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1.
Poland D 《Biopolymers》2006,81(2):127-135
In this article we use the published heat capacity data of Dragan et al. (J Mol Biol 2003, 327, 293-411) for a short DNA duplex to calculate the enthalpy probability distribution for this species as a function of temperature. Our approach is based on a procedure that we developed (Poland, D. J Chem Phys 2000, 112, 6554) whereby one obtains moments of the enthalpy distribution from the temperature dependence of the heat capacity. One then uses the maximum-entropy method to construct the enthalpy probability distribution from the set of enthalpy moments. For the DNA duplex treated here the heat capacity goes through a maximum as a function of temperature reflecting the unwinding of the duplex structure. In the neighborhood of the heat capacity maximum, the enthalpy distribution functions show a clear bimodal structure, indicating the coexistence of two distinct states, the duplex and the single-strand state. The probabilities of theses two states can be estimated from the enthalpy distribution functions and can be used to calculate the temperature dependence of the equilibrium constant for the unwinding of the DNA duplex. This example illustrates that the temperature dependence of the heat capacity can be used to give a detailed picture of conformational transitions in biological macromolecules. In particular, the structure of the enthalpy distribution in this case allows one to see the temperature evolution of the two-state distribution in detail.  相似文献   

2.
Poland D 《Biophysical chemistry》2007,125(2-3):497-507
In this article we use the published heat capacity data of Dragan et al. [A.I. Dragan, et al., The energetics of specific binding of AT-hooks from HMGA1 to target DNA, J. Mol. Biol. 327 (2003) 393-411] on the association of proteins with DNA duplexes to construct enthalpy probability distributions for the protein/DNA complexes formed in these systems. We first analyze the multistep equilibrium that determines the species concentrations in this system to determine whether or not the DNA-peptide complex goes cleanly to DNA single-strands and peptide. Using the heat capacity data for this case we employ the maximum-entropy method to construct enthalpy probability distribution functions for the species involved in this equilibrium. We find that the distribution functions for this system clearly show bimodal behavior indicating a two-state transition from complex to non-complex form.  相似文献   

3.
We have recently shown that one can construct the enthalpy distribution for protein molecules from experimental knowledge of the temperature dependence of the heat capacity. For many proteins the enthalpy distribution evaluated at the midpoint of the denaturation transition (corresponding to the maximum in the heat capacity vs temperature curve) is broad and biphasic, indicating two different populations of molecules (native and unfolded) with distinctly different enthalpies. At temperatures above the denaturation point, the heat capacity for the unfolded state in many proteins is quite large and using the analysis just mentioned, we obtain a gaussian-like enthalpy distribution that is very broad. A large value of the heat capacity indicates that there are structural changes going on in the unfolded state above the transition temperature. In the present paper we investigate the origin of this large heat capacity by considering the presence of changing amounts of secondary structure (specifically, alpha-helix) in the unfolded state. For this purpose we use the empirical estimates of the Zimm-Bragg sigma and s factors for all of the native amino acids in water as determined by Scheraga and co-workers. Using myoglobin as an example, we calculate probability profiles and distribution functions for the total number of helix states in the specific-sequence molecule. Given the partition function for the specific-sequence molecule, we can then calculate a set of enthalpy moments for the molecule from which we obtain a good estimate of the enthalpy distribution in the unfolded state. This distribution turns out to be quite narrow when compared with the distribution obtained from the raw heat capacity data. We conclude that there must be other major structural changes (backbone and solvent) that are not accounted for by the inclusion of alpha-helix in the unfolded state.  相似文献   

