A framework for designing and analyzing binary decision-making strategies in cellular systems.

Cells make many binary (all-or-nothing) decisions based on noisy signals gathered from their environment and processed through noisy decision-making pathways. Reducing the effect of noise to improve the fidelity of decision-making comes at the expense of increased complexity, creating a tradeoff between performance and metabolic cost. We present a framework based on rate distortion theory, a branch of information theory, to quantify this tradeoff and design binary decision-making strategies that balance low cost and accuracy in optimal ways. With this framework, we show that several observed behaviors of binary decision-making systems, including random strategies, hysteresis, and irreversibility, are optimal in an information-theoretic sense for various situations. This framework can also be used to quantify the goals around which a decision-making system is optimized and to evaluate the optimality of cellular decision-making systems by a fundamental information-theoretic criterion. As proof of concept, we use the framework to quantify the goals of the externally triggered apoptosis pathway.

An information-theoretic characterization of the optimal gradient sensing response of cells.

Many cellular systems rely on the ability to interpret spatial heterogeneities in chemoattractant concentration to direct cell migration. The accuracy of this process is limited by stochastic fluctuations in the concentration of the external signal and in the internal signaling components. Here we use information theory to determine the optimal scheme to detect the location of an external chemoattractant source in the presence of noise. We compute the minimum amount of mutual information needed between the chemoattractant gradient and the internal signal to achieve a prespecified chemotactic accuracy. We show that more accurate chemotaxis requires greater mutual information. We also demonstrate that a priori information can improve chemotaxis efficiency. We compare the optimal signaling schemes with existing experimental measurements and models of eukaryotic gradient sensing. Remarkably, there is good quantitative agreement between the optimal response when no a priori assumption is made about the location of the existing source, and the observed experimental response of unpolarized Dictyostelium discoideum cells. In contrast, the measured response of polarized D. discoideum cells matches closely the optimal scheme, assuming prior knowledge of the external gradient-for example, through prolonged chemotaxis in a given direction. Our results demonstrate that different observed classes of responses in cells (polarized and unpolarized) are optimal under varying information assumptions.

Control analysis of bacterial chemotaxis signaling.

Bacteria such as Escherichia coli demonstrate the remarkable ability to migrate up gradients of attractants and down gradients of repellents in a rapid and sensitive fashion. They employ a temporal sensing strategy in which they estimate the concentration of ligand at different time points and continue moving in the same direction if the concentration is increasing in time, and randomly reorient if the concentration is decreasing in time. The key to success is accurate sensing of ligand levels in the presence of extracellular and intracellular disturbances. Research from a control theory perspective has begun to characterize the robustness of the bacterial chemotaxis signal transduction system to these perturbations. Modeling and theory can describe the optimal performance of such a sensor and how it can be achieved, thereby illuminating the design of the network. This chapter describes some basic principles of control theory relevant to the analysis of this sensing system, including sensitivity analysis, Bode plots, integral feedback control, and noise filters (i.e., Kalman filters).

Optimal noise filtering in the chemotactic response of Escherichia coli.

Information-carrying signals in the real world are often obscured by noise. A challenge for any system is to filter the signal from the corrupting noise. This task is particularly acute for the signal transduction network that mediates bacterial chemotaxis, because the signals are subtle, the noise arising from stochastic fluctuations is substantial, and the system is effectively acting as a differentiator which amplifies noise. Here, we investigated the filtering properties of this biological system. Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell. Then, using a mathematical model to describe the signal, noise, and system, we formulated and solved an optimal filtering problem to determine the cutoff frequency that bests separates the low-frequency signal from the high-frequency noise. There was good agreement between the theory, simulations, and published experimental data. Finally, we propose that an elegant implementation of the optimal filter in combination with a differentiator can be achieved via an integral control system. This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.