Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms

<p>Abstract</p> <p>Background</p> <p>Simulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models.</p> <p>Results</p> <p>We construct a 3D model of epidermal development and provide a set of GPU algorithms that executes significantly faster than sequential central processing unit (CPU) code. We provide a parallel implementation of the subcellular element method for individual cells residing in a lattice-free spatial environment. Each cell in our epidermal model includes an internal gene network, which integrates cellular interaction of Notch signaling together with environmental interaction of basement membrane adhesion, to specify cellular state and behaviors such as growth and division. We take a pedagogical approach to describing how modeling methods are efficiently implemented on the GPU including memory layout of data structures and functional decomposition. We discuss various programmatic issues and provide a set of design guidelines for GPU programming that are instructive to avoid common pitfalls as well as to extract performance from the GPU architecture.</p> <p>Conclusions</p> <p>We demonstrate that GPU algorithms represent a significant technological advance for the simulation of complex biological models. We further demonstrate with our epidermal model that the integration of multiple complex modeling methods for heterogeneous multicellular biological processes is both feasible and computationally tractable using this new technology. We hope that the provided algorithms and source code will be a starting point for modelers to develop their own GPU implementations, and encourage others to implement their modeling methods on the GPU and to make that code available to the wider community.</p

Blood Vessel Tortuosity Selects against Evolution of Agressive Tumor Cells in Confined Tissue Environments: a Modeling Approach

Cancer is a disease of cellular regulation, often initiated by genetic mutation within cells, and leading to a heterogeneous cell population within tissues. In the competition for nutrients and growth space within the tumors the phenotype of each cell determines its success. Selection in this process is imposed by both the microenvironment (neighboring cells, extracellular matrix, and diffusing substances), and the whole of the organism through for example the blood supply. In this view, the development of tumor cells is in close interaction with their increasingly changing environment: the more cells can change, the more their environment will change. Furthermore, instabilities are also introduced on the organism level: blood supply can be blocked by increased tissue pressure or the tortuosity of the tumor-neovascular vessels. This coupling between cell, microenvironment, and organism results in behavior that is hard to predict. Here we introduce a cell-based computational model to study the effect of blood flow obstruction on the micro-evolution of cells within a cancerous tissue. We demonstrate that stages of tumor development emerge naturally, without the need for sequential mutation of specific genes. Secondly, we show that instabilities in blood supply can impact the overall development of tumors and lead to the extinction of the dominant aggressive phenotype, showing a clear distinction between the fitness at the cell level and survival of the population. This provides new insights into potential side effects of recent tumor vasculature renormalization approaches

Modeling Morphogenesis in silico and in vitro: Towards Quantitative, Predictive, Cell-based Modeling

Cell-based, mathematical models help make sense of morphogenesis—i.e. cells organizing into shape and pattern—by capturing cell behavior in simple, purely descriptive models. Cell-based models then predict the tissue-level patterns the cells produce collectively. The &#64257;rst step in a cell-based modeling approach is to isolate sub-processes, e.g. the patterning capabilities of one or a few cell types in cell cultures. Cell-based models can then identify the mechanisms responsible for patterning in vitro. This review discusses two cell culture models of morphogenesis that have been studied using this combined experimental-mathematical approach: chondrogenesis (cartilage patterning) and vasculogenesis (de novo blood vessel growth). In both these systems, radically dif- ferent models can equally plausibly explain the in vitro patterns. Quantitative descriptions of cell behavior would help choose between alternative models. We will brie&#64258;y review the experimental methodology (micro&#64258;uidics technology and traction force microscopy) used to measure responses of individual cells to their micro-environment, including chemical gradients, physical forces and neighboring cells. We conclude by discussing how to include quantitative cell descriptions into a cell-based model: the Cellular Potts model

Multiscale developments of cellular Potts models

Multiscale problems are ubiquitous and fundamental in all biological phenomena that emerge naturally from the complex interaction of processes which occur at various levels. A number of both discrete and continuous mathematical models and methods have been developed to address such an intricate network of organization. One of the most suitable individual cell-based model for this purpose is the well-known cellular Potts model (CPM). The CPM is a discrete, lattice-based, flexible technique that is able to accurately identify and describe the phenomenological mechanisms which are responsible for innumerable biological (and nonbiological) phenomena. In this work, we first give a brief overview of its biophysical basis and discuss its main limitations. We then propose some innovative extensions, focusing on ways of integrating the basic mesoscopic CPM with accurate continuous models of microscopic dynamics of individuals. The aim is to create a multiscale hybrid framework that is able to deal with the typical multilevel organization of biological development, where the behavior of the simulated individuals is realistically driven by their internal state. Our CPM extensions are then tested with sample applications that show a qualitative and quantitative agreement with experimental data. Finally, we conclude by discussing further possible developments of the metho

