Xenopus extracts. Predictions based on the analysis of the reference state were used iteratively to develop a more refined model from which we analyzed the effects of prolonged and transient Wnt stimulation on β-catenin and axin turnover. We predict several unusual features of the Wnt pathway, some of which we tested experimentally. An insight from our model, which we confirmed experimentally, is that the two scaffold proteins axin and APC promote the formation of degradation complexes in very different ways. We can also explain the importance of axin degradation in amplifying and sharpening the Wnt signal, and we show that the dependence of axin degradation on APC is an essential part of an unappreciated regulatory loop that prevents the accumulation of β-catenin at decreased APC concentrations. By applying control analysis to our mathematical model, we demonstrate the modular design, sensitivity, and robustness of the Wnt pathway and derive an explicit expression for tumor suppression and oncogenicity.Wnt signaling plays an important role in both oncogenesis and development. Activation of the Wnt pathway results in stabilization of the transcriptional coactivator β-catenin. Recent studies have demonstrated that axin, which coordinates β-catenin degradation, is itself degraded. Although the key molecules required for transducing a Wnt signal have been identified, a quantitative understanding of this pathway has been lacking. We have developed a mathematical model for the canonical Wnt pathway that describes the interactions among the core components: Wnt, Frizzled, Dishevelled, GSK3β, APC, axin, β-catenin, and TCF. Using a system of differential equations, the model incorporates the kinetics of protein–protein interactions, protein synthesis/degradation, and phosphorylation/dephosphorylation. We initially defined a reference state of kinetic, thermodynamic, and flux data from experiments using  Wnt signaling is important in both oncogenesis and development. Mathematical modeling predicts several unusual features of the Wnt pathway, some of which are tested experimentally Considerable effort employing biochemistry, genetics, and pharmacology has been invested in identifying the web of interactions that characterize signal transduction pathways in metazoan organisms. Several conclusions can be drawn from these efforts. Despite the large number of receptors, ligands, and downstream targets, the number of signal transduction pathways in metazoans is relatively small, arguably less than 20 . This liXenopus embryo, it is widely used in many different contexts in development, and it is also very important in human cancer. Although the design features of the Wnt pathway are highly conserved in evolution, it is not clear what purposes those features serve. This paper is in part an answer to that question.Many of these questions require a more quantitative understanding of the behavior of signaling pathways. Such information is rarely available. Most mathematical models have to be satisfied with a general conceptual understanding and are seldom testable, as most parameters must be assumed or inferred. It is partly for this reason that such theoretical efforts up to now have had limited impact on experimentalists, who prefer powerful qualitative tools to construct logical and formal models of pathway structures. Mathematical modeling is more advanced for metabolic networks, where the pathways have been known for more than a half-century and where more kinetic data have been available, including more recent data on in vivo dynamics . To deveThe pivotal player in Wnt signaling is the scaffold protein axin, which is required for the constitutive degradation of β-catenin. Axin coordinates the assembly of a large complex that includes the glycogen synthase kinase 3β (GSK3β); another scaffold protein, adenomatous polyposis coli (APC); and the negative regulators Dsh and GSK3β-binding protein (glycogen synthase kinase-binding protein [GBP]/Frat). Binding of Wnt to its receptor, Frizzled, activates Dsh through an as-yet-unknown process. In the absence of Wnt, GSK3β bound to axin phosphorylates β-catenin bound to both axin and APC. Phosphorylated β-catenin is a substrate for ubiquitination and subsequent degradation through the F-box protein β-TRCP, which is part of an SCF ubiquitin ligase complex. In the presence of the Wnt signal, the activated Dsh protein binds to axin and, through bound GBP, inhibits β-catenin phosphorylation; this inhibits its ubiquitination and consequent degradation. The buildup in β-catenin in the presence of a Wnt signal leads to transcription of specific genes.Numerous questions arise from this general model. Why are two scaffold proteins, APC and axin, both necessary? Do their roles differ? Recently it has been discovered that axin, like β-catenin, is an unstable protein . In receTo answer such questions, we collected what we initially thought were sufficient quantitative data on rates, affinities, and fluxes to derive a reference state model of the Wnt pathway in this system. The provisional reference state model reflected most of the known properties of the system, but from this model we identified several rates and affinity constants whose values were critical to the behavior of the model. We then went back and measured these. Thus this paper contains a reference model, a large number of experimental measurements needed to define this model, theoretical predictions, and experimental tests of those predictions, where possible. A general test of the validity of the model is its predictive ability under a wide range of conditions. From this analysis, several unexpected properties emerged with significance for understanding the biological function of the Wnt pathway.The model was based on the reaction scheme shown in The centerpiece of the model is the formation of the unstable core complexes involved in β-catenin phosphorylation and subsequent destruction. In addition to β-catenin, this set of complexes contains GSK3β and the scaffold proteins APC and axin. The complexes assemble in several steps: (1) binding of axin to APC (forward reaction of step 7); (2) binding of GSK3β (forward reaction of step 6); (3) phosphorylation of axin and APC by GSK3β (step 4). Dephosphorylation of the core complex (step 5) is mediated by PP2A. The first step in β-catenin degradation is its binding to APC*/axin*/GSK3β (step 8), after which it is phosphorylated by GSK3β (step 9) and released from the complex (step 10). Our model assumes that the phosphorylation of β-catenin by GSK3β is negligible in the absence of axin. Indeed, recent work indicates that axin stimulates the phosphorylation of β-catenin by GSK3β at least 24,000-fold . Free, pXenopus egg extracts indicate that the turnover of GSK3β, Dsh, and TCF is relatively slow , the synthesis and degradation of these proteins are not explicitly modeled. The activation of the pathway in vivo, which results in the stabilization of β-catenin, is initiated by binding of Wnt ligands to Frizzled receptors and the subsequent transition of Dsh from its inactive form (Dshi) to its active form (Dsha). Since these events are still poorly defined, both processes have been combined in step 1. Interaction of Dsha with the nonphosphorylated complex APC/axin/GSK3β (step 3) activates the release of GSK3β . This latter process requires the activity of the GBP/Frat (not shown on our diagram). Deactivation of Dsha occurs through an as-yet-unidentified mechanism (step 2).The dynamic properties of the model, such as the flux through the pathway, are also affected by binding of β-catenin to other partners, such as TCF (step 16) and free APC (step 17). In special cases (high axin concentrations), the flux through the system is affected by the binding of axin to GSK3β (step 19) as well as β-catenin (step 18). We have previously shown experimentally that TCF reduces the rate of β-catenin degradation . TurnoveWnt(t). Since Dsh, TCF, and GSK3β are degraded very slowly, we assume that their concentrations remain constant throughout the timecourse of a Wnt signaling event. The conservation equations for Dsh, TCF, and GSK3β are as follows:The mathematical analysis is based on a series of balance equations that describe the concentrations and complexes of proteins in the Wnt pathway, as depicted in GSK3β0 = GSK3β. Similarly, we omitted the concentration of complexes containing axin in the conservation relationship for APC, which leads to the following equation:Since the concentration of axin is very low (see below) compared to the concentration of GSK3β, we replaced Equation (3) with the simple relationship We will, however, take into account the contribution of axin-containing complexes for GSK3β and APC conservation equations when we later consider the effect of large increases in axin concentration.νi. Unimolecular reactions are assumed to be irreversible and are described by linear rate equations νi = ik · jX, where ik denotes the first-order rate constant and jX denotes the concentration of the reactants. Reversible binding steps (double-headed arrows in νi = +iXjYlk − −ik(jX.lY), where jX and lY denote the concentrations of the binding partners and (jX.lY) the concentration of their complex. The Dsh-mediated release of GSK3β from the destruction complex is described by an irreversible reaction that is bimolecular in the concentrations of Dsh and the degradation complex. The model is simplified by assuming that the reversible binding steps between axin, β-catenin, APC, and TCF are very fast, such that the corresponding protein complexes are in rapid equilibrium, so that only the dissociation constants iK = ki−/ki+ are considered in the kinetic description of these steps. The conservation equations and the binding equilibria reduce the number of independent dynamic variables. Accordingly, the original set of 15 differential equations is transformed into a set of only seven ordinary differential equations coupled to four conservation equations and four relationships for binding equilibria. For a detailed mathematical description of the model and the procedure for reducing the number of systems variables, see The simplest possible equation was chosen to describe the kinetics of each individual reaction. Synthesis of β-catenin and axin are described by constant rates Wnt = 0). In this unstimulated stationary state, Dsh is inactive and does not affect the degradation complex. β-Catenin concentration is kept low by continuous phosphorylation and degradation. The reference state can be characterized by the special values for its rate constants, its equilibrium constants, and its conservation quantities. If one can obtain values for all of these system parameters, the model equations should allow for a straightforward calculation of the variables in the reference state. Currently, we have experimental data for many of these parameters (see below). For the remaining system parameters that were not directly measured, we were able to derive numbers based on experimental data of steady-state concentrations and fluxes. A number of parameters were set