Harmonic oscillator model of the insulin and IGF1 receptors’ allosteric binding and activationстатья из журнала
Аннотация: Article17 February 2009Open Access Harmonic oscillator model of the insulin and IGF1 receptors' allosteric binding and activation Vladislav V Kiselyov Corresponding Author Vladislav V Kiselyov Receptor Systems Biology Laboratory, Hagedorn Research Institute, Gentofte, Denmark Search for more papers by this author Soetkin Versteyhe Soetkin Versteyhe Receptor Systems Biology Laboratory, Hagedorn Research Institute, Gentofte, Denmark Search for more papers by this author Lisbeth Gauguin Lisbeth Gauguin Receptor Systems Biology Laboratory, Hagedorn Research Institute, Gentofte, Denmark Search for more papers by this author Pierre De Meyts Pierre De Meyts Receptor Systems Biology Laboratory, Hagedorn Research Institute, Gentofte, Denmark Search for more papers by this author Vladislav V Kiselyov Corresponding Author Vladislav V Kiselyov Receptor Systems Biology Laboratory, Hagedorn Research Institute, Gentofte, Denmark Search for more papers by this author Soetkin Versteyhe Soetkin Versteyhe Receptor Systems Biology Laboratory, Hagedorn Research Institute, Gentofte, Denmark Search for more papers by this author Lisbeth Gauguin Lisbeth Gauguin Receptor Systems Biology Laboratory, Hagedorn Research Institute, Gentofte, Denmark Search for more papers by this author Pierre De Meyts Pierre De Meyts Receptor Systems Biology Laboratory, Hagedorn Research Institute, Gentofte, Denmark Search for more papers by this author Author Information Vladislav V Kiselyov 1, Soetkin Versteyhe1, Lisbeth Gauguin1 and Pierre De Meyts1 1Receptor Systems Biology Laboratory, Hagedorn Research Institute, Gentofte, Denmark *Corresponding author. Receptor Systems Biology Laboratory, Hagedorn Research Institute, Niels Steensens Vej 6, Gentofte 2820, Denmark. Tel.: +44 420 266; Fax: +45 444 392 03; E-mail: [email protected] Molecular Systems Biology (2009)5:243https://doi.org/10.1038/msb.2008.78 PDFDownload PDF of article text and main figures. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions Figures & Info The insulin and insulin-like growth factor 1 receptors activate overlapping signalling pathways that are critical for growth, metabolism, survival and longevity. Their mechanism of ligand binding and activation displays complex allosteric properties, which no mathematical model has been able to account for. Modelling these receptors' binding and activation in terms of interactions between the molecular components is problematical due to many unknown biochemical and structural details. Moreover, substantial combinatorial complexity originating from multivalent ligand binding further complicates the problem. On the basis of the available structural and biochemical information, we develop a physically plausible model of the receptor binding and activation, which is based on the concept of a harmonic oscillator. Modelling a network of interactions among all possible receptor intermediaries arising in the context of the model (35, for the insulin receptor) accurately reproduces for the first time all the kinetic properties of the receptor, and provides unique and robust estimates of the kinetic parameters. The harmonic oscillator model may be adaptable for many other dimeric/dimerizing receptor tyrosine kinases, cytokine receptors and G-protein-coupled receptors where ligand crosslinking occurs. Synopsis Insulin and insulin-like growth factor 1 (IGF1) have similar structures and exert their action by activating two closely related receptor tyrosine kinases—insulin receptor (IR) and IGF1 type I receptor (IGF1R), which have virtually identical signalling pathways (De Meyts and Whittaker, 2002). Despite this similarity, the two hormones produce markedly different responses: mostly metabolic for insulin and mitogenic for IGF1 (Kim and Accili, 2002). So far, there is poor understanding of how these hormones produce such markedly different biological effects using basically the same machinery (Kim and Accili, 2002). In recent years, it has become clear that a systems biology approach is required to understand the combinatorial nature of signalling specificity (Kholodenko, 2007). However, the two receptors' mechanism of ligand binding and activation displays complex allosteric properties (i.e. negative cooperativity and ligand dependence of the receptor dissociation rate), which no mathematical model has been able to account for. Therefore, development of a reliable mathematical model describing the two receptors' binding kinetics and activation is a critical first step in a systems biology approach to understand the function of these receptors. Both IR and IGF1R exist in the membrane as pre-formed covalent dimers of two identical moieties. Their extracellular domains comprise two leucine-rich (L1 and L2) modules separated by a cystein-rich domain, followed by three fibronectin type III (Fn1–3) modules (see Figure 1A) (McKern et al, 2006). The bivalent