Effective Dissociation Constant Research Articles

Water-Based Polyurethane Dispersions: A Detailed Analysis of the Particle Charge Using Soft and Hard Particle Model.

Water-based polyurethane dispersions (PUDs) show a characteristic dependency of the electrophoretic mobility on the electrolyte concentration, which can be investigated by hard and soft particle models. For this purpose, additional information can be obtained by determining particle charges and electrostatic potentials. PUDs with different contents of an intrinsic ionic stabilizer and various polyol components were synthesized according to the acetone process. The particle charge was characterized by potentiometric acid-base titration, and the data of the titration curve were fitted assuming multiple functional groups with adaptable acid strengths. To investigate the electrostatic potentials, electrophoretic mobilities were measured as a function of electrolyte concentration and analyzed by soft and hard particle theory. Acid-base titration experiments indicated that not all detected ionic groups are located on the surface but are partly arranged inside the polymer particle, as evidenced by a significant decrease of the corresponding effective dissociation constant. The evaluation of the titration data and the electrokinetic experiments showed that the soft particle model of Ohshima is not suitable to reflect the actual particle charge. In contrast, the hard particle model can describe the measured electrophoretic mobility of the dispersions very well if the relaxation effect is taken into account. The dependency of the corresponding zeta potentials on the electrolyte concentration can be excellently modeled assuming a constant surface potential ψ0 and distance of the shear plane xs. Reasonable results are obtained for both parameters with only minor differences between the PUD series. Nonetheless, the electrokinetic surface charge densities calculated with respect to the surface potential are lower than expected from the titration results. Although our results indicate a more complex charge distribution in a peripheral layer, the hard particle model currently shows the best description of the electrokinetic behavior of the PUDs.

Utility of FRET in studies of membrane protein oligomerization: The concept of the effective dissociation constant

The activity of many membrane receptors is controlled through their lateral association into dimers or higher-order oligomers. Although Förster resonance energy transfer (FRET) measurements have been used extensively to characterize the stability of receptor dimers, the utility of FRET in studies of larger oligomers has been limited. Here we introduce an effective equilibrium dissociation constant that can be extracted from FRET measurements for EphA2, a receptor tyrosine kinase (RTK) known to form active oligomers of heterogeneous distributions in response to its ligand ephrinA1-Fc. The newly introduced effective equilibrium dissociation constant has a well-defined physical meaning and biological significance. It denotes the receptor concentration for which half of the receptors are monomeric and inactive, and the other half are associated into oligomers and are active, irrespective of the exact oligomer size. This work introduces a new dimension to the utility of FRET in studies of membrane receptor association and signaling in the plasma membrane.

Streaming Potentials of Hyaluronic Acid Hydrogel Films.

The streaming potentials of hyaluronic acid (HA) hydrogel films are measured and theoretically interpreted by systematically varying the HA concentration and the streaming electrolyte pH and ionic strength. While Donnan potentials are expected to vanish with sufficient added salt, apparent ζ-potentials from the Helmholtz-Smoluchowski interpretation remain of the order -20 mV. To theoretically interpret these data, we derived an electrokinetic model (valid in the Debye-Hückel regime) that accounts for ionic and hydrodynamic permeability of the gels. The films could then be ascribed an effective acid dissociation constant pKa ≈ 4.2, specific HA charge ≈-0.1e mmol g-1, and Brinkman/hydrodynamic permeability ∼ S1/3, where is the Brinkman length for HA solutions in the as-prepared reference state and S is the hydrogel swelling ratio. At an ionic strength of 10 mmol L-1, for example, the HA surface potentials are only ψD/2 ≈ -8 mV, where ψD is the Donnan potential, considerably lower than ζ-potentials furnished by the Helmholtz-Smoluchowski interpretation. This insight significantly changes how the films are expected to interact with other surfaces and colloids via Derjaguin-Landau-Vervey-Overbeek-type forces. Our analysis furnishes formulas for the swelling ratio S and hydrodynamic permeability , expressed explicitly as simple power-law functions of the as-prepared HA concentration cha (wt %), consistent with independent assessments of the HA solution permeability and polyelectrolyte-hydrogel swelling theory. These may prove valuable for extrapolating the results to other combinations of ionic strength, pH, and HA and cross-linking concentrations.

Displacement of Strong Acids or Bases by Weak Acids or Bases in Aerosols: Thermodynamics and Kinetics.

