Competitive Binding Model Research Articles

Competitive Interactions of Ligands and Macromolecular Crowders with Maltose Binding Protein

Cellular signaling involves a cascade of recognition events occurring in a complex environment with high concentrations of proteins, polysaccharides, and other macromolecules. The influence of macromolecular crowders on protein binding affinity through hard-core repulsion is well studied, and possible contributions of protein-crowder soft attraction have been implicated recently. Here we present direct evidence for weak association of maltose binding protein (MBP) with a polysaccharide crowder Ficoll, and that this association effectively competes with the binding of the natural ligand, maltose. Titration data over wide ranges of maltose and Ficoll concentrations fit well with a three-state competitive binding model. Broadening of MBP 1H­15N TROSY spectra by the addition of Ficoll indicates weak protein-crowder association, and subsequent recovery of sharp NMR peaks upon addition of maltose indicates that the interactions of the crowder and the ligand with MBP are competitive. We hypothesize that, in the Escherichia coli periplasm, the competitive interactions of polysaccharides and maltose with MBP could allow MBP to shuttle between the peptidoglycan attached to the outer membrane and the ATP-binding cassette transporter in the inner membrane.

Identification of nucleotides and amino acids that mediate the interaction between ribosomal protein L30 and the SECIS element

BackgroundRibosomal protein L30 belongs to the L7Ae family of RNA-binding proteins, which recognize diverse targets. L30 binds to kink-turn motifs in the 28S ribosomal RNA, L30 pre-mRNA, and mature L30 mRNA. L30 has a noncanonical function as a component of the UGA recoding machinery that incorporates selenocysteine (Sec) into selenoproteins during translation. L30 binds to a putative kink-turn motif in the Sec Insertion Sequence (SECIS) element in the 3’ UTR of mammalian selenoprotein mRNAs. The SECIS also interacts with SECIS-binding protein 2 (SBP2), an essential factor for Sec incorporation. Previous studies showed that L30 and SBP2 compete for binding to the SECIS in vitro. The SBP2:SECIS interaction has been characterized but much less is known about how L30 recognizes the SECIS.ResultsHere we use enzymatic RNA footprinting to define the L30 binding site on the SECIS. Like SBP2, L30 protects nucleotides in the 5’ side of the internal loop, the 5’ side of the lower helix, and the SECIS core, including the GA tandem base pairs that are predicted to form a kink-turn. However, L30 has additional determinants for binding as it also protects nucleotides in the 3’ side of the internal loop, which are not protected by SBP2. In support of the competitive binding model, we found that purified L30 repressed UGA recoding in an in vitro translation system, and that this inhibition was rescued by SBP2. To define the amino acid requirements for SECIS-binding, site-specific mutations in L30 were generated based on published structural studies of this protein in a complex with its canonical target, the L30 pre-mRNA. We identified point mutations that selectively inhibited binding of L30 to the SECIS, to the L30 pre-mRNA, or both RNAs, suggesting that there are subtle differences in how L30 interacts with the two targets.ConclusionsThis study establishes that L30 and SBP2 bind to overlapping but non-identical sites on the SECIS. The amino acid requirements for the interaction of L30 with the SECIS differ from those that mediate binding to the L30 pre-mRNA. Our results provide insight into how L7Ae family members recognize their cognate RNAs.

Using a two species competitive binding model to predict expanded bed breakthrough of a recombinant protein expressed in a high cell density fermentation

Expanded Bed experiments were conducted using a mixed mode (MM) resin to capture and purify a recombinant protein produced in yeast fermentation. Expanded bed breakthrough profiles show an overshoot in column effluent concentration of the target protein in the presence of cells and other broth proteins, similar to that seen by other researchers when loading two competing species onto packed beds. In this research, a numerical model assuming negligible axial dispersion is developed and first validated for columns loads that contain only the target protein. This model is solved by finite differences in a unique way that uses an embedded analytical-solution to increase solution speed and stability. To model expanded bed breakthrough of the target protein in the actual cell broth, it was assumed that the other non-product proteins in the broth compete for MM resin binding sites and might be represented as a second “average” species via a traditional two-component competitive Langmuir isotherm. Estimates of the Langmuir constant and broth concentration of this second species were then calculated from batch adsorption data. Using these parameters for the second species, and other batch-derived parameters for the target protein with this resin, this unique numerical modeling approach provided results that compare favorably to experimental breakthrough data at various flow rates. Finally, the model was employed for a parameter sensitivity analysis that shows which process variables are most important in determining breakthrough time and the shape and magnitude of the concentration overshoot.

