**Cellular signaling**

An individual eukaryotic cell senses identity and quantity of ligands through molecular receptors and signaling pathways, dynamically activating signaling effectors. A distinct ligand often activates multiple different effectors, and a distinct effector is activated by numerous different ligands, which results in cross-wired signaling. In apparently identical cells, the activity of signaling effectors can vary considerably, raising questions about the accuracy of cellular signaling and the interpretation of heterogeneous responses, as either functional or simply noise. Cell-to-cell variability of signaling outcomes, signaling dynamics, and cross-wiring all give rise to signaling complexity, complicating the analysis of signaling mechanisms. How can cells function reliably with highly variable signaling outputs? What is the explanation for cross-wired architecture? What are the implications of variable cross-wired signaling for health and disease? These questions reflect tangible gaps in our understanding of how cellular signaling functions, which we are addressing in our work.

**Deciphering cellular signaling with information theory**

Within information theory, a signaling pathway can be interpreted as a communication device, which for a given stimulus level x (input), for example, ligand concentration, generates a response y (output), for example, activation of a transcription factor biochemical signaling pathway, which can be represented as a probabilistic input–output relationship, P(Y|X = x), which encodes input, x, using output, y **(A)**. Because of stochastic factors, decoding is possible only with limited precision. Fisher information quantifies the inverse of the minimal variance with which a given input x can be decoded, which is known as Cramér-Rao inequality . How precisely can x be decoded depends on sensitivity of the response distribution to changes in x ** (B)**. Therefore, formally, Fisher information is defined as the average sensitivity of the logarithm of the probability, P(Y|X = x), to changes in the input, x. Shannon information capacity, C*, quantifies the overall signaling accuracy. It can be interpreted as log2 of a number of inputs that a signaling system can resolve and is approximated by the integration of Fisher information

**(C)**. How much information can be transferred, broadly speaking, depends on the overlap between response distributions to different inputs (e.g. ligand concentrations). Completely overlapping distributions do not allow for information transfer and imply the capacity of 0 bits. Information capacity increases for more distinct distributions and reaches 2 bits for completely distinct distributions to four considered inputs

**(D)**.

For more information on information-theory perspective at signaling see our review:

**Information-theoretic analyses of cellular strategies for achieving high signaling capacity — dynamics, cross-wiring and heterogeneity of cellular states**Topolewski P, Komorowski M.

Current Opinion in Systems Biology, 2021.

**Cell-to-cell variability of signaling responses**

While reliable, high-fidelity signaling appears to be essential for cell function, signaling responses show substantial cell-to-cell heterogeneity. A fraction of cells treated with one dose typically have levels of signaling effectors that are similar to cells stimulated with some other dose, as in the IFN-γ shown above. If we suppose that the cell-to-cell heterogeneity results from molecular noise, then each cell should induce, on average, the same level of response to a given dose, and the differences between cells should arise from the inherent randomness of the signaling biochemistry. Then, the following question arises. What is the probability that a cell exposed to a given dose can decode the dose correctly, based on the signaling output? We know from statistics that the error minimizing decoding strategy is to assign a given response to the dose for which it is most likely. This strategy is known as the maximum likelihood decoding. The maximum likelihood decoding is equivalent to the way in which we the overlaps between the response distributions are quantified in the above figure. Responses to each dose are divided into regions that are most likely for any of the doses. If the cell-to-cell heterogeneity results predominantly from noise then the quantified overlaps between distributions can be interpreted as decoding probabilities. In the above pie-charts, the diagonal elements show the probabilities of correct decoding. Off-diagonal elements show the probabilities of confusing one concentration with another. If the cell-to-cell heterogeneity results from molecular noise the potential of single cells to discriminate between different doses is strongly limited, suggesting that individual cells could not adapt precisely to the external cues. It leaves, therefore, unexplained how cells could function reliably with such a noisy sensing apparatus. In our work, we intend to reconcile cell-to-cell signaling heterogeneity with the reliable functioning of cell signaling pathways.

For more information on how we proposed to interpret and analyze cell-to-cell heterogeneity of signaling responses see:

**Fractional response analysis reveals logarithmic cytokine responses in cellular populations**Nienaltowski K, Rigby RE, Walczak J, Zakrzewska KE, Głów E, Rehwinkel J, Komorowski M.

Nature Communications, 2021.

**Cross-wired signaling**

The cross-wired architecture of signaling is in the simplest instance demonstrated by a single stimulus activating multiple signaling effectors. The degree of crosstalk present in signaling networks varies widely across evolution. For instance, bacterial two-component signaling networks possess little crosstalk. In contrast, pathways of metazoans can hardly be considered to be distinct due to the dense connectivity. The specific advantages of cross-wired architecture and its evolutionary origins are not well understood. It has been, for instance, postulated that the highly-cross wired architecture of signaling could have evolved based on the need for multiple cell types to respond differently to the same environmental conditions. Under this hypothesis, the configuration of cross-wiring varies between cell types, which enables the generation of different responses to the same stimuli. On the other hand, we have recently hypothesized that effective information transfer could be achieved even with minor divergence, implying low evolutionary pressure for independent pathways. Overall, however, evolutionary origins, advantages, and vulnerabilities of cross-wired architecture, as well as their implications for applied life sciences, which we are trying to explore, are only beginning to be understood.

For more information on our evolutionary perspective at cross-wired signaling see:

**The Limited Information Capacity of Cross-Reactive Sensors Drives the Evolutionary Expansion of Signaling**Komorowski M, Tawfik DS.

Cell Systems, 2019.