Partial Redundancy and Morphological Homeostasis: Reliable Development through Overlapping Mechanisms

How might organisms grow into their desired physical forms in spite of environmental and genetic variation? How do they maintain this form in spite of physical insults? This article presents a case study in simulated morphogenesis, using a physics-based model for embryonic epithelial tissue. The challenges of the underlying physics force the introduction of closed-loop controllers for both spatial patterning and geometric structure. Reliable development is achieved not through elaborate control procedures or exact solutions, but through crude layering of independent, overlapping mechanisms. As a consequence, development and regeneration together become one process, morphological homeostasis, which, owing to its internal feedbacks and partially redundant architecture, is remarkably robust to both knockout damage and environmental variation. The incomplete nature of such redundancy furnishes an evolutionary rationale for its preservation, in spite of individual knockout experiments that may suggest it has little purpose.National Science Foundation (U.S.) (Grant No. CNS-1116294)Google (Firm

Multicellular Systems Biology of Development

Embryonic development depends on the precise coordination of cell fate specification, patterning and morphogenesis. Although great strides have been made in the molecular understanding of each of these processes, how their interplay governs the formation of complex tissues remains poorly understood. New techniques for experimental manipulation and image quantification enable the study of development in unprecedented detail, resulting in new hypotheses on the interactions between known components. By expressing these hypotheses in terms of rules and equations, computational modeling and simulation allows one to test their consistency against experimental data. However, new computational methods are required to represent and integrate the network of interactions between gene regulation, signaling and biomechanics that extend over the molecular, cellular and tissue scales. In this thesis, I present a framework that facilitates computational modeling of multiscale multicellular systems and apply it to investigate pancreatic development and the formation of vascular networks. This framework is based on the integration of discrete cell-based models with continuous models for intracellular regulation and intercellular signaling. Specifically, gene regulatory networks are represented by differential equations to analyze cell fate regulation; interactions and distributions of signaling molecules are modeled by reaction-diffusion systems to study pattern formation; and cell-cell interactions are represented in cell-based models to investigate morphogenetic processes. A cell-centered approach is adopted that facilitates the integration of processes across the scales and simultaneously constrains model complexity. The computational methods that are required for this modeling framework have been implemented in the software platform Morpheus. This modeling and simulation environment enables the development, execution and analysis of multi-scale models of multicellular systems. These models are represented in a new domain-specific markup language that separates the biological model from the computational methods and facilitates model storage and exchange. Together with a user-friendly graphical interface, Morpheus enables computational modeling of complex developmental processes without programming and thereby widens its accessibility for biologists. To demonstrate the applicability of the framework to problems in developmental biology, two case studies are presented that address different aspects of the interplay between cell fate specification, patterning and morphogenesis. In the first, I focus on the interplay between cell fate stability and intercellular signaling. Specifically, two studies are presented that investigate how mechanisms of cell-cell communication affect cell fate regulation and spatial patterning in the pancreatic epithelium. Using bifurcation analysis and simulations of spatially coupled differential equations, it is shown that intercellular communication results in a multistability of gene expression states that can explain the scattered spatial distribution and low cell type ratio of nascent islet cells. Moreover, model analysis shows that disruption of intercellular communication induces a transition between gene expression states that can explain observations of in vitro transdifferentiation from adult acinar cells into new islet cells. These results emphasize the role of the multicellular context in cell fate regulation during development and may be used to optimize protocols for cellular reprogramming. The second case study focuses on the feedback between patterning and morphogenesis in the context of the formation of vascular networks. Integrating a cell-based model of endothelial chemotaxis with a reaction-diffusion model representing signaling molecules and extracellular matrix, it is shown that vascular network patterns with realistic morphometry can arise when signaling factors are retained by cell-modified matrix molecules. Through the validation of this model using in vitro assays, quantitative estimates are obtained for kinetic parameters that, when used in quantitative model simulations, confirm the formation of vascular networks under measured biophysical conditions. These results demonstrate the key role of the extracellular matrix in providing spatial guidance cues, a fact that may be exploited to enhance vascularization of engineered tissues. Together, the modeling framework, software platform and case studies presented in this thesis demonstrate how cell-centered computational modeling of multi-scale and multicellular systems provide powerful tools to help disentangle the complex interplay between cell fate specification, patterning and morphogenesis during embryonic development