Silica Adsorbents and Peroxide Functionality for Removing Paraquat from Wastewater

To treat wastewater containing paraquat, the interaction of the herbicide with unmodified and modified (i.e., chemically treated) proprietary silicas is explored using liquid chromatography—mass spectrometry and ultraviolet-visible spectrometry. Strong adsorption and rapid exchange kinetics (i.e., more than 80% within 30 s) of the contaminant onto both unmodified and modified silica surfaces indicate that paraquat adsorption is inherent to the unmodified silica. Although activated carbon sequesters paraquat more effectively than silica at long times (i.e., after 2 h), considering both constant mass and constant area approaches in loading the adsorbents, the best performance in the short-term (i.e., at least up to 150 s) interaction was achieved by using unmodified silicas. Comparison of data fitting to a competitive binding model with or without consideration of homogeneous solid diffusion indicates that, at least for times relevant to water-treatment applications, the competitive binding model is an appropriate mathematical tool to explain experimental adsorption data. Addition of H2O2 is also attempted to initiate paraquat decomposition; however, silica is not an effective catalyst for peroxide decomposition paraquat.

The Effect of Parenterally Administered Cyclodextrins on the Pharmacokinetics of Coadministered Drugs

Cyclodextrins are used increasingly to formulate otherwise poorly soluble molecules for clinical use. Cyclodextrins, such as 2-hydroxypropyl-β-cyclodextrin (HPβCD) and sulfobutylether β-cyclodextrin (SBEβCD), are found in marketed parenteral drug formulations. Depending upon the relative affinities of a coadministered medication for cyclodextrin and plasma proteins, complexation with HPβCD or SBEβCD may alter its pharmacokinetics (PK). To explore this possibility, we applied a previously developed model for competitive binding of drugs with HPβCD and human serum albumin to a variety of commonly administered medications. We modeled this potential interaction in medications chosen on the basis of a hypothetical detrimental effect of HPβCD complexation with their therapeutic action (e.g., antibiotics), supplemented by a composite listing of concurrent medications. Stability constant (K(1:1)) values for drug-HPβCD 1:1 inclusion complexes were extracted from our own data and the literature. The K(1:1) values for the drugs tested ranged from 2 to 40,000 M(-1) and the plasma protein binding from about 20% to over 99%. None of the 63 drugs examined in the present study had a sufficiently high K(1:1) value for HPβCD complexation to affect plasma protein binding to a degree that would be expected to alter their PK substantively, for example, to require increased doses.

Metal mobilization in soil by two structurally defined polyphenols

Polyphenols including tannins comprise a large percentage of plant detritus such as leaf litter, and affect soil processes including metal dynamics. We tested the effects of tannins on soil metal mobilization by determining the binding stoichiometries of two model polyphenols to Al(III) and Fe(III) using micelle-mediated separation and inductively coupled plasma optical emission spectroscopy (ICP-OES). By fitting the data to the Langmuir model we found the higher molecular weight polyphenol (oenothein B) was able to bind more metal than the smaller polyphenol (epigallocatechin gallate, EGCg). For example, oenothein B bound 9.43molFemol−1, while EGCg bound 4.41mol of Femol−1. Using the parameters from the binding model, we applied the Langmuir model for competitive binding to predict binding for mixtures of Al(III) and Fe(III). Using the parameters from the single metal experiments and information about polyphenol sorption to soils we built a model to predict metal mobilization from soils amended with polyphenols. We tested the model with three natural soils and found that it predicted mobilization of Fe and Al with r2=0.92 and r2=0.88, respectively. The amount of metal that was mobilized was directly proportional to the maximum amount of metal bound to the polyphenol. The secondary parameter in each model was the amount of weak organically chelated Fe or Al that was in the soil. This study provides the first compound-specific information about how natural polyphenols interact with metals in the environment. We propose a model that is applicable to developing phytochelation agents for metal detoxification, and we discuss how tannins may play a role in metal mobilization from soils.