insulin molecule can bind to a site consisting of residues located in L1 and a 12 amino-acid peptide from the insert in Fn2, which combine to form 'site 1', and also to a site consisting of residues located in L2, Fn1 and Fn2 ('site 2') (De Meyts and Whittaker, 2002). A crystal structure of the extracellular (unliganded) IR dimer (McKern et al, 2006) in the inactive conformation displays a symmetrical antiparallel arrangement of the receptor's binding sites for insulin (as previously suggested by De Meyts (1994)) (see Figure 1A–C). Binding of insulin to both sites simultaneously is thought to produce a conformational change in IR, which is necessary for its activation. The crystal structure is consistent with an assumption (as previously suggested by De Meyts, 1994) that this conformational change is produced by a tilt of the receptor subunits, leading to a movement of sites 1 and 2 towards each other and to a corresponding movement of the other sites away from each other (Figure 1D and E). Mathematical modelling of the insulin binding to the inactive conformation of IR requires four parameters: association rate constants for sites 1 and 2 (designated a1 and a2, respectively) and dissociation rate constants for sites 1 and 2 (designated d1 and d2, respectively). However, the precise mechanism of the IR activation required for mathematical modelling is not known. On the basis of the available structural data, we developed a physically plausible model of the IR activation, which builds on a thermodynamically and structurally justified assumption that the IR conformational change (required for activation) can be described by harmonic oscillations of the receptor subunits. Analysis of the behaviour of an ensemble of the IR 'harmonic oscillators' in thermal equilibrium with the surrounding allows to model the receptor activation in a simple way (Figure 4A) and substantially reduces the combinatorial complexity. Binding of insulin to IR in the context of the model leads to a network of interactions shown in a simplified way in Figure 4B. Fitting of the model to the experimental data results in accurate reproduction of all the kinetic properties of IR and IGF1R and in robust estimation of the parameters, thus providing insight into the differences in kinetics between the two receptors. Recently, it has become clear that kinetics of the receptor activation contribute to, and sometimes play an essential role in, determining signalling specificity by means of kinetic proofreading (McKeithan, 1995), which states that the activated receptor must complete a cascade of reversible modifications before a cellular response can occur. If the receptor becomes inactive before the full set of modifications is complete, the receptor reverts to its basal unmodified state. The presented model predicts that upon ligand binding IR and IGF1R exist in the ligand-bound state for a long time: on average for 2 and 6 h, respectively. However, in the ligand-bound state the two receptors shuttle between the inactive and active states, and the average lifetimes in the activated states are approximately 76 s for IR and 135 s for IGF1R. This difference in the average lifetimes is expected to favour activation of the Ras–MAP kinase pathway (involved in cell growth control) by IGF1, as this pathway seems to require that the activated state is maintained for 3–5 min (Krüger et al, 2007), thus providing a possible explanation for the fact that IGF1 is more mitogenic than insulin. Thus, our model represents an essential first step in building a systems biology analysis of the insulin/IGF-I signalling networks to explain the combinatorial nature of their biological specificity. Furthermore, the model can potentially contribute to analysis of signalling specificity of other receptors as well, as it may be adaptable for a large number of dimeric or dimerizing receptor tyrosine kinases, cytokine receptors and G-protein-coupled receptors where a ligand crosslinking occurs. Introduction Insulin and insulin-like growth factors (IGF) 1 and 2 have similar structures and exert their action by activating two closely related receptor tyrosine kinases—the insulin receptor and the IGF1 type I receptor (IGF1 receptor), which share largely overlapping signalling pathways (Adams et al, 2000; De Meyts and Whittaker, 2002; De Meyts, 2004; Denley et al, 2005). Despite this similarity, the two hormones produce different responses: mostly metabolic for insulin and mitogenic for IGF1 (Kim and Accili, 2002). Dysregulation of their signalling may lead to two different life-threatening diseases: type II diabetes and cancer, which are among the largest global health challenges in the world. So far, there is poor understanding of how these hormones produce such different biological effects using similar signalling networks (Kim and Accili, 2002). It has become clear that a systems biology approach is required to understand the combinatorial nature of signalling specificity (Shymko et al, 1997; Kholodenko, 