Tip growth is a common mode of cell morphogenesis observed in root hairs, fungal hyphae, pollen tubes, and many unicellular algae. These organisms have cell walls with distinct polymer compositions and structures. Despite these molecular differences, the mechanical aspect of their morphogenesis shows striking similarities, suggesting that these organisms share mechanical constraints that transcend the molecular details of their walls. We are conducting comparative work in a wide range of tip-growing cells to determine what these constraints are.

The defining feature of tip growth is that surface expansion is limited to one extremity of the cell (Fig. 1). The steady advancement of the tip relies on a precisely regulated equilibrium between the localized deposition of building material and its subsequent deformation to expand the cell surface.

Fig.1: Time lapse sequence of a growing lily pollen tube. Note that the morphology of the tube is drawn by the expanding tip and does not change behind it.

Tip growth is a dynamical process that requires new tools and methods to be adequately investigated. We have developed imaging protocols that can be used to quantify the dynamics of tip growth under a wide range of conditions. Some of these tools are used to quantify the cell geometry and measure the rate of wall expansion by labelling the surface of actively growing cells with fluorescent microspheres (Shaw et al., 2000; Dumais et al., 2004). Using time-lapse imaging, we can track the displacement of the microspheres and determine from it the rates of wall expansion (Fig. 2).

Fig. 2: Kinematic and mechanical analysis of tip growth in Medicago root hairs.

In Medicago truncatula root hairs, wall expansion exhibits a strong meridional gradient with a maximum near the pole of the cell. Root hair cells also show a striking expansion anisotropy, i.e., over most of the dome surface the rate of circumferential wall expansion exceeds the rate of meridional expansion. The tensional stresses present in the cell wall can be calculated from the tip geometry and the measured hydrostatic pressure of the cell. Using these data, we have shown that the expansion anisotropy can be predicted from the calculated stresses and a simple constitutive model for the cell wall based on the observed pattern of cellulose microfibrils (Dumais et al., 2004).

Morphogenesis is foremost an explanation of how shape is created. To reconstruct the shape sequence shown in Fig. 1 and Fig. 2, three morphogenetic variables must be known: the tip shape, the tip velocity, and the direction of growth; all of which may evolve in time. Tip-growth morphogenesis can thus be addressed by answering three fundamental questions:
i) What sets the shape of the tip?
ii) What sets the tip velocity?
iii) What maintains the direction of growth?
As natural as these questions may seem, they have attracted little attention in the literature. The questions listed above are linked to three outstanding problems in the field: Reinhardt's Rule, pulsatile growth, and helical growth .

Tip Shape and Reinhardt's Rule: In 1892, Reinhardt formulated a basic rule for tip growth morphogenesis stating that the cell tip gets more pointed as the tip velocity increases. Reinhardt's empirical observation has been validated on numerous occasions (Wessels, 1988) but never quantified. Reinhardt drew putative trajectories of wall elements, all perpendicular to the cell surface, to demonstrate that more pointed tips arise from steeper gradients of wall expansion (Fig. 3). The connection between the tip velocity and the gradient of wall expansion remains, however, unexplained.

Fig. 3: Trajectory of material points according to Reinhardt.

Fig. 4: Tip geometry across a wide range of tip-growing cells. The cells are represented at different scales.

Pulsatile Growth: Most tip-growing cells show slight random variations in the tip velocity during elongation. However, in some cells these variations attain such high amplitudes and temporal regularity that the cell can be described as pulsing. The trigger of pulsatile growth as well as the quantitative interactions that set the amplitude and period of the oscillations are still not understood.

Fig. 5: Pulsatile growth in a lily pollen tube. (Top) Outline of the cell shown every five seconds. (Bottom) Velocity of the tip as a function of time. There is a clear period of about 25 seconds in the velocity.

Helical Growth in Pollen Tubes: Steering during tip growth is such that the cells keep a more or less straight direction over length scales that far exceed the length of the growth zone. However, some cells show transient helical growth when the normal steering dynamics is disrupted. The instability that leads to helical growth has not yet been studied.

Fig. 6: Helical pollen tubes observed in culture (A) A cell undergoing helical growth. (B) In the same cell, helices can show different amplitudes and wavelengths. (C) At high magnification, the shape of the cell is seen to be truly helical.

Fig. 7: Segmentation of cells into straight and helical segments

Fig. 8: Two classes of trajectories that can create an helical cell