Rate distortion theory in cellular signaling

Cells often use signal transduction networks to make decisions critical to proper cell functioning. For example, Mitogen-activated protein kinase (MAPK) cascades control the hormone-induced Xenopus oocyte maturation decision [1] as well as the budding response in the mating pathway of yeast [2], receptor modification mechanisms in the signal transduction pathway of E. coli control the direction of flagella rotation and hence the run-or-tumble decision [3], and Ca2+ signaling plays a primary role in T cell activation [4], The underlying mechanisms and molecular interactions governing systems such as these have been the focus of much work, and the recent emergence of the area of systems biology has provided fruitful insight into the dynamics of complex signaling networks. However, the performance and efficiency of many cellular decision-making systems is relatively unclear. How well does the signal transduction network of a cell make decisions based on the signaling cues available? Can improvements be made by altering the parameters or structure of the network? How efficiently are resources such as metabolic energy used? Here we provide a framework with which to answer such questions using concepts from signal processing and information theory, and we study the gradient sensing mechanism in Dictyostelium discoideum as an example. The utility of information theory for the study of biology has been suggested for some time [5]-[8] and has received considerable attention in the fields of neuroscience [9] and genetics [10]-[12]. However, the full breadth of this utility for biological signaling systems in general has not been realized, primarily because of the difficulty of defining " information" in a biological system. Unlike neural signals, which are easily decomposed into discrete events (and thus translated directly into bits of information in the usual engineering sense), the information content of a general signal transduction network, such as the signaling pathway of E. coli or a MAPK cascade, is embedded directly in the dynamics of the system itself [6], [7], Our approach is to maintain a high-level description of biological information in the sense of Shannon [13] without concern for the specific information content of the signal of interest. This allows for a sufficient yet relatively simple and intuitive characterization of information that we hope motivates the study of other biological signaling networks in a similar light. Here we use rate distortion theory as theoretical tool for studying performance-cost tradeoffs in cellular decision making. The rate distortion function provides a lower bound on the rate at which information must be transmitted through the cellular signal transduction network in order to achieve a given performance criterion. To study gradient sensing performance of D. discoideum cells, we developed a model of the cell's directional response to a chemoattractant gradient that arises from a random direction. The distribution of the gradient angle represents a priori knowledge of the chemoattractant source location from the perspective of the cell. Using a distortion function closely related to the chemotactic index - a widely used measure of chemotactic performance - we computed the rate distortion function that minimizes the mutual information between the gradient angle and the directional response of the cell. We found that the input-output maps that optimally achieve the rate distortion function closely match published models that capture key characteristics of the signaling network in D. discoideum, implying that these cells have evolved to respond to chemoattractant sources in an efficient manner. Our results help explain differences in observed behavioral responses of polarized and unpolarized D. discoideum cells. Unpolarized cells are very responsive to changes in the location of a source of attractant, quickly realigning key signaling components with the new gradient direction [14]. On the other hand, polarized cells chemotaxing towards an attractant source respond to a change in source location with gradual turns that initially maintain the predisposition towards the previous source location [14], [15]. Furthermore, gradient amplification in the response of polarized cells is larger than that in unpolarized cells [16]. Our results, verified in simulation, indicate that these dissimilar responses are necessary to cope with the different gradient angle distributions that are associated with each environmental situation.