Related papers: A mathematical model of p62-ubiquitin aggregates i…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
Similarly-charged polymers in solution, known as polyelectrolytes, are known to form aggregated structures in the presence of oppositely charged counterions. Understanding the dependence of the equilibrium phases and the dynamics of the…
The formation and proliferation of protein aggregates play a central role in a number of devastating neuro-degenerative diseases. Many experimental studies indicate that the ability of existing aggregates to replicate is a key property in…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
In this paper, for a family of second-order parabolic system or equation with rapidly oscillating and time-dependent periodic coefficients over rough boundaries, we obtain the large-scale boundary estimates, by a quantitative approach. The…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
Autophagy is an intracellular degradation process that employs complex membrane dynamics to isolate and break down cellular components. However, many unanswered questions remain concerning remodeling of autophagic membranes. Here, we focus…
We consider a multiscale stochastic compartmental model with three types of cells (stem cells, immature cells and mature cells) which combines cell proliferation and cell differentiation. We derive a hydrodynamic limit when the number of…
New model equations are derived for dynamics of self-aggregation of finite-size particles. Differences from standard Debye-Huckel and Keller-Segel models are: the mobility of particles depends on the configuration of their neighbors and…
The Branched Polymer Growth Model (BPGM) has been employed to study the kinetic growth of ramified polymers in the presence of impurities. In this article, the BPGM is revisited on the square lattice and a subtle modification in its…
Neurodegenerative diseases are driven by the accumulation of protein aggregates in the brain of affected individuals. The aggregation behaviour in vitro is well understood and driven by the equilibration of a super-saturated protein…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
Recently, a hypothesis on the complexity growth of unitarily evolving operators was presented. This hypothesis states that in generic, non-integrable many-body systems the so-called Lanczos coefficients associated with an autocorrelation…
The formation of dynamical clusters of proteins is ubiquitous in cellular membranes and is in part regulated by the recycling of membrane components. Mean-field models of out-of-equilibrium cluster formation with recycling predict a broad…
Bacterial microcompartments are large, roughly icosahedral shells that assemble around enzymes and reactants involved in certain metabolic pathways in bacteria. Motivated by microcompartment assembly, we use coarse-grained computational and…
Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key…
The phase diagram of prolate and oblate particles in the restricted orientations approximation (Zwanzig model) is calculated. Transitions to different inhomogeneous phases (smectic, columnar, oriented, or plastic solid) are studied through…
In this paper we are interested in a degenerate parabolic system of reaction-diffusion equations arising in biology when studying cell adhesion at the protein level. In this modeling the unknown is the couple of the distribution laws of the…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
We revisit the modeling of the diauxic growth of a pure microorganism on two distinct sugars which was first described by Monod. Most available models are deterministic and make the assumption that all cells of the microbial ecosystem…