Depletion of chloride, nitrate, or ammonium from atmospheric aerosols represents a unique class of displacement reactions in which strong acids (HCl and HNO3) or bases (NH3) are substituted by weaker ones (i.e., dicarboxylic acids or dicarboxylate salts, respectively). These reactions alter the aerosol composition and perturb the atmospheric cycle of volatile compounds, thereby affecting environmental systems and climate. Despite the profound implications, the mechanism of these unique displacement reactions remains unclear. Here, we elucidate the thermodynamics and kinetics of these reactions using the multiphase buffer theory and a diffusion-controlled mass-transfer function, respectively. On the thermodynamic aspect, we find that the effective dissociation constants of the strong acids and bases in aerosols are 2 to 10 orders of magnitude lower than those in bulk solutions. On the kinetic aspect, we find that displacement reactions occur rapidly in aerosol microdroplets with a radius below 10 μm. Within this size range, the characteristic reaction time is always shorter than the lifetime of the aerosols in the atmosphere. Our findings suggest that the unique displacement reactions can significantly modify the composition of atmospheric aerosols, and consequentially, these aerosols may manifest distinct properties unforeseen by the chemistry of homogeneous bulk systems.

Discovery and characterization of a potent activator of the BKCa channel that relives overactive bladder syndrome in rats

The large-conductance Ca2+-activated K+ channel (BKCa channel) is involved in repolarizing the membrane potential and has a variety of cellular functions. The BKCa channel is highly expressed in bladder smooth muscle and mediates muscle relaxation. Compounds that activate the BKCa channel have therapeutic potential against pathological symptoms associated with the overactivity of bladder smooth muscle. In this regard, we screened a chemical library of 9938 compounds to identify novel BKCa channel activators. A cell-based fluorescence assay identified a structural family of compounds containing a common tricyclic quinazoline ring that activated the BKCa channel. The most potent compound TTQC-1 (7-bromo-N-(3-methylphenyl)-5-oxo-1-thioxo-4,5-dihydro[1,3]thiazolo[3,4-a]quinazoline-3-carboxamide) directly and reversibly activated the macroscopic current of BKCa channels expressed in Xenopus oocytes from both sides of the cellular membrane. TTQC-1 increased the maximum conductance and shifted the half activation voltage to the left. The apparent half-maximal effective concentration and dissociation constant were 2.8 μM and 7.95 μM, respectively. TTQC-1 delayed the kinetics of channel deactivation without affecting channel activation. The activation effects were observed over a wide range of intracellular Ca2+ concentrations and dependent on the co-expression of β1 and β4 auxiliary subunits, which are highly expressed in urinary bladder. In the isolated smooth muscle cells of rat urinary bladder, TTQC-1 increased the K+ currents which can be blocked by iberiotoxin. Finally, oral administration of TTQC-1 to hypertensive rats decreased the urination frequency. Therefore, TTQC-1 is a BKCa channel activator with a novel structure that is a potential therapeutic candidate for BKCa channel-related diseases, such as overactive bladder syndrome.

Impact of non-ideality on reconstructing spatial and temporal variations in aerosol acidity with multiphase buffer theory

Abstract. Aerosol acidity is a key parameter in atmospheric aqueous chemistry and strongly influences the interactions of air pollutants and the ecosystem. The recently proposed multiphase buffer theory provides a framework to reconstruct long-term trends and spatial variations in aerosol pH based on the effective acid dissociation constant of ammonia (Ka,NH3∗). However, non-ideality in aerosol droplets is a major challenge limiting its broad applications. Here, we introduced a non-ideality correction factor (cni) and investigated its governing factors. We found that besides relative humidity (RH) and temperature, cni is mainly determined by the molar fraction of NO3- in aqueous-phase anions, due to different NH4+ activity coefficients between (NH4)2SO4- and NH4NO3-dominated aerosols. A parameterization method is thus proposed to estimate cni at a given RH, temperature and NO3- fraction, and it is validated against long-term observations and global simulations. In the ammonia-buffered regime, with cni correction, the buffer theory can reproduce well the Ka,NH3∗ predicted by comprehensive thermodynamic models, with a root-mean-square deviation ∼ 0.1 and a correlation coefficient ∼ 1. Note that, while cni is needed to predict Ka,NH3∗ levels, it is usually not the dominant contributor to its variations, as ∼ 90 % of the temporal or spatial variations in Ka,NH3∗ are due to variations in aerosol water and temperature.