2007). Insulin analogues with altered kinetic properties show enhanced mitogenic potencies, although they bind to the same insulin receptor; they also cross-react to a variable extent with the IGF-I receptor (Shymko et al, 1997; Kurtzhals et al, 2000). Differences in kinetics of ligand binding and receptor activation by the insulin and IGF1 receptors may be one of the factors determining their specificity (Shymko et al, 1997). The two receptors' mechanism of ligand binding and activation displays complex allosteric properties (i.e. negative cooperativity and ligand dependence of the receptor dissociation rate), which no mathematical model has been able to fully account for (Jeffrey, 1982; Kohanski and Lane, 1983; Hammond et al, 1997; Wanant and Quon, 2000; Sedaghat et al, 2002). Thus, the development of a reliable mathematical model describing the two receptors' binding kinetics and activation is a critical first step in a systems biology approach to understand the function and specificity of these receptors. The insulin and IGF1 receptors exist in the membrane as pre-formed covalent dimers of two identical moieties. Their extracellular domains comprise two leucine-rich repeat-containing large domains (L1 and L2) separated by a cystein-rich (CR) domain, followed by three fibronectin type III (Fn1–3) domains (Adams et al, 2000; De Meyts and Whittaker, 2002; De Meyts, 2004). A crystal structure of this extracellular (unliganded) insulin receptor dimer has recently been solved (McKern et al, 2006; Lawrence et al, 2007; Ward et al, 2007, 2008). The intracellular portion of the two receptors consists of a kinase domain flanked by regulatory regions (Hubbard and Miller, 2007). The insulin and IGF1 receptors exhibit complex binding properties. The Scatchard plots for both receptors are concave up, indicating the presence of high- and low-affinity binding sites and/or negative cooperativity (De Meyts et al, 1973, 1976; De Meyts, 1994). The receptors bind only one ligand molecule with high affinity and at least another one with lower affinity. The ligand dissociation rate is dependent on its concentration (De Meyts et al, 1973, 1976; De Meyts, 1994). Furthermore, this dependence is bell-shaped for the insulin receptor, whereas for the IGF1 receptor, it is sigmoid (Christoffersen et al, 1994). When the insulin receptor is in a monomeric form, its affinity is reduced 30-fold, the Scatchard plot becomes linear and the dissociation rate of the ligand becomes independent of its concentration (De Meyts, 1994, 2004; De Meyts and Whittaker, 2002). Insulin has two receptor-binding surfaces on the 'opposite' sides of the molecule. The first 'classical' binding surface, also involved in insulin dimerization, was defined in the early 1970s (Pullen et al, 1976; De Meyts et al, 1978), and later validated by alanine-scanning mutagenesis (Kristensen et al, 1997), whereas the second surface, also involved in insulin hexamerization, was mapped by alanine-scanning mutagenesis more recently (De Meyts, 2004; Gauguin et al, 2008). The dimerization surface interacts with a site located in the L1 module of the insulin receptor, as well as a 12 amino-acid peptide from the insert in Fn2, which combine to form 'site 1' (Wedekind et al, 1989; Kurose et al, 1994; Williams et al, 1995; Mynarcik et al, 1996; De Meyts and Whittaker, 2002; Kristensen et al, 2002; Huang et al, 2004), whereas the hexamerization surface interacts with a site consisting of residues located in the C-terminal portion of L2 and in the Fn1 and Fn2 modules (site 2) (Fabry et al, 1992; De Meyts and Whittaker, 2002; Hao et al, 2006; Benyoucef et al, 2007; Whittaker et al, 2008). Schäffer (1994) suggested that the high-affinity binding could result from insulin crosslinking site 1 of one receptor half and site 2 of the other half of the receptor dimer, thus leaving the other two sites free for interaction with the ligand. However, this model had difficulty in explaining the ligand dependence of the ligand dissociation rate. De Meyts (1994) suggested that this problem could be solved by assuming that the four sites of the receptor dimer are arranged in a symmetrical antiparallel way, a postulate that was supported by the recent structure determination of the insulin receptor extracellular domain (McKern et al, 2006). Despite its seeming simplicity, this model turned out to be notoriously difficult for a quantitative analysis and some researchers even concluded that it did not explain the ligand dependence of the dissociation rate (Hammond et al, 1997). The problem is that the qualitative crosslinking models suggested by Schäffer (1994) and De Meyts (1994) are not detailed enough from a biochemical and structural viewpoint for mathematical modelling (especially concerning the precise mechanism that leads to receptor crosslinking). The modelling problem is further aggravated by combinatorial complexity arising from multivalent ligand binding to the receptor in multiple possible conformations. We have now solved this