The effect of diffusion on the trapping of membrane-bound receptors by localized coated pits

Localized coated pits are considered in the primary steps of receptor-mediated endocytosis. According to the pit reinsertion mechanism, we have modified our previous kinetic model and studied the effect of diffusion on the trapping rate constant (k+). Using experimental data for low density lipoprotein (LDL) receptors on fibroblast cells, we found that the binding of receptors to coated pits is not totally diffusion controlled. For example, the process is less than 78% diffusion controlled if receptors are not allowed to escape the coated pits. However, due to the large uncertainties in the experimental parameters, a diffusion-controlled process cannot be ruled out. The greatest differences between localized and random reinsertion were found when the escaping rate constant (k-) is much greater than the rate constant for invagination of the pits (lambda 1). Under this condition, k+ for localized reinsertion is no less than 39% diffusion controlled, while k+ for random reinsertion shows no diffusion effect at all.     

Diffusion-limited forward rate constants in two dimensions. Application to the trapping of cell surface receptors by coated pits.

A variety of receptors are known to aggregate in specialized cell surface structures called coated pits, prior to being internalized when the coated pits close off. At 37 degrees C on human fibroblasts, as well as on other cell types, a recycling process maintains a constant number of coated pits on the cell surface. In this paper, we explore implications for receptor aggregation and internalization of the two types of recycling models that have been proposed for the maintenance of the coated pit concentration. In one model, coated pits alternate between accessible and inaccessible states at fixed locations on the cell surface, while in the other model, coated pits recycle to random locations on the cell surface. We consider receptors that are randomly inserted in the membrane, move by pure diffusion with diffusion coefficient D, and are instantly and irreversibly trapped when they reach a coated pit boundary (the diffusion limit). For such receptors, we calculate for each of the two models: the mean time tau to reach a coated pit, the forward rate constant k+ for the interaction of a receptor with a coated pit, and the fraction phi of receptors aggregated in coated pits. We show that for the parameters that characterize coated pits on human fibroblasts, the way in which coated pits return to the surface has a negligible effect on the values of tau, k+, and phi for mobile receptors, D greater than or equal to 1.0 X 10(-11) cm2/s, but has a substantial effect for "immobile" receptors, D much less than 1 X 10(-11) cm2/s. We present numerical examples to show that it may be possible to distinguish between these models if one can monitor slowly diffusing receptors (D less than 1 X 10(-11) cm2/s) on cells whose coated pits have relatively short lifetimes (less than or equal to 1 min). Finally, we show that for the low-density lipoprotein (LDL) receptor on human fibroblasts (D = 4.5 X 10(-11) cm2/s), the predicted and observed values of K+ and phi are in close agreement. Therefore, even for slowly diffusing LDL receptor, unaided diffusion as the transport mechanism of receptors to coated pits is consistent with measured rates of LDL internalization.     

Induction of mutant dynamin specifically blocks endocytic coated vesicle formation

Dynamin is the mammalian homologue to the Drosophila shibire gene product. Mutations in this 100-kD GTPase cause a pleiotropic defect in endocytosis. To further investigate its role, we generated stable HeLa cell lines expressing either wild-type dynamin or a mutant defective in GTP binding and hydrolysis driven by a tightly controlled, tetracycline- inducible promoter. Overexpression of wild-type dynamin had no effect. In contrast, coated pits failed to become constricted and coated vesicles failed to bud in cells overexpressing mutant dynamin so that endocytosis via both transferrin (Tfn) and EGF receptors was potently inhibited. Coated pit assembly, invagination, and the recruitment of receptors into coated pits were unaffected. Other vesicular transport pathways, including Tfn receptor recycling, Tfn receptor biosynthesis, and cathepsin D transport to lysosomes via Golgi-derived coated vesicles, were unaffected. Bulk fluid-phase uptake also continued at the same initial rates as wild type. EM immunolocalization showed that membrane-bound dynamin was specifically associated with clathrin-coated pits on the plasma membrane. Dynamin was also associated with isolated coated vesicles, suggesting that it plays a role in vesicle budding. Like the Drosophila shibire mutant, HeLa cells overexpressing mutant dynamin accumulated long tubules, many of which remained connected to the plasma membrane. We conclude that dynamin is specifically required for endocytic coated vesicle formation, and that its GTP binding and hydrolysis activities are required to form constricted coated pits and, subsequently, for coated vesicle budding.     

