Agent-based modeling of multicell morphogenic processes during development

A central challenge in the field of developmental biology is to understand how mechanisms at one level of biological scale (i.e., cell-level) interact to produce higher-level (i.e., tissue-level) phenomena. This challenge is particularly relevant to the study of tissue morphogenesis, the process that generates newly formed, remodeled, or regenerated tissue structures. Morphogenesis arises from the spatially- and temporally-dynamic interactions of individual cells with each other and their local environment. Computational models have been combined with experimental efforts to accelerate the discovery processes. Agent-based modeling (ABM) is a computational technique that can be used to model collections of individual biological cells and compute their interactions, which generate emergent tissue-level results. Recently, ABM has been applied to the study of various developmental morphogenic processes, and the purpose of this review is to summarize these studies in order to demonstrate the types of advances that can be expected from pursuing a multicell ABM approach. We also highlight some challenges associated with ABM and suggest strategies for overcoming them. While ABM's application to the study of ecology, epidemiology, and social sciences has a much longer history, we suggest that the application of ABM to the study of morphogenesis has great utility, and when paired with benchtop experimentation, ABM can provide new insights and direct future experimentation.     

A microfabricated array bioreactor for perfused 3D liver culture

We describe the design, fabrication, and performance of a bioreactor that enables both morphogenesis of 3D tissue structures under continuous perfusion and repeated in situ observation by light microscopy. Three-dimensional scaffolds were created by deep reactive ion etching of silicon wafers to create an array of channels (through-holes) with cell-adhesive walls. Scaffolds were combined with a cell-retaining filter and support in a reactor housing designed to deliver a continuous perfusate across the top of the array and through the 3D tissue mass in each channel. Reactor dimensions were constructed so that perfusate flow rates meet estimated values of cellular oxygen demands while providing fluid shear stress at or below a physiological range (<2 dyne cm(2)), as determined by comparison of numerical models of reactor fluid flow patterns to literature values of physiological shear stresses. We studied the behavior of primary rat hepatocytes seeded into the reactors and cultured for up to 2 weeks, and found that cells seeded into the channels rearranged extensively to form tissue like structures and remained viable throughout the culture period. We further observed that preaggregation of the cells into spheroidal structures prior to seeding improved the morphogenesis of tissue structure and maintenance of viability. We also demonstrate repeated in situ imaging of tissue structure and function using two-photon microscopy.     

The Fog signaling pathway: Insights into signaling in morphogenesis

Epithelia form the building blocks of many tissue and organ types. Epithelial cells often form a contiguous 2-dimensional sheet that is held together by strong adhesions. The mechanical properties conferred by these adhesions allow the cells to undergo dramatic three-dimensional morphogenetic movements while maintaining cell–cell contacts during embryogenesis and post-embryonic development. The Drosophila Folded gastrulation pathway triggers epithelial cell shape changes that drive gastrulation and tissue folding and is one of the most extensively studied examples of epithelial morphogenesis. This pathway has yielded key insights into the signaling mechanisms and cellular machinery involved in epithelial remodeling. In this review, we discuss principles of morphogenesis and signaling that have been discovered through genetic and cell biological examination of this pathway. We also consider various regulatory mechanisms and the system?s relevance to mammalian development. We propose future directions that will continue to broaden our knowledge of morphogenesis across taxa.     

A DEAD-box RNA helicase promotes thermodynamic equilibration of kinetically trapped RNA structures in vivo

