Plasma equilibrium in axisymmetric poloidal magnetic field configurations in flux coordinates

A simple derivation is given of equilibrium equations in flux coordinates in the general case of an anisotropic-pressure plasma. The issue of how to formulate the boundary conditions for these equations is discussed for two types of configurations—a straight system and a system with an internal conductor. Examples of numerical solutions to the equilibrium problem for these configurations are presented.     

Linear MHD stability analysis of post-disruption plasmas in ITER

Most of the plasma current can be replaced by a runaway electron (RE) current during plasma disruptions in ITER. In this case the post-disruption plasma current profile is likely to be more peaked than the pre-disruption profile. The MHD activity of such plasma will affect the runaway electron generation and confinement and the dynamics of the plasma position evolution (Vertical Displacement Event), limiting the timeframe for runaway electrons and disruption mitigation. In the present paper, we evaluate the influence of the possible RE seed current parameters on the onset of the MHD instabilities. By varying the RE seed current profile, we search for subsequent plasma evolutions with the highest and the lowest MHD activity. This information can be applied to a development of desirable ITER disruption scenario.     

Tumor-associated carbonic anhydrase 9 spatially coordinates intracellular pH in three-dimensional multicellular growths

CA9 is a membrane-tethered, carbonic anhydrase (CA) enzyme, expressed mainly at the external surface of cells, that catalyzes reversible CO(2) hydration. Expression is greatly enhanced in many tumors, particularly in aggressive carcinomas. The functional role of CA9 in tumors is not well established. Here we show that CA9, when expressed heterologously in cultured spheroids (0.5-mm diameter, ~25,000 cells) of RT112 cells (derived from bladder carcinoma), induces a near-uniform intracellular pH (pH(i)) throughout the structure. Dynamic pH(i) changes during displacements of superfusate CO(2) concentration are also spatially coincident (within 2 s). In contrast, spheroids of wild-type RT112 cells lacking CA9 exhibit an acidic core (~0.25 pH(i) reduction) and significant time delays (~9 s) for pH(i) changes in core versus peripheral regions. pH(i) non-uniformity also occurs in CA9-expressing spheroids after selective pharmacological inhibition of the enzyme. In isolated RT112 cells, pH(i) regulation is unaffected by CA9 expression. The influence of CA9 on pH(i) is thus only evident in multicellular tissue. Diffusion-reaction modeling indicates that CA9 coordinates pH(i) spatially by facilitating CO(2) diffusion in the unstirred extracellular space of the spheroid. We suggest that pH(i) coordination may favor survival and growth of a tumor. By disrupting spatial pH(i) control, inhibition of CA9 activity may offer a novel strategy for the clinical treatment of CA9-associated tumors.     

Real-time three-dimensional graphic reconstructions using Brown-Roberts-Wells frame coordinates in a microcomputer environment

A desktop microcomputer environment that utilizes Brown-Roberts-Wells (BRW) frame coordinates for creation of three-dimensional depiction of operator-defined intracranial structures has been developed. The system allows direct reading of Siemens CT scan images from a floppy disc, structural edge definition, and reconstruction of defined images. The system is used in the operating room to view scans, perform standard BRW stereotactic functions, and create three-dimensional graphics for such tasks as defining tumor margins, conceptualizing positional relationships of intracranial structures, and radiation planning.     

Use of conical wire arrays for modeling three-dimensional MHD implosion effects

Results are presented from experimental studies and numerical simulations of three-dimensional dynamics of the plasma produced in the Angara-5-1 facility by the electrical implosion of conical wire arrays at currents of up to 3 MA. The arrays were made of 6-to 8-μm-diameter tungsten wires, the inclination angle of the generatrix with respect to the axis being from 15° to 42°. The results of two-dimensional MHD simulations are compared with experimental data. The formation dynamics of the plasma precursor is found to be different for cylindrical and conical arrays. As the cone angle increases, the duration of the X-ray pulse increases, while the height of the pinch radiating zone decreases.     

MHD stability of a plasma in an axisymmetric open divertor configuration

For a plasma with confined in a system of two simple axisymmetric mirror cells separated by a divertor cell, a radial plasma pressure profile is obtained that is stable against convective modes and drops off to zero at the separatrix. The shape of the marginally stable pressure profile depends on the geometric parameters (such as mirror ratios and the localization of the divertor cell), the ratio of the pressure in the mirrors cells to the pressure in the divertor cell, and the degree of pressure anisotropy.     

MHD plasma stability in alternative toroidal systems and the local dispersion relation

The local dispersion relation obtained for an inhomogeneous anisotropic high-pressure plasma in the Chew-Goldberger-Low approximation is used to qualitatively study small-scale MHD plasma instabilities in alternative magnetic configurations in which the plasma compressibility plays a significant stabilizing role. It is established that it is important to satisfy the Bernstein-Kadomtsev condition in order to reduce the growth rate of the quasi-flute oscillations. Moderate plasma anisotropy is shown not to have a substantial destabilizing effect on the MHD plasma stability under the Bernstein-Kadomtsev condition in alternative systems. The situation in which the electron compressibility vanishes while the ion compressibility is nonzero is discussed; it is shown that, in this situation, the Bernstein-Kadomtsev condition becomes more stringent as the longitudinal wavenumber increases.     