Effect of membrane flow on the capture of receptors by coated pits. Theoretical results.

Coated pits trap cell surface receptors and mediate their internalization. Once internalized, many receptors recycle back to the cell surface. When recycled receptors are inserted into the plasma membrane, they move until they are again trapped in coated pits. The mechanisms for moving receptors from their insertion sites to coated pits are unknown. Unaided diffusion as the transport mechanism is consistent with the observed kinetics of receptor recycling. Another candidate for the transport mechanism is convection. For receptors that recycle to random positions on the cell surface, or to restricted regions about coated pits, we assess the importance of convective flow in the transport of receptors to coated pits. First we consider local flows set up by the formation of coated pits and their transformation into coated vesicles. As coated pits form and round into coated vesicles, surrounding membrane is drawn inward, creating flows directed toward the coated pit centers. We show that unless the lifetime of a coated pit is very short, 10 s or less, such local flows have a negligible effect on the time it takes receptors to reach coated pits. We also show that they are unlikely to be the mechanism that keeps receptors that have reached coated pits trapped within coated pits until they are internalized. Finally we calculate the mean time tau for a diffusing receptor to reach a coated pit in the presence of membrane flow that is constant in magnitude and direction, as may occur on moving cells. We show that for typical membrane flow velocities, tau can be reduced significantly from its value in the absence of flow. For example, a velocity v = 2.8 micron/min cuts the mean transport time in half.     

Benzodiazepine receptors along the nephron: [3H]PK 11195 binding in rat tubules

Binding of [3H]PK 11195, an isoquinoline carboxamide derivative, was measured in microdissected tubule segments of rat nephron. High specific binding capacities (1.1-1.8 fmol X mm-1) were found in the thick ascending limb of the Henle's loop and in the collecting tubule, whereas specific binding could not be detected in the proximal tubule. In the medullary collecting tubule, the association and dissociation rate constants at 4 degrees C were k1 = 3.0 X 10(6) M-1 X min-1 and k-1 = 0.021 min -1; the ratio k-1/k1 = 7.0 nM was in agreement with the estimated equilibrium dissociation constant (Kd = 2.4 nM). [3H]PK 11195 binding sites from medullary ascending limb and medullary collecting tubule revealed the following sequence of specificity: PK 11195 = Ro 5-4864 much greater than clonazepam, indicating that tubule binding sites might be the peripheral benzodiazepine receptors of the rat kidney.     

On the validity of the quasi-steady state approximation of bimolecular reactions in solution

Two-step binding kinetics are extensively used to study the relative importance of diffusion in biochemical reactions. Classical analysis of this problem assumes ad hoc that the encounter complex is at quasi-steady state (QSS). Using scaling arguments we derive a criterion for the validity of this assumption in the limit of irreversible product formation. We find that the QSS approximation (QSSA) of two-step binding is only valid if the total ligand and receptor concentrations are much smaller than (k2+k-1)/k1, where k1 and k-1 are, respectively, the forward and reverse diffusion encounter rate constants and k2 is the chemical association rate constant. This criterion can be shown to imply that the average time between encounters is much longer than the half-life of the encounter complex and also guarantees that the concentration of the encounter complex is negligible compared to the reactant and product concentrations. Numerical examples of irreversible and reversible cases corroborate our analysis and illustrate that the QSS may be invalid even if k-2相似文献   

A kinetic study of cyclic adenosine 3':5'-monophosphate binding and mode of activation of protein kinase from Drosophila melanogaster embryos.