RNAs must assemble into specific structures in order to carry out their biological functions, but in vitro RNA folding reactions produce multiple misfolded structures that fail to exchange with functional structures on biological time scales. We used carefully designed self-cleaving mRNAs that assemble through well-defined folding pathways to identify factors that differentiate intracellular and in vitro folding reactions. Our previous work showed that simple base-paired RNA helices form and dissociate with the same rate and equilibrium constants in vivo and in vitro. However, exchange between adjacent secondary structures occurs much faster in vivo, enabling RNAs to quickly adopt structures with the lowest free energy. We have now used this approach to probe the effects of an extensively characterized DEAD-box RNA helicase, Mss116p, on a series of well-defined RNA folding steps in yeast. Mss116p overexpression had no detectable effect on helix formation or dissociation kinetics or on the stability of interdomain tertiary interactions, consistent with previous evidence that intracellular factors do not affect these folding parameters. However, Mss116p overexpression did accelerate exchange between adjacent helices. The nonprocessive nature of RNA duplex unwinding by DEAD-box RNA helicases is consistent with a branch migration mechanism in which Mss116p lowers barriers to exchange between otherwise stable helices by the melting and annealing of one or two base pairs at interhelical junctions. These results suggest that the helicase activity of DEAD-box proteins like Mss116p distinguish intracellular RNA folding pathways from nonproductive RNA folding reactions in vitro and allow RNA structures to overcome kinetic barriers to thermodynamic equilibration in vivo.     

VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development

Plant organs, including leaves and roots, develop by means of a multilevel cross talk between gene regulation, patterned cell division and cell expansion, and tissue mechanics. The multilevel regulatory mechanisms complicate classic molecular genetics or functional genomics approaches to biological development, because these methodologies implicitly assume a direct relation between genes and traits at the level of the whole plant or organ. Instead, understanding gene function requires insight into the roles of gene products in regulatory networks, the conditions of gene expression, etc. This interplay is impossible to understand intuitively. Mathematical and computer modeling allows researchers to design new hypotheses and produce experimentally testable insights. However, the required mathematics and programming experience makes modeling poorly accessible to experimental biologists. Problem-solving environments provide biologically intuitive in silico objects ("cells", "regulation networks") required for setting up a simulation and present those to the user in terms of familiar, biological terminology. Here, we introduce the cell-based computer modeling framework VirtualLeaf for plant tissue morphogenesis. The current version defines a set of biologically intuitive C++ objects, including cells, cell walls, and diffusing and reacting chemicals, that provide useful abstractions for building biological simulations of developmental processes. We present a step-by-step introduction to building models with VirtualLeaf, providing basic example models of leaf venation and meristem development. VirtualLeaf-based models provide a means for plant researchers to analyze the function of developmental genes in the context of the biophysics of growth and patterning. VirtualLeaf is an ongoing open-source software project (http://virtualleaf.googlecode.com) that runs on Windows, Mac, and Linux.     

Determination of mechanical stress distribution in Drosophila wing discs using photoelasticity

Morphogenesis, the process by which all complex biological structures are formed, is driven by an intricate interplay between genes, growth, as well as intra- and intercellular forces. While the expression of different genes changes the mechanical properties and shapes of cells, growth exerts forces in response to which tissues, organs and more complex structures are shaped. This is exemplified by a number of recent findings for instance in meristem formation in Arabidopsis and tracheal tube formation in Drosophila. However, growth not only generates forces, mechanical forces can also have an effect on growth rates, as is seen in mammalian tissues or bone growth. In fact, mechanical forces can influence the expression levels of patterning genes, allowing control of morphogenesis via mechanical feedback. In order to study the connections between mechanical stress, growth control and morphogenesis, information about the distribution of stress in a tissue is invaluable. Here, we applied stress-birefringence to the wing imaginal disc of Drosophila melanogaster, a commonly used model system for organ growth and patterning, in order to assess the stress distribution present in this tissue. For this purpose, stress-related differences in retardance are measured using a custom-built optical set-up. Applying this method, we found that the stresses are inhomogeneously distributed in the wing disc, with maximum compression in the centre of the wing pouch. This compression increases with wing disc size, showing that mechanical forces vary with the age of the tissue. These results are discussed in light of recent models proposing mechanical regulation of wing disc growth.     

