Number of natively unfolded proteins scales with genome size

Natively unfolded proteins exist as an ensemble of flexible conformations lacking a well defined tertiary structure along a large portion of their polypeptide chain. Despite the absence of a stable configuration, they are involved in important cellular processes. In this work we used from three indicators of folding status, derived from the analysis of mean packing and mean contact energy of a protein sequence as well as from VSL2, a disorder predictor, and we combined them into a consensus score to identify natively unfolded proteins in several genomes from Archaea, Bacteria and Eukarya. We found a high correlation among the number of predicted natively unfolded proteins and the number of proteins in the genomes. More specifically, the number of natively unfolded proteins scaled with the number of proteins in the genomes, with exponent 1.81 +- 0.10. This scaling law may be important to understand the relation between the number of natively unfolded proteins and their roles in cellular processes.Comment: Submitted to Biophysics and Bioengineering Letters http://padis2.uniroma1.it:81/ojs/index.php/CISB-BB

Percolation and lack of self-averaging in a frustrated evolutionary model

We present a stochastic evolutionary model obtained through a perturbation of Kauffman's maximally rugged model, which is recovered as a special case. Our main results are: (i) existence of a percolation-like phase transition in the finite phase space case; (ii) existence of non self-averaging effects in the thermodynamic limit. Lack of self-averaging emerges from a fragmentation of the space of all possible evolutions, analogous to that of a geometrically broken object. Thus the model turns out to be exactly solvable in the thermodynamic limit.Comment: 22 pages, 1 figur

Long time behavior of quasi-stationary states of the Hamiltonian Mean-Field model

The Hamiltonian Mean-Field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived, out-of-equilibrium, quasi-stationary dynamical states, whose lifetime diverges in the thermodynamic limit. The nature of these states has been the object of a lively debate, in the recent past. We introduce a new numerical tool, based on the fluctuations of the phase of the instantaneous magnetization of the system. Using this tool, we study the quasi-stationary states that arise when the system is started from different classes of initial conditions, showing that the new observable can be exploited to compute the lifetime of these states. We also show that quasi-stationary states are present not only below, but also above the critical temperature of the second order magnetic phase transition of the model. We find that at supercritical temperatures the lifetime is much larger than at subcritical temperatures.Comment: Submitted to Phys. Rev.

Causal influence in linear response models

The intuition of causation is so fundamental that almost every research study in life sciences refers to this concept. However a widely accepted formal definition of causal influence between observables is still missing. In the framework of linear Langevin networks without feedbacks (linear response models) we developed a measure of causal influence based on a decomposition of information flows over time. We discuss its main properties and compare it with other information measures like the Transfer Entropy. Finally we outline some difficulties of the extension to a general definition of causal influence for complex systems.Comment: 9 pages, 9 figure

Bacterial protein interaction networks: connectivity is ruled by gene conservation, essentiality and function

Protein-protein interaction (PPI) networks are the backbone of all processes in living cells. In this work we relate conservation, essentiality and functional repertoire of a gene to the connectivity $k$ of the corresponding protein in the PPI networks. Focusing on a set of 42 bacterial species with reasonably separated evolutionary trajectories, we investigate three issues: i) whether the distribution of connectivity values changes between PPI subnetworks of essential and nonessential genes; ii) how gene conservation, measured both by the evolutionary retention index (ERI) and by evolutionary pressures (evaluated through the ratio $K_a/K_s$ and ENC plots) is related to the the connectivity of the corresponding protein; iii) how PPI connectivities are modulated by evolutionary and functional relationships, as represented by the Clusters of Orthologous Proteins (COGs). We show that conservation, essentiality and functional specialization of genes control in a quite universal way the topology of the emerging bacterial PPI networks. Noteworthy, a structural transition in the network is observed such that, for connectivities $k\ge40$, bacterial PPI networks are mostly populated by genes that are conserved, essential and which, in most cases, belong to the COG cluster J, related to ribosomal functions and to the processing of genetic information