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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. The boundaries of these regimes as well as the finite size in the second case can be computed explicitly. The growth in the third case (quadratic in time) can also be made explicit by formal asymptotic methods. The qualitative results are illustrated by numerical simulations. A comparison with recent experimental results permits a partial parametrization of the model.
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 autophagy, t
We consider a general incompressible finite model protein of size M in its environment, which we represent by a semiflexible copolymer consisting of amino acid residues classified into only two species (H and P, see text) following Lau and Dill. We a
The free energy of globular protein chain is considered to be a functional defined on smooth curves in three dimensional Euclidean space. From the requirement of geometrical invariance, together with basic facts on conformation of helical proteins an
While seemingly straightforward in principle, the reliable estimation of rate constants is seldom easy in practice. Numerous issues, such as the complication of poor reaction coordinates, cause obvious approaches to yield unreliable estimates. When a
Reaction coordinates are widely used throughout chemical physics to model and understand complex chemical transformations. We introduce a definition of the natural reaction coordinate, suitable for condensed phase and biomolecular systems, as a maxim