We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations ("classics") are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The "tipping point" at which a paper becomes a classic is about 25 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 31 for Physical Review D papers published from 1975-1994, and 37 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited.C ommonly observed in nature and in the social sciences are probability distribution functions that appear to involve dual underlying mechanisms, with a "tipping point" between them. Examples of such probability distributions include the distributions of city sizes (1, 2); fluctuations in stock market indices (3, 4); U.S. firm sizes (5, 6); degrees of Internet nodes (7, 8); numbers of followers of religions (8); gamma-ray intensities of solar flares (9); sightings of bird species (8); and citations of scientific papers (10-13). In these situations, a distribution pðkÞ may have exponential behavior for small k and a power-law tail for large k. Here we develop a generative model for one such dual-mechanism process, scientific citations, for which databases are large and readily available. Here, k represents the number of citations a paper receives, ranging from zero to hundreds or, sometimes, thousands. pðkÞ is the distribution of the relative numbers of such citations, taken over a database of papers.There have been several important studies of power-law tails of distributions, including those involving scientific citations. Price noted that highly cited scientific papers accumulate additional citations more quickly than papers that have fewer citations (14). He called this "cumulative advantage" (CA): the probability that a paper receives a citation is proportional to the number of citations it already contains. Price showed that this rule asymptotically gives a power law for large k. Power-law tails have been widely explored in various contexts and under different names -"the rich get richer," the Yule process (15, 16), the Matthew effect (17), or preferential attachment (18). Barabási and Albert noted that networks, such as the World Wide Web, often have power-law distributions of vertex connectivities, called "scalefree" behavior (18). Their model, called preferential attachment, leads to a fixed power-law exponent of −3. Because many propertie...

Some human cancers maintain telomeres using alternative lengthening of telomeres (ALT), a process thought to be due to recombination. In Kluyveromyces lactis mutants lacking telomerase, recombinational telomere elongation (RTE) is induced at short telomeres but is suppressed once telomeres are moderately elongated by RTE. Recent work has shown that certain telomere capping defects can trigger a different type of RTE that results in much more extensive telomere elongation that is reminiscent of human ALT cells. In this study, we generated telomeres composed of either of two types of mutant telomeric repeats, Acc and SnaB, that each alter the binding site for the telomeric protein Rap1. We show here that arrays of both types of mutant repeats present basally on a telomere were defective in negatively regulating telomere length in the presence of telomerase. Similarly, when each type of mutant repeat was spread to all chromosome ends in cells lacking telomerase, they led to the formation of telomeres produced by RTE that were much longer than those seen in cells with only wild-type telomeric repeats. The Acc repeats produced the more severe defect in both types of telomere maintenance, consistent with their more severe Rap1 binding defect. Curiously, although telomerase deletion mutants with telomeres composed of Acc repeats invariably showed extreme telomere elongation, they often also initially showed persistent very short telomeres with few or no Acc repeats. We suggest that these result from futile cycles of recombinational elongation and truncation of the Acc repeats from the telomeres. The presence of extensive 3 overhangs at mutant telomeres suggests that Rap1 may normally be involved in controlling 5 end degradation.

We model the evolution of eukaryotic protein-protein interaction (PPI) networks. In our model, PPI networks evolve by two known biological mechanisms: (1) Gene duplication, which is followed by rapid diversification of duplicate interactions. (2) Neofunctionalization, in which a mutation leads to a new interaction with some other protein. Since many interactions are due to simple surface compatibility, we hypothesize there is an increased likelihood of interacting with other proteins in the target protein’s neighborhood. We find good agreement of the model on 10 different network properties compared to high-confidence experimental PPI networks in yeast, fruit flies, and humans. Key findings are: (1) PPI networks evolve modular structures, with no need to invoke particular selection pressures. (2) Proteins in cells have on average about 6 degrees of separation, similar to some social networks, such as human-communication and actor networks. (3) Unlike social networks, which have a shrinking diameter (degree of maximum separation) over time, PPI networks are predicted to grow in diameter. (4) The model indicates that evolutionarily old proteins should have higher connectivities and be more centrally embedded in their networks. This suggests a way in which present-day proteomics data could provide insights into biological evolution.

Scien, 23,13-47, 2004). Usually the rate of this process is predicted using QSAR or other knowledge-based predictors (R Gozalbes, et al., Bioorganic & Med Chem,19, 2615-2624, 2011. However, this approach is not always accurate. Moreover, it does not provide the atomistic details of the process, and thus its prediction cannot be directly exploited to rationally design drugs with higher permeation rate. We developed a protocol for studying the permeation of small organic molecules (e.g. drugs) through lipid membranes by atomistic simulations. This protocol allows computing accurately the permeability coefficient, and provides a detailed atomistic picture of the process. The approach is based on an enhanced sampling technique, bias exchange metadynamics (S. Piana and A. Laio, J Phys Chem B, 111, 4553-4559, 2007), that allows deriving from atomistic simulations a multidimensional free energy landscape and an accurate kinetic model describing the transitions between the relevant metastable states of the system (F Marinelli, et al., Plos Comp Biol, 5, e1000452, 2009). As a benchmark, we applied this protocol on the permeation of ethanol through palmitoyloleoylphosphatidylcholine (POPC) membrane. We are applying the same procedure to study the permeation of two anti-HIV drugs where unbiased simulation of the permeation process is not possible.