Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position.

We present a novel optical technique for three-dimensional tracking of single fluorescent particles using a modified epifluorescence microscope containing a weak cylindrical lens in the detection optics and a microstepper-controlled fine focus. Images of small, fluorescent particles were circular in focus but ellipsoidal above and below focus; the major axis of the ellipsoid shifted by 90 degrees in going through focus. Particle z position was determined from the image shape and orientation by applying a peak detection algorithm to image projections along the x and y axes; x, y position was determined from the centroid of the particle image. Typical spatial resolution was 12 nm along the optical axis and 5 nm in the image plane with a maximum sampling rate of 3-4 Hz. The method was applied to track fluorescent particles in artificial solutions and living cells. In a solution of viscosity 30 cP, the mean squared distance (MSD) traveled by a 264 nm diameter rhodamine-labeled bead was linear with time to 20 s. The measured diffusion coefficient, 0.0558 +/- 0.001 micron2/s (SE, n = 4), agreed with the theoretical value of 0.0556 micron2/s. Statistical variability of MSD curves for a freely diffusing bead was in quantitative agreement with Monte Carlo simulations of three-dimensional random walks. In a porous glass matrix, the MSD data was curvilinear and showed reduced bead diffusion. In cytoplasm of Swiss 3T3 fibroblasts, bead diffusion was restricted. The water permeability in individual Chinese Hamster Ovary cells was measured from the z movement of a fluorescent bead fixed at the cell surface in response osmotic gradients; water permeability was increased by > threefold in cells expressing CHIP28 water channels. The simplicity and precision of this tracking method may be useful to quantify the complex trajectories of fluorescent particles in living cells.     

Correlation of nuclear acceptor sites for oestrogen receptors with gene transcription in vitro

1. Membrane particles prepared from ultrasonically-disrupted, aerobically-grown Escherichia coli were centrifuged on to a plastic film that was supported perpendicular to the centrifugal field to yield oriented membrane multilayers. In such preparations, there is a high degree of orientation of the planes of the membranes such that they lie parallel to each other and to the supporting film. 2. When dithionite- or succinate-reduced multilayers are rotated in the magnetic field of an e.p.r. spectrometer, about an axis lying in the membrane plane, angular-dependent signals from an iron-sulphur cluster at g(x)=1.92, g(y)=1.93 and g(z)=2.02 are seen. The g=1.93 signal has maximal amplitude when the plane of the multilayer is perpendicular to the magnetic field. Conversely, the g=2.02 signal is maximal when the plane of the multilayer is parallel with the magnetic field. 3. Computer simulations of the experimental data show that the cluster lies in the cytoplasmic membrane with the g(y) axis perpendicular to the membrane plane and with the g(x) and g(z) axes lying in the membrane plane. 4. In partially-oxidized multilayers, a signal resembling the mitochondrial high-potential iron-sulphur protein (Hipip) is seen whose g(z)=2.02 axis may be deduced as lying perpendicular to the membrane plane. 5. Appropriate choice of sample temperature and receiver gain reveals two further signals in partially-reduced multilayers: a g=2.09 signal arises from a cluster with its g(z) axis in the membrane plane, whereas a g=2.04 signal is from a cluster with the g(z) axis lying along the membrane normal. 6. Membrane particles from a glucose-grown, haem-deficient mutant contain dramatically-lowered levels of cytochromes and exhibit, in addition to the iron-sulphur clusters seen in the parental strain, a major signal at g=1.90. 7. Only the latter may be demonstrated to be oriented in multilayer preparations from the mutant. 8. Comparisons are drawn between the orientations of the iron-sulphur proteins in the cytoplasmic membrane of E. coli and those in mitochondrial membranes. The effects of diminished cytochrome content on the properties of the iron-sulphur proteins are discussed.     

A scapular coordinate frame for clinical and kinematic analyses

The aim of this study was to define a body-fixed coordinate frame for the scapula that minimises axes variability and is closely related to the clinical frame of reference. Medical images of 21 scapulae were used to quantify 14 different axes from identifiable landmarks. The plane of the blade of the scapula was defined. The orientations of the quantified axes were calculated. The angular relationships between axes were quantified and applied to grade the sensitivity of each axis to inter-scapular variations in the others. The volume of data required to define an axis was noted for its dependency on pathology and the three criteria were weighted according to relative importance. The two axes with the highest weighting were applied to define a body-fixed Cartesian coordinate frame for the scapula. A least square medio-lateral line through the centre of the spine root was the most optimal axis. The plane formed by the spine root line and a least square line through the centre of the lateral border ridge was the most optimal scapular plane. This body-fixed Cartesian coordinate frame is closely aligned to the cardinal planes in the anatomical position and thus is a clinically applicable, specimen invariant coordinate frame that can be used in patient-specific kinematics modelling.     

