Spatial and temporal specificity of Ca2+signalling inChlamydomonas reinhardtiiin response to osmotic stress

Ca2+-dependent signalling processes enable plants to perceive and respond to diverse environmental stressors, such as osmotic stress. A clear understanding of the role of spatiotemporal Ca2+ signalling in green algal lineages is necessary in order to understand how the Ca2+ signalling machinery has evolved in land plants. We used single-cell imaging of Ca2+-responsive fluorescent dyes in the unicellular green alga Chlamydomonas reinhardtii to examine the specificity of spatial and temporal dynamics of Ca2+ elevations in the cytosol and flagella in response to salinity and osmotic stress. We found that salt stress induced a single Ca2+ elevation that was modulated by the strength of the stimulus and originated in the apex of the cell, spreading as a fast Ca2+ wave. By contrast, hypo-osmotic stress induced a series of repetitive Ca2+ elevations in the cytosol that were spatially uniform. Hypo-osmotic stimuli also induced Ca2+ elevations in the flagella that occurred independently from those in the cytosol. Our results indicate that the requirement for Ca2+ signalling in response to osmotic stress is conserved between land plants and green algae, but the distinct spatial and temporal dynamics of osmotic Ca2+ elevations in C. reinhardtii suggest important mechanistic differences between the two lineages.

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.