ABSTRACT:
This model is from the article:
Root gravitropism is regulated by a transient lateral auxin gradient controlled by a tipping-point mechanism.
Band LR, Wells DM, Larrieu A, Sun J, Middleton AM, French AP, Brunoud G, Sato EM, Wilson MH, Péret B, Oliva M, Swarup R, Sairanen I, Parry G, Ljung K, Beeckman T, Garibaldi JM, Estelle M, Owen MR, Vissenberg K, Hodgman TC, Pridmore TP, King JR, Vernoux T, Bennett MJ.
Proc Natl Acad Sci U S A.2012 Mar 20;109(12):4668-73
22393022,
Abstract:
Gravity profoundly influences plant growth and development. Plants respond to changes in orientation by using gravitropic responses to modify their growth. Cholodny and Went hypothesized over 80 years ago that plants bend in response to a gravity stimulus by generating a lateral gradient of a growth regulator at an organ's apex, later found to be auxin. Auxin regulates root growth by targeting Aux/IAA repressor proteins for degradation. We used an Aux/IAA-based reporter, domain II (DII)-VENUS, in conjunction with a mathematical model to quantify auxin redistribution following a gravity stimulus. Our multidisciplinary approach revealed that auxin is rapidly redistributed to the lower side of the root within minutes of a 90° gravity stimulus. Unexpectedly, auxin asymmetry was rapidly lost as bending root tips reached an angle of 40° to the horizontal. We hypothesize roots use a "tipping point" mechanism that operates to reverse the asymmetric auxin flow at the midpoint of root bending. These mechanistic insights illustrate the scientific value of developing quantitative reporters such as DII-VENUS in conjunction with parameterized mathematical models to provide high-resolution kinetics of hormone redistribution.
This model corresponds to the simplified model described in the article. It is assumed that, on the timescale of DII-VENUS degradation, the concentrations of auxin, TIR1/AFB, and their complexes can be approximated by quasi-steady-state expressions. This reduced the full model to a single ODE that describes how the DII-VENUS dynamics depend on the auxin influx and four parameter groupings.
Leah Band 