Can axes conventions of the trunk reference frame influence breast displacement calculation during running?

To obtain breast motion relative to the trunk, skin markers are used to define a local coordinate system (trunk), with respect to the global reference frame. This study aimed to quantify any differences in multiplanar breast displacement relative to the trunk using the first axis of rotation as either the mediolateral or longitudinal axis. Ten female participants ran on a treadmill (10 kph) in three different breast supports (no bra, everyday bra, sports bra). Four reflective markers placed on the trunk and right nipple were tracked using eight infrared cameras (200 Hz) during five running gait cycles in each breast support condition. Following marker identification, right breast multiplanar displacements were calculated relative to the trunk using either the mediolateral axis or the longitudinal axis as the first rotational axis to define the orthogonal local coordinate system. Results showed that there was a significant difference (8.2%) in superioinferior breast displacement in the sports bra condition when calculated using different axes conventions for the trunk segment. Furthermore, the greatest magnitude of breast displacement occurred in a different direction depending upon the selection of the first rotational axis. The definition of the primary reference axis of the trunk significantly alters the magnitude of superioinferior breast displacement and therefore it is recommended that the previously reported ‘stable’ longitudinal axis should be defined as the first rotational axis during running. Caution should also be used as the axes convention influences the magnitude and direction of breast support requirements, which has important implications for bra design.     

The finite displacements vector's method: an application to the scoliotic spine

This paper presents a vectorial method to directly obtain the components of the screw displacement between two positions of a body in a three-dimensional space (position of the helical axis of motion, rotation around this axis and translation along it). This method can be applied either to the case of a bone, moving with respect to the reference frame, or to the case of the relative motion of a joint; it gives exact formulae even if the displacements are finite; it generalizes the results (already published) obtained for finite displacements in the plane. The involved computation is easy, and the use of this method deals with only a small magnification of experimental errors. The technique of a screw displacement is applied to the vertebral segments of a scoliolic spine. The necessary data is taken from a couple of in-vivo X-rays. The goals of this study are: first, to describe the shape of the spine at each step of its evolution and second, to quantify the evolution in time of any segment of the spine between two states.     

Object localization with whiskers

Rats use their large facial hairs (whiskers) to detect, localize and identify objects in their proximal three-dimensional (3D) space. Here, we focus on recent evidence of how object location is encoded in the neural sensory pathways of the rat whisker system. Behavioral and neuronal observations have recently converged to the point where object location in 3D appears to be encoded by an efficient orthogonal scheme supported by primary sensory-afferents: each primary-afferent can signal object location by a spatial (labeled-line) code for the vertical axis (along whisker arcs), a temporal code for the horizontal axis (along whisker rows), and an intensity code for the radial axis (from the face out). Neuronal evidence shows that (i) the identities of activated sensory neurons convey information about the vertical coordinate of an object, (ii) the timing of their firing, in relation to other reference signals, conveys information about the horizontal object coordinate, and (iii) the intensity of firing conveys information about the radial object coordinate. Such a triple-coding scheme allows for efficient multiplexing of 3D object location information in the activity of single neurons. Also, this scheme provides redundancy since the same information may be represented in the activity of many neurons. These features of orthogonal coding increase accuracy and reliability. We propose that the multiplexed information is conveyed in parallel to different readout circuits, each decoding a specific spatial variable. Such decoding reduces ambiguity, and simplifies the required decoding algorithms, since different readout circuits can be optimized for a particular variable.     

A spatial property of the retino-cortical mapping

Striate cortex topography derives from a stretching of retinal space along the optic axis. At the retina, relative distances are preserved in a mapping of retinal space onto a spherical surface in the environment. At the cortex, relative distances along visual meridia in the cortical map are preserved in a mapping of striate cortex onto an environmental conic surface whose base is in the plane of the eye. This eco-cortical relationship can be considered a reference frame through which spatial relationships at the cortex might provide information about the environment. The present analysis provides an explanation of changes in cortical magnification with visual eccentricity in the primate and a detailed three-dimensional model of striate topography for the macaque monkey. In man, a conic environmental surface is shown to be uniformly resolvable along meridia in the visual field. Finally, the implications of this analysis of the structural properties of the retino-striate pathway and visual resolution are considered in relation to depth and distance perception.     