Ectodysplasin regulates activator-inhibitor balance in murine tooth development through Fgf20 signaling

Uncovering the origin and nature of phenotypic variation within species is the first step in understanding variation between species. Mouse models with altered activities of crucial signal pathways have highlighted many important genes and signal networks regulating the morphogenesis of complex structures, such as teeth. The detailed analyses of these models have indicated that the balanced actions of a few pathways regulating cell behavior modulate the shape and number of teeth. Currently, however, most mouse models studied have had gross alteration of morphology, whereas analyses of more subtle modification of morphology are required to link developmental studies to evolutionary change. Here, we have analyzed a signaling network involving ectodysplasin (Eda) and fibroblast growth factor 20 (Fgf20) that subtly affects tooth morphogenesis. We found that Fgf20 is a major downstream effector of Eda and affects Eda-regulated characteristics of tooth morphogenesis, including the number, size and shape of teeth. Fgf20 function is compensated for by other Fgfs, in particular Fgf9 and Fgf4, and is part of an Fgf signaling loop between epithelium and mesenchyme. We showed that removal of Fgf20 in an Eda gain-of-function mouse model results in an Eda loss-of-function phenotype in terms of reduced tooth complexity and third molar appearance. However, the extra anterior molar, a structure lost during rodent evolution 50 million years ago, was stabilized in these mice.     

DNA methylation control of tissue polarity and cellular differentiation in the mammary epithelium

Alterations in gene expression accompany cell-type-specific differentiation. In complex systems where functional differentiation depends on the organization of specific cell types into highly specialized structures (tissue morphogenesis), it is not known how epigenetic mechanisms that control gene expression influence this stepwise differentiation process. We have investigated the effect of DNA methylation, a major epigenetic pathway of gene silencing, on the regulation of mammary acinar differentiation. Our in vitro model of differentiation encompasses human mammary epithelial cells that form polarized and hollow tissue structures (acini) when cultured in the presence of basement membrane components. We found that acinar morphogenesis was accompanied with chromatin remodeling, as shown by alterations in histone 4 acetylation, heterochromatin 1 protein, and histone 3 methylated on lysine 9, and with an increase in expression of MeCP2, a mediator of DNA-methylation-induced gene silencing. DNA hypomethylation induced by treatment with 5-aza-2' deoxycytidine during acinar differentiation essentially prevented the formation of apical tissue polarity. This treatment also induced the expression of CK19, a marker of cells that are in a transitional differentiation stage. These results suggest that DNA methylation is a mechanism by which mammary epithelial differentiation is coordinated both at the tissue and cellular levels.     

Morphogenesis of Mouse Mammary Epithelium In Vivo in Response to Biomatrix Prepared from a Stimulatory Fetal Mesenchyme

Insoluble "biomatrix" of mesenchyme is a stimulator of mammary cell differentiation in vitro , but its effect in the morphogenesis is unknown. Fetal salivary mesenchyme induces intense local duct formation when implanted into adult mammary gland. We have therefore tested whether biomatrix prepared from fetal salivary mesenchyme retains this abillity to stimulate duct formation in vivo . Salivary mesenchyme isolated from mouse fetuses at 13.5–14.0 days of gestation, extracted sequentially with water and with 1 M NaCl, then digested with DNAse and RNAse was implanted into mammary glands of female mice and left for periods of 1–35 days. In approximately 40% of recipients, the local epithelium either formed cyst like structures, or else "spikes" of mammary epithelium penetrated the matrix forming a simplified ductwork inside it. Similar responses were elicited by salivary mesenchyme killed by freezing and also by biomatrix prepared from fetal mammary fat pad precursor tissue, mesenchyme of fetal lung, and fetal heart, liver, and brain. However when mesenchyme was either fixed with glutaraldehyde or sonicated and embedded in polymer blocks before implantation, no epithelial response was noted. These observations suggest that the biomatrix provides a passive scaffolding that contributes to morphogenesis of mammary ducts, is insufficient to support normal morphogenesis.     

Elevated expression of pp60c-src alters a selective morphogenetic property of epithelial cells in vitro without a mitogenic effect.

