Motion of particles adhering to the leading lamella of crawling cells.

Time-lapsed films of particle motion on the leading lamella of chick heart fibroblasts and mouse peritoneal macrophages were analyzed. The particles were composed of powdered glass or powdered aminated polystyrene and were 0.5-1.0 micrometer in radius. Particle motions were described by steps in position from one frame to the time-lapse movies to the next. The statistics of the step-size distribution of the particles were consistent with a particle in Brownian motion subject to a constant force. From the Brownian movement, we have calculated the two-dimensional diffusion coefficient of different particles. These vary by more than an order of magnitude (10(-11)-10(-10) cm2/s) even for particles composed of the same material and located very close to each other on the surface of the cell. This variation was not correlated with particle size but is interpretable as a result of different numbers of adhesive bonds holding the particles to the cells. The constant component of particle movement can be interpreted as a result of a constant force acting on each particle (0.1-1.0 x 10(-8) dyn). Variations in the fractional coefficient for particles close to each other on the cell surface do not yield corresponding differences in velocity, suggesting that the frictional coefficient and the driving force vary together. This is consistent with the hypothesis that the particles are carried by flow of the membrane as a whole or by flow of some submembrane material. The utility of our methods for monitoring cell motile behavior in biologically interesting situations, such as a chemotactic gradient, is discussed.

Separation of propulsive and adhesive traction stresses in locomoting keratocytes.

Strong, actomyosin-dependent, pinching tractions in steadily locomoting (gliding) fish keratocytes revealed by traction imaging present a paradox, since only forces perpendicular to the direction of locomotion are apparent, leaving the actual propulsive forces unresolved. When keratocytes become transiently "stuck" by their trailing edge and adopt a fibroblast-like morphology, the tractions opposing locomotion are concentrated into the tail, leaving the active pinching and propulsive tractions clearly visible under the cell body. Stuck keratocytes can develop approximately 1 mdyn (10,000 pN) total propulsive thrust, originating in the wings of the cell. The leading lamella develops no detectable propulsive traction, even when the cell pulls on its transient tail anchorage. The separation of propulsive and adhesive tractions in the stuck phenotype leads to a mechanically consistent hypothesis that resolves the traction paradox for gliding keratocytes: the propulsive tractions driving locomotion are normally canceled by adhesive tractions resisting locomotion, leaving only the pinching tractions as a resultant. The resolution of the traction pattern into its components specifies conditions to be met for models of cytoskeletal force production, such as the dynamic network contraction model (Svitkina, T.M., A.B. Verkhovsky, K.M. McQuade, and G.G. Borisy. 1997. J. Cell Biol. 139:397-415). The traction pattern associated with cells undergoing sharp turns differs markedly from the normal pinching traction pattern, and can be accounted for by postulating an asymmetry in contractile activity of the opposed lateral wings of the cell.

Nascent focal adhesions are responsible for the generation of strong propulsive forces in migrating fibroblasts.

Fibroblast migration involves complex mechanical interactions with the underlying substrate. Although tight substrate contact at focal adhesions has been studied for decades, the role of focal adhesions in force transduction remains unclear. To address this question, we have mapped traction stress generated by fibroblasts expressing green fluorescent protein (GFP)-zyxin. Surprisingly, the overall distribution of focal adhesions only partially resembles the distribution of traction stress. In addition, detailed analysis reveals that the faint, small adhesions near the leading edge transmit strong propulsive tractions, whereas large, bright, mature focal adhesions exert weaker forces. This inverse relationship is unique to the leading edge of motile cells, and is not observed in the trailing edge or in stationary cells. Furthermore, time-lapse analysis indicates that traction forces decrease soon after the appearance of focal adhesions, whereas the size and zyxin concentration increase. As focal adhesions mature, changes in structure, protein content, or phosphorylation may cause the focal adhesion to change its function from the transmission of strong propulsive forces, to a passive anchorage device for maintaining a spread cell morphology.

Distinct roles of frontal and rear cell-substrate adhesions in fibroblast migration.

