Bolus contaminant dispersion in oscillating flow in curved tubes.

The investigation of longitudinal dispersion of tracer substances in unsteady flows has biomechanical application in the study of heat and mass transport within the bronchial airways during normal, abnormal, and artificial pulmonary ventilation. To model the effects of airway curvature on intrapulmonary gas transport, we have measured local gas dispersion in axially uniform helical tubes of slight pitch during volume-cycled oscillatory flow. Following a small argon bolus injection into the flow field, the time-averaged effective diffusion coefficient (Deff/Dmol) for axial transport of the contaminant was evaluated from the time-dependent local argon concentration measured with a mass spectrometer. The value of (Deff/Dmol) is extracted from the curve of concentration versus time by two techniques yielding identical results. Experiments were conducted in two helical coiled tubes (delta = 0.031, lambda = 0.022 or delta = 0.085, lambda = 0.060) over a range of 2 < alpha < 15, 3 < A < 15, where delta is the ratio of tube radius to radius of curvature, lambda is the ratio of pitch height to radius of curvature, alpha is the Womersley parameter or dimensionless frequency, and A is the stroke amplitude or dimensionless tidal volume. Experimental results show that, when compared to transport in straight tubes, the effective diffusivity markedly increases in the presence of axial curvature. Results also compare favorably to mathematical predictions of bolus dispersion in a curved tube over the ranges of frequency and tidal volume studied.     

Viscoelastic and rheological properties of concentrated solutions of proteoglycan subunit and proteoglycan aggregate

The oscillatory and steady shear rheological properties of concentrated solutions of proteoglycan subunit (PGS) and aggregate (PGA) from bovine articular cartilage have been studied using a Rheometrics fluids spectrometer. At comparable concentrations in the physiological range tan delta increases from 0.5 to 1.0 for PGA as the oscillation frequency (omega) increases from 10(-1) to 10(2) rads/s, compared to a decrease from 40 to 5 for PGS. Thus PGA solutions exhibit predominantly elastic response whereas those of PGS exhibit primarily viscous behavior. PGA solutions show pronounced shear-thinning behavior at all shear rates (gamma) in the range 10(-2) less than gamma (s-1) less than 10(2), whereas PGS solutions exhibit predominantly Newtonian flow. For PGA, the small-strain complex viscosity eta* (omega) is substantially smaller than the steady-flow viscosity eta(gamma) at comparable values of omega and gamma. These observations indicate that the presence of proteoglycan aggregates leads to formation of a transient or weak-gel network. Since aggregation leads to a large increase in molecular hydrodynamic volume and hence in the relaxation times for macromolecular rotation, it appears that role of aggregate formation is to shift the linear viscoelastic response from the terminal viscous flow into the plateau elastomeric regime of relaxational behavior. Normal or pathological changes that produce a decrease in aggregation will result in a loss of elastomeric behavior of the proteoglycan matrix.     

Healthy and diseased coronary bifurcation geometries influence near-wall and intravascular flow: A computational exploration of the hemodynamic risk

Local hemodynamics has been identified as one main determinant in the onset and progression of atherosclerotic lesions at coronary bifurcations. Starting from the observation that atherosensitive hemodynamic conditions in arterial bifurcation are majorly determined by the underlying anatomy, the aim of the present study is to investigate how peculiar coronary bifurcation anatomical features influence near-wall and intravascular flow patterns. Different bifurcation angles and cardiac curvatures were varied in population-based, idealized models of both stenosed and unstenosed bifurcations, representing the left anterior descending (LAD) coronary artery with its diagonal branch. Local hemodynamics was analyzed in terms of helical flow and exposure to low/oscillatory shear stress by performing computational fluid dynamics simulations.Results show that bifurcation angle impacts lowly hemodynamics in both stenosed and unstenosed cases. Instead, curvature radius influences the generation and transport of helical flow structures, with smaller cardiac curvature radius associated to higher helicity intensity. Stenosed bifurcation models exhibit helicity intensity values one order of magnitude higher than the corresponding unstenosed cases. Cardiac curvature radius moderately affects near-wall hemodynamics of the stenosed cases, with smaller curvature radius leading to higher exposure to low shear stress and lower exposure to oscillatory shear stress. In conclusion, the proposed controlled benchmark allows investigating the effect of various geometrical features on local hemodynamics at the LAD/diagonal bifurcation, highlighting that cardiac curvature influences near wall and intravascular hemodynamics, while bifurcation angle has a minor effect.     

