Simulation of saturation transfer electron paramagnetic resonance spectra for rotational motion with restricted angular amplitude.

We have simulated both conventional (V1) and saturation transfer (V'2) electron paramagnetic resonance spectra for the case of Brownian rotational diffusion restricted in angular amplitude. Numerical solutions of the diffusion-coupled Bloch equations were obtained for an axially symmetric 14N nitroxide spin label with its principal axis rotating within a Gaussian angular distribution of full width delta theta at half maximum. Spectra were first calculated for a macroscopically oriented system with cylindrical symmetry (e.g., a bundle of muscle fibers or a stack of membrane bilayers), with the Gaussian angular distribution centered at theta 0 with respect to the magnetic field. These spectra were then summed over theta 0 to obtain the spectrum of a randomly oriented sample (e.g., a dispersion of myofibrils or membrane vesicles). The angular amplitude delta theta was varied from 0 degrees, corresponding to isotropic motion (order parameter = 0). For each value of delta theta, the rotational correlation time, tau r, was varied from 10(-7) to 10(-2) s, spanning the range from maximal to minimal saturation transfer. We provide plots that illustrate the dependence of spectral parameters on delta theta and tau r. For an oriented system, the effects of changing delta theta and tau r are easily distinguishable, and both parameters can be determined unambiguously by comparing simulated and experimental spectra. For a macroscopically disordered system, the simulated spectra are still quite sensitive to delta theta, but a decrease in tau r produces changes similar to those from an increase in delta theta. If delta theta can be determined independently, then the results of the present study can be used to determine tau r from experimental spectra. Similarly, if tau r is known, then delta theta can be determined.     

High resolution 1H nuclear magnetic resonance of a transmembrane peptide.

Although the strong 1H-1H dipolar interaction is known to result in severe homogeneous broadening of the 1H nuclear magnetic resonance (NMR) spectra of ordered systems, in the fluid phase of biological and model membranes the rapid, axially symmetric reorientation of the molecules about the local bilayer normal projects the dipolar interaction onto the motional symmetry axis. Because the linewidth then scales as (3 cos2 theta-1)/2, where theta is the angle between the local bilayer normal and the magnetic field, the dipolar broadening has been reduced to an "inhomogeneous" broadening by the rapid axial reorientation. It is then possible to obtain high resolution 1H-NMR spectra of membrane components by using magic angle spinning (MAS). Although the rapid axial reorientation effectively eliminates the homogeneous dipolar broadening, including that due to n = 0 rotational resonances, the linewidths observed in both lipids and peptides are dominated by low frequency motions. For small peptides the most likely slow motions are either a "wobble" or reorientation of the molecular diffusion axis relative to the local bilayer normal, or the reorientation of the local bilayer normal itself through surface undulations or lateral diffusion over the curved surface. These motions render the peptide 1H-NMR lines too broad to be observed at low spinning speeds. However, the linewidths due to these slow motions are very sensitive to spinning rate, so that at higher speeds the lines become readily visible.(ABSTRACT TRUNCATED AT 250 WORDS)     

Distribution and kinetics of membrane dielectric polarization. II. Frequency domain studies of gating currents

We have studied the admittance of the membrane of squid giant axon under voltage clamp in the absence of ionic conductances in the range of 0-12 kHz for membrane potentials (V) between --130 and 70 mV. The admittance was measured at various holding potentials (HP) or 155 ms after pulsing from a given holding potential. Standard P/4 procedure was used to study gating currents in the same axons. We found that the membrane capacity Cm (omega) is voltage as well as frequency dependent. For any given V, the voltage-dependent part of the membrane capacitance has a maximum as the frequency approaches zero and requires at least a two-time constant equivalent circuit to be described. When the holding potential is varied, the voltage-dependent capacitance follows a bell- shaped curve with a maximum change of 0.15 muF/cm2 at about --60 mV. With the pulse method, the maximum is at --40 mV for HP = --70 and it shifts to --70 mV for HP = 0. The shift in the maximum of the voltage- dependent capacitance is consistent with the shift in the charge (Q) vs. V curve observed in our experiments with regular P/4 procedure when the HP is varied. Our data can be explained qualitatively by a four- state model for the sodium channel gating, where a charged particle can move within the field and interact with another particle not affected by the field.     

