Related papers: Sequence determines degree of knottedness in a coa…
We investigate the formation of beta-sheet structures in proteins without taking into account specific sequence-dependent hydrophobic interactions. To accomplish this, we introduce a model which explicitly incorporates both solvation…
An increasing number of proteins are being discovered with a remarkable and somewhat surprising feature, a knot in their native structures. How the polypeptide chain is able to knot itself during the folding process to form these highly…
Mapping between sequence and structure is currently an open problem in structural biology. Despite many experimental and computational efforts it is not clear yet how the structure is encoded in the sequence. Answering this question may…
Proteins are responsible for the most diverse set of functions in biology. The ability to extract information from protein sequences and to predict the effects of mutations is extremely valuable in many domains of biology and medicine.…
We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through…
The mechanics of complex soft matter often cannot be understood in the classical physical frame of flexible polymers or rigid rods. The underlying constituents are semiflexible polymers, whose finite bending stiffness ($\kappa$) leads to…
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…
Synthetic copolymers and biopolymers, such as polypeptides and double-stranded DNA, often exhibit strong variations in bending stiffness along their contour, which can significantly impact conformational behavior at larger scales. To…
Hydrophobicity is thought to be one of the primary forces driving the folding of proteins. On average, hydrophobic residues occur preferentially in the core, whereas polar residues tends to occur at the surface of a folded protein. By…
After a discussion of the definition and number of pseudoknots, we reconsider the self-attracting homopolymer paying particular attention to the scaling of the number of pseudoknots at different temperature regimes in two and three…
The effect of sequence heterogeneity on the dynamics of molecular motors is reviewed and analyzed using a set of recently introduced lattice models. First, we review results for the influence of heterogenous tracks such as a single-strand…
The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular…
Modeling of DNA-protein interactions is a complex process involving many important time and length scales. This can be facilitated through the use of coarse-grained models which reduce the number of degrees of freedom and allow efficient…
The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice…
Recent advances in coarse-grained lattice and off-lattice protein models are reviewed. The sequence dependence of thermodynamical folding properties are investigated and evidence for non-randomness of the binary sequences of good folders…
We study folding in 16-monomer heteropolymers on the square lattice. For a given sequence, thermodynamic properties and stability of the native state are unique. However, the kinetics of folding depends on the model of dynamics adopted for…
We study the impact of mutations (changes in amino acid sequence) on the thermodynamics of simple protein-like heteropolymers consisting of N monomers, representing the amino acid sequence. The sequence is designed to fold into its native…
Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by…
Protein sequences serve as a natural record of the evolutionary constraints that shape their functional structures. We show that it is possible to use only sequence information to go beyond predicting native structures and global stability…
We explore the effect of Couette flow on knotted linear polymer chains with extensive Molecular Dynamics (MD) simulations. Hydrodynamic interactions are accounted for by means of Multi-Particle Collision Dynamics (MPCD). The polymer chain,…