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F W Wiegel

Publications and source records attributed to F W Wiegel.

18 recordsLinked to original sources
PubMed1994

Kinetics of ligand binding to a cluster of membrane-associated receptors.

The process of ligand binding to a cluster of membrane-associated receptors is examined theoretically. The theoretical model proposed involves the diffusion of ligands from the solution to the disc-like cluster of receptors on the surface of the spherical cell. When the ligand hits the internal part of the disc-like cluster, it begins to move laterally until it leaves the disc through its outer surface or is bound by one of the receptors inside the disc. If the ligand leaves the cluster, it returns to the solution and hits the disc again after a certain period, etc. According to our model the transition from a diffusion-limited to a reaction-limited process of binding is determined by the dimensionless parameter lambda identical to Dtc/a2, where D is the lateral diffusion coefficient, tc is the characteristic time of reaction, and a is the radius of the disc-like cluster. The forward rate constant kf turns out to be a function of lambda. Comparing the results of our calculations of kf with some experimental data we found that agreement is achieved at high lambda, i.e. the process of ligand binding by clustered receptors is predominantly reaction-limited.

Cell Membrane↗
PubMed1990

Chemoreception by a cell with age-dependent receptor binding sites.

The authors determine the time-dependent ligand current into a spherical cell that is covered with a large number of age-dependent receptors. These receptors can be in either of two states: active (i.e., available for ligand binding) or inactive. An active receptor turns inactive upon binding a ligand, and it can reappear as active at some later time. The transition inactive----active is treated as a probabilistic process. The ligand distribution around the cell is determined analytically in terms of this distribution at the cell surface. A set of nonlinear integral equations is derived for the distribution at the cell surface, which is solved numerically. In this way the time-dependent ligand current into the cell as well as the average active receptor population at the cell surface are determined.

Binding Sites↗
PubMed1988

Time-dependent ligand current into a saturating cell performing chemoreception.

We determine the ligand current into a single spherical cell whose receptors become permanently blocked after binding ligands. Initially the cell is placed in a medium which contains ligands at uniform concentration. The analytical solution for the ligand distribution is obtained in terms of an integral over the solution at the cell surface. For the solution at the cell surface a nonlinear integral equation is derived which is solved numerically. We determine the time-dependent ligand current into the cell and the average number of free receptors in the cell surface as a function of time.

Cells↗
PubMed1988

The distribution of cell surface proteins on spreading cells. Comparison of theory with experiment.

Bretscher (1983) has shown that on uniformly spread giant HeLa cells, the receptors for low density lipoprotein (LDL) and transferrin are concentrated toward the periphery of the cells. To explain these nonuniform distributions, he proposed that on giant HeLa cells, recycling receptors return to the cell surface at the cell's leading edge. Since the distribution of coated pits on these cells is uniform, Bretscher and Thomson (1983) proposed that there is a bulk membrane flow toward the cell centers. Here we present a mathematical model that allows us to predict the distribution of cell surface proteins on a thin circular cell, when exocytosis occurs at the cell periphery and endocytosis occurs uniformly over the cell surface. We show that on such a cell, a bulk membrane flow will be generated, whose average velocity is zero at the cell center and increases linearly with the distance from the cell center. Our model predicts that proteins that aggregate in coated pits will have concentrations that are maximal at the cell periphery. We fit our theory to the data of Bretscher and Thomson (1983) on the distribution of ferritin receptors for the following cases: the receptors move by diffusion alone; they move by bulk membrane flow alone; they move by a combination of diffusion and bulk membrane flow. From our fits we show that tau m greater than 3.5 tau p, where tau m and tau p are the lifetimes of the membrane and the ferritin receptor on the cell surface, and that tau pD less than 6.9 X 10(-7) cm2, where D is the ferritin receptor diffusion coefficient. Surprisingly, we obtain the best fits to the data when we neglect membrane flow. Our model predicts that for proteins that are excluded from coated pits, the protein concentration will be Gaussian, being maximal at the cell center and decreasing with the distance from the cell center. If on giant HeLa cells a protein with such a distribution could be found, it would strongly support Bretcher's proposal that there is an inward membrane flow.

