Team:Waterloo/Aggregation
Aggregation Model
-Usefulness of the Model -Lab Collaboration - timescale to check up on the yeast (psi+ state ones) --> 48 hours - results of lab to confirming results produced by model - usage of lab results to help make a better model?
The life cycle of an prion protein can be summarized down into 4 stages: synthesis, conversion, fragmentation, and transmission (Sindi and Olofsson, 2013).
Synthesis is when healthy Sup35 is created by the the yeast cell. It is then possible for it to be converted into the prion state either through spontaneous changes (Lancaster et al., 2009) or recruited to a growing aggregate, and then converted to the prion state as a part of the aggregate (Collins et al., 2004).
The aggregate later fragments into smaller aggregates (Sindi and Olofsson, 2013), and is eventually transmitted through cell division into the daughter cell (Liebman and Chernoff, 2012).
This is shown in the figure below, where the squares are the [PSI+] Sup35 and the triangles are healthy Sup35.
Aggregate fragmentation is crucial to spreading the aggregates throughout the population, due to aggregates larger than 20 monomers being unable to be transmitted to daughter cell and thus propagated (Sindi and Olofsson, 2013). Fragmentation can be induced by several factors, such as the chaperone molecule, Hsp104 (Shorter and Lindquist, 2008).
It has been found that the concentration of Hsp104 induces three different responses in the [PSI+] of the yeast population. Higher concentrations of Hsp 104 will "cure" the [PSI+] state and revert the Sup35 to its [psi-] soluble form (Shorter and Lindquist, 2004) due to a large increase in fragmentation induced by the Hsp104 (Romanova and Chernoff, 2009).
Under-expression of Hsp104 will also decrease of the portion of the yeast population infected with prions, due to a lack of fragmentation, thus forming aggregates too large to pass to a daughter cell, allowing the aggregates to remain in the mother until cell death (Shorter and Lindquist, 2008).
However, a more medial concentration will propagate the production of [PSI+] Sup35 through fragmentation of aggregates, producing smaller aggregates able to be inherited by the daughter cell.
These three responses are shown in the figure below, where the yellow pentagons represent the Hsp104 hexamers.
Algorithm
The agent-based model was written in Python with Cell objects each containing a list of amyloids with associated sizes, and a number of healthy Sup35 molecules.
When the cell buds every 1.5 hours (Brewer et al., 1984), the aggregates under the 20 monomer size threshold (Sindi and Olofsson, 2013) are passed to the mother cell with a binomial distribution with a probability of 0.4 (Olofsson and Sindi, 2014), as well as a number of healthy Sup35.
Between budding times, a Gillespie algorithm with 6 different "reactions" simulates the different Hsp104, Sup35 and aggregate interactions in the cell, and are as follows in the table below. The spontaneous appearance of [PSI+] cells was considered to be included in the model, but due to its low probability of occurrence (in the order of 10-7 (Lancaster et al., 2009)) in relation to the sample size of the model, it was excluded in favour of a faster simulation.
The propensities associated with the Gillespie's algorithm are based on rates found in literature and adjusted with different factors, such as healthy Sup35 levels, number of amyloids present in the system, as well as the total number of bonds connecting aggregate monomers.
Modelling Curing of [PSI+] State
The initial state of the cell population was that of 100% of the cells in the [PSI+]. Through adjustments of different curing rates of Hsp104, where a monomer was broken off during a single reaction, the effects of Hsp104 concentration on [PSI+] cells populations could be effectively simulated and in agreement with results found in literature. (CITATION)
Image of propagation of Sup35
Image of overexpression curing curve
Image of underexpression curing curve
The curing curves produced during the simulated under-expression of Hsp104 confirms the effectiveness of this method in curing the prion states of a cell population. In the future, tools to induce this Hsp104 under-expression, such as using CRISPR, could possibly be utilized to help cure prion-based diseases.
[1] Sindi, S. S., & Olofsson, P. (2013). A Discrete-Time Branching Process Model of Yeast Prion Curing Curves*. Mathematical Population Studies, 20(1), 1–13. doi:10.1080/08898480.2013.748566
[2] Lancaster, A. K., Bardill, J. P., True, H. L., & Masel, J. (2010). The spontaneous appearance rate of the yeast prion [PSI+] and its implications for the evolution of the evolvability properties of the [PSI+] system. Genetics, 184(2), 393–400. doi:10.1534/genetics.109.110213
[3] Collins, S. R., Douglass, A., Vale, R. D., & Weissman, J. S. (2004). Mechanism of prion propagation: amyloid growth occurs by monomer addition. PLoS Biology, 2(10), e321. doi:10.1371/journal.pbio.0020321
[4] Liebman, S. W., & Chernoff, Y. O. (2012). Prions in yeast. Genetics, 191(4), 1041–72. doi:10.1534/genetics.111.137760
[5] Shorter, J., & Lindquist, S. (2008). Hsp104, Hsp70 and Hsp40 interplay regulates formation, growth and elimination of Sup35 prions. The EMBO Journal, 27(20), 2712–24. doi:10.1038/emboj.2008.194
[6] Shorter, J., & Lindquist, S. (2004). Hsp104 catalyzes formation and elimination of self-replicating Sup35 prion conformers. Science (New York, N.Y.), 304(5678), 1793–7. doi:10.1126/science.1098007
[7] Romanova, N. V, & Chernoff, Y. O. (2009). Hsp104 and prion propagation. Protein and Peptide Letters, 16(6), 598–605. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/19519517
[8] Brewer, B. J., Chlebowicz-Sledziewska, E., & Fangman, W. L. (1984). Cell cycle phases in the unequal mother/daughter cell cycles of Saccharomyces cerevisiae. Molecular and Cellular Biology, 4(11), 2529–31. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/6392855
[9] Olofsson, P., & Sindi, S. S. (2014). A Crump-Mode-Jagers branching process model of prion loss in yeast. Journal of Applied Probability, 51(2), 453–465. doi:10.1239/jap/1402578636
[10] Olofsson, P., & Sindi, S. S. (2014). A Crump-Mode-Jagers branching process model of prion loss in yeast. Journal of Applied Probability, 51(2), 453–465. doi:10.1239/jap/1402578636
