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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…
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…
The robustness of complex networks with dependencies has been studied in recent years. However, previous studies focused on the robustness of networks composed of dependency links without network topology. In this study, we will analyze the…
Neither of the two prevalent theories, namely thermodynamic stability and kinetic stability, provides a comprehensive understanding of protein folding. The thermodynamic theory is misleading because it assumes that free energy is the…
While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the three--dimensional, biologically active, native conformation of…
The native conformation of structured proteins is stabilized by a complex network of interactions. We analyzed the elementary patterns that constitute such network and ranked them according to their importance in shaping protein sequence…
An effective potential function is critical for protein structure prediction and folding simulation. For simplified models of proteins where coordinates of only $C_\alpha$ atoms need to be specified, an accurate potential function is…
Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in…
We consider six different secondary structures of proteins and construct two types of Go-type off-lattice models: with the steric constraints and without. The basic aminoacid-aminoacid potential is Lennard Jones for the native contacts and…
The primary structure of proteins, that is their sequence, represents one of the most abundant set of experimental data concerning biomolecules. The study of correlations in families of co--evolving proteins by means of an inverse…
Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states lying energetically between folded and unfolded conformations. While there are different ways to test for two-state…
Interactions between elements, which are usually represented by networks, have to delineate potentially unequal relationships in terms of their relative importance or direction. The intrinsic unequal relationships of such kind, however, are…
In this letter, the possible dynamic scaling properties of protein molecules in folding are investigated theoretically by assuming that the protein molecules are percolated networks. It is shown that the fractal character and the fractal…
The overall structure of the transition state and intermediate ensembles experimentally observed for Dihydrofolate Reductase and Interleukin-1beta can be obtained utilizing simplified models which have almost no energetic frustration. The…
We study folding dynamics of protein-like sequences on square lattice using physical move set that exhausts all possible conformational changes. By analytically solving the master equation, we follow the time-dependent probabilities of…
This paper studies the controllability of networked relative coupling systems (NRCSs), in which subsystems are of fixed high-order linear dynamics and coupled through relative variables depending on their neighbors, from a structural…
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…
We present a theoretical study of the folding of small proteins inside confining potentials. Proteins are described in the framework of an effective potential model which contains the Ramachandran angles as degrees of freedom and does not…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…