A stochastic model of root gravitropism

Gravitropism is a vital process determining plant architecture. As plant architecture is key to resource aquisition a better understanding of gravitropic behaviour may have a great impact on our future food security. Recent models of gravitropism have focussed on understanding specific mechanisms involved in gravitopic response. However our understanding of gravitropism at the behavioural level remains limited, with little known about the factors that determine a response and the timescales involved. We show that gravitropic behaviour is best treated as an angle dependent stochastic system exhibiting fast angle detection and relatively slow response with limited to no hysteresis. A minimal stochastic model of root gravitropism is presented which provides a description of gravitropic behaviour at the population level as well making informative predictions about the behaviour of the mechanisms involved. The root is treated as having a probability of making a discrete bend in a given time that is directly proportional to the current angle. The angle dependent probability combined with the size of a bend determines the expected response, while the bend size determines the variation in response. The time step of a bend limits the timescale of the response to a few minutes. The need to analyse the noisy response of roots to gravity has necessitated the development of equipment to precisely control the angle of a root tip over long time periods, as well as automated data analysis tools capable of handling large datasets.