Changes in surface area of intact guard cells are correlated with membrane internalization

Guard cells must maintain the integrity of the plasma membrane as they undergo large, rapid changes in volume. It has been assumed that changes in volume are accompanied by changes in surface area, but mechanisms for regulating plasma membrane surface area have not been identified in intact guard cells, and the extent to which surface area of the guard cells changes with volume has never been determined. The alternative hypothesis-that surface area remains approximately constant because of changes in shape-has not been investigated. To address these questions, we determined surface area for intact guard cells of Vicia faba as they underwent changes in volume in response to changes in the external osmotic potential. We also estimated membrane internalization for these cells. Epidermal peels were subjected to external solutions of varying osmotic potential to shrink and swell the guard cells. A membrane-specific fluorescent dye was used to identify the plasma membrane, and confocal microscopy was used to acquire a series of optical paradermal sections of the guard cell pair at each osmotic potential. Solid digital objects representing the guard cells were created from the membrane outlines identified in these paradermal sections, and surface area, volume, and various linear dimensions were determined for these solid objects. Surface area decreased by as much as 40% when external osmotic potential was increased from 0 to 1.5 MPa, and surface area varied linearly with volume. Membrane internalization was approximated by determining the amount of the fluorescence in the cell's interior. This value was shown to increase approximately linearly with decreases in the cell's surface area. The changes in surface area, volume, and membrane internalization were reversible when the guard cells were returned to a buffer solution with an osmotic potential of approximately zero. The data show that intact guard cells undergo changes in surface area that are too large to be accommodated by plasma membrane stretching and shrinkage and suggest that membrane is reversibly internalized to maintain cell integrity.     

Estimating surface area in early hominins

Height and weight-based methods of estimating surface area have played an important role in the development of the current consensus regarding the role of thermoregulation in human evolution. However, such methods may not be reliable when applied to early hominins because their limb proportions differ markedly from those of humans. Here, we report a study in which this possibility was evaluated by comparing surface area estimates generated with the best-known height and weight-based method to estimates generated with a method that is sensitive to proportional differences. We found that the two methods yield indistinguishable estimates when applied to taxa whose limb proportions are similar to those of humans, but significantly different results when applied to taxa whose proportions differ from those of humans. We also found that the discrepancy between the estimates generated by the two methods is almost entirely attributable to inter-taxa differences in limb proportions. One corollary of these findings is that we need to reassess hypotheses about the role of thermoregulation in human evolution that have been developed with the aid of height and weight-based methods of estimating body surface area. Another is that we need to use other methods in future work on fossil hominin body surface areas.     

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.     

Effect of surface tension on alveolar surface area.

At fixed lung volume (VL), alterations in surface tension change alveolar surface area (S) and lung recoil (PL). Wilson (26), using data from fixed lungs (1, 9), quantified the isovolume change in S with PL. We reexamined this question in fresh excised rabbit lungs, with two important differences. First, we measured fractional changes in S by using diffuse light scattering, avoiding the potential upset of the balance of tissue and surface forces during fixation. Second, we altered surface tension by ventilating the lungs with nebulized polydimethylsiloxane, with much less residual fluid compared with lavage. We found that S decreased at low and mid VL (treatment surface tension > control) by about half of Wilson's estimates and was nearly unaffected by treatment at high VL. This suggests that with increased surface tension there is 1) greater septal retraction in lungs fixed by vascular perfusion compared with unfixed lungs and 2) a greater increase in PL and less loss of S than would have been predicted.     

Variation of folded polypeptide surface area with probe size

Three types of polypeptide surface area (contact, accessible, and molecular) have been studied as a function of the radius of a probe sphere used to map the surface. The surfaces are: (1) three alpha-helices, the H-helix of myoglobin, the E-helix of leghemoglobin, and an artificial polyalanine helix, each with 26 residues; (2) two globins, myoglobin and leghemoglobin, each with 153 residues; and (3) a two-center model system for which the three types of surface area have been calculated analytically. The two globin helices have almost identical surface areas as a function of probe size as do the two globins. The polyalanine helix surface area is smaller but similar in shape to the globin helix areas. All three helix contact areas tend to the same limit as the probe size increases, and the globin contact areas behave similarly. Fractal dimensions were calculated for the helix and globin contact and molecular surfaces. All fractal dimensions showed strong dependence on probe size. The contact fractal dimension peaks at larger values for both the helices and globins. Most residues do not make contact with large probes (15 A).     

