Interaxial Separation Research Articles

Interference of high-order perfect optical vortex beams

We investigate the interference of high-order perfect optical vortex (POV) beams with different topological charges. Through numerical simulations, we reveal a remarkable phenomenon: keeping the beam width, and beam radius fixed while changing the topological charge, the splitting of the composite POV beam into two distinct individual perfect vortices occurs exactly at the same inter-axial separation. The observed interference pattern exhibits pronounced sensitivity to factors such as axial separation, phase shift, beam radius, and topological charges of the constituent beams. Notably, our findings are contrasted with the interference of high-order Laguerre-Gauss (LG) beams, highlighting that the splitting of composite vortices into their individual components is more rapid in the case of LG beams. We also investigate the evolution of the interference pattern for both POV, and LG beams along the propagation direction in free-space. Our research provides significant insights into the distinct interference properties of high-order POV beams, presenting potential applications in the fields of optical manipulation and communication systems.

Water structural effects on DNA–DNA interactions and homologous recognition

Comprehending the principles underlying the interaction between DNA molecules in electrolyte solution is of crucial importance for understanding the phenomena of DNA condensation, recognition of homologous genes, and properties of DNA liquid crystals. Although DNA was considered in all its helical complexity over the last two decades, only a primitive, local, electrostatic model of the aqueous solution was considered. The forces acting between DNA molecules however must be influenced by the structure of the liquid separating them. In this paper we make a step towards unravelling earlier neglected effects of water structure on DNA–DNA interactions. We develop a model of DNA interaction accounting for the nonlocal dielectric response of water and of the electrolyte plasma dissolved in it. We focus particularly on the study of the dipolar overscreening effect, which leads to decaying oscillations of the electrostatic potential about DNA, and how it will affect electrostatic energy surfaces as a function of interaxial separation and mutual azimuthal orientation of the parallelly aligned interacting DNAs. We found that going beyond the classical electrostatic description of water (the so-called primitive model) reveals a complex oscillatory interaction surface in space, with many possible metastable configurations. These however vanish rapidly with smearing of the DNA charge distribution, due to dephasing of the oscillatory components of the interaction. This dephasing results in the suppression of oscillation amplitudes and leads to the dominance of non-oscillatory components in spatial dipolar correlations and the Debye screening. These dominant correlation patterns are shown to lead to a substantial enhancement of the difference between the interaction of homologous and nonhomologous DNA sequences, deepening and sharpening the homology recognition well.

Unusual behavior of the magnetization reversal process of interacting nanostructures with wire-tube morphology

We have studied the magnetostatic interactions between two parallel cylindrical nanostructures with wire-tube morphology as a function of their interaxial separation and the magnetic field applied using micromagnetic simulations. We find that the hysteresis curves of the system can exhibit one, two or three Barkhausen jumps as a function of the separation between the nanostructures and the angle at which the external magnetic field is applied, which are related to the reversal of the magnetic moments of certain segments of the nanostructures. In addition, by studying the averages of magnetization we obtain that for angles less than or equal to 60 degrees, the nanostructures reverse their magnetization through the nucleation and propagation of domain walls (vortex for the tube segment and transverse for the wire segment), while for higher angles the nanostructures revert their magnetization by quasi-coherent rotation.

Polarizing aperture stereoscopic cinema camera

The art of stereoscopic cinematography has been held back because of the lack of a convenient way to reduce the stereo camera lenses' interaxial to less than the distance between the eyes. This article describes a unified stereoscopic camera and lens design that allows for varying the interaxial separation to small values using a unique electro-optical polarizing aperture design for imaging left and right perspective views onto a large single digital sensor, the size of the standard 35 mm frame, with the means to select left and right image information. Even with the added stereoscopic capability, the appearance of existing camera bodies will be unaltered.

OSCAM - optimized stereoscopic camera control for interactive 3D

This paper presents a controller for camera convergence and interaxial separation that specifically addresses challenges in interactive stereoscopic applications like games. In such applications, unpredictable viewer- or object-motion often compromises stereopsis due to excessive binocular disparities. We derive constraints on the camera separation and convergence that enable our controller to automatically adapt to any given viewing situation and 3D scene, providing an exact mapping of the virtual content into a comfortable depth range around the display. Moreover, we introduce an interpolation function that linearizes the transformation of stereoscopic depth over time, minimizing nonlinear visual distortions. We describe how to implement the complete control mechanism on the GPU to achieve running times below 0.2ms for full HD. This provides a practical solution even for demanding real-time applications. Results of a user study show a significant increase of stereoscopic comfort, without compromising perceived realism. Our controller enables 'fail-safe' stereopsis, provides intuitive control to accommodate to personal preferences, and allows to properly display stereoscopic content on differently sized output devices.

