Stability threshold approach for complex dynamical systems

Acknowledgments This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP, and supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with the Institute of Applied Physics RAS). The first author thanks Dr Roman Ovsyannikov for valuable discussions regarding estimation of the mistake probability.

On the acidity and reactivity of HNO in aqueous solution and biological systems

The gas phase and aqueous thermochemistry and reactivity of nitroxyl (nitrosyl hydride, HNO) were elucidated with multiconfigurational self-consistent field and hybrid density functional theory calculations and continuum solvation methods. The pKa of HNO is predicted to be 7.2 ± 1.0, considerably different from the value of 4.7 reported from pulse radiolysis experiments. The ground-state triplet nature of NO− affects the rates of acid-base chemistry of the HNO/NO− couple. HNO is highly reactive toward dimerization and addition of soft nucleophiles but is predicted to undergo negligible hydration (Keq = 6.9 × 10−5). HNO is predicted to exist as a discrete species in solution and is a viable participant in the chemical biology of nitric oxide and derivatives.

Reverse biochemistry: Use of macromolecular protease inhibitors to dissect complex biological processes and identify a membrane-type serine protease in epithelial cancer and normal tissue

Serine proteases of the chymotrypsin fold are of great interest because they provide detailed understanding of their enzymatic properties and their proposed role in a number of physiological and pathological processes. We have been developing the macromolecular inhibitor ecotin to be a “fold-specific” inhibitor that is selective for members of the chymotrypsin-fold class of proteases. Inhibition of protease activity through the use of wild-type and engineered ecotins results in inhibition of rat prostate differentiation and retardation of the growth of human PC-3 prostatic cancer tumors. In an effort to identify the proteases that may be involved in these processes, reverse transcription–PCR with PC-3 poly(A)+ mRNA was performed by using degenerate oligonucleotide primers. These primers were designed by using conserved protein sequences unique to chymotrypsin-fold serine proteases. Five proteases were identified: urokinase-type plasminogen activator, factor XII, protein C, trypsinogen IV, and a protease that we refer to as membrane-type serine protease 1 (MT-SP1). The cloning and characterization of the MT-SP1 cDNA shows that it encodes a mosaic protein that contains a transmembrane signal anchor, two CUB domains, four LDLR repeats, and a serine protease domain. Northern blotting shows broad expression of MT-SP1 in a variety of epithelial tissues with high levels of expression in the human gastrointestinal tract and the prostate. A His-tagged fusion of the MT-SP1 protease domain was expressed in Escherichia coli, purified, and autoactivated. Ecotin and variant ecotins are subnanomolar inhibitors of the MT-SP1 activated protease domain, suggesting a possible role for MT-SP1 in prostate differentiation and the growth of prostatic carcinomas.

Sticky ions in biological systems.

Aqueous gel sieving chromatography on Sephadex G-10 of the Group IA cations (Li+, Na+, K+, Rb+, Cs+) plus NH4+ as the Cl- salts, in combination with previous results for the halide anions (F-, Cl-, Br-, I-) as the Na+ salts [Washabaugh, M.W. & Collins, K.D. (1986) J. Biol. Chem. 261, 12477-12485], leads to the following conclusions. (i) The small monovalent ions (Li+, Na+, F-) flow through the gel with water molecules attached, whereas the large monovalent ions (K+, Rb+, Cs+, Cl-, Br-, I-) adsorb to the nonpolar surface of the gel, a process requiring partial dehydration of the ion and implying that these ions bind the immediately adjacent water molecules weakly. (ii) The transition from strong to weak hydration occurs at a radius of about 1.78 A for the monovalent anions, compared with a radius of about 1.06 A for the monovalent cations (using ionic radii), indicating that the anions are more strongly hydrated than the cations for a given charge density. (iii) The anions show larger deviations from ideal behavior (an elution position corresponding to the anhydrous molecular weight) than do the cations and dominate the chromatographic behavior of the neutral salts. These results are interpreted to mean that weakly hydrated ions (chaotropes) are "pushed" onto weakly hydrated surfaces by strong water-water interactions and that the transition from strong ionic hydration to weak ionic hydration occurs where the strength of ion-water interactions approximately equals the strength of water-water interactions in bulk solution.

Topological structures of complex belief systems

The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join-semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology.

Topological structures of complex belief systems (II): Textual materialization

Mythical and religious belief systems in a social context can be regarded as a conglomeration of sacrosanct rites, which revolve around substantive values that involve an element of faith. Moreover, we can conclude that ideologies, myths and beliefs can all be analyzed in terms of systems within a cultural context. The significance of being able to define ideologies, myths and beliefs as systems is that they can figure in cultural explanations. This, in turn, means that such systems can figure in logic-mathematical analyses.

Shock tube studies of the effects of sharp-rising, long-duration overpressures on biological systems /

Shock tubes have been used successfully by a number of investigators to study the biological effects of variations in environmental pressures (1,2,3). Recently an unusually versatile laboratory pressurization source became available with the capability of consistently reproducing a wide variety of pressure-time phenomena of durations equal to and well beyond those associated with the detonation of nuclear devices (4). Thus it became possible to supplement costly full-scale field research in blast biology carried out at the Nevada Test Site (5,6) by using an economical yet realistic laboratory tool. In one exploratory study employing pressure pulses of 5 to 10 sec duration wherein the times to max overpressure and the magnitudes of the overpressures were varied, a relatively high tolerance of biological media to pressures well over 150 psi was demonstrated (7). In contrast, the present paper will describe the relatively high biological susceptibility to long duration overpressures in which the pressure rises occurred in single and double fast-rising steps.

The prediction and representation of phase equilibria and physicochemical properties in complex slag systems

The development of new experimental techniques for the determination of phase equilibria in complex slag systems, chemical thermodynamic, and viscosity models is reported. The new experimental data, and new thermodynamic and viscosity models, have been combined in a custom-designed computer software package to produce limiting operability diagrams for slag systems. These diagrams are used to describe phase equilibria and physicochemical properties in complex slag systems. The approach is illustrated with calculations on the system FeO-Fe2O3-CaO-SiO-Al2O3 at metallic iron saturation, slags produced in coal slagging gasifiers, and in the reprocessing of nonferrous smelting slags. This article was presented at the Mills Symposium Molten Metals, Slags and Glasses-Characterisation of Properties and Phenomena held in London in August 2000.

Robustness of mathematical models for biological systems

The robustness of mathematical models for biological systems is studied by sensitivity analysis and stochastic simulations. Using a neural network model with three genes as the test problem, we study robustness properties of synthesis and degradation processes. For single parameter robustness, sensitivity analysis techniques are applied for studying parameter variations and stochastic simulations are used for investigating the impact of external noise. Results of sensitivity analysis are consistent with those obtained by stochastic simulations. Stochastic models with external noise can be used for studying the robustness not only to external noise but also to parameter variations. For external noise we also use stochastic models to study the robustness of the function of each gene and that of the system.