such that the results of the model were in agreement with previous experimental data, specifically with the experimentally determined rate of β-catenin degradation  and steady-state concentrations . The total concentrations of Dsh, TCF, GSK3β, axin, β-catenin, and APC in Xenopus egg extract were determined experimentally using Western blot analysis by comparing the intensity of the signal to that of known amounts of recombinant protein. The concentration of phosphorylated β-catenin w as estimated because we have not been able to directly determine its level in extracts. However, we estimate that this value is small compared to that of nonphosphorylated β-catenin for the following reasons: (1) Addition of axin to Xenopus extracts dramatically increases the rate of β-catenin degradation. Since the role of axin is to promote phosphorylation of β-catenin, which is subsequently degraded, this would suggest that normally a significant pool of β-catenin exists in the nonphosphorylated form. (2) Western blot analysis of Xenopus extracts demonstrates that only a small percentage (<10%) of total β-catenin can be detected as migrating with a slower mobility, which likely represents the phosphorylated form of β-catenin.The first group of input data contains both total concentrations  and phosphatase(s), respectively. By contrast, the concentration ratio of the two β-catenin-containing degradation complexes represents the relative activities of β-catenin phosphorylation and the rate of release of phosphorylated β-catenin from the complex. These parameters were chosen rather arbitrarily to indicate roughly equal kinase and phosphatase activities and yielded realistic values for the overall fluxes, given the known concentrations and kinetic rate constants.ν11 for the degradation of β-catenin via the Wnt pathway and the flux ratio ν13/ν11 describing the extent to which β-catenin is degraded via non-Wnt mechanisms . We havK.P = 1/(k4 + k5) for the kinase/phosphatase cycle that mediates phosphorylation/dephosphorylation of both APC and axin in the degradation complex (steps 4 and 5), τGSK3β.ass = 1 / (k6GSK3β + k−6) for the binding equilibrium of GSK3β with the APC/axin complex (step 6), and τax.deg for axin degradation (step 15). Values for the rate of axin degradation were determined directly from experiments performed in Xenopus egg extracts (unpublished data). Experiments to determine the rate of APC and axin dephosphorylation (τK.P ≈ 2.5 min) were performed using in vitro 32P-labeled recombinant APC and axin. Radiolabeled proteins were added to Xenopus egg extracts, and the loss of radioactivity over time was assessed by SDS-PAGE and autoradiography  of selected processes. This is the time it takes for the concentration to drop to 1/e of its initial value. These characteristic times include τiography . The legW = Wnt/Wnt0 that represents the ratio of the Wnt concentration with respect to its concentration Wnt0 in a “standard” stimulated  state. W = 0 and W = 1 characterize the reference state and a standard stimulated state, respectively, with the hyperstimulated state defined as W > 1. In order to calculate concentrations in the standard stimulated state, additional input quantities are required. These include the ratio of the active and inactive forms of Dsh (a/DshiDsh), the relation between non-Dsh-mediated and Dsh-mediated release of GSK3β from the destruction complex (the flux ratio ν−6/ν3), and the characteristic time for the Dsh activation/inactivation cycle (τDsh.act). These values are not at present measurable. The values for these input quantities are listed in the legend of Using the reference state as a starting point, we consider other stationary states that are attained when the pathway is permanently stimulated. To describe the strength of Wnt stimulation, we introduce a dimensionless quantity W = 1 and fixing all other parameters, we arrive at steady-state solutions of the systems equations  is a fixed value and the rate of degradation depends solely on the concentration of free axin .By setting ions see . A compaW ≤ 1.4) on the steady-state concentrations of β-catenin and axin reveal a nearly hyperbolic saturation of increasing concentrations of nonphosphorylated and total β-catenin with increasing strength of Wnt stimulation. Furthermore, Wnt stimulation affects the steady-state concentrations of axin and β-catenin in an opposite direction   A. We thetration) , adding )  and β-catenin (ν12 = 0). This reference curve is in close agreement with our experimental data . We examined a new state, where we have increased the amount of endogenous axin (0.02 nM) by 0.2 nM. As shown in t½ = 11.8 min) in agreement with the experimentally obtained values (t½ = 12 min). Theoretically, the effect of axin on β-catenin degradation is primarily due to the large concentration difference between the two scaffold proteins, APC and axin. Owing to the high concentration of APC, an increase in axin concentration results in a sharp increase in the concentration of the APC/axin complex, thereby accelerating β-catenin binding to the destruction complex.The straight line for Curve d in a, as well as the experimental support for it (Xenopus extracts since we see the same effect with Dsh protein that has been “activated” with extracts prior to its use in our degradation assay. As shown in K.P of phosphorylation and dephosphorylation of APC and axin in the destruction complex is relatively slow (2.5 min), and it therefore takes 5 min for 75% of the complex to be dephosphorylated. If Dsha acted only on the dephosphorylated complex (through step 3) to remove GSK3β and thus block phosphorylation of the complex, then we would predict the biphasic kinetics shown in The immediate inhibition by LiCl is in contrast with the action of Dsh that inhibits only after a significant delay. We were intrigued by the theoretical biphasic degradation curves of β-catenin in the presence of Dsht > 2 h in both curves a and b again suggests the existence of a slow degradation process mediated by non-Wnt pathway mechanisms.To test this prediction beyond consistency with experimental data, we performed an experiment in which Dsh was either preincubated with extract before or added at the same time as radiolabeled β-catenin . If β-caa required to inhibit β-catenin degradation, but the pathway is much more sensitive to axin concentration than it is to GSK3β concentration. In the presence of high concentrations of axin, the effect of Dsha should be blocked; high concentrations of axin will lead to high concentrations of the phosphorylated destruction complex no matter what level of Dsha activity is present. High levels of the destruction complex will require even higher levels of Dsh to overcome the inhibition. The interaction between Dsha and GSK3β is similar in principle: Dsh-mediated release of GSK3β (step 3) from the degradation complex can simply be reversed by sufficiently high concentrations of GSK3β (step 6). In this case, however, the effect is small. Thus, axin blocks the action of Dsh so effectively that it renders the Dsh pathway inoperable.In establishing quantities for our model in In Sf9 cells and bacteria, respectively) may be low and that a significant fraction of the recombinant proteins may not be active. Alternatively, the low activity of GSK3β may point to an unidentified inhibitory activity present in our Xenopus egg extracts.Our experimental results, however, show a smaller effect on the half-life of β-catenin degradation at high concentrations of Dsh as GSK3β levels are increased. Also, the concentrations of added axin in the theoretical curve and the experimental curves are very different. The quantitative difference between the model and experimental may simply reflect the fact that the specific activity of our GSK3β and axin preparations  changes with changes in the concentrations of CF0 see .MK represents a half-saturation constant for the activating effect of APC.We chose to focus on the effects of changes in the concentrations of pathway components in the reference state, because similar effects were also seen for the stimulated state. Recently, we investigated a new and important property of the Wnt pathway, namely that the degradation of axin (reaction 15) is dependent on APC (unpublished data). The degradation rate of axin is mathematically expressed in the following manner:ν15 = k15axin is applied). With APC-mediated axin degradation, β-catenin degradation is affected very little by changes in the concentration of APC (25% decrease with a 2-fold increase in APC concentration). This resistance to changes of β-catenin levels upon changes in APC concentration is due to the APC-dependence of axin degradation  and axin (ν14) synthesis on both β-catenin and axin levels  and after diminution of the Wnt signal; however, during active signaling, the differences in the dynamic nature of signal output at differing rates of axin turnover are dramatically revealed.Regulating axin turnover is important for Wnt signaling. Wnt-stimulated axin turnover has been reported in cultured mammalian cells  and in Dosophila . In a fuThus, β-catenin degradation is effectively inhibited for a certain time period due to a reduced availability of the scaffold axin.Interestingly, an increase in the turnover rate of axin leads to higher amplitudes and shorter durations of the β-catenin signal. This can be explained by the faster degradation of axin after its Dsh-mediated release from the destruction complex.W = 0 to W = 1, a fast axin turnover favors rapid replenishment of the axin pool after the decline of the Wnt stimulus and, in this way, fast recovery of the destruction complex. This explains why the β-catenin signal is not only amplified, but becomes more spike-like. Increasing the turnover rate of axin affects the response of axin to temporary Wnt stimulation in a similar way as the response of β-catenin; i.e., the signal is amplified and sharpened  during the transition from harpened . Closer K18 = 1 nM), a moderate increase in axin concentration should theoretically accelerate β-catenin degradation, whereas a much higher concentration should result in inhibition of β-catenin degradation, due to the formation of partial complexes on axin. A more extensive analysis of β-catenin half-lives over a range of axin concentrations shows such a biphasic curve  only becomes inhibitory at higher than micromolar concentration (curve c), whereas the combined effect of binding to both β-catenin and GSK3β  shows inhibition at less than 500 nM (curve d). If, however, we model an ordered process of binding to axin, then abortive inhibitory complexes cannot form. We show this in ½ at high axin concentrations . In this case, increasing concentrations of APC greater than the reference concentrations does not lead to inhibition of β-catenin degradation even at very high concentrations of APC. In cultured cells, overexpression of APC stimulates β-catenin degradation . The alternative pathways have very little effect on the half-life of β-catenin at normal and supranormal concentrations of APC. However, the effect of