Independent control of the thermodynamic and kinetic properties of aptamer switches

Molecular switches that change their conformation upon target binding offer powerful capabilities for biotechnology and synthetic biology. Aptamers are useful as molecular switches because they offer excellent binding properties, undergo reversible folding, and can be engineered into many nanostructures. Unfortunately, the thermodynamic and kinetic properties of the aptamer switches developed to date are intrinsically coupled, such that high temporal resolution can only be achieved at the cost of lower sensitivity or high background. Here, we describe a design strategy that decouples and enables independent control over the thermodynamics and kinetics of aptamer switches. Starting from a single aptamer, we create an array of aptamer switches with effective dissociation constants ranging from 10 μM to 40 mM and binding kinetics ranging from 170 ms to 3 s. Our strategy is broadly applicable to other aptamers, enabling the development of switches suitable for a diverse range of biotechnology applications.

Interaction of Glutathione-Stabilized Gold Nanoclusters with Doxorubicin and Polycation

Glutathione-capped gold nanoclusters display polyanionic properties that are manifested in the interaction with cationic species. The nanoclusters form complexes with doxorubicin with effective dissociation constant about 10 µM that increased by an order of magnitude in the presence of 0.15 M NaCl confirming electrostatic character of binding. Adsorption of polylysine arose an increase in the fluorescence of gold nanoclusters due to aggregation induced emission enhancement effect. Fluorescence of the complexes increased several-fold upon addition of up to 1 M of KCl suggesting contribution of non-Coulombic forces in the stabilization of aggregates of gold nanoclusters.

Monomeric state of S100P protein: Experimental and molecular dynamics study

S100 proteins constitute a large subfamily of the EF-hand superfamily of calcium binding proteins. They possess one classical EF-hand Ca2+-binding domain and an atypical EF-hand domain. Most of the S100 proteins form stable symmetric homodimers. An analysis of literature data on S100 proteins showed that their physiological concentrations could be much lower than dissociation constants of their dimeric forms. It means that just monomeric forms of these proteins are important for their functioning. In the present work, thermal denaturation of apo-S100P protein monitored by intrinsic tyrosine fluorescence has been studied at various protein concentrations within the region from 0.04–10 μM. A transition from the dimeric to monomeric form results in a decrease in protein thermal stability shifting the mid-transition temperature from 85 to 75 °C. Monomeric S100P immobilized on the surface of a sensor chip of a surface plasmon resonance instrument forms calcium dependent 1 to 1 complexes with human interleukin-11 (equilibrium dissociation constant 1.2 nM). In contrast, immobilized interleukin-11 binds two molecules of dimeric S100P with dissociation constants of 32 nM and 288 nM. Since effective dissociation constant of dimeric S100P protein is very low (0.5 μM as evaluated from our data) the sensitivity of the existing physical methods does not allow carrying out a detailed study of S100P monomer properties. For this reason, we have used molecular dynamics methods to evaluate structural changes in S100P upon its transition from the dimeric to monomeric state. 80-ns molecular dynamics simulations of kinetics of formation of S100P, S100B and S100A11 monomers from the corresponding dimers have been carried out. It was found that during the transition from the homo-dimer to monomer form, the three S100 monomer structures undergo the following changes: (1) the helices in the four-helix bundles within each monomer rotate in order to shield the exposed non-polar residues; (2) almost all lost contacts at the dimer interface are substituted with equivalent and newly formed interactions inside each monomer, and new stabilizing interactions are formed; and (3) all monomers recreate functional hydrophobic cores. The results of the present study show that both dimeric and monomeric forms of S100 proteins can be functional.

Electro-lyotropic equilibrium and the utility of ion-pair dissociation constants

• Ion-pairing with effective dissociation constants in millimolar to molar range. • Combined electrostatic and lyotropic equilibrium at surfaces • Determination of dissociation constants using polymer brush electrokinetics.

Selectivity enhancements in gel-based DNA-nanoparticle assays by membrane-induced isotachophoresis: thermodynamics versus kinetics.