Madin-Darby canine kidney (MDCK) cells are highly differentiated and have retained the morphogenetic properties necessary to form polarized, multicellular epithelial structures (cysts) in vitro that resemble epithelial tissues in vivo. We introduced the c-src gene into MDCK cells to elevate the level of the plasma membrane-associated cellular tyrosine kinase, pp60c-src, to levels two- to ninefold higher than that expressed in parent MDCK cells. Our results revealed a highly discriminatory biological action of pp60c-src on the morphogenetic properties of MDCK cells. Elevated expression of pp60c-src conferred on MDCK cells the ability to undergo dramatic changes of cell shape that includes the formation of long cell processes (100 to 200 microns), never observed in control MDCK cells. The morphogenesis of multicellular epithelial cysts was altered by elevated levels of pp60c-src and led to predictable distortions of their three-dimensional architecture. However, these cells established morphologically normal cell polarity, formed adhesive epithelial cell-cell contacts indistinguishable from those of control MDCK cells, and exhibited neither focus-forming ability or anchorage-independent growth potential. Finally, we showed that MDCK cells expressing elevated levels of pp60c-src exhibit increased phosphorylation of a more limited number of phosphotyrosine-containing proteins than MDCK cells expressing pp60v-src. We suggest that a natural function of pp60c-src is to regulate the morphogenetic properties which determine the shape of differentiated cells and multicellular structures.     

In pursuit of the whole hypha.

We know organisms first of all by their forms. Rabbit and carrot, Neurospora, and Paramecium represent particular shapes and structures, patterns in space and time. Each pattern integrates innumerable molecules into a coherent whole, reproduces itself from one generation to the next, and may persist in this manner for millions of years. In this lecture, I shall discuss efforts to render a dynamic and causal account of biological morphogenesis, using fungal hyphae as a concrete exemplar. Molecular structures and interactions are necessary but not sufficient to specify patterns on a scale three to five orders of magnitude larger. The search for alternatives leads to the importation of the concept of dynamic fields, exemplified by the proposal of Bartnicki-Garcia and Gierz that apical growth and morphogenesis report the operation of a mobile vesicle-supply center. Application of field theories to biological morphogenesis is still at an early stage, but is necessary in order to resolve the paradoxical relationship between genes and form.     

Polyhedron geometry of skeletons of Mesozoic radiolarian Pantanellium

We considered the geometrical properties of skeletons of the genus Pantanellium, a type of Mesozoic radiolarian. We constructed four 3D models of fossil specimens of Pantanellium, using X-ray Micro-CT and layered manufacturing technology. Focusing on cortical shells, we approximated the skeletal structures with convex polyhedrons and investigated their geometrical properties. We summarized these properties using planar graphs. The geometrical properties differ for fossils that are believed to belong to the same species. The results of numerical simulations based on a mathematical model for spherical radiolarians were partially consistent with the skeletal structures of the specimens. We conclude that the skeletal structure of the genus Pantanellium is not fixed and is not completely optimized from the viewpoint of symmetry.     

Synthetic matrices reveal contributions of ECM biophysical and biochemical properties to epithelial morphogenesis

Epithelial cells cultured within collagen and laminin gels proliferate to form hollow and polarized spherical structures, recapitulating the formation of a rudimentary epithelial organ. However, the contributions of extracellular matrix (ECM) biochemical and biophysical properties to morphogenesis are poorly understood because of uncontrolled presentation of multiple adhesive ligands, limited control over mechanical properties, and lot-to-lot compositional variability in these natural ECMs. We engineered synthetic ECM-mimetic hydrogels with independent control over adhesive ligand density, mechanical properties, and proteolytic degradation to study the impact of ECM properties on epithelial morphogenesis. Normal cyst growth, polarization, and lumen formation were restricted to a narrow range of ECM elasticity, whereas abnormal morphogenesis was observed at lower and higher elastic moduli. Adhesive ligand density dramatically regulated apicobasal polarity and lumenogenesis independently of cell proliferation. Finally, a threshold level of ECM protease degradability was required for apicobasal polarity and lumen formation. This synthetic ECM technology provides new insights into how cells transduce ECM properties into complex morphogenetic behaviors.     

