Propagation of fluctuations in interaction networks governed by the law of mass action

Using an example of physical interactions between proteins, we study how perturbations propagate in interconnected networks whose equilibrium state is governed by the law of mass action. We introduce a comprehensive matrix formalism which predicts the response of this equilibrium to small changes in total concentrations of individual molecules, and explain it using a heuristic analogy to a current flow in a network of resistors. Our main conclusion is that on average changes in free concentrations exponentially decay with the distance from the source of perturbation. We then study how this decay is influenced by such factors as the topology of a network, binding strength, and correlations between concentrations of neighboring nodes. An exact analytic expression for the decay constant is obtained for the case of uniform interactions on the Bethe lattice. Our general findings are illustrated using a real biological network of protein-protein interactions in baker's yeast with experimentally determined protein concentrations.Comment: 4 pages; 2 figure

On the superfluidity of classical liquid in nanotubes

In 2001, the author proposed the ultra second quantization method. The ultra second quantization of the Schr\"odinger equation, as well as its ordinary second quantization, is a representation of the N-particle Schr\"odinger equation, and this means that basically the ultra second quantization of the equation is the same as the original N-particle equation: they coincide in 3N-dimensional space. We consider a short action pairwise potential V(x_i -x_j). This means that as the number of particles tends to infinity, $N\to\infty$, interaction is possible for only a finite number of particles. Therefore, the potential depends on N in the following way: $V_N=V((x_i-x_j)N^{1/3})$. If V(y) is finite with support $\Omega_V$, then as $N\to\infty$ the support engulfs a finite number of particles, and this number does not depend on N. As a result, it turns out that the superfluidity occurs for velocities less than $\min(\lambda_{\text{crit}}, \frac{h}{2mR})$, where $\lambda_{\text{crit}}$ is the critical Landau velocity and R is the radius of the nanotube.Comment: Latex, 20p. The text is presented for the International Workshop "Idempotent and tropical mathematics and problems of mathematical physics", Independent University of Moscow, Moscow, August 25--30, 2007 and to be published in the Russian Journal of Mathematical Physics, 2007, vol. 15, #

Expansion Around the Mean-Field Solution of the Bak-Sneppen Model

We study a recently proposed equation for the avalanche distribution in the Bak-Sneppen model. We demonstrate that this equation indirectly relates $\tau$,the exponent for the power law distribution of avalanche sizes, to $D$, the fractal dimension of an avalanche cluster.We compute this relation numerically and approximate it analytically up to the second order of expansion around the mean field exponents. Our results are consistent with Monte Carlo simulations of Bak-Sneppen model in one and two dimensions.Comment: 5 pages, 2 ps-figures iclude

Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are added. arXiv admin note: significant text overlap with arXiv:1111.610

Hierarchy Measures in Complex Networks

Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally hierarchical. Comparison with these extremal cases as well as with random scale-free networks allows us to better understand hierarchical versus modular features in several real-life complex networks. For random scale-free topologies the extent of topological hierarchy is shown to smoothly decline with $\gamma$ -- the exponent of a degree distribution -- reaching its highest possible value for $\gamma \leq 2$ and quickly approaching zero for $\gamma>3$.Comment: 4 pages, 4 figure

Promise and Pitfalls of Extending Google's PageRank Algorithm to Citation Networks

We review our recent work on applying the Google PageRank algorithm to find scientific "gems" among all Physical Review publications, and its extension to CiteRank, to find currently popular research directions. These metrics provide a meaningful extension to traditionally-used importance measures, such as the number of citations and journal impact factor. We also point out some pitfalls of over-relying on quantitative metrics to evaluate scientific quality.Comment: 3 pages, 1 figure, invited comment for the Journal of Neuroscience. The arxiv version is microscopically different from the published versio

Leishmania tarentolae: taxonomic classification and its application as a promising biotechnological expression host

In this review, we summarize the current knowledge concerning the eukaryotic protozoan parasite Leishmania tarentolae, with a main focus on its potential for biotechnological applications. We will also discuss the genus, subgenus, and species-level classification of this parasite, its life cycle and geographical distribution, and similarities and differences to human-pathogenic species, as these aspects are relevant for the evaluation of biosafety aspects of L. tarentolae as host for recombinant DNA/protein applications. Studies indicate that strain LEM-125 but not strain TARII/UC of L. tarentolae might also be capable of infecting mammals, at least transiently. This could raise the question of whether the current biosafety level of this strain should be reevaluated. In addition, we will summarize the current state of biotechnological research involving L. tarentolae and explain why this eukaryotic parasite is an advantageous and promising human recombinant protein expression host. This summary includes overall biotechnological applications, insights into its protein expression machinery (especially on glycoprotein and antibody fragment expression), available expression vectors, cell culture conditions, and its potential as an immunotherapy agent for human leishmaniasis treatment. Furthermore, we will highlight useful online tools and, finally, discuss possible future applications such as the humanization of the glycosylation profile of L. tarentolae or the expression of mammalian recombinant proteins in amastigotelike cells of this species or in amastigotes of avirulent human-pathogenic Leishmania species