Related papers: A mathematical model of p62-ubiquitin aggregates i…
The qualitative behavior of a recently formulated ODE model for the dynamics of heterogenous aggregates is analyzed. Aggregates contain two types of particles, oligomers and cross-linkers. The motivation is a preparatory step of cellular…
We consider a linear integro-differential equation which arises to describe both aggregation-fragmentation processes and cell division. We prove the existence of a solution $(\lb,\U,\phi)$ to the related eigenproblem. Such eigenelements are…
We extend our previous stochastic cellular automata based model for areal aggregation of prion proteins on neuronal surfaces. The new anisotropic model allow us to simulate both strong beta-sheet and weaker attachment bonds between…
The presence of protein aggregates in cells is a known feature of many human age-related diseases, such as Huntington's disease. Simulations using fixed parameter values in a model of the dynamic evolution of expanded polyglutamine (PolyQ)…
We consider fully nonlinear uniformly elliptic cooperative systems with quadratic growth in the gradient, such as $$ -F_i(x, u_i, Du_i, D^2 u_i)- \langle M_i(x)D u_i, D u_i \rangle =\lambda c_{i1}(x) u_1 + \cdots + \lambda c_{in}(x) u_n…
This work presents a mathematical model which describes both the genesis and growth of oxygenic photogranules (OPGs) and the related treatment process. The photogranule has been modelled as a free boundary domain with radial symmetry, which…
Cellular aggregates play a significant role in the evolution of biological systems such as tumor growth, tissue spreading, wound healing, and biofilm formation. Analysis of such biological systems, in principle, includes examining the…
We develop a theory of aggregation using statistical mechanical methods. An example of a complicated aggregation system with several levels of structures is peptide/protein self-assembly. The problem of protein aggregation is important for…
We investigate aggregation mechanism of two proteins in a thermodynamically unambiguous manner by considering the finite size effect of free energy landscape of HP lattice protein model. Multi-Self-Overlap-Ensemble Monte Carlo method is…
This paper deals with a general system of equations and conditions arising from a mathematical model of prostate cancer growth with chemotherapy and antiangiogenic therapy that has been recently introduced and analyzed (see [P. Colli et…
This paper unravels the problem of an idealised pile-up of n infinite, equi-spaced walls of edge dislocations at equilibrium. We define a dimensionless parameter that depends on the geometric, constitutive and loading parameters of the…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
We explore the statistics of assembling soft-matter building blocks to investigate the uptake and encapsulation of cargo particles by carriers engulfing their load. While the such carrier-cargo complexes are important for many applications…
We present a continuous time model of maturation and survival, obtained as the limit of a compartmental evolution model when the number of compartments tends to infinity. We establish in particular an explicit formula for the law of the…
The aggregation of particles in the free molecular regime is determined approximately for situations with a high degree of translational energy equilibration. The mean particle sizes develop linearly in time. Scaling relations are used to…
Cellular functions are established through biological evolution, but are constrained by the laws of physics. For instance, the physics of protein folding limits the lengths of cellular polypeptide chains. Consequently, many cellular…
The stochastic Eden model of charged particles aggregation in two-dimensional systems is presented. This model is governed by two parameters: screening length of electrostatic interaction, $\lambda $, and short range attraction energy, $E$.…
The possibility for proteins to aggregate in different superstructures, i.e. large-scale polymorphism, has been widely observed, but an understanding of the physico-chemical mechanisms behind it is still out of reach. Here we present a…
The evolution of occupied volume under progressive fragmentation of granular matter is studied using a purely geometric model. Rather than modelling disorder directly, properties are investigated by analysing highly ordered reference…
In this thesis, we develop multiscale models for particle simulations in population dynamics. These models are characterised by prescribing particle motion on two spatial scales: microscopic and macroscopic. At the microscopic level, each…