How computational models can help unlock biological systems

AbstractWith computation models playing an ever increasing role in the advancement of science, it is important that researchers understand what it means to model something; recognize the implications of the conceptual, mathematical and algorithmic steps of model construction; and comprehend what models can and cannot do. Here, we use examples to show that models can serve a wide variety of roles, including hypothesis testing, generating new insights, deepening understanding, suggesting and interpreting experiments, tracing chains of causation, doing sensitivity analyses, integrating knowledge, and inspiring new approaches. We show that models can bring together information of different kinds and do so across a range of length scales, as they do in multi-scale, multi-faceted embryogenesis models, some of which connect gene expression, the cytoskeleton, cell properties, tissue mechanics, morphogenetic movements and phenotypes. Models cannot replace experiments nor can they prove that particular mechanisms are at work in a given situation. But they can demonstrate whether or not a proposed mechanism is sufficient to produce an observed phenomenon. Although the examples in this article are taken primarily from the field of embryo mechanics, most of the arguments and discussion are applicable to any form of computational modelling

Inferring cellular forces from image stacks

Although the importance of cellular forces to a wide range of embryogenesis and disease processes is widely recognized, measuring these forces is challenging, especially in three dimensions. Here, we introduce CellFIT-3D, a force inference technique that allows tension maps for three-dimensional cellular systems to be estimated from image stacks. Like its predecessors, video force microscopy and CellFIT, this cell mechanics technique assumes boundary-specific interfacial tensions to be the primary drivers, and it constructs force-balance equations based on triple junction (TJ) dihedral angles. The technique involves image processing, segmenting of cells, grouping of cell outlines, calculation of dihedral planes, averaging along three-dimensional TJs, and matrix equation assembly and solution. The equations tend to be strongly overdetermined, allowing indistinct TJs to be ignored and solution error estimates to be determined. Application to clean and noisy synthetic data generated using Surface Evolver gave tension errors of 1.6?7%, and analyses of eight-cell murine embryos gave estimated errors smaller than the 10% uncertainty of companion aspiration experiments. Other possible areas of application include morphogenesis, cancer metastasis and tissue engineering.authorsversionPeer reviewe

On the origins of the mitotic shift in proliferating cell layers

Background: During plant and animal development, monolayer cell sheets display a stereotyped distribution of polygonal cell shapes. In interphase cells these shapes range from quadrilaterals to decagons, with a robust average of six sides per cell. In contrast, the subset of cells in mitosis exhibits a distinct distribution with an average of seven sides. It remains unclear whether this ‘mitotic shift’ reflects a causal relationship between increased polygonal sidedness and increased division likelihood, or alternatively, a passive effect of local proliferation on cell shape. Methods: We use a combination of probabilistic analysis and mathematical modeling to predict the geometry of mitotic polygonal cells in a proliferating cell layer. To test these predictions experimentally, we use Flp-Out stochastic labeling in the Drosophila wing disc to induce single cell clones, and confocal imaging to quantify the polygonal topologies of these clones as a function of cellular age. For a more generic test in an idealized cell layer, we model epithelial sheet proliferation in a finite element framework, which yields a computationally robust, emergent prediction of the mitotic cell shape distribution. Results: Using both mathematical and experimental approaches, we show that the mitotic shift derives primarily from passive, non-autonomous effects of mitoses in neighboring cells on each cell’s geometry over the course of the cell cycle. Computationally, we predict that interphase cells should passively gain sides over time, such that cells at more advanced stages of the cell cycle will tend to have a larger number of neighbors than those at earlier stages. Validating this prediction, experimental analysis of randomly labeled epithelial cells in the Drosophila wing disc demonstrates that labeled cells exhibit an age-dependent increase in polygonal sidedness. Reinforcing these data, finite element simulations of epithelial sheet proliferation demonstrate in a generic framework that passive side-gaining is sufficient to generate a mitotic shift. Conclusions: Taken together, our results strongly suggest that the mitotic shift reflects a time-dependent accumulation of shared cellular interfaces over the course of the cell cycle. These results uncover fundamental constraints on the relationship between cell shape and cell division that should be general in adherent, polarized cell layers

