Searching Through Cellular Landscapes

Target search processes by molecular components underlie a broad variety of cellular functions, from signal processing to sorting and export, to transcriptional regulation. These processes take place on an immensely complex landscape that encompasses both the geometry of intracellular structures and the localized interactions that modulate molecular motion and encounter times. The subcellular world includes subdomains with different dimensionalities, such as 1D filaments, and 2D sheets, as well as more complex morphologies such as networks and trees. Here, we summarize cellular applications of mathematical models for geometry-dependent kinetics. In addition, we discuss how the energetic landscape emerging from transient interactions within cellular condensates, and with extended filamentous and membrane structures, can serve to accelerate some searchers while filtering out others. The landscape picture provides a unifying framework linking molecular and cellular search processes, together with the mathematics of random walks in complex spatial architectures.