Numerical simulation of cellular tip growth

Computational morphodynamics: a modeling framework to understand plant growth

Computational morphodynamics utilizes computer modeling to understand the development of living organisms over space and time. Results from biological experiments are used to construct accurate and predictive models of growth. These models are then used to make novel predictions that provide further insight into the processes involved, which can be tested experimentally to either confirm or rule out the validity of the computational models. This review highlights two fundamental challenges: (a) to understand the feedback between mechanics of growth and chemical or molecular signaling, and (b) to design models that span and integrate single cell behavior with tissue development. We review different approaches to model plant growth and discuss a variety of model types that can be implemented to demonstrate how the interplay between computational modeling and experimentation can be used to explore the morphodynamics of plant development.

Model for calcium dependent oscillatory growth in pollen tubes

Experiments have shown that pollen tubes grow in an oscillatory mode, the mechanism of which is poorly understood. We propose a theoretical growth model of pollen tubes exhibiting such oscillatory behaviour. The pollen tube and the surrounding medium are represented by two immiscible fluids separated by an interface. The physical variables are pressure, surface tension, density and viscosity, which depend on relevant biological quantities, namely calcium concentration and thickness of the cell wall. The essential features generally believed to control oscillating growth are included in the model, namely a turgor pressure, a viscous cell wall which yields under pressure, stretch-activated calcium channels which transport calcium ions into the cytoplasm and an exocytosis rate dependent on the cytosolic calcium concentration in the apex of the cell. We find that a calcium dependent vesicle recycling mechanism is necessary to obtain an oscillating growth rate in our model. We study the variation in the frequency of the growth rate by changing the extracellular calcium concentration and the density of ion channels in the membrane. We compare the predictions of our model with experimental data on the frequency of oscillation versus growth speed, calcium concentration and density of calcium channels.

Growth of walled cells: from shells to vesicles

The growth of isolated walled cells is investigated. Examples of such cells range from bacteria to giant algae, and include cochlear hair, plant root hair, fungi, and yeast cells. They are modeled as elastic shells containing a liquid. Cell growth is driven by fluid pressure and is is similar to a plastic deformation of the wall. The requirement of mechanical equilibrium leads to two new scaling laws for cell size that are in quantitative agreement with the compiled biological data. Given these results, possible shapes for growing cells are computed by analogy with those of vesicle membranes.

Quantitative analysis of concentration gradient and ionic currents associated with hyphal tip growth in fungi

It has been shown previously that the nutrient gradient generated by a tip growing elongated cell induces an ionic current entering the cell tip and looping back in the extracellular medium [L. Limozin, B. Denet and P. Pelcé, Phys. Rev. Lett. 78, 4881 (1997)]. We apply this mechanism to the case of hyphae of fungi, using realistic cell geometries, symport kinetics, proton pump permeabilities, and buffer concentrations. We show that this mechanism contributes to a noticeable part of the external current intensity, related inner electrical field and pH gradient, in agreement with experimental measurements. This provides a good example in biological cells of interaction between shape and field, a common property of growing nonliving systems, such as crystalline dendrites or electrodeposition.

Algal morphogenesis: modelling interspecific variation inMicrasteriaswith reaction–diffusion patterned catalysis of cell surface growth

Semi–cell morphogenesis in unicellular desmid algae of the genusMicrasteriasgenerates a stellar shape by repeated dichotomous branching of growing tips of the cell surface. The numerous species of the genus display variations of the branching pattern that differ markedly in number of branchings, lobe width and lobe length. We have modelled this morphogenesis, following previous work by D. M. Harrison and M. Kolár (1988), on the assumptions that patterning occurs by chemical reaction–diffusion activity within the plasma membrane, leading to morphological expression by patterned catalysis of the extension of the cell surface. The latter has been simulated in simplified form by two–dimensional computations. Our results indicate that for generation of repeated branchings and for the control of diverse species–specific shapes, the loss of patterning activity and of rapid growth in regions separating the active growing tips is an essential feature. We believe this conclusion to be much more general than the specific details of our model. We discuss the limitations of the model especially in terms of what extra features might be addressed in three–dimensional computation.

Predicted acetylcholine layer around embryonic motoneurones

The secretion of acetylcholine (ACh) from cultures of dissociated rat purified embryonic motoneurones into the medium was measured at different times using a chemiluminescent assay. From these results it is proposed that a motoneurone is able to generate an extracellular ACh layer surrounding its membrane. This layer is expected to modulate the ACh concentration at the membrane in a range where ACh receptors can be sensitive, and thus to affect the response of the motoneurone. The influences of both membrane-bound and soluble-secreted acetylcholinesterase (AChE) were simulated and a local ACh membrane efflux was deduced. Since ACh usually exerts an inhibitory effect on neurite outgrowth, a possible autocrine influence of the ACh layer in motoneurone morphogenesis is discussed.