Selectivity against mutant nontargets with a few mismatches remains challenging in nucleic acid sensing. Sensitivity enhancement by analyte concentration does not improve selectivity because it affects targets and nontargets equally. Hydrodynamic or electrical shear enhanced selectivity is often accompanied by substantial losses in target signals, thereby leading to poor limits of detection. We introduce a platform based on depletion isotachophoresis in agarose gel generated by an ion-selective membrane that allows both selectivity and sensitivity enhancement with a two-step assay involving concentration polarization at an ion-selective membrane. By concentrating both the targets and probe-functionalized nanoparticles by ion enrichment at the membrane, the effective thermodynamic dissociation constant is lowered from 40nM to below 500pM, and the detection limit is 10pM as reported previously. A dynamically optimized ion depletion front is then generated from the membrane with a high electrical shear force to selectively and irreversibly dehybridize nontargets. The optimized selectivity against a two-mismatch nontarget (in a 35-base pairing sequence) is shown to be better than the thermodynamic equilibrium selectivity by more than a hundred-fold, such that there is no detectable signal from the two-mismatch nontarget. We offer empirical evidence that irreversible cooperative dehybridization plays an important role in this kinetic selectivity enhancement and that mismatch location controls the optimum selectivity even when there is little change in the corresponding thermodynamic dissociation constant.

Dynamic equilibrium on DNA defines transcriptional regulation of a multidrug binding transcriptional repressor, LmrR

LmrR is a multidrug binding transcriptional repressor that controls the expression of a major multidrug transporter, LmrCD, in Lactococcus lactis. Promiscuous compound ligations reduce the affinity of LmrR for the lmrCD operator by several fold to release the transcriptional repression; however, the affinity reduction is orders of magnitude smaller than that of typical transcriptional repressors. Here, we found that the transcriptional regulation of LmrR is achieved through an equilibrium between the operator-bound and non-specific DNA-adsorption states in vivo. The effective dissociation constant of LmrR for the lmrCD operator under the equilibrium is close to the endogenous concentration of LmrR, which allows a substantial reduction of LmrR occupancy upon compound ligations. Therefore, LmrR represents a dynamic type of transcriptional regulation of prokaryotic multidrug resistance systems, where the small affinity reduction induced by compounds is coupled to the functional relocalization of the repressor on the genomic DNA via nonspecific DNA adsorption.

Effect of the Protein Corona on Antibody-Antigen Binding in Nanoparticle Sandwich Immunoassays.

We investigated the effect of the protein corona on the function of nanoparticle (NP) antibody (Ab) conjugates in dipstick sandwich immunoassays. Ab specific for Zika virus nonstructural protein 1 (NS1) were conjugated to gold NPs, and another anti-NS1 Ab was immobilized onto the nitrocellulose membrane. Sandwich immunoassay formation was influenced by whether the strip was run in corona forming conditions, i.e., in human serum. Strips run in buffer or pure solutions of bovine serum albumin exhibited false positives, but those run in human serum did not. Serum pretreatment of the nitrocellulose also eliminated false positives. Corona formation around the NP-Ab in serum was faster than the immunoassay time scale. Langmuir binding analysis determined how the immobilized Ab affinity for the NP-Ab/NS1 was impacted by corona formation conditions, quantified as an effective dissociation constant, KDeff. Results show that corona formation mediates the specificity and sensitivity of the antibody-antigen interaction of Zika biomarkers in immunoassays, and plays a critical but beneficial role.

Elucidation of design rules for integrin ligand clustering in biomaterials using protein-engineered fabrics

