Green function method for calculating properties of static magnetic fields

Given complete information about the normal component of a magnetic field in a plane, it is possible to directly calculate all aspects of the field at any point in a source-free, homogeneous volume above that plane. The magnetic scalar potential, the magnetic field, and its gradient have direct representations as integrals of the boundary data. This paper provides a Green function method for this problem, as well as examples of such calculations.     

Steady-state vortex structure in a plasma with a strong magnetic field

A study is made of nonquasineutral vortex structures in a plasma with a magnetic field B _z in which the charges separate on a spatial scale equal to the magnetic Debye radius r _B=B _z/4πen _e. The electric field arising due to charge separation leads to radial expansion of the ions, thereby destroying the initial electron vortex. It is shown that the ion pressure gradient stops ion expansion in a nonquasineutral electron vortex and gives rise to a steady structure with a characteristic scale on the order of r _B. With the electron inertia taken into account in the hydrodynamic approximation, the magnetic vortex structure in a hot plas mamanifests itself in the appearance of a “hole” in the plasma density.     

The organelle of differentiation in embryos: the cell state splitter

The cell state splitter is a membraneless organelle at the apical end of each epithelial cell in a developing embryo. It consists of a microfilament ring and an intermediate filament ring subtending a microtubule mat. The microtubules and microfilament ring are in mechanical opposition as in a tensegrity structure. The cell state splitter is bistable, perturbations causing it to contract or expand radially. The intermediate filament ring provides metastability against small perturbations. Once this snap-through organelle is triggered, it initiates signal transduction to the nucleus, which changes gene expression in one of two readied manners, causing its cell to undergo a step of determination and subsequent differentiation. The cell state splitter also triggers the cell state splitters of adjacent cells to respond, resulting in a differentiation wave. Embryogenesis may be represented then as a bifurcating differentiation tree, each edge representing one cell type. In combination with the differentiation waves they propagate, cell state splitters explain the spatiotemporal course of differentiation in the developing embryo. This review is excerpted from and elaborates on “Embryogenesis Explained” (World Scientific Publishing, Singapore, 2016).     

Quantum chemical studies of protein structure

Quantum chemical methods now permit the prediction of many spectroscopic observables in proteins and related model systems, in addition to electrostatic properties, which are found to be in excellent accord with those determined from experiment. I discuss the developments over the past decade in these areas, including predictions of nuclear magnetic resonance chemical shifts, chemical shielding tensors, scalar couplings and hyperfine (contact) shifts, the isomer shifts and quadrupole splittings in M?ssbauer spectroscopy, molecular energies and conformations, as well as a range of electrostatic properties, such as charge densities, the curvatures, Laplacians and Hessians of the charge density, electrostatic potentials, electric field gradients and electrostatic field effects. The availability of structure/spectroscopic correlations from quantum chemistry provides a basis for using numerous spectroscopic observables in determining aspects of protein structure, in determining electrostatic properties which are not readily accessible from experiment, as well as giving additional confidence in the use of these techniques to investigate questions about chemical bonding and chemical reactions.     

Hydromagnetic modes in an inhomogeneous collisionless plasma of finite pressure

The spatial structure and growth rate of hydromagnetic waves with frequencies are considered in a one-dimensional model. It is shown that the wave under consideration is an Alfvén mode modified by the inhomogeneity and anisotropy of the plasma and its finite pressure. Because of these factors, the magnetic field lines oscillate differently in the radial and azimuthal directions and the wave frequency depends on the radial wavenumber. There may be two types of mode structure in the direction across the magnetic shells. When the magnetospheric parameters vary monotonically along the radial coordinate, the mode propagates across the magnetic field lines; because of its resonance with high-energy particles, the radial wavenumber acquires a nonzero imaginary part, which vanishes at the Alfvén resonance surface. In the magnetospheric regions where the main plasma parameters (density or pressure) reach their extreme values, the mode is a standing wave in a direction transverse to the magnetic field lines. In this case, because of the instability, the eigen-frequency of the cavity has a nonzero imaginary part. Under certain, very specific conditions, there can exist drift-mirror waves in the magnetosphere. Such conditions, however, are unlikely to occur in reality. In terms of the modes to be described, it is possible to explain some types of oscillations of the geomagnetic field.     

