Related papers: Sequence determines degree of knottedness in a coa…
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…
Site-specific recombination on supercoiled circular DNA molecules can yield a variety of knots and catenanes. Twist knots are some of the most common conformations of these products and they can act as substrates for further rounds of…
The Knot Entropy Conjecture states that the exponential growth rate of the number of $n$-edge lattice polygons with knot-type $K$ is the same as that for unknot polygons. Moreover, the next order growth follows a power law in $n$ with an…
The time evolution of the formation probability of native bonds has been studied for designed sequences which fold fast into the native conformation. From this analysis a clear hierarchy of bonds emerge a) local, fast forming highly stable…
Folding channels and free-energy landscapes of hydrophobic-polar heteropolymers are discussed on the basis of a minimalistic off-lattice coarse-grained model. We investigate how rearrangements of hydrophobic and polar monomers in a…
We study the medium effects on the selection of sequences in protein folding by taking account of the surface potential in HP-model. Our analysis on the proportion of H and P monomers in the sequences gives a direct interpretation that the…
A general strategy is described for finding which amino acid sequences have native states in a desired conformation (inverse design). The approach is used to design sequences of 48 hydrophobic and polar aminoacids on three-dimensional…
The relationship between interactions, flexibility and disorder in proteins has been explored from many angles: folding upon binding, flexibility of the core relative to the periphery, entropy changes, etc. In this work, we provide…
Advanced Monte Carlo simulations are used to study the effect of nano-slit confinement on metric and topological properties of model DNA chains. We consider both linear and circularised chains with contour lengths in the 1.2--4.8 $\mu$m…
Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…
We assume that the protein folding process follows two autonomous steps: the conformational search for the native, mainly ruled by the hydrophobic effect; and, the final adjustment stage, which eventually gives stability to the native. Our…
Detailed thermodynamic analysis of complex systems with multiple stable configurational states allows for insight into the cooperativity of each individual transition. In this work we derive a heat capacity decomposition comprising…
With the help of a simple 20 letters, lattice model of heteropolymers, we investigate the energy landscape in the space of designed good-folder sequences. Low-energy sequences form clusters, interconnected via neutral networks, in the space…
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…
Site-specific recombination on supercoiled circular DNA yields a variety of knotted or catenated products. We develop a model of this process, and give extensive experimental evidence that the assumptions of our model are reasonable. We…
A model for soliton dynamics on a hydrogen-bond network in helical proteins is proposed. It employs in three dimensions the formalism of fully integrable Toda lattices which admits phonons as well as solitons along the hydrogen-bonds of the…
We consider how beads can diffuse along a chain that wraps them, without becoming displaced from the chain; our proposed mechanism is analogous to the reptation of "stored length" in more familiar situations of polymer dynamics. The problem…
A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The…
The predominant structural protein in vertebrates is collagen, which plays a key role in extracellular matrix and connective tissue mechanics. Despite its prevalence and physical importance in biology, the mechanical properties of molecular…
The idea that the knottedness (hydrodynamic Helicity) of a fluid flow is conserved has a long history in fluid mechanics. The quintessential example of a knotted flow is a knotted vortex filament, however, owing to experimental…