problem. Here, we present the first mathematical model that accurately reproduces all the kinetic properties of the insulin receptor such as negative cooperativity and the bell-shaped ligand dependence of the receptor dissociation rate. On the basis of the available structural information, we develop a physically plausible model of the receptor activation, which is based on the concept of a harmonic oscillator. We justify thermodynamically that the symmetrically arranged subunits of the insulin receptor dimer experience harmonic oscillatory movements. Analysis of the behaviour of an ensemble of such harmonic oscillators in thermal equilibrium with the surrounding milieu allows to model the receptor activation in a simple way and to substantially reduce the combinatorial complexity. This model is the first one that gives a description of the insulin receptor binding and activation mechanism in terms of interactions between the molecular components and fully takes into account the combinatorial binding complexity (employing 35 insulin receptor intermediaries). Fitting of the model to experimental data provides unique and robust estimates of the kinetic parameters. With a small modification, the model can also be used for the IGF1 receptor. Furthermore, the harmonic oscillator model may be adaptable for many other dimeric or dimerizing receptor tyrosine kinases, cytokine receptors and G-protein-coupled receptors where ligand crosslinking occurs (De Meyts, 2008). Theory and results Our goal is to develop a physically plausible mathematical model of the insulin receptor-binding and activation mechanism in terms of interactions between the molecular components. This, however, requires the knowledge of the precise mechanism of interaction between the components involved, for which some biochemical and structural details are still missing. Thus, some assumptions are unavoidable. All of the assumptions made in this article are justified from the physicochemical point of view and are therefore physically plausible. Binding of insulin to the inactive conformation of the insulin receptor The structure of the insulin receptor dimer in the unliganded conformation displays a symmetrical antiparallel arrangement of the receptor's two binding sites for insulin (McKern et al, 2006) (see Figure 1A and C). From now on, a pair of sites 1 and 2 from the different receptor subunits will be referred to as a 'crosslink'. The structure shows that the distance between sites 1 and 2 (within the same crosslink) is rather small (see Figure 1B), indicating that if an insulin molecule binds to either of these sites, there is not enough room for binding of a second insulin molecule. Thus, it is reasonable to assume that only one insulin molecule can bind to the same crosslink (either to site 1 or 2), when the receptor dimer is in the inactive conformation. Mathematical modelling of insulin binding to the inactive conformation of the insulin receptor is straightforward and requires only four parameters: association rate constants for sites 1 and 2 (designated a1 and a2, respectively) and dissociation rate constants for sites 1 and 2 (designated d1 and d2, respectively). The four sites will from now on be designated as sites 1, 2, 3 and 4, where sites 3 and 4 are identical to sites 1 and 2, respectively, but from a different crosslink (see Figure 2A). Binding of insulin to the inactive conformation of the insulin receptor gives rise to nine intermediaries, designated r0, r1, r2, r3, r4, r13, r14, r23 and r24 (where indices i and j in ri and rij designate the number of the site to which insulin is bound) (see Figure 2A). Figure 1.Insulin receptor structure. In all of the panels, the individual monomers of the insulin receptor dimer are coloured in green and blue, respectively, and location of the binding sites is shown approximately, as the residues involved in binding to insulin are not known precisely. (A) Crystal structure of the ecto-domain of the insulin receptor dimer (PDB code: 2DTG). Labelling of the modules is shown only for the blue-coloured monomer. (B) Half of the insulin receptor dimer is shown. The placement of insulin in the binding cavity is shown approximately. (C) A view of the insulin receptor dimer (shown in (A)) as seen from the 'top'. (D) Simplified representation of the insulin receptor dimer, in which the insulin-binding subunits are represented as rigid bodies. (E) Crosslinked (tilted) conformations of the rigid-body representation of the insulin receptor dimer. Insulin is depicted as a black dot. Download figure Download PowerPoint Figure 2.Inactive (A) and crosslinked (B, C) insulin receptor intermediaries used in the model. S1 and S2 stand for sites 1 and 2, respectively. Insulin is depicted as a black dot. Download figure Download PowerPoint Conformational change in the insulin receptor upon insulin binding Currently, the precise mechanism of the insulin receptor crosslinking reaction required for mathematical modelling is not known. Therefore, we will