Quantitative calculations of fluorescence polarization and absorption anisotropy kinetics of double- and triple-chromophore complexes with energy transfer.

A new method is presented for calculation of the fluorescence depolarization and kinetics of absorption anisotropy for molecular complexes with a limited number of chromophores. The method considers absorption and emission of light by both chromophores, and also energy transfer between them, with regard to their mutual orientations. The chromophores in each individual complex are rigidly positioned. The complexes are randomly distributed and oriented in space, and there is no energy transfer between them. The new "practical" formula for absorption anisotropy and fluorescence depolarization kinetics, P(t) = [3B(t) - 1 + 2A(t)]/[3 + B(t) + 4A(t)], is derived both for double- and triple-chromophore complexes with delta-pulse excitation. The parameter B(t) is given by (a) B(t) = cos2(theta) for double-chromophore complexes, and (b) B(t) = q12(t)cos2(theta 12) + q13(t)-cos2(theta 13) + q23(t)cos2(theta 23) for triple-chromophore complexes, where q12(t) + q13(t) + q23(t) = 1. Here theta ij are the angles between the chromophore transition dipole moments in the individual molecular complex. The parameters qij(t) and A(t) are dependent on chromophore spectroscopic features and on the rates of energy transfer.     

Three new familial hemiplegic migraine mutants affect P/Q-type Ca(2+) channel kinetics

Missense mutations in the pore-forming human alpha(1A) subunit of neuronal P/Q-type Ca(2+) channels are associated with familial hemiplegic migraine. We studied the functional consequences on P/Q-type Ca(2+) channel function of three recently identified mutations, R583Q, D715E, and V1457L after introduction into rabbit alpha(1A) and expression in Xenopus laevis oocytes. The potential for half-maximal channel activation of Ba(2+) inward currents was shifted by > 9 mV to more negative potentials in all three mutants. The potential for half-maximal channel inactivation was shifted by > 7 mV in the same direction in R583Q and D715E. Biexponential current inactivation during 3-s test pulses was significantly faster in D715E and slower in V1457L than in wild type. Mutations R583Q and V1457L delayed the time course of recovery from channel inactivation. The decrease of peak current through R583Q (30.2%) and D715E (30. 1%) but not V1457L (18.7%) was more pronounced during 1-Hz trains of 15 100-ms pulses than in wild type (18.2%). Our data demonstrate that the mutations R583Q, D715E, and V1457L, like the previously reported mutations T666M, V714A, and I1819L, affect P/Q-type Ca(2+) channel gating. We therefore propose that altered channel gating represents a common pathophysiological mechanism in familial hemiplegic migraine.     

Recruitment of a foreign quinone into the A(1) site of photosystem I. II. Structural and functional characterization of phylloquinone biosynthetic pathway mutants by electron paramagnetic resonance and electron-nuclear double resonance spectroscopy

Electron paramagnetic resonance (EPR) and electron-nuclear double resonance studies of the photosystem (PS) I quinone acceptor, A(1), in phylloquinone biosynthetic pathway mutants are described. Room temperature continuous wave EPR measurements at X-band of whole cells of menA and menB interruption mutants show a transient reduction and oxidation of an organic radical with a g-value and anisotropy characteristic of a quinone. In PS I complexes, the continuous wave EPR spectrum of the photoaccumulated Q(-) radical, measured at Q-band, and the electron spin-polarized transient EPR spectra of the radical pair P700(+) Q(-), measured at X-, Q-, and W-bands, show three prominent features: (i) Q(-) has a larger g-anisotropy than native phylloquinone, (ii) Q(-) does not display the prominent methyl hyperfine couplings attributed to the 2-methyl group of phylloquinone, and (iii) the orientation of Q(-) in the A(1) site as derived from the spin polarization is that of native phylloquinone in the wild type. Electron spin echo modulation experiments on P700(+) Q(-) show that the dipolar coupling in the radical pair is the same as in native PS I, i.e. the distance between P700(+) and Q(-) (25.3 +/- 0.3 A) is the same as between P700(+) and A(1)(-) in the wild type. Pulsed electron-nuclear double resonance studies show two sets of resolved spectral features with nearly axially symmetric hyperfine couplings. They are tentatively assigned to the two methyl groups of the recruited plastoquinone-9, and their difference indicates a strong inequivalence among the two groups when in the A(1) site. These results show that Q (i) functions in accepting an electron from A(0)(-) and in passing the electron forward to the iron-sulfur clusters, (ii) occupies the A(1) site with an orientation similar to that of phylloquinone in the wild type, and (iii) has spectroscopic properties consistent with its identity as plastoquinone-9.     

