Oscillations in a neurite growth model with extracellular feedback

•A new model of neurite outgrowth accounting extracellular signalling is proposed.•The model predicts three different scenarios of the neurite development.•It has been demonstrated that the elongation dynamics is angle-specific. We consider the influence of extracellular signalling on neurite elongation in a model of neurite growth mediated by building proteins (e.g., tubulin). The tubulin production dynamics were supplied by a function describing the influence of extracellular signalling, which can promote or depress neurite elongation. We found that this extracellular feedback could generate neurite length oscillations consisting of a periodic sequence of elongations and retractions. The oscillations prevent further outgrowth of the neurite, which becomes trapped in the non-uniform extracellular field. We analysed the characteristics of the elongation process for different distributions of attracting and repelling sources of the extracellular signalling molecules. The model predicts three different scenarios of neurite development in the extracellular field, including monotonic and oscillatory outgrowth, localised limit cycle oscillations and complete growth depression.