Cell Membrane↗
PubMed1987

Fractional exponential decay of a membrane protein population due to capture by coated pits.

We consider the lateral diffusion of receptors, or other membrane proteins, in the outer membranes of certain cells, and their capture by coated pits. It is shown, for the case in which the coated pits are in fixed random positions, that the long-time decay of the total number of uncaptured proteins is of the fractional exponential form, N(t) = N0 exp [-square root of (t/tau)], and not of the pure exponential form, N(t) = N0 exp(-t/tau), which is usually assumed.

Coated Pits, Cell-Membrane↗
PubMed1987

Time-dependent ligand current into a single cell performing chemoreception.

We determine the ligand current into a single spherical cell which carries a large number of receptors on its surface. Initially, this cell is placed into a medium which contains ligands at uniform concentration. The time-dependent ligand distribution is calculated, from which the time-dependent ligand current into the cell is derived. If the ligand concentration is kept constant at distances comparable to the radius of the cell the stationary state sets in at times comparable to the T1 necessary for ligands to travel a distance of the order of the radius of the cell. If the ligand concentration is kept constant at infinity the stationary state sets in at a time which is about 1000T1 for typical values of the parameters.

Cell Physiological Phenomena↗
PubMed1984

Forward rate constants for receptor clusters. Variational methods for upper and lower bounds.

We are interested in the effect of receptor clustering on k+, the diffusion-limited forward rate constant for the binding of a ligand to a cell surface receptor. Here we estimate the reduction in k+ when receptors are clustered in various configurations. We obtain two alternative expressions for the flux of ligands into receptors distributed on a surface. Next we show through a variational principle that these provide both upper and lower bounds on the flux when evaluated for trial concentration functions which satisfy only the boundary conditions of the Laplace equation. We use an analogy with electrostatics to calculate rigorous bounds within approx. 10% of the exact result for a variety of planar clusters of hemispherical receptor sites. We also obtain an exact result for the flux into a spheroidal receptor and use this result to obtain bounds on the flux into certain receptor clusters.

Animals↗
PubMed1983

Membrane fluidity and the probability of complement fixation.

We develop a mathematical theory of the role of membrane fluidity in the initiation of the IgG mediated complement cascade. The basic assumption is that C1q must be at least doubly bound to activate C1r, but that once C1q is doubly bound, C1r still requires some mean finite time tau to become enzymatically active. If C1q dissociates during this time interval, C1r cannot be activated. We consider the consequences of the simplest model of fluidity--one in which the difference between "fluid phase" lipids and "non-fluid phase" lipids is to allow protein mobility, but not a change in protein conformation. We show that under these conditions fluidity will effect C1r activation only if the rate of formation of multiply bound C1q is limited by diffusion in the membrane. If diffusion in the membrane is not rate-limiting, then, within the framework of this model, fluidity has no effect whatsoever on C1r activation. Thus, an experimental determination that C1q binding is not rate-limited by diffusion in the surface, but that fluidity does effect activation, would suggest a protein conformational change resulting perhaps from altered lipid composition. If diffusion in the surface does rate limit multiple C1q binding, we predict the possibility of an optimum diffusion coefficient for activation. For suitably chosen and reasonable parameter values this optimum will occur in the range (10(-11) less than or equal to D less than or equal to 10(-8) cm2/sec. We predict further, under these circumstances, a precipitous drop in the probability of activation above the optimum. The abrupt switch from a high probability of activation to essentially no probability of activation suggests the possibility of a very sensitive control mechanism exploitable by relatively small changes in membrane lipid composition.

Animals↗
PubMed1983

The effect of receptor clustering on diffusion-limited forward rate constants.

The effect of receptor clustering on the diffusion-limited forward rate constant (k+) is studied theoretically by modeling cell surface receptors by hemispheres distributed on a plane. We give both exact results and bounds. The exact results are obtained using an electrostatic analogue and applying the method of the images. Accurate upper bounds on k+ are found from a variational principle.

Cell Membrane↗
PubMed1982

The equilibrium size distribution of rouleaux.

