C R Worthington's research while affiliated with Carnegie Mellon University and other places
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Publications (75)
We reconsider the use of stiffness measurements to estimate N, the number of myosin heads acting (working at any instant to produce tension) on a single actin filament in vertebrate striated muscle, and give reasons for our rejection of numbers produced from such measurements. We go on to present a different approach to the problem, citing and exte...
Piazzesi et al. [G. Piazzesi, L. Lucii, V. Lombardi, J. Physiol. 545 (2002) 145-151] made a study on the muscle transients due to step changes in force using improved time resolution and recorded filament movement and shortening velocities in the four phases. They point to Phase 2 and to Phase 4 (working muscle) and claim that their results do not...
We derive the energy rate equation for muscle contraction. Our equation has only two parameters m, the maintenance heat rate and 1/S, the shortening heat coefficient. The impulsive model (previously described in earlier papers) provides a physical basis for parameter 1/S as well as for constants a and b in Hill's force-velocity equation. We develop...
Apart from a few experimental studies muscle viscosity has not received much recent analytical attention as a determinant of the contractile process. This is surprising, since any muscle cell is 80% water, and may undergo large shape changes during its working cycle. Intuitively, one might expect the viscosity of the solvent to be an important dete...
We use the step-size distance equation z = u/n developed in our two previous papers (z is the step-size distance, u is the actin filament relative velocity and n is the rate of ATP splitting on a given actin filament), and introduce one additional concept: that the impulsive contractile forces developed on an actin filament should proceed sequentia...
The step-size distance in muscle contraction is obtained using the step-size distance equation z = u/n, where z is the step-size distance, u is the actin filament velocity and n is the ATPase rate of splitting. In a previous study a step-size distance of about 17 A at no load was determined for intact frog muscle. Some properties of the step-size e...
We derive the step-size distance, and the impulse time per ATP split, from a consideration of Hill's energy rate equation coupled with the enthalpy available per ATP split. This definition of step-size distance is model-independent, and is calculated to have a maximum of 17 A at no load and to reduce to zero at isometric tension, since it will depe...
A new molecular model is proposed for muscle contraction, that involves the electrical charging of the long (C-terminal) alpha-helical part of the head of the myosin molecule (S1) while the head is attached to actin; as it charges the alpha-helical part moves in the radial electric field between the filaments. The alpha-helical part snaps back when...
A new molecular model is proposed for muscle contraction, that involves the electrical charging of the long (C-terminal) α-helical part of the head of the myosin molecule (S1) while the head is attached to actin; as it charges the α-helical part moves in the radial electric field between the filaments. The α-helical part snaps back when the myosin...
We have performed x-ray scattering measurements of the wide-angle region of the gel phase of fully hydrated unoriented multilamellar vesicles of dipalmitoylphosphatidylcholine that quantitate two satellite peaks in addition to the usual (20) and (11) peaks. All the peaks in the wide-angle region are adequately fit using an electron density model co...
The tilt angle theta tilt of the hydrocarbon chains has been determined for fully hydrated gel phase of a series of saturated lecithins. Oriented samples were prepared on glass substrates and hydrated with supersaturated water vapor. Evidence for full hydration was the same intensity pattern of the low angle lamellar peaks and the same lamellar rep...
The intermolecular and interfibrillar spacings of collagen in bovine corneal stroma have been measured as a function of tissue hydration. Data were recorded from low- and high-angle x-ray diffraction patterns obtained using a high intensity synchrotron source. The most frequently occurring interfibrillar spacing varied from 34 nm in dry corneas to...
X-ray diffraction spacings in multilayered membranes obtained from frog sciatic nerves were found to increase in discrete steps of approx. 5 A during swelling. These observed jumps in the repeat period suggest that the lipid bilayers exist in distinct states of hydration, and perhaps the swelling occurs by step-wise addition of water layers between...
In paper I of helical diffraction [Worthington & Elliott (1989). Acta Cryst. A45, 645-654] an expression for the autocorrelation function (a.c.f.) for a helix was obtained. The Fourier transform of this a.c.f. gave a new expression for the diffracted intensity. In paper II the theory is extended to real helices containing subunits of finite size. T...
In a new approach to helical diffraction a helix generating function is defined, and thence an expression for the autocorrelation function (a.c.f.) for a helix is obtained. The Fourier transform of this a.c.f. gives a new expression for the diffracted intensity, which is shown to be equivalent formally to the classical expression of Cochran, Crick...
