (modules) to values appropriate for almond, based on data from field experiments. However, the L-PEACH model accommodated manual pruning of simulated trees and pruning was always practiced when simulating tree growth over multiple years. This resulted in substantial reduction in tree (and L-string) complexity after each pruning when running the L-PEACH model.  Since almond trees are rarely pruned much after the 2nd year in an orchard, simulation of almond tree growth without pruning resulted in unrealistically dense simulated canopies, exponentially increased L-string complexity with time and unsatisfactory rates of virtual tree simulation.  To overcome this, a function for simulating stem/spur mortality based on within-canopy shading was developed. However, the current L-ALMOND model, while capable of realistic simulations of almond tree growth over the first four years of growth, approaches the limit of usefulness for simulations beyond four years because of computational times required for each hourly time step.

 

The revival of an old enigma: Phyllotaxis at the era of molecular and computational biology

Christophe Godin, Director of the INRIA project on plant modeling, Head of the Inria/Cirad/Inra project-team Virtual Plants, Université Montpellier 2, France
 

Over the last two centuries, multidisciplinary research on phyllotaxis has led to a common deterministic explanation of the striking symmetries displayed by the arrangement of organs along plant axes. In this view, recently created primodia at the tip of axes locally inhibit the formation of other primordia in their immediate vicinity. Due to growth, these already existing primordia get progressively away from the initiation zone, leaving periodically space for new initiations at the tip. The frequency and position of these initiations emerge from this dynamical process and produce these familiar spiral and whorl patterns. This deterministic vision, based on the production of a field of inhibition by each primordium, largely prevailed at the end of the 20th century as the “classical model” of phyllotaxis. But no clear physical or molecular interpretation of these fields was known. In recent years, however, due to the spectacular progresses of molecular biology and imaging techniques, it became possible to seek for the mechanistic causes of these inhibitory interactions. In this talk, I will sketch the progresses that have been made in the last 15 years in trying to find out the bio-chemical and/or physical actors underlying the classical model’s hypotheses. I will emphasize how a deeper understanding of the phyllotaxis mechanism and model extensions have progressively emerged from the fertile dialogue between biology, mathematics and computer science.

 

Exocytosis-centered mechanisms for tip growth underlie growth guidance in pollen tubes

Nan Luo, Department of Botany and Plant Sciences, University of California Riverside
 

Rapid tip growth, an extreme form of self-organizing polar growth that generates highly elongated cells, is essential for growth guidance, e.g. targeting to long-distance destinations in response to external vectorial cues. Using mathematical modeling and experimental approaches, here we have established an exocytosis-centered mechanism underlying the tip growth and growth guidance of Arabidopsis pollen tubes: Exocytosis maintains the polarity of intracellular signaling and modulates cell wall mechanics required for cell growth and morphogenesis, and by coupling with external guidance signal, this system is responsible for efficient and robust growth guidance. Experimental perturbations of key factors in this system alter the behavior of pollen tubes as predicted by computational simulations, providing quantitative insights into how the system is maintained and regulated.

 

Collective Cell Migration: Where the Experimental Rubber Meets the Theoretical Road

Rebecca McLennan (1), Linus Schumacher (2), Jason Morrison (1), Jessica Teddy (1), Ruth Baker (2), Philip Maini (2) and Paul Kulesa (1).

1 - Stowers Institute for Medical Research / 2 - Wolfson Centre for Mathematical Biology, Mathematical Institute, Oxford University

The neural crest is an excellent model to study collective cell migration since cells invade throughout the entire embryo in discrete migratory streams. Failure of proper neural crest cell migration often results in major birth defects to the craniofacial, cardiovascular, and peripheral nervous systems since multipotent neural crest cells contribute to nearly every major organ. Furthermore, the neural crest is an important model system for cancer cell invasion, given that two of the most aggressive cancers (neuroblastoma and melanoma) are derived from this embryonic population. Here, I will present a study of neural crest migration and describe a cell-induced gradient model in which lead cells readout guidance cues in the embryonic microenvironment and transfer information to trailing cells in order to move as a collective.

 

Multiscale cell-based modeling of mechanical cell-cell communication and tissue-level responses to mechanical strain

Roeland Merks, Centrum Wiskunde & Informatica (CWI), Amsterdam, the Netherlands

Apart from molecular signals, mechanical cell-cell communication is key to explaining collective cell behavior during biological morphogenesis. Using a novel, hybrid Cellular Potts and finite element computational model we study how mechanical interactions between cells and the extracellular matrix (ECM) can regulate single cell behavior and collective cell behavior during biological morphogenesis. Our model describes the contractile forces that cells exert on the ECM, the resulting strains fields in the ECM, and the cellular response to local strains. The model simulations reproduce the behavior of individual endothelial cells on compliant matrices, and show that local cell-ECM interactions suffice for explaining interactions of endothelial cell pairs and collective cell behavior, including network formation and sprouting from spheroids.  If an external strain is exerted on the ECM, the cells rapidly align with the strain field, even in response to very subtle strain cues.  We will also present recent simulation results on chick somitogenesis under external strain. Altogether, our models suggest simple mechanisms by which local, mechanical cell-ECM interactions can assist in integrating morphological information across organization levels.

