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Modelling: Big Data and Society Conference
A new PhD student publication
CoMPLEX Fellowship Report - Zena Hadjivasiliou
Professor Yoh Iwasa’s Mathematical Biology Laboratory, Department of Biology, Kyushu University, Fukuoka. (See pictures!)
My PhD focuses on the evolution of two distinct sexes in most sexual organisms. Most theoretical attempts to understand the evolution of the sexes are based on arguments relevant to uniparental mitochondrial inheritance. My previous research results however incorporated a new modeling approach which suggested that binary mating systems are unlikely to evolve as a response to the need to uniparental inheritance of mitochondria. The natural next step would be to explore other possible explanations for the prominent existence of binary mating systems. Professor Yoh Iwasa is amongst the leading mathematical biologists and mathematical ecologists in Japan and worldwide and is one of the very few scientists to have studied alternative explanations for the evolution of two sexes not involving mitochondrial inheritance. The purpose of our collaboration was to explore the possibility that two sexes is the most efficient configuration for successful gamete attraction and fusion in sexual populations. In particular, we investigated this hypothesis in a system where pheromone release and detection acts as instigation for gamete fusion (these systems are present in a variety of organism such as Green Algae). Professor Iwasa has previously worked on a diversity of mathematical biology problems ranging from pattern formation in development and morphogenesis, to pathogen interaction and evolutionary dynamics. It is thus not surprising that our collaboration was incredibly rewarding both in terms of the progress of my project itself but also my academic development as a whole.
The persistence of binary mating systems in sexual organisms constitutes a well-known conundrum in evolutionary biology. In the majority of sexual organisms two different types of sex cells (gametes) are necessary for reproduction. Even in organisms with more than one “sex” or mating type, such as slime molds, only gametes of different type can fuse to form a zygote. In fact, no sexual organism without some form of sexual asymmetry is known suggesting that mating types or sexes are fundamental to sex. Why this is the case is unclear. Dividing the population in specialized mating types or sexes at first glance appears to give rise to a mating system less efficient than one where any cell could mate with any other. This is due to the difficulty of finding a mate in a population where 50% of the gametes become incompatible with each other. Given this apparent disadvantage and the prominent persistence of sexes we expect the role of this asymmetry to be paramount.
Although different organisms have evolved various means of sexual reproduction, there is a common underlying process where specialized sexual cells (the gametes) need to recognize each other and fuse. For this process to successfully take place, two gametes of the same species need to recognize each other, somehow approach each other and effectively fuse. Living organisms have the incredible capacity to both create and respond to cues in their environment. This is typically manifested via the generation and detection of chemical gradients. Various experimental reports support the idea that gametes of different sex or mating type are attracted to each other via the release of and response to pheromones. What is more, the majority of these reports indicate that gametes of different type or sex take up different roles in this communication. In particular, gametes of one type generally are responsible of producing a particular pheromone whereas gametes of the opposite type tend to recognize and be attracted to this pheromone.
In this project we studied the role of this asymmetric role the gametes assume. We developed a mathematical model to explore the hypothesis that by being restricted to either secreting or releasing a pheromone gametes achieve a more efficient mechanism of attraction whereby the speed at which they approach each other is optimized. The underlying hypothesis is that when a moving cell secretes a pheromone it generates a local asymmetry in chemical concentration presumably interfering with its ability to find other gametes.
We developed a simple one-dimensional model of chemical diffusion in one dimension described by the equation:
This is the inhomogeneous diffusion equation in one dimension where C(x,
t) is the chemical concentration at point x and time t, D is the
diffusion coefficient, u is the decomposition rate, s is the rate of
chemical production at the cell’s position and δ(.) is the Dirac delta
function signifying the release of a chemical at rate s at the current
position of the cell, xcell. Using this equation we obtained the
concentration around a moving cell which is shown graphically on Fig.1.
We found that the cell’s motion creates an asymmetry in the chemical
concentration around it. The higher the speed of the cell, the stronger
the asymmetry (Fig.1).
Fig. 1 - Travelling wave solutions for D=0.05; u=0.02 and s=0.03. (1): Wave speed v=0.03; (2): Wave speed v=0.06.
We then considered the chemotactic movement of the cell. We assume (based on known mechanisms for cellular gradient sensing) that the speed of the cell is determined by equation (2)
Where gamma and alpha are parameters determining the strength of the chemoattractant force and R is the cell’s radius.
Using this and the solution of Equation (1) we were able to determine the speed at which a cell would in theory approach a source releasing a chemoattractant when the cell itself does and does not release the same chemoattractant. We found a significant decrease in the cell’s speed when it did release the chemoattractant (Fig.2).
Fig. 2 Speed at which cell approaches target source when it releases (blue) and when it does not release (back) the chemoattractant for different values of gamma and alpha.
Fig.3 Trajectory of cell in one dimension from its initial position to the target source’s position when it releases (black) and when it does not release (red) the chemoattractant. The left plot is for alpha=5 and the right one for alpha=1.
These results were all in one dimension but a two dimensional model was developed with some preliminary results agreeing with the one-dimensional case.
The next step would be to consider multiple moving cells in two and three dimensions and ask how an asymmetric role in secreting and being attracted to a chemoattractant would affect the ability of gametes to find each other. This is currently under development. Although this work is far from completed my collaboration in Japan formed a great foundation for further development of the ideas laid out here and lead to some exciting and encouraging first results.
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