Chemical waves in cell and developmental biology

Abstract

Many biological events, such as the propagation of nerve impulses, the synchronized cell cycles of early embryogenesis, and collective cell migration, must be coordinated with remarkable speed across very large distances. Such rapid coordination cannot be achieved by simple diffusion of molecules alone and requires specialized mechanisms. Although active transport can provide a directed and efficient way to travel across subcellular structures, it cannot account for the most rapid examples of coordination found in biology. Rather, these appear to be driven by mechanisms involving traveling waves of chemical activities that are able to propagate information rapidly across biological or physical systems. Indeed, recent advances in our ability to probe the dynamics of signaling pathways are revealing many examples of coordination of cellular and developmental processes through traveling chemical waves. Here, we will review the theoretical principles underlying such waves; highlight recent literature on their role in different contexts, ranging from chemotaxis to development; and discuss open questions and future perspectives on the study of chemical waves as an essential feature of cell and tissue physiology.

Figure 1.

Sending biochemical signals in cells. (A) Schematic of a biochemical signal diffusing through a cell. (B) Distance traveled as a function of time by diffusion. Shaded regions represent relative range over which different-sized molecules diffuse. (C) Spreading of the concentration profile of a biochemical signal by diffusion. (D) Molecular motors can carry cargo through a cell by moving along cytoskeletal filaments in a process called active transport. (E) Distance traveled as a function of time by active transport. A narrower range of velocities (shaded area, E) has been observed for systems relying on active transport than for systems relying on chemical waves (shaded area, H). (F) Propagation of the concentration profile of a biochemical signal by active transport. (G) Chemical waves are the basis by which action potentials can rapidly spread signals through a neuron. Depicted is a traveling action potential. (H) Distance traveled as a function of time by chemical waves. (I) Propagation of the concentration profile of a biochemical signal by chemical waves. Diffusive transport dampens signal, whereas active transport and chemical waves preserve the amplitude of the traveling signal. Peaks are closer together in I compared with F to convey that chemical waves can travel much faster.

Figure 2.

Theoretical mechanisms of chemical waves. (A and B) Introduction of a physical barrier in a tissue/embryo allows the distinction between an active (A) and a phase wave (B). (C) Wave-like spreading of farming through Italy, adapted from Baggaley et al. (2012). (D and E) Propagation of Fisher–Kolmogorov unstable waves spreading through space. (F) Diagram representing bistable regulation of the cell cycle transition from interphase to mitosis. Cdk1 activity exhibits a switch-like/bistable response as a function of cyclin concentration. (G and H) Propagation of bistable chemical waves. (I) Diagram representing the spreading of an action potential through an axon in a neuron. (J and K) Excitable wave spreading through space and time.

Figure 3.

Examples of bistable and excitable chemical waves in biology. (A) Schematic of mitotic waves in Xenopus egg extracts. Teal blobs represent interphase assemblies of sperm chromatin and nuclear-targeted GFP in a Teflon tube. Upon mitotic entry, blobs disassemble in a wave-like fashion. (B) Waves of mitotic entry (pink circles) and exit (blue circles) in Xenopus egg extracts. Adapted from Chang and Ferrell (2013). (C) Uncoupled mitotic waves upon physical separation of the extract in two halves. Adapted from Chang and Ferrell (2013). (D) Schematic of cytokinetic ring formation. (E) Starfish embryo coexpressing GFP–rGBD (cyan; Rho activity) and GFP-Utr (pink; F-actin) undergoing cytokinesis. Adapted from Bement et al. (2015). (F) Kymograph of an activated frog egg overexpressing Ect-2 depicting Rho-activity (cyan) and actin (pink) waves. Adapted from Bement et al. (2015). (G) Schematic of mitotic waves in a developing Drosophila embryo. (H) Schematic of Cdk1 FRET sensor: active Cdk1 complex induces a conformational change that increases FRET efficiency. (I) Heatmap of Cdk1 wave in a cell cycle 13 Drosophila embryo. Black line, mitotic entry wavefront; white circles, wave origins. (J) Uncoupled Cdk1 waves after the introduction of a barrier during S phase. Dotted line, mitotic entry front; solid line, mitotic exit front; shaded region, barrier. Adapted from Deneke et al. (2016).

Figure 4.

Additional examples of chemical waves in biological systems. (A) Schematic of clock-wavefront model for somitogenesis. The PSM exhibits oscillatory gene expression that generates waves that sweep from posterior to anterior. (B) Schematic of PSM showing how gene expression oscillations have different frequencies along the anterior-posterior axis. (C) Heat map showing waves generated by a gradient of frequency through space. (D) Schematic of clot formation upon injury. Upon contact with collagen layer (gray), thrombin (navy circles) gets recruited to the site of injury and spreads in a wave-like manner. The thrombin wave is followed by a delayed antagonistic wave that results in the formation of a localized blood clot (red). (E) Spatiotemporal distribution of thrombin activity wave. Adapted from Dashkevich et al. (2012). (F) Schematic of a Drosophila eye imaginal disc, showing a morphogenetic furrow moving from posterior to anterior and organizing cell differentiation and cell proliferation.