Differential polarization imaging. II. Symmetry properties and calculations

Various differential polarization images or Mueller images of model objects are generated using the equations derived in the previous paper (paper I of this series). These calculated images include models of the higher-order organization of metaphase chromosomes, and show the applicability of the differential polarization imaging method to the elucidation of complex molecular organizations. Then, the symmetry behavior of the Mueller matrix elements upon infinitesimal rotations of the optical components about the optical axis of the imaging system is presented. It is shown that the rotational properties of the Mueller images can be used to eliminate the linear polarization contributions to the M14 and M44 images, which appear when these images are generated with imperfect circular polarizations. The relationships between the 16 bright-field Mueller images for four different media, i.e., linearly and circularly isotropic, circularly anisotropic, linearly anisotropic, and linearly and circularly anisotropic, are also derived. For the first three cases simple relationships between the Mueller images are found and phenomenological equations in terms of the optical coefficients are derived. In the last case there are no specific relationships between the Mueller images and instead we briefly present Schellman and Jensen's method for treating this type of medium. The criterion of spatial resolution between adjacent domains of different optical anisotropy is then derived. It is found that in transitions between domains of opposite anisotropy the classical Rayleigh limit must be replaced by a magnitude criterion which depends on the limits of the sensitivity of the detection. Finally, the feasibility of optical sectioning in differential polarization imaging is demonstrated.     

Differential polarization imaging. IV. Images in higher Born approximations.

The theory of differential polarization imaging developed previously within the framework of the first Born approximation is extended to higher Born approximations, taking into account interactions among the polarizable groups in the object. Several properties of differential polarization images, originally described using first Born approximation are modified when higher Born approximations are used. In particular, (a) when the polarizable groups are spherically symmetric, the off-diagonal Mueller elements Mij (i not equal to j) in bright field do not vanish in higher Born approximations, as they do in the first Born approximation case. (b) In higher Born approximations, the dark field Mi4 and M4i (i = 1, 2, 3) images do not vanish as in the first Born approximation, due to the anisotropy induced by the interactions among the groups. (c) When the polarizability tensor of each group is symmetric and real, the bright field M14 and M41 images always vanish in the first Born approximation. In higher Born approximations, these terms do not vanish if the groups bear a chiral relationship to each other. Quantitative criteria for the validity of the first Born approximation in differential polarization imaging are explicitly derived for three different types of media: (a) linearly anisotropic, (b) circularly anisotropic, and (c) linearly and circularly anisotropic (medium displaying linear birefringence and circular birefringence). These criteria define the limits of thickness and the degree of anisotropy of optically thin media. Finally, the possibility to perform optical sectioning in differential polarization imaging in the presence and absence of group interactions is discussed.     

Differential polarization imaging. V. Numerical aperture effects and the contribution of preferential scattering and absorption to the circular dichroism images.

Chiral objects which scatter and absorb preferentially left versus right circularly polarized light give rise to bright-field circular dichroism (CD) images containing contributions from both these two phenomena. These contributions are separated and characterized mathematically, and the effect of the dimensions of the chiral object on their relative magnitude is discussed. CD images of the long-range chiral organization of the thylakoid membranes in chloroplasts are obtained at two different wavelengths to illustrate the diverse wavelength dependence of the preferential absorption and scattering contributions to the images. The bright field CD images not only depend on the magnitude and sign of the preferential scattering and preferential absorption contributions, but also on the numerical aperture of the lens used. This dependence is obtained formally and a method to extract the angle dependent preferential scattering contributions to the images is presented. The validity of this method is confirmed experimentally.     