Fast approximations for accessible surface area and molecular volume of protein segments

Equations are presented that approximate the accessible surface area of a continuous protein segment using the surface area of an inertial ellipsoid and that approximate the molecular volume from the number of non-hydrogen atoms in the segment. These approximations, which are appropriate for segments of four or more residues in length, are much faster to calculate than the exact solutions, yet suffer only a 3–8% error. Included in an appendix are FORTRAN subroutines that calculate the surface area of an ellipsoid from its three principal moments of inertia.     

The relative importance of habitat complexity and surface area in assessing biodiversity: Fractal application on rocky shores

Theoretical work predicts that complex habitats allow more species to co-exist in a given area. However, more field studies are still needed to clarify this relationship, especially in intertidal habitats. Furthermore, the potential separate effects of surface complexity and area on species richness and abundance have rarely been addressed. We tested the hypotheses that a more complex substratum or larger surface area will support a greater number of individuals and species of mobile macrofauna on three rocky shores in Hong Kong. Surface complexity, assessed by using fractals, was an important factor in species–area relationships. The number of species increased proportionally to habitat complexity and this relationship was homogeneous among different shores. Total abundance of animals, however, was more dependent on the available surface area. The slope of the size–frequency distribution of animals in samples taken on surfaces with different fractal dimensions (D) was significantly steeper with an increase in fractal dimension, showing that the relative abundance of small animals increased with surface complexity. Thus, surface complexity and area may be important in determining different aspects of the macrofaunal community structure on rocky shores. The resulting increase in surface area on more rough surfaces may introduce bias in density and species number assessments when two-dimensional sampling units (i.e., quadrats) are employed. It is necessary, therefore, to account for the surface complexity in the design and interpretation of the results of benthic studies. Using D as an index of surface complexity is very useful, but also involves some practical problems, e.g., surfaces may be anisotropic and different methods may give different estimates of D. Therefore, these different methods need to be calibrated before comparisons of D values between them are meaningful.     

On the relationship between common amplitude surface roughness parameters and surface area: Implications for the study of cell–material interactions

In order to show that surface area is not always a quantity proportional to the surface roughness, we have constructed simple surfaces consisting of boxes of the same height equally spaced, and rms roughness and surface area have been computed. We have shown how we can get examples of surface configurations for which an increment in the surface roughness corresponds to a decrease in the surface area, although this is observed only for surfaces having similar rms roughness. We have also shown that even in the more intuitive situations where an increase in the surface roughness leads to an increase in the surface area, this increase is not necessarily equivalent. Analogous conclusions have been found when roughness was evaluated through the average roughness. These results could be interesting when analyzing interfacial phenomena such as cell adhesion, especially from a microscopic point of view, where the exact contact area between interacting phases governs these phenomena, and an exact-as-possible approximation to its real value is desirable. Also, the results of this paper could be of interest in various biomedical applications where the modulation of material surface-by-surface roughness may play a significant role. It can be concluded that care should be taken when using roughness parameters as estimators or indicators of the contact area between phases, since the relationship is not always simple.     

MASKER: improved solvent-excluded molecular surface area estimations using Boolean masks

A fast algorithm for computing the solvent-accessible molecular surface area (SAS) using Boolean masks [Le Grand,S.M. and Merz,K.M.J. (1993). J. Comput. Chem., 14, 349-352) has been modified to estimate the solvent-excluded molecular surface area (SES), including contact, toroidal and re-entrant surface components. Numerical estimates of arc lengths of intersecting atomic SAS are used to estimate the toroidal surface and intersections between those arcs are used to estimate the re-entrant surface area. The new method is compared with an exact analytical method. Boolean molecular surface areas are continuous and pairwise differentiable and should be useful for molecular dynamics simulations, especially as the basis for an implicit solvent model.     

A colloidal gold labeling technique for the direct determination of the surface area of eukaryotic cells

We have developed a colloidal gold labeling technique for the direct quantitation of the cell surface area. The method is based on coating the cell surface with [195Au] colloidal gold-protein complexes followed by morphometric determination of the labeling density (gold particles/micron2 cell surface) and radiometric determination of the total number of gold particles bound per cell. The ratio of both values directly gives the cell surface area. The accuracy of the method was shown using Staphylococcus aureus cells as a model system, where the cell surface area determined with our assay (4.0 microns2) corresponded well to the value calculated from the radius of the cells (3.6 microns2). In a more complex model system J-774 mouse macrophages were labeled with different amounts of [195Au] gold-protein complexes to show that the assay is independent of the degree of saturation of the cell surface binding sites. Both high (135 Au/microns2) and low (65 Au/microns2) labeling densities resulted in a surface area of about 1200 microns2. The technique finally was applied to L-929 fibroblasts to determine the increase of the cell surface area when the cells change from a spherical to a flat monolayer state. We found that the cell surface area increased 3-fold during the spreading process. The results show that the colloidal gold labeling technique allows the direct determination of the surface area of complex eukaryotic cells. The technique is suitable for the quantitation of changes in the surface architecture known to occur in different functional states of eukaryotic cells.     