Frequency dependence of dynamic curvature effects on flow through coronary arteries

The flow through a curved tube model of a coronary artery was investigated computationally to determine the importance of time-varying curvature on flow patterns that have been associated with the development of atherosclerosis. The entry to the tube was fixed while the radius of curvature varied sinusoidally in time at a frequency of 1 or 5 Hz. Angiographic data from other studies suggest that the radius of curvature waveform contains significant spectral content up to 6 Hz. The overall flow patterns were similar to those observed in stationary curved tubes; velocity profile skewed toward the outer wall, secondary flow patterns, etc. The effects of time-varying curvature on the changes in wall shear rate were expressed by normalizing the wall shear rate amplitude with the shear rate calculated at the static mean radius of curvature. It was found that the wall shear rate varied as much as 94 percent of the mean wall shear rate at the mid wall of curvature for a mean curvature ratio of 0.08 and a 50 percent change in radius of curvature. The effects of 5 Hz deformation were not well predicted by a quasi-static approach. The maximum values of the normalized inner wall shear rate amplitude were found to scale well with a dimensionless parameter equivalent to the product of the mean curvature ratio (delta), normalized change in radius of curvature (epsilon), and a Womersley parameter (alpha). This parameter was less successful at predicting the amplitudes elsewhere in the tube, thus additional studies are necessary. The mean wall shear rate was well predicted with a static geometry. These results indicate that dynamic curvature plays an important role in determining the inner wall shear rates in coronary arteries that are subjected to deformation levels of epsilon delta alpha > 0.05. The effects were not always predictable with a quasi-static approach. These results provide guidelines for constructing more realistic models of coronary artery flow for atherogenesis research.     

Dependence of central airway resistance on frequency and tidal volume: a model study

The resistance of a hollow cast of human central airways was measured during true sinusoidal airflow oscillations over a wide range of frequencies (0.5-40 Hz) and for various flow amplitudes up to 8 l/s. Pressure and flow were measured in the trachea with high-performance transducers, digitized and averaged over 100 cycles. Data were studied at two points in the flow cycle: at peak inspiratory and expiratory flows and in the two neighborhoods around zero flow where airway resistance (Rv approximately equal to o) was taken as the average slope of the pressure-flow (P-V) curve in each zone. When data obtained near peak flow were plotted in terms of dimensionless pressure drop vs. peak Reynolds number (Rem) and compared with steady-state data, we found no difference up to 2 Hz as previously reported (Isabey and Chang, J. Appl. Physiol. 51: 1338-1348, 1981), a slight decay in pressure drop between 4 and 8 Hz, a frequency-dependent increase in peak flow resistance at high frequencies (10-40 Hz) governed by the Strouhal number alpha 2/Rem beyond alpha 2/Rem = 0.5. On the other hand RV approximately equal to o was found to increase relative to steady state as local acceleration increases, e.g., as peak flow increases at a fixed frequency; this differs from the classical linear theory of oscillatory flow in a long straight tube. To explain these results, we had to use, as in our previous study, an alternative expression for the Strouhal number, i.e., epsilon = L X A X (dV/dt)/V2 (where L and A are the length and cross-sectional area of the trachea and V is a constant flow range over which resistance around flow reversal was computed), which accurately reflects the ratio of local acceleration [d(V/A)/dt)] to convective acceleration [(V/A)2/L] in developing branching flow. Finally, to delineate the regions of dominance of each of the dimensionless parameters, we compiled frequency-tidal volume diagrams for peak flows as well as for reversal. Epsilon, which is negligible near peak flows, appeared to govern the oscillatory P-V relationship near flow reversal in a transitional region of the diagram located between regions of steadiness, or moderate unsteadiness, and a region of dominant unsteadiness governed by alpha.     

