Search

In response to the COVID-19 pandemic, many higher educational institutions moved their courses on-line in hopes of slowing disease spread. The advent of multiple highly-effective vaccines offers the promise of a return to "normal" in-person operations, but it is not clear if-or for how long-campuses should employ non-pharmaceutical interventions such as requiring masks or capping the size of in-person courses. In this study, we develop and fine-tune a model of COVID-19 spread to UC Merced's student and faculty population. We perform a global sensitivity analysis to consider how both pharmaceutical and non-pharmaceutical interventions impact disease spread. Our work reveals that vaccines alone may not be sufficient to eradicate disease dynamics and that significant contact with an infectious surrounding community will maintain infections on-campus. Our work provides a foundation for higher-education planning allowing campuses to balance the benefits of in-person instruction with the ability to quarantine/isolate infectious individuals.

Amyloid appearance is a rare event that is promoted in the presence of other aggregated proteins. These aggregates were thought to act by templating the formation of an assembly-competent nucleation seed, but we find an unanticipated role for them in enhancing the persistence of amyloid after it arises. Specifically, Saccharomyces cerevisiae Rnq1 amyloid reduces chaperone-mediated disassembly of Sup35 amyloid, promoting its persistence in yeast. Mathematical modeling and corresponding in vivo experiments link amyloid persistence to the conformationally defined size of the Sup35 nucleation seed and suggest that amyloid is actively cleared by disassembly below this threshold to suppress appearance of the [PSI+] prion in vivo. Remarkably, this framework resolves multiple known inconsistencies in the appearance and curing of yeast prions. Thus, our observations establish the size of the nucleation seed as a previously unappreciated characteristic of prion variants that is key to understanding transitions between prion states.

Prions are proteins capable of adopting misfolded conformations and transmitting these conformations to other normally folded proteins. Prions are most commonly known for causing fatal neurodegenerative diseases in mammals but are also associated with several harmless phenotypes in yeast. A distinct feature of prion propagation is the existence of different phenotypical variants, called strains. It is widely accepted that these strains correspond to different conformational states of the protein, but the mechanisms driving their interactions remain poorly understood. This study uses mathematical modeling to provide insight into this problem. We show that the classical model of prion dynamics allows at most one conformational strain to stably propagate. In order to conform to biological observations of strain coexistence and co-stability, we develop an extension of the classical model by introducing a novel prion species consistent with biological studies. Qualitative analysis of this model reveals a new variety of behavior. Indeed, it allows for stable coexistence of different strains in a wide parameter range, and it also introduces intricate initial condition dependency. These new behaviors are consistent with experimental observations of prions in both mammals and yeast. As such, our model provides a valuable tool for investigating the underlying mechanisms of prion propagation and the link between prion strains and strain specific phenotypes. The consideration of a novel prion species brings a change in perspective on prion biology and we use our model to generate hypotheses about prion infectivity.

Prions adopt alternative, self-replicating protein conformations and thereby determine novel phenotypes that are often irreversible. Nevertheless, dominant-negative prion mutants can revert phenotypes associated with some conformations. These observations suggest that, while intervention is possible, distinct inhibitors must be developed to overcome the conformational plasticity of prions. To understand the basis of this specificity, we determined the impact of the G58D mutant of the Sup35 prion on three of its conformational variants, which form amyloids in S. cerevisiae. G58D had been previously proposed to have unique effects on these variants, but our studies suggest a common mechanism. All variants, including those reported to be resistant, are inhibited by G58D but at distinct doses. G58D lowers the kinetic stability of the associated amyloid, enhancing its fragmentation by molecular chaperones, promoting Sup35 resolubilization, and leading to amyloid clearance particularly in daughter cells. Reducing the availability or activity of the chaperone Hsp104, even transiently, reverses curing. Thus, the specificity of inhibition is determined by the sensitivity of variants to the mutant dosage rather than mode of action, challenging the view that a unique inhibitor must be developed to combat each variant.

Prions are proteins most commonly associated with fatal neurodegenerative diseases in mammals but are also responsible for a number of harmless heritable phenotypes in yeast. These states arise when a misfolded form of a protein appears and, rather than be removed by cellular quality control mechanisms, persists. The misfolded prion protein forms aggregates and is capable of converting normally folded protein to the misfolded state through direct interaction between the two forms. The dominant mathematical model for prion aggregate dynamics has been the nucleated polymerization model (NPM) which considers the dynamics of only the normal protein and the aggregates. However, for yeast prions the molecular chaperone Hsp104 is essential for prion propagation. Further, although mammals do not express Hsp104, experimental assays have shown Hsp104 also interacts with mammalian prion aggregates. In this study, we generalize the NPM to account for molecular chaperones and develop what we call the enzyme-limited nucleated polymerization model (ELNPM). We discuss existence, uniqueness and stability of solutions to our model and demonstrate that the NPM represents a quasi-steady-state reduction of our model. We validate the ELNPM by demonstrating agreement with experimental results on the yeast prion PSI(+) that could not be supported by the NPM. Finally, we demonstrate that, in contrast to the NPM, the ELNPM permits the coexistence of multiple prion strains.

The nucleated polymerization model is a mathematical framework that has been applied to aggregation and fragmentation processes in both the discrete and continuous setting. In particular, this model has been the canonical framework for analyzing the dynamics of protein aggregates arising in prion and amyloid diseases such as as Alzheimer's and Parkinson's disease. We present an explicit steady-state solution to the aggregate size distribution governed by the discrete nucleated polymerization equations. Steady-state solutions have been previously obtained under the assumption of continuous aggregate sizes; however, the discrete solution allows for direct computation and parameter inference, as well as facilitates estimates on the accuracy of the continuous approximation.