these alternative pathways becomes much more prominent when the APC concentration is lowered, a situation that may be significant under pathological conditions. As seen in β-Catenin can also be degraded by nonaxin-dependent mechanisms, which include Siah-1 and presenilin-mediated degradation. Though they are expected to contribute very little to the total flux through the pathway, the nonaxin-dependent processes may have very important influences under certain conditions. In our +ik and −ik, we use control coefficients for the total concentration of β-cateninThe model contains many parameters that affect the system behavior in different ways and to various extents. We can systematically investigate these parameters and look for those whose perturbation the system is most sensitive or most robust against. We focus on the concentrations of β-catenin and axin and calculate the responses in the total concentrations of these two compounds upon changes in the rates of the individual processes. For quantifying the effects of the rate constants axin±iC for the total axin concentration. These coefficients, originally proposed for quantifying control in metabolic networks . This group includes the reactions participating in assembling the destruction complex APC*/axin*/GSK3β. The corresponding parameters involve the rate constants k7 for the binding of axin to APC, k6 for the association of GSK3β to the APC/axin complex, and k4 for the phosphosphorylation of axin and APC in the destruction complex. Similar strong negative control is exerted by β-catenin binding to the phosphorylated destruction complex (rate constant: k8), the phosphorylation of β-catenin in the destruction complex (rate constant: k9), and the synthesis of axin (ν14).For the reference state, there are six steps exerting strong negative control on the total β-catenin concentration (βcatiC ≅ 1). To this group belong the reactions participating in the disassembly of the destruction complex APC*/axin*/GSK3β, which are described by the rate constants −k7 for the dissociation of the APC/axin complex, −k6 for the dissociation of GSK3β from the destruction complex, and k5 for the dephosphorylation of the APC and axin in the destruction complex. Other steps with a high positive control are the dissociation of β-catenin from the destruction complex (rate constant: −k8), axin degradation (rate constant: k15), and β-catenin synthesis (ν12).Six other reactions exert strong positive control in the reference state on the total concentration of β-catenin (concentration (k16 and k17), and the corresponding dissociation processes . Interestingly, the effects of the two β-catenin degradation processes (rate constants: k11 and k13) are also small. Calculation of control coefficients for the standard stimulated state reveals that some steps that exert no control in the reference state become important. These are the activation and inactivation of Dsh (rate constants: k1 and k2) and, more pronounced, the Dsh-mediated release of GSK3β from the destruction complex (k3). For all other processes, the signs of the control coefficients for β-catenin and axin do not change at the transition from the reference state to the standard stimulated state. The effects of parameter changes on axin are generally opposite to those on β-catenin; i.e., processes with a positive control coefficient for β-catenin have negative control coefficients for axin and vice versa. A significant exception is the synthesis of β-catenin, which exerts a positive control not only on β-catenin but also on axin, as expected from the results obtained in the last section.There are many reactions exerting almost no control on β-catenin levels in the reference state. This group includes binding of β-catenin to TCF and APC .Closer inspection of For those more familiar with genetic manipulation, it is more common to vary the concentrations of individual components rather than vary the rate constant of a reaction. σ of the control coefficients from their mean value. According to the summation theorem, the mean value of all control coefficients for a given variable is zero. Thus, we get for the standard deviation for the control coefficients of β-catenin:σ indicate that the given variable is on average very sensitive towards changes of rate constants. We propose to introduce a measure for the robustness ρ of a variable towards changes of all parameters in the following way:Clearly, the robustness of a variable towards parameter changes is higher the lower the corresponding concentration control coefficient. To arrive at an estimation of the overall effects of parameter perturbations on the system as a whole, we consider first the standard deviation σ may vary between zero and infinity, the range of ρ is confined to the interval 1≥ ρ ≥ 0. High values of ρ resulting from low σ values for the control coefficients indicate that the variable is robust against parameter perturbations. The standard deviations σ of the control coefficients and the ρ values for β-catenin and axin are presented in the last two rows of σ values for β-catenin as well as for axin are rather small. Since all values for σ are lower than unity, a 1% change in a rate constant leads, on average, to a response of <1% in the overall level of β-catenin. The total concentration of axin is more robust against parameter perturbations than the total concentration of β-catenin, particularly in the standard stimulated state. A transition from the reference to the standard stimulated state results in a lower robustness for β-catenin and a higher robustness for axin.As Xenopus egg extracts was to acquire the kind of detailed kinetic data required to build a realistic model. There are several unusual advantages to the extract system that contributed to this effort. The Xenopus egg extract is essentially neat cytoplasm; it reproduces the in vivo rate of β-catenin degradation and responds to known regulators as expected from in vivo experiments. Kinetic experiments with high time resolution are possible in this system, since a well-stirred extract is presumably synchronous in ways in which collections of cells may not be. In extracts it is possible to precisely set the level of components by depletion or addition. The direct output of the canonical Wnt pathway is an easily measured cytoplasmic event, the degradation of β-catenin. Thus, in this unusual system it is possible to acquire quantitative information about signaling pathways, not achievable in vivo. At the same time, these extracts have limitations. We have not considered the receptor events, and it is likely that reactions at the plasma membrane contribute to dynamic features. Also, our analysis is incomplete, as there are other components of Wnt signaling, such as casein kinase Iδ, casein kinase Iɛ, and PAR1, as well as cross-talk from other pathways, that influence the behavior of the system. We have also oversimplified the multiple phosphorylation steps. We have assumed a simple interconversion of the phosphorylated and unphosphorylated complex of axin, APC, and GSK3β, whereas in reality multiple phosphorylation states exist within the complex; the states may be random or sequential. We simply do not have the information to provide a much more specific model of phosphorylation interconversions at this time, although the model could easily be extended. Finally, there is the question of what Wnt process we are studying. We are looking at events in the cytoplasm of unfertilized eggs. Though endowed with all of the core components of the Wnt pathway, the egg is, as far as we know, transcriptionally silent and not involved in Wnt signaling, though this system is active very soon in embryogenesis. Thus, there is no biological in vivo behavior with which to compare the in vitro behavior. Nevertheless, the basic core circuitry is intact and is presumably prepared for the early Wnt events in the embryo. All the properties of the egg extract system are very similar to that circuitry in vertebrate somatic cells.Theory and quantitation are mutually dependent activities. It would seem unlikely that one would go to the trouble to measure detailed kinetic quantities without a specific model to test, and it is equally unlikely that realistic models can be constructed without the constraints of quantitative experimental data. Our intent in trying to reproduce a substantial part of the Wnt pathway in Xenopus embryos and mammalian cells, whose similarity to the in vitro system we had already confirmed. We derived a system of differential equations that described the time-dependent variations of the system variables, i.e., the concentrations of the pathway components and their complexes. Parameters of the model are binding constants of proteins, rate constants of phosphorylations and dephosphorylations, rate constants of protein degradation, and rates of protein synthesis. Model reduction was achieved by considering conservation relations and by applying rapid equilibrium approximations for selected binding processes. Despite these simplifications, the model consists of a nonlinear system of differential equations whose solution requires the use of computers. Not all of these parameters were accessible to measurement. To circumvent this problem, we used as primary inputs not only kinetic parameters characterizing individual steps, but quantities that are more easily accessible from experiment, such as the overall flux of β-catenin degradation. This allowed us to derive rate constants as well as protein concentrations in a reference state, where there was no Wnt signal. This state serves as a starting point for predicting the system behavior during Wnt signaling as well as after experimental perturbations.To build a mathematical description of the Wnt signaling system, we started with the basic circuitry discerned from previous studies in The basic model reproduced quantitatively the behavior of the reference state, including perturbations of this state achieved by varying the concentration of axin, GSK3β, and TCF. It also reproduced extensions of this to the signaling state. A wide variety of different sets of experimental data could be simulated by the same model, employing the same sets of kinetic parameters. We approached this process iteratively. For example, the early model did not include nonaxin-dependent degradation of β-catenin, but inclusion of this process improved the fit to the experimental data. More significantly, addition of this process had interesting biological implications, which we discuss.Xenopus extracts. Axin levels in other organisms may similarly be very low: Drosophila axin can be detected by Western blotting only following its immunoprecipitation  has another design feature potentially very general and important for the modularity of metazoan signaling pathways. Axin is a critical node point for controlling β-catenin levels, but it also interacts with components shared with several other important pathways. The interaction of these components with axin fluctuates due to Wnt signals (reflecting changes in binding as well as changes in axin