The cellular basis of cell sorting kinetics

Cell sorting is a dynamical cooperative phenomenon that is fundamental for tissue morphogenesis and tissue homeostasis. According to Steinberg's differential adhesion hypothesis, the structure of sorted cell aggregates is determined by physical characteristics of the respective tissues, the tissue surface tensions. Steinberg postulated that tissue surface tensions result from quantitative differences in intercellular adhesion. Several experiments in cell cultures as well as in developing organisms support this hypothesis.The question of how tissue surface tension might result from differential adhesion was addressed in some theoretical models. These models describe the cellular interdependence structure once the temporal evolution has stabilized. In general, these models are capable of reproducing sorted patterns. However, the model dynamics at the cellular scale are defined implicitly and are not well-justified. The precise mechanism describing how differential adhesion generates the observed sorting kinetics at the tissue level is still unclear.It is necessary to formulate the concepts of cell level kinetics explicitly. Only then it is possible to understand the temporal development at the cellular and tissue scales. Here we argue that individual cell mobility is reduced the more the cells stick to their neighbors. We translate this assumption into a precise mathematical model which belongs to the class of stochastic interacting particle systems. Analyzing this model, we are able to predict the emergent sorting behavior at the population level. We describe qualitatively the geometry of cell segregation depending on the intercellular adhesion parameters. Furthermore, we derive a functional relationship between intercellular adhesion and surface tension and highlight the role of cell mobility in the process of sorting. We show that the interaction between the cells and the boundary of a confining vessel has a major impact on the sorting geometry.     

Morphogenesis of fingers and branched organs: how collagen and fibroblasts break the symmetry of growing biological tissue

Understanding the growth of branching organs is an important scientific endeavour. It has crucial applications, from saving premature newborns, to repairing or even regenerating organs. Despite differences in timing and shape, branching morphogenesis of all branching organs or glands (lung, kidney, salivary, lachrymal, mammary glands, sebaceous and sweat glands, prostate, guts papillae etc.) is similar: an epithelial sheet of cells, forming a 2D layer, penetrates into a 3D mass of mesenchymal cells. Inside the epithelium, a lumen is filled with fluid. As the epithelium grows, it evolves into a branched structure. The pattern of branches is in some cases stereotypic, deterministic, and it has memory effects. We present a simple line of reasoning that predicts that viscous fingering of biological tissue will exhibit all of these features. The line of reasoning is based on the idea that surface tension selects the shape of a growing branch, as is well known in the context of moving boundary problems, except that in this case, the surface is akin to a liquid-crystal. The anisotropy of the surface tension comes from a symmetry breaking by collagen and fibroblasts. The equilibrium shape of the corresponding boundary is that of an actual fingertip, and the out-of-equilibrium shape is that of branched organs, such as the lung.     

Emergent morphogenesis: Elastic mechanics of a self-deforming tissue

Multicellular organisms are generated by coordinated cell movements during morphogenesis. Convergent extension is a key tissue movement that organizes mesoderm, ectoderm, and endoderm in vertebrate embryos. The goals of researchers studying convergent extension, and morphogenesis in general, include understanding the molecular pathways that control cell identity, establish fields of cell types, and regulate cell behaviors. Cell identity, the size and boundaries of tissues, and the behaviors exhibited by those cells shape the developing embryo; however, there is a fundamental gap between understanding the molecular pathways that control processes within single cells and understanding how cells work together to assemble multicellular structures. Theoretical and experimental biomechanics of embryonic tissues are increasingly being used to bridge that gap. The efforts to map molecular pathways and the mechanical processes underlying morphogenesis are crucial to understanding: (1) the source of birth defects, (2) the formation of tumors and progression of cancer, and (3) basic principles of tissue engineering. In this paper, we first review the process of tissue convergent extension of the vertebrate axis and then review models used to study the self-organizing movements from a mechanical perspective. We conclude by presenting a relatively simple “wedge-model” that exhibits key emergent properties of convergent extension such as the coupling between tissue stiffness, cell intercalation forces, and tissue elongation forces.     