Imaging linear and circular polarization features in leaves with complete Mueller matrix polarimetry

Spectropolarimetry of intact plant leaves allows to probe the molecular architecture of vegetation photosynthesis in a non-invasive and non-destructive way and, as such, can offer a wealth of physiological information. In addition to the molecular signals due to the photosynthetic machinery, the cell structure and its arrangement within a leaf can create and modify polarization signals. Using Mueller matrix polarimetry with rotating retarder modulation, we have visualized spatial variations in polarization in transmission around the chlorophyll a absorbance band from 650?nm to 710?nm. We show linear and circular polarization measurements of maple leaves and cultivated maize leaves and discuss the corresponding Mueller matrices and the Mueller matrix decompositions, which show distinct features in diattenuation, polarizance, retardance and depolarization. Importantly, while normal leaf tissue shows a typical split signal with both a negative and a positive peak in the induced fractional circular polarization and circular dichroism, the signals close to the veins only display a negative band. The results are similar to the negative band as reported earlier for single macrodomains. We discuss the possible role of the chloroplast orientation around the veins as a cause of this phenomenon. Systematic artefacts are ruled out as three independent measurements by different instruments gave similar results. These results provide better insight into circular polarization measurements on whole leaves and options for vegetation remote sensing using circular polarization.     

Dichrometer errors resulting from large signals or improper modulator phasing

A single-beam spectrometer equipped with a photoelastic modulator can be configured to measure a number of different parameters useful in characterizing chemical and biochemical materials including natural and magnetic circular dichroism, linear dichroism, natural and magnetic fluorescence-detected circular dichroism, and fluorescence polarization anisotropy as well as total absorption and fluorescence. The derivations of the mathematical expressions used to extract these parameters from ultraviolet, visible, and near-infrared light-induced electronic signals in a dichrometer assume that the dichroic signals are sufficiently small that certain mathematical approximations will not introduce significant errors. This article quantifies errors resulting from these assumptions as a function of the magnitude of the dichroic signals. In the case of linear dichroism, improper modulator programming can result in errors greater than those resulting from the assumption of small signal size, whereas for fluorescence polarization anisotropy, improper modulator phase alone gives incorrect results. Modulator phase can also impact the values of total absorbance recorded simultaneously with linear dichroism and total fluorescence. Chirality 24:706-717, 2012. ? 2012 Wiley Periodicals, Inc.(?).     

Assessment of tissue polarimetric properties using Stokes polarimetric imaging with circularly polarized illumination

Tissue‐depolarization and linear‐retardance are the main polarization characteristics of interest for bulk tissue characterization, and are normally interpreted from Mueller polarimetry. Stokes polarimetry can be conducted using simpler instrumentation and in a shorter time. Here, we use Stokes polarimetric imaging with circularly polarized illumination to assess the circular‐depolarization and linear‐retardance properties of tissue. Results obtained were compared with Mueller polarimetry in transmission and reflection geometry, respectively. It is found that circular‐depolarization obtained from these 2 methods is very similar in both geometries, and that linear‐retardance is highly quantitatively similar for transmission geometry and qualitatively similar for reflection geometry. The majority of tissue circular‐depolarization and linear‐retardance image information (represented by local image contrast features) obtained from Mueller polarimetry is well preserved from Stokes polarimetry in both geometries. These findings can be referred to for further understanding tissue Stokes polarimetric data, and for further application of Stokes polarimetry under the circumstances where short acquisition time or low optical system complexity is a priority, such as polarimetric endoscopy and microscopy.      

Calculations of the circular dichroism of double-helical nucleic acids. I. Effects involving pi leads to pi transitions

The circular dichroism of double-helical nucleic acids was calculated as a function of geometry using the theory of Tinoco and Johnson. This theory does not include contributions of near ultraviolet transitions that are not π → π* in nature. The calculated circular dichroism shows a strong dependence on the distance of base pairs from the helix axis and the tilt of the base pair. Smaller dependences are predicted for the propeller-like twist of a base pair and for variation of the angular increment per base pair. Moderately good agreement between calculated and many experimentally observed spectra could be generated.     

Alignment maps of tissues: I. Microscopic elliptical polarimetry

An automated method for generating a fiber alignment map in tissues, tissue-equivalents, and other fibrillar materials exhibiting linear and circular optical properties and scattering is presented. This method consists of interrogating the sample with elliptically polarized light from a rotated quarter-wave plate and an effective circular analyzer, and implementing nonlinear regression techniques to estimate parameters defining the optical properties of the optic train and the sample. Thus, an account is made for imperfect and misaligned optic elements. The optic train was modeled using the Mueller matrix representation and the combined sample properties by an exponential matrix. Because a sample's Mueller matrix does not uniquely determine the linear, circular, or scattering properties, the circular properties and effective scattering are estimated for a matched isotropic sample to determine and correct for the linear birefringence of an aligned sample. The method's utility is demonstrated by generating an alignment map of an arterial media-equivalent, a relevant test case because of its circumferential alignment and thus showing the method's sample orientation independence.     

