Timothy J. Newman

Modeling cell rheology with the Subcellular Element Model

Recently, the Subcellular Element Model (SEM) has been introduced, primarily to compute the dynamics of large numbers of three-dimensional deformable cells in multicellular systems. Within this model framework, each cell is represented by a collection of elastically coupled elements, interacting with one another via short-range potentials, and dynamically updated using over-damped Langevin dynamics. The SEM can also be used to represent a single cell in more detail, by using a larger number of subcellular elements exclusively identified with that cell. We have tested whether, in this context, the SEM yields viscoelastic properties consistent with those measured on single living cells. Employing virtual methods of bulk rheology and microrheology we find that the SEM successfully captures many cellular rheological properties at intermediate time scales and moderate strains, including weak power law rheology. In its simplest guise, the SEM cannot describe long-time/large-strain cell responses. Capturing these cellular properties requires extensions of the SEM which incorporate active cytoskeletal rearrangement. Such extensions will be the subject of a future publication.

Emergent cell and tissue dynamics from subcellular modeling of active biomechanical processes

Cells and the tissues they form are not passive material bodies. Cells change their behavior in response to external biochemical and biomechanical cues. Behavioral changes, such as morphological deformation, proliferation and migration, are striking in many multicellular processes such as morphogenesis, wound healing and cancer progression. Cell-based modeling of these phenomena requires algorithms that can capture active cell behavior and their emergent tissue-level phenotypes. In this paper, we report on extensions of the subcellular element model to model active biomechanical subcellular processes. These processes lead to emergent cell and tissue level phenotypes at larger scales, including (i) adaptive shape deformations in cells responding to slow stretching, (ii) viscous flow of embryonic tissues, and (iii) streaming patterns of chemotactic cells in epithelial-like sheets. In each case, we connect our simulation results to recent experiments.

Grid-Free Models of Multicellular Systems, with an Application to Large-Scale Vortices Accompanying Primitive Streak Formation

This paper is comprised of two parts. In the first we provide a brief overview of grid-free methods for modeling multicellular systems. We focus on an approach based on Langevin equations, in which inertia is ignored, and stochastic effects on cell motion are included. The discussion starts with simpler models, in which cells are modeled as adhesive spheres. We then turn to more sophisticated approaches in which nontrivial cell shape is accommodated, including the recently introduced Subcellular Element Model, in which each cell is described as a cluster of adhesively coupled over-damped subcellular elements, representing patches of cytoskeleton. In the second part of the paper we illustrate the use of a standard grid-free cell-based model to computationally probe interesting new features associated with primitive streak formation in the chick embryo. Streak formation is a key developmental step in amniotes (i.e., birds, reptiles, and mammals), and can be observed in detail in the chick embryo, where the streak extends across a tightly-packed two-dimensional sheet (the epiblast) comprised of about 50,000 cells. The Weijer group [Cui, Yang, Chuai, Glazier, and Weijer, Dev. Biol. 284 (2005) 37-47] recently observed that streak formation is accompanied by coordinated cell movement lateral to the streak, resulting in two large counter-rotating vortices. We study a mechanism based on cell polarity (in the plane of the epiblast) that provides an explanation for these vortices, and test it successfully using computer simulations. This mechanism is robust, since the emergent vortex formation depends only on the gross features of the initial spatial distribution of planar polarity in the epiblast.

A 'chemotactic dipole' mechanism for large-scale vortex motion during primitive streak formation in the chick embryo

Primitive streak formation in the chick embryo involves significant coordinated cell movement lateral to the streak, in addition to the posterior-anterior movement of cells in the streak proper. Cells lateral to the streak are observed to undergo polonaise movements, i.e. two large counter-rotating vortices, reminiscent of eddies in a fluid. In this paper, we propose a mechanism for these movement patterns which relies on chemotactic signals emitted by a dipolar configuration of cells in the posterior region of the epiblast. The chemotactic dipole consists of adjacent regions of cells emitting chemo-attractants and chemo-repellents. We motivate this idea using a mathematical analogy between chemotaxis and electrostatics, and test this idea using large-scale computer simulations. We implement active cell response to both neighboring mechanical interactions and chemotactic gradients using the Subcellular Element Model. Simulations show the emergence of large-scale vortices of cell movement. The length and time scales of vortex formation are in reasonable agreement with experimental data. We also provide quantitative estimates for the robustness of the chemotaxis dipole mechanism, which indicate that the mechanism has an error tolerance of about 10% to variation in chemotactic parameters, assuming that only 1% of the cell population is involved in emitting signals. This tolerance increases for larger populations of cells emitting signals.

