Related papers: Topology, Geometry, and Stability: Protein Folding…

A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths --- the rare trajectories that transit between the folded and unfolded ensembles --- using only thermodynamic information, such as a…

Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…

Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…

Proteins with nontrivial topology, containing knots and slipknots, have the ability to fold to their native states without any additional external forces invoked. A mechanism is suggested for folding of these proteins, such as YibK and…

We review some of our recent results obtained within the scope of simple lattice models and Monte Carlo simulations that illustrate the role of native geometry in the folding kinetics of two state folders.

Methods of local topology are introduced to the field of protein physics. This is achieved by explaining how the folding and unfolding processes of a globular protein alter the local topology of the protein's C-alpha backbone through…

Quantification and classification of protein structures, such as knotted proteins, often requires noise-free and complete data. Here we develop a mathematical pipeline that systematically analyzes protein structures. We showcase this…

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…

Repeat proteins are made with tandem copies of similar amino acid stretches that fold into elongated architectures. Due to their symmetry, these proteins constitute excellent model systems to investigate how evolution relates to structure,…

Biological diversity has evolved despite the essentially infinite complexity of protein sequence space. We present a hierarchical approach to the efficient searching of this space and quantify the evolutionary potential of our approach with…

Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied to study protein structure and its implications. More that…

We carry out a theoretical study of the vibrational and relaxation properties of naturally-occurring proteins with the purpose of characterizing both the folding and equilibrium thermodynamics. By means of a suitable model we provide a full…

An all-atom model of proteins is used to show that the same sequence of amino acids can have many alternative structures, that are very distant from, and that can be as stable as, the corresponding native structure. Such alternative…

In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be ``protein-like'', heteropolymers must be thermodynamically stable, stable against…

A reduced model, which can fold both helix and sheet structures, is proposed to study the problem of protein folding. The goal of this model is to find an unbiased effective potential that has included the effects of water and at the same…

The root is an important organ of a plant since it is responsible for water and nutrient uptake. Analyzing and modelling variabilities in the geometry and topology of roots can help in assessing the plant's health, understanding its growth…

Recently described stochastic models of protein evolution have demonstrated that the inclusion of structural information in addition to amino acid sequences leads to a more reliable estimation of evolutionary parameters. We present a…

Monte Carlo simulations of a simple lattice model of protein folding show two distinct regimes depending on the chain length. The first regime well describes the folding of small protein sequences and its kinetic counterpart appears to be…

Proteins work only if folded in their native state, but changes in temperature T and pressure P induce their unfolding. Therefore for each protein there is a stability region (SR) in the T-P thermodynamic plane outside which the biomolecule…

Natural protein molecules are exceptional polymers. Encoded in apparently random strings of amino-acids, these objects perform clear physical tasks that are rare to find by simple chance. Accurate folding, specific binding, powerful…