Introduction
In my master’s and PhD project, I explore the world of mathematical biology. More specifically, I aim to better understand the growth patterns and behaviour of yeast colonies commonly used for making bread and alcoholic beverages. I find this interdisciplinary collaboration extremely rewarding because it empowers me to make contributions to benefit winemakers, bioengineers, material scientists etc.
My work is done under the wonderful supervision of A/Prof Benjamin Binder and Dr Edward Green, where we are developing new mathematical models to predict the spatial patterns in yeast colonies. We employ both continuous partial differential equations and discrete agent-based approaches to better understand different types of yeast growths from experimental results. Very exciting! Note this blog is just a short summary of my master’s project, hence I have left out many details.
Why Study Yeast?
There are several important reasons to understand the growth modes of yeast which is why yeast are among one of the most widely studied organisms in biology. For instance, the yeast strain was the first eukaryote to have its genome fully sequenced. With over 1,500 recognized strains, yeast are considered a key model organism for understanding the molecular mechanisms underlying the basic functions of other eukaryotic cells (e.g. plant and animal). This makes yeast an important biological model in many experimental studies. Additionally, yeast are crucial in the production of baked goods, beer, and wine through fermentation. However, some yeast strains can also cause pathogenic infections in humans. Therefore, expanding our understanding of yeast growth can have far-reaching benefits, from disease research to the food and biotechnology industries.
Part I: Modelling Unixial Growth (1D Model)
The figure below was produced by (Vulin et al. 2014) where yeast colonies was restricted to grow in the uniaxial direction with no lateral expansion. The scientist made an interesting observation where the colony grew linearly with time. This is interesting because things in nature tend to exhibit exponential growth.
Therefore, the first part of my project focused on modelling cylindrical yeast colonies with the aim to understand how this growth mode occurs. We employed a continuous partial differential equation (PDE) approach to model this scenario by coupling nutrient transport and cellular proliferation. More specifically, we utilize reaction-diffusion theory and derive a system of reaction-advection-diffusion equations. We then solve this system using the method of lines. This part of the project has now being completed and a manuscript have been submitted and is currently under review.
Part II: Spatial Quantification of Filamentous and Invasive Growth
The second part of my project aims to quantify the top-view, two-dimensional spatial patterning of non-uniform growth in Saccharomyces cerevisiae yeast colonies. Examples of such as colonies is shown below (Gontar et al. 2018).
The biologist that my supervisors collaborate closely with have provided us with a bank of these experimental images for different strains under varying nutrient conditions (see above). Hence, one component of the second part of my project is to find robust methods that can quantify the different strains under varies nutrient environment. In addition, it was observed in experiments that these yeast colonies can borrow into the Agar plate known as invasive growth. Hence, we also would like to quantify such behavior with the goal to extract useful information from our mathematical metrics. Previously, there have being metrics proposed (Binder et al. 2015), however, they are not great at distinguishing between different strains of yeast. Hence, the need for new robust metrics. This work is currently still in progress.
Part III: Modelling Filamentous Growth (2D Model)
Finally, the final part of my project involves modelling the filamentous yeast colony as shown above with a discrete agent based model. Previously, (Tronnolone et al. 2017) proposed a lattice-based model. However, there are limitations to the model as it struggles to capture the finer filamentous structure seen in the experimental images. Hence, we wish to develop a new off-lattice model that can capture the colony morphology and coupling it with nutrient transport. Once we fully developed the model, we then wish to use Approximate Bayesian Computation (ABC) to estimate parameters of our model.
Thank you for reading this far. I hope you found (or at least bits) my master’s project interesting. As a reward here is a cool (I think anyways) gif I made.
