Gravitropism Shapes the Pareto Front of Root System Architecture

The root systems of wild tomatoes (S. Pimpinellifolium) can be understood as biological networks in which the lateral roots branch from a single main root and together balance two competing objectives: minimizing the material cost of building the network (wiring cost) and minimizing the transport time from the root tips to the shoot (conduction delay). Our prior work showed that S. Pimpinellifolium root architectures cluster near the Pareto-optimal front defined by these two objectives, with morphological diversity resolving into four qualitative topologies ((Chandrasekhar and Julkowska, 2022)). That framework assumed lateral roots grow as straight lines - ignoring gradual onset of lateral root gravitropism, the tendency of roots to curve toward the gravity vector. Because curved trajectories are longer than straight lines, gravitropism directly increases both wiring cost and conduction delay, constraining which architectures are physically realizable and thereby reshaping the Pareto front itself. Here we extend the model to explicitly incorporate lateral root gravitropism, producing predicted architectures that align much more closely with observed S. Pimpinellifolium root systems. We present a computational method to infer gravitropic sensitivity directly from anatomical tracing data - without reorientation assays - and apply it to 2423 arbors across different root topologies, growth conditions, and hormone treatments. Incorporating gravitropism reveals variation invisible to the straight-line model:notably, lateral roots show reduced gravitropic sensitivity under salt stress, mirroring a phenomenon previously described only for main roots and overlooked in lateral roots until now.