Fig 1.
Overview of the FIDES pipeline and FFI.
A: Pipeline for force inference. Confocal microscopy time-lapses are segmented using SDT-PiCS into 3D meshes of cells. The cell shapes serve as a starting point for DCM simulations and FIDES finds the optimal parameters that stabilize the cell shapes. In this example, a difference in surface tension is established, while the bottom cell also has a contractile ring. B: Description of the DCM. Single cells are represented as a triangulated shell, with surface tension γ, pressure P, viscosity η, cortical thickness t, and volume conservation regulated by bulk modulus K. Between cells, adhesive tension ω and friction ξ applies. C: Force model for cytokinetic ring. A ring of elastic springs is applied on a cell, which results in inward forces and creates the furrow. Two spherical coordinates determine the normal vector for the division plane, while distance d controls its offset from the mass center. An elastic spring constant k results in a ring force FR, which is distributed over neighboring nodes, making the furrow more smooth. The position of the ring is stabilized using an area modulus that resists changes in cell area on both sides of the ring with pressure force FPi. D: Force model for protrusion. The direction of the protrusion is controlled by two spherical coordinates, pointing from the mass center of the cell. The angle α controls the width of the protrusion and FP controls the total pushing force. The forces are smoothly distributed over the mesh according to a Difference of Gaussian kernels, with an outward force in the center of the protrusion, while the edges are pulled inwards to ensure an overall net force of zero. E: Overview of curved FFI. By assuming that cells behave like soap bubbles, we can write a series of equations that give observable variables, the contact angles θ at triple membrane junctions and the curvature H of the membranes, as a function of tensions γ and pressures P. This system of equations is next parametrized with measurements from segmented images and solved by least squares fitting.
Fig 2.
Performance of FFI and FIDES on synthetic embryos.
A: Simple synthetic embryo, consisting of four cells having different volumes and surface tensions, and five unique cell-cell contacts with varying interfacial tension. B: Performance comparison of FFI and FIDES on the simple synthetic embryo. Both have an excellent correlation with the ground truth. C: Advanced synthetic embryo, modeled after the 7-cell C. elegans embryo. This sample features seven differently parametrized cells, 15 contacts with varying interfacial tension, a contractile ring on P2 and a total of four protrusions on ABpl and ABpr, two of which are visible. D: Performance comparison on the advanced synthetic embryo.
Table 1.
Contribution of factors disrupting FFI methods.
Fig 3.
Cortical laser ablation as validation for cell surface tension inferences.
A: Cortical laser ablation procedure for cell P0. A cut measuring 8 μm is made in the cortex, causing the cortex to recoil perpendicularly to the cut. Here, this cut happens in the anterior side of the polarizing zygote (P0-A). B: Highlights of the cortex are tracked over the duration of the ablation experiment, resulting in velocity measurements for the myosin marker (green) and the actin marker (red). An exponential curve is then fitted on measured ablation velocities, providing an initial recoil velocity as estimation for the cortical tension. C: Ablation speeds differ between two sides of the polarizing zygote, and between two directions of ABpl. 95% confidence intervals and p-values were approximated using bootstrap, 2000 samples. The difference is significant with p < 0.0005 for both cases. D: Comparison of cortical tension measurements with tangent FFI tension inference for the 7-cell stage embryo. The positive correlation is significant (p < 0.01, using bootstrap, 10,000 samples). E: Comparison of cortical tension measurements with FIDES tension inference for the 7-cell stage embryo. The positive correlation is significant (p < 0.0001, using bootstrap, 10,000 samples). F: Exponential decay rate for ablations of the 7-cell stage cells, showing 95% CI.
Fig 4.
FIDES tension inference over early development.
A: We show six snapshots of a developing C. elegans embryo, each representing the aggregated force inferences at their respective cell stage. The 4-cell stage is split in two equal halves (4A and 4B), as it is a long-lasting stage with significant ongoing changes. B: Inferred cell surface tension results for every cell. The surface tension bars have 95% confidence intervals, calculated via bootstrap, 1000 samples. C: Inferred adhesive tension results for every cell-cell contact.
Fig 5.
Inference comparisons to literature and protein presence.
Data is aggregated from 15 time-lapses (see S4 Fig). A: Inferred adhesive tensions of the 4-cell stage (n = 43). Bootstrap (2000 samples) was used to calculate 95% confidence intervals. B: Timeline of inferred surface tension for the 4-cell stage cells. Data is smoothed using a lowess regression. Surface tensions are normalized so they average 1 at each time instance. C: Comparison of inferred surface tension to experimental measurements of cortical actin and myosin, measured across the free cell surface. Points are aggregated per cell for all cells between the 2- and 8-cell stage. Regression band with 95% confidence interval via bootstrap, 1000 samples. D: Comparison of inferred adhesive tension to experimental measurements of E-cadherin on the cell-cell interfaces, aggregated per contact for different cell stages. Regression band with 95% confidence interval via bootstrap, 1000 samples. E: Orientation of inferred cytokinetic rings for different cell stages. Division planes are projected to the most meaningful axis and standard deviations of the planes are shown in gray. F: Asymmetry of inferred cytokinetic ring offsets for every cell division, with 95% confidence intervals. Difference from zero is significant for P0 (p = 0.00004) and P2 (p = 0.009). G: Orientation of inferred protrusions for ABpl and ABpr. Individual observations are 3D unit vectors projected on the plane perpendicular to the LR axis, while the weighted average orientation is shown as an arrow. H: Rotation of the ventral protrusion of ABpl over time. Weighted least squares regression finds a significant effect of the AP axis component over time (p<0.0001), meaning that the protrusion moves from pointing slightly posterior to slightly anterior over the course of 10 minutes.