Identification of messenger RNA for human type II collagen

The fluorescence polarization of acridine orange-stained, oriented lambda phages was measured. The parameters of DNA packing within the phage head cos2 theta and cos4 theta were calculated (theta, angle between the direction of a small segment of DNA and the phage axis). It is shown that simple models of lambda phage DNA tertiary structure are not consistent with calculated values. A new model is proposed.     

Transport properties of rigid bent-rod macromolecules and of semiflexible broken rods in the rigid-body treatment. Analysis of the flexibility of myosin rod.

The translational diffusion coefficients, rotational relaxation times and intrinsic viscosities of rigid bent rods, composed by two rodlike arms joined rigidly at an angle alpha, have been evaluated for varying conformation using the latest advances in hydrodynamic theory. We have considered semiflexible rods in which the joint is an elastic hinge or swivel, with a potential V(alpha) = 1/2Q alpha 2 with constant Q. Accepting the rigid-body treatment, we calculate properties of broken rods by averaging alpha-dependent values for rigid rods. The results are finally used to interpret literature values of the properties of myosin rod. Q is regarded as an adjustable parameter, and the value fitted is such that the average bending angle of myosin rod is approximately 60 degrees.     

Direction reversal of fluctuation-induced biased Brownian motion on distorted ratchets

The biased movement of Brownian particles on a fluctuating two-state periodic potential made of identical distorted ratchets is studied. The purpose is to investigate how the direction of the particle movement is related to the asymmetry of the potential. In general, distorting one of the two linear arms of a regular symmetric ratchet (with equal arm lengths) can create a driving force for the Brownian particle to execute biased movement. The direction of the induced biased movement depends on the type of the distortion. It has been found that if one linear arm is kinked into two linear sub-arms, the direction of the movement can be either positive or negative depending on the frequency of the fluctuation and the location and the degree of the kink. In contrast, if one arm of the symmetric ratchet is replaced by a continuous nonlinear sinusoidal function, the movement is always unidirectional. Thus, for the latter case to generate the direction reversal phenomenon, the ratchets have to have an additional asymmetry. We also have found that two potentials with different distorted ratchets can generate identical fluxes if the distortions are polar symmetric about the mid-point of the arm(s) of the basic linear two-arm ratchet. The results are useful for designing experimental apparatuses for the separation of protein particles based on their sizes and charges and the viscosity of the medium.     

Efficient analysis of macromolecular rotational diffusion from heteronuclear relaxation data

A novel program has been developed for the interpretation of ¹⁵N relaxation rates in terms of macromolecular anisotropic rotational diffusion. The program is based on a highly efficient simulated annealing/minimization algorithm, designed specifically to search the parametric space described by the isotropic, axially symmetric and fully anisotropic rotational diffusion tensor models. The high efficiency of this algorithm allows extensive noise-based Monte Carlo error analysis. Relevant statistical tests are systematically applied to provide confidence limits for the proposed tensorial models. The program is illustrated here using the example of the cytochrome c from Rhodobacter capsulatus, a four-helix bundle heme protein, for which data at three different field strengths were independently analysed and compared.     

Dynamics of an integral membrane peptide: a deuterium NMR relaxation study of gramicidin.