levels), yet because the concentration of axin is so low, there will be no appreciable change in the overall levels of GSK3β, Dsh, or APC . The very low axin concentration thus isolates the Wnt pathway from perturbing other systems, a simple mechanism to achieve modularity. Other scaffold proteins may serve similar functions in other pathways. These insights follow from a very simple measurement of axin concentration and suggest the utility of measuring the levels of signaling pathway components in different cell types and circumstances. Since quantitative and kinetic features may be important in defining modules, it suggests that qualitative circuit diagrams of signal transduction may overlook very important design features. Modularity within the Wnt pathway can be defined by an extension of the summation theorem of In addition to work by +, but rather is focused on the two scaffolding proteins. This was apparent from the biphasic nature of both the theoretical and experimental curves, which suggested that Dsh inhibited the rephosphorylation of axin/APC, but still allowed many cycles of β-catenin phosphorylation, ubiquitination, and degradation. This mechanism was further proven by a timing-of-addition experiment. It needs to be further confirmed and extended by looking specifically at individual phosphorylation sites on all the components of the complex. Another insight into the mechanisms of complex formation and control of β-catenin degradation concerns the inhibition of β-catenin degradation at concentrations of axin approaching those of other components. This suggests that axin binds APC, GSK3β, and β-catenin in random order. As discussed above, the axin concentration is limited by other factors; owing to the low concentration of axin, random binding is not likely ever to be a problem. The situation for APC seems very different. The concentration of APC is comparable to that of the other components. Overexpression studies show no inhibitory effects. These theoretical and experimental observations suggest that APC as a scaffold must be very different from axin as a scaffold. Most likely, APC binds components in an ordered manner.Despite considerable progress in identifying components of the Wnt pathway, many important mechanistic details are still lacking. In this analysis we have shown that Dsh seems to act to prevent the phosphorylation of the axin/APC complex, not the phosphorylation of β-catenin. Dsh (complexed to GBP) does not seem to be a general GSK3β inhibitor, like LiMetabolic pathways are understandable in terms of the familiar logic of chemical synthesis; signal transduction pathways, by contrast, often do not seem to conform to simple design principles. It is not clear at all whether signaling pathways have been optimized for a specific function or instead whether they are remnants of some early and rather arbitrary evolutionary experiment, now embedded in other processes that are difficult to change. Systems analysis, along with experiment, offers some hope of uncovering latent principles of design. For example, the modeling of the Wnt pathway gave a theoretical insight into the function of axin degradation in Wnt signaling. The degree of axin instability dramatically affects the amplitude and duration of the β-catenin response to a transient Wnt signal. If axin turnover were designed to be slow, then β-catenin would rise slowly to a low amplitude and persist for many hours. In a system where axin turnover was more rapid, the amplitude could increase several-fold and would persist a shorter time. The duration and amplitude of the response are likely to be important factors in developmental systems, which may respond differently to different amplitudes and durations of a signal. In addition, some developmental processes occur with such rapidity that the same signal would be interpreted differently at different times, hence the need to quickly terminate a signal. The very different effects of transient and persistent signals in the same pathway have been studied in PC12 cells in the MAP kinase pathway activated by EGF or NGF . FinallyRobustness has also been considered an important design principle for signaling processes , and conAnother aspect of robustness is susceptibility to mutation or pharmacologic or environmental perturbation. The unexpected minimal phenotypes observed in numerous mouse knockout experiments have underscored our ignorance of the adaptable responses of organisms and in particular the adaptable nature of signaling pathways. One unexpected theoretical observation in this paper was the potential importance of the nonaxin-dependent degradation for β-catenin, under conditions where the APC levels are reduced. In our model, the nonaxin-dependent degradation contributed only a few percent to the overall flux of β-catenin degradation. Yet if the APC levels fall only 50%, the exact level of the alternative pathway made a large difference in the steady-state level of β-catenin. If the activity of the alternative pathways varied in different tissues, then this simple but largely silent effect could explain the tissue specificity of APC mutations. Similarly, variations in the alternative pathway might also explain some aspect of individual risk to loss of a single copy of the APC gene.An experiment can better be judged by how many questions it raises than by how many it answers. The same may be said about theoretical analysis. Such analysis is always a work in progress, in that the experimental basis is continually changing to some degree. Some of the experimental changes, though significant mechanistically, may have little effect on the model and its interpretation. Some may require major revision. In the case of the Wnt pathway, the theoretical analysis and modeling have already raised several interesting questions of biological importance. They have already stimulated further experimentation. More than anything, the modeling has increased the urgency for obtaining accurate quantitative information about both steady-state and transient processes in Wnt signaling and for obtaining information about the differences in parameters in different tissues and in different organisms.Xenopus egg extracts were prepared as described previously (eviously . Extracteviously .Xenopus egg extracts were either supplemented with 25 mM LiCl in Xenopus buffer (XB) or XB and an aliquot were withdrawn for β-catenin degradation assays. The free methionine pool in Xenopus embryos is approximately 90 μM, and based on this number, [35S]methionine was added to the extract to a give a final activity of 1,000 counts per picomole methionine. Extracts were incubated at 20°C, and aliquots were withdrawn at the indicated times for SDS-PAGE, trichloroacetic acid (TCA) precipitation, and β-catenin pull-downs. To assay protein synthesis in the extract, total methionine incorporation was measured by TCA precipitation. In brief, Xenopus extracts (2 μl), metabolically labeled with [35S]methionine as above, were diluted to 100 μl with PBS and supplemented with 2 μl of 2% deoxycholate and TCA to 5%. The reaction was pelleted at 20,000 × g for 10 min at 4°C. After washing with ice-cold acetone and air drying, the radioactivity of the pellet was measured in a scintillation counter.Freshly prepared Xenopus extracts, we used His-tagged APCm3 cross-linked to Ultralink beads . Since phosphorylated APC has a much higher affinity for β-catenin, APCm3 beads were first phosphorylated with 300 nM His-tagged GSK3β in 25 mM HEPES (pH 7.7), 1 mM EDTA, 300 mM NaCl, 10 mM MgCl2, 1 mM DTT, and 1 mM ATP for 1 h at room temperature with shaking. The beads were washed three times with 25 mM HEPES (pH 7.7), 1 mM EDTA, 300 mM NaCl, 1% Tween, and 1 mM DTT and were then used to pull down β-catenin. Extracts (50 μl) labeled with [35S]methionine (see above) were diluted 5× with XB containing 1% Tween and protease inhibitors. The diluted extracts were incubated with phosphorylated APCm3 beads (20 μl) at 4°C for 2 h. The beads were washed and bound protein was eluted by boiling in SDS-PAGE loading buffer. Labeled β-catenin was detected following SDS-PAGE and autoradiography.To isolate metabolically labeled β-catenin from 4, and 50 mM NaCl. For the nonphorphorylated control, β-catenin was incubated as above, except that 50 mM LiCl was used instead of NaCl to inhibit GSK3β. The kinase reactions were incubated in a shaker for 30 min at 20°C and then added to 50 μl of MBP–axin, bound to amylose beads (1 mg of protein per milliliter of beads), and brought up to 250 μl with XB containing 50 mM LiCl. After phorsphorylated and nonphosphorylated β-catenin, respectively, bound to axin beads, the beads were washed three times with 500 μl of XB containing 50 mM LiCl. Dissociation of the bound β-catenin was initiated by adding 1 μM unlabeled recombinant β-catenin  and incubated at 20°C in a shaker. At the appropriate times, 5 μl aliquots of beads were quickly removed, filtered through Wizard minicolumns , and washed with ice-cold XB (3 ml). Proteins bound to beads were eluted from the minicolumns with 20 μl of hot sample buffer, followed by SDS-PAGE and autoradiography.Radiolabeled β-catenin (5 μl) was phosphorylated using 300 nM His-tagged GSK3β and 100 nM maltose-binding protein (MBP)–axin in 20 μl of XB containing 10 mM ATP, 20 mM MgSOSf9 cells.The expression and purification of all recombinant proteins have been previously described . Dsh wasDataset S1(287 KB DOC).Click here for additional data file.Figure S1W of Wnt stimulation. Curve a: free unphosphorylated β-catenin; curve b: free phosphorylated β-catenin; curve c: total β-catenin; curve d: total axin. All concentrations are scaled with respect to their values in the reference state. It is worth mentioning that in the model “without regulatory loop,” the steady-state concentration of free axin is determined by the condition X12 =ν14/k15, and is, therefore, independent of Wnt stimulation.The curves represent steady-state concentrations of β-catenin (solid lines) and axin (broken lines) as functions of the strength .Click here for additional data file.Figure S2W = 1. All concentrations and synthesis rates are scaled with respect to their values in the stimulated stationary state.This figure gives additional information with respect to the effects of Dsh, TCF, and GSK3β on the steady-state concentrations of total β-catenin (solid lines) and total axin (dashed lines) for the case of permanent Wnt-stimulation, .Click here for additional data file.Figure S3The curves represent steady-state values of total concentrations of β-catenin (solid lines) and axin (dashed lines), depending on the rates of synthesis of β-catenin and axin. All concentrations and synthesis rates are scaled with respect to their values in the stimulated stationary state..Click here for additional data file.Table S1(45 KB DOC).Click here for additional data file.Table S2W ≠ 0. Note that some of the numerical values are given in a higher precision compared to The rate constants marked with “#” play a role only in stimulated states where (111 KB DOC).Click here for additional data file.