 

Declarative modeling methods for multiscale morphodynamics

Eric Mjolsness, Departments of Computer Science and Mathematics, University of California, Irvine
 

In developmental biology, especially plant development, modelers must integrate a wide variety of relevant molecular biochemical and biomechanical mechanisms and processes that can be described at different lengthscales. In addition to the molecular level these descriptions include dynamically changing networks (both regulatory and mechanical) and geometries. I argue that this complexity favors the use of modeling frameworks that can both be solved and optimized numerically but also manipulated and transformed symbolically: declarative modeling languages. Examples include computer algebra systems and grammar-like languages. I will show recent modeling methods and biological examples that fit into this approach: graph-constrained dynamical model reduction, sparse gene regulation network inference, and theoretical work towards an adaptive version of algebraic multigrid methods.

 

Data-Driven multiscale modeling of cell fate dynamics
Qing Nie, Departments of Mathematics and Bioengineering, University of California, Irvine
 

Fates of cells are not preordained. Cells make fate decisions in response to different and dynamic environmental and pathological stimuli. Recently, there has been an explosion of experimental data at various biological scales, including gene expression and epigenetic measurements at the single cell level, lineage tracing, and live imaging. While such data provide tremendous detail on individual elements, many gaps remain in our knowledge and understanding of how cells make their dynamic decisions in complex environments. In addition to developing new models to analyze data at each scale, we are working on multiscale modeling challenges in analyzing single-cell molecular data (data-rich scale) and their connections with spatial tissue dynamics (data-poor scale). Our approach requires new and challenging mathematical and computational tools in machine learning, stochastic analysis and simulations, and PDEs with moving boundaries. We then use our novel data-driven multiscale modeling approach to uncover new principles for cell fate dynamics in development, regeneration, and disease.

 

How variable cells make reproducible organs—a view from the experimentalist’s side

Adrienne Roeder, Weill Institute for Cell & Molecular Biology, Department of Plant Biology, Cornell University
 

Floral organ sizes are strikingly precise, despite the stochastic growth and division of individual cells within them. To reveal what mechanisms enable this precision, we screened for Arabidopsis mutants with variably sized sepal organs and identified mutations in the mitochondrial i-AAA protease FtsH4. Surprisingly, through live imaging, we observed reduced cellular growth variability in ftsh4 sepals compared to wild type sepals. Through computational modeling and quantitative phenotypic analysis, we found that regular organ size results from spatiotemporal averaging of the cellular variability in wild type sepals, whereas in ftsh4 mutants the averaging process is disrupted. Reactive oxygen species (ROS) accumulated in ftsh4 mutants, abnormally increasing organ size variability. ROS also accumulated in the maturing cells of wild type sepals, and lowering ROS enzymatically produced larger sepals. Our results demonstrate an inverse relationship between the robustness of plant organ size and ROS, which we show is a key regulator terminating organogenesis.

 

Tissue flow genetics: Using tissue cartography to explore stresses driving tissue morphogenesis

Sebastian Streichan, Kavli Institute for Theoretical Physics, University of California, Santa Barbara
 

Developmental biology established principles of how the body plan is laid out, morphogens setup axes, and gene expression patterns determine cell fates. Although we know organ architecture is often composed of laminar tissue, how shape is determined remains elusive. How are behaviors of multiple cell types coordinated to build complex organs? D’Arcy Thompson’s theory of shape evolution uses transformations of ‘measured’ coordinate lines to map organs between related species. Gene expression patterns established on embryos and organs setup a coordinate system that lends itself naturally to adapt this idea in a framework for tissue layer morphogenesis. Debates on mechanical aspects of tissue transformations illustrate the need of a multi-scale understanding that explains how physical stress coordinates molecular processes with tissue flows. Here, we deploy multi view light sheet microscopy to study tissue flows using D. melanogaster gastrulation as a model system. To facilitate data analysis and extract tissue flows, we designed the Image Surface Analysis Environment (ImSAnE), a cartography toolbox tailored towards analysis of layered and curved bio-image data. At the organ scale, we find the flow fields on the embryo surface exhibit simple topological configurations arranged in a sequence of three phases. Each phase associates with a typical spatial arrangement of myosin motors, that display long range modulation along major tissue axes. Quantifications of flow and myosin activation patterns feed into a quantitative physical model, that describes a viscous fluid driven by myosin generated stresses. This model explains observed flow field configurations with 80% accuracy, and predicts non-local control of tissue flows by sources generated in the germband through an incompressibility transition.