Before revision:  We then extend coarse-grained population models and derive an analytical approximation for the drift velocity in rugged landscapes that includes the relevant time and length scales. Our model explains the improved velocity, and recovers standard Keller-Segel gradient-sensing results in the limits of no cellular memory, no ruggedness of the landscape, and when memory and fluctuation timescales are well separated.
After revision:  We then extend coarse-grained population models and derive an analytical approximation for the drift velocity in rugged landscapes that explains the enhanced velocity, and recovers standard Keller-Segel gradient-sensing results in the limits of no cellular memory, no ruggedness of the landscape, and when memory and fluctuation timescales are well separated.