Related papers: Asymptotics of Stochastic Protein Assembly Models
Biopolymer self-assembly pathways are central to biological activity, but are complicated by the ability of the monomeric subunits of biopolymers to adopt different conformational states. As a result, biopolymer nucleation often involves a…
The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon…
We present a theoretical model for predicting the phase behavior of polymer solutions in which phase separation competes with oligomerization. Specifically, we consider scenarios in which the assembly of polymer chains into stoichiometric…
Autocatalytic fibril nucleation has recently been proposed to be a determining factor for the spread of neurodegenerative diseases, but the same process could also be exploited to amplify minute quantities of protein aggregates in a…
The intrinsic stochasticity of gene expression can lead to large variability in protein levels for genetically identical cells. Such variability in protein levels can arise from infrequent synthesis of mRNAs which in turn give rise to…
Proteins are polymerized by cyclic machines called ribosome which use their messenger RNA (mRNA) track also as the corresponding template and the process is called translation. We explore, in depth and detail, the stochastic nature of the…
Autonomous oscillations in biological systems may have a biochemical origin or result from an interplay between force-generating and visco-elastic elements. In molecular motor assemblies the force-generating elements are molecular engines…
Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not…
We investigate the selective forces that promote the emergence of modularity in nature. We demonstrate the spontaneous emergence of modularity in a population of individuals that evolve in a changing environment. We show that the level of…
Random heteropolymers do not display the typical equilibrium properties of globular proteins, but are the starting point to understand the physics of proteins and, in particular, to describe their non-native states. So far, they have been…
The importance of understanding the mechanism of protein aggregation into insoluble amyloid fibrils relies not only on its medical consequences, but also on its more basic properties of self--organization. The discovery that a large number…
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 solve a model that takes into account entropic barriers, frustration, and the organization of a protein-like molecule. For a chain of size $M$, there is an effective folding transition to an ordered structure. Without frustration, this…
Protein folding, peptide aggregation and crystallization, as well as adsorption of molecules on soft or solid substrates have an essential feature in common: In all these processes, structure formation is guided by a collective, cooperative…
Molecules provide the ultimate language in terms of which physiology and pathology must be understood. Myriads of proteins participate in elaborate networks of interactions and perform chemical activities coordinating the life of cells. To…
Advances in experimental techniques and in theoretical models have improved our understanding of protein crystallization. But they have also left open questions regarding the protein phase behavior and self-assembly kinetics, such as why…
An important goal of self-assembly is to achieve a preprogrammed structure with high fidelity. Here, we control the valence of DNA-functionalized emulsions to make linear and branched model polymers, or `colloidomers'. The distribution of…
Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with…
In this paper we analyze the equilibrium properties of a large class of stochastic processes describing the fundamental biological process within bacterial cells, {\em the production process of proteins}. Stochastic models classically used…
The asymptotic behavior of a stochastic network represented by a birth and death processes of particles on a compact state space is analyzed. Births: Particles are created at rate $\lambda_+$ and their location is independent of the current…