scholarly journals Multi-Scale Mathematical Modeling of Prion Aggregate Dynamics and Phenotypes in Yeast Colonies

2020 ◽  
Author(s):  
Mikahl Banwarth-Kuhn ◽  
Suzanne Sindi
Keyword(s):  
Mathematical Modeling ◽  
Multi Scale ◽  
Aggregate Dynamics

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

2020 ◽  
Author(s):  
Lemarre Paul ◽  
Sindi S. Suzanne ◽  
Pujo-Menjouet Laurent
Keyword(s):  
Mathematical Modeling ◽  
Guanidine Hydrochloride ◽  
Impulsive Differential Equations ◽  
Valuable Insight ◽  
Mathematical Framework ◽  
Yeast Prion ◽  
Modeling Framework ◽  
Yeast Prions ◽  
Multi Scale ◽  
Insight Into

AbstractThe 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 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 summaryIn 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.

scholarly journals Mathematical Modeling Predicts That Strict Social Distancing Measures Would Be Needed to Shorten the Duration of Waves of COVID-19 Infections in Vietnam

2021 ◽  
Vol 8 ◽  
Author(s):  
Anass Bouchnita ◽  
Abdennasser Chekroun ◽  
Aissam Jebrane
Keyword(s):  
Mathematical Modeling ◽  
Urban Areas ◽  
Reproduction Number ◽  
Global Public Health ◽  
Social Distancing ◽  
Multi Scale ◽  
Major Threat ◽  
Reported Data ◽  
The Impact ◽  
Pharmaceutical Interventions

Coronavirus disease 2019 (COVID-19) emerged in Wuhan, China in 2019, has spread throughout the world and has since then been declared a pandemic. As a result, COVID-19 has caused a major threat to global public health. In this paper, we use mathematical modeling to analyze the reported data of COVID-19 cases in Vietnam and study the impact of non-pharmaceutical interventions. To achieve this, two models are used to describe the transmission dynamics of COVID-19. The first model belongs to the susceptible-exposed-infectious-recovered (SEIR) type and is used to compute the basic reproduction number. The second model adopts a multi-scale approach which explicitly integrates the movement of each individual. Numerical simulations are conducted to quantify the effects of social distancing measures on the spread of COVID-19 in urban areas of Vietnam. Both models show that the adoption of relaxed social distancing measures reduces the number of infected cases but does not shorten the duration of the epidemic waves. Whereas, more strict measures would lead to the containment of each epidemic wave in one and a half months.

scholarly journals Characteristics of mathematical modeling languages that facilitate model reuse in systems biology: A software engineering perspective

2019 ◽  
Author(s):  
Christopher Schölzel ◽  
Valeria Blesius ◽  
Gernot Ernst ◽  
Andreas Dominik
Keyword(s):  
Mathematical Modeling ◽  
Systems Biology ◽  
Software Engineering ◽  
Cardiac Conduction ◽  
Modeling Language ◽  
Modeling Languages ◽  
Model Reuse ◽  
Multi Scale ◽  
Trade Offs ◽  
Language Characteristics

AbstractReproducible, understandable models that can be reused and combined to true multi-scale systems are required to solve the present and future challenges of systems biology. However, many mathematical models are still built for a single purpose and reusing them in a different context can be challenging due to an inflexible monolithic structure, confusing code, missing documentation or other issues. These challenges are very similar to those faced in the engineering of large software systems. It is therefore likely that addressing model design at the software engineering level will also be beneficial in systems biology. To do this, researchers cannot just rely on using an accepted standard language. They need to be aware of the characteristics that make this language desirable and they need guidelines on how to utilize them to make their models more reproducible, understandable, reusable, and extensible. Drawing upon our experience with translating and extending a model of the human baroreflex, we therefore propose a list of desirable language characteristics and provide guidelines and examples for incorporating them in a model: In our opinion, a mathematical modeling language used in systems biology should be modular, human-readable, hybrid (i.e. support multiple formalisms), open, declarative, and support the graphical representation of models. We compare existing modeling languages with respect to these characteristics and show that there is no single best language but that trade-offs always have to be considered. We also illustrate the benefits of the individual language characteristics by translating a monolithic model of the human cardiac conduction system to a modular version using the modeling language Modelica as an example. Our experiment can be seen as emblematic for model reuse in a multi-scale setting. It illustrates how each characteristic, when applied consistently, can facilitate the reuse of the resulting model. We therefore recommend that modelers consider these criteria when choosing a programming language for any biological modeling task and hope that our work sparks a discussion about the importance of software engineering aspects in mathematical modeling languages.

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