# 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 assess 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, Alpha pheromone) to output (GFP Fluorescence) or put differently:

**From Signal (S) to Response (R).**This information flow from signal to response can be quantified with the following equation:

With R and S being the Response and Signal respectively. Using this equation and obtained experimental data from single cells we determined the mutual information I(R;S) in the yeast pheromone cascade from signal to response, with the real nice property that no assumption has to be made about the distributions of this system. Regardless of the distribution the mutual information of this system can then be expressed with one clarifying number: The BioBit.

###### Figure 1: The Biobit, the ultimate measurement for

the information processing capacity of a biological system.

The BioBit (mutual information) 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. For instance a biological system with a BioBit of 2.02 is able to reliably distinguish 22.02 = 4.06 values in the signal. If this certain biological system is a cell then this BioBit tells us that the cell can reliably sense 4.06 (or about 4) different environmental conditions (or put different: Signal,S). Below a picture is shown which gives visual interpretation of the concept on the level of a biological system, in this case on a single cell level.

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

**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]. As described in the reporter section of the Wetlab part, 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. 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-through-put Fluorescence 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 glass bottom plate and imaged under an automated Fluorescence Microscope. Several pictures were taken over a time of 8 hours. More information about how these experimental results were obtained can be found in the Reporter section of the Wetlab part. After the experiment was completed the pictures were analyzed 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-through-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 ΔFAR1 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

**0.8 for the BioBit**, which seems reasonable in the light of the finding that the BioBit value usually does not reach beyond 1 and is often lower.

## Discussion & Future Outlook

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**'0.8' which is equal to 2^0.8 =1.74 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. A Bioengineer could for instance be interested in designing a biosynthetic system that has sensing capabilities and must eventually be able to be able to distinguish between 3 different environmental conditions. In this case the Bioengineer could be interested in using the yeast pheromone cascade as part of this biosynthesis system. To assess if the yeast pheromone cascade is a suitable systems in this case, the Bioengineer would go to the parts registry and he or she would discover that the BioBit is in this specific case 0.8, which directly applied would not have a high enough information processing capacity. This would lead the Bioengineer to explore new biosynthetic designs that would lead to an overall BioBit value of 1.58 (corresponding to the 3 required distinguishable values). The Bioengineer could by example in this case use quorum sensing systems to group the information into one node thereby improving the overall BioBit/Information processing capacity of the envisioned biosynthetic system. By assuming the following bush like information processing topology and by using the following relation as described by Cheong, et al [1]. the Bioengineer would be able to compute the amount of yeast cells that would need be grouped into the quorum sensing enabled information node to attain the desirable BioBit value.

Where σ

^{2}

_{S }is the variance of the signal distribution and σ

^{2}

_{S->R}is the noise (variance) introduced in each branch of this bush model function. Thus the BioBit value can grow logarithmically with the number of yeast cells in the bush. The Bioengineer would with knowing that with σ

^{2}

_{S }and σ

^{2}

_{S->R}having a value of for instance 4 and 3, the amount of grouped yeast cell would have to be larger than 48 (47.25 rounded up), which would help the Bioengineer much in the design process. The BioBit therefore provides a new tool for rational genetic circuit design.