Related papers: Are there Unfoldable Proteins in Dimension Three?
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
We examined what determines the designability of 2-letter codes (H and P) lattice proteins from three points of view. First, whether the native structure is searched within all possible structures or within maximally compact structures.…
The evolutionary trajectory of a protein through sequence space is constrained by function and three-dimensional (3D) structure. Residues in spatial proximity tend to co-evolve, yet attempts to invert the evolutionary record to identify…
In this work, we discovered a fundamental connection between selection for protein stability and emergence of preferred structures of proteins. Using standard exact 3-dimensional lattice model we evolve sequences starting from random ones…
Theory of multi-dimensional representation of free energy surface of protein folding is developed by adopting structural order parameters of multiple regions in protein as multiple coordinates. Various scenarios of folding are classified in…
An infinite regular three-dimensional network is composed of identical resistors each of resistance joining adjacent nodes. What is the equivalent resistance between the lattice site and the lattice site, when two bonds are removed from the…
The protein folding problem has attracted an increasing attention from physicists. The problem has a flavor of statistical mechanics, but possesses the most common feature of most biological problems -- the profound effects of evolution. I…
When materials are patterned in three dimensions, there exist opportunities to tailor and create functionalities associated with an increase in complexity, the breaking of symmetries, and the introduction of curvature and non-trivial…
In this paper, we introduce a three-dimensional mathematical model of collagen contraction with microbuckling based on the two-dimensional model previously developed by the authors. The model both qualitatively and quantitatively replicates…
This paper extends the recently obtained complete and continuous map of the Lattice Isometry Space (LISP) to the practical case of dimension 3. A periodic 3-dimensional lattice is an infinite set of all integer linear combinations of basis…
The thermodynamic behavior of a three-dimensional off-lattice model for protein folding is probed. The model has only two types of residues, hydrophobic and hydrophilic. In absence of local interactions, native structure formation does not…
Protein folds are highly designable, in the sense that many sequences fold to the same conformation. In the present work we derive an expression for the designability in a 20 letter lattice model of proteins which, relying only on the…
Inspired by protein folding, we explored the construction of three-dimensional structures and machines from one-dimensional chains of simple building blocks. This approach not only allows us to recreate the self-replication mechanism…
The beautiful structures of single and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein…
Predicting the three-dimensional (3D) functional structures of proteins remains an important computational milestone in molecular biology to be achieved. This feat is hinged on a clear understanding of the mechanism which proteins use to…
The human proteome is enriched in proteins that do not fold into a stable 3D structure. These intrinsically disordered proteins (IDPs) spontaneously fluctuate between a large number of configurations in their native form. Remarkably, the…
We use the lattice model of directed walks to investigate the conformational as well as the adsorption properties of a semiflexible homopolymer chain immersed in a good solvent in two and three dimensions. To account for the stiffness in…
Many recent papers deal with the enumeration of 2-dimensional walks with prescribed steps confined to the positive quadrant. The classification is now complete for walks with steps in $\{0, \pm 1\}^2$: the generating function is D-finite if…
Understanding the principles of protein folding is a cornerstone of computational biology, with implications for drug design, bioengineering, and the understanding of fundamental biological processes. Lattice protein folding models offer a…
The three dimensional structure of a protein is an outcome of the interactions of its constituent amino acids in 3D space. Considering the amino acids as nodes and the interactions among them as edges we have constructed and analyzed…