Control of Spatially Heterogeneous and Time-Varying Cellular Reaction Networks: A New Summation Law

A hallmark of a plethora of intracellular signaling pathways is the spatial separation of activation and deactivation processes that potentially results in precipitous gradients of activated proteins. The classical Metabolic Control Analysis (MCA), which quantifies the influence of an individual process on a system variable as the control coefficient, cannot be applied to spatially separated protein networks. The present paper unravels the principles that govern the control over the fluxes and intermediate concentrations in spatially heterogeneous reaction networks. Our main results are two types of the control summation theorems. The first type is a non-trivial generalization of the classical theorems to systems with spatially and temporally varying concentrations. In this generalization, the process of diffusion, which enters as the result of spatial concentration gradients, plays a role similar to other processes such as chemical reactions and membrane transport. The second summation theorem is completely novel. It states that the control by the membrane transport, the diffusion control coefficient multiplied by two, and a newly introduced control coefficient associated with changes in the spatial size of a system (e.g., cell), all add up to one and zero for the control over flux and concentration. Using a simple example of a kinase/phosphatase system in a spherical cell, we speculate that unless active mechanisms of intracellular transport are involved, the threshold cell size is limited by the diffusion control, when it is beginning to exceed the spatial control coefficient significantly.Comment: 19 pages, AMS-LaTeX, 6 eps figures included with geompsfi.st

Serially-regulated biological networks fully realize a constrained set of functions

We show that biological networks with serial regulation (each node regulated by at most one other node) are constrained to {\it direct functionality}, in which the sign of the effect of an environmental input on a target species depends only on the direct path from the input to the target, even when there is a feedback loop allowing for multiple interaction pathways. Using a stochastic model for a set of small transcriptional regulatory networks that have been studied experimentally, we further find that all networks can achieve all functions permitted by this constraint under reasonable settings of biochemical parameters. This underscores the functional versatility of the networks.Comment: 9 pages, 3 figure

Elementary derivation of Spitzer's asymptotic law for Brownian windings and some of its physical applications

A simple derivation of Spitzer'z asymptotic law for Brownian windings [Trans.Am.Math.Soc.87,187 (1958)]is presented along with its generalizations >.These include the cases of planar Brownian walks interacting with a single puncture and Brownian walks on a single truncated cone with variable conical angle interacting with the truncated conical tip.Such situations are typical in the theories of quantum Hall effect and 2+1 quantum gravity, respectively .They also have some applications in polymer physic

Integrated assessment of the environmental hazard level of technologies of drilling and blasting operations with using emulsion explosives in quarries

Purpose. Adaptation of the “unified method of quantitative and qualitative assessment of the level of environmental hazard of the operation of industrial enterprises, facilities and introduced technologies in the field of production and ecology” to the technologies of drilling and blasting operations in quarries for extraction of ore and nonmetallic materials with the use of various types of explosives. The methods. They are based on a heuristic evaluation of the impact of priority man-made factors of the technologies used according to the 4-point scale (0, 1, 2, 3), and then – of the complex level of their environmental hazard – according to the total 15-point scale, evenly divided into three qual-itative levels. Findings. The identification of types and sources of environmental hazard for natural environments (atmosphere, hydrosphere, lithosphere, soils and biota) was performed when using emulsion and TNT-containing explosives during drilling and blasting operations in quarries. The intensity, perio-dicity and consequences of various accompanying man-made factors were taken as the criteria of influence of dangerous impact of technological processes on the condition of the above natural en-vironments. It was found that the integrated level of the environmental hazard of man-made impacts of drilling and blasting operations using emulsion explosives was 2.33, in other words, it was “low”. When using TNT-containing explosives it was 5.00, i.e. appeared on the boundary of the first and the second ranges, where the “low” hazard level changes to “moderate”. This is an evi-dence of a higher (more than 2 times) environmental efficiency of using emulsion explosives com-pared to the use of TNT-containing explosives. The originality. The system of identification and management of environmental and technology-related risks under conditions of extraction of ore and nonmetallic materials in quarries by the drill and blast method was proposed, whereupon an integrated assessment of the level of environmental hazard of mining enterprises is proposed to be defined as a sum of average grade points (for each of the man-made factors) according to quantitative-qualitative scale. Practical implications. The developed methods allow determining with a sufficient degree of reli-ability the level of environmental hazard of existing technologies of drilling and blasting operations and substantiating expediency of change-over to emulsion explosive materials

Conformational transformations induced by the charge-curvature interaction at finite temperature

The role of thermal fluctuations on the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo transformation to polygonal shape. The transition occurs both in the case of hardening and softening charge-bending interaction. In the former case the charge and curvature are smoothly distributed along the chain while in the latter spontaneous kink formation is initiated. The transition to a non-circular conformation is analogous to the phase transition of the second kind.Comment: 23 pages (Latex), 10 figures (Postscript), 2 biblio file (bib-file and bbl-file

Veneziano Amplitudes, Spin Chains and String Models

In a series of recently published papers we reanalyzed the existing treatments of Veneziano and Veneziano-like amplitudes and the models associated with these amplitudes. In this work we demonstrate that the already obtained new partition function for these amplitudes can be exactly mapped into that for the Polychronakos-Frahm (P-F) spin chain model. This observation allows us to recover many of the existing string-theoretic models, including the most recent ones.Comment: 38 page