LIM kinase 1 coordinates microtubule stability and actin polymerization in human endothelial cells

Microtubule (MT) destabilization promotes the formation of actin stress fibers and enhances the contractility of cells; however, the mechanism involved in the coordinated regulation of MTs and the actin cytoskeleton is poorly understood. LIM kinase 1 (LIMK1) regulates actin polymerization by phosphorylating the actin depolymerization factor, cofilin. Here we report that LIMK1 is also involved in the MT destabilization. In endothelial cells endogenous LIMK1 co-localizes with MTs and forms a complex with tubulin via the PDZ domain. MT destabilization induced by thrombin or nocodazole resulted in a decrease of LIMK1 colocalization with MTs. Overexpression of wild type LIMK1 resulted in MT destabilization, whereas the kinase-dead mutant of LIMK1 (KD) did not affect MT stability. Importantly, down-regulation of endogenous LIMK1 by small interference RNA resulted in abrogation of the thrombin-induced MTs destabilization and the inhibition of thrombin-induced actin polymerization. Expression of Rho kinase 2, which phosphorylates and activates LIMK1, dramatically decreases the interaction of LIMK1 with tubulin but increases its interaction with actin. Interestingly, expression of KD-LIMK1 or small interference RNA-LIMK1 prevents thrombin-induced microtubule destabilization and F-actin formation, suggesting that LIMK1 activity is required for thrombin-induced modulation of microtubule destabilization and actin polymerization. Our findings indicate that LIMK1 may coordinate microtubules and actin cytoskeleton.     

MHD stability of a collisionless anisotropic plasma in a system with an internal conductor

A study is made of the MHD stability of a collisionless anisotropic-pressure plasma in a nonparaxial magnetic configuration with an internal conductor in cylindrical geometry. A stability criterion for flutelike modes is obtained, and the families of marginally stable profiles of the longitudinal and transverse plasma pressures are calculated by using the Chew-Goldberger-Low anisotropic MHD equations. Possible marginally stable plasma states are considered with allowance for the expected turbulent relaxation and self-organization processes, on the one hand, and isotropization processes, on the other. A stability criterion for Alfvén modes is also derived in the Chew-Goldberger-Low model.     

MHD stability of a finite-pressure plasma in axisymmetric configurations of the poloidal magnetic field

A set of linear integrodifferential equations is presented for the plasma displacement components that minimize the Kruskal-Oberman functional of the potential energy of an MHD perturbation. Marginal stability results when the smallest eigenvalue of this set of equations is zero.     

A partially buried site in homologous HPr proteins is not optimized for stability

The energetic consequences of site-specific replacement of a residue at a partially buried site in the two homologous HPr proteins from Escherichia coli and Bacillus subtilis is described. We determined previously that the replacement of a partially buried Lys residue with Glu at position 49 in E.coli HPr increased the conformational stability of the protein substantially because the side-chain of the latter residue could act as a hydrogen-bond acceptor. Here, we extend this analysis to other side-chains with different chemical properties and abilities to form hydrogen bonds to compare the properties of this position in the backgrounds of two different homologous HPr proteins. We find that the variants with polar residues that can form a tertiary hydrogen bond with a nearby site in the protein are more stable than either hydrophobic residues or polar residues that become buried yet are incapable of forming a new hydrogen bond. Furthermore, the protein with the wild-type residue in each HPr variant is not among the most stable of the proteins studied. These results suggest a general strategy for designing variants in which the overall stability of a protein can be modulated in a defined fashion.     

Constant rate population harvesting: equilibrium and stability.

The paper studies the effect of constant rate harvesting on population models described by ordinary differential equations. The dependence of limits of populations on the harvest rate, the possibility of extinction in finite time, and the effect of the introduction of a time-lag delay on stability are studied. Various models for one population are analysed, and a geometric technique for the study of two-population models is discussed.     

Longitudinal structure of MHD perturbations at the boundary of convective stability in the Kruskal-Oberman model

It is shown that, in contrast to the MHD model, a perturbation at the boundary of convective stability of a finite-pressure plasma in confinement systems without an averaged minB in the Kruskal-Oberman model is not generally a purely flute one. The reasons for this discrepancy are clarified. The analysis is carried out for axisymmetric configurations formed by a poloidal magnetic field.     

