James S. Beck

Relations between membrane monolayers in some red cell shape transformations.

Abstract Analytic expressions for cell volume and for the areas of the component monolayers of the membrane of red blood cells of different shapes have been derived from geometric models. The results show differences between outer and inner monolayers of 0·41, 0·42, 0·39 and 0·93 μm2, respectively for discocyte, spherocyte, stomatocyte and spheroechinocyte of surface area 138 μm2. These results can be applied to the evaluation of various hypotheses about red cell shape transformations.

Hypotonic hemolysis of human red blood cells: a two-phase process

SummaryPrevious use of hemolysis time measurement to determine permeability coefficients for the red blood cell membrane rested on the assumption that cells swelling in a hypotonic medium hemolyzed immediately on reaching critical volume. By preswelling red cells to various volumes prior to immersion in hemolytic solutions we extrapolate to the hemolysis time of red cells immersed at critical volume and thereby find a significant period of time during which the cells apparently remain in a spherical form prior to release of hemoglobin. Revised estimates of permeability coefficients follow from including this spherical (nonswelling) phase. In addition, the appreciation of a characteristic time period during which the membrane is under tension provides new opportunity to study physical and chemical properties of the membrane.

Area under the curve, bioavailability, and clearance

It is a well-known fact that the area under the curve (AUC) representing the concentration of a drug in the plasma as a function of time is related in a simple way to the fraction of the dose reaching the plasma and to its clearance from the same. Indeed if the drug clears the ptasma in such a way that its concentration c(t) at the point of exit can be considered uniform, call C1 the volume cleared per unit time, then Cl. c(t) 9 dt is the amount of drug cleared from the plasma in the interval of time from t to t + dt; supposing also that the drug administered to the individual subject will eventually leave the plasma completely, then

Probability Density Function of the Red Cell Membrane Permeability Coefficient

The distribution of a random variable is determined by the probability density functions (PDF) of all other random variables with which the variable in question is jointly distributed. If the PDF of the random variable of interest is normal, or skewed normal, then the distributions with which it is jointly distributed determine its mean and standard deviation. In the case described here (where hemolysis time of the red blood cell is a function of the permeability coefficient and geometric variables of the cell) the mean and standard deviation of the permeability coefficient and the known distributions of the geometric variables on which the hemolysis time depends determine a predicted distribution of hemolysis time. An observed distribution of the hemolysis time is obtained spectrophotometrically. By choosing the mean and standard deviation of the permeability coefficient so that the predicted PDF of the hemolysis time matches the observed PDF best by least-squares criterion, the complete distribution of the permeability coefficient is determined.

Echinocyte formation: a test case for mechanisms of cell shape changes.

Abstract That cell shape changes result from monolayer condensation and/or expansion of plasma membranes when clustering of intrinsic membrane proteins occurs is a feasible hypothesis to explain important aspects of cell behaviour. Information about the human red blood cell membrane is consistent with the hypothesis. The formation of echinocytes (red cells with regular outward projections) constitutes a tractable test case for the hypothesis. Critical experiments can be done on red cells with available techniques.

On internalization of hormone-receptor complex and receptor recycling

Experimental evidence for recycling of receptors and for discontinuous internalization of the hormone-receptor complex by endocytosis, suggests a number of variations on this theme. Simulations based on models of these processes show the possible effects of the variations and suggest experimental strategies. Two examples from the experimental literature are explored. The new parameters associated with endocytosis are threshold for internalization of clusters of the complex, composition of clusters with respect to the complex and uncomplexed receptor and rate constant for cluster formation.

Determination of dependence of binding parameters on receptor occupancy

Measurements of the binding of ligand to receptors that are macromolecules, either free or components of biomembranes, often show deviation from what is expected of a simple reaction described by an association and a dissociation rate constant. A more versatile model and more discriminating experiments are required for a satisfactory explanation. This paper is based on a general model of the binding reaction in which the rate constants and equilibrium constant are dependent upon occupancy of receptors. The analysis of the model leads to three kinds of experiments: (1) equilibrium measurements which permit quantitative determination of a dissociation equilibrium parameter as a function of receptor occupancy; (2) measurements prior to equilibrium which yield the same information; and (3) measurements prior to equilibrium which reveal quantitatively the dependence of both association and dissociation rate parameters separately, on occupancy.

Determination of binding parameters in the presence of coupled reactions

Components of a binding reaction may undergo nonbinding reactions: receptors may be degraded, internalized, or exchanged with cryptic sites; ligand may be degraded or compartmented. In such cases the parameters that characterize the system are not obtained from the usual equilibrium analyses. We have simulated the reactions of such systems and generated association curves, “Scatchard” plots, and “Scatchard-like” plots that permit the calculation of binding affinity and receptor number not normally calculable under non-equilibrium binding conditions. In particular, we show that certain coupled reactions produce local maxima and sigmoid shapes in association curves and that the maxima can be used to obtain affinities and receptor numbers.

Coagulation in cell suspensions: Extensions of the von Smoluchowski model

Recently, a long-range interactive force between erythrocytes has been proposed (Rowlands et al., 1981, 1982a,b) based on an apparent increase in the rate of aggregation of erythrocytes in an aqueous suspension over that predicted by one model of Brownian aggregation. Here, we examine the assumptions underlying this model and propose modifications compatible with the biological constraints on the model. The refined model is represented as a series of coupled differential equations representing the change in particle number density as a function of time. Numerical solution of these equations is consistent with the absence of an intercellular force.

Conceptual Foundations and Uses of Models in Pharmacokinetics

The word “model” is overused in the biomedical literature. And it is often misused in a way that blurs the distinction between the system under study and someone’s concept of the system- We can get involved in wasteful disputes and fruitless efforts with such sloppy thinking. Because these failings appear so frequently and because rational uses of models can be very helpful, I will sketch here a brief picture of what — I suggest — a model should be and what it can do for us. Along the way I will point out some pitfalls I see as taking a toll on our scientific and therapeutic enterprizes.