Generalizing a mathematical model of prion aggregation allows strain coexistence and co-stability by including a novel misfolded species

Measuring prion propagation in single bacteria elucidates a mechanism of loss

Prions are self-propagating protein aggregates formed by specific proteins that can adopt alternative folds. Prions were discovered as the cause of the fatal transmissible spongiform encephalopathies in mammals, but prions can also constitute nontoxic protein-based elements of inheritance in fungi and other species. Prion propagation has recently been shown to occur in bacteria for more than a hundred cell divisions, yet a fraction of cells in these lineages lost the prion through an unknown mechanism. Here, we investigate prion propagation in single bacterial cells as they divide using microfluidics and fluorescence microscopy. We show that the propagation occurs in two distinct modes. In a fraction of the population, cells had multiple small visible aggregates and lost the prion through random partitioning of aggregates to one of the two daughter cells at division. In the other subpopulation, cells had a stable large aggregate localized to the pole; upon division the mother cell retained this polar aggregate and a daughter cell was generated that contained small aggregates. Extending our findings to prion domains from two orthologous proteins, we observe similar propagation and loss properties. Our findings also provide support for the suggestion that bacterial prions can form more than one self-propagating state. We implement a stochastic version of the molecular model of prion propagation from yeast and mammals that recapitulates all the observed single-cell properties. This model highlights challenges for prion propagation that are unique to prokaryotes and illustrates the conservation of fundamental characteristics of prion propagation.

Eco-evolutionary trade-offs in the dynamics of prion strain competition

Prion and prion-like molecules are a type of self-replicating aggregate protein that have been implicated in a variety of neurodegenerative diseases. Over recent decades, the molecular dynamics of prions have been characterized both empirically and through mathematical models, providing insights into the epidemiology of prion diseases and the impact of prions on the evolution of cellular processes. At the same time, a variety of evidence indicates that prions are themselves capable of a form of evolution, in which changes to their structure that impact their rate of growth or fragmentation are replicated, making such changes subject to natural selection. Here we study the role of such selection in shaping the characteristics of prions under the nucleated polymerization model (NPM). We show that fragmentation rates evolve to an evolutionary stable value which balances rapid reproduction of PrPSc aggregates with the need to produce stable polymers. We further show that this evolved fragmentation rate differs in general from the rate that optimizes transmission between cells. We find that under the NPM, prions that are both evolutionary stable and optimized for transmission have a characteristic length of three times the critical length below which they become unstable. Finally, we study the dynamics of inter-cellular competition between strains, and show that the eco-evolutionary trade-off between intra- and inter-cellular competition favours coexistence.

Measuring prion propagation in single bacteria elucidates mechanism of loss

Prions are self-propagating protein aggregates formed by specific proteins that can adopt alternative folds. Prions were discovered as the cause of the fatal transmissible spongiform encephalopathies in mammals, but prions can also constitute non-toxic protein-based elements of inheritance in fungi and other species. Prion propagation has recently been shown to occur in bacteria for more than a hundred cell divisions, yet a fraction of cells in these lineages lost the prion through an unknown mechanism. Here, we investigate prion propagation in single bacterial cells as they divide using microfluidics and fluorescence microscopy. We show that the propagation occurs in two distinct modes with distinct stability and inheritance characteristics. We find that the prion is lost through random partitioning of aggregates to one of the two daughter cells at division. Extending our findings to prion domains from two orthologous proteins, we observe similar propagation and loss properties. Our findings also provide support for the suggestion that bacterial prions can form more than one self-propagating state. We implement a stochastic version of the molecular model of prion propagation from yeast and mammals that recapitulates all the observed single-cell properties. This model highlights challenges for prion propagation that are unique to prokaryotes and illustrates the conservation of fundamental characteristics of prion propagation across domains of life.