Cyclic AMP-dependent protein kinase and its regulatory subunit were isolated from Drosophila melanogaster embryos. The profiles of cyclic AMP binding by these proteins were significantly different. In order to explain such a difference and to find the mode of enzyme activation by cyclic AMP, a kinetic study of cyclic AMP binding was carried out. First, the association rate constant k1 and dissociation rate constant k-1 in the cyclic AMP-regulatory subunit interaction at 0 degrees C were estimated to be 2.3 X 10(6)M-1s-1 and 1.1 X 10(-3)s-1, respectively. Secondly, the three possible modes of enzyme activation by cyclic AMP were mathematically considered and could be described by a unique formula: r=APt + BQt (A + B=1) in which the parameters A, B, P, and Q are equivalent to rate constants in the sense that the rate constants are simply expressed by these parameters. Thirdly, the values of the parameters and subsequently the values of rate constants involved in the possible mechanisms were evaluated using a curve-fitting technique and compared with experimental observation. It was then found that the following mechanism was the only one which fitted the experimental observations. Namely, RC + L k3 equilibrium k-3 LRC k4 equilibrium k-4 RL + C where R, C, and L represent the regulatory and catalytic subunits and cyclic AMP as a ligand. Thus, our results indicate that in the presence of cyclic AMP the active enzyme (C) is released from a ternary intermediate which is the primary product of the cyclic AMP-holoenzyme interaction. The estimated values of the rate constants are: k3=3.5 X 10(6)M-1s-1;k-3=7.3 X 10(-1)s-1;and k4=3.8 X 10(-2)s. These estimates indicate that the reaction LRC leads to RL + C is relatively slow and limits the rate of the overall reaction. By comparing k-3 and k4, it is apparent that a large part of newly formed ternary intermediate reverts to the holoenzyme.     

Kinetic properties of binding of myosin subfragment-1 with F-actin in the absence of nucleotide

The rate constant for the binding of myosin subfragment-1 (S-1) with F-actin in the absence of nucleotide, k1, and that for dissociation of the F-actin-myosin subfragment-1 complex (acto-S-1), k-1, were measured independently. The rate of S-1 binding with F-actin was measured from the time course of the change in the light scattering intensity after mixing S-1 with various concentrations of F-actin and k1 was found to be 2.55 X 10(6) M-1 X S-1 at 20 degrees C. The dissociation rate of acto-S-1 was determined using F-actin labeled with pyrenyl iodoacetamide (Pyr-FA). Pyr-FA, with its fluorescence decreased by binding with S-1, was mixed with acto-S-1 complex and the rate of displacement of F-actin by Pyr-FA was measured from the decrease in the Pyr-FA fluorescence intensity. The k-1 value was calculated to be 8.5 X 10(-3) S-1 (or 0.51 min-1). The value of the dissociation constant of S-1 from acto-S-1 complex, Kd, was calculated from Kd = k-1/k1 to be 3.3 X 10(-9) M at 20 degrees C. Kd was also measured at various temperatures (0-30 degrees C), and the thermodynamic parameters, delta G degree, delta H degree, and delta S degree, were estimated from the temperature dependence of Kd to be -11.3 kcal/mol, +2.5 kcal/mol, and +47 cal/deg . mol, respectively. Thus, the binding of the myosin head with F-actin was shown to be endothermic and entropy-driven.     