Cell migration involves complex physical and chemical interactions with the substrate. To probe the mechanical interactions under different regions of migrating 3T3 fibroblasts, we have disrupted cell-substrate adhesions by local application of the GRGDTP peptide, while imaging stress distribution on the substrate with traction force microscopy. Both spontaneous and GRGDTP-induced detachment of the trailing edge caused extensive cell shortening, without changing the overall level of traction forces or the direction of migration. In contrast, disruption of frontal adhesions caused dramatic, global loss of traction forces before any significant shortening of the cell. Although traction forces and cell migration recovered within 10-20 min of transient frontal treatment, persistent treatment with GRGDTP caused the cell to develop traction forces elsewhere and reorient toward a new direction. We conclude that contractile forces of a fibroblast are transmitted to the substrate through two distinct types of adhesions. Leading edge adhesions are unique in their ability to transmit active propulsive forces. Their functions cannot be transferred directly to existing adhesions upon detachment. Trailing end adhesions create passive resistance during cell migration and readily redistribute their loads upon detachment. Our results indicate the distinct nature of mechanical interactions at the leading versus trailing edges, which together generate the mechanical interactions for fibroblast migration.

Antifolate transport in L1210 leukemia cells. Kinetic evidence for the non-identity of carriers for influx and efflux.

The kinetics of methotrexate transport in L1210 cells are described. Data derived from the measurmenets of initial influx, the complete time-course of uptake, intracellular steady-state level and unidirectional efflux were found to be consistent with a simple empirical equation containing three constants. Properties of the system include the following: (1) saturability of initial influx: (2) approach to steady state during uptake is exponential; (3) the half-time for drug uptake is independent of external concentration and equal to half-time for efflux; and (4) transport is concentrative at low external concentrations, whereas the reverse is true at high external concentrations. These observations are incorporated into a kinetic model which quantitatively accounts for the data on the basis of the hypothesis that influx and efflux take place via different carriers.

A method for measuring membrane microviscosity using pyrene excimer formation. Application to human erythrocyte ghosts.

In order to determine the microviscosity of human erythrocyte membrane suspensions, a method has been developed which is based on pyrene excimer formation. First, measurements of partitioning of pyrene into membranes, in conjunction with known values for the volume of the lipid compartment of erythrocyte ghosts are used to determine the concentration of pyrene in the membrane lipid. Secondly, reported measurements of the diffusion constants of aromatic hydrocarbons similar in structure to pyrene, are used to derive an empirical equation relating solvent viscosity and the diffusion constant of pyrene. Then, measurements of pyrene excimer formation in a series of solvents ranging up to several poise in viscosity are used to determine that the interaction diameter of the excimer formation reaction is 3 +/- 1 A. Finally all these data are brought together in order to conclude that the viscosity of the lipid in the human erythrocyte ghost is 8.0, 4.0 and 1.6 P at 10, 25 and 40 degrees C, respectively.

Binding of bivalent ligand to cell surface IgE: can one detect ring formation?

It is well established that aggregation of cell surface immunoglobulin is involved in signal transduction by cells of the immune system. It is less well understood what special properties of these cell surface aggregates are important in initiating the signal cascade. Several authors have proposed that cells respond to the size (Fewtrell and Metzger (1980) J. Immun. 125, 701-710) as well as the stereochemistry (Ortega et al. (1989) Eur. J. Immun. 19, 2251-2256) of receptor aggregates. One approach to arriving at data relevant to this question has been to construct simple bivalent ligands that can bind to surface immunoglobulin. Several authors have suggested that when these bivalent ligands interact with surface immunoglobulin the formation of small stable cyclic complexes is highly favored. In this paper we consider whether it is possible to completely determine the parameters that describe the binding of a bivalent ligand to a bivalent receptor with the available experimental technology. We show that with the appropriate analysis procedure, using a modified equivalent site model, these parameters can be reliably determined from only three experiments even when there is a large amount of ring formation.

Kinetic analysis of histamine release due to covalently linked IgE dimers.

We present a kinetic model of histamine release from human basophils due to covalently linked IgE dimers. Comparison of theory with experiment shows that the model gives a good description of histamine release by IgE dimers and allows a number of the parameters of the model to be determined. Comparison with previous models of release by conventional antigens indicates that despite their covalent structure, IgE dimers are subject to the same laws governing inactivation as are antigen produced crosslinks. In addition, the kinetic equation which relates the rate of histamine release to the number of crosslinked Fc epsilon receptors per cell is the same for crosslinks formed by IgE dimers as for antigen induced crosslinks. Quantitative fitting of histamine release data also yields a value for the rate constant for crosslink formation by IgE dimer on the cell surface (rx approximately 5 x 10(-10) cm2/sec). This rate constant is remarkably high and indicates that the reaction is diffusion controlled.