Differential stability of DNA crossovers in solution mediated by divalent cations

The assembly of DNA duplexes into higher-order structures plays a major role in many vital cellular functions such as recombination, chromatin packaging and gene regulation. However, little is currently known about the molecular structure and stability of direct DNA–DNA interactions that are required for such functions. In nature, DNA helices minimize electrostatic repulsion between double helices in several ways. Within crystals, B-DNA forms either right-handed crossovers by groove–backbone interaction or left-handed crossovers by groove–groove juxtaposition. We evaluated the stability of such crossovers at various ionic concentrations using large-scale atomistic molecular dynamics simulations. Our results show that right-handed DNA crossovers are thermodynamically stable in solution in the presence of divalent cations. Attractive forces at short-range stabilize such crossover structures with inter-axial separation of helices less than 20 Å. Right-handed crossovers, however, dissociate swiftly in the presence of monovalent ions only. Surprisingly, left-handed crossovers, assembled by sequence-independent juxtaposition of the helices, appear unstable even at the highest concentration of Mg2+studied here. Our study provides new molecular insights into chiral association of DNA duplexes and highlights the unique role divalent cations play in differential stabilization of crossover structures. These results may serve as a rational basis to understand the role DNA crossovers play in biological processes.

Homology recognition funnel

The recognition of homologous sequences of DNA before strand exchange is considered to be the most puzzling stage of homologous recombination. A mechanism for two homologous dsDNAs to recognize each other from a distance in electrolytic solution without unzipping had been proposed in an earlier paper [A. A. Kornyshev and S. Leikin, Phys. Rev. Lett. 86, 366 (2001)]. In that work, the difference in the electrostatic interaction energy between homologous duplexes and between nonhomologous duplexes, termed the recognition energy, has been calculated. That calculation was later extended in a series of papers to account for torsional elasticity of the molecules. A recent paper [A. A. Kornyshev and A. Wynveen, Proc. Natl. Acad. Sci. U.S.A. 106, 4683 (2009)] investigated the form of the potential well that homologous DNA molecules may feel when sliding along each other. A simple formula for the shape of the well was obtained. However, this latter study was performed under the approximation that the sliding molecules are torsionally rigid. Following on from this work, in the present article we investigate the effect of torsional flexibility of the molecules on the shape of the well. A variational approach to this problem results in a transcendental equation that is easily solved numerically. Its solutions show that at large interaxial separations the recognition well becomes wider and shallower, whereas at closer distances further unexpected features arise related to an abrupt change in the mean azimuthal alignment of the molecules. The energy surface as a function of interaxial separation and the axial shift defines what we call the recognition funnel. We show that it depends dramatically on the patterns of adsorption of counterions on DNA.

Evidence that collagen and tendon have monolayer water coverage in the native state

This paper investigates an alternative explanation for widely reported paradoxical intracellular water properties. The most frequent biological explanation assumes water structure extending multiple layers from surfaces of compactly folded macromolecules to explain large amounts of perturbed water. Long range water structuring, however, contradicts molecular models widely accepted by the scientific majority. This study questions whether the paradoxical cell water could result from larger than expected amounts of first layer interfacial water on internal protein surfaces rather than structured multilayers. Native mammalian tendon is selected for the study because (1) the organ consists of highly compact structures of a single macromolecular protein--collagen, (2) molecular structure and geometry of collagen is well characterized by X-ray diffraction, (3) molecular structure extends to the macroscopic tendon level and (4) perturbed water behavior similar to cellular water is reported on tendon. Native tendon holds 1.6 g water/g dry mass. The 62% native water content simulates the water content of many cell types. MicroCT studies of tendon dilatometry as a function of hydration are measured and correlated to X-ray diffraction measurements of interaxial separation. Correlations show that native tendon has sufficient water for only a single monolayer of interfacial water. Thus the paradoxical properties of water in native tendon are first-layer interfacial water properties. Similar water behavior on globular proteins suggests that paradoxical cell water behavior could be caused by larger than expected amounts of first layer interfacial water on internal and external macromolecular surfaces of cell components.

Azimuthal Frustration and Bundling in Columnar DNA Aggregates

The interaction between two stiff parallel DNA molecules is discussed using linear Debye-Hückel screening theory with and without inclusion of the dielectric discontinuity at the DNA surface, taking into account the helical symmetry of DNA. The pair potential furthermore includes the amount and distribution of counterions adsorbed on the DNA surface. The interaction does not only depend on the interaxial separation of two DNA molecules, but also on their azimuthal orientation. The optimal mutual azimuthal angle is a function of the DNA-DNA interaxial separation, which leads to azimuthal frustrations in an aggregate. On the basis of the pair potential, the positional and orientational order in columnar B-DNA assemblies in solution is investigated. Phase diagrams are calculated using lattice sums supplemented with the entropic contributions of the counterions in solution. A variety of positionally and azimuthally ordered phases and bundling transitions is predicted, which strongly depend on the counterion adsorption patterns.

