Related papers: CoHSI III: Long proteins and implications for prot…
Protein evolution underpins life, and understanding its behavior as a system is of great importance. However, our current models of protein evolution are arguably too simplistic to allow quantitative interpretation and prediction of…
The structure of molecular networks derives from dynamical processes on evolutionary time scales. For protein interaction networks, global statistical features of their structure can now be inferred consistently from several…
Simple hidden Markov models are proposed for predicting secondary structure of a protein from its amino acid sequence. Since the length of protein conformation segments varies in a narrow range, we ignore the duration effect of length…
Natural protein sequences somehow encode the structural forms that these molecules adopt. Recent developments in structure-prediction are agnostic to the mechanisms by which proteins fold and represent them as static objects. However, the…
Much information is stored in amino acid composition of protein and base composition of DNA. We simulated the evolution of amino acid frequencies and genomic GC content by a linguistic model. It is showed that the evolution of genetic code…
The evolution of the full repertoire of proteins encoded in a given genome is mostly driven by gene duplications, deletions, and sequence modifications of existing proteins. Indirect information about relative rates and other intrinsic…
The Conservation of Energy plays a pivotal part in the development of the physical sciences. With the growth of computation and the study of other discrete token based systems such as the genome, it is useful to ask if there are…
The coding space of protein sequences is shaped by evolutionary constraints set by requirements of function and stability. We show that the coding space of a given protein family--the total number of sequences in that family--can be…
Using three-dimensional Go lattice models with side chains for proteins, we investigate the dependence of folding times on protein length. In agreement with previous theoretical predictions, we find that the folding time grows as a power…
Proteins are sequences of amino acids that serve as the basic building blocks of living organisms. Despite rapidly growing databases documenting structural and functional information for various protein sequences, our understanding of…
Proteins employ the information stored in the genetic code and translated into their sequences to carry out well-defined functions in the cellular environment. The possibility to encode for such functions is controlled by the balance…
We analyse a simple discrete-time stochastic process for the theoretical modeling of the evolution of protein lengths. At every step of the process a new protein is produced as a modification of one of the proteins already existing and its…
Proteins must fold quickly to acquire their biologically functional three-dimensional native structures. Hence, these are mainly stabilized by local contacts, while intricate topologies such as knots are rare. Here, we reveal the existence…
Recently described stochastic models of protein evolution have demonstrated that the inclusion of structural information in addition to amino acid sequences leads to a more reliable estimation of evolutionary parameters. We present a…
In this paper, we mathematically describe the time evolution of protein folding features via Iori et al.'s heteropolymer model. More specifically, we identify that the folding amino acid chain evolve according to a power law $D \sim…
A new approach to estimate the Shannon entropy of a long-range correlated sequence is proposed. The entropy is written as the sum of two terms corresponding respectively to power-law (\emph{ordered}) and exponentially (\emph{disordered})…
This paper summarizes previous work linking protein aggregation to the heterozygosity of organisms. It also cites the literature showing a correlation between species' morphological complexity and the lengths of their proteins. These two…
An important question in molecular evolution is whether an amino acid that occurs at a given position makes an independent contribution to fitness, or whether its effect depends on the state of other loci in the organism's genome, a…
A number of recently discovered protein structures incorporate a rather unexpected structural feature: a knot in the polypeptide backbone. These knots are extremely rare, but their occurrence is likely connected to protein function in as…
Protein design is the inverse approach of the three-dimensional (3D) structure prediction for elucidating the relationship between the 3D structures and amino acid sequences. In general, the computation of the protein design involves a…