Rouleaux are formed by the aggregation of red blood cells in the presence of macromolecules that bridge the membranes of adherent erythrocytes. We compute the size and degree of branching of rouleaux for macroscopic systems in thermal equilibrium in the absence of fluid flow. Using techniques from statistical mechanics, analytical expressions are derived for (a) the average number of rouleaux consisting of n cells and having m branch points; (b) the average number of cells per rouleau; (c) the average number of branch points per rouleau; and (d) the number of rouleaux with n cells, n = 1, 2, ..., in a system containing a total of N cells. We also present the results of numerical evaluations to establish the validity of asymptotic expressions that simplify our formal analytic results.

Erythrocyte Aggregation↗
PubMed1982

Evaluation of reaction rate enhancement by reduction in dimensionality.

The paths followed by ligands as they react with or dissociate from cell surface receptors may include weak association with nonreceptor portions of the surface followed by lateral diffusion in the plane of the membrane to a receptor. The change in dimensionality of the diffusion process by utilization of these nonspecific paths has been invoked by a number of investigators as a mechanism for enhancing reaction rate in biological systems. This paper extends our previous work on the calculation of diffusive rate constants for ligand-receptor paths. We find that they have little effect on rate constants unless the number of free receptors per cell has been reduced to less than or equal to 10(2). This number represents better than 90% occupancy for most eukaryotes, suggesting that the dimensional change mechanism is of limited consequence. We show further that when the free receptor number is low enough for rate enhancement, then the primary parameter of consequence is D'K*/D, where D' and D are the two- and three-dimensional diffusion coefficients, respectively, and K* the nonspecific affinity. A 10-fold rate enhancement with 100 free receptors requires that this parameter be of order 10(-3). This value is barely within the lower limit imposed by currently available experimental information, casting doubt on the relevance of nonspecific paths in cellular systems.

Animals↗
PubMed1981

Effect of nonspecific forces and finite receptor number on rate constants of ligand--cell bound-receptor interactions.

We develop a theory of ligand diffusion in the presence of a central potential toward or away from receptor patches that are uniformly distributed over a spherical cell. The current onto the receptors is reduced to less than that onto the sphere by a factor that is a nonlinear function of the number of free receptors, their size, and their potential energy. Similarly, under conditions defined by the theory, the dissociation rate from a receptor is reduced by the probability of rebinding to some other receptor on the same cell. This complicates the kinetic analysis, leading to the possibility of an occupancy-dependent dissociation rate, but has no effect on the interpretation of thermodynamic data.

Cell Membrane↗
PubMed1981

Theoretical considerations of the role of antigen structure in B cell activation.

Thymus-independent antigens generally are polymeric molecules with repeating arrays of antigenic determinants. Immunological studies of the activity of haptenated thymus-independent antigens have shown that small changes in hapten density can transform a polymeric antigen from nonimmunogenic to immunogenic, and from immunogenic to tolerogenic. In this paper we compute the equilibrium configuration of a linear flexible, haptenated polymer absorbed to a B cell surface, and correlate configurational features of the molecule with its immunological functioning. A polymeric molecule bound to a cell generally will not lie entirely on the surface; rather there will be sections that form loops extending into solution, separated by tightly bound sections, or trains. Trains link antibody receptors on the B cell surface in a fashion that restricts their mobility. Thus trains cause restrictive cross-linking. Our computations show that there is a critical hapten density below which the polymer does not bind to the surface. At hapten densities slightly above the critical density, the polymer binds weakly to the surface with a configuration dominated by a few, rather long loops. These loops cross-link receptors, but do so without bringing the cross-linked receptors into close proximity and without substantially restricting their motion. Long loops thus cause unrestrictive cross-linking. As the hapten density increases, the average loop length decreases and the average train length increases. Thus cross-linking becomes restrictive. In this density range, immune stimulation is observed. At high hapten densities long trains form, separated by few, very short loops and almost all receptors are cross-linked. Consequently cross-linking may be overly restrictive, freezing receptors into place and generating an abundance of cross-linking or other signals that induce a state of immunological tolerance.

Antigens↗