Excitable behavior in amoeboid chemotaxis

The ability of cells to direct movement in response to spatial differences in the concentration of external chemoattractants has fascinated biologists for over a century. Chemotaxis is of great important for the proper functioning of both single-cell and multicellular organisms. It allows single cell organisms to search for nutrients. It guides cells of the immune system to sites of infection. Unfortunately, chemotaxis is not always beneficial, as it also directs cancer cells during metastasis. There are two fundamental approaches that allow cells to sense and respond to chemoattractant gradients. Cells performing temporal sensing compare concentrations of chemoattractants over time, and make directional decisions based on the temporal changes in receptor occupancy levels. The chemotactic behaviour of bacteria, particularly E. coli, is the best understood temporal sensing mechanism in biology. The temporal sensing strategy is appropriate for small, fast moving cells that can cover an area quickly – E. coli cells move at approximately ten body lengths per second – but also have chemoattractant receptors that are localized in the cell. Larger, slower cells – a classification that includes most if not all of chemotactic eukaryotic cells – employ a spatial sensing mechanism. In this strategy, cell surface receptors need to be spaced sufficiently far that a gradient of receptor occupancy is formed and can serve as the basis for making directional decisions. Probably the best-studied chemotactic, eukaryotic cells are the social amoeba, Dictyostelium discoideum, as well as the biochemically-similar system in mammalian neutrophils1, 2. Dictyostelium carries out two forms of chemotaxis. During their normal life cycle, they use folic acid gradients to direct their movement in search of bacteria. However, in starvation conditions, Dictyostelium cells develop the ability to produce and secrete cAMP, which is used by cells to aggregate chemotactically. These aggregates eventually form fruiting bodies and spores that allow cells to survive. While the response to these two chemotactic signals is similar, there are some differences. Chemotaxis to cAMP, which is mediated by G-protein coupled receptors, is better understood. To date, the identity of the folic acid receptor is unknown. The spatial sensing strategy involves the coordinated action of three separate processes3–5. Clearly, cells must be able to discern receptor occupancy gradients – what we refer to as static spatial sensing – independent of any motility. Cells must respond to the sensed gradient by focusing motility in the direction of the gradients. Finally, cells polarize by developing distinct leading and trailing edges. This polarization, which need not be permanent is usually induced by migrating in gradients, but can also appear after spatially uniform stimulation or even in the absence of any chemoattractant. In recent years, we have seen a fundamental change in our understanding of chemotaxis in Dictyostelium and neutrophils, prompted by the growing evidence that the actin cytoskeleton and other signalling proteins display behaviour, such as propagating waves, that is consistent with the presence of an excitable system6–14 (Fig. 1; sidebar). We and others have hypothesized that an excitable system couples receptor occupancy to actin polymerization. Here, we review some of the basic features of the chemotactic response in amoeboid cells, and highlight the role played by the excitable network hypothesis. Sidebar Excitable systems The study of excitable systems and media dates to the Hodgkin-Huxley equations describing action potentials in neurons though is now an active area of applied mathematics. An excitable system is a dynamical system that operates at a stable point (Fig. 2a–c). A small amplitude perturbation away from this equilibrium leads to a small responses. However, if the size of the perturbation is sufficiently large, then the system undergoes a large scale, transient response referred to as a “firing”. After the activation of the system there is a refractory period during which the state goes below the equilibrium point. Moreover, during this period no further firings can take place. Activator-inhibitor systems are a common form of a two-component excitable system, where the activator includes a strong autocatalytic positive feedback loop, as well as a negative feedback loop through the inhibitor (Fig. 2b). Substrate depletion systems are the other common form of an excitable system – in this case, the basic double feedback topology (one positive, one negative) is maintained, but the interaction “arrows” are reversed. The term excitable medium is used if the components of the system are diffusible, in which case the components of the system will be seen to propagate as waves (Fig. 2d). In this case, the refractory period means that after a wave goes through a point, a certain period of time must pass before a second wave may go through. Colliding waves thus appear to annihilate each other. Figure 2 Dynamical description of excitable behaviour Figure 1 Excitable behaviour in chemotactic, eukaryotic cells