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Molecular motors are specialized proteins which perform active, directedtransport of cellular cargoes on cytoskeletal filaments. In many cases, cargomotion powered by motor proteins is found to be bidirectional, and may beviewed as a biased random walk with fast unidirectional runs interspersed withslow `tug-of-war' states. The statistical properties of this walk are not knownin detail, and here, we study memory and bias, as well as directionalcorrelations between successive runs in bidirectional transport. We show, basedon a study of the direction reversal probabilities of the cargo using a purelystochastic (tug-of-war) model, that bidirectional motion of cellular cargoesis, in general, a correlated random walk. In particular, while the motion of acargo driven by two oppositely pulling motors is a Markovian random walk,memory of direction appears when multiple motors haul the cargo in one or bothdirections. In the latter case, the Markovian nature of the underlying singlemotor processes is hidden by internal transitions between degenerate run andpause states of the cargo. Interestingly, memory is found to be a non-monotonicfunction of the number of motors. Stochastic numerical simulations of thetug-of-war model support our mathematical results and extend them tobiologically relevant situations.

Memory, Bias and Correlations in Bidirectional Transport of Molecular Motor-driven Cargoes