Mathematical model linking telomeres to senescence in Saccharomyces cerevisiae reveals cell lineage versus population dynamics.

Telomere shortening ultimately causes replicative senescence. However, identifying the mechanisms driving replicative senescence in cell populations is challenging due to the heterogeneity of telomere lengths and the asynchrony of senescence onset. Here, we present a mathematical model of telomere shortening and replicative senescence in Saccharomyces cerevisiae which is quantitatively calibrated and validated using data of telomerase-deficient single cells.

A mathematical model of p62-ubiquitin aggregates in autophagy.

Aggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. Three different parameter regimes are identified, where either aggregates are unstable, or their size saturates at a finite value, or their size grows indefinitely as long as free particles are abundant.

Telomere shortening causes distinct cell division regimes during replicative senescence in Saccharomyces cerevisiae.

Background: Telomerase-negative cells have limited proliferation potential. In these cells, telomeres shorten until they reach a critical length and induce a permanently arrested state. This process called replicative senescence is associated with genomic instability and participates in tissue and organismal ageing.

Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.

The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of 'pure fragmentation'. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is of importance in biology and biomedicine for instance in governing the creation of amyloid seeds and the propagation of prions. Here, we devised from mathematical theory inversion formulae to recover the division rates and division kernel information from time-dependent experimental measurements of filament size distribution.

A purely mechanical model with asymmetric features for early morphogenesis of rod-shaped bacteria micro-colony.

To model the morphogenesis of rod-shaped bacterial micro-colony, several individual-based models have been proposed in the biophysical literature. When studying the shape of micro-colonies, most models present interaction forces such as attraction or filial link. In this article, we propose a model where the bacteria interact only through non-overlapping constraints.

The Division of Amyloid Fibrils: Systematic Comparison of Fibril Fragmentation Stability by Linking Theory with Experiments.

The division of amyloid protein fibrils is required for the propagation of the amyloid state and is an important contributor to their stability, pathogenicity, and normal function. Here, we combine kinetic nanoscale imaging experiments with analysis of a mathematical model to resolve and compare the division stability of amyloid fibrils. Our theoretical results show that the division of any type of filament results in self-similar length distributions distinct to each fibril type and the conditions applied.

Early stage prion assembly involves two subpopulations with different quaternary structures and a secondary templating pathway.

The dynamics of aggregation and structural diversification of misfolded, host-encoded proteins in neurodegenerative diseases are poorly understood. In many of these disorders, including Alzheimer's, Parkinson's and prion diseases, the misfolded proteins are self-organized into conformationally distinct assemblies or strains. The existence of intrastrain structural heterogeneity is increasingly recognized.

A bi-monomeric, nonlinear Becker-Döring-type system to capture oscillatory aggregation kinetics in prion dynamics.

In this article, in order to understand the appearance of oscillations observed in protein aggregation experiments, we propose, motivate and analyse mathematically the differential system describing the kinetics of the following reactions: [Formula: see text] with n finite or infinite. This system may be viewed as a variant of the seminal Becker-Döring system, and is capable of displaying sustained though damped oscillations.

Bidirectional sliding of two parallel microtubules generated by multiple identical motors.

It is often assumed in biophysical studies that when multiple identical molecular motors interact with two parallel microtubules, the microtubules will be crosslinked and locked together. The aim of this study is to examine this assumption mathematically. We model the forces and movements generated by motors with a time-continuous Markov process and find that, counter-intuitively, a tug-of-war results from opposing actions of identical motors bound to different microtubules.

Pressure Reveals Unique Conformational Features in Prion Protein Fibril Diversity.

The prion protein (PrP) misfolds and assembles into a wide spectrum of self-propagating quaternary structures, designated PrP. These various PrP superstructures can be functionally different, conferring clinically distinctive symptomatology, neuropathology and infectious character to the associated prion diseases. However, a satisfying molecular basis of PrP structural diversity is lacking in the literature.

The mechanism of monomer transfer between two structurally distinct PrP oligomers.

In mammals, Prion pathology refers to a class of infectious neuropathologies whose mechanism is based on the self-perpetuation of structural information stored in the pathological conformer. The characterisation of the PrP folding landscape has revealed the existence of a plethora of pathways conducing to the formation of structurally different assemblies with different biological properties. However, the biochemical interconnection between these diverse assemblies remains unclear.