Correlating cell behavior with tissue topology in embryonic epithelia.

Measurements on embryonic epithelial tissues in a diverse range of organisms have shown that the statistics of cell neighbor numbers are universal in tissues where cell proliferation is the primary cell activity. Highly simplified non-spatial models of proliferation are claimed to accurately reproduce these statistics. Using a systematic critical analysis, we show that non-spatial models are not capable of robustly describing the universal statistics observed in proliferating epithelia, indicating strong spatial correlations between cells. Furthermore we show that spatial simulations using the Subcellular Element Model are able to robustly reproduce the universal histogram. In addition these simulations are able to unify ostensibly divergent experimental data in the literature. We also analyze cell neighbor statistics in early stages of chick embryo development in which cell behaviors other than proliferation are important. We find from experimental observation that cell neighbor statistics in the primitive streak region, where cell motility and ingression are also important, show a much broader distribution. A non-spatial Markov process model provides excellent agreement with this broader histogram indicating that cells in the primitive streak may have significantly weaker spatial correlations. These findings show that cell neighbor statistics provide a potentially useful signature of collective cell behavior.

Modeling Multicellular Structures Using the Subcellular Element Model

This chapter describes a new method for simulating grid-free multicellular structures, in which the three-dimensional shape of each cell is dynamically adaptive to its local environment. This is achieved by constructing each cell from “subcellular elements.” I describe in detail the underlying mathematical equation of motion for the elements, and the additional algorithms which allow for cell growth and cell division. The model is illustrated with the simple example of a growing three dimensional cluster of cells.

Quantifying metastatic inefficiency: rare genotypes versus rare dynamics.

We introduce and solve a null model of stochastic metastatic colonization. The model is described by a single parameter θ: the ratio of the rate of cell division to the rate of cell death for a disseminated tumour cell in a given secondary tissue environment. We are primarily interested in the case in which colonizing cells are poorly adapted for proliferation in the local tissue environment, so that cell death is more likely than cell division, i.e. θ < 1. We quantify the rare event statistics for the successful establishment of a metastatic colony of size N. For N >> 1, we find that the probability of establishment is exponentially rare, as expected, and yet the mean time for such rare events is of the form ~log (N)/(1 - θ) while the standard deviation of colonization times is ~1/(1 - θ). Thus, counter to naive expectation, for θ < 1, the average time for establishment of successful metastatic colonies decreases with decreasing cell fitness, and colonies seeded from lower fitness cells show less stochastic variation in their growth. These results indicate that metastatic growth from poorly adapted cells is rare, exponentially explosive and essentially deterministic. These statements are brought into sharper focus by the finding that the temporal statistics of the early stages of metastatic colonization from low-fitness cells (θ < 1) are statistically indistinguishable from those initiated from high-fitness cells (θ > 1), i.e. the statistics show a duality mapping (1 - θ) --> (θ - 1). We conclude our analysis with a study of heterogeneity in the fitness of colonising cells, and describe a phase diagram delineating parameter regions in which metastatic colonization is dominated either by low or high fitness cells, showing that both are plausible given our current knowledge of physiological conditions in human cancer.

Biology is simple

This paper explores the potential for simplicity to reveal new biological understanding. Borrowing selectively from physics thinking, and contrasting with Cricks reductionist philosophy, the author argues that greater emphasis on simplicity is necessary to advance biology and its applications.

Water is a molecular liquid

Science and society are failing to grapple with the public health burden of cancer. In this short perspective piece, I contrast reductionism and complexity in cancer research, using water as a simple example, arguing for more ecological approaches to cancer. This is a call to arms to physical scientists, ecologists and others to get involved, to link up with cancer clinicians and cancer biologists, and an appeal to funding agencies to link up across disciplines to make a difference.