4.
Poland D 《Biopolymers》2001,58(1):89-105
Experimental data on the temperature dependence of the heat capacity of proteins can be used to calculate approximate enthalpy distributions for these molecules using the maximum-entropy method. C(p) (T) data is first used to calculate a set of moments of the enthalpy distribution, and these are then used to estimate the enthalpy distribution. If one knows the temperature expansion of the heat capacity through the (n - 2)th power of DeltaT (measured from the expansion center), then this is enough information to calculate the nth moment of the enthalpy distribution. Using four or more moments is in turn enough information to resolve bimodal behavior in the distribution. If the enthalpy distribution of a protein exhibits two distinct peaks, then this is direct experimental confirmation of a two-state mechanism of denaturation, the two peaks corresponding to the enthalpy of the native and unfolded species respectively. If the heat capacity of a protein exhibits a maximum at the denaturation temperature, then there is the possibility that the enthalpy distribution will be bimodal, but the presence of a maximum in the heat capacity is not a sufficient condition for this kind of behavior. We construct a phase diagram in terms of the appropriate variables to indicate when a maximum in the heat capacity will also give rise to bimodal behavior in the enthalpy distribution. We illustrate the phase diagram using literature data for a set of proteins.  相似文献   

5.
The temperature dependence of the heat capacity of myoglobin depends dramatically on pH. At low pH (near 4.5), there are two weak maxima in the heat capacity at low and intermediate temperatures, respectively, whereas at high pH (near 10.7), there is one strong maximum at high temperature. Using literature data for the low-pH form (Hallerbach and Hinz, 1999) and for the high-pH form (Makhatadze and Privalov, 1995), we applied a recently developed technique (Poland, 2001d) to calculate the free energy distributions for the two forms of the protein. In this method, the temperature dependence of the heat capacity is used to calculate moments of the protein enthalpy distribution function, which in turn, using the maximum-entropy method, are used to construct the actual distribution function. The enthalpy distribution function for a protein gives the fraction of protein molecules in solution having a given value of the enthalpy, which can be interpreted as the probability that a molecule picked at random has a given enthalpy value. Given the enthalpy distribution functions at several temperatures, one can then construct a master free energy function from which the probability distributions at all temperatures can be calculated. For the high-pH form of myoglobin, the enthalpy distribution function that is obtained exhibits bimodal behavior at the temperature corresponding to the maximum in the heat capacity (Poland, 2001a), reflecting the presence of two populations of molecules (native and unfolded). For this form of myoglobin, the temperature evolution of the relative probabilities of the two populations can be obtained in detail from the master free energy function. In contrast, the enthalpy distribution function for the low-pH form of myoglobin does not show any special structure at any temperature. In this form of myoglobin the enthalpy distribution function simply exhibits a single maximum at all temperatures, with the position of the maximum increasing to higher enthalpy values as the temperature is increased, indicating that in this case there is a continuous evolution of species rather than a shift between two distinct population of molecules.  相似文献   

6.
D Poland 《Proteins》2001,45(4):325-336
Protein molecules in solution have a broad distribution of enthalpy states. A good approximation to the distribution function for enthalpy states can be calculated, using the maximum-entropy method, from the moments of the distribution that, in turn, are obtained from the experimental temperature dependence of the heat capacity. In the present paper, we show that the enthalpy probability distribution can then be formulated in terms of a free energy function that gives the free energy of the protein corresponding to a particular value of the enthalpy. By the location of the minima in this function, the free energy distribution graphically indicates the most probable values of the enthalpy for the protein. We find that the behavior of the free energy functions for proteins falls somewhere between two different cases: a two-state like function with two minima, the relative levels of the two states changing with temperature; and, a single-minimum function where the position of the minimum shifts to higher enthalpy values as the temperature is increased. We show that the temperature dependence of the free energy function can be expressed in terms of a central free energy distribution for a given, fixed temperature (which is most conveniently chosen as the temperature of the maximum in the heat capacity). The nature of this central free energy function for a given protein thus yields all of the thermodynamic behavior of that protein over the temperature range of the denaturation process.  相似文献   

