Mathematical modelling of fungal growth and function

Phase-field modeling of constrained interactive fungal networks

Fungi develop structures that interact with their surroundings and evolve adaptively in the presence of geometrical constraints, finding optimal solutions for complex combinatorial problems. The pathogenic fungus Ophiocordyceps constitutes a perfect model for the study of constrained interactive networks. Modeling these networks is challenging due to the highly coupled physics involved and their interaction with moving boundaries. In this work, we develop a computational phase-field model to elucidate the mechanics of the emerging properties observed in fungal networks. We use a variational approach to derive the equations governing the evolution in time of the mycelium biomass and the nutrients in the medium. We present an extensive testing of our model, reproduce growing and decaying phenomena, and capture spatial and temporal scales. We explore the variables interplay mechanism that leads to different colony morphologies, and explain abrupt changes of patterns observed in the laboratory. We apply our model to simulate analogous processes to the evolution of Ophiocordyceps as it grows through confined geometry and depletes available resources, demonstrating the suitability of the formulation to study this class of biological networks.

The Mycelium as a Network

The characteristic growth pattern of fungal mycelia as an interconnected network has a major impact on how cellular events operating on a micron scale affect colony behavior at an ecological scale. Network structure is intimately linked to flows of resources across the network that in turn modify the network architecture itself. This complex interplay shapes the incredibly plastic behavior of fungi and allows them to cope with patchy, ephemeral resources, competition, damage, and predation in a manner completely different from multicellular plants or animals. Here, we try to link network structure with impact on resource movement at different scales of organization to understand the benefits and challenges of organisms that grow as connected networks. This inevitably involves an interdisciplinary approach whereby mathematical modeling helps to provide a bridge between information gleaned by traditional cell and molecular techniques or biophysical approaches at a hyphal level, with observations of colony dynamics and behavior at an ecological level.

Spatial organization of organelles in fungi: Insights from mathematical modelling

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Modelling of dynein motility reveals a stochastic role in dynein comet formation.

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Modelling helps to elucidate mechanisms in spatial organization of early endosomes.

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A combination of diffusion and directed motion distributes ribosomes and peroxisomes.

Mathematical modelling in cellular systems aims to describe biological processes in a quantitative manner. Most accurate modelling is based on robust experimental data. Here we review recent progress in the theoretical description of motor behaviour, early endosome motility, ribosome distribution and peroxisome transport in the fungal model system Ustilago maydis and illustrate the power of modelling in our quest to understand molecular details and cellular roles of membrane trafficking in filamentous fungi.

A framework for an organelle-based mathematical modeling of hyphae

Background

Although highly desirable, a mechanistic explanation for the outstanding protein secretion capabilities of fungi such as Aspergilli is missing. As a result, a rational and predictive design of strains as cell factories for protein production is still out of reach. The analysis of the secretion apparatus is not only hampered by open issues concerning molecular cell biological processes, but as well by their spatial fragmentation and highly dynamic features. Whereas the former issues are addressed by many groups, an account of the space- and time-dependent processes, which is best done by means of mathematical models, is lacking. Up to now, mathematical models for hyphal organisms mainly focus on one of two extremes. Either macroscopic morphology, such as pellet or mycelium growth, is addressed, or a microscopic picture is drawn predicting, for instance, the form of a hyphal tip. How intra-hyphal transport and organelle distribution works, however, has not been tackled so far mathematically.

Results

The main result of this contribution is a generic modeling framework to describe the space- and time-dependent evolution of intracellular substances and organelles. It takes intrahyphal, passive and active transport of substances into account and explains exponential and then linear length growth by tugor-driven uptake of water. Experimentally observed increasing concentration levels of organelles towards the tip can be well explained within the framework without resorting to complex biological regulations. It is shown that the accumulation can be partly explained by geometrical constraints, besides a necessary deceleration of the active transport velocity. The model is formulated such that more intricate intracellular processes can be included.

Conclusions

Results from steady-state experiments are easy to be interpreted. In a hyphal network, however, new branches are produced at an exponential rate. Moreover, passive and active transport processes give rise to a spatial distribution of organelles and other cytoplasmatic constituents inside hyphae. As a result, most of the data obtained in experiments will be from a non-steady and space dependent state. A quantitative and mechanistic explanation of the processes occurring will only be possible if these dependencies are taking into account while evaluating experimental findings.

The Cell Factory Aspergillus Enters the Big Data Era: Opportunities and Challenges for Optimising Product Formation

Living with limits. Getting more from less. Producing commodities and high-value products from renewable resources including waste. What is the driving force and quintessence of bioeconomy outlines the lifestyle and product portfolio of Aspergillus, a saprophytic genus, to which some of the top-performing microbial cell factories belong: Aspergillus niger, Aspergillus oryzae and Aspergillus terreus. What makes them so interesting for exploitation in biotechnology and how can they help us to address key challenges of the twenty-first century? How can these strains become trimmed for better growth on second-generation feedstocks and how can we enlarge their product portfolio by genetic and metabolic engineering to get more from less? On the other hand, what makes it so challenging to deduce biological meaning from the wealth of Aspergillus -omics data? And which hurdles hinder us to model and engineer industrial strains for higher productivity and better rheological performance under industrial cultivation conditions? In this review, we will address these issues by highlighting most recent findings from the Aspergillus research with a focus on fungal growth, physiology, morphology and product formation. Indeed, the last years brought us many surprising insights into model and industrial strains. They clearly told us that similar is not the same: there are different ways to make a hypha, there are more protein secretion routes than anticipated and there are different molecular and physical mechanisms which control polar growth and the development of hyphal networks. We will discuss new conceptual frameworks derived from these insights and the future scientific advances necessary to create value from Aspergillus Big Data.

Structural and functional organization of growing tips of Neurospora crassa Hyphae

Data are presented on a variety of intracellular structures of the vegetative hyphae of the filamentous fungus Neurospora crassa and the involvement of these structures in the tip growth of the hyphae. Current ideas on the molecular and genetic mechanisms of tip growth and regulation of this process are considered. On the basis of comparison of data on behaviors of mitochondria and microtubules and data on the electrical heterogeneity of the hyphal apex, a hypothesis is proposed about a possible supervisory role of the longitudinal electric field in the structural and functional organization of growing tips of the N. crassa hyphae.