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.     

Coupling of cell structure to cell metabolism and function

The fact that cells make directed decisions regarding how to use energy, i.e., where to direct intracellular particles or where to move, suggests that energy can be, and is, harnessed in specific ways. It is now well established that the chemical reactions of the cell do not occur in nonorganized soup, but rather in the context of ordered structure. The physical components that make up this ordered structure of the cell are part of the tissue matrix, which consists of the dynamic linkages between the skeletal networks of the nucleus (the nuclear matrix), the cytoplasm (the cytoskeleton), and the extracellular environment (the extracellular matrix). To understand gene function and how the energy of the cell is directed towards accomplishing the tasks directed by DNA (gene expression), a further understanding of how cell structure is tied to cellular energy and function is required. We propose that the structural components of the cell harness cellular energy to direct cell functions by providing a dynamic bridge between thermodynamics and gene expression. © 1994 Wiley-Liss, Inc.     

Electromagnetic field generation by ATP-induced reverse electron transfer

This paper describes a mechanism to explain low-level light emission in biology. A biological analog of the electrical circuitry, modeled on the parallel plate capacitor, traversed by a helical structure, required to generate electromagnetic radiation in the optical spectral range, is described. The charge carrier required for the emissions is determined to be an accelerating electron driven by an ATP-induced reverse electron transfer. The radial velocity component, the emission trajectory, of the moving charges traversing helical protein structures in a cyclotron-type mechanism is proposed to be imposed by the ferromagnetic field components of the iron in the iron-sulfur proteins. The redox systems NADH, riboflavin, and chlorophyll were examined with their long-wavelength absorption maxima determining the energetic parameters for the calculations. Potentials calculated from the axial velocity components for the riboflavin and NADH systems were found to equal the standard redox potentials of these systems as measured electrochemically and enzymatically. The mechanics for the three systems determined the magnetic moments, the angular momenta, and the orbital magnetic fluxes to be adiabatic invariant parameters. The De Broglie dual wave-particle equation, the fundamental equation of wave mechanics, and the key idea of quantum mechanics, establishes the wavelengths for accelerating electrons which, divided into a given radial velocity, gives its respective emission frequency. Electrons propelled through helical structures, traversed by biologically available electric and magnetic fields, make accessible to the internal environment the optical spectral frequency range that the solar spectrum provides to the external environment.     

Simultaneous analysis of the cardiac electric and magnetic fields using the scalar multipole expansion

A theoretical analysis of electric and magnetic fields of the heart, based solely upon the scalar multipole expansion, is carried out in order to gain an insight into the interrelation of the data contained in electro- and magnetocardiological measurements. The usual multipole expansion is applied for the electric field, however corresp[nding equivalent multipoles are formulated as idealized generators, having not only flow sources, but also vortex sources of the field. Furthermore, the magnetic field in a homogeneous infinite volume conductor is expressed as a sum of two series, the first being the usual multipole expansion of the nonvortex component of the magnetic field, and the second being a sequence of magnetic fields set up by the aforementioned electric multipole generators reduced to axial form. The former term is uniquely defined by the electric multipole components, but the latter reflects properties of the cardiogenerator that can be revealed only by means of magnetic measurements. Features of the electric and magnetic multipole components as integral characteristics of the cardiogenerator are discussed and concepts of the magnetic centre and magnetic axis of the cardiogenerator are proposed. The analysis is illustrated by examples of simple generator configurations.     

The nuclear matrix: a heuristic model for investigating genomic organization and function in the cell nucleus.

Despite significant advances in deciphering the molecular events underlying genomic function, our understanding of these integrated processes inside the functioning cell nucleus has, until recently, met with only very limited success. A major conundrum has been the "layers of complexity" characteristic of all cell structure and function. To understand how the cell nucleus functions, we must also understand how the cell nucleus is put together and functions as a whole. The value of this neo-holistic approach is demonstrated by the enormous progress made in recent years in identifying a wide variety of nuclear functions associated with the nuclear matrix. In this article we summarize basic properties of in situ nuclear structure, isolated nuclear matrix systems, nuclear matrix-associated functions, and DNA replication in particular. Emphasis is placed on identifying current problems and directions of research in this field and illustrating the intrinsic heuristic value of this global approach to genomic organization and function.     