Event Abstract Back to Event Elucidation of design rules for integrin ligand clustering in biomaterials using protein-engineered fabrics Patrick Benitez1, Shamik Mascharak1 and Sarah Heilshorn1, 2 1 Stanford University, Bioengineering, United States 2 Stanford University, Materials Science & Engineering, United States Introduction: While ligand clustering is known to enhance integrin activation, this insight has been difficult to apply to implantable materials due to a lack of suitable technologies to design biomaterials with precisely tunable local and global ligand densities. Historically, ligand-clustering experiments relied on non-scalable fabrication techniques (e.g. e-beam lithography) and rigid materials (e.g. glass substrates) [1],[2]. As an alternative, we present a novel combination of recombinant protein engineering to tune local ligand density and electrospinning to tune global ligand density of implantable biomaterial fabrics. Studies of cell spreading, integrin signaling, focal adhesion formation, and cell proliferation on these fabrics have revealed two general design principles for ligand presentation in implantable biomaterials. Materials and Methods: Local ligand density was controlled by genetically engineering a fibronectin-derived arginine-glycine-aspartate- (RGD-) based αVβ3 integrin ligand into an elastin-like polypeptide (ELP) sequence. An otherwise identical, non-cell-adhesive control protein was produced by simply switching the positions of the glycine and aspartate amino acid residues. The two ELP variants were blended to achieve local ligand densities of 0 to 122,000 RGD µm-2, and the solutions were electrospun into fabrics to yield global ligand densities of 0 to 71,000 RGD µm-2. Fabrics were characterized by scanning electron microscopy and mechanical testing [3]. Specific adhesion of human umbilical vein endothelial cells (HUVECs) on the fabrics was confirmed with integrin blocking studies. Cell proliferation was analyzed by DNA quantification and Ki67 immunostaining; cell morphology and focal adhesion formation were quantified by nuclear (DAPI), actin (phalloidin), and vinculin (antibody) staining; and integrin signaling was quantified by immunoblotting with antibodies targeting FAK and pFAK-397. Results and Discussion: Clustering of ligands was found to have the greatest influence on cell proliferation, focal adhesion number, and focal adhesion kinase expression near the ligand’s effective thermodynamic dissociation constant (KD,eff ~12,000 RGD µm-2). Near this global ligand density, HUVECs on ligand-clustered fabrics behaved similarly to cells grown on fabrics with significantly larger global ligand densities but without clustering. However, this ligand-clustering effect was found to have a threshold cut-off: at a local ligand density of 122,000 RGD µm-2, cell division, focal adhesion number, and focal adhesion kinase expression were significantly reduced relative to fabrics with identical global ligand density and lesser local ligand densities. Thus, when clustering results in overcrowding of ligands, integrin receptors are no longer able to effectively engage with their target ligands. Conclusion: Two general design principles for implantable materials were elucidated: clustering ligands enhances integrin-dependent signals via increased focal adhesion formation provided that (i) the global ligand density, i.e., the ligand density across the cellular length scale, is near the ligand’s effective dissociation constant and (ii) the local ligand density, i.e., the ligand density across the length scale of individual focal adhesions, is less than an overcrowding threshold. This fundamental understanding was made possible through the design of implantable fabrics based on protein-engineering technology, which enables the precise specification of ligand presentation. These results support the further design and exploration of protein-engineered biomaterials as ideal substrates for fundamental studies of cell-biomaterial interactions.

Study of o-fluorbenzonal electrochemical behavior with the carbon electrode using voltammetry

A high sensitive stripping voltammetric method was for the first time proposed for determination of o-fluorbenzonal. This method is based on the ability to be electrochemically reduced with the carbon electrodes of different types. The working conditions of o-fluorbenzonal voltammetric determination are: pH of the background electrolyte, electrolysis potential and time scan rate. The effective dissociation constant of various forms of o-fluorbenzonal, number of electrons involved in the electrode process were calculated.

Mechanism of Immobilized Protein A Binding to Immunoglobulin G on Nanosensor Array Surfaces

Protein A is often used for the purification and detection of antibodies such as immunoglobulin G (IgG) because of its quadrivalent domains that bind to the Fc region of these macromolecules. However, the kinetics and thermodynamics of the binding to many sensor surfaces have eluded mechanistic description due to complexities associated with multivalent interactions. In this work, we use a near-infrared (nIR) fluorescent single-walled carbon nanotube sensor array to obtain the kinetics of IgG binding to protein A, immobilized using a chelated Cu(2+)/His-tag chemistry to hydrogel dispersed sensors. A bivalent binding mechanism is able to describe the concentration dependence of the effective dissociation constant, KD,eff, which varies from 100 pM to 1 μM for IgG concentrations from 1 ng mL(-1) to 100 μg mL(-1), respectively. The mechanism is shown to describe the unusual concentration-dependent scaling demonstrated by other sensor platforms in the literature as well, and a comparison is made between resulting parameters. For comparison, we contrast IgG binding with that of human growth hormone (hGH) to its receptor (hGH-R) which displays an invariant dissociation constant at KD = 9 μM. These results should aid in the use of protein A and other recognition elements in a variety of sensor types.