The sterologic method of determining the surface area of the mammalian neocortex]

A method for calculation of the square surface area of the cerebral cortex is proposed which represents a combination of the method of averaged reconstruction after a continuous series of histological sections and the stereological method of determination of the length of any curve disposed on the surface. A comparative analysis of the proposed method with curvometrical and stereological (after Hennig's formula) method used earlier for this purpose is made taking as an example the calculation of the neocortex square surface area of some mammals. The results of calculation of the surface by the proposed method were found to coincide with curvometrical data within the range of 5% while the data obtained by stereological method of determination of the absolute square surface area differ from curvometrical data by more than 22%. The proposed method is very convenient and allows considerable acceleration in obtaining results.     

Bead method for measuring the root surface area in conifers

A method of determining the surface area of mycorrhizous conifer roots is described. The roots are cleaned from soil particles by washing, slightly dried and covered with a monolayer of plastic beads. The surface area is estimated on the basis of the weight of adhered beads.The method has been tested against the surface area measurements by a photographic-planimetric method. The estimates of the surface area by both methods compare fairly well.An analysis of model root systems shows that the accuracy of the method for measuring the roots of 0.3mm diameter is about 5%.     

A quick method of determining rock surface area for quantification of the invertebrate community

Stone and rock substrates provide important habitat for many types of stream-dwelling invertebrates. Measures of the invertebrate communities inhabiting rock substrates are often an important component of ecological, monitoring and disturbance studies in streams. A major obstacle to researchers examining rock-inhabiting invertebrates is the time and effort expended on currently used methods of determining rock surface area to derive invertebrate densities on these substrates. In an attempt to more efficiently determine invertebrate densities from rock substrates in streams, we tested a direct method of calculating rock surface area from rock weight or displacement volume. This method allows very quick determinations of rock surface area in the field. Surface area estimates made using this technique were highly correlated to those from a widely used and more time-consuming method. Measurements made using this new method should theoretically give better surface area estimates than any other commonly used technique.     

Body surface area prediction in normal-weight and obese patients

None of the equations frequently used to predict body surface area (BSA) has been validated for obese patients. We applied the principles of body size scaling to derive an improved equation predicting BSA solely from a patient's weight. Forty-five patients weighing from 51.3 to 248.6 kg had their height and weight measured on a calibrated scale and their BSA calculated by a geometric method. Data were combined with a large series of published BSA estimates. BSA prediction with the commonly used Du Bois equation underestimated BSA in obese patients by as much as 20%. The equation we derived to relate BSA to body weight was a power function: BSA (m(2)) = 0.1173 x Wt (kg)(0.6466). Below 10 kg, this equation deviated significantly from the BSA vs. body weight curve, necessitating a different set of coefficients: BSA (m(2)) = 0.1037 x Wt (kg)(0.6724). Covariance of height and weight for patients weighing <80 kg reduced the Du Bois BSA-predicting equation to a power function, explaining why it provides good BSA predictions for normal-size patients but fails with obesity.     

Computation of the average shear-induced deformation of red blood cells as a function of osmolality

A model was developed for computing the average deformation of red cells as a function of suspending medium osmolality. It assumes a population of red cells characterized by a single value for surface area and for isotonic volume, but having a Gaussian distribution in mean intracellular hemoglobin concentration (MCHC). The ability of cells of a given hemoglobin concentration to deform is assumed to be limited by either the amount of redundant surface area available or the intracellular viscosity, determined by the intracellular hemoglobin concentration. The surface area limitation is calculated by finding the dimensions of a prolate ellipsoid having the volume and surface area of the red cell. The viscosity limitation is incorporated in two ways. First, the ratio of intracellular to extracellular viscosity must lie below a certain threshold to permit deformation, and second, its magnitude determines the extent of cell elongation. This model gave a reasonable fit to experimental data for a threshold viscosity ratio close to 1. Extension to cell populations for which either mean cell hemoglobin concentration or surface area had been modified also provided a close reproduction of the experimental curves.     

Reexamination of the Byczkowska-Smyk gill surface area data for European teleosts, with new measurements on the pikeperch, Sander lucioperca

This paper reexamines the gill morphometrics of 20 European teleosts first reported in the early gill literature by Byczkowska-Smyk and colleagues in attempt to clarify the long-recognized discrepancies between these data and those obtained in subsequent works. Determination of gill dimensions for the pikeperch, Sander lucioperca, in this study (a species for which Byczkowska-Smyk reported data), along with a literature review for other European teleosts, reveals inaccurate estimation of the total gill surface area by up to 18× for 19 of the 20 species reexamined. This error results primarily from imprecise determination of the bilateral surface area of individual gill lamellae and, to a lesser extent, the incorrect assumption that lamellar area and frequency are species-specific constants that do not vary with fish body mass. This review compiles gill morphometric data from various sources to be used in place of the inaccurate gill area estimates of Byczkowska-Smyk and colleagues and thereby clears the way for higher resolution in the comparative analysis of gill morphology and its correlation to fish habitat and life history characteristics.     