Transcription from the second heavy-strand promoter of human mtDNA is repressed by transcription factor A in vitro

Cell-based studies support the existence of two promoters on the heavy strand of mtDNA: heavy-strand promoter 1 (HSP1) and HSP2. However, transcription from HSP2 has been reported only once in a cell-free system, and never when recombinant proteins have been used. Here, we document transcription from HSP2 using an in vitro system of defined composition. An oligonucleotide template representing positions 596-685 of mtDNA was sufficient to observe transcription by the human mtRNA polymerase (POLRMT) that was absolutely dependent on mitochondrial transcription factor B2 (TFB2M). POLRMT/TFB2M-dependent transcription was inhibited by concentrations of mitochondrial transcription factor A (TFAM) stoichiometric with the transcription template, a condition that activates transcription from the light-strand promoter (LSP) in vitro. Domains of TFAM required for LSP activation were also required for HSP2 repression, whereas other mtDNA binding proteins failed to alter transcriptional output. Binding sites for TFAM were located on both sides of the start site of transcription from HSP2, suggesting that TFAM binding interferes with POLRMT and/or TFB2M binding. Consistent with a competitive binding model for TFAM repression of HSP2, the impact of TFAM concentration on HSP2 transcription was diminished by elevating the POLRMT and TFB2M concentrations. In the context of our previous studies of LSP and HSP1, it is now clear that three promoters exist in human mtDNA. Each promoter has a unique requirement for and/or response to the level of TFAM present, thus implying far greater complexity in the regulation of mammalian mitochondrial transcription than recognized to date.

General analysis of competitive binding in drug–interceptor–DNA systems

A general model of competitive binding in drug-interceptor-DNA systems has been developed in order to quantify both the interceptor and protector mechanisms. The model involves full parameterization of the basic equations governing the mutual competition between drugs binding to DNA and incorporates as partial cases various similar models existing in the literature. The generality of the model results from strict accounting of the statistical effects of the binding of the drug and interceptor with DNA according to the McGhee-von Hippel formalism, and to the strict treatment of hetero-association between the drug and interceptor, which includes formation of all possible types of self- and hetero-complexes in solution. Indirect experimental evidence is provided for the importance of the protector mechanism in drug-caffeine-DNA systems, which is sometimes ignored in the literature because of the small magnitude of the CAF-DNA binding constant.

Quantification of the interceptor action of caffeine on the in vitro biological effect of the anti-tumour agent topotecan

Using published invitro data on the dependence of the percentage of apoptosis induced by the anti-cancer drug topotecan in a leukaemia cell line on the concentration of added caffeine, and a general model of competitive binding in a system containing two aromatic drugs and DNA, it has been shown to be possible to quantify the relative change in the biological effect just using a set of component concentrations and equilibrium constants of the complexation of the drugs. It is also proposed that a general model of competitive binding and parameterization of that model may potentially be applied to any system of DNA-targeting aromatic drugs under invitro conditions. The main reasons underpinning the proposal are the general feature of the complexation of aromatic drugs with DNA and their interaction in physiological media via hetero-association.

Competitive Binding to Cuprous Ions of Protein and BCA in the Bicinchoninic Acid Protein Assay

Although Bicinchoninic acid (BCA) has been widely used to determine protein concentration, the mechanism of interaction between protein, copper ion and BCA in this assay is still not well known. Using the Micro BCA protein assay kit (Pierce Company), we measured the absorbance at 562 nm of BSA solutions with different concentrations of protein, and also varied the BCA concentration. When the concentration of protein was increased, the absorbance exhibited the known linear and nonlinear increase, and then reached an unexpected plateau followed by a gradual decrease. We introduced a model in which peptide chains competed with BCA for binding to cuprous ions. Formation of the well-known chromogenic complex of BCA-Cu1+-BCA was competed with the binding of two peptide bonds (NTPB) to cuprous ion, and there is the possibility of the existence of two new complexes. A simple equilibrium equation was established to describe the correlations between the substances in solution at equilibrium, and an empirical exponential function was introduced to describe the reduction reaction. Theoretical predictions of absorbance from the model were in good agreement with the measurements, which not only validated the competitive binding model, but also predicted a new complex of BCA-Cu1+-NTPB that might exist in the final solution. This work provides a new insight into understanding the chemical bases of the BCA protein assay and might extend the assay to higher protein concentration.