HERC2/USP20 coordinates CHK1 activation by modulating CLASPIN stability

CLASPIN is an essential mediator in the DNA replication checkpoint, responsible for ATR (ataxia telangiectasia and Rad3-related protein)-dependent activation of CHK1 (checkpoint kinase 1). Here we found a dynamic signaling pathway that regulates CLASPIN turn over. Under unperturbed conditions, the E3 ubiquitin ligase HERC2 regulates the stability of the deubiquitinating enzyme USP20 by promoting ubiquitination-mediated proteasomal degradation. Under replication stress, ATR-mediated phosphorylation of USP20 results in the disassociation of HERC2 from USP20. USP20 in turn deubiquitinates K48-linked-polyubiquitinated CLASPIN, stabilizing CLASPIN and ultimately promoting CHK1 phosphorylation and CHK1-directed checkpoint activation. Inhibition of USP20 expression promotes chromosome instability and xenograft tumor growth. Taken together, our findings demonstrated a novel function of HERC2/USP20 in coordinating CHK1 activation by modulating CLASPIN stability, which ultimately promotes genome stability and suppresses tumor growth.     

Microtubule stability studied by three-dimensional molecular theory of solvation

We study microtubular supramolecular architectures of tubulin dimers self-assembling into linear protofilaments, in turn forming a closed tube, which is an important component of the cytoskeleton. We identify the protofilament arrangements with the lowest free energy using molecular dynamics to optimize tubulin conformations. We then use the three-dimensional molecular theory of solvation to obtain the hydration structure of protofilaments built of optimized tubulins and the solvent-mediated effective potential between them. The latter theoretical method, based on first principles of statistical mechanics, is capable of predicting the structure and thermodynamics of solvation of supramolecular architectures. We obtained a set of profiles of the potential of mean force between protofilaments in a periodic two-dimensional sheet in aqueous solution. The profiles were calculated for a number of amino acid sequences, tubulin conformations, and spatial arrangements of protofilaments. The results indicate that the effective interaction between protofilaments in aqueous solution depends little on the isotypes studied; however, it strongly depends on the M loop conformation of beta-tubulin. Based on the analysis of the potential of mean force between adjacent protofilaments, we found the optimal arrangement of protofilaments, which is in good agreement with other studies. We also decomposed the potential of mean force into its energetic and entropic components, and found that both are considerable in the free-energy balance for the stabilized protofilament arrangements.     

Synapse adhesion: a dynamic equilibrium conferring stability and flexibility

Cell adhesion molecules (CAMs) linked to cytoskeleton generate stable cell-cell junctions. Cadherins provide a canonical example, but paradoxically, they participate in a multitude of transient and regulatable interactions. Their extracellular binding generates weak adhesion that is modified by clustering; interactions with F-actin are regulated, can be transient, and can alter F-actin dynamics. Additionally, cadherin recycling from the cell surface can modify the size and location of junctions and strength of adhesion. In epithelial cells, this ongoing dynamic behavior is important for maintaining stable junctions. Recent work supports that cadherins act similarly at synapses where their actions are likely to be shared by integrins and other actin-linked CAMs. Together the collaborative activities of such CAMs provide a stable, but flexible structure that can promote and support changes in synapse shape and size while maintaining stable junctions to permit information flow.     

Preferential mating in symmetric multilocus systems: stability conditions of the central equilibrium

Several multilocus models that incorporate both preferential mating and viability selection are studied. Specifically, a class of symmetric heterozygosity models are considered that assign individuals to phenotypic classes according to which loci are in heterozygous state regardless of the actual allelic content. Otherwise, an arbitrary number of loci, number of alleles per locus, and arbitrary recombination scheme, viability parameters and preferential mating pattern based on phenotypes are allowed. The conditions for the stability of a central polymorphism are indicated and interpreted. The effects of viability and preference selection may be summarized in a single quantity for each phenotypic class, a generalized fitness. Preferential assortative mating alone can produce stability for a central polymorphism as in the case of viability selection when sexual attractiveness or general fitness increases with higher levels of heterozygosity. The situation is more complex with sexual selection.     

Effects of diffusion on the stability of the equilibrium in multi-species ecological systems

Continuous population distributions that undergo self-diffusion, migrational cross-diffusion and interaction in a region of (1-, 2- or 3-dimensional) space are described dynamically by a governing system of nonlinear reaction-diffusion equations. It is shown that the constants associated with migrational cross-diffusion are ordinarily nonnegative or nonpositive, contingent on the type of species interaction. A simple sign relationship obtains between the latter diffusivity constants and the rate constants for species interaction in the neighborhood of a spatially uniform equilibrium state, and this relationship of signs serves to simplify the general stability theory for the growth or decay of arbitrary perturbations on a spatially uniform equilibrium state. The stability of the equilibrium state is analyzed and discussed in detail for the case of a generic two-species model, where the self-diffusion and migrational cross-diffusion of species act to either stabilize or destabilize the equilibrium, depending essentially on the character of the species interaction and also on the magnitude of the Helmholtz eigenvalues associated with the region and boundary conditions. In particular, for a prey-predator or host-parasite model, self-diffusion usually helps to stabilize the equilibrium state and migrational cross-diffusion can only act as an additional stabilizing influence, as evidenced generally by the experiments on such two-species systems. Sufficient conditions are derived for stability of the equilibrium state in the general case for an arbitrarily large number of interacting species. It is shown that the equilibrium state is always stable if all species undergo significant self-diffusion and the Helmholtz eigenvalues are suitably large.