A novel iterative strategy for protein design

We propose and discuss a novel strategy for protein design. The method is based on recent theoretical advancements which showed the importance to treat carefully the conformational free energy of designed sequences. In this work we show how computational cost can be kept to a minimum by encompassing negative design features, i.e. isolating a small number of structures that compete significantly with the target one for being occupied at low temperature. The method is succesfully tested on minimalist protein models and using a variety of amino acid interaction potentials.Comment: 9 pages, 8 figure

Phase diagram of force-induced DNA unzipping in exactly solvable models

The mechanical separation of the double helical DNA structure induced by forces pulling apart the two DNA strands (``unzipping'') has been the subject of recent experiments. Analytical results are obtained within various models of interacting pairs of directed walks in the (1,1,...,1) direction on the hypercubic lattice, and the phase diagram in the force-temperature plane is studied for a variety of cases. The scaling behaviour is determined at both the unzipping and the melting transition. We confirm the existence of a cold denaturation transition recently observed in numerical simulations: for a finite range of forces the system gets unzipped by {\it decreasing} the temperature. The existence of this transition is rigorously established for generic lattice and continuum space models.Comment: 19 pages, 5 eps figures; revised version with minor changes, presentation simplified in the text with details in appendix. Accepted for publication in Phys. Rev.

Swollen-Collapsed Transition in Random Hetero-Polymers

A lattice model of a hetero-polymer with random hydrophilic-hydrophobic charges interacting with the solvent is introduced, whose continnuum counterpart has been proposed by T. Garel, L. Leibler and H. Orland {J. Phys. II France 4, 2139 (1994)]. The transfer matrix technique is used to study various constrained annealed systems which approximate at various degrees of accuracy the original quenched model. For highly hydrophobic chains an ordinary $\theta$-point transition is found from a high temperature swollen phase to a low temperature compact phase. Depending on the type of constrained averages, at very low temperatures a swollen phase or a coexistence between compact and swollen phases are found. The results are carefully compared with the corresponding ones obtained in the continuum limit, and various improvements in the original calculations are discussed.Comment: 13 pages, 8 figures; revised version with minor changes, accepted for publication in European Physical Journal

Global protein function prediction in protein-protein interaction networks

The determination of protein functions is one of the most challenging problems of the post-genomic era. The sequencing of entire genomes and the possibility to access gene's co-expression patterns has moved the attention from the study of single proteins or small complexes to that of the entire proteome. In this context, the search for reliable methods for proteins' function assignment is of uttermost importance. Previous approaches to deduce the unknown function of a class of proteins have exploited sequence similarities or clustering of co-regulated genes, phylogenetic profiles, protein-protein interactions, and protein complexes. We propose to assign functional classes to proteins from their network of physical interactions, by minimizing the number of interacting proteins with different categories. The function assignment is made on a global scale and depends on the entire connectivity pattern of the protein network. Multiple functional assignments are made possible as a consequence of the existence of multiple equivalent solutions. The method is applied to the yeast Saccharomices Cerevisiae protein-protein interaction network. Robustness is tested in presence of a high percentage of unclassified proteins and under deletion/insertion of interactions.Comment: 5 pages, 2 figures, 2 supplementary table

Heteropolymers in a Solvent at an Interface

Exact bounds are obtained for the quenched free energy of a polymer with random hydrophobicities in the presence of an interface separating a polar from a non polar solvent. The polymer may be ideal or have steric self-interactions. The bounds allow to prove that a ``neutral'' random polymer is localized near the interface at any temperature, whereas a ``non-neutral'' chain is shown to undergo a delocalization transition at a finite temperature. These results are valid for a quite general a priori probability distribution for both independent and correlated hydrophobic charges. As a particular case we consider random AB-copolymers and confirm recent numerical studies.Comment: 4 pages, no figure

Species lifetime distribution for simple models of ecologies

Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher order taxa, such as families or genera, follow a broader distribution, compatible with power law decay. We show that both these evidences are consistent with a simple evolutionary model that does not require specific assumptions on species interaction. The model provides a zero-order description of the dynamics of ecological communities and its species lifetime distribution can be computed exactly. Different behaviors are found: an initial $t^{-3/2}$ power law, emerging from a random walk type of dynamics, which crosses over to a steeper $t^{-2}$ branching process-like regime and finally is cutoff by an exponential decay which becomes weaker and weaker as the total population increases. Sampling effects can also be taken into account and shown to be relevant: if species in the fossil record were sampled according to the Fisher log-series distribution, lifetime should be distributed according to a $t^{-1}$ power law. Such variability of behaviors in a simple model, combined with the scarcity of data available, cast serious doubts on the possibility to validate theories of evolution on the basis of species lifetime data.Comment: 19 pages, 2 figure

Hidden scaling patterns and universality in written communication

The temporal statistics exhibited by written correspondence appear to be media dependent, with features which have so far proven difficult to characterize. We explain the origin of these difficulties by disentangling the role of spontaneous activity from decision-based prioritizing processes in human dynamics, clocking all waiting times through each agent's `proper time' measured by activity. This unveils the same fundamental patterns in written communication across all media (letters, email, sms), with response times displaying truncated power-law behavior and average exponents near -3/2. When standard time is used, the response time probabilities are theoretically predicted to exhibit a bi-modal character, which is empirically borne out by our new years-long data on email. These novel perspectives on the temporal dynamics of human correspondence should aid in the analysis of interaction phenomena in general, including resource management, optimal pricing and routing, information sharing, emergency handling.Comment: 27 pages, 10 figure

Entropy production in systems with unidirectional transitions

The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each transition between two states also the reverse one is allowed. Nevertheless, several physical systems may exhibit a mixture of both unidirectional and bidirectional transitions, and how to properly define the entropy production in this case is still an open question. Here, we present a solution to such a challenging problem. The average entropy production can be consistently defined, employing a mapping that preserves the average fluxes, and its physical interpretation is provided. We describe a class of stochastic systems composed of unidirectional links forming cycles and detailed-balanced bidirectional links, showing that they behave in a pseudo-deterministic fashion. This approach is applied to a system with time-dependent stochastic resetting. Our framework is consistent with thermodynamics and leads to some intriguing observations on the relation between the arrow of time and the average entropy production for resetting events.Comment: (Accepted for publication in Physical Review Research

Geometry of compact tubes and protein structures

Proteins form a very important class of polymers. In spite of major advances in the understanding of polymer science, the protein problem has remained largely unsolved. Here, we show that a polymer chain viewed as a tube not only captures the well-known characteristics of polymers and their phases but also provides a natural explanation for many of the key features of protein behavior. There are two natural length scales associated with a tube subject to compaction -- the thickness of the tube and the range of the attractive interactions. For short tubes, when these length scales become comparable, one obtains marginally compact structures, which are relatively few in number compared to those in the generic compact phase of polymers. The motifs associated with the structures in this new phase include helices, hairpins and sheets. We suggest that Nature has selected this phase for the structures of proteins because of its many advantages including the few candidate strucures, the ability to squeeze the water out from the hydrophobic core and the flexibility and versatility associated with being marginally compact. Our results provide a framework for understanding the common features of all proteins.Comment: 15 pages, 3 eps figure