The auto-regulation model: a unified concept of how HIV regulates its infectivity, pathogenesis and persistence.

The life cycle of HIV can be divided into two distinct stages: intracellular and extracellular. The prevailing view is that the intracellular stage provides the only locus for regulating the virus in response to physiologic stimuli. Such regulation is accomplished by modulating the rates of transcription, translation and viral assembly. The extracellular stage consists of physical processes such as diffusion, adhesion and penetration of cells by viral particles. These latter processes are commonly thought to be "automatic" and not subject to regulation. For the past several years, we have developed means of more carefully measuring and characterizing the extracellular stage of HIV infection, and we have obtained evidence indicating that novel regulatory processes do, in fact, take place during this extracellular stage. We believe that this extracellular regulation permits HIV to adapt to a wide range of physiologic cell densities, to maintain persistent but slow growing infection, and to defeat the protective activity of humoral blockers. The overall purpose of this review is to consider our evidence for this hypothesis.

Cytoplasm dynamics and cell motion: two-phase flow models.

The motion of amoeboid cells is characterized by cytoplasmic streaming and by membrane protrusions and retractions which occur even in the absence of interactions with a substratum. Cell translocation requires, in addition, a transmission mechanism wherein the power produced by the cytoplasmic engine is applied to the substratum in a highly controlled fashion through specific adhesion proteins. Here we present a simple mechano-chemical model that tries to capture the physical essence of these complex biomolecular processes. Our model is based on the continuum equations for a viscous and reactive two-phase fluid model with moving boundaries, and on force balance equations that average the stochastic interactions between actin polymers and membrane proteins. In this paper we present a new derivation and analysis of these equations based on minimization of a power functional. This derivation also leads to a clear formulation and classification of the kinds of boundary conditions that should be specified at free surfaces and at the sites of interaction of the cell and the substratum. Numerical simulations of a one-dimensional lamella reveal that even this extremely simplified model is capable of producing several typical features of cell motility. These include periodic 'ruffle' formation, protrusion-retraction cycles, centripetal flow and cell-substratum traction forces.

Properties of behavior under different random ratio and random interval schedules: A parametric study.

Four pigeons were trained to peck a key under different values of a temporally defined independent variable (T) and different probabilities of reinforcement (p). Parameter T is a fixed repeating time cycle and p the probability of reinforcement for the first response of each cycle T. Two dependent variables were used: mean response rate and mean postreinforcement pause. For all values of p a critical value for the independent variable T was found (T=1 sec) in which marked changes took place in response rate and postreinforcement pauses. Behavior typical of random ratio schedules was obtained at T 1 sec and behavior typical of random interval schedules at T 1 sec.

[Properties of cholinesterase preparations from human erythroyctes]. / Nekotorye svoistva preparatov atsetilkholinésterazy iz éritrotsitov cheloveka.

A modified method is described for isolation of acetylcholinesterase from human erythrocytes using an additional step of gel filtration on Sephadex G-75. Preparations of acetylcholinesterase were liberated from thromaboplastic activity and their specific activity was increased due to removal of low molecular proteins and of the products of destruction of hemoglobin. Content of A and B isoantigens in the preparations obtained was rather low and content of hemoglobin, combined with other proteins in the form of oxyhemoglobin, did not exceed 12% of the total protein.

Mechanics and control of the cytoskeleton in Amoeba proteus.

Many models of the cytoskeletal motility of Amoeba proteus can be formulated in terms of the theory of reactive interpenetrating flow (Dembo and Harlow, 1986). We have devised numerical methodology for testing such models against the phenomenon of steady axisymmetric fountain flow. The simplest workable scheme revealed by such tests (the minimal model) is the main preoccupation of this study. All parameters of the minimal model are determined from available data. Using these parameters the model quantitatively accounts for the self assembly of the cytoskeleton of A. proteus: for the formation and detailed morphology of the endoplasmic channel, the ectoplasmic tube, the uropod, the plasma gel sheet, and the hyaline cap. The model accounts for the kinematics of the cytoskeleton: the detailed velocity field of the forward flow of the endoplasm, the contraction of the ectoplasmic tube, and the inversion of the flow in the fountain zone. The model also gives a satisfactory account of measurements of pressure gradients, measurements of heat dissipation, and measurements of the output of useful work by amoeba. Finally, the model suggests a very promising (but still hypothetical) continuum formulation of the free boundary problem of amoeboid motion. by balancing normal forces on the plasma membrane as closely as possible, the minimal model is able to predict the turgor pressure and surface tension of A. proteus. Several dynamical factors are crucial to the success of the minimal model and are likely to be general features of cytoskeletal mechanics and control in amoeboid cells. These are: a constitutive law for the viscosity of the contractile network that includes an automatic process of gelation as the network density gets large; a very vigorous cycle of network polymerization and depolymerization (in the case of A. proteus, the time constant for this reaction is approximately 12 s); control of network contractility by a diffusible factor (probably calcium ion); and control of the adhesive interaction between the cytoskeleton and the inner surface of the plasma membrane.