Solid state deuterium (2H) NMR inversion-recovery and Jeener-Broekaert relaxation experiments were performed on oriented multilamellar dispersions consisting of 1,2-dilauroyl-sn-glycero-3-phosphatidylcholine and 2H exchange-labeled gramicidin D, at a lipid to protein molar ratio (L/P) of 15:1, in order to study the dynamics of the channel conformation of the peptide in a liquid crystalline phase. Our dynamic model for the whole body motions of the peptide includes diffusion of the peptide around its helix axis and a wobbling diffusion around a second axis perpendicular to the local bilayer normal in a simple Maier-Saupe mean field potential. This anisotropic diffusion is characterized by the correlation times, tau R parallel and tau R perpendicular. Aligning the bilayer normal perpendicular to the magnetic field and graphing the relaxation rate, 1/T1Z, as a function of (1-S2N-2H), where S2N-2H represents the orientational order parameter, wer were able to estimate the correlation time, tau R parallel, for rotational diffusion. Although in the quadrupolar splitting, which varies as (3 cos2 theta D-1), has in general two possible solutions to theta D in the range 0 < or = theta D < or = 90 degrees, the 1/T1Z vs. (1-S2N-2H) curve can be used to determine a single value of theta D in this range. Thus, the 1/T1Z vs. (1-S2N-2H) profile can be used both to define the axial diffusion rate and to remove potential structural ambiguities in the splittings. The T1Z anisotropy permits us to solve for the two correlation times (tau R parallel = 6.8 x 10(-9) s and tau R perpendicular = 6 x 10(-6) s). The simulated parameters were corroborated by a Jeener-Broekaert experiment where the bilayer normal was parallel to the principal magnetic field. At this orientation the ratio, J2(2 omega 0)/J1(omega 0) was obtained in order to estimate the strength of the restoring potential in a model-independent fashion. This measurement yields the rms angle, <theta 2>1/2 (= 16 +/- 2 degrees at 34 degrees C), formed by the peptide helix axis and the average bilayer normal.     

The functional asymmetry of cosN, the nicking site for bacteriophage lambda DNA packaging, is dependent on the terminase binding site, cosB.

cosN is the site at which terminase, the DNA packaging enzyme of phage lambda, introduces staggered nicks into viral concatemeric DNA to initiate genome packaging. Although the nick positions and many of the base pairs of cosN show 2-fold rotational symmetry, cosN is functionally asymmetric. That is, the cosN G2C mutation in the left half-site (cosNL) causes a strong virus growth defect whereas the symmetrically disposed cosN C11G mutation in the right half-site (cosNR) does not affect virus growth. The experiments reported here test the proposal that the genetic asymmetry of cosN results from terminase interactions with cosB, a binding site to the right of cosN. In the presence of cosB, the left half-site mutation, cosN G2C, strongly affected the cos cleavage reaction, while the symmetric right half-site mutation, cosN C11G, had little effect. In the absence of cosB, the two mutations moderately reduced the rate of cos cleavage by the same amount. The results indicated that the functional asymmetry of cosNdepends on the presence of cosB. A model is discussed in which terminase-cosN interactions in the nicking complex are assisted by anchoring of terminase to cosB.     

Kinetics and pathways of charge recombination in photosystem II

The mechanism of charge recombination of the S(2)Q(A)(-) state in photosystem II was investigated by modifying the free energy gap between the quinone acceptor Q(A) and the primary pheophytin acceptor Ph. This was done either by changing the midpoint potential of Ph (using mutants of the cyanobacterium Synechocystis with a modified hydrogen bond to this cofactor), or that of Q(A) (using different inhibitors of the Q(B) pocket). The results show that the recombination rate is dependent on the free energy gap between Ph and Q(A), which confirms that the indirect recombination pathway involving formation of Ph(-) has a significant contribution. In the mutant with the largest free energy gap, direct electron transfer from Q(A)(-) to P(+) predominates. The temperature dependence of the recombination rate was investigated, showing a lower activation enthalpy in this mutant compared with the WT. The data allow the determination of the rate of the direct route and of its relative weight in the various strains. The set of currently accepted values for the midpoint potentials of the Q(A)/Q(A)(-), Ph/Ph(-), and P(+)/P* couples is not consistent with the relatively rapid rate of the indirect recombination pathway found here, nor with the 3% yield of delayed fluorescence as previously estimated by de Grooth and van Gorkom (1981, Biochim. Biophys. Acta 635, 445-456). It is argued that a likely explanation is that the midpoint potentials of the two latter couples are more positive than believed due to electrostatic interactions. If such is the case, the estimation of the midpoint potential of the P(+)/P and S(2)/S(1) couples must also be revised upward, with values of 1260 and 1020 mV, respectively.     

