In a canonical example, cells detect extracellular stimuli (input) with specific transmembrane receptors binding a ligand at the surface, which results in a biochemical activity on the inside of the cell, for example, the activation of a receptor associated kinase. The initial stimuli are processed in a relay mechanism along intracellular signalling pathways and culminate in effectors (output), which might be transcription factors. The effectors carry information about the identity, intensity and duration of the stimuli in order to initiate distinct cellular responses, which might involve gene transcription, metabolism, cell cycle or any other cellular process.
The overall molecular and biochemical mechanisms how individual cells transduce signals to effectors are widely understood. Biochemical descriptions, however, do not directly lead to understanding how the stimuli are translated into distinct responsesas signalling processes are immensely complex. Many components of signalling pathways are functionally pleiotropic: (i) a single stimulus often activates multiple effectors, (ii) a distinct effector can be activated by numerous stimuli, and (iii) signals triggered by different stimuli often travel through shared network components. Moreover, conventional approaches to studying intracellular signalling pathways have measured the averaged response at a fixed time point after stimulation of a population of identical cells. Such population-based measurements hide the variability and dynamics of individual cells, and therefore misleadingly suggest precise input-output relationships. Recent studies of cellular signalling at the single-cell level have revealed that (iv) biochemical signalling processes are intrinsically stochastic and responding cells exhibit quite varied behaviours when examined individually, and (v) temporal dynamics of signalling in individual cells is correlated with physiological responses. These observations (i-v) raised questions that are fundamental for understanding biochemical signalling processes: (i) how is a complex mixture of ligands translated into activities of a variety of different effectors (ii), how is the identity and quantity of ligands encoded in temporal activity of the pathway’s effectors? (iii) how precisely can individual cells sense the concentrations of a specific ligand? In light of these questions, how information about complex mixture of extracellular stimuli is processed and translated into distinct cellular responses remains elusive. Therefore, biochemical descriptions require quantitative support to explain how complex stimuli are translated and encoded in distinct activities of the pathway’s effectors.
Mathematical methods of information theory appear to provide a natural mathematical language to describe how stimuli are encoded in activities of signaling effectors. Exploring the information-theoretic perspective, however, remains conceptually, experimentally, and computationally challenging. In particular, it is not entirely clear how the information transfer of cellular systems should be defined and quantified. Current approaches inherit methodologies developed for electronic communication, which usually transfers information by means of long sequences of symbols. Cellular signaling however is different. Typically, signaling pathways transfer information about the identity and quantity of chemical ligands over a given period of time by inducing activity of signaling effectors, e.g. transcription factors. Therefore, we Intend to reshape information-theory approaches in order to match the realm of biochemical signaling.
Biochemical signal transduction is analogous to the statistical inference: an activation level of pathways’ effector contains information about levels of extracellular ligands analogously as data contain information about parameters of a statistical model. Therefore, methods originated from the theory of statistical inference can be employed to analyze information flow in signaling pathways. Statistics developed a rich set of tools that allow quantifying what information about parameters can be inferred from data. Most importantly this includes Fisher information that provides an upper limit for the precision of estimates in frequentists statistics and so-called referenced priors that describe when maximal information about unknown parameters can be maximized in the setting of the Bayesian paradigm; sufficient statistics that defines how information about parameters is encoded in data. We intend to take inspiration from these tools and ways of thinking to understand the functioning of biochemical signaling.