Search

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 a group of proteins that can adopt a spectrum of metastable conformations in vivo. These alternative states change protein function and are self-replicating and transmissible, creating protein-based elements of inheritance and infectivity. Prion conformational flexibility is encoded in the amino acid composition and sequence of the protein, which dictate its ability not only to form an ordered aggregate known as amyloid but also to maintain and transmit this structure in vivo. But, while we can effectively predict amyloid propensity in vitro, the mechanism by which sequence elements promote prion propagation in vivo remains unclear. In yeast, propagation of the [PSI+] prion, the amyloid form of the Sup35 protein, has been linked to an oligopeptide repeat region of the protein. Here, we demonstrate that this region is composed of separable functional elements, the repeats themselves and a repeat proximal region, which are both required for efficient prion propagation. Changes in the numbers of these elements do not alter the physical properties of Sup35 amyloid, but their presence promotes amyloid fragmentation, and therefore maintenance, by molecular chaperones. Rather than acting redundantly, our observations suggest that these sequence elements make complementary contributions to prion propagation, with the repeat proximal region promoting chaperone binding to and the repeats promoting chaperone processing of Sup35 amyloid., Competing Interests: The authors have declared that no competing interests exist.

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 self-assembly of alternative conformations of normal proteins into amyloid aggregates has been implicated in both the acquisition of new functions and in the appearance and progression of disease. However, while these amyloidogenic pathways are linked to the emergence of new phenotypes, numerous studies have uncoupled the accumulation of aggregates from their biological consequences, revealing currently underappreciated complexity in the determination of these traits. Here, to explore the molecular basis of protein-only phenotypes, we focused on the Saccharomyces cerevisiae Sup35/[PSI(+)] prion, which confers a translation termination defect and expression level-dependent toxicity in its amyloid form. Our studies reveal that aggregated Sup35 retains its normal function as a translation release factor. However, fluctuations in the composition and size of these complexes specifically alter the level of this aggregate-associated activity and thereby the severity and toxicity of the amyloid state. Thus, amyloid heterogeneity is a crucial contributor to protein-only phenotypes.

According to the prion hypothesis, atypical phenotypes arise when a prion protein adopts an alternative conformation and persist when that form assembles into self-replicating aggregates. Amyloid formation in vitro provides a model for this protein-misfolding pathway, but the mechanism by which this process interacts with the cellular environment to produce transmissible phenotypes is poorly understood. Using the yeast prion Sup35/[PSI(+)], we found that protein conformation determined the size distribution of aggregates through its interactions with a molecular chaperone. Shifts in this range created variations in aggregate abundance among cells because of a size threshold for transmission, and this heterogeneity, along with aggregate growth and fragmentation, induced age-dependent fluctuations in phenotype. Thus, prion conformations may specify phenotypes as population averages in a dynamic system.

According to the prion hypothesis, proteins may act in atypical roles as genetic elements of infectivity and inheritance by undergoing self-replicating changes in physical state. While the preponderance of evidence strongly supports this concept particularly in fungi, the detailed mechanisms by which distinct protein forms specify unique phenotypes are emerging concepts. A particularly active area of investigation is the molecular nature of the heritable species, which has been probed through genetic, biochemical, and cell biological experimentation as well as by mathematical modeling. Here, we suggest that these studies are converging to implicate small aggregates composed of prion-state conformers as the transmissible genetic determinants of protein-based phenotypes.

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.

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.

The use of yeast systems to study the propagation of prions and amyloids has emerged as a crucial aspect of the global endeavor to understand those mechanisms. Yeast prion systems are intrinsically multi-scale: the molecular chemical processes are indeed coupled to the cellular processes of cell growth and division to influence phenotypical traits, observable at the scale of colonies. We introduce a novel modeling framework to tackle this difficulty using impulsive differential equations. We apply this approach to the [PSI+] yeast prion, which is associated with the misconformation and aggregation of Sup35. We build a model that reproduces and unifies previously conflicting experimental observations on [PSI+] and thus sheds light onto characteristics of the intracellular molecular processes driving aggregate replication. In particular our model uncovers a kinetic barrier for aggregate replication at low densities, meaning the change between prion or prion-free phenotype is a bi-stable transition. This result is based on the study of prion curing experiments, as well as the phenomenon of colony sectoring, a phenotype which is often ignored in experimental assays and has never been modeled. Furthermore, our results provide further insight into the effect of guanidine hydrochloride (GdnHCl) on Sup35 aggregates. To qualitatively reproduce the GdnHCl curing experiment, aggregate replication must not be completely inhibited, which suggests the existence of a mechanism different than Hsp104-mediated fragmentation. Those results are promising for further development of the [PSI+] model, but also for extending the use of this novel framework to other yeast prion or amyloid systems. Author summary: In the study of yeast prions, mathematical modeling is a powerful tool, in particular when it comes to facing the difficulties of multi-scale systems. In this study, we introduce a mathematical framework for investigating this problem in a unifying way. We focus on the yeast prion [PSI+] and present a simple molecular scheme for prion replication and a model of yeast budding. In order to qualitatively reproduce experiments, we need to introduce a non-linear mechanism in the molecular rates. This transforms the intracellular system into a bi-stable switch and allows for curing to occur, which is a crucial phenomenon for the study of yeast prions. To the best of our knowledge, no model in the literature includes such a mechanism, at least not explicitly. We also describe the GdnHCl curing experiment, and the propagon counting procedure. Reproducing this result requires challenging hypotheses that are commonly accepted, and our interpretation gives a new perspective on the concept of propagon. This study may be considered as a good example of how mathematical modeling can bring valuable insight into biological concepts and observations. [ABSTRACT FROM AUTHOR]

The nucleated polymerization model is a mathematical framework that has been applied to aggregation and fragmentation processes in both the discrete and continuous settings. In particular, this model has been the canonical framework for analyzing the dynamics of protein aggregates arising in prion and amyloid diseases such 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. [ABSTRACT FROM AUTHOR]