The Role of the α2 Chain in the Stabilization of the Collagen Type I Heterotrimer: A Study of the Type I Homotrimer in oim Mouse Tissues

We have previously reported that the fragility of skin, tendon and bone from the oim mouse is related to a significant reduction in the intermolecular cross-linking. The oim mutation is unlikely to affect the efficacy of the lysyl oxidase, suggesting that the defect is in the molecule and fibre. We have therefore investigated the integrity of both the oim collagen molecules and the fibre by differential scanning calorimetry. The denaturation temperature of the oim molecule in solution and the fibre from tail tendon were found to be higher than the wild-type by 2.6 deg. C and 1.9 deg. C, respectively. With the loss of the α2 chain, the hydroxyproline content of the homotrimer is higher than the heterotrimer, which may account for the increase. There is a small decrease in the enthalpy of the oim fibres but it is not significant, suggesting that the amount of disorder of the triple-helical molecules and of the fibres is small and involves only a small part of the total bond energy holding the helical structure together. The difference in denaturation temperature of the skin collagen molecules ( t m) and fibres ( t d) is significantly lower for the oim tissues, 19.9 deg. C against 23.1 deg. C, indicating reduced molecular interactions and hence packing of the molecules in the fibre. Computation of the volume fraction of the water revealed that the interaxial separation of the oim fibres was indeed greater, increasing from 19.6 Å to 21.0 Å. This difference of 1.4 Å, equivalent to a C–C bond, would certainly decrease the ability of the telopeptide aldehyde to interact with the ε-amino group from an adjacent molecule and form a cross-link. We suggest, therefore, that the reduction of the cross-linking is due to increased water content of the fibre rather than a distortion of the molecular structure. The higher hydrophobicity of the α2 chain appears to play a role in the stabilisation of heterotrimeric type I collagen, possibly by increasing the hydrophobic interactions between the heterotrimeric molecules, thereby reducing the water content and increasing the binding of the molecules in the fibre.

Nature of collagen–water hydration forces: a problem in water structure

The detailed make up of the total hydration force, F TOT, or its osmotic pressure equivalent, π, for the collagen–water system has been revealed by Raman spectroscopy, thermodynamics, and statistical mechanics. π is composed of three terms: (1) the pure water internal pressure, p i H 2O , (2) a collagen–water stochastic electric field term, p i FIELD, and (3) a thermal term, nRT ST/( V− V 0)= ρRT ST/MW H 2O . V− V 0 is the water volume, ρ is the density of pure water at the structural temperature, T ST, and MW H 2O is the molecular weight. An electric field modified, van der Waal’s type, equation of state results, namely, ( π+ p i ′) ( V− V 0)= nRT ST. p i ′ is the total internal pressure including the electric field, namely, p i ′≡ p i H 2O − p i FIELD. p i H 2O ≡(∂ E/∂ V) T =[ βT ST/ κ T − P], where β and κ T are the expansion coefficient and compressibility of pure water. The structural temperature, T ST, of the hydration water, was obtained from Raman OH-stretching component intensity ratios, K(T)≡(I 3250 cm −1 /I 3400 cm −1 ) , measured for collagen, but using the known T dependence of K( T) for pure water [1]. P= P external=1 atm. The electric field contribution, p i FIELD, to the total internal pressure, p i ′, comes from the negative V derivative of the stochastic electric field energy, U E. However, the sign of − p i H 2O , alone, determines the overall hydrophobicity or hydrophilicity; changing from (+), hydrophobic, positive force, for low T ST; to (−), hydrophilic, negative force, for high T ST; with increasing interaxial separation, X, in Å. T ST is ≈220–230 K for the driest collagen and the smallest X≈13 Å, implying, from Raman measurements of supercooled water [2], a dominance of pentagon-based, hydrophobic, clathrate-like rings of H-bonded water molecules in excellent agreement with X-ray measurements, although some hydrophilic interactions remain. T ST for the wettest collagen, X≈18 Å, is ≈296 K ( T i=293 K, is the constant experimental temperature) which signals the dominance of hydrophilic forces with high water content or large X. An excellent fit to the experimentally measured osmotic pressure was obtained for the collagen–water system using only well-known, short-range forces.