Effect of preferential insertion of LDL receptors near coated pits

Recent experiments suggest that low density lipoprotein (LDL) receptors on human fibroblasts are not inserted into the plasma membrane uniformly, as earlier experiments indicated, but are inserted into specialized regions, called plaques, where coated pits form. If the consequent reduction in the time required for LDL receptors to diffuse to coated pits were significant, this could alter conclusions drawn from previous calculations based on the assumption that LDL receptors are inserted uniformly. In particular, the conclusion could be wrong that diffusion of LDL receptors to coated pits is the rate limiting step in the interaction of cell surface LDL receptors with coated pits. Here we calculate the extent of the reduction in mean travel time of an LDL receptor to a coated pit, as a function of the plaque radius. We find that only if LDL receptor insertion is limited to a very small portion of the plasma membrane near coated pit sites is there a substantial decrease in the average time it would take an LDL receptor to diffuse to a coated pit. In order for preferential insertion of LDL receptors into plaques to cut the mean receptor travel time in half, plaques would have to take up no more than 10% of the cell surface area; to reduce the travel time by a factor of 10 plaques would have to cover only 2% of the cell surface, approximately twice the area covered by coated pits at 37°C.     

The role of dynamin and its binding partners in coated pit invagination and scission

Plasma membrane clathrin-coated vesicles form after the directed assembly of clathrin and the adaptor complex, AP2, from the cytosol onto the membrane. In addition to these structural components, several other proteins have been implicated in clathrin-coated vesicle formation. These include the large molecular weight GTPase, dynamin, and several Src homology 3 (SH3) domain-containing proteins which bind to dynamin via interactions with its COOH-terminal proline/arginine-rich domain (PRD). To understand the mechanism of coated vesicle formation, it is essential to determine the hierarchy by which individual components are targeted to and act in coated pit assembly, invagination, and scission.To address the role of dynamin and its binding partners in the early stages of endocytosis, we have used well-established in vitro assays for the late stages of coated pit invagination and coated vesicle scission. Dynamin has previously been shown to have a role in scission of coated vesicles. We show that dynamin is also required for the late stages of invagination of clathrin-coated pits. Furthermore, dynamin must bind and hydrolyze GTP for its role in sequestering ligand into deeply invaginated coated pits.We also demonstrate that the SH3 domain of endophilin, which binds both synaptojanin and dynamin, inhibits both late stages of invagination and also scission in vitro. This inhibition results from a reduction in phosphoinositide 4,5-bisphosphate levels which causes dissociation of AP2, clathrin, and dynamin from the plasma membrane. The dramatic effects of the SH3 domain of endophilin led us to propose a model for the temporal order of addition of endophilin and its binding partner synaptojanin in the coated vesicle cycle.     

Effect of preferential insertion of LDL receptors near coated pits

Recent experiments suggest that low density lipoprotein (LDL) receptors on human fibroblasts are not inserted into the plasma membrane uniformly, as earlier experiments indicated, but are inserted into specialized regions, called plaques, where coated pits form. If the consequent reduction in the time required for LDL receptors to diffuse to coated pits were significant, this could alter conclusions drawn from previous calculations based on the assumption that LDL receptors are inserted uniformly. In particular, the conclusion could be wrong that diffusion of LDL receptors to coated pits is the rate limiting step in the interaction of cell surface LDL receptors with coated pits. Here we calculate the extent of the reduction in mean travel time of an LDL receptor to a coated pit, as a function of the plaque radius. We find that only if LDL receptor insertion is limited to a very small portion of the plasma membrane near coated pit sites is there a substantial decrease in the average time it would take an LDL receptor to diffuse to a coated pit. In order for preferential insertion of LDL receptors into plaques to cut the mean receptor travel time in half, plaques would have to take up no more than 10% of the cell surface area; to reduce the travel time by a factor of 10, plaques would have to cover only 2% of the cell surface, approximately twice the area covered by coated pits at 37 degrees C.     

Sodium binding sites of gramicidin A: sodium-23 nuclear magnetic resonance study.

In ethanol-water mixtures (90:10), the gramicidin dimer binds Na+ cations at well-defined sites, with a binding constant K = 4 M-1. Partial desolvation of Na+ occurs upon binding, as judged from the magnitude of the quadrupolar coupling constant (1.7 MHz) for bound sodium. The binding sites are identified with the outer sites flanking the channel entrances. The rate constants for binding and release are k+ less than or equal to 2.2 X 10(9) M-1 s-1 and k- less than or equal to 5.5 X 10(8) s-1, respectively.     