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.     

Magnetic forces and DNA mechanics in multiplexed magnetic tweezers

Magnetic tweezers (MT) are a powerful tool for the study of DNA-enzyme interactions. Both the magnet-based manipulation and the camera-based detection used in MT are well suited for multiplexed measurements. Here, we systematically address challenges related to scaling of multiplexed magnetic tweezers (MMT) towards high levels of parallelization where large numbers of molecules (say 10³) are addressed in the same amount of time required by a single-molecule measurement. We apply offline analysis of recorded images and show that this approach provides a scalable solution for parallel tracking of the xyz-positions of many beads simultaneously. We employ a large field-of-view imaging system to address many DNA-bead tethers in parallel. We model the 3D magnetic field generated by the magnets and derive the magnetic force experienced by DNA-bead tethers across the large field of view from first principles. We furthermore experimentally demonstrate that a DNA-bead tether subject to a rotating magnetic field describes a bicircular, Limaçon rotation pattern and that an analysis of this pattern simultaneously yields information about the force angle and the position of attachment of the DNA on the bead. Finally, we apply MMT in the high-throughput investigation of the distribution of the induced magnetic moment, the position of attachment of DNA on the beads, and DNA flexibility. The methods described herein pave the way to kilo-molecule level magnetic tweezers experiments.     

Structural specificity of steroids in stimulating DNA synthesis and protooncogene expression in primary rat hepatocyte cultures

Among the chemical compounds of varied structure which possess liver tumour-promoting are steroids, such as estrogens, pregnenolone derivatives and anabolic steroids. Although the mechanism(s) of tumour promotion in liver by these xenobiotics is not well understood, it is clear that growth stimulation is one important element in their action. As a basis for better defining whether steroids stimulate growth by a common mechanism or fall into sub-groups with differing actions, the effects of 46 steroids on DNA synthesis and the expression of protooncogenes c-fos and c-myc were examined in primary cultures of normal rat hepatocytes. Tentative groupings of steroids have been identified based on apparent structural requirements for stimulation of DNA synthesis, and effects of auxiliary factors in modulating this growth stimulus. For a "progestin" group, insulin appeared to be permissive for stimulation of DNA synthesis, and presence of an ester or hydroxyl group at 17alpha-position in combination with a non-polar group at C(6) appeared to be required for stimulation. For the pregnenes, dexamethasone was stimulatory. Structural requirements include a non-polar substitution at 16alpha-position and presence of a 6alpha-methyl group. Androgens were weak or ineffective stimulators of DNA synthesis. Anabolic steroids were weak to strong stimulators and alteration to A ring structure in combination with non-polar substitution at 17alpha-position appeared to be required for the activity. With the exception of the anabolic steroid, dianabol, there do not appear to be strong correlation between ability to stimulate DNA synthesis and ability to induce protooncogene expression among the steroids. This study provides a starting point for future more detailed examination of growth-stimulatory mechanism(s) of action of steroids in the liver.     

The use of NMR residual dipolar couplings in aqueous dilute liquid crystalline medium for conformational studies of complex oligosaccharides

C-H dipolar coupling values were measured for a natural-abundance sample of the pentasaccharide beta-D-Galp-(1-->3)-[alpha-L-Fucp-(1-->4)]-beta-D-GlcNAcp-(1 -->3)-beta-D- Galp-(1-->4)-beta-D-Glcp ('lacto-N-fucopentaose 2') (LNF-2), in a 7.5% solution of dimyristoyl phosphatidylcholine-dihexanoyl phosphatidylcholine bicelle liquid crystals oriented in the NMR magnetic field. Interpretation of the dipolar coupling data and NOE confirms the conformational model for the Lewis(a) trisaccharide epitope based on NOE, molecular dynamics simulations, and scalar coupling data and provided new structural information for the remaining residues of the pentasaccharide. Since residual dipolar coupling provides information on long-range order, it is a valuable complement to other types of NMR data such as NOE and scalar coupling for exploring conformations of complex oligosaccharides.     