Coupled analysis of in vitro and histology tissue samples to quantify structure-function relationship

The structure/function relationship is fundamental to our understanding of biological systems at all levels, and drives most, if not all, techniques for detecting, diagnosing, and treating disease. However, at the tissue level of biological complexity we encounter a gap in the structure/function relationship: having accumulated an extraordinary amount of detailed information about biological tissues at the cellular and subcellular level, we cannot assemble it in a way that explains the correspondingly complex biological functions these structures perform. To help close this information gap we define here several quantitative temperospatial features that link tissue structure to its corresponding biological function. Both histological images of human tissue samples and fluorescence images of three-dimensional cultures of human cells are used to compare the accuracy of in vitro culture models with their corresponding human tissues. To the best of our knowledge, there is no prior work on a quantitative comparison of histology and in vitro samples. Features are calculated from graph theoretical representations of tissue structures and the data are analyzed in the form of matrices and higher-order tensors using matrix and tensor factorization methods, with a goal of differentiating between cancerous and healthy states of brain, breast, and bone tissues. We also show that our techniques can differentiate between the structural organization of native tissues and their corresponding in vitro engineered cell culture models.     

Developmental biology and tissue engineering

Morphogenesis implies the controlled spatial organization of cells that gives rise to tissues and organs in early embryonic development. While morphogenesis is under strict genetic control, the formation of specialized biological structures of specific shape hinges on physical processes. Tissue engineering (TE) aims at reproducing morphogenesis in the laboratory, i.e., in vitro, to fabricate replacement organs for regenerative medicine. The classical approach to generate tissues/organs is by seeding and expanding cells in appropriately shaped biocompatible scaffolds, in the hope that the maturation process will result in the desired structure. To accomplish this goal more naturally and efficiently, we set up and implemented a novel TE method that is based on principles of developmental biology and employs bioprinting, the automated delivery of cellular composites into a three-dimensional (3D) biocompatible environment. The novel technology relies on the concept of tissue liquidity according to which multicellular aggregates composed of adhesive and motile cells behave in analogy with liquids: in particular, they fuse. We emphasize the major role played by tissue fusion in the embryo and explain how the parameters (surface tension, viscosity) that govern tissue fusion can be used both experimentally and theoretically to control and simulate the self-assembly of cellular spheroids into 3D living structures. The experimentally observed postprinting shape evolution of tube- and sheet-like constructs is presented. Computer simulations, based on a liquid model, support the idea that tissue liquidity may provide a mechanism for in vitro organ building.     

What do we mean by biological complexity?

The purpose of the present paper is to offer a precise definition of the concepts of integration, emergence and complexity in biological networks through the use of the information theory. If two distinct properties of a network are expressed by two discrete variables, the classical subadditivity principle of Shannon's information theory applies when all the nodes of the network are associated with these properties. If not, the subadditivity principle may not apply. This situation is often to be encountered with enzyme and metabolic networks, for some nodes may well not be associated with these two properties. This is precisely what is occurring with an enzyme that binds randomly its two substrates. This situation implies that an enzyme, or a metabolic network, may display a joint entropy equal, smaller, or larger than the corresponding sum of individual entropies of component sub-systems. In the first case, the collective properties of the network can be reduced to the individual properties of its components. Moreover, the network is devoid of any information. In the second case, the system displays integration effects, behaves as a coherent whole, and has positive information. But if the joint entropy of the network is smaller than the sum of the individual entropies of its components, then the system has emergent collective properties and can be considered complex. Moreover, under these conditions, its information is negative. The extent of negative information is enhanced if the enzyme, or the metabolic network, is far away from equilibrium.