7.
D Pederson  D Gabriel  J Hermans 《Biopolymers》1971,10(11):2133-2145
We have performed potentiometric titrations of poly-L -lysine. From these data we have calculated the free energy and enthalpy changes for the folding of the random coil to the α-helix in 10% ethanol (?120 and ?120 cal/mole) and from the random coil to the β-structure in water (?140 and 870 cal/mole) and in 10% ethanol (?180 and 980 cal mole). Comparison of these values with each other and with values for the coil → α- helix transition in water (?78 and ?880 cal/mole) led to the following conclusions. The stabilization by ethanol of ethanol of the α-helix with respect to the coil is that predicted from the known free energy of transfer of the peptide group from water to 10% ethanol. Similar data to explain the enthalpy difference are not available. The thermodynamic functions for the transition from α-helix to β-structure, obtained by subtracting those for the coil → α-helix and coil → β-structure transitions, are explained from a consideration of the structural differences: non bonded interactions of the polypeptide backbone are less favorable in the β-structure than in the α-helix, causing an increase in the energy, while hydrophobic contacts between side chains raise the entropy of the β-structure as compared with the α-helix, so that the free energy difference between the two structures is small, but enthalpy and entropy differences are large. The observation of only small differences in the free energy and enthalpy changes for the transition from coil β-structure upon going from water to 10% ethanol is expected by considering both the free energy of transfer of the peptide group (as for the α-helix) and the free energy and enthalpy of transfer of the apolar part of the side chain involved in hydrophobic bond formation.  相似文献   

8.
alphabeta T-cell receptors (TCRs) recognize peptide antigens presented by class I or class II major histocompatibility complex molecules (pMHC). Here we review the use of thermodynamic measurements in the study of TCR-pMHC interactions, with attention to the diversity in binding thermodynamics and how this is related to the variation in TCR-pMHC interfaces. We show that there is no enthalpic or entropic signature for TCR binding; rather, enthalpy and entropy changes vary in a compensatory manner that reflects a narrow free energy window for the interactions that have been characterized. Binding enthalpy and entropy changes do not correlate with structural features such as buried surface area or the number of hydrogen bonds within TCR-pMHC interfaces, possibly reflecting the myriad of contributors to binding thermodynamics, but likely also reflecting a reliance on van't Hoff over calorimetric measurements and the unaccounted influence of equilibria linked to binding. TCR-pMHC binding heat capacity changes likewise vary considerably. In some cases, the heat capacity changes are consistent with conformational differences between bound and free receptors, but there is little data indicating these conformational differences represent the need to organize disordered CDR loops. In this regard, we discuss how thermodynamics may provide additional insight into conformational changes occurring upon TCR binding. Finally, we highlight opportunities for the further use of thermodynamic measurements in the study of TCR-pMHC interactions, not only for understanding TCR binding in general, but also for understanding specifics of individual interactions and the engineering of TCRs with desired molecular recognition properties.  相似文献   

9.
Bakk A 《Physical biology》2004,1(3-4):152-158
Many small globular proteins are traditionally classified as thermodynamical two-state systems, i.e., the protein is either in the native, active state (folded) or in the denatured state (unfolded). We challenge this view and show that there may exist (protein) systems for which a van't Hoff analysis of experimental data cannot determine whether the system corresponds to two or three thermodynamical states when only temperatures in a narrow temperature region around the transition are considered. We generalize a widely employed two-state protein folding model to include a third, transition state. For this three-state system we systematically study the deviation of the calorimetric enthalpy (heat of transition) from the van't Hoff enthalpy, a measure of the two-stateness of a transition. We show that under certain conditions the heat capacity of the three-state system can be almost indistinguishable from the heat capacity for the two-state system over a broad temperature interval. The consequence may be that some three-state (or even more than three-states) systems have been misinterpreted as two-state systems when the conclusion is drawn solely upon the van't Hoff enthalpy. These findings are important not only for proteins, but also for the interpretation of thermodynamical systems in general.  相似文献   