Biological membrane assemblies with two membranes per unit cell and with well defined fluid layers are treated. In membrane diffraction the minus fluid model is used. A method for the determination of the zero-order amplitude using knowledge of the membrane-pair width is described. Sampling-theorem expressions for the Fourier transform of the indiv...
Low-angle X-ray diffraction patterns have been recorded from the cornea. A fibre diagram was obtained: the reflections from the axial period of collagen were on the equator while reflections from the collagen fibril lattice structure were on the meridian. Only the reflections from tha array of collagen fibrils have been studied. These reflections c...
The anatomy and physiology of cornea has been described in reviews (Maurice, 1969; Davson, 1980). We are primarily concerned with the structure of the stroma of cornea. There are two levels of organization in the stroma: the collagen fibrils and the lamellae. Each lamella contains an array of collagen fibrils which appear as long thin cylinders in...
Differential scanning calorimetry has been used to study thermal properties of the frog sciatic nerve. Heating scans of whole peripheral nervous system nerves show three endotherms: A (48°C), B (54°C) and C (62°C), which disappear in second heating scans. Homogenized myelin prepared from the sciatic nerves does not display any of these endotherms....
It has been known for more than two decades that peripheral nerve shows X-ray reflections other than those originating from the myelin sheath. These extra reflections are at small angles of diffraction and arise from a variation of electron density in the radial direction. X-ray diffraction studies since 1973 have identified these reflections as co...
Improved X-ray diffraction data from dry nerve myelin are presented. In addition to the spacing of approx. 150 A, 44 A and 34.6 A, which have been previously reported, we identify a 14 A series. The data suggests that the hydrocarbon chains in the single bilayer (approximately equal to 60 A) is ordered, whereas in the double bilayer (approximately...
A method of deconvolution using the modulus of the continuous Fourier transform of the unit cell is described. This method differs from previous deconvolution methods in membrane diffraction in that calculations are carried out in reciprocal space. The modulus profile is obtained from the continuous intensity transform which is itself the Fourier t...
The problem of assigning the phase to the first-order reflection in membrane diffraction is treated. Biological membrane assemblies with two membranes per unit cell and the special case of lipid bilayers are treated. Phase assignment is dependent on the origin value of the minus fluid or the minus lipid model and on the actual asymmetry of the memb...
Low-angle X-ray diffraction patterns have been recorded from frog sciatic nerves in Ringer's solution after heat treatment from 20 to 80°C. The X-ray patterns were obtained from the heat treated specimens after cooling to room temperature. The normal X-ray pattern of frog sciatic nerve in Ringer's solution with was maintained from 20 to 58°C. Above...
Procedures for correcting experimental diffraction intensities in the small-angle region for the determination of one-dimensional structures are presented. The diffraction patterns in question consist of meridional streaks which are transversely broadened due to: (1) finite fibril radius, (2) imperfect fibrillar orientation, (3) lamellar curvature...
Low-angle X-ray diffraction patterns have been recorded from frog sciatic nerve after digestion with trypsin and Pronase. Reproducible X-ray patterns were obtained by swelling the nerves in distilled water before treatment with enzymes. The X-ray patterns of enzyme-treated nerves are distinctly different from the X-ray pattern of normal (live) nerv...
The Fourier-transform values are obtained by multiplying the integrated intensities of X-ray patterns by the correction factor C(h). The problem of determining C(h) for biological specimens which have a planar multi-layered structure and which remain stationary during the X-ray experiment is treated. Parameters for evaluating C(h) can be obtained f...
The protein compositions of peripheral nervous system myelin proteins from rat, rabbit, and frog Rana pipiens were examined by gel electrophoresis after discontinuous sucrose gradient purification. The major P0 protein and the basic proteins P1 and P2 were shown to be doublets. Gel patterns of frog sciatic nerve after digestion in trypsin and Prona...
Low-angle X-ray diffraction patterns have been recorded from frog sciatic nerve in pH solutions of 0.1–13.0. The normal X-ray pattern of frog sciatic nerve in Ringer's solution is maintained at pH 4.0–10.0. In acid pH, 2.5–4.0, and in alkaline pH, 10.0–11.0, the nerve myelin is in the partial swollen state. The partial swollen state and the normal...
The Fourier transform values are obtained by multiplying the integrated intensities by the correction factor C(h). The problem of calculating the correction factor for biological specimens which have a multilayered structure is treated. Allowance is made for the transverse size of the specimen, the disorientation in the specimen (ω), the divergence...
