Team:TU-Delft/informationtheory

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Introduction

Signaling pathways and genetic circuitry have the capacity to transmit and process information about certain states in its environment. They are used by the cell to make decisions about whether to take certain actions to remain well adapted. Until now we have used models to describe these dynamics with the goal of eventually having enough insight into the systems so we can develop rational approaches to engineer them. Because of the apparent random nature of many biochemical systems interest in stochastic modeling has increased over the years. Complex stochastic biochemical pathways can now be simulated and models keep coming closer to reality.
The only problem is that we as users of these models do not have many tools to evaluate the stochastic output of these systems. A new objective and quantitative way to assess the stochastic characteristics and thus also the information processing capacity of a cellular system is therefore needed. The way to do this is to use the tools from information theory and apply this to biological problems. Because we will be using the tools of information theory the right way to asses the properties of our biological systems would be at the single cell level as this is the environment were our genetic circuitry actually functions. Therefore we used Fluorescence Microscopy to acquire data on single cells to assess the processed information from input (Ligand) to output (Fluorescence) or put differently: From Signal (S) to Response (R). This information flow from signal to response can be quantified with the following equation:



Using this equation and experimental data we determine the mutual information in the yeast pheromone cascade from signal to response. The mutual signal/response information can then be expressed in one clarifying number:
The BioBit.

Figure 1: The Biobit, the ultimate measurement for
the information processing capacity of a biological system.

The BioBit is a number that represents the length of a string of ones and zeros in which information can be encoded, thus quantifying the amount of information a certain biological system can process. As described in the reporter section, data from single cells was gathered by a Robotic High-through-put Fluorescence Microscopy Setup. This enabled us to assess the temporal dynamics of single cells which can also be useful for validating cellular stochastic models of the yeast pheromone cascade. Below a picture is shown which indicates the problem on a single cell level.

Figure 2: From Signa (S) to Response (R) in our case from Alpha pheromone to GFP fluoresence.

How many Signal values can the cell reliably distinguish? This is what the biobit value quantifies.

The above picture illustrates the concept that was further discussed [1]. Using this approach we could also determine the temporal dynamics of the information processing capacity for many time points. With this data we could also analyze the maximum response for individual cells and thereby getting more insight into the system than would be possible with flow cytometry.

Methods & Results

To arrive at this result a High-trough-put Fluoresence microscopy pipeline was developed. The cells were grown for 24 hours, remaining in exponential phase and then live fixed with Concanavalin-A to a 24-wells plate and imaged under an automated Fluoresence Microscope. Several pictures were taken over a time of 8 hours. After that time the pictures were analysed with VCell-ID software and a dataset was produced that could be imported into MATLAB for computational analysis, which was performed as in [1]. The flow chart of the experimental pipeline is shown below:

Figure 3: Experimental Flow Chart of High-through-put Microscopy pipeline.

The result that was obtained with High-trough-put Microscopy is shown below. Because temporal fluorescence optima did occur in a relatively small time period the fluorescence value for all the individual yeast cells was determined at the mean experimental maximum of t = 3.5 h.

Figure 4: Fluorescence Cell Histograms for FUS-GFP ΔFAR at t=3.5 for different concentrations of Ligand (S) of Alpha pheromone.

As one can see the response has a longer tail for high concentrations of ligand ( Signal,S) of Alpha pheromone. There are however several cells that have low Fluorescence upon induction with ligand. Data was corrected for dead cells. Subsequent analysis of the data in MATLAB yielded a value of 0.6 for the BioBit, which seems reasonable in the light of the finding that the BioBit value usually does not cross 1.0 and is often lower.

Conclusion

Eventually we used this data to compute the information bit value to get BioBit for the yeast pheromone cascade. This value was calculated to be '0.6' which is equal to 2^0.6=1.51 detectable values on the single cell level. In the future this technique can be used to classify and evaluate the information processing capacity of genetic circuits. Therefore providing a new tool for rational genetic circuit design.

References

[1] Raymond Cheong, Alex Rhee, Chiaochun Joanne Wang, Ilya Nemenman, Andre Levchenko. Information Transduction Capacity of Noisy Biochemical Signaling Networks, Science. (2011)