A numerical scheme for the early steps of nucleation-aggregation models.

In the formation of large clusters out of small particles, the initializing step is called the nucleation, and consists in the spontaneous reaction of agents which aggregate into small and stable polymers called nuclei. After this early step, the polymers are involved in a number of reactions such as polymerization, fragmentation and coalescence. Since there may be several orders of magnitude between the size of a particle and the size of an aggregate, building efficient numerical schemes to capture accurately the kinetics of the reaction is a delicate step of key importance.

Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly.

Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with human diseases such as Alzheimer's disease. Amyloid fibrils also have potential applications in nano-engineering of biomaterials. The kinetics of amyloid assembly show an exponential growth phase preceded by a lag phase, variable in duration as seen in bulk experiments and experiments that mimic the small volumes of cells.

Estimation from moments measurements for amyloid depolymerisation.

Estimating reaction rates and size distributions of protein polymers is an important step for understanding the mechanisms of protein misfolding and aggregation, a key feature for amyloid diseases. This study aims at setting this framework problem when the experimental measurements consist in the time-dynamics of a moment of the population (i.e.

The asymmetry of telomere replication contributes to replicative senescence heterogeneity.

In eukaryotes, the absence of telomerase results in telomere shortening, eventually leading to replicative senescence, an arrested state that prevents further cell divisions. While replicative senescence is mainly controlled by telomere length, the heterogeneity of its onset is not well understood. This study proposes a mathematical model based on the molecular mechanisms of telomere replication and shortening to decipher the causes of this heterogeneity.

Information content in data sets for a nucleated-polymerization model.

We illustrate the use of statistical tools (asymptotic theories of standard error quantification using appropriate statistical models, bootstrapping, and model comparison techniques) in addition to sensitivity analysis that may be employed to determine the information content in data sets. We do this in the context of recent models [S. Prigent, A.

Division in Escherichia coli is triggered by a size-sensing rather than a timing mechanism.

Background: Many organisms coordinate cell growth and division through size control mechanisms: cells must reach a critical size to trigger a cell cycle event. Bacterial division is often assumed to be controlled in this way, but experimental evidence to support this assumption is still lacking. Theoretical arguments show that size control is required to maintain size homeostasis in the case of exponential growth of individual cells.

Data-driven modeling of SRC control on the mitochondrial pathway of apoptosis: implication for anticancer therapy optimization.

Src tyrosine kinases are deregulated in numerous cancers and may favor tumorigenesis and tumor progression. We previously described that Src activation in NIH-3T3 mouse fibroblasts promoted cell resistance to apoptosis. Indeed, Src was found to accelerate the degradation of the pro-apoptotic BH3-only protein Bik and compromised Bax activation as well as subsequent mitochondrial outer membrane permeabilization.

An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation.

Protein polymerization consists in the aggregation of single monomers into polymers that may fragment. Fibrils assembly is a key process in amyloid diseases. Up to now, protein aggregation was commonly mathematically simulated by a polymer size-structured ordinary differential equations (ODE) system, which is infinite by definition and therefore leads to high computational costs.

Estimating the division rate for the growth-fragmentation equation.

Growth-fragmentation equations arise in many different contexts, ranging from cell division, protein polymerization, neurosciences etc. Direct observation of temporal dynamics being often difficult, it is of main interest to develop theoretical and numerical methods to recover reaction rates and parameters of the equation from indirect observation of the solution. Following the work done in Perthame and Zubelli (Inverse Probl 23:1037-1052, 2007) and Doumic et al.

A new model for the estimation of cell proliferation dynamics using CFSE data.

CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and divisionlinked changes in cell behavior. Recently Banks et al. (2011), Luzyanina et al.

On the calibration of a size-structured population model from experimental data.

The aim of this work is twofold. First, we survey the techniques developed in Perthame and Zubelli (Inverse Probl 23(3):1037-1052, 2007), Doumic et al. (Inverse Probl 25, 2009) to reconstruct the division (birth) rate from the cell volume distribution data in certain structured population structured population models.

Prion dynamics with size dependency-strain phenomena.

Models for the polymerization process involved in prion self-replication are well-established and studied [H. Engler, J. Pruss, and G.