Visualisation of mycorrhizal fungal structures and quantification of their surface area and volume using laser scanning confocal microscopy

 A method has been developed for the visualisation and three-dimensional (3D) measurement of mycorrhizal fungal structures inside plant roots. Sections of Allium porrum L. roots colonised by Glomus sp. 'City Beach' (WUM 16) and Lilium sp. roots colonised by Scutellospora calospora (Nicol. & Gerd.) Walker & Sanders (WUM 12(2)) were stained with acid fuchsin. This allowed fluorescence from the fungal structures to be observed under a laser scanning confocal microscope (LSCM) without interference from the plant cells. A series of horizontal optical sections were collected from a Glomus sp. arbuscule and from a hyphal coil of S. calospora. These data were used to produce extended focus images. Axial distortion in microscopic visualisation due to the refractive index mismatch between the immersion and mounting media was quantified using vertical scanning of the hyphae. A correction factor of 0.71 μm was used for the z-interval between the xy-slices. A series of binary xy-images from each structure was rendered into a 3D graphical model for viewing. The volume and surface area of the structures were estimated using computerised 3D measurement and also by stereological integration of binary xy-images. With both structures, the surface area estimates varied greatly between the two measuring systems, whereas differences in volume estimates were small. Computerised 3D measurement was considered more accurate than stereological integration of confocal binary images. Accepted: 25 August 1999     

The surface area of mudfish

The surface area of two closely related mudfish species have been determined by coating the animals with masking tape. The results indicate that Labeo capensis specimens above 95 g body weight have a larger surface area than corresponding L. umbratus animals. The same is true for the fin surface area above 50 g body weight. Below these weights L. umbratus specimens have higher surface areas. The body surface area of L. capensis is always lower than that of L. umbratus in the range studied.     

The relation between surface area and anchorage dependence of growth in hamster and mouse fibroblasts.

Anchorage dependence can be defined as an increase in proliferation which is seen when cells are allowed to attach to a solid surface. We have measured this increase by time-lapse cinematography and other methods, and have compared it with measurements of the change in surface area which also occurs. Anchorage dependence can be varied over very wide limits in cells of the NIL-8 hamster fibroblast line by varying the concentration of serum in the medium. Thus in a concentration of 5% serum, the transition probability (a measure of growth rate) of attached cells is 8 times greater than in suspension. When the serum concentration is raised to 66%, attached and suspended cells grow at the same rate. We have found that this change in growth is accompanied by a corresponding change in the exposed surface area of the cells. Thus in 5% serum, the area of attached is 3 times greater than suspended cells, while in 66% serum, the areas of attached and suspended cells are equal. There is also a significant relationship between the area and the total amount of growth achieved, since both suspended colonies and attached confluent monolayers appear to stop growing at the same surface: volume ratio. Several aspects of this relationship between anchorage dependence and area are also seen when other different types of cell are cultured in the suspended and attached state, all at the same serum concentration. These experiments show that change in exposed surface area can provide a complete explanation for the anchorage dependence of NIL-8 cells and suggest the possibility that this might also be true of animal cells in general.     

A simple procedure for estimation of total body surface area and determination of a new value of Meeh's constant in rats

Precise calculation of total body surface area (TBSA) or premarked surface areas (P-MSAs) is of great importance in many biomedical applications. The aim of the paper was to present a simple procedure of measurement of P-MSAs in small animals and to determine a more accurate Meeh's constant (k), for a commonly used weight range of laboratory rats. A series of 30 Wistar rats, weighing 195-240 g, were anaesthetized and weighted. The TBSA of each animal was measured using a clear pocket and a planimeter. The data obtained were entered into the Meeh's formula (TBSA = kW(2/3)), the most commonly used for small experimental animals, so that a k value for each animal as well as a mean k value (9.83) were obtained. The TBSA of the animals was also calculated using the aforementioned mean k value and compared with that obtained using k values reported in previous studies. According to our findings, the new mean k value, determined with the use of our procedure of surface area measurement, ensured greater accuracy in the determination of the TBSA of experimental rats of a specific weight range. We also suggest a new procedure of surface area measurement which is easy, accurate and does not require animal sacrifice.