10.
The 32-residue leucine zipper subsequence, called here Jun-lz, associates in benign media to form a parallel two-stranded coiled coil. Studies are reported of its thermal unfolding/folding transition by circular dichroism (CD) on samples of natural isotopic abundance and by both equilibrium and spin inversion transfer (SIT) nuclear magnetic resonance (NMR) on samples labeled at the leucine-18 alpha-carbon with 99% 13C. The data cover a wide range of temperature and concentration, and show that Jun-lz unfolds below room temperature, being far less stable than some other leucine zippers such as GCN4. 13C-NMR shows two well-separated resonances. We ascribe the upfield one to 13C spins on unfolded single chains and the downfield one to 13C spins on coiled-coil dimers. Their relative intensities provide a measure of the unfolding equilibrium constant. In SIT NMR, the recovery of the equilibrium magnetization after one resonance is inverted is modulated in part by the unfolding and folding rate constants, which are accessible from the data. Global Bayesian analysis of the equilibrium and SIT NMR data provide values for the standard enthalpy, entropy, and heat capacity of unfolding, and show the latter to be unusually large. The CD results are compatible with the NMR findings. Global Bayesian analysis of the SIT NMR data yields the corresponding activation parameters for unfolding and folding. The results show that both reaction directions are activated processes. Activation for unfolding is entropy driven, enthalpy opposed. Activation for folding is strongly enthalpy opposed and somewhat entropy opposed, falsifying the idea that the barrier for folding is solely due to a purely entropic search for properly registered partners. The activation heat capacity is much larger for folding, so almost the entire overall change is due to the folding direction. This latter finding, if it applies to GCN4 leucine zippers, clears up an extant apparent disagreement between folding rate constants for GCN4 as determined by chevron analysis and NMR in differing temperature regimes.  相似文献   

11.
The temperature-induced helix to coil transition in a series of host peptides was monitored using circular dichroism spectroscopy (CD) and differential scanning calorimetry (DSC). Combination of these two techniques allowed direct determination of the enthalpy of helix-coil transition for the studied peptides. It was found that the enthalpy of the helix-coil transition differs for different peptides and this difference is related to the difference in the temperature for the midpoint of helix-coil transition. The enthalpy of the helix-coil transition decreases with the increase in temperature, thus providing the first experimental estimate for the heat capacity changes upon helix-coil transition, DeltaC(p). The values for DeltaC(p) of helix-coil transition are found to be negative, which is in contrast to the positive DeltaC(p) for protein unfolding. Analysis suggests that this negative DeltaC(p) of helix-coil transition is due to the exposure of the polar peptide backbone to solvent upon helix unfolding.  相似文献   

12.
A frequent outcome in differential scanning calorimetry (DSC) experiments carried out with large proteins is the irreversibility of the observed endothermic effects. In these cases, DSC profiles are analyzed according to methods developed for temperature-induced denaturation transitions occurring under kinetic control. In the one-step irreversible model (native → denatured) the characteristics of the observed single-peaked endotherm depend on the denaturation enthalpy and the temperature dependence of the reaction rate constant, k. Several procedures have been devised to obtain the parameters that determine the variation of k with temperature. Here, we have elaborated on one of these procedures in order to analyze more complex DSC profiles. Synthetic data for a heat capacity curve were generated according to a model with two sequential reactions; the temperature dependence of each of the two rate constants involved was determined, according to the Eyring's equation, by two fixed parameters. It was then shown that our deconvolution procedure, by making use of heat capacity data alone, permits to extract the parameter values that were initially used. Finally, experimental DSC traces showing two and three maxima were analyzed and reproduced with relative success according to two- and four-step sequential models.  相似文献   

13.
The thermodynamics of self-assembly of a 14 base pair DNA double helix from complementary strands have been investigated by titration (ITC) and differential scanning (DSC) calorimetry, in conjunction with van't Hoff analysis of UV thermal scans of individual strands. These studies demonstrate that thermodynamic characterization of the temperature-dependent contributions of coupled conformational equilibria in the individual "denatured" strands and in the duplex is essential to understand the origins of duplex stability and to derive stability prediction schemes of general applicability. ITC studies of strand association at 293 K and 120 mM Na+ yield an enthalpy change of -73 +/- 2 kcal (mol of duplex)-1. ITC studies between 282 and 312 K at 20, 50, and 120 mM Na+ show that the enthalpy of duplex formation is only weakly salt concentration-dependent but is very strongly temperature-dependent, decreasing approximately linearly with increasing temperature with a heat capacity change (282-312 K) of -1.3 +/- 0.1 kcal K-1 (mol of duplex)-1. From DSC denaturation studies in 120 mM Na+, we obtain an enthalpy of duplex formation of -120 +/- 5 kcal (mol of duplex)-1 and an estimate of the corresponding heat capacity change of -0.8 +/- 0.4 kcal K-1 (mol of duplex)-1 at the Tm of 339 K. van't Hoff analysis of UV thermal scans on the individual strands indicates that single helix formation is noncooperative with a temperature-independent enthalpy change of -5.5 +/- 0.5 kcal at 120 mM Na+. From these observed enthalpy and heat capacity changes, we obtain the corresponding thermodynamic quantities for two fundamental processes: (i) formation of single helices from disordered strands, involving only intrastrand (vertical) interactions between neighboring bases; and (ii) formation of double helices by association (docking) of single helical strands, involving interstrand (horizontal and vertical) interactions. At 293 K and 120 mM Na+, we calculate that the enthalpy change for association of single helical strands is approximately -64 kcal (mol of duplex)-1 as compared to -210 kcal (mol of duplex)-1 calculated for duplex formation from completely unstructured single strands and to the experimental ITC value of -73 kcal (mol of duplex)-1. The intrinsic heat capacity change for association of single helical strands to form the duplex is found to be small and positive [ approximately 0.1 kcal K-1 (mol of duplex)-1], in agreement with the result of a surface area analysis, which also predicts an undetectably small heat capacity change for single helix formation.  相似文献   