X-ray diffraction from oriented bilayers of sphingomyelin gave up to 14 orders of diffraction of a lamellar repeat of 68.5 A on the merididan and up to eight reflections, including a strong reflection at 4.2 A, on the equator. The diffraction spacings did not change when the sphingomyelin bilayers were exposed to different humidities. A direct anal...
A method of determining the phases of X-ray reflections from oriented model membrane systems at low resolution is described. The method involves deconvolution and requires that d less than or equal to 2v where v is the width of the head group region within the bilayer and d is the thickness of the bilayer. The method can be used with a single set o...
Oriented samples of sphingomyelin (SM), cholesterol (CHOL) and their mixtures in SM : CHOL molar proportions of 4 : 1, 3 : 1, 2 : 1, 1 : 1 and 1 : 2 were studied by x-ray diffraction. These samples were in multilayered form such that a series of discrete series of x-ray reflections were recorded from a well-defined lamellar repeating distance. Samp...
THE structure of photoreceptor membranes in the rod outer segments of
vertebrates has been studied using X-ray diffraction1-3, and
electron density profiles of the disk membrane at a resolution of 14
Å have been obtained4. The ultra-structure of
invertebrate rhabdomeric visual cells have been studied using electron
microscopy5 and birefringence6, b...
Low-angle X-ray diffraction patterns of peripheral nerve myelin after modification by either rehydration in various solutions or by chemical treatment have been recorded. These X-ray patterns and the previously reported modified nerve myelin patterns demonstrate that nerve myelin has at least five different states: the normal state, condensed state...
Low-angle X-ray diffraction patterns have been recorded from cattle and rabbit optic nerves swollen in glycerol solutions. The new X-ray data have a resolution of about 15 to 16 Å. Analysis of the low-angle X-ray data indicates that the myelin layers of optic nerves swell in units of four membranes, that is, two membrane pairs adhere together durin...
Low-angle X-ray diffraction patterns have been recorded from normal nerve and nerve swollen in glycerol solutions. The new X-ray data have a resolution of 7 A. Direct methods of structure analysis which include deconvolution of the auto-correlation function and sampling theorem reconstructions have been used in the interpretation of the X-ray data....
Low-angle X-ray diffraction has been recorded from oriented preparations of sacroplasmic reticulum membranes in fluid media containing glycerol solutions in different concentrations. Discrete diffraction orders of a lamellar repeat distance ranging from 200 Å to 250 Å have been recorded. Fourier synthesis at a resolution of 17 Å for 0, 10, 20, and...
New low-angle X-ray diffraction data have been obtained from nerve myelin after rehydration. The X-ray patterns show the first six orders of diffraction of a lamellar repeat unit of about 100 Å. Direct methods of structure analysis have been used to determine uniquely the phases of the first three orders of diffraction. The electron density profile...
New X-ray diffraction data from normal nerve and nerve swollen in glycerol solutions have been recorded. Direct methods of structure analysis have been used in the interpretation of the X-ray data, and the phases of the first five orders of diffraction of peripheral nerve myelin have been uniquely determined. The direct methods include deconvolutio...
The use of the low-angle x-ray diffraction method in biology is described. Some x-ray diffraction patterns have been known since the early 1930's but, in the last decade, many new patterns, which show more reflections than previously, have been recorded. An interpretation of these improved patterns of biological systems provides detailed informatio...
X-ray diffraction intensities from frog and cattle retinal rod segments have been interpreted in terms of an electron density distribution along the rod axis. Phases were uniquely determined using direct methods of structure analysis. The correction factor was derived in explicit form and its value was obtained experimentally. The average electron...
This chapter discusses the results of recent X-ray diffraction studies on cell membranes. Membrane ultra-structure is more often studied by electron microscopy, but the X-ray diffraction method has an important advantage in that membranes can be maintained in a living condition during the X-ray experiment. X-Ray studies on membranes have their own...
Evidence is presented for the structure of the Gaucher cell deposit existing as a series of bilayers that are each 60 Å thick and are gradually twisted along their length. This evidence was obtained by freeze-etching studies and by X-ray diffraction studies that were used to calculate possible electron density profiles for each bilayer. A model is...
Electron density profile of nervemyel in at a resolution of 7 Å has been determined using a direct method of structure analysis. The results provide a basis for interpreting the molecular distribution of the nerve myelin membrane.
Vesicles of fragmented sarcoplasmic reticulum membranes have been prepared and centrifuged into a multilayered form suitable for analysis by X-ray diffraction. X-ray diffraction has been recorded from a regular stacking of flattened vesicles in the presence of excess fluid. Discrete orders of a lamellar repeat distance ranging from 220 to 270 Å hav...