Theory of interaction between helical molecules

This work builds a basis for understanding electrostatic and solvation forces between various types of helical molecules by explicitly incorporating the helical structure and symmetries into the theory. We derive exact expressions for interaction between molecules with cylindrical inner cores and arbitrary distribution of discrete surface charges and analyze forces between single-stranded, double-stranded, and multistranded helices. For example, we demonstrate that the traditional approximation by a homogeneously charged rod becomes inappropriate when even less than a third of the strand charge on a single-stranded helix is neutralized by countercharges (adsorbed or intrinsic to the helix by their nature). The traditionally expected force is then complemented by helix-specific interactions. These helix-specific forces allow commensurate helices (with the ratio of pitches equal to a rational number) to recognize each other at a distance and self-assemble into an aggregate. Under certain conditions, these forces may induce a spontaneous symmetry loss, e.g., two DNA-type double helices rotate around their long axes to a separation-dependent angle when the molecules come closer than a critical interaxial separation. In general, while a longer-range helix-specific attraction induces the self-assembly, a shorter-range helix-specific repulsion prevents the tight molecular contact creating a force balance responsible for a nonzero surface separation in equilibrium. The decay rates and the amplitudes of the attraction and of the repulsion depend on the helical pitch and on the number and relative disposition of the helical strands. The theory of these forces allows us to explain a number of puzzling features of interactions measured between biological helices, including DNA, collagen, and four-stranded guanosine macromolecules.

Identification of structural motifs from protein coordinate data: secondary structure and first-level supersecondary structure.

A computer program is described that produces a description of the secondary structure and supersecondary structure of a polypeptide chain using the list of alpha carbon coordinates as input. Restricting the term "secondary structure" to the conformation of contiguous segments of the chain, the program determines the initial and final residues in helices, extended strands, sharp turns, and omega loops. This is accomplished through the use of difference distance matrices. The distances in idealized models of the segments are compared with the actual structure, and the differences are evaluated for agreement within preset limits. The program assigns 90-95% of the residues in most proteins to at least one type of secondary element. In a second step the now-defined helices and strands are idealized as straight line segments, and the axial directions and locations are compiled from the input C alpha coordinate list. These data are used to check for moderate curvature in strands and helices, and the secondary structure list is corrected where necessary. The geometric relations between these line segments are then calculated and output as the first level of supersecondary structure. A maximum of six parameters are required for a complete description of the relations between each pair. Frequently a less complete description will suffice, for example just the interaxial separation and angle. Both the secondary structure and one aspect of the supersecondary structure can be displayed in a character matrix analogous to the distance matrix format. This allows a quite accurate two-dimensional display of the three-dimensional structure, and several examples are presented. A procedure for searching for arbitrary substructures in proteins using distance matrices is also described. A search for the DNA binding helix-turn-helix motif in the Protein Data Bank serves as an example. A further abstraction of the above data can be made in the form of a metamatrix where each diagonal element represents an entire secondary segment rather than a single atom, and the off-diagonal elements contain all the parameters describing their interrelations. Such matrices can be used in a straightforward search for higher levels of supersecondary structure or used in toto as a representation of the entire tertiary structure of the polypeptide chain.

Bacterial flagella rotating in bundles: a study in helical geometry.

Bacterial flagella are semi-rigid helices that undergo true rotation. In peritrichously flagellated bacteria (e.g., Escherichia and Salmonella) there are many flagella on each cell; during translational cell movement these operate as a coordinated bundle that actively disperses upon reversal of the rotation sense. The dynamic behavior of a set of helices originating on separate rotational axes is explored by a working model, geometrical analysis, and hydrodynamic calculations. A critical relationship exists between the interaxial separation and phase difference of parallel helices with overlapping domains; in the subcritical case the filaments are not intertwisted, whereas in the supercritical case they are intertwisted in the same sense (left-handed) as the helices, with one twist per helical turn. During counter-clockwise rotation (the sense operative in forward swimming) any preexisting twists of this kind are automatically cancelled and the helices brought progressively into phase. Hydrodynamic calculations suggest that some wrapping then occurs in a right-handed sense, opposite to that of the helices; this necessitates a distortion from true helical geometry which is minimized by maintaining a coaxial in-phase relationship. A highly coordinated helical bundle results that is capable of operating smoothly for an indefinite period, in agreement with the observed behavior of swimming bacteria. During reverse rotation, the supercritical case develops to cause jamming of the bundle, as has been observed with bacteria in high-viscosity medium. The explosive dispersal of the bundle during reversal in low-viscosity medium is a consequence of a complicating phenomenon, namely, a drastic change in flagellar quaternary structure. The overall conclusion is that bundle formation and function are perfectly compatible with a rotational mechanism for the individual flagella.

Stereoscopic Perceptions of Size, Shape, Distance and Direction

Most of the distortions perceived in stereoscopic pictures are caused by false perspective. False perspective cannot be corrected by variation of the camera interaxial separation. Parallax movements, which result from head movements in ordinary experience, are lacking in stereoscopic pictures, and are replaced by perverse twists of the scene. This lack is felt as a real shortcoming of stereoscopic motion pictures, and is best masked by frequent movement of the camera during shots.