Mathematical modeling of combinatorial regulation suggests that apparent positive regulation of targets by miRNA could be an artifact resulting from competition for mRNA

MicroRNAs bind to and regulate the abundance and activity of target messenger RNA through sequestration, enhanced degradation, and suppression of translation. Although miRNA have a predominantly negative effect on the target protein concentration, several reports have demonstrated a positive effect of miRNA, i.e., increase in target protein concentration on miRNA overexpression and decrease in target concentration on miRNA repression. miRNA–target pair-specific effects such as protection of mRNA degradation owing to miRNA binding can explain some of these effects. However, considering such pairs in isolation might be an oversimplification of the RNA biology, as it is known that one miRNA interacts with several targets, and conversely target mRNA are subject to regulation by several miRNAs. We formulate a mathematical model of this combinatorial regulation of targets by multiple miRNA. Through mathematical analysis and numerical simulations of this model, we show that miRNA that individually have a negative effect on their targets may exhibit an apparently positive net effect when the concentration of one miRNA is experimentally perturbed by repression/overexpression in such a multi-miRNA multitarget situation. We show that this apparent unexpected effect is due to competition and will not be observed when miRNA interact noncompetitively with the target mRNA. This result suggests that some of the observed unusual positive effects of miRNA may be due to the combinatorial complexity of the system rather than due to any inherently unusual positive effect of the miRNA on its target.     

Validation of fractal-like kinetic models by time-resolved binding kinetics of dansylamide and carbonic anhydrase in crowded media

Kinetic studies of biochemical reactions are typically carried out in a dilute solution that rarely contains anything more than reactants, products, and buffers. In such studies, mass-action-based kinetic models are used to analyze the progress curves. However, intracellular compartments are crowded by macromolecules. Therefore, we investigated the adequacy of the proposed generalizations of the mass-action model, which are meant to describe reactions in crowded media. To validate these models, we measured time-resolved kinetics for dansylamide binding to carbonic anhydrase in solutions crowded with polyethylene glycol and Ficoll. The measured progress curves clearly show the effects of crowding. The fractal-like model proposed by Savageau was used to fit these curves. In this model, the association rate coefficient k_a allometrically depends on concentrations of reactants. We also considered the fractal kinetic model proposed by Schnell and Turner, in which k_a depends on time according to a Zipf-Mandelbrot distribution, and some generalizations of these models. We found that the generalization of the mass-action model, in which association and dissociation rate coefficients are concentration-dependent, represents the preferred model. Other models based on time-dependent rate coefficients were inadequate or not preferred by model selection criteria.     

Parameterization and classification of the protein universe via geometric techniques

We present a scheme for the classification of 3487 non-redundant protein structures into 1207 non-hierarchical clusters by using recurring structural patterns of three to six amino acids as keys of classification. This results in several signature patterns, which seem to decide membership of a protein in a functional category. The patterns provide clues to the key residues involved in functional sites as well as in protein-protein interaction. The discovered patterns include a "glutamate double bridge" of superoxide dismutase, the functional interface of the serine protease and inhibitor, interface of homo/hetero dimers, and functional sites of several enzyme families. We use geometric invariants to decide superimposability of structural patterns. This allows the parameterization of patterns and discovery of recurring patterns via clustering. The geometric invariant-based approach eliminates the computationally explosive step of pair-wise comparison of structures. The results provide a vast resource for the biologists for experimental validation of the proposed functional sites, and for the design of synthetic enzymes, inhibitors and drugs.     

A stochastic analysis of first-order reaction networks

A stochastic model for a general system of first-order reactions in which each reaction may be either a conversion reaction or a catalytic reaction is derived. The governing master equation is formulated in a manner that explicitly separates the effects of network topology from other aspects, and the evolution equations for the first two moments are derived. We find the surprising, and apparently unknown, result that the time evolution of the second moments can be represented explicitly in terms of the eigenvalues and projections of the matrix that governs the evolution of the means. The model is used to analyze the effects of network topology and the reaction type on the moments of the probability distribution. In particular, it is shown that for an open system of first-order conversion reactions, the distribution of all the system components is a Poisson distribution at steady state. Two different measures of the noise have been used previously, and it is shown that different qualitative and quantitative conclusions can result, depending on which measure is used. The effect of catalytic reactions on the variance of the system components is also analyzed, and the master equation for a coupled system of first-order reactions and diffusion is derived. All authors contributed equally to this work.     

A synthetic S6 segment derived from KvAP channel self-assembles, permeabilizes lipid vesicles, and exhibits ion channel activity in bilayer lipid membrane

KvAP is a voltage-gated tetrameric K(+) channel with six transmembrane (S1-S6) segments in each monomer from the archaeon Aeropyrum pernix. The objective of the present investigation was to understand the plausible role of the S6 segment, which has been proposed to form the inner lining of the pore, in the membrane assembly and functional properties of KvAP channel. For this purpose, a 22-residue peptide, corresponding to the S6 transmembrane segment of KvAP (amino acids 218-239), and a scrambled peptide (S6-SCR) with rearrangement of only hydrophobic amino acids but without changing its composition were synthesized and characterized structurally and functionally. Although both peptides bound to the negatively charged phosphatidylcholine/phosphatidylglycerol model membrane with comparable affinity, significant differences were observed between these peptides in their localization, self-assembly, and aggregation properties onto this membrane. S6-SCR also exhibited reduced helical structures in SDS micelles and phosphatidylcholine/phosphatidylglycerol lipid vesicles as compared with the S6 peptide. Furthermore, the S6 peptide showed significant membrane-permeabilizing capability as evidenced by the release of calcein from the calcein-entrapped lipid vesicles, whereas S6-SCR showed much weaker efficacy. Interestingly, although the S6 peptide showed ion channel activity in the bilayer lipid membrane, despite having the same amino acid composition, S6-SCR was significantly inactive. The results demonstrated sequence-specific structural and functional properties of the S6 wild type peptide. The selected S6 segment is probably an important structural element that could play an important role in the membrane interaction, membrane assembly, and functional property of the KvAP channel.