On the Measurement of Cooperativity and the Physico-Chemical Meaning of the Hill Coefficient.

Cooperative ligand binding is a fundamental property of many biological macromolecules, notably transport proteins, hormone receptors, and enzymes. Positive homotropic cooperativity, the form of cooperativity that has greatest physiological relevance, causes the ligand affinity to increase as ligation proceeds, thus increasing the steepness of the ligand-binding isotherm. The measurement of the extent of cooperativity has proven difficult, and the most commonly employed marker of cooperativity, the Hill coefficient, originates from a structural hypothesis that has long been disproved. However, a wealth of relevant biochemical data has been interpreted using the Hill coefficient and is being used in studies on evolution and comparative physiology. Even a cursory analysis of the pertinent literature shows that several authors tried to derive more sound biochemical information from the Hill coefficient, often unaware of each other. As a result, a perplexing array of equations interpreting the Hill coefficient is available in the literature, each responding to specific simplifications or assumptions. In this work, we summarize and try to order these attempts, and demonstrate that the Hill coefficient (i) provides a minimum estimate of the free energy of interaction, the other parameter used to measure cooperativity, and (ii) bears a robust statistical correlation to the population of incompletely saturated ligation intermediates. Our aim is to critically evaluate the different analyses that have been advanced to provide a physical meaning to the Hill coefficient, and possibly to select the most reliable ones to be used in comparative studies that may make use of the extensive but elusive information available in the literature.

Stationary growth and unique invariant harmonic measure of cylindrical diffusion limited aggregation.

We prove that the harmonic measure is stationary, unique, and invariant on the interface of diffusion limited aggregation (DLA) growing on a cylinder surface. We provide a detailed theoretical analysis puzzling together multiscaling, multifractality, and conformal invariance, supported by extensive numerical simulations of clusters built using conformal mappings and on a lattice. The growth properties of the active and frozen zones are clearly elucidated. We show that the unique scaling exponent characterizing the stationary growth is the DLA fractal dimension.

A stochastic local search algorithm for distance-based phylogeny reconstruction.

In many interesting cases, the reconstruction of a correct phylogeny is blurred by high mutation rates and/or horizontal transfer events. As a consequence, a divergence arises between the true evolutionary distances and the differences between pairs of taxa as inferred from available data, making the phylogenetic reconstruction a challenging problem. Mathematically, this divergence translates in a loss of additivity of the actual distances between taxa. In distance-based reconstruction methods, two properties of additive distances have been extensively exploited as antagonist criteria to drive phylogeny reconstruction: On the one hand, a local property of quartets, that is, sets of four taxa in a tree, the four-points condition; on the other hand, a recently proposed formula that allows to write the tree length as a function of the distances between taxa, Pauplin's formula. Here, we introduce a new reconstruction scheme that exploits in a unified framework both the four-points condition and the Pauplin's formula. We propose, in particular, a new general class of distance-based Stochastic Local Search algorithms, which reduces in a limit case to the minimization of Pauplin's length. When tested on artificially generated phylogenies, our Stochastic Big-Quartet Swapping algorithmic scheme significantly outperforms state-of-art distance-based algorithms in cases of deviation from additivity due to high rate of back mutations. A significant improvement is also observed with respect to the state-of-art algorithms in the case of high rate of horizontal transfer.

Compressing proteomes: the relevance of medium range correlations.

We study the nonrandomness of proteome sequences by analysing the correlations that arise between amino acids at a short and medium range, more specifically, between amino acids located 10 or 100 residues apart; respectively. We show that statistical models that consider these two types of correlation are more likely to seize the information contained in protein sequences and thus achieve good compression rates. Finally, we propose that the cause for this redundancy is related to the evolutionary origin of proteomes and protein sequences.

Language trees and zipping.

In this Letter we present a very general method for extracting information from a generic string of characters, e.g., a text, a DNA sequence, or a time series. Based on data-compression techniques, its key point is the computation of a suitable measure of the remoteness of two bodies of knowledge. We present the implementation of the method to linguistic motivated problems, featuring highly accurate results for language recognition, authorship attribution, and language classification.