A nonlinear single-mode structure in a plasma with anisotropic temperature

An exact solution is derived to the equations of vortex electron anisotropic hydrodynamics for a plasma that is unstable against the Weibel instability driven by the electron temperature anisotropy. This solution describes saturation of the Weibel instability in the single-mode regime with an arbitrary wavelength and corresponds to a standing helical wave of magnetic perturbations in which the amplitude of the generated magnetic field varies periodically over time. The longitudinal and transverse (with respect to the rotating anisotropy axis) plasma temperatures are subject to the same periodic variations. In this case, the maximum magnetic field energy can be on the order of the plasma thermal energy.

     

Acridine orange-induced precipitation of mouse testicular sperm cell DNA reveals new patterns of chromatin structure

Precipitate resulting from interaction between certain intercalators, such as acridine orange (AO), and nucleic acids can be detected by electron microscopy. Formation of precipitate in nuclei of live cells is modulated by chromatin structure. Susceptibility of in situ DNA to precipitation was studied in mouse testicular germ cells during various stages of sperm maturation. DNA in round spermatid chromatin, similar to somatic cell euchromatin, was rather resistant to precipitation; the electron-dense precipitate was granular and randomly distributed. DNA in elongated spermatids was more susceptible to precipitation; the products were in the form of fibers. At early stages of spermatid maturation these fibers were distributed uniformly throughout the entire nucleus. At later stages, the products appeared as approximately 25-nm-thick fibers arranged longitudinally in arrays within the nucleus. With further cell maturation, fibers in the anterior portion of the nucleus appeared to fuse, forming homogeneously dense product. These fibrous products likely represent AO interactions with DNA in chromatin in which transition proteins had replaced histones. Changing patterns of these precipitated fibers likely reflect progressive stages of chromatin condensation, which starts at the center and anterior portion of the nucleus where the fibers coalesce. Mature sperm cell DNA, known to be complexed with protamines, was more resistant to AO-induced precipitation. The data suggest that precipitation induced by AO and monitored by electron microscopy may be a useful probe of nuclear chromatin structure.     

Nucleus size and its effect on nucleosome stability in living cells

DNA architectural proteins play a major role in organization of chromosomal DNA in living cells by packaging it into chromatin, whose spatial conformation is determined by an intricate interplay between the DNA-binding properties of architectural proteins and physical constraints applied to the DNA by a tight nuclear space. Yet, the exact effects of the nucleus size on DNA-protein interactions and chromatin structure currently remain obscure. Furthermore, there is even no clear understanding of molecular mechanisms responsible for the nucleus size regulation in living cells. To find answers to these questions, we developed a general theoretical framework based on a combination of polymer field theory and transfer-matrix calculations, which showed that the nucleus size is mainly determined by the difference between the surface tensions of the nuclear envelope and the endoplasmic reticulum membrane as well as the osmotic pressure exerted by cytosolic macromolecules on the nucleus. In addition, the model demonstrated that the cell nucleus functions as a piezoelectric element, changing its electrostatic potential in a size-dependent manner. This effect has been found to have a profound impact on stability of nucleosomes, revealing a previously unknown link between the nucleus size and chromatin structure. Overall, our study provides new insights into the molecular mechanisms responsible for regulation of the nucleus size, as well as the potential role of nuclear organization in shaping the cell response to environmental cues.     

The use of fractal features from the periphery of cell nuclei as a classification tool.

A polygonization-based method is used to estimate the fractal dimension and several new scalar lacunarity features from digitized transmission electron micrographs (TEM) of mouse liver cell nuclei. The fractal features have been estimated in different segments of 1D curves obtained by scanning the 2D cell nuclei in a spiral-like fashion called "peel-off scanning". This is a venue to separate estimates of fractal features in the center and periphery of a cell nucleus. Our aim was to see if a small set of fractal features could discriminate between samples from normal liver, hyperplastic nodules and hepatocellular carcinomas. The Bhattacharyya distance was used to evaluate the features. Bayesian classification with pooled co-variance matrix and equal prior probabilities was used as the rule for classification. Several single fractal features estimated from the periphery of the cell nuclei discriminated samples from the hyperplastic nodules and hepatocellular carcinomas from normal ones. The outer 25-30% of the cell nuclei contained important texture information about the differences between the classes. The polygonization-based method was also used as an analysis tool to relate the differences between the classes to differences in the chromatin structure.