This symposium will focus on modeling of biological systems using single-cells as a natural level of abstraction. Unlike continuum models where cells are represented in the form of density, cell-level modeling provides modelers with deeper insights into biological phenomena and ultimately allows for easy integration with subcellular models. This method is capable of determining single cell phenomena based on more detailed subcellular models than those employed by continuum methods. Currently, various cell-level models are being explored (lattice-based, off-lattice, cellular automata, etc.). As of now, there is little to no consensus amongst scientists and developers to easily and correctly model multicellular systems with single cell resolution. During this symposium, we will explore how different single cell-level models are capable of describing and reproducing biological phenomena at the single-cell and tissue levels. Following scheduled talks, we will have a roundtable discussion covering the gambit of current models and noting similarities and differences in techinques and scientific contents. We hope this discussion will lead to consensus or possible motivation for unification/integration of presented models and modeling methods.

Back to Minisymposium_planning.

ABSTRACTS

• James Glazier, Maciej Swat (glazier@indiana.edu, mswat@indiana.edu)

Multi-Cell Modeling of Biological Development using the GGH Model and CompuCell3D—Applications, Technology and Open Problems

While bioinformatics tools for the analysis of DNA sequences, reaction kinetics models of biomolecular networks and molecular dynamics simulations of biomolecules, are all widely used, multi-cell modeling of developmental processes at the tissue scale is still relatively undeveloped. One of the key reasons for this neglect has been the lack of widely-accepted modeling approaches and the computational difficulty of building such models. Now, a growing community of modelers has settled on the GGH Model, a modeling approach that derives from the familiar Potts model of statistical mechanics, as a convenient methodology to create sophisticated multi-cell simulations of tissue development, creating a de facto common modeling approach. The GGH’s use of an Effective Energy and constraints to describe cell behaviors simplifies integration of multiple biological mechanisms, while the availability of open-source tools like CompuCell3D for building GGH models makes developing, validating and sharing such simulations much easier for non-specialists. I will introduce the GGH and the modeling environment CompuCell3D (http://www.compucell3d.org/), then apply the GGH to modeling somitogenesis in vivo, and to angiogenesis and vasculogenesis in vitro (see pictures), illustrating some of the questions this type of modeling can address (e.g. error correction mechanisms in development) and discussing its application to other developmental-biology problems including tumor growth, gastrulation, and biofilms. I will also discuss some of the key mathematical and computational issues which GGH models and modeling environments still need to address.

• Tim Newman, Arizona State University (Timothy.Newman@asu.edu)

Modeling multicellularity: from cell rheology to gastrulation

I will present an overview of recent work focused on constructing computer models of developmental systems. In particular, we have devised an off-lattice algorithm, called the Subcellular Element Model, which is able to simulate large numbers (thousands) of deformable cells in three dimensions. I will describe the inner workings of the algorithm, and indicate that the method is capable of modeling developmental systems over a wide range of scales - capturing cell visco-elasticity at small scales, and long-ranged coordinated cell movement at large scales. Modeling of primitive streak extension in the chick embryo will be discussed as a concrete application.

• Roger Kamm (rdkamm@mit.edu)

Multi-Scale Analysis of Cellular Force Transmission and Biochemical Activation

Mechanical force plays an important role in numerous cellular processes such as migration, adhesion and apoptosis. The dynamic framework of the cytoskeleton provides a cell with structural integrity and transmits the physical cues to the targets that respond to the external force. We have studied the structure and mechanical properties of the cytoskeleton using computational models and experimental measurements. In the computational studies, we have developed a rigorous three-dimensional computational model of the cytoskeleton based on Brownian dynamics and used it to investigate cytoskeletal morphology and rheology. Through a parametric study, we found that the morphological properties of the cytoskeleton are effectively captured by a relatively small number of parameters. The developed model demonstrates how the actin cytoskeleton responds to external force exhibiting power-law rheology, strain-stiffening, and stress relaxation. In the experiments, interactions between actin filaments and actin binding proteins (ABPs) were probed at both molecular and network scales using optical tweezers. Unbinding and unfolding force of ABPs were measured by pulling one of actin filaments in the ABP/F-actin complex. Mechanical deformation of an actin network cross-linked with ABPs under external shear was visualized by confocal microscopy and the network elasticity was characterized by both passive and active methods using optical tweezers. We have also developed a two-dimensional coarse-grained membrane/cortex model with dynamic protein associations for human erythrocytes or other cell types to elucidate the roles of shear stress, specific chemical agents, and thermal fluctuations in cortex remodeling. The human erythrocyte demonstrates extraordinary ability to undergo reversible large deformations and fluidity. Such mechanical responses cannot be consistently rationalized on the basis of fixed connectivity of the spectrin network tethered to the phospholipid membrane. In this study, we have demonstrated a clear solid-to-fluid transition depending on the metabolic energy influx. The solid network’s plastic deformation also manifests creep and yield regimes depending on the strain rate. This cytoskeletal dynamics model offers a means to resolve long-standing questions regarding the reference state used in red blood cell elasticity theory for determining the equilibrium shape and deformation response.