The mechanics of motility in dissociated cytoplasm.

We stimulate the dynamical behavior of dissociated cytoplasm using the Reactive Flow Model (Dembo, M., and F. Harlow, 1986, Biophys. J., 50:109-121). We find that for the most part the predicted dynamical behavior of the cytoplasm is governed by three nondimensional numbers. Several other nondimensional parameters, the initial conditions, and boundary conditions are found to have lesser effects. Of the three major nondimensional parameters, one (D#) controls the percentage of ectoplasm, the second (C#) controls the sharpness of the endoplasm-ectoplasm boundary, and the third (R#) controls the topological complexity of the endoplasm-ectoplasm distribution. If R# is very small, then the cytoplasm contracts into a single uniform mass, and there is no bulk streaming. If R# is very large, then the cytoplasmic mass breaks up into a number of clumps scattered throughout the available volume. Between these clumps the solution undergoes turbulent or chaotic patterns of streaming. Intermediate values of R# can be found such that the mass of cytoplasm remains connected and yet undergoes coherent modes of motility similar to flares (Taylor, D.L., J.S. Condeelis, P.L. Moore, and R.D. Allen, 1973, J. Cell Biol., 59:378-394) and rosettes (Kuroda, K., 1979, Cell Motility: Molecules and Organization, 347-362).

A thermodynamic model of hemoglobin suitable for physiological applications.

We propose a quantitative model of the thermodynamics of hemoglobin in contact with its five major ligands (O2, CO2, Cl-, 2,3-bisphosphoglycerate, and H+). Our model incorporates the two-state formalism of J. Monod, J. Wyman, and J.P. Changeux (J. Mol. Biol. 12: 88-118, 1965) for treatment of quanternary transitions and also the mean field formalism of K. Linderstrom-Lang (C. R. Trav. Lab. Carlsberg Ser. Chim. 15: 1-30, 1924) for treatment of electrostatic interactions. On the basis of this approach, we develop an algorithm for the efficient computation of observable quantities, such as the occupancy of various ligand binding sites, and an objective statistical procedure for determining both maximum likelihood values and confidence limits of all the intrinsic thermodynamic parameters of hemoglobin. Finally, we show that the predictions of our theory are in good agreement with independent experimental observations.

Approximating the effects of diffusion on reversible reactions at the cell surface: ligand-receptor kinetics.

We consider the problem of determining the time dependence of the bound ligand concentration for the reversible binding of a diffusing monovalent ligand to receptors uniformly distributed over the surface of a spherical cell. We start by formulating a boundary value problem that captures the essential physics of this situation. We then introduce a systematic approximation scheme based on the method of weighted residuals. By this means we convert the initial boundary value problem into a simpler problem that requires solving only a small number of ordinary differential equations. We show how, at the lowest order of approximation, the method can be used to obtain modified chemical rate equations where, in place of fundamental rate constants, effective rate coefficients appear. These rate coefficients are functions of the ligand diffusion coefficient, the cell radius, the receptor density and other variables. We compare exact and approximate solutions and discuss under what conditions the approximate equations can be used. We also apply the method of weighted residuals to obtain approximate descriptions of the binding kinetics when (1) there are two different cell surface receptor populations that bind the ligand and (2) the cell secretes a ligand that can bind back to receptors on the cell (autocrine binding).

On the mechanics of the first cleavage division of the sea urchin egg.

We describe a continuum model of the sea urchin egg during the first cleavage division. Using estimated values of the relevant mechanical parameters we then carry out numerical simulations of cytokinesis and conduct a systematic comparison of these computations with a variety of published experimental data.