In-vitro study on the competitive binding of diflunisal and uraemic toxins to serum albumin and human plasma using a potentiometric ion-probe technique

The competitive binding of diflunisal and three well-known uraemic toxins (3-indoxyl sulfate, indole-3-acetic acid and hippuric acid) to bovine serum albumin (BSA), human serum albumin (HSA) and human plasma was studied by direct potentiometry. The method used the potentiometric drug ion-probe technique with a home-made ion sensor (electrode) selective to the drug anion. The site-oriented Scatchard model was used to describe the binding of diflunisal to BSA, HSA and human plasma, while the general competitive binding model was used to calculate the binding parameters of the three uraemic toxins to BSA. Diflunisal binding parameters, number of binding sites, n(i) and association constants for each class of binding site, K(i), were calculated in the absence and presence of uraemic toxins. Although diflunisal exhibits high binding affinity for site I of HSA and the three uraemic toxins bind primarily to site II, strong interaction was observed between the drug and the three toxins, which were found to affect the binding of diflunisal on its primary class of binding sites on both BSA and HSA molecules and on human plasma. These results are strong evidence that the decreased binding of diflunisal that occurs in uraemic plasma may not be solely attributed to the lower albumin concentration observed in many patients with renal failure. The uraemic toxins that accumulate in uraemic plasma may displace the drug from its specific binding sites on plasma proteins, resulting in increased free drug plasma concentration in uraemic patients.

An ensemble model of competitive multi-factor binding of the genome

Hundreds of different factors adorn the eukaryotic genome, binding to it in large number. These DNA binding factors (DBFs) include nucleosomes, transcription factors (TFs), and other proteins and protein complexes, such as the origin recognition complex (ORC). DBFs compete with one another for binding along the genome, yet many current models of genome binding do not consider different types of DBFs together simultaneously. Additionally, binding is a stochastic process that results in a continuum of binding probabilities at any position along the genome, but many current models tend to consider positions as being either binding sites or not. Here, we present a model that allows a multitude of DBFs, each at different concentrations, to compete with one another for binding sites along the genome. The result is an "occupancy profile," a probabilistic description of the DNA occupancy of each factor at each position. We implement our model efficiently as the software package COMPETE. We demonstrate genome-wide and at specific loci how modeling nucleosome binding alters TF binding, and vice versa, and illustrate how factor concentration influences binding occupancy. Binding cooperativity between nearby TFs arises implicitly via mutual competition with nucleosomes. Our method applies not only to TFs, but also recapitulates known occupancy profiles of a well-studied replication origin with and without ORC binding. Importantly, the sequence preferences our model takes as input are derived from in vitro experiments. This ensures that the calculated occupancy profiles are the result of the forces of competition represented explicitly in our model and the inherent sequence affinities of the constituent DBFs.

Fast Pressure Jumps Can Perturb Calcium and Magnesium Binding to Troponin C F29W

We have used rapid pressure jump and stopped-flow fluorometry to investigate calcium and magnesium binding to F29W chicken skeletal troponin C. Increased pressure perturbed calcium binding to the N-terminal sites in the presence and absence of magnesium and provided an estimate for the volume change upon calcium binding (-12 mL/mol). We observed a biphasic response to a pressure change which was characterized by fast and slow reciprocal relaxation times of the order 1000/s and 100/s. Between pCa 8-5.4 and at troponin C concentrations of 8-28 muM, the slow relaxation times were invariant, indicating that a protein isomerization was rate-limiting. The fast event was only detected over a very narrow pCa range (5.6-5.4). We have devised a model based on a Monod-Wyman-Changeux cooperative mechanism with volume changes of -9 and +6 mL/mol for the calcium binding to the regulatory sites and closed to open protein isomerization steps, respectively. In the absence of magnesium, we discovered that calcium binding to the C-terminal sites could be detected, despite their position distal to the calcium-sensitive tryptophan, with a volume change of +25 mL/mol. We used this novel observation to measure competitive magnesium binding to the C-terminal sites and deduced an affinity in the range 200-300 muM (and a volume change of +35 mL/mol). This affinity is an order of magnitude tighter than equilibrium fluorescence data suggest based on a model of direct competitive binding. Magnesium thus indirectly modulates binding to the N-terminal sites, which may act as a fine-tuning mechanism in vivo.

