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Topological constraints (TCs) between polymers determine the behaviour of complex fluids such as creams, oils and plastics. Most of the polymer solutions used every day life employ linear chains; their behaviour is accurately captured by…
It is well-established that many physical properties of DNA at sufficiently long length scales can be understood by means of simple polymer models. One of the most widely used elasticity models for DNA is the twistable worm-like chain…
A gordian unlink is a finite number of unknots that are not topologically linked, each with prescribed length and thickness, and that cannot be disentangled into the trivial link by an isotopy preserving length and thickness throughout. In…
RNA molecules exhibit various biological functions intrinsically dependent on their diverse ecosystem of highly flexible structures. This flexibility arises from complex hydrogen-bonding networks defined by canonical and non-canonical base…
Proteins encoded by genes containing regions of variable number tandem repeats (VNTRs) are known to be polymorphic within species but the influence of their instability in molecular interactions remains unclear. VNTRs are overrepresented in…
We present an analytical theory for heteropolymer deformation, as exemplified experimentally by stretching of single protein molecules. Using a mean-field replica theory, we determine phase diagrams for stress-induced unfolding of typical…
Large scale molecular dynamics simulations on graphic processing units (GPUs) are employed to study the scaling behavior of ring polymers with various topological constraints in melts. Typical sizes of rings containing $3_1$, $5_1$ knots…
A microscopic theory of the free energy barriers and folding routes for minimally frustrated proteins is presented, greatly expanding on the presentation of the variational approach outlined previously [J. J. Portman, S. Takada, P. G.…
Semiflexible polymers are widely used as a paradigm for understanding structural phases in biomolecules including folding of proteins. Here, we compare bead-spring and bead-stick variants of coarse-grained semiflexible polymer models that…
Protein-protein binding enables orderly and lawful biological self-organization, and is therefore considered a miracle of nature. Protein-protein binding is steered by electrostatic forces, hydrogen bonding, van der Waals force, and…
New results on the groundstate energy of tight, magnetic knots are presented. Magnetic knots are defined as tubular embeddings of the magnetic field in an ideal, perfectly conducting, incompressible fluid. An orthogonal, curvilinear…
The mechanical properties of DNA play a critical role in many biological functions. For example, DNA packing in viruses involves confining the viral genome in a volume (the viral capsid) with dimensions that are comparable to the DNA…
Links and knots are exotic topological structures that have garnered significant interest across multiple branches of natural sciences. Coherent links and knots, such as those constructed by phase or polarization singularities of coherent…
Lattice models, for their coarse-grained nature, are best suited for the study of the ``designability problem'', the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a…
Natural protein sequences that self-assemble to form globular structures are compact with high packing densities in the folded states. It is known that proteins unfold upon addition of denaturants, adopting random coil structures. The…
We have shown recently that the notion of poking pairwise interactions along a chain provides a unifying framework for understanding the formation of both secondary and the tertiary protein structure based on symmetry and geometry.…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
Optical knots and links, consisting of trajectories of phase or polarisation singularities, are intriguing nontrivial three-dimensional topologies. They are theoretically predicted and experimentally observed in paraxial and non-paraxial…
Neural Tangent Kernel (NTK) is widely used to analyze overparametrized neural networks due to the famous result by Jacot et al. (2018): in the infinite-width limit, the NTK is deterministic and constant during training. However, this result…
Mutations in proteins can have deleterious effects on a protein's stability and function, which ultimately causes particular diseases. Genetically inherited muscular dystrophies (MDs) include several genetic diseases, which cause increasing…