Theoretical constraints imposed by gradient detection and dispersal on microbial size in astrobiological environments

The capacity to sense gradients efficiently and acquire information about the ambient environment confers many advantages like facilitating movement toward nutrient sources or away from toxic chemicals. The amplified dispersal evinced by organisms endowed with motility is possibly beneficial in related contexts. Hence, the connections between information acquisition, motility, and microbial size are explored from an explicitly astrobiological standpoint. By using prior theoretical models, the constraints on organism size imposed by gradient detection and motility are elucidated in the form of simple heuristic scaling relations. It is argued that environments such as alkaline hydrothermal vents, which are distinguished by the presence of steep gradients, might be conducive to the existence of "small" microbes (with radii of $\gtrsim 0.1$ $\mu$m) in principle, when only the above two factors are considered; other biological functions (e.g., metabolism and genetic exchange) could, however, regulate the lower bound on microbial size and elevate it. The derived expressions are potentially applicable to a diverse array of settings, including those entailing solvents other than water; for example, the lakes and seas of Titan. The paper concludes with a brief exposition of how this formalism may be of practical and theoretical value to astrobiology.