Preparation and analysis of anodic aluminum oxide films with continuously tunable interpore distances

Nanoporous anodic aluminum oxides are often used as templates for preparation of nanostructures such as nanodot, nanowire and nanotube arrays. The interpore distance of anodic aluminum oxide is the most important parameter in controlling the periodicity of these nanostructures. Herein we demonstrate a simple and yet powerful method to fabricate ordered anodic aluminum oxides with continuously tunable interpore distances. By using mixed solution of citric and oxalic acids with different molar ratio, the range of anodizing voltages within which self-ordered films can be formed were extended to between 40 and 300V, resulting in the interpore distances change from 100 to 750nm. Our work realized very broad range of interpore distances in a continuously tunable fashion and the experiment processes are easily controllable and reproducible. The dependence of the interpore distances on acid ratios in mixed solutions was discussed through analysis of anodizing current and it was found that the effective dissociation constant of the mixed acids is of great importance. The interpore distances achieved are comparable to wavelengths ranging from UV to near IR, and may have potential applications in optical meta-materials for photovoltaics and optical sensing.

The influence of concentration on specific ion effects at the silica/water interface

Second harmonic generation spectroscopy is a useful tool for monitoring changes in interfacial potential at buried insulator/liquid interfaces. Here we apply this technique to the silica/aqueous interface and monitor the changes in interfacial potential while varying the pH in the presence of different alkali halides at 0.1M concentration. Within the pH range explored, the bimodal distribution of acidic sites on planar silica is clearly observed, corresponding to two types of acidic SiOH groups. Comparing these data with previous work at 0.5M sheds light on whether the presence of the ions stabilizes the charged or neutral state of the surface sites. For the alkali chlorides, with the exception of NaCl, we observe that the presence of the alkali chlorides stabilize the less acidic site in the protonated (SiOH) rather than deprotonated (SiO−) form. This unusual influence of the cation is attributed to the combination of interactions at the interface between water, surface sites and the electrolyte. Overall, we observe that the influence of the alkali ion on the ratio of the two types of sites and their effective acid dissociation constants is minor at 0.1M, unlike that observed at 0.5M. In contrast, the influence of the anion on the cooperative dissociation of surface sites and their relative distribution is little affected upon decreasing the concentration, which indicates that these specific anion effects are prevalent in nature.

Preparation of Porous Hollow Polyaniline Microspheres and Study on Their <I>In Vitro</I> Release Behavior

We report the synthesis of porous hollow polyaniline (PANI) microspheres loaded with Acid Red 8 dye (200-600 nm diameters under different reaction conditions) by using spherically mesoporous aggregates of Fe3O4 particles as soft templates and ammonium persulfate (APS) as the oxidant at 2.5 degrees C. Since the as-prepared spherical aggregates of Fe3O4 particles are readily dissolved in acidic aqueous solution, these spherical aggregates can be treated as soft template for the fabrication of hollow spheres. This process is therefore more convenient than other reported methods which require the post-treatment to remove the templates under strict conditions. The influence of the synthetic conditions on the formation and size of PANI microspheres was investigated. The morphology was confirmed by transmission electron microscopy (TEM). The chemical and electronic structures of the PANI microspheres were also studied by FTIR and UV-Vis spectrometry, respectively. The experimental in vitro release showed that these porous hollow PANI microspheres provided a controlled release of the entrapped dye, which was regulated by pH. Furthermore, the releasing behavior was qualitatively explained based on effective dissociation constant as a function of the pH.

Quantitative Measurement of Protein Relocalization in Live Cells

Microscope cytometry provides a powerful means to study signaling in live cells. Here we present a quantitative method to measure protein relocalization over time, which reports the absolute fraction of a tagged protein in each compartment. Using this method, we studied an essential step in the early propagation of the pheromone signal in Saccharomyces cerevisiae: recruitment to the membrane of the scaffold Ste5 by activated Gβγ dimers. We found that the dose response of Ste5 recruitment is graded (EC50 = 0.44 ± 0.08 nM, Hill coefficient = 0.8 ± 0.1). Then, we determined the effective dissociation constant (Kde) between Ste5 and membrane sites during the first few minutes when the negative feedback from the MAPK Fus3 is first activated. Kde changed during the first minutes from a high affinity of <0.65 nM to a steady-state value of 17 ± 9 nM. During the same period, the total number of binding sites decreased slightly, from 1940 ± 150 to 1400 ± 200. This work shows how careful quantification of a protein relocalization dynamic can give insight into the regulation mechanisms of a biological system.