Kinetics and mechanism of bilirubin binding to human serum albumin

The kinetics of bilirubin binding to human serum albumin at pH 7.40, 4 degrees C, was studied by monitoring changes in bilirubin absorbance. The time course of the absorbance change at 380 nm was complex: at least three kinetic events were detected including the bimolecular association (k1 = 3.8 +/- 2.0 X 10(7) M-1 S-1) and two relaxation steps (52 = 40.2 +/- 9.4 s-1 and k3 = 3.8 +/- 0.5 s-1). The presence of the two slow relaxations was confirmed under pseudo-first order conditions with excess albumin. Curve-fitting procedures allowed the assignment of absorption coefficients to the intermediate species. When the bilirubin-albumin binding kinetics was observed at 420 nm, only the two relaxations were seen; apparently the second order association step was isosbestic at this wavelength. The rate of albumin-bound bilirubin dissociation was measured by mixing the pre-equilibrated human albumin-bilirubin complex with bovine albumin. The rate constant for bilirubin dissociation measured at 485 nm was k-3 = 0.01 s-1 at 4 degrees C. A minimum value of the equilibrium constant for bilirubin binding to human albumin determined from the ratio k1/k-3 is therefore approximately 4 X 10(9) M-1.     

Kinetic analysis of the dual phospholipid model for phospholipase A2 action

A kinetic scheme is proposed for the action of cobra venom phospholipase A2 on mixed micelles of phospholipid and the nonionic detergent Triton X-100, based on the "dual phospholipid model." (formula; see text) The water-soluble enzyme binds initially to a phospholipid molecule in the micelle interface. This is followed by binding to additional phospholipid in the interface and then catalytic hydrolysis. A kinetic equation was derived for this process and tested under three experimental conditions: (i) the mole fraction of substrate held constant and the bulk substrate concentration varied; (ii) the bulk substrate concentration held constant and the Triton X-100 concentration varied (surface concentration of substrate varied); and (iii) the Triton X-100 concentration held constant and the bulk substrate concentration varied. The substrates used were chiral dithiol ester analogs of phosphatidylcholine (thio-PC) and phosphatidylethanolamine (thio-PE), and the reactions were followed by reaction of the liberated thiol with a colorimetric thiol reagent. The initial binding (Ks = k1/k-1) was apparently similar for thio-PC and thio-PE (between 0.1 and 0.2 mM) as were the apparent Michaelis constants (Km = (k-2 + k3)/k2) (about 0.1 mol fraction). The Vmax values for thio-PC and thio-PE were 440 and 89 mumol min-1 mg-1, respectively. The preference of cobra venom phospholipase A2 for PC over PE in Triton X-100 mixed micelles appears to be an effect on k3 (catalytic rate) rather than an effect on the apparent binding of phospholipid in either step of the reaction.     

A study of the cholinolytic actions of strychnine using the technique of concentration jump relaxation analysis

The blocking actions of strychnine on excitatory acetylcholine (ACh) responses in isolated, voltage clamped Aplysia neuronal cell bodies has been studied using a rapid drug application technique. Rapid microperfusion of strychnine (10-50 microM) produced a reduction of the steady-state ACh-induced inward current in Aplysia neurons which decayed exponentially with a highly dose-dependent time constant. At the cessation of strychnine perfusion the ACh-induced current recovered to its original value with an exponential time course which was not sensitive to the dose of strychnine previously applied. The calculated association (k1) and dissociation (k-1) constants for a pseudo-first-order reaction between strychnine and its binding site were k1 = 1.2 X 10(4) M-1. sec-1 and k-1 = 0.12 sec-1 (KD = 1 X 10(-5) M-1). These results demonstrate that concentration jump relaxation experiments can be performed on isolated neurons for the study of voltage-independent antagonists by the use of rapid microperfusion systems and provide the first direct estimates to date of the rate constants of the cholinolytic effect of strychnine.     