Mometasone furoate (MF) is a highly potent glucocorticoid used topically to treat inflammation in the lung, nose and on the skin. However, so far no information has been published on the human glucocorticoid receptor activity of the metabolites or degradation products of MF. We have now determined the relative receptor binding affinities of the known metabolite 6β-OH MF and the degradation product 9,11-epoxy MF to understand their possible contribution to undesirable systemic side effects. In competition experiments with human lung glucocorticoid receptors we have determined the relative receptor affinities (RRA) of these substances with reference to dexamethasone (RRA = 100). We have discovered that 6β-OH MF and 9,11-epoxy MF display RRAs of 206 ± 15 and 220 ± 22, respectively. This level of activity is similar to that of the clinically used inhaled corticosteroid flunisolide (RRA 180 ± 11). Furthermore we observed that 9,11-epoxy MF is a chemically reactive metabolite. In recovery experiments with human plasma and lung tissue we found a time dependent decrease in extractability of the compound. Hence, we provide data that might contribute to the understanding of the pharmacokinetics as well as the clinical effects of MF. Mometasone furoate (MF) is a highly potent topical glucocorticoid for the treatment of asthma , allergiBesides the efficacy of a corticosteroid, safety issues have to be taken into consideration. For topically applied glucocorticoids, the high local anti-inflammatory activity should be paralleled by a low systemic exposure. Therefore, a prolonged redistribution from lung tissue into systemic circulation and a rapid and complete hepatic metabolism of the compounds to inactive derivatives are favorable. For MF, a very low systemic bioavailability of less than 1 % has been reported . HoweverThere had been, however, not much information on the extent and site of metabolite formation in humans. Recent studies now provided some of the required information ,13,15,16Despite the recent discovery of the major metabolite 6β-OH MF and the abundant degradation product 9,11-epoxy MF it is still not clear whether these compounds retain any significant binding affinity to the human glucocorticoid receptor. In the present study we addressed this open question and we present some evidence that the degradation product might bind tightly, most possibly covalently, to protein structures in human lung tissue and plasma.3H]-Dexamethasone was obtained from Amersham . All other chemicals were obtained from Sigma-Aldrich-Chemie  or E. Merck .Mometasone furoate (MF), 6-hydroxy mometasone furoate (6-OH MF), mometasone and 9,11-epoxy mometasone furoate  were generous gifts from GlaxoSmithKline .  labelled dexamethasone by various concentrations of 6-OH MF, mometasone and 9,11-epoxy MF was determined.The competition experiments were performed according to the procedure described earlier . The disMF or 9,11-epoxy MF, respectively, were added to human plasma, lung tissue suspension (0.5 g / 20 ml) or buffer  yielding an initial concentration of 0.3 μg/ml. Only glass lab ware was used for these experiments to exclude any non-specific binding effects of the highly lipophilic compounds to plastic material. Samples were incubated at 37°C in a shaking water bath. At designated time intervals samples of 1.0 ml were removed, subjected to a fluid extraction with diethylether and analyzed by HPLC.18 column .Samples were prepared and analyzed as described previously . The HPLWe determined the relative receptor affinities (RRAs) of 6β-OH MF, 9,11-epoxy MF and mometasone base by competition assays with reference to dexamethasone (RRA = 100). Both, the metabolite 6β-OH MF and the degradation product 9,11-epoxy MF displayed residual receptor binding affinities about twice as high as dexamethasone  metabolite 6β-OH MF and its degradation product 9,11-epoxy MF to understand their possible contribution to undesirable systemic side effects. For the first time we provide data that both compounds are significantly active at the human glucocorticoid receptor with binding affinities twice as high as dexamethasone and similar to that of the clinically used inhaled corticosteroids flunisolide and triamcinolone acetonide . Furtherin vivo formation of these compounds was still lacking. Studies of Teng et al. identified 6β-OH MF and 9,11-epoxy MF as candidate compounds that can indeed be formed in vivo either by hepatic metabolism or by simple degradation of MF [Glucocorticoids currently used for topical application in asthma therapy all share the safety relevant property of extensive metabolism and formation of inactive metabolites. For MF, however, data was sparse so far. Though putative metabolites and degradation products with binding affinity to the rat glucocorticoid receptor have been previously suggested , it was on of MF ,16. We don of MF .Usually hydroxylation at the 6β position results in inactivation of the corticosteroid. The 6-OH metabolite of various glucocorticoids displays little or no residual binding affinity to the receptor (e.g.) ,18. Thiset al. [The MF degradation product 9,11-epoxy MF also displays a significant receptor binding affinity with an RRA of about 200. This RRA is within the range that could be expected from the studies of Isogai et al. . Since 9et al. , it can Besides the significant residual receptor binding affinity of 9,11-epoxy MF we discovered that this compound undergoes follow-up reactions. After incubation with plasma clearly less of 9,11-epoxy MF compared to the parent compound MF was recovered by extraction with an organic solvent. This extraction procedure usually reliably retrieves all non-covalently bound substance from the incubation mixture. In human lung tissue, it was even more obvious that 9,11-epoxy MF was recovered completely from buffer, but not from the tissue suspension. About 17 % of 9,11-epoxy MF was "lost" after three hours of incubation. This observation cannot be explained by simple non-specific tissue binding since the tissue adsorption reaches equilibrium very quickly after about 20 min  seems toIn contrast to other inhaled corticosteroids MF generates an active metabolite, 6β-OH MF, in the liver. The degradation product 9,11-epoxy MF, which is formed in human lung tissue and plasma, exhibits significant receptor affinity as well. Additionally, we found that 9,11-epoxy MF undergoes follow-up reactions. Our data contribute to the understanding of how the claimed low bioavailability of MF parent compound after inhalation might still be accompanied by HPA axis suppression. Thus, our findings are consistent with both pharmacokinetic and clinical data. We strongly suggest a clinical trial that determines both efficacy and safety in parallel as well as all known metabolites and degradation products after application of MF.AV carried out all experiments and the data analysis and participated in the design of the study. PH conceived of and designed the study and wrote the manuscript. All authors read and approved the final manuscript.


Isolation and separation of specific molecules is used in almost all areas of biosciences and biotechnology. Diverse procedures can be used to achieve this goal. Recently, increased attention has been paid to the development and application of magnetic separation techniques, which employ small magnetic particles. The purpose of this review paper is to summarize various methodologies, strategies and materials which can be used for the isolation and purification of target proteins and peptides with the help of magnetic field. An extensive list of realised purification procedures documents the efficiency of magnetic separation techniques. Isolation, separation and purification of various types of proteins and peptides, as well as of other specific molecules, is used in almost all branches of biosciences and biotechnologies. Separation science and technology is thus very important area necessary for further developments in bio-oriented research and technology. New separation techniques, capable of treating dilute solutions or solutions containing only minute amounts of target molecules in the presence of vast amounts of accompanying compounds in both small and large-scale processes, even in the presence of particulate matter, are necessary.In the area of biosciences and biotechnology the isolation of proteins and peptides is usually performed using variety of chromatography, electrophoretic, ultrafiltration, precipitation and other procedures, affinity chromatography being one of the most important techniques. Affinity ligand techniques represent currently the most powerful tool available to the downstream processing both in term of their selectivity and recovery. The strength of column affinity chromatography has been shown in thousands of successful applications, especially in the laboratory scale. However, the disadvantage of all standard column liquid chromatography procedures is the impossibility of the standard column systems to cope with the samples containing particulate material so they are not suitable for work in early stages of the isolation/purification process where suspended solid and fouling components are present in the sample. In this case magnetic affinity, ion-exchange, hydrophobic or adsorption batch separation processes, applications of magnetically stabilized fluidized beds or magnetically modified two-phase systems have shown their usefulness.The basic principle of batch magnetic separation is very simple. Magnetic carriers bearing an immobilized affinity or hydrophobic ligand or ion-exchange groups, or magnetic biopolymer particles having affinity to the isolated structure, are mixed with a sample containing target compound(s). Samples may be crude cell lysates, whole blood, plasma, ascites fluid, milk, whey, urine, cultivation media, wastes from food and fermentation industry and many others. Following an incubation period when the target compound(s) bind to the magnetic particles the whole magnetic complex is easily and rapidly removed from the sample using an appropriate magnetic separator. After washing out the contaminants, the isolated target compound(s) can be eluted and used for further work.Magnetic separation techniques have several advantages in comparison with standard separation procedures. This process is usually very simple, with only a few handling steps. All the steps of the purification procedure can take place in one single test tube or another vessel. There is no need for expensive liquid chromatography systems, centrifuges, filters or other equipment. The separation process can be performed directly in crude samples containing suspended solid material. In some cases  it is even possible to integrate the disintegration and separation steps and thus shorten the total separation time . Due to Magnetic separation is usually very gentle to the target proteins or peptides. Even large protein complexes that tend to be broken up by traditional column chromatography techniques may remain intact when using the very gentle magnetic separation procedure . Both thSeparation of target proteins using standard chromatography techniques often leads to the large volume of diluted protein solution. In this case appropriate magnetic particles can be used for their concentration instead of ultrafiltration, precipitation etc. .The purpose of this review is to summarize various methodologies and strategies which can be employed for the isolation and purification of target proteins and peptides with the help of magnetic materials. An extensive list of realised purification procedures documents the efficiency of magnetic separation techniques. All these information will help the scientists to select the optimal magnetic material and the purification procedure.The basic equipment for laboratory experiments is very simple. Magnetic carriers with immobilized affinity or hydrophobic ligands, magnetic particles prepared from a biopolymer exhibiting affinity for the target compound(s) or magnetic ion-exchangers are usually used to perform the isolation procedure. Magnetic separators of different types can be used for magnetic separations, but many times cheap strong permanent magnets are equally efficient, especially in preliminary experiments.Magnetic carriers and adsorbents can be either prepared in the laboratory, or commercially available ones can be used. Such carriers are usually available in the form of magnetic particles prepared from various synthetic polymers, biopolymers or porous glass, or magnetic particles based on the inorganic magnetic materials such as surface modified magnetite can be used. Many of the particles behave like superparamagnetic ones responding to an external magnetic field, but not interacting themselves in the absence of magnetic field. This is important due to the fact that magnetic particles can be easily resuspended and remain in suspension for a long time. In most cases, the diameter of the particles differs from ca 50 nm to approx. 