High-resolution magnetoencephalography--studies with a small-volume phantom]

To investigate the spatiotemporal organisation of neuronal processes in an animal model using magnetoencephalography (MEG), a high temporal resolution (ms) and an appropriate spatial resolution of about 1 mm is necessary. With the aim of determining the localization error and the resolution power of high-resolution MEG systems, we developed a phantom capable of simulating the characteristics of animal models. The phantom enables us to variably position at least two magnetic field sources to within 0.1 mm. For source localization on the basis of the magnetic field data, a spatial filtering algorithm was used. The investigation of a 16-channel micro SQUID-MEG system with a current dipole orientated tangentially to the phantom surface produced the following localization data (min ... max, x, y--horizontal plane, z--depth); systematic localization error e(x) = 1.16 ... 1.67 mm, e(y) = -1.01 ... -1.28 mm, e(z) = -5.22 ... -7.64 mm, standard deviation of the individual measurements perpendicular to the dipole axis s(perp) = 0.05 ... 0.22 mm, along this axis s(long) = 0.20 ... 1.73 mm, in the depths sz = 0.17 ... 3.17 mm. The "goodness of fit" was > 95%. Separation of two dipoles was still possible for parallel dipoles at a distance apart of d(parallel) = 0.03 mm and for those oriented perpendicularly to each other at a distance apart of d(perp) = 0.10 mm. On the basis of these results we conclude that the MEG system can achieve a resolution sufficient to permit the investigation of neuronal microstructures. The spatial errors detected were related to sensor position in the cryostatic vessel as well as to external low-frequency noise.     

Quantitation of secondary structure in ATR infrared spectroscopy

Polarized attenuated total reflection infrared spectroscopy of aligned membranes provides essential information on the secondary structure content and orientation of the associated membrane proteins. Quantitation of the relative content of different secondary structures, however, requires allowance for geometric relations of the electric field components (E(x), E(y), E(z)) of the evanescent wave, and of the components of the infrared transition moments, in combining absorbances (A() and A( perpendicular)) measured with radiation polarized parallel with and perpendicular to, respectively, the plane of incidence. This has hitherto not been done. The appropriate combination for exact evaluation of relative integrated absorbances is A() + (2E(z)(2)/E(y)(2) - E(x)(2)/E(y)(2))A( perpendicular), where z is the axis of ordering that is normal to the membrane plane, and the x-axis lies in the membrane plane within the plane of incidence. This combination can take values in the range approximately from A() - 0.4A( perpendicular) to A() + 2.7A( perpendicular), depending on experimental conditions and the attenuated total reflection crystal used. With unpolarized radiation, this correction is not possible. Similar considerations apply to the dichroic ratios of multicomponent bands, which are also treated.     

Muscle forces predicted using optimization methods are coordinate system dependent

Optimization methods are widely used to predict in vivo muscle forces in musculoskeletal joints. Moment equilibrium at the joint center (usually chosen as the origin of the joint coordinate system) has been used as a constraint condition for optimization procedures and the joint reaction moments were assumed zero. This study, through the use of a three-dimensional elbow model, investigated the effect of coordinate system origin (joint center) location on muscle forces predicted using a nonlinear static optimization method. The results demonstrated that moving the origin of the coordinate system medially and laterally along the flexion-extension axis caused dramatic variations in the predicted muscle forces. For example, moving the origin of the coordinate system from a position 5mm medial to 5mm lateral of the geometric elbow center caused the predicted biceps force to vary from 12% to 46% and the brachialis force to vary from 80% to 34% of the total muscle loading. The joint reaction force reduced by 24% with this medial to lateral variation of the coordinate system origin location. This data revealed that the muscle forces predicted using the optimization method are sensitive to the coordinate system origin location due to the zero joint reaction moment assumption in the moment constraint condition. For accurate prediction of muscle load distributions using optimization methods, it is necessary to determine the accurate coordinate system origin location where the condition of a zero joint reaction moment is satisfied.     

Label-free quantitative proteomics using large peptide data sets generated by nanoflow liquid chromatography and mass spectrometry

We developed an integrated platform consisting of machinery and software modules that can apply vast amounts of data generated by nanoflow LC-MS to differential protein expression analyses. Unlabeled protein samples were completely digested with modified trypsin and separated by low speed (200 nl/min) one-dimensional HPLC. Mass spectra were obtained every 1 s by using the survey mode of a hybrid Q-TOF mass spectrometer and displayed in a two-dimensional plane with m/z values along the x axis, and retention time was displayed along the y axis. The time jitter of nano-LC was adjusted using newly developed software based on a dynamic programming algorithm. The comprehensiveness (60,000-160,000 peaks above the predetermined threshold detectable in 60-microg cell protein samples), reproducibility (average coefficient of variance of 0.35-0.39 and correlation coefficient of over 0.92 between duplicates), and accurate quantification with a wide dynamic range (over 10(3)) of our platform warrant its application to various types of experimental and translational proteomics.     

