Table 1.
Variables and Parameters.
Table 2.
Models.
Figure 1.
Geometric description of organ shape.
The median line of an organ of total length L is in a plane defined by coordinates x, y. The arc length s is defined along the median line with s = 0 referring to the base and s = L referring to the apex. A(s) is the local orientation of the organ with respect to the vertical, and C(s) the local curvature. The orientation of the gravity field vector g is parallel to the y axis. The orientation of the light field vector l forms an angle AP with the y axis. The resulting angle of the two tropisms is called AR.
Figure 2.
A. −1 + AP/AR as a function of the fluence rate of the light.
Data are reprocessed from Figs. 4, 5 and 6 in [17] Solid lines correspond to the fit . An etiolated Avena coleoptile is tilted from the vertical for different values of the angle A0 (0, 10, 30, 90 and 120) while a light beam is collimated on the tip of the coleoptile. For different fluence rates, controlled by a neutral density filter, the apical angle is measured after variable duration. This is said to be the equilibrium angle. B. −1 + AP/AR as a function of the fluence rate of the light; data are reprocessed from Figs. 4, 5 and 6 of [17]. Solid lines correspond to the fit . C. −1 + Ap/AR as a function of the fluence rate of the light; data are reprocessed from Figure 8 in in [17]. The solid lines correspond to the fits from A. The empty black symbols (circles and squares) correspond to the measured fluence rates that precisely compensate the gravitropic reaction. The equilibrium state then corresponds to the case in which no movement is observed and AR = A0. Empty circles: A0<90°; empty squares: A0>90°. D. Ap/AR as a function of the fluence rate of the light. Solid lines correspond to the fits from A.
Table 3.
Steady states of the different models.
Figure 3.
A. Timelapse of a coleoptile during phototropic movement, 50 minutes between each picture.
The source light is collimated on the right of the organ and is perpendicular to the vertical. The white bar is 1cm. B. The kinematics of the angle A(s, t) plotted with respect to time t and curvilinear abscissa s (from the base to the apex of the organ). C. The kinematics of the curvature C(s, t) plotted with respect to time t and curvilinear abscissa s (from the base to the apex of the organ). At first, the whole organ curves; then the curvature concentrates near the base.
Figure 4.
Variation of the reference orientation AR as a function of M.
When photoception dominates, M << 1, AR = AP. When graviception dominates, M >> 1, AR = 0.
Table 4.
Parameters of the fit .
Figure 5.
A. Straightening dynamics of the AaC model (D = 4).
At each time the shape is an arc of circle. B. Steady-state shape of the AaC model. The shape is an arc of circle. As photoception dominates over proprioception, D increases (from blue to red); the apical angle reorients in the direction of the light field vector.
Figure 6.
A. Steady-state shape of the model for D = 4.
The black line is the solution when B = 0. As B increases (solid colored line from red to blue), the orientation and the shape of the organ is modified. The dashed line shows the steady-state shape of the graviceptive equation. The expected orientation of the organ AR is shown at the bottom. B. Steady-state shape of the model for B = 4. The black line is the solution when D = 0. As D increases (solid colored line from red to blue), the organ’s orientation and shape are modified. The dashed line shows the steady-state shape of the photoceptive equation, AaC model. The expected orientation of the organ AR is shown at the bottom.
Figure 7.
A. Steady-state shape of the model for B = 2.
The solid black line is the solution when D = 0; the dashed line is the solution when D → ∞ and B = 0. As M increases (from red to blue), the organ’s orientation and shape are modified. B. Straightening dynamics of the model (B = 2 D = 20). The solid black line is the solution when D = 0; the dashed line is the solution when D → ∞ and B = 0. During the movement, the organ reaches the steady state of the photoceptive equation but then goes to the steady state of the gravi-photo-proprioceptive equation. C. Space-time mapping of the curvature C(s, t) during straightening.