Applying dimorphic yeasts as model organisms to study mycelial growth: Part 1. Experimental investigation of the spatio-temporal development of filamentous yeast colonies

Ramified Challenges: Monitoring and Modeling of Hairy Root Growth in Bioprocesses--A Review

The review presents a comprehensive overview on available solutions for the monitoring and modeling of various aspects of hairy root growth processes. Several online and offline measurement principles get explained exemplary and are being compared. It was found that no direct online measurement principle for hairy root biomass in submerged and solid-state culturing environment is available. However, certain indirect methods involving one or more measurement values have been developed for biomonitoring of hairy roots especially in bioreactors. In the field of modeling of hairy root growth processes, four independent architectures (continuous models, metabolic flux analysis, agent-based models, and artificial neural networks) are described and compared including literature references. The discussion is structured into microscopic model approaches, addressing only certain aspects of growth, and macroscopic model approaches, describing the hairy root network as a whole. An agent-based macroscopic model based on phenomenological data acquired with systematic imaging of hairy roots on culture dishes together with a 3D visualization of simulation results is presented in detail.

A simple mathematical model that describes the growth of the area and the number of total and viable cells in yeast colonies

We propose a model, based on the Gompertz equation, to describe the growth of yeasts colonies on agar medium. This model presents several advantages: (i) one equation describes the colony growth, which previously needed two separate ones (linear increase of radius and of the squared radius); (ii) a similar equation can be applied to total and viable cells, colony area or colony radius, because the number of total cells in mature colonies is proportional to their area; and (iii) its parameters estimate the cell yield, the cell concentration that triggers growth limitation and the effect of this limitation on the specific growth rate. To elaborate the model, area, total and viable cells of 600 colonies of Saccharomyces cerevisiae, Debaryomyces fabryi, Zygosaccharomyces rouxii and Rhodotorula glutinis have been measured. With low inocula, viable cells showed an initial short exponential phase when colonies were not visible. This phase was shortened with higher inocula. In visible or mature colonies, cell growth displayed Gompertz-type kinetics. It was concluded that the cells growth in colonies is similar to liquid cultures only during the first hours, the rest of the time they grow, with near-zero specific growth rates, at least for 3 weeks.

SIGNIFICANCE AND IMPACT OF THE STUDY

Mathematical models used to predict microbial growth are based on liquid cultures data. Models describing growth on solid surfaces, highlighting the differences with liquids cultures, are scarce. In this work, we have demonstrated that a single Gompertz equation describes accurately the increase of the yeast colonies, up to the point where they reach their maximum size. The model can be used to quantify the differences in growth kinetics between solid and liquid media. Moreover, as all its parameters have biological meaning, it could be used to build secondary models predicting yeast growth on solid surfaces under several environmental conditions.

Modeling hairy root tissue growth in in vitro environments using an agent-based, structured growth model

An agent-based model for simulating the in vitro growth of Beta vulgaris hairy root cultures is described. The model fitting is based on experimental results and can be used as a virtual experimentator for root networks. It is implemented in the JAVA language and is designed to be easily modified to describe the growth of diverse biological root networks. The basic principles of the model are outlined, with descriptions of all of the relevant algorithms using the ODD protocol, and a case study is presented in which it is used to simulate the development of hairy root cultures of beetroot (Beta vulgaris) in a Petri dish. The model can predict various properties of the developing network, including the total root length, branching point distribution, segment distribution and secondary metabolite accumulation. It thus provides valuable information that can be used when optimizing cultivation parameters (e.g., medium composition) and the cultivation environment (e.g., the cultivation temperature) as well as how constructional parameters change the morphology of the root network. An image recognition solution was used to acquire experimental data that were used when fitting the model and to evaluate the agreement between the simulated results and practical experiments. Overall, the case study simulation closely reproduced experimental results for the cultures grown under equivalent conditions to those assumed in the simulation. A 3D-visualization solution was created to display the simulated results relating to the state of the root network and its environment (e.g., oxygen and nutrient levels).