Development of vacuum-ultraviolet circular dichroism measurement system using a polarizing undulator

We have developed an improved circular dichroism (CD) and linear dichroism (LD) simultaneous measurement system for the vacuum ultraviolet (VUV) region by polarization modulation techniques using a four-period Onuki-type crossed undulator as a polarized light source. The system has been constructed at the VUV beamline BL-5 in the electron storage ring TERAS, at AIST. Our improvements, in particular the adoption of an optical chopper as the detection method of incident light, have resulted in a flat baseline and a consequent simplification of the Mueller matrix calculation for our optical system. Based on the Mueller matrix calculation, we have successfully measured real VUV-CD and LD spectra of leucine films for wavelengths down to 160 nm with absolute optical constants. The obtained spectra show good consistency with spectra measured by conventional methods.     

Circular differential scattering and circular differential absorption of DNA-protein condensates and of dyes bound to DNA-protein condensates

DNA-protein condensates that give positive and negative psi-type circular dichroism (CD) spectra (psi condensates) bind intercalative and nonintercalative dyes. CD depends both on circular differential scattering and on circular differential absorption; scattering-corrected CD measurements are approximations to circular differential absorption. The circular differential scattering and scattering-corrected CD patterns observed in the DNA absorption band of psi condensates are mimicked in the induced CD band of intercalators bound to psi condensates. The induced scattering-corrected CD and circular differential scattering patterns of the groove-binding dye Hoechst 33342 bound to psi condensates are the inverse of the patterns seen with intercalative dyes, whereas the groove-binding dye manganese(III) meso-tetrakis(4-N-methylpyridyl)porphine [MnIIITMpyP-4] shows no significant induced CD patterns. The large circular differential scattering and scattering-corrected CD bands are interpreted as resulting from long-range chiral packing, rather than near-neighbor short-range interactions. Dyes intercalated into the DNA of the psi condensates have the same type of long-range chiral packing as the DNA bases. Therefore, the psi-type CD spectra seen in the UV spectra originating from the long-range packing of the DNA bases are also observed in the visible spectra when dyes are intercalated in the DNA of the psi condensates. Our interpretation comes from the observation that the induced circular differential scattering and circular differential absorption of the dye bound to the psi condensates depend only upon the sign of the circular differential absorption and the pattern of the circular differential scattering of the psi condensates without bound dye.(ABSTRACT TRUNCATED AT 250 WORDS)     

Model computations on the differential scattering of circularly polarized light (CIDS) by dense macromolecular particles

Circular intensity differential scattering (CIDS) patterns have been calculated for two general types of chiral arrangements. The calculations were done using the second Born approximation. The geometries considered are (a) a linear array of anisotropic scattering groups with a spiraling orientation (a twisted ladder) and (b) a helical array of scattering groups with arbitrary anisotropy and orientation. The CIDS expressions for the first of these models (twisted ladder) reduces to a simple analytical form and clearly illustrates many properties of CIDS patterns. The second geometry (helix) is more general. Calculations were done for oriented scatterers and for rotationally averaged scatterers as would be found in solution.     

Circular dichroism analyses of membrane proteins: an examination of differential light scattering and absorption flattening effects in large membrane vesicles and membrane sheets

The circular dichroism spectra of membrane suspensions are distorted by differential light scattering and absorption flattening effects, which arise as a consequence of the large size of the membrane particles relative to the wavelength of light and the high concentration of proteins in the membranes. In this paper, the consequences of these phenomena on the protein spectra of large membrane particles are discussed, and methods for eliminating them are examined. The distortions due to differential light scattering are relatively small in membrane systems, and can be compensated for by use of a large detector acceptance angle geometry. Several methods for correcting for differential flattening, which introduces a substantial distortion, have been evaluated, and a new method, the flattening quotient approach, which produces by far the best results, is described. Since the secondary structures calculated from circular dichroism spectra are highly dependent on accurate spectral shape and magnitude, this method for correcting the spectra may find general application in circular dichroism studies of membrane proteins.     