Oscillatory flow and gas transport through a symmetrical bifurcation

Axial gas transport due to the interaction between radial mixing and radially nonuniform axial velocities is responsible for gas transport in thick airways during High-frequency oscillatory ventilation (HFO). Because the airways can be characterized by a bifurcating tube network, the secondary flow in the curved portion of a bifurcating tube contributes to cross-stream mixing. In this study the oscillatory flow and concentration fields through a single symmetrical airway bifurcating tube model were numerically analyzed by solving three-dimensional Navier-Stokes and mass concentration equations with the SIMPLER algorithm. The simulation conditions were for a Womersley number, alpha = 9.1 and Reynolds numbers in the parent tube between 200 and 1000, corresponding to Dn2/alpha 4 in the curved portion between 2 and 80, where Dn is Dean number. For comparison with the results from the bifurcating tube, we calculated the velocity and concentration fields for fully developed oscillatory flow through a curved tube with a curvature rate of 1/10, which is identical to the curved portion of the bifurcating tube. For Dn2/alpha 4 < or = 10 in the curved portion of the bifurcating tube, the flow divider and area changes dominate the axial gas transport, because the effective diffusivity is greater than in either a straight or curved tube, in spite of low secondary velocities. However, for Dn2/alpha 4 > or = 20, the gas transport characteristics in a bifurcation are similar to a curved tube because of the significant effect of secondary flow.     

Theory of fluorescence recovery after photobleaching measurements on cylindrical surfaces.

The theory of fluorescence recovery after photobleaching measurements of isotropic diffusion on a cylindrical surface is developed for Gaussian beam illumination centered perpendicular to an infinitely-long cylinder. A general analytical solution is obtained which is a function of the ratio of the cylindrical radius (r) to the beam exp [-2] radius omega. Numerical analysis of this solution demonstrates that significant deviations from one dimensional recovery are observed for omega less than 3r and from two-dimensional recovery for omega greater than or equal to 0.5r. Numerical data and an algorithm for analysis of recovery data where 0.5r less than or equal to omega less than or equal to 3r is presented.     

Structural heterogeneity of the Fe(2+)-N epsilon (HisF8) bond in various hemoglobin and myoglobin derivatives probed by the Raman-active iron histidine stretching mode.

We have examined the Fe(2+)-N epsilon (HisF8) complex in hemoglobin A (HbA) by measuring the band profile of its Raman-active nu Fe-His stretching mode at pH 6.4, 7.0, and 8.0 using the 441-nm line of a HeCd laser. A line shape analysis revealed that the band can be decomposed into five different sublines at omega 1 = 195 cm-1, omega 2 = 203 cm-1, omega 3 = 212 cm-1, omega 4 = 218 cm-1, and omega 5 = 226 cm-1. To identify these to the contributions from the different subunits we have reanalyzed the nu Fe-His band of the HbA hybrids alpha(Fe)2 beta(Co)2 and alpha(Co)2 beta(Fe)2 reported earlier by Rousseau and Friedman (D. Rousseau and J. M. Friedman. 1988. In Biological Application on Raman Spectroscopy. T. G. Spiro, editor, 133-216). Moreover we have reanalyzed other Raman bands from the literature, namely the nu Fe-His band of the isolated hemoglobin subunits alpha SH- and beta SH-HbA, various hemoglobin mutants (i.e., Hb(TyrC7 alpha-->Phe), Hb(TyrC7 alpha-->His), Hb M-Boston and Hb M-Iwate), N-ethylmaleimide-des(Arg141 alpha) hemoglobin (NES-des(Arg141 alpha)HbA) and photolyzed carbonmonoxide hemoglobin (Hb*CO) measured 25 ps and 10 ns after photolysis. These molecules are known to exist in different quaternary states. All bands can be decomposed into a set of sublines exhibiting frequencies which are nearly identical to those found for deoxyhemoglobin A. Additional sublines were found to contribute to the nu Fe-His band of NES-des(Arg141 alpha) HbA and the Hb*CO species. The peak frequencies of the bands are determined by the most intensive sublines. Moreover we have measured the nu Fe-His band of deoxyHbA at 10 K in an aqueous solution and in a 80% glycerol/water mixture. Its subline composition at this temperature depends on the solvent and parallels that of more R-like hemoglobin derivatives. We have also measured the optical charge transfer band III of deoxyHbA at room temperature and found, that at least three subbands are required to fit its asymmetric band shape. This corroborates the findings on the nu Fe-His band in that it is indicative of a heterogeneity of the Fe(2+)-N epsilon(HisF8) bond. Finally we measured the nu Fe-His band of horse heart deoxyMb at different temperatures and decomposed it into three different sublines. In accordance with what was obtained for HbA their intensities rather than their frequencies are temperature-dependent.(ABSTRACT TRUNCATED AT 400 WORDS)     

