John E. Fletcher

Binding of long chain fatty acids to β-lactoglobulin.

Abstractβ-lactoglobulin (BLG), a bovine milk protein that is available commercially in crystalline form, binds long chain free fatty acids (FFA). The binding data were analyzed with a model containing one primary FFA binding site and a large number of weak secondary binding sites. At 37C and pH 7.4, the apparent association constant for binding of FFA to the primary site was of the order of 105 M−1 and that for binding to the secondary sites was approximately 103 M−1. The strength of binding was: palmitate > stearate > oleate > laurate. The affinity of BLG for palmitate increased as the pH of the incubation medium was raised from 6.5 to 8.7 and decreased as the ionic strength of the medium was raised. Palmitate binding was decreased in the presence of 6 M urea and when the protein either was exposed to elevated temperature or was acetylated prior to incubation. BLG took up methyl palmitate, cetyl alcohol, hexadecane and cholesterol to a lesser extent than FFA. Binding of FFA to BLG was associated with a small increase in the intensity of the fluorescent emission of the protein at 333 mμ. BLG can serve as an FFA acceptor or carrier in biological experiments. FFA released from adipose tissue during in vitro incubation was taken up by BLG. Net transfer of fatty acid to the incubation medium ceased when the molar ratio of FFA to BLG exceeded 1.1.14C-1-Palmitate bound to BLG was taken up by Ehrlich ascites tumor cells in vitro. At a given palmitate-protein molar ratio, much more labeled fatty acid was taken up by these cells from media containing BLG than from those containing bovine albumin, apparently because FFA is bound less firmly to BLG than to albumin.

A procedure for computer analysis of data from macromolecule-ligand binding studies

Abstract A procedure for fitting macromolecule-ligand binding data to a mathematical model using computer techniques is described. The computer algorithm for carrying out this procedure together with a flow diagram of the main program are presented. Using this procedure, the choice of an appropriate model is made from computed results, and the subjective bias often associated with hand-drawn graphical methods is avoided. In addition, estimates of the statistical standard errors of the binding constants are obtained, and information concerning the validity of the model is provided. The output obtained from the computer is displayed in both tabular and graphical form.

COMPUTER ANALYSIS OF DRUG-PROTEIN BINDING DATA*

The therapeutic action of a drug often depends upon its effective concentration as well as upon its drug activity. This effective concentration is the concentrktion of free drug. The differences among sulfa drugs and among penicillins depend largely upon differences in binding to serum albumin because of different side chains. By varying the chemical structure of a drug, the pharmacologist has the opportunity of regulating both the duration and the intensity of its action. Often the two may be varied nearly independently. For high activity of short duration, a drug should not be bound to the plasma proteins, but for the prolonged action, it should be largely bound.

The binding of palmitoyl-CoA to bovine serum albumin.

Bovine serum albumin (BSA) is routinely utilized in vitro to prevent the adverse detergent effects of long-chain acyl-CoA esters (i.e., palmitoyl-CoA) in enzyme assays. Determination of substrate saturation kinetics in the presence of albumin would only be valid if the relationship between bound and free substrate concentrations was known. To elucidate the relationship between bound and free palmitoyl-CoA concentrations in the presence of BSA, several different techniques including equilibrium dialysis, equilibrium partitioning, fluorescence polarization and direct fluorescence enhancement were investigated. Direct fluorescence enhancement using a custom synthesized fluorescent probe, 16-(9-anthroyloxy)palmitoyl-CoA (AP-CoA), was the best approach to this question. Measurement of the relationship between mol of palmitoyl-CoA bound per mol of BSA (nu) versus -log[free palmitoyl-CoA] revealed that the binding of palmitoyl-CoA to BSA, like palmitate was nonlinear, suggesting the presence of more than one class of acyl-CoA binding sites. Computer analyses of the binding data gave a best fit to the 2,4 two-class Scatchard model, suggesting the presence of two high-affinity primary binding sites (k1 = (1.55 +/- 0.46) x 10(-6) M-1) and four lower affinity secondary binding sites (k2 = (1.90 +/- 0.09) x 10(-8) M-1). Further analyses using the six parameter stoichiometric (stepwise) ligand binding model supports the existence of six binding sites with the higher affinities associated with the binding of the first mole of palmitoyl-CoA and weaker binding occurring after the first two sites are occupied. The association constants from this model of multiple binding diminish sequentially (i.e., K1 greater than K2 greater than K3 greater than...greater than or equal to K6), suggesting that each mol of long-chain acyl-CoA binds to BSA with decreasing affinities.