Calibration of the angular dependence of the amide proton-C alpha proton coupling constants, 3JHN alpha, in a globular protein. Use of 3JHN alpha for identification of helical secondary structure

The vicinal amide proton-C alpha proton spin-spin coupling constants, JHN alpha, in the globular protein basic pancreatic trypsin inhibitor (BPTI) have been measured using phase-sensitive correlated spectroscopy at high digital resolution. In conjunction with the crystal structure of BPTI, these data were used to calibrate the correlation between 3JHN alpha and the dihedral angle phi. The resulting "BPTI curve" is 3JHN alpha = 6.4 cos2 theta - 1.4 cos theta + 1.9 (theta = [phi - 60 degrees]). It is further shown that measurement of the spin-spin couplings 3JHN alpha presents an independent, reliable method for identification of the location of helical structure in the amino acid sequence of proteins.     

Analysis of the backbone dynamics of interleukin-1 beta using two-dimensional inverse detected heteronuclear 15N-1H NMR spectroscopy

The backbone dynamics of uniformly 15N-labeled interleukin-1 beta are investigated by using two-dimensional inverse detected heteronuclear 15N-1H NMR spectroscopy. 15N T1, T2, and NOE data at a spectrometer frequency of 600 MHz are obtained for 90% of the backbone amide groups. The data provide evidence for motions on three time scales. All the residues exhibit very fast motions on a time scale of approximately less than 20-50 ps that can be characterized by a single-order parameter with an average value of 0.82 +/- 0.05. For a model comprising free diffusion within a cone, these residue-specific order parameters translate to an average cone semiangle of 20.7 +/- 3.3 degrees. Thirty-two residues also display motions on a time scale of 0.5-4 ns, slightly less than the overall rotational correlation time of the protein (8.3 ns). These additional motions must be invoked to account for the discrepancy between experiment and the simplest theoretical formulation in which the internal motions are described by only two parameters, a generalized order parameter and an effective correlation time [Lipari, G., & Szabo, A. (1982a) J. Am. Chem. Soc. 104, 4546-4559]. In particular, while the simple formulation can account for the 15N T1 and T2 data, it fails to account for the 15N-1H NOE data and yields calculated values for the NOEs that are either too small or negative, whereas the observed NOEs are positive. With the introduction of two internal motions that are faster than the rotational correlation time and differ in time scales by at least 1-2 orders of magnitude [Clore, G. M., Szabo, A., Bax, A., Kay, L. E., Driscoll, P. C., & Gronenborn, A. M. (1990) J. Am. Chem. Soc. 112, 4989-4991], all the relaxation data for these 32 residues can be fitted by two order parameters and an effective correlation time for the slower of the two internal motions. A simple model for these two motions is one in which the very fast motion involves axially symmetric diffusion within a cone, while the slower motion comprises jumps between two different orientations of the NH vector. For such a model the jump angle (excluding the C-terminal residue) ranges from 15 degrees to 69 degrees with a mean value of 28.6 +/- 14.0 degrees. Another 42 residues are characterized by some sort of motion on the 30-ns-10-ms time scale, which results in 15N line broadening due to chemical exchange between different conformational substates with distinct 15N chemical shifts.(ABSTRACT TRUNCATED AT 400 WORDS)     

Matrix simulation of duodenal crypt cell kinetics. I. The steady state.

Steady state crypt cell kinetics have been simulated using matrix algebra. The model crypt cell population is distributed through two proliferation compartments (P1 and P2) and a quiescent state (Q). Under steady state conditions half the daughter cells produced on completion of P1 enter G1 of P2 and half enter G1 of P1. Both P2 daughter cells enter Q. Cells in Q are non-dividing but retain the potential to divide. On completion of Q, cells lose the potential to divide and move up onto the villi. The model has been developed by simultaneously simulating the following biological data: (1) the per cent labeled mitosis (PML) curve, (2) the number of labeled cells per crypt as a function of time following an injection of 3H-thymidine, and (3) the total number of cells per crypt.     