Dynamic shear stress in parallel-plate flow chambers

An in vitro model using a parallel-plate fluid flow chamber is supposed to simulate in vivo fluid shear stresses on various cell types exposed to dynamic fluid flow in their physiological environment. The metabolic response of cells in vitro is associated with the wall shear stress. However, parallel-plate flow chambers have not been characterized for dynamic fluid flow experiments. We use a dimensionless ratio h / lambda(v), in determining the exact magnitude of the dynamic wall shear stress, with its oscillating components scaled by a shear factor T. It is shown that, in order to expose cells to predictable levels of dynamic fluid shear stress, two conditions have to be met: (1) h / lambda(v) < 2, where h is the distance between the plates and lambda(v) is the viscous penetration depth; and (2) f(0) < f(c) / m, where the critical frequency f(c) is the upper threshold for this flow regime, m is the highest harmonic mode of the flow, and f(0) is the fundamental frequency of fluid flow.     

pH-induced conformational changes of the Fe(2+)-N epsilon (His F8) linkage in deoxyhemoglobin trout IV detected by the Raman active Fe(2+)-N epsilon (His F8) stretching mode.

To investigate heme-protein coupling via the Fe(2+)-N epsilon (His F8) linkage we have measured the profile of the Raman band due to the Fe(2+)-N epsilon (His F8) stretching mode (nu Fe-His) of deoxyHb-trout IV and deoxyHbA at various pH between 6.0 and 9.0. Our data establish that the band of this mode is composed of five different sublines. In deoxyHb-trout IV, three of these sublines were assigned to distinct conformations of the alpha-subunit (omega alpha 1 = 202 cm-1, omega alpha 2 = 211 cm-1, omega alpha 3 = 217 cm-1) and the other two to distinct conformations of the beta-subunit (omega beta 1 = 223 cm-1 and omega beta 2 = 228 cm-1). Human deoxyHbA exhibits two alpha-chain sublines at omega alpha 1 = 203 cm-1, omega alpha 2 = 212 cm-1 and two beta-chain sublines at omega beta 1 = 217 cm-1 and omega beta 2 = 225 cm-1. These results reveal that each subunit exists in different conformations. The intensities of the nu Fe-His sublines in deoxyHb-trout IV exhibit a significant pH dependence, whereas the intensities of the corresponding sublines in the deoxyHbA spectrum are independent on pH. This finding suggests that the structural basis of the Bohr effect is different in deoxyHbA and deoxyHb-trout IV. To analyse the pH dependence of the deoxyHb-trout IV sublines we have applied a titration model describing the intensity of each nu Fe-His subline as an incoherent superposition of the intensities from sub-sublines with the same frequency but differing intrinsic intensities due to the different protonation states of the respective subunit. The molar fractions of these protonation states are determined by the corresponding Bohr groups (i.e., pK alpha 1 = pK alpha 2 = 8.5, pK beta 1 = 7.5, pK beta 2 = 7.4) and pH. Hence, the intensities of these sublines reflect the pH dependence of the molar fractions of the involved protonation states. Fitting this model to the pH-dependent line intensities yields a good reproduction of the experimental data.(ABSTRACT TRUNCATED AT 400 WORDS)     

Cooperative ligand-lattice binding. Approximate Gaussian binding distribution

Nearest-neighbor cooperative binding of a ligand covering n sites and binding with equilibrium constant K and cooperativity factor omega to a large molecule with m binding sites (m much greater than n omega, n/omega) can be approximately described by a Gaussian distribution P(q-qmax), where q is the number of ligands bound and qmax the most probable value of q. The variance of the Gaussian is equal to the derivative dqmax/d ln(L), where L is the free ligand concentration. This variance, sigma 2, is a complicated function of qmax. However, in the limits of very large cooperativity, omega much greater than 1, very large anticooperativity, omega much less than 1, or noncooperativity, omega = 1, simpler expressions for sigma 2 can be given. For qmax = m/(n + 1), where the most probable number of bound ligands equals the number of free binding sites, sigma 2 has a particularly simple form: sigma 2 = 2m omega 1/2/(n + 1)3. The Gaussian and the infinite lattice approximations for the average number of ligands bound are good approximations only if sigma is much smaller than the number of binding sites. The variance may therefore provide an easy check on the validity of the infinite lattice approximation, which is commonly used to analyze experimental binding data.     

