Origin of cellular ionic currents

Competition of energy between active transport and vesicle fusion at the origin of intracellular gradient fields

It has been reported that the ionic patterns of hyphal growth can be explained by a weakening of the active transport at the tip at the expense of other biosynthesis processes, from which results energy transport from the proximal cells to the apical ones (Potapova et al. 1988). We present here a theory to support this hypothesis, whose extent is much more general than the initial frame where it has been formulated. It can be summarized in two basics mechanisms, one coupling active transport of the plasma membrane, electric potential and vesicle fusion, the other coupling the Ca²⁺-ATPase of the endoplasmic reticulum and vesicle fusion. For some values of parameters introduced in the theory, the uniform state of the cell becomes unstable, at the origin of intracellular gradient fields. Theoretical ionic patterns are spontaneously produced, which can be satisfactorily compared to several observed in and around tip-growing cells.

A computational model of dendrite elongation and branching based on MAP2 phosphorylation

We introduce a new computational model of dendritic development in neurons. In contrast to previous models, our model explicitly includes cellular mechanisms involved in dendritic development. It is based on recent experimental data which indicates that the phosphorylation state of microtubule-associated protein 2 (MAP2) may play a key role in controlling dendritic elongation and branching (Audesirk et al., 1997). Dephosphorylated MAP2 favours elongation by promoting microtubule polymerization and bundling, whilst branching is more likely to occur when MAP2 is phosphorylated and microtubules are spaced apart. In the model, the rate of elongation and branching is directly determined by the ratio of phosphorylated to dephosphorylated MAP2. This is regulated by calmodulin-dependent protein kinase II (CaMKII) and calcineurin, which are both dependent on the intracellular calcium concentration. Results from computer simulations of the model suggest that the wide variety of branching patterns observed among different cell types may be generated by the same underlying mechanisms and that elongation and branching are not necessarily independent processes. The model predicts how the branching pattern will change following manipulations with calcium, CaMKII and MAP2 phosphorylation.

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.

Diffusion-regulated control of cellular dendritic morphogenesis

Highly branched dendritic shapes are distinguishing characteristics of neurons and certain other cell types, but the physical mechanisms responsible for their formation are not well understood. Here, we model the growth of cells under the control of diffusible growth-regulating factors (morphogens such as calcium ion) whose local internal concentration results from influx and active extrusion across the cell membrane. Nonlinearities in voltage-dependent ionic permeabilities enhance unstable growth, so that branching dendritic outgrowths results from self-sustaining internal morphogen gradients. Simulations display complex patterns of branching growth, influenced by membrane conductance, galvanotropism and chemotropism. This self-organizing pattern formation is in agreement with the development of real neurons under corresponding conditions.