The combination of peripheral nerve grafts and acidic fibroblast growth factor enhances arginase I and polyamine spermine expression in transected rat spinal cords

Dual-focus imaging optics for three-dimensional tracking of individual quantum dots has been developed to study the molecular mechanisms of motor proteins in cells. The new system has a high spatial and temporal precision, 2 nm in the x-y sample plane and 5 nm along the z-axis at a frame time of 2 ms. Three-dimensional positions of the vesicles labeled with quantum dots were detected in living cells. Vesicles were transported on the microtubules using 8-nm steps towards the nucleus. The steps had fluctuation of approximately 20 nm which were perpendicular to the axis of the microtubule but with the constant distance from the microtubule. The most of perpendicular movement was not synchronized with the 8-nm steps, indicating that dynein moved on microtubules without changing the protofilaments. When the vesicles changed their direction of movement toward the cell membrane, they moved perpendicular with the constant distance from the microtubule. The present method is powerful tool to investigate three dimensional movement of molecules in cells with nanometer and millisecond accuracy.     

In-vivo measurement of dynamic joint motion using high speed biplane radiography and CT: application to canine ACL deficiency

Dynamic assessment of three-dimensional (3D) skeletal kinematics is essential for understanding normal joint function as well as the effects of injury or disease. This paper presents a novel technique for measuring in-vivo skeletal kinematics that combines data collected from high-speed biplane radiography and static computed tomography (CT). The goals of the present study were to demonstrate that highly precise measurements can be obtained during dynamic movement studies employing high frame-rate biplane video-radiography, to develop a method for expressing joint kinematics in an anatomically relevant coordinate system and to demonstrate the application of this technique by calculating canine tibio-femoral kinematics during dynamic motion. The method consists of four components: the generation and acquisition of high frame rate biplane radiographs, identification and 3D tracking of implanted bone markers, CT-based coordinate system determination, and kinematic analysis routines for determining joint motion in anatomically based coordinates. Results from dynamic tracking of markers inserted in a phantom object showed the system bias was insignificant (-0.02 mm). The average precision in tracking implanted markers in-vivo was 0.064 mm for the distance between markers and 0.31 degree for the angles between markers. Across-trial standard deviations for tibio-femoral translations were similar for all three motion directions, averaging 0.14 mm (range 0.08 to 0.20 mm). Variability in tibio-femoral rotations was more dependent on rotation axis, with across-trial standard deviations averaging 1.71 degrees for flexion/extension, 0.90 degree for internal/external rotation, and 0.40 degree for varus/valgus rotation. Advantages of this technique over traditional motion analysis methods include the elimination of skin motion artifacts, improved tracking precision and the ability to present results in a consistent anatomical reference frame.     

Determination of 3D spinal kinematics without defining a local vertebral coordinate system

In this paper a method is presented to calculate Euler's angles of rotation of a body segment during locomotion without a priori defining the location of the center of rotation, and without defining a local vertebral coordinate system. The method was applied to in vivo spinal kinematics. In this method, the orientation of each segment is identified by a set of three markers. The orientation of the axes of rotation is calculated based on the average position of the markers during one stride cycle. Some restrictions and assumptions should be made. The approach is viable only when the average orientation of the anatomical axes of rotation of each spinal segment during a stride cycle coincides with the three axes of the laboratory coordinate system. Furthermore, the rotations should be symmetrical with respect to both sides of the plane of symmetry of the spinal segment, and the subject should move parallel to one axis of the laboratory coordinate system. Since in experimental conditions these assumptions will only be met approximately, errors will be introduced in the calculated angles of rotation. The magnitude of the introduced errors was investigated in a computer simulation experiment. Since the maximal errors did not exceed 0.7° in a range of misalignments up to 10° between the two coordinate systems, the approach proved to be a valid method for the estimation of spinal kinematics.     

