Regulatory memory and growth-coupled inheritance shape nutrient-dependent flagella number variation in Salmonella

Bacteria must balance the advantage of movement against the cost of building flagella, yet how nutrient availability shapes variation in flagellar number across single cells remains unclear. Here, we combine time-resolved basal-body measurements in Salmonella enterica with a mechanistically constrained stochastic model of flagellar remodeling. The model separates two routes from nutrient availability to flagellar number: an RflP-dependent regulatory memory that sets a synthesis target via a latent sensing-memory variable, and a physical inheritance process in which synthesis, binomial partitioning, and division reshape the flagellar-number distribution. Coarse-graining this process yields leaky-integrator dynamics in which the mean flagellar number tracks a regulatory target, while the latent correlation follows acquisition-decay dynamics. In wild-type cells, nutrient-dependent acquisition raises the target and increases flagellar investment; in {Delta}rflP cells, loss of acquisition produces a transient overshoot that isolates the intrinsic decay (memory) timescale of the regulatory state. The fitted model predicts a held-out nutrient condition and reveals which parameter combinations are identifiable from the data. Analysis of the fitted dynamics suggests that precision is tuned primarily by sensing-dependent signal amplitude, rather than integration time, with an apparent [~]1.7-fold increase in effective wild-type noise amplitude after mean normalization, consistent with a precision cost of active regulation relative to the mutant. A model-free, information-geometric (Cramer-Rao) speed limit further shows that active remodeling approaches the statistical speed allowed by the observed distributional variability. Together, these results reveal how Salmonella cells couple regulatory memory with growth-dependent inheritance to record recent nutrient history in their flagellar number.