10 μm. However, also larger magnetic affinity particles, with the diameters up to millimetre range, have been successfully used [lly used . MagnetiCommercially available magnetic particles can be obtained from a variety of companies. In most cases polystyrene is used as a polymer matrix, but carriers based on cellulose, agarose, silica, porous glass or silanized magnetic particles are also available. Examples of magnetic particles used (or usable) for proteins and peptides separation can be found elsewhere -7.Particles with immobilised affinity ligands are available for magnetic affinity adsorption. Streptavidin, antibodies, protein A and Protein G are used most often in the course of protein and peptides isolation. Magnetic particles with above mentioned immobilised ligands can also serve as generic solid phases to which native or modified affinity ligands can be immobilised .2 are used for immobilisation, in some cases magnetic particles are available already in the activated form .Also some other affinity ligands  are already immobilised to commercially available carriers. To immobilise other ligands of interest to both commercial and laboratory made magnetic particles standard procedures used in affinity chromatography can be employed. Usually functional groups available on the surface of magnetic particles such as -COOH, -OH or -NHIn the laboratory magnetite  particles can be surface modified by silanization. This process modifies the surface of the inorganic particles so that appropriate functional groups become available, which enable easy immobilisation of affinity ligands . In exceBiopolymers such as agarose, chitosan, kappa carrageenan and alginate can be easily prepared in a magnetic form. In the simplest way the biopolymer solution is mixed with magnetic particles and after bulk gel formation the magnetic gel formed is mechanically broken into fine particles . AlternaBasically the same procedures can be used to prepare magnetic particles from synthetic polymers such as polyacrylamide, poly and many others .In another approach used standard affinity or ion-exchange chromatography material was post-magnetised by interaction of the sorbent with water-based ferrofluid. Magnetic particles accumulated within the pores of chromatography adsorbent thus modifying this material into magnetic form ,13. AlteMagnetoliposomes (magnetic derivatives of standard liposomes), either in the original form or after immobilization of specific proteins, have the potential for the separation of antiphospholipid antibodies , IgG antRecently also non-spherical magnetic structures, such as magnetic nanorods have been tested as possible adsorbent material for specific separation of target proteins .Magnetic separators are necessary to separate the magnetic particles from the system. In the simplest approach, a small permanent magnet can be used, but various magnetic separators employing strong rare-earth magnets can be obtained at reasonable prices. Commercial laboratory scale batch magnetic separators are usually made from magnets embedded in disinfectant-proof material. The racks are constructed for separations in Eppendorf micro-tubes, standard test tubes or centrifugation cuvettes, some of them have a removable magnetic plate to facilitate easy washing of separated magnetic particles. Other types of separators enable separations from the wells of microtitration plates and the flat magnetic separators are useful for separation from larger volumes of suspensions (up to approx. 500 – 1000 ml). Examples of typical batch magnetic separators are shown in Fig. Flow-through magnetic separators are usually more expensive, and high gradient magnetic separators (HGMS) are the typical examples. Laboratory scale HGMS is composed from a column packed with fine magnetic grade stainless steel wool or small steel balls which is placed between the poles of an appropriate magnet. The suspension is pumped through the column, and magnetic particles are retained within the matrix. After removal the column from the magnetic field, the particles are retrieved by flow and usually by gentle vibration of the column.For work in dense suspensions, open gradient magnetic separators may be useful. A very simple experimental set-up for the separation of magnetic affinity adsorbents from litre volumes of suspensions was described .Currently many projects require the analysis of a high number of individual proteins or variants. Therefore, methods are required that allows multiparallel processing of different proteins. There are several multiple systems for high throughput nucleic acid and proteins preparation commercially available. The most often used approach for proteins isolation is based on the isolation and assay of 6xHis-tagged recombinant proteins using magnetic beads with Ni-nitriloacetic acid ligand . The comMagnetic separations of proteins and peptides are usually convenient and rapid. Nevertheless, several hints may be helpful to obtain good results.Proteins and peptides in the free form can be directly isolated from different sources. Membrane bound proteins have to be usually solubilized using appropriate detergents. When nuclei are broken during sample preparation, DNA released into the lysate make the sample very viscous. This DNA may be sheared by repeated passage up and down through a 21 gauge hypodermic syringe needle before isolation of a target protein. Alternatively, DNase can be added to enzymatically digest the DNA.Magnetic beads in many cases exhibit low non-specific binding of non-target molecules present in different samples. Certain samples may still require preclearing to remove molecules which have high non-specific binding activity. If preclearing is needed, the sample can be mixed with magnetic beads not coated with the affinity ligand. In the case of immunomagnetic separation, magnetic beads coated with secondary antibody or with irrelevant antibodies have been used. The non-specific binding can also be minimised by adding a non-ionic detergent both in the sample and in the washing buffers after isolation of the target.In general, magnetic affinity separations can be performed in two different modes. In the direct method, an appropriate affinity ligand is directly coupled to the magnetic particles or biopolymer exhibiting the affinity towards target compound(s) is used in the course of preparation of magnetic affinity particles. These particles are added to the sample and target compounds then bind to them. In the indirect method the free affinity ligand (in most cases an appropriate antibody) is added to the solution or suspension to enable the interaction with the target compound. The resulting complex is then captured by appropriate magnetic particles. In case antibodies are used as free affinity ligands, magnetic particles with immobilised secondary antibodies, protein A or protein G are used for capturing of the complex. Alternatively the free affinity ligands can be biotinylated and magnetic particles with immobilised streptavidin or avidin are used to capture the complexes formed. In both methods, magnetic particles with isolated target compound(s) are magnetically separated and then a series of washing steps is performed to remove majority of contaminating compounds and particles. The target compounds are then usually eluted, but for specific applications  they can be used still attached to the particles, such as in the case of polymerase chain reaction, magnetic ELISA etc.The two methods perform equally well, but, in general, the direct technique is more controllable. The indirect procedure may perform better if affinity ligands have poor affinity for the target compound.In most cases, magnetic batch adsorption is used to perform the separation step. This approach represents the simplest procedure available, enabling to perform the whole separation in one test-tube or flask. If larger magnetic particles (with diameters above ca 1 μm) are used, simple magnetic separators can be employed. In case magnetic colloids (diameters ranging between tens and hundreds of nanometres) are used as affinity adsorbents, high-gradient magnetic separators have usually to be used to remove the magnetic particles from the system.Alternatively magnetically stabilised fluidised beds (MSFB), which enable a continuous separation process, can be used. The use of MSFB is an alternative to conventional column operation, such as packed-bed or fluidised bed, especially for large-scale purification of biological products. Magnetic stabilisation enables the expansion of a packed bed without mixing of solid particles. High column efficiency, low pressure drop and elimination of clogging can be reached ,22.Also non-magnetic chromatographic adsorbents can be stabilized in magnetically stabilized fluidized beds if sufficient amount of magnetically susceptible particles is also present. The minimum amount of magnetic particles necessary to stabilize the bed is a function of various parameters including the size and density of both particles, the magnetic field strength, and the fluidization velocity. A variety of commercially available affinity, ion-exchange, and adsorptive supports can be used in the bed for continuous separations .Biocompatible two phase systems, composed for example from dextran and polyethylene glycol, are often used for isolation of biologically active compounds, subcellular organelles and cells. One of the disadvantages of this system is the slow separation of the phases when large amounts of proteins and cellular components are present. The separation of the phases can be accelerated by the addition of fine magnetic particles or ferrofluids to the system followed by the application of a magnetic field. This method seems to be useful when the two phases have very similar densities, the volumetric ratio between the phases is very high or low, or the systems are viscous. Magnetically enhanced phase separation usually increases the speed of phase separation by a factor of about 10 in well-behaved systems, but it may increase by a factor of many thousands in difficult systems. The addition of ferrofluids and/or iron oxide particles was shown to have usually no influence on enzyme partioning or enzyme activity ,25.Proteins and peptides isolated using magnetic techniques have to be usually eluted from the magnetic separation materials. In most cases bound proteins and peptides can be submitted to standard elution methods such as the change of pH, change of ionic strength, use of polarity reducing agents  or the