analyse the available structural information from a physicochemical point of view to derive a plausible model. In the absence of insulin, the insulin receptor adopts an inactive, symmetrical conformation (McKern et al, 2006) (see Figure 1A and C). Binding of insulin to both sites of a crosslink is thought to produce a conformational change in the insulin receptor, which is necessary for its activation. The crystal structure of the insulin receptor (McKern et al, 2006) is consistent with an assumption (as previously suggested by De Meyts, 1994) that this conformational change is produced by a tilt of the receptor subunits, leading to a movement of sites 1 and 2 towards each other and to a corresponding movement of sites from the second crosslink away from each other. This structural rearrangement is schematically shown in Figure 1D and E, in which the symmetrically arranged subunits of the receptor dimer are approximated by rigid bodies. Obviously, the tilted (activated) conformation has higher free energy than the symmetrical, inactive conformation (otherwise there would be a substantial receptor activation in the absence of insulin), probably due to slight distortion of bond angles and lengths. Thus, it is reasonable to assume that receptor molecules can exist in both inactive and active conformations, with equilibrium being strongly shifted towards the inactive (energetically more favourable) conformation in the absence of the ligand. However, when the ligand is present, it may bind simultaneously to sites 1 and 2 of the same crosslink when the receptor molecules are in the tilted conformation and thus stabilize the active conformation. Insulin receptor as a harmonic oscillator: a physically plausible model of the receptor conformational change As discussed above, the tilted (active) conformation of the insulin receptor has higher free energy compared with the non-tilted (inactive) conformation. It is reasonable to assume that larger tilt angles result in larger free energy values, and that the insulin receptor free energy has a local minimum at the zero tilt angle. Therefore, in a sufficiently small vicinity around the zero tilt angle, the system behaviour can be approximated by harmonic oscillations (Bloch, 1997). Let us consider the energy of the insulin receptor oscillations when the insulin receptor is in thermal equilibrium with the buffer. Then, the receptor molecules will have various energies (received from accidental collisions with the buffer molecules), and their distribution will be according to the Maxwell–Boltzmann formula (Bloch, 1997), which for a one-dimensional harmonic oscillator takes the form: where P, E, k and T stand for probability, energy, Boltzmann constant and absolute temperature, respectively. As appears from Figure 3A, the most likely state of the receptor is that with the zero energy of oscillations (corresponding to the zero tilt angle, or an inactive conformation), with the probability density of finding receptor molecules with higher energies decreasing exponentially as a function of energy. The Maxwell–Boltzmann distribution implies that a small fraction of receptor molecules will have sufficient energy to reach the tilt angle of the activated receptor in the absence of insulin (Figure 3A). This fraction can be easily derived from the Maxwell–Boltzmann distribution if the activation energy (designated Eact), corresponding to the tilt angle of the activated receptor, is known: Figure 3.Harmonic oscillator model of the insulin receptor activation mechanism. (A) Plot of the Maxwell–Boltzmann distribution for a one-dimensional harmonic oscillator and reaction scheme for the spontaneous receptor activation. The 5% fraction of the activated receptor molecules (with energy of oscillations ranging from the activation energy to 'infinity') is indicated by the hatched region. (B) Reaction scheme for the insulin receptor activation. The forces acting to restore the inactive/symmetrical conformation of the receptor subunits are represented by elastic springs, which can be compressed and stretched during movement of the receptor subunits. E stands for energy of oscillations, Eactivation—activation energy, F—random force vector acting on the receptor subunits, υ—vector showing direction of movement of the crosslinking subunits. S1 and S2 stand for sites 1 and 2, respectively. Insulin is depicted as a black dot. Download figure Download PowerPoint To estimate the fraction of the activated insulin receptor molecules in the absence of insulin, we note that the insulin receptor basal autophosphorylation rate is increased 10- to 20-fold in the presence of insulin (Flores-Riveros et al, 1989; Kohanski, 1993). It is reasonable to assume that the autophosphorylation rate is proportional to the fraction of the activated receptor molecules and that the basal rate is proportional to this fraction in the absence of insulin. Thus, around 5–10% of the receptor molecules are estimated to be activated in the absence of insulin. From