Searching for generic behaviors has been one of the driving forces leading to a deep understanding and classification of diverse phenomena. Usually a starting point is the development of a phenomenology based on observations. Such is the case for power law distributions encountered in a wealth of situations coming from physics, geophysics, biology, lexicography as well as social and financial networks. This finding is however restricted to a range of values outside of which finite size corrections are often invoked. Here we uncover a universal behavior of the way in which elements of a system are distributed according to their rank with respect to a given property, valid for the full range of values, regardless of whether or not a power law has previously been suggested. We propose a two parameter functional form for these rank-ordered distributions that gives excellent fits to an impressive amount of very diverse phenomena, coming from the arts, social and natural sciences. It is a discrete version of a generalized beta distribution, given by f(r) = A(N+1-r)^b/r^a, where r is the rank, N its maximum value, A the normalization constant and (a, b) two fitting exponents. Prompted by our genetic sequence observations we present a growth probabilistic model incorporating mutation-duplication features that generates data complying with this distribution. The competition between permanence and change appears to be a relevant, though not necessary feature. Additionally, our observations mainly of social phenomena suggest that a multifactorial quality resulting from the convergence of several heterogeneous underlying processes is an important feature. We also explore the significance of the distribution parameters and their classifying potential. The ubiquity of our findings suggests that there must be a fundamental underlying explanation, most probably of a statistical nature, such as an appropriate central limit theorem formulation.

Spermatozoa sea urchin swimming behaviour is regulated by small peptides from the egg outer envelope. Speract, such a peptide, after binding to its receptor inStrongylocentrotus purpuratussperm flagella, triggers a signaling pathway that culminates with a train of intracellular calcium oscillations, correlated with changes in sperm swimming pattern. This pathway has been widely studied but not fully characterized. Recent work onArbacia punctulatasea urchin spermatozoa has documented the presence of the Ca²⁺CatSper channel in their flagella and its involvement in chemotaxis. However, if other calcium channels participate in chemotaxis remains unclear. Here, based on an experimentally-backed logical network model, we conclude that CatSper is fundamental in theS. purpuratussperact-activated sea urchin sperm signaling cascade, although other Ca²⁺channels could still be relevant. We also present for the first time experimental corroboration of its active presence inS. purpuratussperm flagella. We argue, prompted byin silicoknock-out calculations, that CatSper is the main generator of calcium oscillations in the signaling pathway and that other calcium channels, if present, have a complementary role. The approach adopted here allows us to unveil processes, which are hard to detect exclusively by experimental procedures.

The dynamical exponent z for a single polymer chain in good and theta solvents is obtained to order ε (= 4 - d) for the bead-spring (Rouse-Zimm) model by means of a renormalization transformation along the chain. In the free-draining limit z = 4 - ε/4 + … for a good solvent. In the non-draining limit z = 4 - ε + … for both good and theta solvents, all in agreement with the phenomenological predictions of de Gennes

Understanding how spermatozoa approach the egg is a central biological issue. Recently a considerable amount of experimental evidence has accumulated on the relation between oscillations in intracellular calcium ion concentration ([Ca ] ) in the sea urchin sperm flagellum, triggered by peptides secreted from the egg, and sperm motility. Determination of the structure and dynamics of the signaling pathway leading to these oscillations is a fundamental problem. However, a biochemically based formulation for the comprehension of the molecular mechanisms operating in the axoneme as a response to external stimulus is still lacking. Based on experiments on the S. purpuratus sea urchin spermatozoa, we propose a signaling network model where nodes are discrete variables corresponding to the pathway elements and the signal transmission takes place at discrete time intervals according to logical rules. The validity of this model is corroborated by reproducing previous empirically determined signaling features. Prompted by the model predictions we performed experiments which identified novel characteristics of the signaling pathway. We uncovered the role of a high voltage-activated channel as a regulator of the delay in the onset of fluctuations after activation of the signaling cascade. This delay time has recently been shown to be an important regulatory factor for sea urchin sperm reorientation. Another finding is the participation of a voltage-dependent calcium-activated channel in the determination of the period of the fluctuations. Furthermore, by analyzing the spread of network perturbations we find that it operates in a dynamically critical regime. Our work demonstrates that a coarse-grained approach to the dynamics of the signaling pathway is capable of revealing regulatory sperm navigation elements and provides insight, in terms of criticality, on the concurrence of the high robustness and adaptability that the reproduction processes are predicted to have developed throughout evolution.