First passage time problems in time-dependent fields

This paper discusses the simplest first passage time problems for random walks and diffusion processes on a line segment. When a diffusing particle moves in a time-varying field, use of the adjoint equation does not lead to any simplification in the calculation of moments of the first passage time as is the case for diffusion in a time-invariant field. We show that for a discrete random walk in the presence of a sinusoidally varying field there is a resonant frequency ϖ* for which the mean residence time on the line segment is a minimum. It is shown that for a random walk on a line segment of lengthL the mean residence time goes likeL2 for largeL when ϖ≠ϖ*, but when ϖ=ϖ* the dependence is proportional toL. The results of our simulation are numerical, but can be regarded as exact. Qualitatively similar results are shown to hold for diffusion processes by a perturbation expansion in powers of a dimensionless velocity. These results are extended to higher values of this parameter by a numerical solution of the forward equation.

Analysis of protein ligand equilibria

Abstract A method is described for analyzing ligand-binding data for proteins. The method has the advantages of objectivity and minimal computer requirements. Its use is illustrated for synthetic data and for real data. The method is shown to be particularly advantageous in the case of co-operative binding.

Axial diffusion and wall permeability effects in perfused capillary-tissue structures

Attempts to experimentally examine oxygen supply and distribution in the isolated perfused heart and brain have renewed interest in mathematical models of artificially perfused capillary-tissue structures. The need to understand histograms of PO2 measurements from these isolated-perfused organ studies (modified Lagendorf preparations) has required that existing mathematical models and their boundary conditions be re-examined in the context of these experiments. A unifying system of equations and boundary conditions are examined here for the purpose of studying the effects of anisotropic diffusion, and capillary vessel wall permeability on both the capillary and tissue substrate supply. The mathematical models are explored for parameters of physiologic interest, and some comparisons are made with experimental determinations. The comparisons with data suggest an anisotropic transport of oxygen in the tissue that is unexplained by known physiologic mechanisms.

On the computation of substrate levels in perfused tissues

Abstract The recent development of experimental techniques to study the isolated perfused heart and brain have renewed interest in the mathematical modeling of capillary-tissue structures. A new analytical representation is developed for the Krogh cylinder model for blood-tissue structures, and a scheme is presented for determining an asymptotic series approximation for this solution. This solution is explored for model parameters of experimental interest, and the contribution and effect of axial diffusion is demonstrated.

A kinetic model of CD4+ lymphocytes with the human immunodeficiency virus (HIV)☆

This report describes a kinetic model of in vitro cytopathology involving interactions of human immunodeficiency virus (HIV) with CD4+ helper T lymphocytes. The model uses nonlinearly coupled, ordinary differential equations to simulate the dynamics of infected and uninfected cells and free virions. It is assumed that resting cells are more readily infected than activated cells, but once infected, only activated cells produce more virus. Resting cells can be activated by some appropriate stimulus (e.g. phytohemagglutinin, soluble antigen). The model predicts that the initial inoculum of virus is taken up by resting cells and without stimulation the system comes to a steady state of two populations, namely infected and uninfected cells. Stimulation of this system produces two additional populations, namely infected and uninfected activated cells which, along with the previous populations, exhibit cyclic behavior of growth, viral expression/release, and death. Additional stimuli enhance or diminish the cyclic behavior depending upon their occurrence in time. These simulations suggest a similar dynamics in human HIV infection and may explain a major factor responsible for the widely varying depletion rate of (CD4+) helper T cells in AIDS patients.

An analytical model for axial diffusion in the Krogh cylinder.

The tissue level distribution of oxygen (O2) in the hemoglobinless perfused heart has been measured under controlled conditions with Whalen PO2 microelectrodes (Schubert, Whalen, and Nair, 19 78). In an attempt to understand tissue level details of O2 transport we compared that PO2 distribution to those predicted by mathmatical models. Models incorporating only radial transport in the tissue compared poorly with the measured histograms. Blum’s (1960) model with radial and axial diffusion was found to be in error (Schubert, 1976), and a correct solution had not been published. A unique analytic model was derived by modifying the radial transport phenomena so that the axial diffusional transport could be included. This model displays trends seen in the experimental data. Unfortunately the best match was obtained by increasing the value of the axial diffusion coefficient, D, considerably beyond the value accepted in the literature. This led to questions about the appropriateness of the radial transport assumptions which could be answered only be seeking the correct solution to the problem originally posed by Blum.