A structured model and likelihood approach to estimate yeast prion propagon replication rates and their asymmetric transmission

Prion proteins cause a variety of fatal neurodegenerative diseases in mammals but are generally harmless to Baker’s yeast (Saccharomyces cerevisiae). This makes yeast an ideal model organism for investigating the protein dynamics associated with these diseases. The rate of disease onset is related to both the replication and transmission kinetics of propagons, the transmissible agents of prion diseases. Determining the kinetic parameters of propagon replication in yeast is complicated because the number of propagons in an individual cell depends on the intracellular replication dynamics and the asymmetric division of yeast cells within a growing yeast cell colony. We present a structured population model describing the distribution and replication of prion propagons in an actively dividing population of yeast cells. We then develop a likelihood approach for estimating the propagon replication rate and their transmission bias during cell division. We first demonstrate our ability to correctly recover known kinetic parameters from simulated data, then we apply our likelihood approach to estimate the kinetic parameters for six yeast prion variants using propagon recovery data. We find that, under our modeling framework, all variants are best described by a model with an asymmetric transmission bias. This demonstrates the strength of our framework over previous formulations assuming equal partitioning of intracellular constituents during cell division.

In this work we investigate the transmissible [PSI⁺] phenotype in yeast. The agents responsible for this phenotype are propagons, misfolded protein aggregates of a naturally occurring protein. These propagons increase in number within a cell and are distributed between cells during division. We use mathematical modeling to infer the replication rate of propagons within cells and if propagons are transmitted equally or unequally during cell division. Prior models in this area assumed only symmetric transmission when fitting replication rates. We couple this model with a novel likelihood framework allowing us to exclude influential outliers from our datasets when inferring parameters. We find that for all six protein variants we study, propagons are transmitted asymmetrically with different biases. Our results can be reproduced with the code and data available at https://github.com/FS-CodeBase/propagon_replication_and_transmission/.

Protein Aggregation Landscape in Neurodegenerative Diseases: Clinical Relevance and Future Applications

Intrinsic disorder is a natural feature of polypeptide chains, resulting in the lack of a defined three-dimensional structure. Conformational changes in intrinsically disordered regions of a protein lead to unstable β-sheet enriched intermediates, which are stabilized by intermolecular interactions with other β-sheet enriched molecules, producing stable proteinaceous aggregates. Upon misfolding, several pathways may be undertaken depending on the composition of the amino acidic string and the surrounding environment, leading to different structures. Accumulating evidence is suggesting that the conformational state of a protein may initiate signalling pathways involved both in pathology and physiology. In this review, we will summarize the heterogeneity of structures that are produced from intrinsically disordered protein domains and highlight the routes that lead to the formation of physiological liquid droplets as well as pathogenic aggregates. The most common proteins found in aggregates in neurodegenerative diseases and their structural variability will be addressed. We will further evaluate the clinical relevance and future applications of the study of the structural heterogeneity of protein aggregates, which may aid the understanding of the phenotypic diversity observed in neurodegenerative disorders.

Proposing a minimal set of metrics and methods to predict probabilities of amyloidosis disease and onset age in individuals

Many amyloid-driven pathologies have both genetic and stochastic components where assessing risk of disease development requires a multifactorial assessment where many of the variables are poorly understood. Risk of transthyretin-mediated amyloidosis is enhanced by age and mutation of the transthyretin (TTR) gene, but amyloidosis is not directly initiated by mutated TTR proteins. Nearly all of the 150+ known mutations increase dissociation of the homotetrameric protein structure and increase the probability of an individual developing a TTR amyloid disease late in life. TTR amyloidosis is caused by dissociated monomers that are destabilized and refold into an amyloidogenic form. Therefore, monomer concentration, monomer proteolysis rate, and structural stability are key variables that may determine the rate of development of amyloidosis. Here we develop a unifying biophysical model that quantifies the relationships among these variables in plasma and suggest the probability of an individual developing a TTR amyloid disease can be estimated. This may allow quantification of risk for amyloidosis and provide the information necessary for development of methods for early diagnosis and prevention. Given the similar observation of genetic and sporadic amyloidoses for other diseases, this model and the measurements to assess risk may be applicable to more proteins than just TTR.

A unifying model for the propagation of prion proteins in yeast brings insight into the [PSI+] prion

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.