Components of the ubiquitin-proteasome pathway compete for surfaces on Rad23 family proteins

BackgroundThe delivery of ubiquitinated proteins to the proteasome for degradation is a key step in the regulation of the ubiquitin-proteasome pathway, yet the mechanisms underlying this step are not understood in detail. The Rad23 family of proteins is known to bind ubiquitinated proteins through its two ubiquitin-associated (UBA) domains, and may participate in the delivery of ubiquitinated proteins to the proteasome through docking via the Rad23 ubiquitin-like (UBL) domain.ResultsIn this study, we investigate how the interaction between the UBL and UBA domains may modulate ubiquitin recognition and the delivery of ubiquitinated proteins to the proteasome by autoinhibition. We have explored a competitive binding model using specific mutations in the UBL domain. Disrupting the intramolecular UBL-UBA domain interactions in HHR23A indeed potentiates ubiquitin-binding. Additionally, the analogous surface on the Rad23 UBL domain overlaps with that required for interaction with both proteasomes and the ubiquitin ligase Ufd2. We have found that mutation of residues on this surface affects the ability of Rad23 to deliver ubiquitinated proteins to the proteasome.ConclusionWe conclude that the competition of ubiquitin-proteasome pathway components for surfaces on Rad23 is important for the role of the Rad23 family proteins in proteasomal targeting.

Structural basis for the recruitment of ERCC1-XPF to nucleotide excision repair complexes by XPA

The nucleotide excision repair (NER) pathway corrects DNA damage caused by sunlight, environmental mutagens and certain antitumor agents. This multistep DNA repair reaction operates by the sequential assembly of protein factors at sites of DNA damage. The efficient recognition of DNA damage and its repair are orchestrated by specific protein-protein and protein-DNA interactions within NER complexes. We have investigated an essential protein-protein interaction of the NER pathway, the binding of the XPA protein to the ERCC1 subunit of the repair endonuclease ERCC1-XPF. The structure of ERCC1 in complex with an XPA peptide shows that only a small region of XPA interacts with ERCC1 to form a stable complex exhibiting submicromolar binding affinity. However, this XPA peptide is a potent inhibitor of NER activity in a cell-free assay, blocking the excision of a cisplatin adduct from DNA. The structure of the peptide inhibitor bound to its target site reveals a binding interface that is amenable to the development of small molecule peptidomimetics that could be used to modulate NER repair activities in vivo.

Complexation of daunomycin with a DNA oligomer in the presence of an aromatic vitamin (B 2) determined by NMR spectroscopy

The effect of simultaneous binding of the anthracycline antibiotic Daunomycin (DAU) and the Vitamin B 2 derivative, Flavin-mononucleotide (FMN), with the DNA oligomer, d(TGCA) 2, in solution has been investigated quantitatively by 1Í-NMR spectroscopy (500 MHz). The equilibrium reaction constants and the thermodynamical parameters (Δ H, Δ S) of the hetero-association FMN-DAU and complexation of FMN with d(TGCA) 2 have been determined by analysis of the concentration and temperature dependences of chemical shifts of the aromatic protons in terms of a competitive binding model. A criterion for discrimination between hetero-association and DNA complexation has been developed and applied to the analysis of the simultaneous binding of the antibiotic and the vitamin with DNA. Under the conditions of the experiment, it is found that both the hetero-association of FMN with DAU and the complexation of FMN with DNA contribute approximately equally to the decrease of DAU binding with DNA oligomer. Such competitive complexation of aromatic vitamin and drug with DNA could affect the biological activity of such drugs.

A competitive low-affinity binding model for determining the mutual and specific sites of two ligands on protein

A competitive low-affinity binding model was proposed for determining the number of mutual (overlapped) and specific binding sites of two ligands (A, B) on a protein (P). To use the model, one needs to carry out a titration experiment by adding either ligand A or B into a three-component system (A–B–P), and to monitor the spectroscopic parameter changes. Fitting the titration curve to the proposed model, one can get the mutual and specific binding sites of the two ligands on the protein. The model was examined by using human serum albumin (HSA) as a receptor and tolmetin (TOL) and salicylic acid (SAL) as ligands. Proton longitudinal relaxation rates ( R 1) were measured on a 500-MHz NMR spectrometer during the titration and used to derive the mutual binding sites. It was found that among the binding sites of 32 ± 4 for SAL and 28 ± 2 for TOL on HSA, there were 17 ± 5 mutual sites for the two ligands. This result indicates that, although HSA has large binding capacities for most ligands, there are still a reasonable amount of the low-affinity binding sites that are structure selective.