Active site control of myosin cross-bridge zeta potential

The electrical properties of contractile proteins contribute to muscle structure and perhaps function but have not been characterized adequately. Electrophoretic mobility, mu(e), is sensitive to the net electric charge and hydrodynamic size of a molecule in solution. Zeta potential, zeta, particle charge, Q(e), and particle charge-to-mass ratio are proportional to mu(e). We measured mu(e) for nucleotide complexes of skeletal muscle heavy meromyosin (HMM) and subfragment 1 (S1). The results indicate that mu(e) for HMM changes depending on the ligand bound in the active site. The changes in electric charge appear to occur mainly on the S1 moieties. For HMM(MgATPgammaS)(2) and HMM(MgADP.P(i))(2) the values of mu(e) are -0.077 and -0.17 (microm/s)/(V/cm), respectively. For these complexes, mu(e) is independent of [ATP], [ADP], and [P(i)]. When P(i) dissociates from HMM(MgADP.P(i))(2) to form HMM(MgADP)(2), mu(e) decreases to -0.61 (microm/s)/(V/cm). This large decrease in mu(e) is independent of free [ADP] or [ATP]. Increasing [P(i)], on the other hand, increases mu(e) for HMM(MgADP)(2) to values near those observed for the steady-state intermediate. For HMM, mu(e) = -0.34 and is independent of P(i). MgADP binding to HMM decreases mu(e) to -0.57 (microm/s)/(V/cm), and the dissociation constant is 9 microM. Taken together, these data indicate that mu(e) and, thus, zeta are controlled by ligand binding to the active site. The magnitudes of the particle charge-to-mass ratios for the HMM complexes are all in a range that falls within published values determined for a variety of other proteins. Possible roles that the observed nucleotide-dependent changes in cross-bridge electric charge might have in the contractile cycle in muscle are considered.     

A theoretical study of rotational diffusion models for rod-shaped viruses. The influence of motion on 31P nuclear magnetic resonance lineshapes and transversal relaxation.

Information about the interaction between nucleic acids and coat proteins in intact virus particles may be obtained by studying the restricted backbone dynamics of the incapsulated nucleic acids using 31P nuclear magnetic resonance (NMR) spectroscopy. In this article, simulations are carried out to investigate how reorientation of a rod-shaped virus particle as a whole and isolated nucleic acid motions within the virion influence the 31P NMR lineshape and transversal relaxation dominated by the phosphorus chemical shift anisotropy. Two opposite cases are considered on a theoretical level. First, isotropic rotational diffusion is used as a model for mobile nucleic acids that are loosely or partially bound to the protein coat. The effect of this type of diffusion on lineshape and transversal relaxation is calculated by solving the stochastic Liouville equation by an expansion in spherical functions. Next, uniaxial rotational diffusion is assumed to represent the mobility of phosphorus in a virion that rotates as a rigid rod about its length axis. This type of diffusion is approximated by an exchange process among discrete sites. As turns out from these simulations, the amplitude and the frequency of the motion can only be unequivocally determined from experimental data by a combined analysis of the lineshape and the transversal relaxation. In the fast motional region both the isotropic and the uniaxial diffusion model predict the same transversal relaxation as the Redfield theory. For very slow motion, transversal relaxation resembles the nonexponential relaxation as observed for water molecules undergoing translational diffusion in a magnetic field gradient. In this frequency region T2e is inversely proportional to the cube root of the diffusion coefficient. In addition to the isotropic and uniaxial diffusion models, a third model is presented, in which fast restricted nucleic acid backbone motions dominating the lineshape are superimposed on a slow rotation of the virion about its length axis, dominating transversal relaxation. In an accompanying article the models are applied to the 31P NMR results obtained for bacteriophage M13 and tobacco mosaic virus.     

Phosphorus nuclear magnetic resonance studies of lipid-protein interactions: human erythrocyte glycophorin and phospholipids

Human erythrocyte glycophorin containing four molecules of phospholipid tightly bound to the protein was isolated from human red cell ghosts. This protein preparation was reconstituted into a digalactosyl diglyceride bilayer. The 31P NMR spectrum of this reconstituted membrane produced an axially symmetric powder pattern arising exclusively from the phospholipids bound to glycophorin. The width of the powder pattern, about 90 ppm, is about twice as broad as that normally exhibited by a phospholipid bilayer. The chemical shift tensor is perturbed relative to phospholipids in a bilayer. The spin-lattice relaxation rate of these protein-bound phospholipids is found to be nearly an order of magnitude faster than phospholipids in a bilayer. The results are consistent with phospholipids tightly bound to the membrane protein and undergoing rotational diffusion, perhaps as a complex of phospholipid and protein.     

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.