Lateral line stimulation patterns and prey orienting behavior in the Lake Michigan mottled sculpin (Cottus bairdi)

Information contained in the spatial excitation pattern along arrayed sensors in the lateral line system of Lake Michigan mottled sculpin, as well as other surface-feeding fish and amphibians, is thought to play a fundamental role in guiding prey-orienting behaviors. However, the way in which prey location is encoded by the excitation pattern and used by the nervous system to direct orienting behaviors is largely unknown. In this study, we test the hypothesis that mottled sculpin use excitation peaks (local ‘hot spots’) to determine the somatotopic location of an artificial prey (vibrating sphere/dipole source) along the body surface. Dipole orientation (axis of sphere vibration re: long axis of the fish) is manipulated to produce excitatory peaks in different body locations without changing the actual sphere location. Our results show that orienting accuracy is largely independent of source orientation, but not source distance and that turning directions are not guided by local hot spots in the somatotopic activation pattern of the lateral line.     

A new coordinate system using the orbital axis for morphological analysis of primate skulls

A new coordinate system for primate skulls was defined by the orbital axis and the validity of the system was examined. This system is thought to be equivalent throughout the primates. With the aid of photogrammetry the three-dimensional coordinates of 39 points on the skulls of 479 individuals comprising 54 species including man were accurately measured. The orbital structure is morphologically stable and its axis represents a comparative horizontal. The midsagittal plane and the bilateral symmetry of the cranium are also stable. The morphological stability in angular dimensions is confirmed by a standard deviation smaller than 2.0°. The major evolutionary change in the neurocranium is the inclination of the cranial base from the orbital horizon, and the inclination is related to the neurocranial size. The ear-eye plane is generally inapplicable to the primates, because it is affected by the orbital size and the descent of the auricular part due to the inclination of the cranial base. The clivus line or the vestibular coordinate system is not desirable as the horizontal, either. The evolutionary development of the facial part of the cranium is independent of that of the neurocranium and these two parts are separated by the orbital horizon.     

Estimation of the longitudinal axis of line symmetrical soft bodies by stereophotogrammetry

The three-dimensional (3-D) position of rigid body segments is generally determined by stereophotogrammetry: the position of markers or marker-trees, fixed onto the rigid body, is identified in each of at least 2 images.Soft bodies like the tongue of a snake are not rigid and difficult to attach marker onto. Therefore, a method is developed to estimate the 3-D position of the central axis from the digitised contours.The 3-D finite spatial curve representing the tongue axis is described by a function of a fourth variable t,tin[0,1]. The projection of this line [x(t),y(t),z(t)], a polynomial curve of a user-defined order, was fitted onto minimally 2 recorded images by means of direct linear transformation. The result is an optimally estimated finite spatial curve defined by the polynomial parameters. The method is applicable for all line symmetrical organs or segments.     

Identification of the functional initiation codons of a phase-variable gene of Haemophilus influenzae, lic2A, with the potential for differential expression

Simple sequence repeats located within reading frames mediate phase-variable ON/OFF switches in gene expression by generating frameshifts. Multiple translation initiation codons in different reading frames are found upstream of most Haemophilus influenzae tetranucleotide repeat tracts, raising the possibility of multiple active reading frames and more than two levels of gene expression for these loci. Phase variation between three levels of gene expression (strong, weak, and none) was observed when lic2A was fused to a lacZ reporter gene. The lic2A 5' CAAT repeat tract is preceded by four 5' ATG codons (x, y, z1, and z2) in two reading frames. Each of these initiation codons was inactivated by site-directed mutagenesis. Strong expression from frame 1 was associated with x but not y. Weak expression from frame 2 was mainly dependent on the z2 codon, and there was no expression from frame 3. Using monoclonal antibodies specific for a digalactoside epitope of lipopolysaccharide whose synthesis requires Lic2A, two levels (strong and undetectable) of antibody reactivity were detected, suggesting that weak expression of lic2A is not discernible at the phenotypic level. Inactivation of the x initiation codon resulted in loss of strong expression of the digalactoside epitope and elevated killing by human serum. The failure to detect more than two phenotypes for lic2A, despite clear evidence of weak expression from the z1/z2 initiation codons, leaves open the question of whether or not multiple initiation codons are associated with more complex patterns of phenotypic variation rather than classical phase-variable switching between two phenotypes.     

Protein structure by solid state nuclear magnetic resonance. Residues 40 to 45 of bacteriophage fd coat protein

The three-dimensional structure of part of the coat protein in the filamentous bacteriophage fd is described by nuclear magnetic resonance (n.m.r.). Residues 40 to 45 are in a somewhat distorted alpha-helix. This n.m.r. approach for determining protein structure relies on the spectral manifestations of chemical shift and heteronuclear dipolar couplings in a symmetrical assembly of protein subunits oriented parallel to the applied magnetic field. The angles between individual peptide linkages and the filament axis of the virion constitute the basic source of structural information. These angles are directly related to x, y, z co-ordinates for describing the protein structure.