Mechanism of osmotic flow in a periodic fiber array

The classic analysis by Anderson and Malone (Biophys J 14: 957-982, 1974) of the osmotic flow across membranes with long circular cylindrical pores is extended to a fiber matrix layer wherein the confining boundaries are the fibers themselves. The equivalent of the well-known result for the reflection coefficient sigma0 = (1 - phi)2, where phi is the partition coefficient, is derived for a periodic fiber array of hexagonally ordered core proteins. The boundary value problem for the potential energy function describing the solute distribution surrounding each fiber is solved by defining an equivalent fluid annulus in which the pressures and osmotic forces are determined. This model is of special interest in the osmotic flow of water across a capillary wall, where recent experimental studies suggest that the endothelial glycocalyx is a quasiperiodic fiber array that serves as the primary molecular sieve for plasma proteins. Results for the reflection coefficient are presented in terms of two dimensionless numbers, alpha = a/R and beta = b/R, where a and b are the solute and fiber radii, respectively, and R is the outer radius of the fluid annulus. In general, the results differ substantially from the classic expression for a circular pore because of the large difference in the shape of the boundary along which the osmotic force is generated. However, as in circular pore theory, one finds that the reflection coefficients for osmosis and filtration are the same.     

1alpha,25-Dihydroxyvitamin D and fish oil synergistically inhibit G1/S-phase transition in prostate cancer cells

Laboratory and epidemiological studies have indicated that 1alpha,25-dihydroxyvitamin D(3) [1alpha,25(OH)(2)D(3)] and dietary omega3-polyunsaturated fatty acids (PUFAs) are capable of inhibiting prostate cancer at the initiation and progression stages. The objective of this study is to investigate the influence of 1alpha,25(OH)(2)D(3) and PUFAs in the form of fish oil applied alone or in combination on cell cycle kinetics in the exponentially growing androgen-dependent and -independent prostate cancer cells. Our data indicate that the high passage androgen-independent cell line, LNCaP-c115 had a much greater inhibitory response at the level of the G(1)/S-phase transition in response to fish oil treatment than androgen-dependent low passage LNCaP-c38 cells. When LNCaP-c38 and LNCaP-c115 cells were treated with fish oil (50mug/ml), 1alpha,25(OH)(2)D(3) (10(-8)M) or fish oil (50mug/ml)+1alpha,25(OH)(2)D(3) (10(-8)M), a synergistic growth inhibitory effect was observed with 1alpha,25(OH)(2)D(3)+fish oil group in LNCaP-c115 cell line at the levels of the G(1)/S-phase transition and cell division. This interaction appears to be specific for androgen-independent prostate cancer cell lines. Based on these results, we hypothesize that dietary components, such as omega3PUFAs and Vitamin D, have the potential to delay the progression of prostate cancer cells to an aggressive and un-treatable state.     