Cell Shape and Forces in Elastic and Structured Environments: From Single Cells to Organoids

With the advent of mechanobiology, cell shape and forces have emerged as essential elements of cell behavior and fate, in addition to biochemical factors such as growth factors. Cell shape and forces are intrinsically linked to the physical properties of the environment. Extracellular stiffness guides migration of single cells and collectives as well as differentiation and developmental processes. In confined environments, cell division patterns are altered, cell death or extrusion might be initiated, and other modes of cell migration become possible. Tools from materials science such as adhesive micropatterning of soft elastic substrates or direct laser writing of 3D scaffolds have been established to control and quantify cell shape and forces in structured environments. Herein, a review is given on recent experimental and modeling advances in this field, which currently moves from single cells to cell collectives and tissue. A very exciting avenue is the combination of organoids with structured environments, because this will allow one to achieve organotypic function in a controlled setting well suited for long-term and high-throughput culture

The Roots of Bioinformatics in Theoretical Biology

From the late 1980s onward, the term “bioinformatics” mostly has been used to refer to computational methods for comparative analysis of genome data. However, the term was originally more widely defined as the study of informatic processes in biotic systems. In this essay, I will trace this early history (from a personal point of view) and I will argue that the original meaning of the term is re-emerging

CompuCell3D model of cell migration reproduces chemotaxis

The introduction and conclusion of the following dissertation serve to support and summarize our research entitled ”CompuCell3D Model of Cell Migration Reproduces Chemotaxis.” In this study, we created a CompuCell3D simulation of single cell chemotaxis, a biological phenomena in which cells move in response to environmental chemical cues. We also developed an analysis scheme to analyze recordings of center of mass and polarization over time to characterize cell dynamics and kinetics. Aiming at individuals with intermediate modeling experience who lack specific understanding in the field, we offer the relevant biology, mathematics, and computational foundation in order to adequately prepare the reader. In the first topic, we discuss the biological cell and its capacity to migrate, discussing both the significance of this capacity for survival and the underlying biochemical mechanism. Second, we explore a few computational and mathematical models of cell migration, focusing on a brand-new analytical model called the Anisotropic OrnsteinUhlenbeck Process, which treats polarization in its stochastic differential equations. Finally, we go over CompuCell3D’s functionality in detail and provide a real-world example for readers to try out (needs access to a computer with Windows installed). Our research on single cell movement aims to completely characterize chemotaxis and offer tools that may be used to analyze experimental data, provided that cell polarization is measured. We discuss the significance of cell polarization measurements and the proper way to handle the issue of cell velocity when short time scales exhibit cell diffusive behavior. We suggest a procedure for measuring chemotactic efficiency as well as a way to discriminate between cell reorientation and cell drift speed modulation as chemotactic response modalities. Our simulation serves as the basis for upcoming collective migration models and may be utilized to investigate the role of particular types of white blood cells during innate immune response

Modeling 3D Cell Shape in Structured Environments with the Cellular Potts Model

In this work, we explore the 3D shape of cells and organoids in structured environments. Understanding the physical determinants of cell shape regulation in structured environments is vital as it plays a crucial role in essential biological processes, including migration, division and tissue development. The cellular Potts model (CPM) has emerged as a powerful computational framework for simulating cell behavior and morphodynamics in complex biological systems. Our research focuses on utilizing the CPM to model 3D single cells on 2D micropatterns and in 3D structured environments. We explicitly consider intracellular structures such as the nucleus and stress fibers and model their impact on cell shape. This allows us to predict morphology and trajectories during the single cell spreading process on micropatterns and demonstrates the effect of nucleus and stress fibers on these processes. Through systematic simulations and comparison with surface minimization approaches and experimental data, we demonstrate the ability of our model to accurately predict cell shapes under different spatial constraints. Additionally, we model the optic cup evagination in fish retina organoids with explicit representation of Matrigel at the surface of the organoid. The findings shed light on the mechanistic basis underlying the shape changes observed in multicellular systems