Original paper: Spreading dynamics and wetting transition of cellular aggregates
In episode one of this series, I presented a research paper by Stéphane Douezan and his colleagues in which they studied a ball of cells (called a cellular aggregate) sitting on a flat surface. After introducing the concept of cellular aggregate wetting by comparing it to the classical system of a drop of water, today I present the main part of the paper which looks at the dynamics of spreading of the cellular aggregate. I strongly suggest that the reader reads the first post before reading this one.
As introduced previously, the spreading of a cellular aggregate is set by the surface tensions of the three interfaces: cells-substrate (
To characterize the dynamics of spreading, Stéphane Douezan and his colleagues measured the area of the cellular aggregate in contact with the surface with respect to time. The authors noticed two distinct regimes: at short times (the first hour) the cellular aggregate flattens, and at longer times, it forms a film which spreads completely. In the first regime, they observed a non-constant spreading speed. More interestingly, it depends on the cellular aggregate size: the bigger the aggregate, the faster the spreading (see Figure 2a).
To understand this non-trivial spreading dynamics, the authors investigated in detail what is driving and what is preventing the cellular aggregate from flattening at short times. The contact area expands because the adhesion between the cells and the substrate is more favorable than the cell-cell adhesion. So increasing the cell/substrate adhesion
First, the energy gain is the work per unit of time of the capillary force
Energy gain =
At early times, the contact angle is very small, so the capillary force
Second, the authors show the dissipation is expressed by
This dynamics of
So if the law is valid, rescaling the measured area by
Table 1. Relative change of the viscosity depending on the E-cadherin expression.
E-cadherin level (controls cell-cell adhesion energy) | 21% | 48% |
Relative viscosity to the 100% expression | 42% | 57% |
To summarize, Stéphane Douezan and his colleagues were able to explain what is driving the initial flattening of the aggregate at short times by showing how this dynamics depends on the aggregate size, and they were able to estimate the ratio of the cell-substrate adhesion energy over the viscosity.
After studying this short-time regime, the authors analyzed the spreading at longer times. Depending on the cell-cell adhesion energy, they noticed two behaviors: either the aggregate flows as a cohesive two-dimensional sheet of cells (like a liquid) when the adhesion is strong, or individual cells escape from the aggregate (analogous to a liquid-to-gas transition) when the adhesion is weak. These two behaviors are shown in Figure 3 and in movie 2 and 3 of the supplementary data. This phenomenon could be used to model an invading tumor for which the biological parameters that control the transition between two kinds of spreadings can be precisely tuned.
In this paper, the authors successfully captured the complexity of a biological system with a predictive law of spreading. By measuring well defined physical variables, such as the viscosity and the cell-substrate adhesion energy, they were able to quantify how cells bind to each other or to their environment. These complex biological processes, which involve many different molecular actors, are often described in a qualitative way. Even more interestingly, the authors showed how they could tune these physical variables by controlling some biological parameters, which directly shows their implications in the processes mentioned above. The approach taken in this paper is very elegant as biology often fails to be predictive because of the important complexity of the processes at stake.
[1] The adhesion energy of an interface is the work that should be spent by unit of area if one were to break this interface. The stronger the energy, the more stable the adhesion. Therefore like the surface tension, it is an energy density (unit:
[2] The capillary force is the sum of the components of the three tensions along the tangent axis to the substrate. This force per unit of length is basically the force that pulls on the drop:
[3] The differential expression of the energy gain is obtained through the following reasoning: during an infinitesimal duration of spreading
[4] A power law is simply a mapping of a variable at some power. They are usually presented on log-log plots, as they appear as a straight line, for which the slope is the power of the function.
Disclosure: The second author of this paper is my Ph.D. supervisor. However, she did this work while she was a postdoc. Consequently, I have never been involved in this work.
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