A General Framework for Development and Data Analysis of Competitive High-Throughput Screens for Small-Molecule Inhibitors of Protein−Protein Interactions by Fluorescence Polarization

Equilibrium binding experiments are widely used for the accurate characterization of binding and competitive binding behavior in biological systems. Modern high-throughput discovery efforts in chemical biology rely heavily upon this principle. Here, we derive exact analytical expressions for general competitive binding models which can also explain a commonly encountered phenomenon in these types of experiments, anticooperative incomplete displacement. We explore the effects of nonspecific binding behavior and parameter misestimation. All expressions are derived in terms of total concentrations determined a priori. We discuss a general framework for high-throughput screening assays based on fluorescence polarization and strategies for assay development, sensitivity regimes, data quality control, analysis, and ranking. Theoretical findings are visualized by simulations using realistic parameter sets. Our results are the basis for the discovery of small-molecule inhibitors of the protein-protein interaction between human calcineurin and NFAT transcription factors, as discussed in the subsequent paper (31).

Application of the local-bulk partitioning and competitive binding models to interpret preferential interactions of glycine betaine and urea with protein surface.

Two thermodynamic models have been developed to interpret the preferential accumulation or exclusion of solutes in the vicinity of biopolymer surface and the effects of these solutes on protein processes. The local-bulk partitioning model treats solute (and water) as partitioning between the region at/or near the protein surface (the local domain) and the bulk solution. The solvent exchange model analyzes a 1:1 competition between water and solute molecules for independent surface sites. Here we apply each of these models to interpret thermodynamic data for the interactions of urea and the osmoprotectant glycine betaine (N,N,N-trimethylglycine; GB) with the surface exposed in unfolding the marginally stable lacI HTH DNA binding domain. The partition coefficient K(P) quantifying accumulation of urea at this protein surface (K(P) approximately equal 1.1) is only weakly dependent on urea concentration up to 6 M urea. However, K(P) quantifying exclusion of GB from the vicinity of this protein surface increases from 0.83 (extrapolated to 0 M GB) to 1.0 (indicating that local and bulk GB concentrations are equal) at 4 M GB (activity > 40 M). We interpret the significant concentration dependence of K(P) for GB, predicted to be general for excluded, nonideal solutes such as GB, as a modest (8%) attenuation of the GB concentration dependence of solute nonideality in the local domain relative to that in the bulk solution. Above 4 M, K(P) for the interaction of GB with the surface exposed in protein unfolding is predicted to exceed unity, which explains the maximum in thermal stability observed for RNase and lysozyme at 4 M GB (Santoro, M. M., Liu, Y. F., Khan, S. M. A., Hou, L. X., and Bolen, D. W. (1992) Biochemistry 31, 5278-5283). Both thermodynamic models provide good two-parameter fits to GB and urea data for lacI HTH unfolding over a wide concentration range. The solute partitioning model allows for a full spectrum of attenuation effects in the local domain, encompasses the cases treated by the competitive binding model, and provides a somewhat better two-parameter fit of effects of high GB concentration on lacI HTH stability. Parameters of this fit should be applicable to isothermal and thermal unfolding data for all proteins with similar compositions of surface exposed in unfolding.

Hidden Markov Model for Competitive Binding and Chain Elongation

Many chemical systems of interest consist of sets of reactions that contain iterated sequences that elongate a molecular chain. For example, such sets of reactions are commonly found in the transcription of DNA or the translation of RNA. However, there are competitive reactions that can prematurely terminate the chain-elongation process. A hidden Markov method appropriate for modeling chains of reactions with competitive processes (i.e., premature chain termination) is developed. The method is an extension of a hidden Markov model suggested by Gibson and Bruck (J. Phys. Chem. A 2000, 104, 1876). The equivalence between results using this method and results from simulation of a system employing the full set of reactions will be demonstrated (Gillespie, D. T. Markov Processes: An Introduction for Physical Scientists; Academic: San Diego, CA, 1992). Examples of its use are shown for several test problems. As an example of a practical application, a comparison among results for a model of terminal modification of ligand-aggregated receptors (Hlavacek, W.; Redondo, A.; Wofsy, C.; Goldstein, B. Bull. Math. Biol. 2002, 64, 887) simulated by ordinary differential equations, the full set of reactions, and the hidden Markov method are shown.