Fourier synthesis of chemically treated nerve indicated that the membrane pair had shrunk by about 9 Å. Although the resolution of the Fourier synthesis was 17 Å, this observed shift in the membrane profile is significant as the X ray diffraction intensities are sensitive to shifts as small as 1 or 2 Å.
The theory of direct methods of structure analysis in the case of multilayered membrane-type systems which contain fluid layers is described. Diffraction formulas for this kind of analysis are derived. Deconvolution methods are used when the centrosymmetrical unit cells contain wide fluid layers. When the membrane systems contain narrow fluid layer...
THE structure of the nerve membranes within the myelin sheath of frog sciatic nerve has been studied by low-angle X-ray diffraction. Many additional orders of diffraction have been recorded from nerve, and, from a structure analysis of this new X-ray data, a twelve-parameter electron density model is proposed. Fourier series representations of the...
A method of phase determination which involves an analytic continuation of the Fourier transform is described. The method has been successfully used to obtain the phases of some of the higher orders of nerve myelin.
A structure analysis of the low-angle X-ray diffraction data from nerve myelin is described. The low-angle X-ray data are interpreted in terms of an electron density strip model which has five parameters, these refer to the dimensions of the membrane pair and their component electron densities. Three sets of low-angle X-ray data from peripheral ner...
Low-angle X-ray data from live myelinated nerve are interpreted in terms of an electron density strip model containing a total of seven parameters. Model parameters are assigned to three varieties of peripheral nerve and two kinds of central nervous system nerve. Cytoplasmic and extracellular fluid channels which occur as independent layers paralle...
A series of low-angle X-ray reflections have been recorded from photoreceptors in four types of intact untreated retinae. The retinae were maintained in a living condition during the X-ray exposure. The X-ray reflections arise from the regular arrangement of disk membranes within the photoreceptors. The recorded X-ray intensities contain informatio...
Low-angle X-ray diffraction patterns from a variety of myelinated nerves are described. Different kinds of patterns are obtained from peripheral nerve and central nervous system myelin. The intensity variation between the first five diffraction orders is the same for each variety of peripheral nerve myelin, and similarly, an intensity variation exi...
The swelling behavior of peripheral nerve myelin has been studied by recording low-angle X-ray diffraction patterns of nerve after various chemical treatments. Peripheral myelin swells in distilled water, hypotonic Ringer's solution and sucrose solutions. The resulting low-angle pattern is called a swollen pattern (by comparison, the normal pattern...
Low-angle X-ray diffraction patterns were obtained from ordered ultracentrifugal pellets of wet receptor disk membranes which had been either treated with antirhodopsin serum, normal rabbit serum, serum albumin, or untreated prior to sedimentation. A preliminary analysis of these patterns indicated: (a) differences between antirhodopsin serum treat...
The use of one-dimensional electron density strip models in interpreting low-angle X-ray data from planar and concentric multilayered structures is described. Diffraction formulas for an n-strip model are given. Fourier transforms, normalization constants, and Patterson functions are derived for certain strip models.
Low-angle X-ray diffraction arising from 40 to 50 Å particles within wet frog retinal receptor disk membranes at 26 °C was not consistent with a planar crystalline lattice of the particles within the disk membranes. The nature of the diffraction suggested the possibility of a planar liquid-like arrangement of the particles. Such an arrangement is s...
THE swelling of freshly dissected frog sciatic nerve myelin in sucrose solutions has been studied by low-angle X-ray diffraction. Our analysis of the X-ray data leads to a choice between two possible triple layered membrane units and also allows us to assign an absolute electron density scale to the favoured model.
The transmittance of a hologram is described in terms of Fresnel transformation. This description facilitates the establishment of requirements for the hologram-recording material and it leads naturally to a classification of holograms made from plane transmitting objects illuminated by a point source. Four subtypes are singled out: the Fresnel-tra...
Low angle X-ray diffraction can be recorded from planar and concentric multilayered (biological) structures. In order to proceed with the X-ray analysis the relation between the observed intensities and the Fourier transform of the unit cell is required. This relation is derived for planar structures such as retinal rods, mitochondria, and collagen...
An optical analogue experiment related to a method of X-ray microscopy by successive Fourier transformation is described. Some experimental design features are discussed. Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/33445/1/0000848.pdf
A convolution formulation of Fresnel diffraction is presented. The diffracted amplitude is expressed as a convolution in either direct or reciprocal space. Approximations involve the use of parabolic wavefronts and the omission of the obliquity factor. The formulation is readily applied to many optical phenomena.
