A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure

We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies are dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control

Robust circadian clocks from coupled protein modification and transcription-translation cycles

The cyanobacterium Synechococcus elongatus uses both a protein phosphorylation cycle and a transcription-translation cycle to generate circadian rhythms that are highly robust against biochemical noise. We use stochastic simulations to analyze how these cycles interact to generate stable rhythms in growing, dividing cells. We find that a protein phosphorylation cycle by itself is robust when protein turnover is low. For high decay or dilution rates (and co mpensating synthesis rate), however, the phosphorylation-based oscillator loses its integrity. Circadian rhythms thus cannot be generated with a phosphorylation cycle alone when the growth rate, and consequently the rate of protein dilution, is high enough; in practice, a purely post-translational clock ceases to function well when the cell doubling time drops below the 24 hour clock period. At higher growth rates, a transcription-translation cycle becomes essential for generating robust circadian rhythms. Interestingly, while a transcription-translation cycle is necessary to sustain a phosphorylation cycle at high growth rates, a phosphorylation cycle can dramatically enhance the robustness of a transcription-translation cycle at lower protein decay or dilution rates. Our analysis thus predicts that both cycles are required to generate robust circadian rhythms over the full range of growth conditions.Comment: main text: 7 pages including 5 figures, supplementary information: 13 pages including 9 figure

Decay rate estimations for linear quadratic optimal regulators

Let $u(t)=-Fx(t)$ be the optimal control of the open-loop system $x'(t)=Ax(t)+Bu(t)$ in a linear quadratic optimization problem. By using different complex variable arguments, we give several lower and upper estimates of the exponential decay rate of the closed-loop system $x'(t)=(A-BF)x(t)$. Main attention is given to the case of a skew-Hermitian matrix $A$. Given an operator $A$, for a class of cases, we find a matrix $B$ that provides an almost optimal decay rate. We show how our results can be applied to the problem of optimizing the decay rate for a large finite collection of control systems $(A, B_j)$, $j=1, \dots, N$, and illustrate this on an example of a concrete mechanical system. At the end of the article, we pose several questions concerning the decay rates in the context of linear quadratic optimization and in a more general context of the pole placement problem.Comment: 25 pages, 1 figur

High mobility group box 1 complexed with heparin induced angiogenesis in a matrigel plug assay

Angiogenesis involves complex processes mediated by several factors and is associated with inflammation and wound healing. High mobility group box 1 (HMGB1) is released from necrotic cells as well as macrophages and plays proinflammatory roles. In the present study, we examined whether HMGB1 would exhibit angiogenic activity in a matrigel plug assay in mice. HMGB1 in combination with heparin strongly induced angiogenesis, whereas neither HMGB1 nor heparin alone showed such angiogenic activity. The heparin-dependent induction of angiogenesis by HMGB1 was accompanied by increases in the expression of tumor necrosis factor-alpha (TNF-alpha) and vascular endothelial growth factor-A120 (VEGF-A120). It is likely that the dependence of the angiogenic activity of HMGB1 on heparin was due to the efficiency of the diffusion of the HMGB1-heparin complex from matrigel to the surrounding areas. VEGF-A165 possessing a heparin-binding domain showed a pattern of heparin-dependent angiogenic activity similar to that of HMGB1. The presence of heparin also inhibited the degradation of HMGB1 by plasmin in vitro. Taken together, these results suggested that HMGB1 in complex with heparin possesses remarkable angiogenic activity, probably through the induction of TNF-alpha and VEGF-A120.</p

Dense attosecond electron sheets from laser wakefields using an up-ramp density transition

Controlled electron injection into a laser-driven wakefield at a well defined space and time is reported based on particle-in-cell simulations. Key novel ingredients are an underdense plasma target with an up-ramp density profile followed by a plateau and a fairly large laser focus diameter that leads to an essentially one-dimensional (1D) regime of laser wakefield, which is different from the bubble (complete blowout) regime occurring for tightly focused drive beams. The up-ramp profile causes 1D wave breaking to occur sharply at the up-ramp-plateau transition. As a result, it generates an ultrathin (few nanometer, corresponding to attosecond duration), strongly overdense relativistic electron sheet that is injected and accelerated in the wakefield. A peaked electron energy spectrum and high charge (∼nC) distinguish the final sheet

Synthesis and Stoichiometry of MgB2

The system MgxB2 has been investigated to investigate possible nonstoichiometry in MgB2. When synthesized at 850oC, MgB2 is a line compound with a possible Mg vacancy content of about 1%. Small changes in lattice constants as a function of starting composition result from grain interaction stresses, whose character is different in the Mg-rich, near-stoichiometric, and Mg-deficient regimes. A small linear decrease of the superconducting transition temperature, Tc, in the Mg-rich regime results from accidental impurity doping.Comment: Accepted for publication in Physica C. 24 pages, 7 figure

Establishment of in Vitro Binding Assay of High Mobility Group Box-1 and S100A12 to Receptor for Advanced Glycation Endproducts: Heparin's Effect on Binding

Interaction between the receptor for advanced glycation end products (RAGE) and its ligands has been implicated in the pathogenesis of various inflammatory disorders. In this study, we establish an in vitro binding assay in which recombinant human high-mobility group box 1 (rhHMGB1) or recombinant human S100A12 (rhS100A12) immobilized on the microplate binds to recombinant soluble RAGE (rsRAGE). The rsRAGE binding to both rhHMGB1 and rhS100A12 was saturable and dependent on the immobilized ligands. The binding of rsRAGE to rhS100A12 depended on Ca2 and Zn2, whereas that to rhHMGB1 was not. Scatchard plot analysis showed that rsRAGE had higher affinity for rhHMGB1 than for rhS100A12. rsRAGE was demonstrated to bind to heparin, and rhS100A12, in the presence of Ca2, was also found to bind to heparin. We examined the effects of heparin preparations with different molecular sizesunfractionated native heparin (UFH), low molecular weight heparin (LMWH) 5000Da, and LMWH 3000Da on the binding of rsRAGE to rhHMGB1 and rhS100A12. All 3 preparations concentration-dependently inhibited the binding of rsRAGE to rhHMGB1 to a greater extent than did rhS100A12. These results suggested that heparin's anti-inflammatory effects can be partly explained by its blocking of the interaction between HMGB1 or S100A12 and RAGE. On the other hand, heparin would be a promising effective remedy against RAGE-related inflammatory disorders.</p

Chronic nitrite treatment activates adenosine monophosphate-activated protein kinase-endothelial nitric oxide synthase pathway in human aortic endothelial cells

Endothelial dysfunction, with impaired bioavailability and/or bioactivity of the vasoprotective molecule, nitric oxide, appears to be a vital step in the initiation of atherosclerosis. Several studies have shown that dietary nitrate/nitrite can have significant benefits on human cardiovascular homeostasis. Although serum nitrite concentrations can reach micromolar levels, the physiological significance of nitrate/nitrite in normal tissues has not been fully elucidated. We investigated in vitro the chronic effects of nitrate/nitrite on endothelial nitric oxide synthase (eNOS) to determine the potential vasoprotective effects of nitrate/nitrite and the underlying molecular mechanisms. Our results demonstrate the expression of phosphorylated eNOS at Ser1177 and phosphorylated adenosine monophosphate activated protein kinase (AMPK) at Thr172 in human aortic endothelial cells were increased after nitrite treatment. We suggest that nitrite stimulation may enhance eNOS activation, which is due, in part, to AMPK activation. The AMPK–eNOS activation by nitrite may be a possible molecular mechanism underlying the vascular protective effects of dietary nitrate