use of deforming eluents containing chaotropic salts. Affinity elution  may be both a very efficient and gentle procedure.Magnetic affinity and ion-exchange separations have been successfully used in various areas, such as molecular biology, biochemistry, immunochemistry, enzymology, analytical chemistry, environmental chemistry etc -29. TablIn the case of proteins and peptides purifications, no simple strategy for magnetic affinity separations exists. Various affinity ligands have been immobilised on magnetic particles, or magnetic particles have been prepared from biopolymers exhibiting the affinity for target enzymes or lectins. Immunomagnetic particles, i.e. magnetic particles with immobilised specific antibodies against the target structures, have been used for the isolation of various antigens, both molecules and cells  and can Magnetic separation procedures can be employed in several ways. Preparative isolation of the target protein or peptide is usually necessary if further detailed study is intended. In other cases, however, the magnetic separation can be directly followed (after elution with an appropriate buffer) with SDS electrophoresis. Magnetically separated proteins and peptides can also be used for further mass spectroscopy characterization ,31. The Enzyme isolation is usually performed using immobilised inhibitors, cofactors, dyes or other suitable ligands, or magnetic beads prepared from affinity biopolymers can be used  are often short-lived and in low abundance. A rapid and sensitive method, based on the immobilization of biotinylated DNA/RNA fragments containing the specific binding sequence to the magnetic streptavidin particles, can be used. The bound DNA/RNA binding proteins are usually eluted with high salt buffer or change of pH .Sc from its conformer which is a cellular protein called PrPC. In fact, plasminogen represents the first endogenous factor discriminating between normal and pathological prion protein. This unexpected property may be exploited for diagnostic purposes [Other types of proteins were isolated using specific affinity-based procedures. For example, plasminogen immobilized on magnetic particles was used to separate scrapie and bovine spongiform encephalopathy associated prion protein PrPpurposes ,40.Magnetic separation was also successfully used for the recovery of proteins expressed in the form of inclusion bodies, involving at first chemical extraction from the host cells, then adsorptive capture of the target protein onto small magnetic adsorbents, followed by rapid collection of the product-loaded supports with the aid of high gradient magnetic fields .A new approach for analytical ion-exchange separation of native proteins and proteins enzymatic digest products has been described recently . MagnetiMagnetic solid phase extraction (MSPE) enables to preconcentrate target analytes from larger volumes of solutions or suspensions using relatively small amount of magnetic specific adsorbent. Up to now this procedure was used for preconcentration of low-molecular weight xenobiotics ,43 but uXenopus egg extracts for analyses of the cell mitosis mechanisms [Sometimes the removal of certain proteins will reveal functions involving the depleted proteins or will help in the course of subsequent protein isolation. As an example, Dynabeads have been used to remove involved proteins from chanisms ,45. Rapichanisms .A combination of mechanical cell disintegration and magnetic batch affinity adsorption was used to simplify the isolation of intracellular proteins. Magnetic glass beads were used because of their hardness and rigidity .Dictyostelium discoideum were separated after magnetic isolation of the vesicles that was accomplished by feeding the amoebae with dextran-stabilized iron oxide particles. The cells were broken, the labelled vesicles were magnetically separated and then disrupted to release proteins which were resolved by SDS-PAGE. After „in-gel“ digestion with endoproteinase Lys-C or Asp-N the generated peptides were used for amino acid sequencing. This strategy allowed the identification of the major protein constituents of the vesicles [An example of quite different protein purification strategy can also be mentioned. Proteins associated with the endocytic vesicles of vesicles . Analogovesicles .Standard liquid column chromatography is currently the most often used technique for the isolation and purification of target proteins and peptides. Magnetic separation techniques are relatively new and still under development. Magnetic affinity particles are currently used mainly in molecular biology , cell biology and microbiology (separation of target cells) and as parts of the procedures for the determination of selected analytes using magnetic ELISA and related techniques . Up to now separations in small scale prevail and thus the full potential of these techniques has not been fully exploited.It can be expected that further development will be focused at least on two areas. The first one will be focused on the laboratory scale application of magnetic affinity separation techniques in biochemistry and related areas (rapid isolation of a variety of both low- and high-molecular weight substances of various origin directly from crude samples thus reducing the number of purification steps) and in biochemical analysis (application of immunomagnetic particles for separation of target proteins from the mixture followed by their detection using ELISA and related principles). Such a type of analysis will enable to construct portable assay systems enabling e.g. near-patient analysis of various protein disease markers. New methodologies, such as the application of chip and microfluidics technologies, may result in the development of magnetic separation processes capable of magnetic separation and detection of extremely small amount of target biologically active compounds .In the second area, larger-scale  systems are believed to be developed and used for the isolation of biologically active compounds directly from crude culture media, wastes from food industry etc., integrating three classical steps  into a single unit operation . It is nIn the near future quite new separation strategies can appear. A novel magnetic separation method, which utilizes the magneto-Archimedes levitation, has been described recently and applied to separation of biological materials. By using the feature that the stable levitation position under a magnetic field depends on the density and magnetic susceptibility of materials, it was possible to separate biological materials such as haemoglobin, fibrinogen, cholesterol, and so on. So far, the difference of magnetic properties was not utilized for the separation of biological materials. Magneto-Archimedes separation may be another way for biological materials separation .It can be expected that magnetic separations will be used regularly both in biochemical laboratories and biotechnology industry in the near future.


Magnetic nanoparticles have been significantly used for coupling with biomolecules, due to their unique properties.Magnetic nanoparticles were synthesized by thermal co-precipitation of ferric and ferrous chloride using two different base solutions. Glucose oxidase was bound to the particles by direct attachment via carbodiimide activation or by thiophene acetylation of magnetic nanoparticles. Transmission electron microscopy was used to characterize the size and structure of the particles while the binding of glucose oxidase to the particles was confirmed using Fourier transform infrared spectroscopy.The direct binding of glucose oxidase via carbodiimide activity was found to be more effective, resulting in bound enzyme efficiencies between 94–100% while thiophene acetylation was 66–72% efficient. Kinetic and stability studies showed that the enzyme activity was more preserved upon binding onto the nanoparticles when subjected to thermal and various pH conditions. The overall activity of glucose oxidase was improved when bound to magnetic nanoparticlesBinding of enzyme onto magnetic nanoparticles via carbodiimide activation is a very efficient method for developing bioconjugates for biological applications The immobilization of biomolecules onto insoluble supports is an important tool for the fabrication of a diverse range of functional materials or devices . Enzyme In the last decade, nanosize materials have been widely used as support for this purpose. Among these materials, magnetic nanoparticles are very popular when used in conjunction with biological materials including proteins, peptides, enzymes -9 antibo3O4) are biocompatible superparamagnetic materials that have low toxicity and strong magnetic properties [in vivo examination including magnetic resonance imaging, contrast enhancement, tissue specific release of therapeutic agents, hyperthermia [in vitro binding of proteins and enzymes [Magnetite  is a homodimer flavoprotein containing two active sites per molecule [Magnetite nanoparticles have been used as support material for binding of enzymes including yeast alcohol dehydrogenase  and lipamolecule ,13. It cmolecule ,14,15. Amolecule  examined3O4 magnetic nanoparticles using two binding methods, the direct binding via carbodiimide activation of amino functionalized particles and binding to thiophene-functionalized acetylated nanoparticles. A comparison of the stability and activity of glucose oxidase immobilized to magnetite using different protocols will lay the foundation for magnetic immunoassays. The size and structure of the nanoparticles were characterized using Transmission electron microscopy (TEM) and Fourier Transform Infrared (FTIR) spectroscopy, respectively. The stability, activity, and kinetic behavior of bound glucose oxidase were also examined.Here, we report the stability and enzymatic activity of glucose oxidase immobilized onto FeAspergillus niger was purchased from VWR international . Carbodiimide-HCl (1-ethyl-3-(3-dimethyl-aminopropyl), ammonium hydroxide, sodium hydroxide, acetic anhydride, glucose, bovine serum albumin (BSA), iron (II) chloride tetrahydrate 97 % and iron (III) chloride hexahydrate 99%, were obtained from Sigma-Aldrich St Louis (USA). 11-bromoundecanoic acid was obtained from TCI America Portland, USA. The Biorad Protein Assay Reagent Concentrate was purchased from Biorad Laboratories . Thiophene-2-thiolate was obtained from Alfa Aesar MA, USA. Iodine was obtained from Mallinckrodt Kentucky, USA, and acetonitrile was obtained from EMD Chemicals . Sodium phosphate monohydrate and potassium phosphate dihydrate were acquired from EM Science . Sodium carbonate was obtained from Orion Research Inc. . Magnetic nanoparticles (Fe3O4) were prepared by chemical co-precipitation of Fe2+ and Fe3+ ions in a solution of ammonium hydroxide (magnetic nanoparticles I or Fe3O4 I), or sodium hydroxide (magnetic nanoparticles II or Fe3O4 II) followed by a treatment under hydrothermal conditions [4OH solution (30%) or NaOH 3 M at a pH 10. The precipitates were heated at 80°C for 35 min under continuous mixing and washed 4 times in water and several times in ethanol. During washing, the magnetic nanoparticles were separated from the supernatant using a magnetic separator of strength greater than 20 megaoersted (MOe). The particles were finally dried in a vacuum oven at 70°C. The dried particles exhibited a strong magnetic attraction.Glucose oxidase (specific activity 200 units/mg protein) from cles Fe3O were prenditions . Iron (I3O4 nanoparticles I and Fe3O4 bound glucose oxidase (GOX-Fe3O4 I) were washed with phosphate buffer pH 7.4 and 0.1 M Tris, pH 8.0, and then used for activity and stability measurements. NaCl was added to enhance the separation of the magnetic nanoparticles [Magnetic nanoparticles I (50 mg) produced, using a solution of ammonium hydroxide were added to 1 mL of phosphate buffer (0.05 M. pH 7.4). After adding 1 mL of carbodiimide solution (0.02 g/mL) in phosphate buffer (0.05 M. pH 7.4), the mixture was sonicated for 15 min. Following the carbodiimide activation, 2 mL of glucose oxidase (1000 units /mL) was added and the reaction mixture was sonicated for 30 min at 4°C in a sonication bath. The magnetic nanoparticles were separated from the mixture using a magnetic separator. The precipitates containing FeCandida rugosa lipase on the γ-Fe2O3[3O4 was added to 5 g of 11-bromoundecanoic acid dissolved in 15 mL of ethanol. 