Ordered arrays of particles about 40 Å in diameter within the outer segment membranes of retinal receptor have been observed by electron microscopy, and low-angle X-ray diffraction studies are in agreement with this finding. Surface-on views of outer segment membranes negatively-stained with phospho-tuhgstate or fixed with permanganate show square...
A theory of Fresnel images is presented. Only the Fresnel images of plane periodic objects viewed in monochromatic light are considered. The theory is in agreement with the experimental and computer research available in the literature. Photographs of Fresnel images of gratings are shown to verify certain aspects of the theory.
Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/32040/1/0000083.pdf
Citations
... In by Rumsby and Crang, 1977, and Kirschner et al., 1984). The changes in myelin period which result from these treatments have been summarized (Worthington, 1982; Kirschner et al., 1984), and the involvement of surface charge in determining membrane packing in myelin has been suggested (Worthington and Blaurock, 1969). The equilibrium separation between membrane surfaces is largely determined by a balance of forces: van der Waals attraction and electrostatic repulsion (Verwey and Overbeek, 1948; Parsegian, 1973; Rand, 1981), the undulation force (Helfrich, 1977), and short-range repulsion due to hydration (Rand, 1981; Marcelja and Radic, 1976) or steric stabilization (Napper, 1977; Bell et al., 1984). ...
... Allowance for this factor would bring the intensity ratio calculated from the model nearer to the observed value. A correction for the effects of specimen disorientation, curvature of the sphere of reflection, and divergence of the incident beam ( Wang and Worthington, 1975) would also decrease the discrepancy between calculated and observed ratios. It is likely, therefore, that the model represents a reasonable approximation to the experimental situation. ...
... The effect of temperature, freezing and drying has been extensively studied in the literature, see e.g. [51,190,[192][193][194] and references therein, however, the values reported in the references cannot be directly compared to the values reported here, primarily because the extracted nerve was typically re-immersed in a buffer solution after freezing or heating. Therefore, future extension of this work has to investigate whether myelin is indeed capable of forming hexatic phases. ...
... [13] There is therefore a compelling case for a smaller-scale mechanism that regulates the mechanical response of the cornea to load. X-ray scattering has been used extensively to study the nanostructure of the cornea in health [14,15] and disease [16], to inform mechanical models [17] and evaluate treatments [18]. The crystalline arrangement of collagen fibrils in the cornea makes it an ideal test bed for the study of collagen mechanics in general. ...
... PMP22 has been demonstrated to act as a membrane stacker [113], but PMP22 cannot rescue myelination when P0 is missing [114]. The periodicity of PNS myelin varies with pH [115], and comprehensive experiments establishing the role of electrostatics and proteins in periodic variation that stem from pH and ionic strength have been conducted [87,88], suggesting that the swelling of the IPL in PNS myelin largely depends on the abundance of negatively charged residues in the P0 Ig-like domain. This, however, was concluded before the structural characterization of the domain, and now, the width of the IPL is thought to be mostly governed by the apposition of Ig-like domains, as illustrated in Figure 2a. ...
... If we consider fractional multiples of this Talbot length 2λ −1 then we have to take into account the cancellation encoded in the quadratic Gauss sums [3]. More technical details of the optical setting of this effect may be found in [4], [5], [6]. ...
... An established technique to recover phase information from scattering experiments on lipid bilayer stacks is the so-called swelling method (e.g. [159] and references therein). It is based on thickness changes of the water layer d w separating adjacent bilayers. ...
... The sVS method results in highly symmetric bilayers, and thus v n can only be +1 or −1. The swelling method [13,33] was then applied in combination with the minus fluid model [69,70]. The resulting minus-fluid form factor F −1 (q z ) is a continuous function of q z and independent of the RH. ...
... Biochemical and structural works on myelin flourished during the 1970s and 1980s (Brunner et al 1989, Chia et al 1984a, 1984b, Worthington and McIntosh 1974, Worthington 1981, Harker 1972, Riccio et al 1985. One of the main reasons for the extended interest in myelin structure studies come from the fact that correlations have been found between its structural modifications and some common neurological degenerative events of pathological nature in humans. ...
... In this case the factor A(h/d) serves the function of an inverse Lorentz factor; it should be noted that this quantity is precisely the correction factor C(h) derived by Worthington & Wang. This method has been applied to the diffraction pattern of two biological structures by Worthington, Worthington & Wang (1980). While Worthington & Wang (1979) did not consider the effects of transverse line broadening due to coherent waviness of the structure within the fibrils (item 3), it can be shown that their approach still applies in the presence of this effect. ...
