Speaker: Andrew Mugler
Department: Department of Physics and Astronomy, Purdue University
Subject: Collective Sensing by Communicating Cells
Location: Delft University of Technology
Date: 16 December 2016
Author: Romano van Genderen
This weeks talk at the department of Bionanoscience was given by prof Mugler of Purdue University. He started by showing us a video of a small cluster of epithelial cells called an organoid growing tentacle shaped protrusions that were growing in the same direction as a chemical gradient, showing that cells can sense gradients and use this information. He told us that he has developed a model capable of explaining this behavior. He said that his talk was split in two sections, one dealing with the fundamental limits to sensing and the other with how cells surpass these limits by communicating.
He started with one of the simplest models, namely E coli chemotaxis. These bacteria can move in two ways, either run forward or change direction by tumbling. The chance that a cell tumbles depends on the concentration gradient. But how accurately can a cell measure its local concentration? To answer this question he modeled the cell very simply, namely as a permeable membrane cube with edges a. So the mean number of molecules in the cell (μ) is equal to a^3*c. Because diffusion is a Poisson process the standard deviation is linearly dependent on the mean. If multiple measurements are done the standard deviation is equal to the mean divided by a refreshing factor T(a^2/D) in which T is the time between 2 measurements and D the diffusion constant. This leads to the Burg-Purcell limit: μ/σ=(TDAc)^-0.5 In real E coli cells this relationship holds true, the cells are almost optimal measurement devices. Next he went on to a bigger cell, namely the amoeba. The amoeba has two detectors, one on the head and one on the tail. This cell also behaves in such a way to make an optimal measurement with a high signal-to-noise ratio.
Next he went on to show models involving cells talking to each other through autocrine signaling. He first showed some models for uniform cell gradients. This model had receptors, ligands and a messenger molecule. For this model he showed some scary looking rate equations with noise terms. He then solved them using a for me completely unknown method. This led to a function for the mean error. It had a term ½ in front for one cell. Two adjacent cells turned this term into 3/8, not ¼ because the cells are sometimes measuring some things twice. Then when he made the cells no longer adjacent the error became a function of the distance. The ideal distance according to this model was 8/3 cell radius. This is a balance between measuring a lot of different points and losing information due to communication. Comparing this to real life cell packing, the cells do in fact pack as predicted. This sparse packing is one of the two ways to minimize noise. They can also be directly attached through gap junctions.
Fig 1. The model used for long-range signaling. Ligand in blue, bound ligand in purple and communication model in green. The communication molecule concentration drops as a power law.
Finally he showed a setup for measuring a gradient. For this setup to work, the gradient must be relatively shallow. Then he placed a single epidermal cell in the gradient. This cell has no preferred growing direction. But an organoid of talking cells do have a bias. When the gap junctions are blocked, they have no bias. So there is juxtacrine signaling through the gap junctions. A new model was made. But the signaling is now done through two molecules, a local signaling molecule that does not diffuse and a global one that does. So the difference between the local and global molecule is a measure for the gradient. Using this model he showed that the optimal distance for a good signal is 4 cells. But like in the telephone tag game, the longer the signal is passed on from cell to cell, the more noise you get.
This was a very interesting talk, but some of the mathematics used was slightly too advanced for me to completely understand the talk. I did like that cells are way more optimal than I usually see them. They behave as “optimal noise reduction machines”. This is most likely something that is selected for a lot in evolution, because problems in signaling lead to swift death.