Chapter 18 - Practical aspects of the cellular force inference toolkit (CellFIT)

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Abstract

If we are to fully understand the reasons that cells and tissues move and acquire their distinctive geometries during processes such as embryogenesis and wound healing, we will need detailed maps of the forces involved. One of the best current prospects for obtaining this information is noninvasive force-from-images techniques such as CellFIT, the Cellular Force Inference Toolkit, whose various steps are discussed here. Like other current quasistatic approaches, this one assumes that cell shapes are produced by interactions between interfacial tensions and intracellular pressures. CellFIT, however, allows cells to have curvilinear boundaries, which can significantly improve inference accuracy and reduce noise sensitivity. The quality of a CellFIT analysis depends on how accurately the junction angles and edge curvatures are measured, and a software tool we describe facilitates determination and evaluation of this information. Special attention is required when edges are crenulated or significantly different in shape from a circular arc. Because the tension and pressure equations are overdetermined, a select number of edges can be removed from the analysis, and these might include edges that are poorly defined in the source image, too short to provide accurate angles or curvatures, or noncircular. The approach works well for aggregates with as many as 1000 cells, and introduced errors have significant effects on only a few adjacent cells. An understanding of these considerations will help CellFIT users to get the most out of this promising new technique.

Introduction

One of the central current questions in biology is, “Why do cells move as they do, and how do they acquire their distinctive and often exacting forms?” It is now clear that cell-level mechanical forces are a key part of the answer to both parts of this important question (Brodland, 2002, Brodland et al., 2014, Chen and Brodland, 2008, Chiou et al., 2012, Ishihara and Sugimura, 2012, Ishihara et al., 2013). Furthermore, as computational models have taught us, subtle changes in driving forces can alter the final cell and tissue forms produced, often with serious clinical implications (Brodland et al., 2010a, Davidson et al., 1995, Hayashi and Carthew, 2004, Kafer et al., 2007). Thus it is clear that if we are to understand how the crucial cell and tissue movements associated with processes such as organogenesis, wound healing, cancer metastasis, and tissue engineering occur, we will need to obtain detailed and accurate maps of the forces at work.

Although a broad range of experimental techniques—such as micropipette aspiration (Maitre et al., 2012), optical tweezers (Capitanio & Pavone, 2013), magnetic cytometry (Kasza, Vader, Koster, Wang, & Weitz, 2011), laser ablations (Hutson et al., 2009), atomic force microscopy (Thomas, Burnham, Camesano, & Wen, 2013), inserted oil droplets (Campas et al., 2014), and FRET (Borghi et al., 2012) (see also Adam A. Lucio et al., 2015, [Chapter 20 of this volume])—are available for measuring forces in cells, these techniques tend to provide force information for single locations and times, only. They are also somewhat invasive, and their use often raises the prospect of unintentional cell and tissue perturbations. One might consider constructing maps from single-point data from multiple experiments, but variations from one animal to another, even within a single clutch, can be 30% or more (Wiebe & Brodland, 2005), making such data collation ideas impractical. One of the few current techniques to offer force maps is traction microscopy (Tambe et al., 2013, Style et al., 2014) (see also Serra-Picamal et al. [Chapter 17 of this volume]), but it is applicable only to planar cell cultures.

A new family of force inference techniques, however, offers the prospect of constructing detailed force maps from images (Brodland et al., 2010b, Brodland et al., 2014, Chiou et al., 2012, Ishihara and Sugimura, 2012, Ishihara et al., 2013, Legant et al., 2010). Indeed, when Video Force Microscopy (VFM), one of the first such techniques, was applied to ventral furrow formation in Drosophila, it provided information about the relative forces acting along each cell membrane and did so with subminute temporal resolution (Brodland, Conte, et al., 2010). It showed that apical constrictions near the embryo midline were key drivers, as expected, but that these forces changed smoothly with respect to position and time, in contrast to most conceptual and computational models of the time. It also demonstrated the action of significant basal contractions in the dorsal and lateral ectoderm and tensions along the membranes normal to the epithelium in a region near the ventral midline. This knowledge was important for understanding how the observed motions were driven and why a variety of mutations caused the furrow to be abnormal or even nonexistent.

The basic idea behind these force-from-shape techniques is that the observed motions or shapes are the consequence of a set of driving forces—generally tensions along cell boundaries and intracellular pressures. VFM included viscous forces, and other kinds of forces could also be incorporated into these methods (Brodland et al., 2014). In a standard computational model, a starting geometry and set of driving forces are specified and the model uses a finite element model or some other numerical engine to predict the motions that will result. In VFM, these equations are inverted, the geometry is specified, and the modified computational engine estimates the driving forces. The inversion process is not straightforward and many of these methods exhibit issues related to equation sufficiency, solution uniqueness, and noise sensitivity, especially when applied to in-plane motions of epithelia.

We recently showed that these issues can be resolved by assuming the cell edges to be curved rather than straight, for rather complex reasons explained elsewhere (Brodland et al., 2014). We also considered a limited number of options for estimating the contact angles at the junctions where cell membranes meet and for approximating membrane curvatures. We called this new approach, including the solution evaluation methods associated with it CellFIT, the Cellular Force Inference Toolkit.

Here, we discuss the steps in CellFIT and examine practical issues related to its implementation, such as determination of edge angles and curvatures, and we introduce a software tool that is useful in these processes. We also consider how to evaluate CellFIT solutions using mathematical tools such as condition numbers, equation residuals, and covariance matrices. Copies of the software used here and an Image-J plug-in with similar capabilities are available at the authors' websites (civil.uwaterloo.ca/brodland and my.vanderbilt.edu/shanehutson).

In principle, CellFIT is equally applicable to cells in 2D and 3D configurations. However, whereas the 2D version can be based on single images and it is easy to visualize and understand, its 3D counterpart is not. The latter requires closely spaced serial sections in which the cell outlines can be identified, cell outlines must be traced and connected together across images cell by cell so that 3D reconstructions can be made of each cell. The apparent angles between the cells seen in individual sections are not true membrane contact angles and special techniques must be used to correctly calculate the needed angles. The cell–cell interfaces are generally nonspherical and curvature calculations are complex. For these reasons, and because it demonstrates the main underlying principles and application considerations, we focus here on a 2D implementation of CellFIT.

Section snippets

The Basic Steps in CellFIT

CellFIT involves extracting geometric information from a source image followed by the formulation and solution of equations based on this information (Figure 1, Figure 2). Two postprocessing steps are also typically carried out, namely, solution visualization and evaluation. In practice, some of these steps are further subdivided in order that they can be carried out using standard computational algorithms. The goal of this section is to describe the steps in the method and their associated

Working with CellFIT Output

The tensions that a CellFIT analysis reports are the effective or equivalent edge or interfacials tensions acting in the cells and their individual edges (Chen and Brodland, 2000, Lecuit et al., 2011). These tensions include the effects of various systems associated with the cell cortex, including actomyosin contractile networks, membrane tensions, and other cortex-bound systems. These tensions are affected by cell–cell adhesion systems, which counterintuitively reduce the edge tensions as

Acknowledgments

Funding was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the National Institutes of Health (1R01-GM099107).

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