Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes being expressed. This information suggests that ourunderstanding of the respective contributions of gene expression and mechanics, and of their crucialentanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assistthe design and interpretation of experiments, point out the main ingredients and assumptions, andultimately lead to predictions. The newly accessible local information thus calls for a reflectionon how to select suitable classes of mechanical models. We review both mechanical ingredientssuggested by the current knowledge of tissue behaviour, and modelling methods that can helpgenerate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and tissue scale ("inter-cell") contributions. We recall the mathematical framework developpedfor continuum materials and explain how to transform a constitutive equation into a set of partialdifferential equations amenable to numerical resolution. We show that when plastic behaviour isrelevant, the dissipation function formalism appears appropriate to generate constitutive equations;its variational nature facilitates numerical implementation, and we discuss adaptations needed in thecase of large deformations. The present article gathers theoretical methods that can readily enhancethe significance of the data to be extracted from recent or future high throughput biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few corrections to the published version, all in Appendix D.2 devoted to large deformation

Comparing individual-based approaches to modelling the self-organization of multicellular tissues.

The coordinated behaviour of populations of cells plays a central role in tissue growth and renewal. Cells react to their microenvironment by modulating processes such as movement, growth and proliferation, and signalling. Alongside experimental studies, computational models offer a useful means by which to investigate these processes. To this end a variety of cell-based modelling approaches have been developed, ranging from lattice-based cellular automata to lattice-free models that treat cells as point-like particles or extended shapes. However, it remains unclear how these approaches compare when applied to the same biological problem, and what differences in behaviour are due to different model assumptions and abstractions. Here, we exploit the availability of an implementation of five popular cell-based modelling approaches within a consistent computational framework, Chaste (http://www.cs.ox.ac.uk/chaste). This framework allows one to easily change constitutive assumptions within these models. In each case we provide full details of all technical aspects of our model implementations. We compare model implementations using four case studies, chosen to reflect the key cellular processes of proliferation, adhesion, and short- and long-range signalling. These case studies demonstrate the applicability of each model and provide a guide for model usage

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

Enhanced metastatic risk assessment in cutaneous squamous cell carcinoma with the 40-gene expression profile test

Aim: To clinically validate the 40-gene expression profile (40-GEP) test for cutaneous squamous cell carcinoma patients and evaluate coupling the test with individual clinicopathologic risk factor-based assessment methods. Patients & methods: In a 33-site study, primary tumors with known patient outcomes were assessed under clinical testing conditions (n = 420). The 40-GEP results were integrated with clinicopathologic risk factors. Kaplan–Meier and Cox regression analyses were performed for metastasis. Results: The 40-GEP test demonstrated significant prognostic value. Risk classification was improved via integration of 40-GEP results with clinicopathologic risk factor-based assessment, with metastasis rates near the general cutaneous squamous cell carcinoma population for Class 1 and ≥50% for Class 2B. Conclusion: Combining molecular profiling with clinicopathologic risk factor assessment enhances stratification of cutaneous squamous cell carcinoma patients and may inform decision-making for risk-appropriate management strategies

Validation of a 40-Gene Expression Profile Test to Predict Metastatic Risk in Localized High-Risk Cutaneous Squamous Cell Carcinoma

Background: Current staging systems for cutaneous squamous cell carcinoma (cSCC) have limited positive predictive value (PPV) for identifying patients who will experience metastasis. Objective: To develop and validate a gene expression profile (GEP) test for predicting risk for metastasis in localized, high-risk cSCC with the goal of improving risk-directed patient management. Methods: Archival formalin-fixed paraffin-embedded primary cSCC tissue and clinicopathologic data (n=586) were collected from 23 independent centers in a prospectively designed study. A GEP signature was developed using a discovery cohort (n=202) and validated in a separate, non-overlaping, independent cohort (n=324). Results: A prognostic, 40-gene expression profile (40-GEP) test was developed and validated, stratifying high-risk cSCC patients into classes based on metastasis risk: Class 1 (low-risk), Class 2A (high-risk), and Class 2B (highest-risk). For the validation cohort, 3-year metastasis-free survival (MFS) rates were 91.4%, 80.6%, and 44.0%, respectively. A PPV of 60% was achieved for the highest-risk group (Class 2B), an improvement over staging systems; while negative predictive value, sensitivity, and specificity were comparable to staging systems. Limitations: Potential understaging of cases could affect metastasis rate accuracy.Conclusion: The 40-GEP test is an independent predictor of metastatic risk that can complement current staging systems for patients with high-risk cSCC

CellFIT: a cellular force-inference toolkit using curvilinear cell boundaries.

Mechanical forces play a key role in a wide range of biological processes, from embryogenesis to cancer metastasis, and there is considerable interest in the intuitive question, "Can cellular forces be inferred from cell shapes?" Although several groups have posited affirmative answers to this stimulating question, nagging issues remained regarding equation structure, solution uniqueness and noise sensitivity. Here we show that the mechanical and mathematical factors behind these issues can be resolved by using curved cell edges rather than straight ones. We present a new package of force-inference equations and assessment tools and denote this new package CellFIT, the Cellular Force Inference Toolkit. In this approach, cells in an image are segmented and equilibrium equations are constructed for each triple junction based solely on edge tensions and the limiting angles at which edges approach each junction. The resulting system of tension equations is generally overdetermined. As a result, solutions can be obtained even when a modest number of edges need to be removed from the analysis due to short length, poor definition, image clarity or other factors. Solving these equations yields a set of relative edge tensions whose scaling must be determined from data external to the image. In cases where intracellular pressures are also of interest, Laplace equations are constructed to relate the edge tensions, curvatures and cellular pressure differences. That system is also generally overdetermined and its solution yields a set of pressures whose offset requires reference to the surrounding medium, an open wound, or information external to the image. We show that condition numbers, residual analyses and standard errors can provide confidence information about the inferred forces and pressures. Application of CellFIT to several live and fixed biological tissues reveals considerable force variability within a cell population, significant differences between populations and elevated tensions along heterotypic boundaries