Peptide-plane flipping in proteins

A peptide-plane flip is a large-scale rotation of the peptide plane that takes the phi,psi angles at residues i and i + 1 to different structural regions in the Ramachandran plot with a comparatively small effect on the relative orientation of their side chains. This phenomenon, which is expected to play an important role during the early stages of protein folding, has been investigated using 76 proteins for which two high-resolution X-ray conformations are available. Peptide-plane flips are identified by looking for those cases where changes in /psi(i)/ + /phi(i + 1)/ are large (>200 degrees), but changes in /psi(i) + phi(i + 1)/ are comparatively small (<50 degrees). Of a total of 23 cases, the most common peptide-plane flip was identified to be the type I to type II beta-turn interconversion. Although individually rarer, there are many other types of flips that are collectively more common. Given the four main accessible regions alpha(R), alpha(L), beta and epsilon, identified from the phi,psi distribution corresponding to non-hydrogen-bonded peptide planes, 32 main types of peptide-plane flip are identified. Only 8 of these are "passive," in that they require only relatively minor adjustments in the orientation of adjacent peptide planes. Of these, only the type I to type II beta-turn interconversion, denoted, beta(i) + alpha(L)(i + 1) <--> alpha(R)(i) + alpha(R)(i + 1), and the rarer alpha(R)(i) + alpha(L)(i + 1) <--> beta(i) + alpha(R)(i + 1), do not involve the epsilon region. "Active" peptide-plane flips affect the orientation of adjacent peptide planes. The flip, alpha(L)(i) + alpha(L)(i + 1) <--> beta(i) + beta(i + 1), of which one example was found, shows how concerted peptide-plane flips can convert the alpha(L) structure to the beta structure without affecting the relative orientations of the side chains.     

X-ray diffraction study of the polymorphic behavior of N-methylated dioleoylphosphatidylethanolamine

The polymorphic phase behavior of aqueous dispersions of dioleoylphosphatidylethanolamine (DOPE) and its N-methylated analogues, DOPE-Me, DOPE-Me2, and DOPC, has been investigated by X-ray diffraction. In the fully hydrated lamellar (L alpha) phase at 2 degrees C, the major structural difference is a large increase in the interlamellar water width from DOPE to DOPE-Me, with minor increases with successive methylation. Consistent with earlier reports, inverted hexagonal (HII) phases are observed upon heating at 5-10 degrees C in DOPE and at 65-75 degrees C in DOPE-Me and are not observed to at least 85 degrees C in DOPE-Me2 or DOPC. In DOPE, the L alpha-HII transition is facile and is characterized by a relatively narrow temperature range of coexistence of L alpha and HII domains, each with long-range order. DOPE-Me exhibits complex nonequilibrium behavior below the occurrence of the HII phase: Upon heating, the L alpha lattice spontaneously disorders on a time scale of days; on cooling from the HII phase, the disorder rises on a time scale of minutes. It is shown that, in copious water, the disordered state transforms very slowly into phases with cubic symmetry. This process is assisted by the generation of small amounts of lipid degradation products. The relative magnitudes of the monolayer spontaneous radius of curvature, R0 [Kirk, G. L., Gruner, S. M., & Stein, D. L. (1984) Biochemistry 23, 1093; Gruner, S. M. (1985) Proc. Natl. Acad. Sci. U.S.A. 82, 3665], are inferred from the HII lattice spacings vs temperature and are shown to increase with increasing methylation. The relative magnitudes of R0 are categorized as small for DOPE, intermediate for DOPE-Me, and large for DOPC. It is suggested, and examples are used to illustrate, that small R0 lipid systems exhibit facile, low-temperature L alpha-HII transitions, intermediate R0 systems exhibit complex nonequilibrium transition behavior and are likely to form cubic phases, and large R0 systems are stable as L alpha phases. The relationship between the cubic phases and minimal periodic surfaces is discussed. It is suggested that minimal periodic surfaces represent geometries in which near constant, intermediate R0 values can be obtained concomitantly with monolayers of near constant thickness, thereby leading to equilibrium cubic phases. Thus, the relative magnitude of the spontaneous radius of curvature may be used to predict mesomorphic behavior.(ABSTRACT TRUNCATED AT 400 WORDS)     

