Actinobacteria and filamentous fungi are just two examples of organisms that use cell elongation for growth. Mathematical models have been used to describe species-specific and more generic polarized growth. In this article in Microbiology Today (pdf) Fordyce Davidson suggests that multi-scale modelling could be the most effective approach to help us understand this morphological phenomenon:
Growth by cell elongation is a morphological process that transcends taxonomic kingdoms. Examples include hyphal tip growth in actinobacteria and filamentous fungi, plant root-hair formation and the development of neurons in animals. Such structures have developed almost certainly because they afford an evolutionary advantage – producing a growth habit well-suited to physically complex environments, facilitating the (internal) redeployment of nutrients or enabling the transfer of information over long spatial scales. The biology involved in producing this polarized growth form is clearly very different in plant, bacterial, fungal or mammalian cells. But its ubiquitous nature suggests that certain ‘”rules” are being followed. Moreover, if we compare fungi and actinobacteria, the foci of this article, it is clear that these rules are scalable: tip growth is similar, irrespective of the orders of magnitude difference in cell size. It appears that these rules form a blueprint for polarized growth.