Mathematical modelling of morphogenesis in fungi: spatial organization of the gravitropic response in the mushroom stem of Coprinus cinereus

Abstract

The purpose of this work was to establish how the distribution of local curvatures changed during the mushroom stem gravitropic reaction and to suggest a suitable mathematical model based on these new data.The gravitropic bending of base-and apex-pinned Coprinus cinereus (Fries) S. F. Gray stems was recorded on videotapes. The images were captured from the tapes after each 10 min, rotated by 45m and transformed into tables of changing co-ordinates of points for each stem. The non-linear regression of these points was performed using Legendre polynomials. From the resulting equations the patterns of changing local curvature for 50 subsections per stem during 400 min of gravitropic reaction were calculated.It was observed that base-pinned stems first bent from the apex, but later the curvature of this part decreased, and in the late stages the apex became nearly completely straight again. Subsections, located about one third of stem length from the base determined the main part of the final curvature. The free basal part of the apex-pinned stems bent upward and after a certain bending time also began to straighten. However, this process started significantly later and was weaker. Bending of the subsections close to the pinned apex did not stop when they reached the vertical position, and the final angle of gravitropic curvature could exceed 180m.Plotting various functions of local bending speed and its derivatives against each other and against local angle indicated that, if the hypothetical signal about reorientation arises in the apex, its propagation towards the base did not follow simple wave or simple diffusion laws. The importance of the local angle of all subsections both for signal origin and transmission was established and a signal transmission equation, involving local angle of each subsection, was derived. After creating a suitable program this partial differential equation was solved numerically. The generated shapes of the bending stem coincided in high degree with experimentally observed images.

The Gravitropic Response of Poplar Trunks: Key Roles of Prestressed Wood Regulation and the Relative Kinetics of Cambial Growth versus Wood Maturation

“…of plant aerial organs (Silk and Erickson, 1978;Moulia et al, 1994;Coutand and Moulia, 2000) and even more seldom used in the area of aerial organ tropisms, except for studies on the gravitropic response of the fruit of Coprinus (Meskauskas et al, 1998). The phenomenology of righting kinematics characterized here for gravitropism due to secondary growth is very similar to that found for the fruit body of Coprinus (Meskauskas et al, 1999b).…”

“…Although two motors appear to exist for gravitropic reactions, most studies have been conducted on organs displaying only primary growth, such as hypocotyls (Cosgrove, 1997), epicotyls (Firn and Digby, 1980), coleoptiles (Tarui and Iino, 1997;Meskauskas et al, 1999a), roots (Selker and Sievers, 1987;Perbal and DrissEcole, 1994;Wolverton et al, 2002;LaMotte and Pickard, 2004), the stipe of Coprinus (Meskauskas et al, 1998), and algae (Kiss, 1997). Studies of gravitropism in aerial organs with secondary radial growth such as tree trunks or branches are less frequent (e.g.…”

“…However, quantitative kinematic analyses of curvature fields during tropic responses are rare (Silk and Erickson, 1978;Meskauskas et al, 1998), and none have been applied to gravitropic responses due to secondary growth.…”

Unifying model of shoot gravitropism reveals proprioception as a central feature of posture control in plants

“…In essence, this has been described as a biphasic pattern of general curving followed by basipetal straightening (GC/BS) (4,17). First, the organ curves up gravitropically, then a phase of decurving starts at the tip and propagates downward, so that the curvature finally becomes concentrated at the base of the growth zone and steady (7)(8)(9)(18)(19)(20). This decurving, which has also been described as autotropic (i.e., the tendency of plants to recover straightness in the absence of any external stimulus) (7,21), may start before the tip reaches the vertical (4).…”

Life History and Developmental Processes in the BasidiomyceteCoprinus cinereus

“…More than half of the upper stipe can be removed without affecting the ability of the remaining stem to show gravitropic bending or its ability to compensate for curvature so induced and adjust to the vertical. However, the greater the part eliminated, the more time is needed to respond, suggesting that graviperception is gradually reduced in zones further from the apex (146,147,319). Gravisensing in fungi is thought to be simple and to occur, for example, just by a static gravistimulus mediated by the fungal mass or by a dynamic stimulus caused by alterations of the rate of cytoplasmic streaming and the slow sedimentation of organelles (such as the nucleus) acting as statoliths (24,347).…”