The effects of gramicidin on the structure of phospholipid assemblies

Gramicidin is an antibiotic peptide that can be incorporated into the monolayers of cell membranes. Dimerization through hydrogen bonding between gramicidin monomers in opposing leaflets of the membrane results in the formation of an iontophoretic channel. Surrounding phospholipids influence the gating properties of this channel. Conversely, gramicidin incorporation has been shown to affect the structure of spontaneously formed lipid assemblies. Using small-angle x-ray diffraction and model systems composed of phospholipids and gramicidin, the effects produced by gramicidin on lipid layers were measured. These measurements explore how peptides are able to modulate the spontaneous curvature properties of phospholipid assemblies. The reverse hexagonal, H(II), phase formed by dioleoylphosphatidylethanolamine (DOPE) monolayers decreased in lattice dimension with increasing incorporation of gramicidin. This indicated that gramicidin itself was adding negative curvature to the lipid layers. In this system, gramicidin was measured to have an apparent intrinsic radius of curvature, R0pgram, of -7.1 A. The addition of up to 4 mol% gramicidin in DOPE did not result in the monolayers becoming stiffer, as measured by the monolayer bending moduli. Dioleoylphosphatidylcholine (DOPC) alone forms the lamellar (L(alpha)) phase when hydrated, but undergoes a transition into the reverse hexagonal (H(II)) phase when mixed with gramicidin. The lattice dimension decreases systematically with increased gramicidin content. Again, this indicated that gramicidin was adding negative curvature to the lipid monolayers but the mixture behaved structurally much less consistently than DOPE/gramicidin. Only at 12 mol% gramicidin in dioleoylphosphatidylcholine could an apparent radius of intrinsic curvature of gramicidin (R0pgram) be estimated as -7.4 A. This mixture formed monolayers that were very resistant to bending, with a measured bending modulus of 115 kT.     

Calculation and application of the anterior surface area of a model human cornea

The macroscopic anterior surface area was calculated for three models of the average human cornea. Two models, a general ellipsoid and a rotational ellipse (rotationally symmetric ellipsoid) gave a surface area of 132 mm2, while a spherical model gave 126 mm2. A general ellipsoidal model having the maximum radius horizontal (with-the-rule corneal astigmatism) has less surface area than a rotational ellipse with the same horizontal radius. For a corneal sagittal height of 2.59 mm, the surface area of an ellipsoidal cornea equals -19.2Q + 16.3R -0.476 which specifies a rotational ellipse (radius R, asphericity Q) of equal surface area. In a cornea with the maximum radius vertical (against-the-rule corneal astigmatism), the ellipsoid has slightly more surface area than a rotational ellipse with the same horizontal radius of curvature. For a given horizontal radius of curvature, the sphere has the lowest surface area. For a corneal sagittal height s of 2.59 mm, the sphere underestimates by 8% the surface area of a rotational ellipse with asphericity -0.5. The anterior corneal surface area of a rotational ellipse model, radius R, asphericity Q is given by 2 pi Rs- 19.2Q. In all three models, the surface area increases with horizontal radius of curvature. In the rotational ellipse model, the rate of increase (slope) is independent of asphericity, and the slope found in with-the-rule astigmatism is less than the slope found with against-the-rule astigmatism. The calculated surface area predicts a precorneal tear volume of 0.86 microliter for a 6.5 micron tear thickness. The apparent, or plane projected are of an epithelial lesion underestimates the curved surface area with a percentage error that increases rapidly with lesion diameter. For a 12 mm diameter lesion on a rotational ellipse model, the apparent area underestimates the surface area by 18%. The average posterior corneal surface in human is not spherical but imitates the anterior surface, and has an area of 137 mm2 or 3.8% greater than the anterior area.     

Flory temperature and upper critical solution temperature of gelatin solutions

The Flory temperatures (theta) measured by turbidity experiments performed on gelatin solutions were found to be 12 +/- 0.3, 13 +/- 0.3, 14 +/- 0.3, 14.5 +/- 0.3, and 15 +/- 0.3 degrees C for salt concentrations 0.1, 0.075, 0.05, 0.025, and 0 M (NaCl), respectively. Estimated persistence length (l(p)) of this weakly charged polyelectrolyte could be deduced from the Benoit and Doty (J. Phys. Chem. 1953, 57, 958) relationship with the approximation that this biopolymer assumes a compact near-globular shape at Flory temperature, implying l(p) = 9(R(h))(2)/(5L(m)), where L(m) is the contour length and R(h) is the hydrodynamic radius. It was found that l(p) approximately 2.2 +/- 0.2 nm at room temperature (20 degrees C), invariant of salt concentration. The Flory expansion factor (alpha= R(h)(T)/R(h)(theta) = 1.5+/-0.2) was found to be almost constant. theta-Composition for this biopolymer was deduced from turbidimitric titration of aqueous gelatin solutions with the alcohols methanol, ethanol, 2-propanol, and tert-butyl alcohol. It appears that hydrophobic interactions play a crucial role in causing chain collapse at theta-temperature and composition.