Changes in DNA superhelical density monitored by polarized light scattering.

Linear and circular lambda-DNA at different ethidium bromide concentrations have been studied by means of polarized light scattering, namely the S14, S34, S33 and S13 elements of Mueller matrix. While S33 at low angle appears well correlated with the total light scattering evaluated by optical density measurements at 632.8 nm for linear and circular DNA of the same mass, the magnitude and slope of the S14, S34 and S13 signals display significant changes for the circular lambda-DNA depending on the degree of negative superhelical density as induced by the different ethidium bromide concentrations. At the same time, for linear lambda-DNA the signal remains invariant, making explicit for the differential scattering of polarized light the possibility to obtain additional information by its angular dependence. Strikingly also the effect of 0.2% glutaraldehyde versus ethanol fixation on the native lambda-DNA structural properties appears to confirm earlier findings by other well-established probes. Results are discussed in terms of first physical principles and of their potential bearings towards our understanding of the mechanism controlling gene expression.     

Investigation on chlorosomal antenna geometries: tube,lamella and spiral-type self-aggregates

Molecular mechanics calculations and exciton theory have been used to study pigment organization in chlorosomes of green bacteria. Single and double rod, multiple concentric rod, lamella, and Archimedean spiral macrostructures of bacteriochlorophyll c molecules were created and their spectral properties evaluated. The effects of length, width, diameter, and curvature of the macrostructures as well as orientations of monomeric transition dipole moment vectors on the spectral properties of the aggregates were studied. Calculated absorption, linear dichroism, and polarization dependent fluorescence-excitation spectra of the studied long macrostructures were practically identical, but circular dichroism spectra turned out to be very sensitive to geometry and monomeric transition dipole moment orientations of the aggregates. The simulations for long multiple rod and spiral-type macrostructures, observed in recent high-resolution electron microscopy images (Oostergetel et al., FEBS Lett 581:5435–5439, 2007) gave shapes of circular dichroism spectra observed experimentally for chlorosomes. It was shown that the ratio of total circular dichroism intensity to integrated absorption of the Q _y transition is a good measure of degree of tubular structures in the chlorosomes. Calculations suggest that the broad Q _y line width of chlorosomes of sulfur bacteria could be due to (1) different orientations of the transition moment vectors in multi-walled rod structures or (2) a variety of Bchl-aggregate structures in the chlorosomes. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Expressions for the interpretation of circular intensity differential scattering of chiral aggregates

The derivation of compact expressions of the circular intensity differential scattering (CIDS) of chiral molecules is presented in the first Born approximation of the fields. The expressions derived are valid for a suspension of scattering chiral particles free to adopt any orientation in solution. The connection is established between the preferential scattering cross section for right- vs left-circularly polarized light for a given scattering angle and the geometrical parameters of the molecule. As observed experimentally, the equations predict that the circular differential scattering patterns must show as a function of the scattering angle a series of lobes of alternating sign. In between these lobes, zeros in the differential scattering cross section occur. For the case of two dipole moments arranged in chiral fashion, an expression is derived that shows how the relative arrangement of the dipoles and their separation relative to the wavelength of light control the number and the position of the zeros. A compact expression predicting the CIDS of a sample for very small angles of scattering is derived for a system of helices whose dimensions are small compared with the wavelength of light. Finally, the presence of CIDS in a sample is related to the appearance of anomalous signals in the CD spectrum of chiral systems. Expressions and computations of the magnitudes and sign of the anomalies are presented. The expressions obtained confirm the main features of the experimental CIDS patterns of chiral molecules previously published.     

An approach to inverse scattering problems

There are several reasons for investigating the inverse scattering problem in medical image processing. A typical case, that of ultrasonic fields, is considered. Assuming that a plane wave illuminates a weakly inhomogeneous two-dimensional object, the fundamental equation is derived for the scattered waves in integral as well as in differential forms. It is shown that the scattered waves observed on a circle surrounding the object is sufficient to specify the structure of the object. This information is summarized in a single term, which is a function of the wavenumber as well as the angles of incidence and observation. A successive approximation is applied to reconstruct the image of the object from this function. Since no analytic solution is available, several methods of approximations are proposed, and examples of computations are shown for the case of a cylindrical object.     