• Dan Beard (dbeard@mcw.edu)

Integration of mitochondrial and cellular metabolism with tissue-level substrate transport to explain emergent phenomena on phosphate metabolite concentations and ATP hydrolysis potential in the heart

To understand how cardiac ATP and CrP remain stable with changes in work rate—a phenomenon that has eluded mechanistic explanation for decades—data from 31phosphate-magnetic resonance spectroscopy (31P-MRS) are analyzed to estimate cytoplasmic and mitochondrial phosphate metabolite concentrations in the normal state, during hypoperfusion, and during acute ischemia and reactive hyperemic recovery. Analysis is based on simulating distributed heterogeneous oxygen transport in the myocardium integrated with a detailed model of cardiac energy metabolism. It is determined that baseline inorganic phosphate (Pi) concentration in the canine myocyte cytoplasm—a variable not accessible to direct noninvasive measurement—is approximately 0.29 mM and increases to 2.3 mM near maximal cardiac work states. This variable is shown to be crucial in controlling oxidative metabolism in vivo. During acute ischemia (from ligation of the left anterior descending artery) Pi increases to approximately 2.8 mM and ATP consumption in the ischemic tissue is reduced to less than half its baseline value before the creatine phosphate (CrP) pool is 16% depleted. It is determined from these experiments that the maximal work rate of the heart is an emergent property and is limited not simply by the maximal rate of ATP synthesis, but by the maximal rate at which ATP can be synthesized at a potential at which it can be utilized.

• Stanislav Shvartsman (stas@princeton.edu )

MAPK SIGNALING IN EQUATIONS AND EMBRYOS

Exploring the robustness and evolvability of developmental signaling mechanisms is essentially impossible without computational modeling approaches. Successful models should integrate large amounts of data, test the feasibility of proposed modes of regulation, and lead to the formulation of new mechanisms. I will describe how we are combining imaging, modeling, and molecular genetics techniques in order to develop and experimentally test multiscale models of the Mitogen Activated Protein Kinase (MAPK) signaling pathway, a key regulator of development across species. We are using the terminal patterning system in the early Drosophila embryo as the main experimental model for studying the MAPK-mediated pattern formation. Our imaging results provide the first quantitative measurements of the gradient of MAPK signaling in the early Drosophila embryo and lead to the model where this gradient is controlled by a cascade of diffusion-trapping systems. We tested this model in a combination of modeling, imaging, and genetic experiments. We are also exploring how the gradient of MAPK signaling is interpreted by giving rise to the gradients of biochemical modifications and subcellular locations of its biochemical targets. Our preliminary data suggest that a substrate competition mechanism coordinates the actions of the anterior and terminal patterning systems in the early embryo. I will present the results of genetic and computational tests of this mechanism.

• Peter Hunter (p.hunter@auckland.ac.nz), Jonna Terkildsen, Catherine Lloyd, Mike Cooling, Poul Nielsen

Bioengineering Institute, University of Auckland, New Zealand

Building integrated cardiac cell models with CellML1.1

CellML (http://www.cellml.org) is an XML standard for encoding differential-algebraic equation (DAE) models and facilitating the building of model repositories and general purpose software tools. The CellML 1.1 standard (available at http://www.cellml.org/specifications/cellml_1.1) supports public and private interfaces that enable encapsulation hierarchies and provide mechanisms for information hiding and abstraction. Model reuse is facilitated by the import element, enabling new models to be constructed by combining existing models into model hierarchies. The process of importing models, developed by different research groups, into a more complex integrated model will be illustrated with three cardiac myocyte models. The 1st is the Pandit et al model [1] of cardiac excitability, the 2nd is the Hinch et al model [2] of calcium dynamics and the 3rd is the Niederer et al model [3] of myofilament mechanics. The resulting coupled electromechanics model is reported in Terkildsen et al [4]. We will also discuss the decomposition of these three models into a library of separate modular components (e.g. individual ion channel models).

1. http://www.cellml.org/models/pandit_clark_giles_demir_2001_version07 2. http://www.cellml.org/models/hinch_greenstein_tanskanen_xu_winslow_2004_version01 3. http://www.cellml.org/models/niederer_hunter_smith_2006_version01 4. Terkildsen, J.R., Niederer, S., Crampin E.J., Hunter, P.J., and Smith N.P. Using Physiome standards to couple cellular functions for cardiac excitation contraction. Exp Physiol; 93, pp919-929, 2008. http://www.cellml.org/models/terkildsen_niederer_crampin_hunter_smith_2008_version01