Brian T. Bulliman

The use of transmembrane differences in saturation transfer for measuring fast membrane transport; application to H13C03− exchange across the human erythrocyte

Abstract We consider the NMR signal intensity of a solute B , that is both in exchange across the membrane of cells in suspension and also in chemical exchange with another solute C , when the nuclei of C are saturated with selective radiofrequency radiation. This extension of the classical saturation transfer experiment potentially enables the measurement of fast unidirectional membrane transport rates of solutes that are in chemical equilibrium, when the chemical shifts of the intra- and extracellular solute are identical. The application of the theory and experimental methods to a biological system is illustrated by using 13 C NMR with the H 13 CO 3 − 13 CO 2 exchange system in human erythrocytes. In the buffer conditions employed the estimated value of the exchange rate of H 13 C0 3 − was comparable to values estimated with NMR and other non-NMR methods.

A series expression for the surface area of an Ellipsoid and its application to the computation of the surface area of avian erythrocytes

Knowledge of the surface area of cells is necessary for biophysical studies in which the permeability coefficient of a cell-type for a solute is defined. Under the microscope, avian erythrocytes have the appearance of an oval discus usually with a central elongated nucleus. The dimensions of these cells have been obtained for a large range of species over the past century. However, estimates of the surface areas have been obtained using mathematically simplistic models such as flattened circular cylinders. We modelled red cells of the domestic chicken (Gallus domesticus) as ellipsoids using the previously published dimensions to obtain the three semi-axis lengths. Although the mathematical expression for the volume of an ellipsoid is well known, an expression for the surface area is not. We present a general expression for the surface area of an ellipsoid that is a power series involving elliptic integrals and functions; the latter being rapidly evaluated by computer using standard series expressions. Our estimates of area are compared with earlier ones and those obtained by numerical integration of the surface.

Mutarotase equilibrium exchange kinetics studied by 13C-NMR

The rates of exchange between the alpha- and beta-anomers of D-[1-13C]glucose, at equilibrium catalyzed by porcine kidney mutarotase (EC 5.1.3.3), were measured using 13C-NMR spin-transfer procedures. This entailed inversion-transfer and saturation-transfer experiments, and two-dimensional exchange spectroscopy (2D EXSY). The concentration and temperature dependences of the fluxes were studied; equilibrium exchange Michaelis constants, and the activation energy of the catalyzed reaction were thereby measured.

Urea exchange across the human erythrocyte membrane measured using 13C NMR lineshape analysis

The 13C NMR spectrum of 13C-urea in a suspension of human red cells of reduced mean cell volume was observed to contain partially resolved resonances arising from the intra- and extracellular populations of the compound. It was shown that at 25°C and a magnetic field strength of 9.4 T, the rate of exchange of urea between the intra- and extracellular populations was such that the NMR lineshape was sensitive to a change in the rate of 13C-urea exchange, induced either by the addition of the urea transport inhibitor phloretin, or by the addition of 12C-urea. Total lineshape analysis of r3C NMR spectra of 13C-urea in red cell suspensions containing different concentrations of 12C-urea resulted in a weighted mean estimate for the Km and Vmax for urea equilibrium exchange from three experiments of 44 ± 18 mM and 3.1 ± 0.6 × 10−8 molcm−2 s−1, respectively (the errors denote the weighted mean standard deviations). These estimates of Km and Vmax, were significantly lower than previous values reported in the literature and determined using other techniques.

In Vivo Determination of ATP in Tumors Using 31P Inversion Spin Transfer

The in vivo exchange kinetics of creatine kinase in the hind leg muscle of rats containing a transplanted mammary adenocarcinoma has been investigated using 31P magnetic resonance spectroscopy. Using a solenoid coil, the adenosine triphosphate (ATP) resonances arising from the tumor could be distinguished from ATP resonances arising from the muscle surrounding the tumor by use of inversion spin transfer techniques. This procedure affords a specific method of evaluating ATP metabolism of tumors in vivo.

31P Magnetization transfer in the phosphoglyceromutase-enolase coupled enzyme system

The rate of exchange of phosphoryl groups between 2-phosphoglycerate, 3-phosphoglycerate and phosphoenolpyruvate by the coupled phosphoglyceromutase-enolase enzyme system using one- and two-dimensional 31P NMR spectroscopy was measured. Magnetization exchange in one-dimensional experiments was achieved by saturation transfer with selective irradiation at both one and two sites in this three-site exchange system using the DANTE pulse sequence. The two-dimensional magnetization exchange experiment avoids the need to selectively saturate at one or more frequencies which may be difficult in complex exchange systems. Analysis of the two-dimensional exchange experiment by the back transformation method yielded exchange rate constants in good agreement with the saturation transfer method.

Bi-cyclide and flat-ring cyclide coordinate surfaces: correction of two expressions

Bi-cyclide and flat-ring cyclide coordinates are three-dimensional rotational coordinate systems based on conformal transformations using the Jacobian elliptic function sn. We have checked the previously published formulae of these systems (P. Moon and D. E. Spencer, Field Theory Handbook, Springer-Verlag, Berlin, 1971). In both cases the expression for the rotation-cyclide surfaces was incorrect: thus we present rederivations. The expressions were verified with the symbolic-algebraic computation package MACSYMA.

Magnetic potential and field gradients of a model cell

The magnetic potential within and outside a nucleated cell placed in a uniform magnetic field is described for a model consisting of two concentric diamagnetic spheres. The analytical description of the magnetic potential in and around a system consisting of a finite number of concentric diamagnetic spheres in a uniform magnetic field was derived. The solution was employed to calculate the field gradients outside and inside a model chicken red blood cell. The form and magnitude of the gradients provide a theoretical basis on which to discuss experimental results relating to the attenuation of signals obtained using proton nuclear magnetic resonance spectroscopy with chicken erythrocyte suspensions. The form of the magnetic field, field difference and field gradients in the external medium of a cell suspension was simulated for a distribution of spheres in a uniform magnetic field, such as might occur in an idealised dilute cell suspension.

Expressions for surfaces in disk-cyclide coordinates : derivations using symbolic computation

Disk-cyclide coordinate systems are orthogonal and curvilinear, and are based on a conformal transformation using the Jacobian elliptic function cn. The expressions for the coordinate surfaces of this system have been presented previously (P. Moon and D.E. Spencer, “Field Theory Handbook”, Springer, Berlin, 1961, 1971). However, they are found to be incorrect. Rederivation of the expressions involved a relatively tedious variable-elimination process which we therefore carried out using symbolic algebraic computation with the MACSYMA package.