Calculations of the circular dichroism of double-helical nucleic acids. II. Effects involving n leads to pi transitions

The circular dichroism of double-helical nucleic acids was calculated as a function of geometry, including terms involving n → π* transitions. The “nonbonding” n or σ orbitals were of the azine type, delocalized, but concentrated at the nitrogen atoms of the purines and pyrimidines. Dynamic coupling of the magnetic moments of the n → π* transitions with the electric moments of π → π* transitions generated important terms. Mixing of electric dipole character into n → π* transitions by the static electric field perturbation of the molecule is of lesser importance. The largest contributions of n → π* transitions to the circular dichroism of double-helical nucleic acids are comparable in magnitude to the sum of π → π* terms only for geometries where the circular dichroism is weak. Using both n → π* and π → π* contributions one is able to match experimental and calculated circular dichroism spectra for DNA's over a much wider range of conditions than was possible previously.     

The multi-mode polarization modulation spectrometer: part 1: simultaneous detection of absorption, turbidity, and optical activity

Circular dichroism (CD) is an important spectroscopic technique for monitoring chirality and biological macromolecule conformation. However, during a CD measurement, absorbance, light scattering/turbidity, and fluorescence can also be detected. The simultaneous measurement of these different spectral features for a single sample is the basis of a multi-mode optical spectrometer. This allows time-efficient gathering of complementary information and provides a scheme to ensure that CD measurements are reliable. Aspects of circular polarization differential light scattering, pH, and temperature variation of a protein (antibody) solution are described. A procedure to help ensure that CD measurements are reliable is described.     

Nucleic acid vibrational circular dichroism, absorption, and linear dichroism spectra. I. A DeVoe theory approach.

Infrared (IR) vibrational circular dichroism (VCD), absorption, and linear dichroism (LD) spectra of four homopolyribonucleotides, poly(rA), poly(rG), poly(rC), and poly(rU), have been calculated, in the 1750-1550 cm-1 spectral region, using the DeVoe polarizability theory. A newly derived algorithm, which approximates the Hilbert transform of imaginaries to reals, was used in the calculations to obtain real parts of oscillator polarizabilities associated with each normal mode. The calculated spectra of the polynucleotides were compared with previously measured solution spectra. The good agreement between calculated and measured polynucleotide spectra indicates, for the first time, that the DeVoe theory is a useful means of calculating the VCD and IR absorption spectra of polynucleotides. For the first time, calculated DeVoe theory VCD and IR absorption spectra of oriented polynucleotides are presented. The calculated VCD spectra for the oriented polynucleotides are used to predict the spectra for such measurements made in the future. The calculated IR spectra for the oriented polynucleotides are useful in interpreting the linear dichroism of the polynucleotides.     

Mapping of retardance,diattenuation and polarizance vector on Poincare sphere for diagnosis and classification of cervical precancer

The mapping of diattenuation, polarizance and retardance vector (normalized Stokes vector) on Poincare sphere, evaluated from Mueller matrix of optically anisotropic stromal region of cervical tissues, is presented for cervical precancer detection and its staging. This reveals that the changes in the polarization states shown by these normalized Stokes vectors corresponds to the degradation of linearly arranged collagen fibers, breakage of the collagen cross links in the stromal region and change in the density of scattering sites when cervical cancer evolves. The distinct nature of real and imaginary parts of the refractive index for linear, linear‐45 and circular polarization from the optically anisotropic stromal region underscore the various polarization structures of the connective tissue region which get modified during the pathological changes. It has been found that versatility of these vectors for normal and precancerous cervical tissue of various grades may be utilized as a key distinction for qualitative staging of cervical precancer tissue. Quantitative classification of precancerous stages of cervical precancer has been determined with 95%–100% sensitivity and 93%–100% specificity through the evaluation of linear and circular diattenuation, linear polarizance and linear birefringence from the components of the respective vectors.