Scales of understanding in biological development

The development of an adult organism from a fertilized egg remains one of the deep mysteries of biology. Great strides have been made in the past three decades, primarily through ever more sophisticated genetic analyses and the advent of live-cell imaging, yet the underlying principles governing development are elusive. Recently, a new generation of biological physicists has entered the field, attracted by the hallmarks of development— coordinated dynamics and pattern formation arising from cell-cell interactions—which reflect tantalizing analogs with many-body systems in condensed matter physics and related fields. There have been corresponding influxes of researchers from other quantitative disciplines. With new workers come new questions and foci at different scales in space, time and complexity. The reductionist philosophy of developmental genetics has become increasingly complemented by a search for effective mechanisms at higher scales, a strategy which has a proven track record of success in the study of complex systems in physics. Are there new and universal mechanisms of development, supra-genetic in nature, waiting to be discovered by focusing on higher scales, or is development fundamentally the intricately scripted unfolding of complex genetic instructions? In this special focus issue of Physical Biology, we present cutting-edge research into embryo development from a broad spectrum of groups representing cell and developmental biology, biological physics, bioengineering and biomathematics. We are provided with a sense of how this multidisciplinary community views the fundamental issue of scale in development and are given some excellent examples of how we can bridge these scales through interdisciplinary collaboration, in order to create new levels of understanding. We start with two reviews which will provide newcomers with a guide to some of the outstanding questions in the field. Winklbauer and Muller use the phenomenon of mesoderm spreading as a platform to discuss the fascinating challenge of connecting cell-level behaviours to tissue-scale dynamics, thereby putting meat on the bones of traditional physical metaphors of the embryonic tissue as a material. A fresh look at natural variation in embryonic phenotypes through the lens of physics, especially mechanics, is provided by von Dassow and Davidson. They stress the importance of environmental scales in providing both physical challenges and an evolutionary backdrop for robust development. The next two papers are concerned with the crucial role of signalling in morphogenesis. Zartman et al study in detail a stage of oogenesis in Drosophila, and show how quantitative experimental determination of pattern formation can be used as a stringent test of proposed underlying molecular mechanisms; in turn, they show how such selected mechanisms can thereafter be tested by newly designed experiments. Streichan et al consider collective cell motion in the zebrafish embryo. They propose an elegant theoretical mechanism to explain how directed collective cell motion can be generated in a uniform signalling landscape through a non-linear chemotactic feedback loop, and propose experimental tests of this idea. The next two papers describe state-of-the-art spatio-temporal quantification of whole embryo dynamics with cell-level resolution. Fernandez-Gonzalez and Zallen study the fascinating phenomenon of cell surface oscillations during axis elongation in Drosophila. They use a newly designed computer algorithm to measure spatio-temporal statistics of the oscillations and connect this information to intracellular actomyosin dynamics. Szabo et al study extracellular matrix (ECM) dynamics during primitive streak extension in the avian embryo. Using computer tracking and analysis they are able to measure spatial and temporal correlations of the ECM during development and use this data to inform the crucial, yet poorly understood, role of cell-ECM interactions. The last two papers are companion articles by Sandersius et al. The first paper describes the integration of active subcellular dynamics into an existing multicellular simulation algorithm. The resulting algorithm, which is parameterized at length and time scales of microns and seconds, is capable of reproducing various experimentally observed phenotypes at significantly higher scales, namely large-strain cell stretching, effective viscosity of embryonic epithelia and streaming patterns of collective cell motion within tissues. The second paper uses this new algorithm to quantitatively test the hypothesis that a dipolar arrangement of chemotactic sources is capable of driving primitive streak formation in amniotes. The hypothesis is found to be consistent with experimental data on cell movement patterns and quantitative estimates are given for the robustness of the chemotaxis mechanism. Is the simplest model of an embryo an embryo? Alternatively, are there higher scales of understanding that will provide predictive and powerful new insights into development? We hope this special focus issue of Physical Biology will provide a snapshot of how quantitative and interdisciplinary approaches are helping to answer these fundamental questions.