Robustness of anisotropic tissue deformation during animal development – RobustTissue

Within this project, we addressed this question from a theoretical perspective.

While there may be several possibilities, we tested one way in which biological tissues may stabilize oriented tissue deformation, which is related to so-called signaling molecules, which are sometimes called morphogens.

Morphogens provide cells with positional information. Take for instance the embryo of the fruit fly, which consists of 6000 cells. Imagine you are one of them, and next to you the only thing you "see" is other cells that do their thing. How are can you know if you are supposed to form a piece of the head, of the middle part, or of the tail end of the animal? One way in which nature solves this problem is through certain molecules, called morphogens, which are produced within some localized region, for instance, the protein Bicoid is produced in the tip of the head end of the fruit fly. It then diffuses through the tissue, and occasionally gets degraded everywhere. The interplay of these three effects will create a graded Bicoid concentration profile across the fly, decreasing from head to tail (Fig. G). How does this help you, as a cell, know where you are in the animal? You just measure the concentration of Bicoid - if it is high your are in the head end, if it is low you are in the tail end. The Bicoid concentration provides you with what biologists call positional information.

Yet, gradients also provide orientational information, e.g. if neighboring cells compare their level of a morphogen, they have an idea of the direction of the gradient. Indeed, in a number of systems, it is known that cell polarity aligns with the local direction of the morphogen gradient.

We thus asked whether the presence of such a morphogen gradient could stabilize oriented tissue deformation during animal development.

To address this question, we studied a so-called continuum models, which describes the behavior averaged over groups of neighboring cells. In our models, we considered the production rate of the proteins, the concentration of proteins, cell polarity, and cell velocities, each as a smooth, spatially varying field. We studied under which conditions the interaction between these field lead to stable oriented tissue deformation.

To probe stability, we used a technique called linear stability analysis: we applied any possible perturbation to the system and computed whether this perturbation would grow or shrink in time. If all possible perturbations shrink, the system is stable, otherwise it is unstable.

While we found that stability of oriented tissue deformation depends on several factors, one factor stood out: whether the forces act to extend the tissue along the direction of the morphogen gradient, which we call gradient-extensile, or whether they contact the tissue asking the gradient direction, which we call gradient-contractile. We found that gradient-contractile tissues are always unstable (Fig. I), while gradient-extensile tissues can be stable depending on some other factors (Fig. H). These other factors include for insurance the storage of the deforming tissue, the size of the region that produces the morphogen, and the rate of morphogen diffusion.

We next compared our results to the biology literature, and we found many examples and potential examples for gradient-extensile systems. However, we found essentially no example for a gradient-contractile system. This would make sense: nature may not have evolved gradient-contractile tissues, because as soon as it would have been "tried out" in some organism, that organism may not have survived since the deformation would be unstable.

In other words, our work suggests that the instability that has been known in the field of active matter physics for 20 years acts as an evolutionary selection criterion.

We also studied other aspects of oriented tissue deformation.

1. For instance, we have shown that the nature of the active forces driving tissue deformation can in part be inferred from the shapes of the cells.

2. We are currently also shedding light on another aspect important for oriented tissue deformation: curvature. As you may know, it is impossible to have a flat map of Earth's surface that shows the correct distances everywhere. Similarly, if you want to flatten an orange peel, this is not ready, because you have to squeeze and/or stretch the peel in different places in order to flatten it.

Both of this is due to the fact that in both cases, the so-called Gaussian curvature of the object changes: a sphere surface has a positive Gaussian curvature while a flat sheet has a Gaussian curvature of zero. And it is known that if the Gaussian curvature of a surface changes, this surface has to undergo tangential deformations.

Because biological tissues often undergo changes of Gaussian curvature, we are current staying how these curvature changes and tissue deformation affect each other in a bi-directional way.

Anisotropic tissue deformation is a key process during animal development. However, the general robustness of such developmental processes is in stark contrast to a known instability of the homogeneously deforming state of active anisotropic materials. Within this project, we ask how active anisotropic deformation of biological tissues can be robust, despite active matter instabilities.

My team and I will study two hypotheses of how anisotropic tissue deformation might be stabilized during development:
(H1) through large-scale protein concentration gradients,
(H2) though externally applied forces.

We will test these hypotheses pursuing two objectives:
Objective 1 - Theory: We will theoretically study continuum models and cell-based tissue models that incorporate tissue flows together with a scalar field representing the protein concentration, a polar field representing cell polarity, and a nematic field representing cell shapes. We will establish general criteria for the robustness of the homogeneously deforming state.
Objective 2 - Experimental system: We will collaborate with the biology group of Thomas Lecuit, who will provide us with experimental image data on the deformation of the germ band tissue during fruit fly embryogenesis. We will analyze these image data to extract the relevant protein concentration, cell polarity, cell shape, and tissue flow data, and fit these data to our continuum model. Based on this approach, we will test our hypotheses by examining data from experimental perturbations of the protein concentration field (H1) and of externally applied forces (H2).

In this project, we address a fundamental open question at the interface between active matter physics and developmental biology. To achieve this, we will also develop new theoretical concepts to examine how scalar and polar fields interact with the cellular material structure.