Digital tracking algorithm reveals the influence of structural irregularities on joint movements in the human cervical spine

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.clinbiomech.2018.04.015 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/Background Disc height loss and osteophytes change the local mechanical environment in the spine; while previous research has examined kinematic dysfunction under degenerative change, none has looked at the influence of disc height loss and osteophytes throughout movement. Methods Twenty patients with pain related to the head, neck or shoulders were imaged via videofluoroscopy as they underwent sagittal-plane flexion and extension. A clinician graded disc height loss and osteophytes as “severe/moderate”, “mild”, or “none”. A novel tracking algorithm quantified motions of each vertebra. This information was used to calculate intervertebral angular and shear displacements. The digital algorithm made it practical to track individual vertebrae in multiple patients through hundreds of images without bias. Findings Cases without height loss/osteophytes had a consistent increase in intervertebral angular displacement from C2/C3 to C5/C6, like that of healthy individuals, and mild height losses did not produce aberrations that were systematic or necessarily discernable. However, joints with moderate to severe disc height loss and osteophytes exhibited reduced range of motion compared to adjacent unaffected joints in that patient and corresponding joints in patients without structural irregularities. Interpretation Digitally-obtained motion histories of individual joints allowed anatomical joint changes to be linked with changes in joint movement patterns. Specifically, disc height loss and osteophytes were found to influence cervical spine movement in the sagittal plane, reducing angular motions at affected joints by approximately 10% between those with and without height loss and osteophytes. Further, these joint changes were associated with perturbed intervertebral angular and shear movements.Natural Sciences and Engineering Research Council (NSERC) Discovery Grant

Control of the Mitotic Cleavage Plane by Local Epithelial Topology

For nearly 150 years, it has been recognized that cell shape strongly influences the orientation of the mitotic cleavage plane (e.g. Hofmeister, 1863). However, we still understand little about the complex interplay between cell shape and cleavage plane orientation in epithelia, where polygonal cell geometries emerge from multiple factors, including cell packing, cell growth, and cell division itself. Here, using mechanical simulations, we show that the polygonal shapes of individual cells can systematically bias the long axis orientations of their adjacent mitotic neighbors. Strikingly, analysis of both animal epithelia and plant epidermis confirm a robust and nearly identical correlation between local cell topology and cleavage plane orientation in vivo. Using simple mathematics, we show that this effect derives from fundamental packing constraints. Our results suggest that local epithelial topology is a key determinant of cleavage plane orientation, and that cleavage plane bias may be a widespread property of polygonal cell sheets in plants and animals.Engineering and Applied Science

DRhoGEF2 Regulates Cellular Tension and Cell Pulsations in the Amnioserosa during Drosophila Dorsal Closure

Coordination of apical constriction in epithelial sheets is a fundamental process during embryogenesis. Here, we show that DRhoGEF2 is a key regulator of apical pulsation and constriction of amnioserosal cells during Drosophila dorsal closure. Amnioserosal cells mutant for DRhoGEF2 exhibit a consistent decrease in amnioserosa pulsations whereas overexpression of DRhoGEF2 in this tissue leads to an increase in the contraction time of pulsations. We probed the physical properties of the amnioserosa to show that the average tension in DRhoGEF2 mutant cells is lower than wild-type and that overexpression of DRhoGEF2 results in a tissue that is more solid-like than wild-type. We also observe that in the DRhoGEF2 overexpressing cells there is a dramatic increase of apical actomyosin coalescence that can contribute to the generation of more contractile forces, leading to amnioserosal cells with smaller apical surface than wild-type. Conversely, in DRhoGEF2 mutants, the apical actomyosin coalescence is impaired. These results identify DRhoGEF2 as an upstream regulator of the actomyosin contractile machinery that drives amnioserosa cells pulsations and apical constriction