this, the activation energy of the insulin receptor can be roughly estimated from the above equation as 5–8 kJ mol−1. Interestingly, the conformational change of the EGF receptor also requires about 4–8 kJ mol−1 (Ozcan et al, 2006), indicating that the above estimation is reasonable. It should be pointed out that large-scale collective motions in a macromolecule are determined mostly by the macromolecule's global topology and are insensitive to structural details, and that the results obtained by assuming subunits to be rigid bodies connected by elastic springs provide a good description of the allosteric dynamics (for review, see Bahar and Rader, 2005). From this perspective, the rigid body model of the symmetrical insulin receptor dimer with elastic springs attached as shown in Figure 3B (compare it with Figure 1C) is expected to provide a decent description of the insulin receptor dynamics. Indeed, such a model will be capable of the conformational changes shown in Figure 1E and the movement of its subunits will be described by harmonic oscillations. In the following, this rigid body model of the insulin receptor dimer will serve as a basis for modelling of the crosslinking reaction. Definition of the crosslinking constant Let us consider the behaviour of the r0 intermediary in the absence of insulin. The harmonic oscillator model implies that in the absence of insulin there are no intermediaries with a certain stable tilt angle, although the zero tilt angle is most likely (see Figure 3A). The tilt angle will be fluctuating (due to collisions of the solvent molecules with the receptor subunits) until an activation state is achieved, which will only be transient because the oscillation will continue its swing in the reverse direction and quickly lose its energy due to interaction with the solvent. The r0 receptor molecules with energy of oscillations less than the energy of activation, designated (and therefore in the inactive state), will reach an active state, *r0, on average after a certain time period, τ. Then, transition from to *r0 can be modelled as a first-order reaction with a rate constant equal to 1/τ, designated from now on as the crosslinking constant, kcr (see Figure 3A). As approximately 5% of receptor molecules are in the active state (see above), the transition from *r0 to can be modelled as a first-order reaction with a rate constant equal to 19 kcr (Figure 3A). Activation of the insulin receptor according to the harmonic oscillator model Let us consider the activation of an inactive r1 intermediary (activation of all other inactive intermediaries can be considered in a similar way). The most likely state of this intermediary (with zero energy of oscillations) is designated as or1 and those states with energy of oscillations less than activation energy (including or1)—as (see Figure 3B), which represent the r1 receptor species in an inactive state. Subunits of the intermediaries will be experiencing random forces acting on them (shown by vectors F in Figure 3B) due to thermal motion of the solvent molecules. These forces will be varying in magnitude, direction and act for various periods of time. When these forces act synergistically for a sufficient period of time, an active state will be achieved, which (as mentioned above) will happen on average after a time period, τ, and transition to the active state, designated as *r1+ (see Figure 3B), from the inactive can be modelled as a first-order reaction with a rate constant, kcr, equal to 1/τ. As in the active state, the distance between insulin and site 2 is zero, the local concentration of insulin in the vicinity of site 2 becomes 'infinite', which means that the subsequent binding of insulin to site 2, and thus formation of r1 × 2, is 'instant' (see Figure 3B). To discriminate between *r1+ and r1 × 2, the *r1+ intermediary is shown in Figure 3B with a small distance between insulin and site 2, which can also be interpreted as a snapshot of *r1+ just before it reaches the active state. The r1 × 2 intermediary will exist until one of the sites of the crosslink dissociates. Let us assume that it is site 2 that dissociates. This leads to the formation of *r1− (see Figure 3B). Similar to the *r1+ intermediary, *r1− is shown with a small distance between site 2 and insulin, which can be interpreted as a snapshot of *r1− just after dissociation of site 2. There is an important difference between *r1− and *r1+. The two intermediaries have identical tilt angles, the same kinetic and potential energies of oscillations. But in *r1+ the crosslinking subunits move towards each other (see Figure 3B, the direction of movement is indicated by vectors υ), meaning that r1 × 2 will be formed in an instant, whereas in *r1− the
Год издания: 2009
Издательство: Springer Nature
Источник: Molecular Systems Biology
Ключевые слова: Growth Hormone and Insulin-like Growth Factors, Metabolism, Diabetes, and Cancer, Diet, Metabolism, and Disease
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