Interaction between prolactin and rabbit mammary prolactin receptor in the presence of environment-modifying agents

The binding assay of prolactin (PRL) to the receptor in the rabbit mammary gland was carried out with varying concentrations of NaCl, KCl, CaCl2, MgCl2, glycerol, glucose, sucrose and urea. The agents did not affect the binding capacity. The ionic bond-breaking agents (NaCl and KCl) had little effect on changes in the association rate constant (k+1) of PRL binding to the receptor and the dissociation rate constant (k-1) of bound PRL. The inclusion of other agents changed the k+1 and the k-1. Among the agents examined, chaotropic salts (CaCl2 and MgCl2) inhibited the binding of PRL greatly, and were the most effective in decreasing the k+1. Both hydrogen- and hydrophobic bonds are involved in the interaction between PRL and the receptor. The data suggest that hydrophobic bonding is primarily an important force participating in the binding of PRL to its receptor.     

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.     

Characterization of the interaction between gastrin and its receptor in rat oxyntic gland mucosa

A gastrin receptor, identified in crude membrane preparations of rat oxyntic gland mucosa, has an equilibrium dissociation constant (Kd) of approx. 4 . 10(-10)M and a binding capacity of 4 fmol/mg protein. The binding capacity was significantly lower after 2 days of fasting, parallel with a significant drop in serum gastrin levels; there was no change in Kd. In order to verify Scatchard analysis and to determine if there was a coincident alteration in the association (k+1) and dissociation (k-1) rates in the fasted rat, a kinetics study was performed. Under our conditions, there appeared to be a single set of binding sites and the binding reaction obeyed first-order dissociation, and second-order association rate kinetics. Second-order association rate kinetics were validated by demonstrating the independence of the rate constants when there were alterations in the concentrations of reactants. The average k+1 was determined to be 2 . 10(6) M-1 . s-1. The average k-1 was determined to be 1 . 10(-3) s-1. There was no significant change in the k+1 and k-1 in fed and fasted rats. Fasting decreased the number of gastrin receptors without altering the affinity of the receptor for the hormone.     

A thermal-variation method for analysing the rate constants of the Michaelis--Menten mechanism.

By analysing the variations of saturation velocity and Michaelis constant with temperature and invoking the mathematical constraint represented by the Arrhenius equation, it becomes possible to estimate k+2 and indistinguishably k+1 and k-1 for the Michaelis--Menten mechanism of one-substrate enzyme reactions. Distinction between k+1 and k-1 may be obtained through the determination of isotopic rate effects. This procedure thus provides a basis for evaluating all three rate constants of the one-substrate mechanism, and disproves the suggestion that k+1 and k-1 are intrinsically unobtainable from steady-state kinetic measurements.     

Multiple GTP-binding proteins participate in clathrin-coated vesicle- mediated endocytosis

We have examined the effects of various agonists and antagonists of GTP- binding proteins on receptor-mediated endocytosis in vitro. Stage- specific assays which distinguish coated pit assembly, invagination, and coat vesicle budding have been used to demonstrate requirements for GTP-binding protein(s) in each of these events. Coated pit invagination and coated vesicle budding are both stimulated by addition of GTP and inhibited by GDP beta S. Although coated pit invagination is resistant to GTP gamma S, A1F4-, and mastoparan, late events involved in coated vesicle budding are inhibited by these antagonists of G protein function. Earlier events involved in coated pit assembly are also inhibited by GTP gamma S, A1F4-, and mastoparan. These results demonstrate that multiple GTP-binding proteins, including heterotrimeric G proteins, participate at discrete stages in receptor- mediated endocytosis via clathrin-coated pits.