11-bromoundecanoic acid was covalently linked to the nanoparticles surfaces by heating the mixture with microwave irradiation for 10 min. Functionalization of the particle was achieved through nucleophilic substitution with the 2-thiophene thiolate. In practice, 2-thiophene thiolate (7 mL) was added to the mixture containing the particles and heated in microwave for 5 minutes. The mixture was washed with ethanol and transferred in a round bottom flask. Acetic anhydride (4 mL) and 34.6 mL of iodine (0.01N) were successively added to the particles and agitated. The mixture was heated for 1 h under reflux condition [A second functionalization protocol using a modification of the strategy adopted to immobilize e γ-Fe2O3 was implondition . The parFor the attachment of glucose to nanoparticles, 2 mL of the GOX solution (1000 units/mL) was added to 50 mg of functionalized magnetic nanoparticles in a test tube and sonicated at 15°C for 3 h. The supernatant containing unbound enzymes was separated from the magnetic nanoparticles using the magnetic separator, and the enzymes bound to magnetic nanoparticles were then used for activity determination. A schematic of the procedures used for both attachments are presented in Figure A = (Ci - Cs)* V     (1)A is the amount of bound enzyme, Ci and Cs are the concentration of the enzyme initially added for attachment and in the supernatant, respectively (mg/mL) and V is the volume of the reaction medium (mL). The size of Fe3O4 magnetic nanoparticles, GOX-Fe3O4 I and GOX-Fe3O4 II were characterized by transmission electron microscopy  and structure by FTIR spectroscopy . The samples for TEM analysis were prepared as follows: a drop of magnetic nanoparticles was dispersed in nanopure water. The resulting solution was sonicated for 4 min to obtain better particle dispersion. A drop of the dispersed solution was then deposited onto a copper grid and dried overnight at room temperature. The binding of GOX onto the magnetic nanoparticles was investigated using FTIR spectroscopy. Samples for FTIR analysis were prepared in phosphate buffer pH 7.4. The activity of bound GOX was determined by measuring the initial rate of formation of hydrogen peroxide at a given temperature following the formation of a red quinoneimine dye. The principle of enzymatic determination of the activity of glucose oxidase is described as follows: Glucose is oxidized by glucose oxidase to gluconate and hydrogen peroxide. Phenol + 4-AAP, in the presence of peroxidase (POX), produces a quinoneimine dye that is measured at 500 nm using a Beckman Du Spectrometer to provide an absorbance that is proportional to the concentration of glucose in the sample. The reaction is described as follows:Where 3O4 and mixed by vortex. A solution of free GOX of the same molar concentration was used to evaluate the activity of the free enzyme for comparison. The solution was incubated at various temperatures (37–80°C) at specific intervals of time (30 min) and the supernatant was separated from GOX-Fe3O4 using a magnetic separator. 10 μL aliquots of the supernatant were then taken for determining the concentration of hydrogen peroxide following the procedure by Trinder [The activity of glucose oxidase was measured as follows. An assay mixture was prepared by mixing 500 U of horseradish peroxidase, 0.015 mmol of 4-aminoantipyrine (4-AAP), 0.025 mmol of phenol and 5 mmol of glucose in 50 mL of phosphate buffer solution (0.05 M. pH 7.4) to result in a glucose concentration of 0.1 M. To start the enzymatic reaction, 2 mL of the assay solution was added to 15 mL centrifuge test tubes containing GOX-Fe Trinder . The actABS sample denotes the absorbance of the sample, ABS Std is the absorbance of the standard solution, and C the concentration of glucose in the sample.Where 3O4 I and GOX-Fe3O4 II was estimated by determining the concentration of glucose in the sample at various temperatures. A solution of the assay mixture was added to the various centrifuge test tubes containing bound or free enzymes. The samples were stored in a water bath at specific temperatures  and the absorbance was monitored at fixed time intervals to determine the glucose content. The effect of pH on GOX was monitored by measuring the initial rate of glucose oxidation by glucose oxidase in different phosphate and carbonate buffer solutions of pH (5–10) at 25°C.The effect of temperature on the free GOX, GOX-Fe3O4 I, and GOX-Fe3O4 II were determined by measuring the residual activity of the enzyme at 25°C, after being exposed to different temperatures (37–80°C) in phosphate buffer  for 30 min. Aliquots of the reacting solutions were taken at periodic intervals (every 30 min for 6 h) and assayed for enzymatic activity as described above. The first-order inactivation rate constant, k was calculated from the equation:The thermal stability of free GOX, GOX-FeA = ln A0 - kt     (5)ln A0 is the initial activity, A is the activity after time t (min) and k is the reaction constant.where 3O4 I, GOX-Fe3O4 II, or free GOX solutions were stored at 25°C in phosphate buffer (0.05 M. pH 7.4) for 33 days. Thereafter, 3 mL of the assay solution was added, and the residual activity of GOX was assayed.The storage stability was examined by measuring the change in the concentration of glucose at room temperature at different time intervals (4 days). Test tubes with samples of GOX-Fe3O4 I and GOX-Fe3O4 II, Km and Vmax were determined by measuring the initial rates of glucose oxidation (0.2–1 mM) by glucose oxidase (0.25 mg/mL) in phosphate buffer (pH 7.4) at 25°C.The kinetic parameters of free GOX, GOX-Fe3O4 I and Fe3O4 II, and their GOX bound counterparts shown in the TEM micrographs in Figures  were estimated from the double reciprocal plots of the initial rates of glucose oxidation by GOX. The double reciprocal plots are presented in Figure Vmax and Km for GOX are shown in Table Vmax of free GOX, GOX- Fe3O4 I and GOX-Fe3O4 II were 0.731, 0.803, and 0766 μmol/min mL and, the corresponding Km values were, 0.383, 0.208, and 0.237 mM, respectively. The Vmax value of GOX immobilized on magnetic nanoparticles (I and II) was higher than that of the free enzyme. The highest Vmax was obtained with GOX-nanoparticles I. Since a low Km indicates a high degree of affinity of the enzyme to substrate [3O4 II and GOD-Fe3O4 I, respectively. The high affinity of the enzyme to the substrate may be explained by a favorable change in the structural organization of the enzyme due to the immobilization procedure [The most important aspect of this study is related to the retention of biocatalytical activity of GOX after binding to magnetic nanoparticles. The amount of bound GOX was estimated using the UV-vis spectrophotometer and the catalytic activity of free and bound GOX was compared. Kinetic parameters . It can be observed that at 37°C, the enzyme retained its activity for about 80 minutes before showing a slight decrease. At 50, 60, 70 and 80°C the activity decreased as the temperature increased in both systems. In GOX- Fe3O4, the remaining activity was 23% at 50°C and 15% at 60°C after 270 min. For this time period and duration, the remaining activities were 9% and 0%, respectively for GOX-Fe3O4 II. A similar trend was observed at 70 and 80°C with a more drastic loss of activity from the GOX-Fe3O4 II protocol. Loss of activity occurred more rapidly in GOX-Fe3O4 II indicating that direct binding through carbodiimide activation provides a greater thermal stability to GOX. The effect of temperature on the activities of free, GOX-Fe3O4 I, and GOX-Fe3O4 II at pH 7.4 are presented in the Arrhenius plots  at 50, 60 70, and 80°C. The rate constants increased with increasing temperature in the order GOX-Fe3O4 I, GOX-Fe3O4 II and free GOX. Here again, binding GOX to magnetic nanoparticles minimized structural denaturation due to heat treatment. Covalent binding was expected to provide the enzyme with the protection against structural denaturation due to the unfavorable solvent-protein interactions, and thus result in activation effect [3O4 II had a lower stability at higher temperatures compared to GOX-Fe3O4 I. The reason for this difference could reside in the stability of the binding, since the binding methods are so far the major difference between these systems. Indeed with GOX-Fe3O4 I, the binding of the enzyme occurred through the amino groups on the surfaces of the particles and the carboxylic groups of proteins in the enzymes [3O4 II the N atom to which the enzyme is attached shared a double bond with the carbon atom which is less stable than the amide bond.The effect of temperature on the activity of free GOX was examined by measuring its relative activity when stored at various temperatures. Figure n effect , a possi3O4 I, and GOX-Fe3O4 II at 25°C at pH 7.4. Each data point was the average of duplicate measurements (coefficient of variation of the measurements was between 1 and 5%). The activity decreased with time in all the systems. Total loss of activity was observed after 20 days for the free GOX and 28 days for GOX-Fe3O4 II while GOX-Fe3O4 I retained 26% activity after 33 days of storage under identical conditions. The stability of the enzyme was found to improve upon binding to the magnetic nanoparticles but the most significant improvement in stability was observed for the GOX-Fe3O4 I nanoparticle complex. The fixation on the surface of the magnetic nanoparticles has been a tangible argument supporting the prevention of auto-digestion of the enzyme and lysis, and the subsequent conservation of its activity [Loss of storage stability is a major concern in enzyme preservation. The storage stability of the enzyme was examined for 33 days. Figure activity . This maactivity  and a su3O4 II complex. Kinetic and stability studies showed that the enzyme activity was more preserved upon binding onto the nanoparticles when the complex was subjected to thermal and pH variations. This study shows that binding onto magnetic nanoparticles can allow the enzyme to acquire the conformational and structural arrangement for a better activity and stability, and suggests that binding of enzyme onto magnetic nanoparticles via carbodiimide activation was efficient for creating bioconjugates for a variety of applications in health and food safety.Magnetic nanoparticles were synthesized by thermal co-precipitation of ferric and ferrous chlorides using two different base solutions. GOX was bound to the particles by direct attachment via carbodiimide activation and chemically via covalent attachment onto thiophene acetylated magnetic nanoparticles. Confirmation of the binding was demonstrated by FTIR spectroscopy and the sizes of the particles were characterized by TEM. The direct binding of GOX via carbodiimide activation was more effective and resulted in binding efficiency in the range between 94–100% while the binding efficiency was only between 66–72% for the GOX-FeDrs. Gilles Kouassi and Joseph Irudayaraj were the primary authors. They were responsible for the concept and experimental plan of the article. Dr Gregory MacCarty was the secondary author and contributed to the overall effort.