14.
15.
Outer surface protein A (OspA) from Borrelia burgdorferi is a predominantly beta-sheet protein comprised of beta-strands beta1-beta21 and a short C-terminal alpha-helix. It contains two globular domains (N and C-terminal domains) and a unique single-layer beta-sheet (central beta-sheet) that connects the two domains. OspA contains an unusually large number of charged amino acid residues. To understand the mechanism of stabilization of this unique beta-sheet protein, thorough thermodynamic investigations of OspA and its truncated mutant lacking a part of the C-terminal domain were conducted using calorimetry and circular dichroism. The stability of OspA was found to be sensitive to pH and salt concentration. The heat capacity curve clearly consisted of two components, and all the thermodynamic parameters were obtained for each step. The thermodynamic parameters associated with the two transitions are consistent with a previously proposed model, in which the first transition corresponds to the unfolding of the C-terminal domain and the last two beta-strands of the central beta-sheet, and the second transition corresponds to that of the N-terminal domain and the first beta-strand of the central beta-sheet in the second peak. The ratio of calorimetric and van't Hoff enthalpies indicates that the first peak includes another thermodynamic intermediate state. Large heat capacity changes were observed for both transitions, indicative of large changes in the exposure of hydrophobic surfaces associated with the transitions. This observation demonstrates that hydrophobic parts are buried efficiently in the native structure in spite of the low content of hydrophobic residues in OspA. By decomposing the enthalpy, entropy, and Gibbs free energy into contributions from different interactions, we found that the enthalpy changes for hydrogen bonding and polar interactions are exceptionally large, indicating that OspA maintains its stability by making full use of its unique beta-sheet and high content of polar residues. These thermodynamic analyses demonstrated that it is possible to maintain protein tertiary structure by making effective use of an unusual amino acid composition.  相似文献   

16.
Unfolding of the small alpha-amylase inhibitor tendamistat (74 residues, 2 disulfide bridges) has been characterized thermodynamically by high sensitivity scanning microcalorimetry. To link the stability parameters with structural information we use heat capacity group parameters and water accessible surface areas to calculate the change in heat capacity on unfolding of tendamistat. Our results show that both the group parameter and surface area approaches provide a reasonable, though not perfect, basis for delta Cp calculations. When using the experimentally determined temperature-independent heat capacity increase of 2.89 kJ mol-1 K-1 tendamistat exhibits convergence of thermodynamic parameters at about 140 degrees C, in agreement with recent predictions of the temperature at which the hydrophobic hydration is supposed to disappear. Despite the apparent support of this new view of the hydrophobic effect, there are inconsistencies in the interpretation of the thermodynamic parameters and these are addressed in the Discussion. The specific stability of tendamistat is similar to that of modified bovine pancreatic trypsin inhibitor, with only two of the native three disulfide bridges intact. This observation confirms our previous conclusion that disulfide bridges affect significantly the enthalpy and entropy of unfolding. The recent study by Doig & Williams provides additional convincing support for this conclusion. The predictive scheme proposed by these authors permits a fair estimate of the Gibbs free energy and enthalpy changes of these two proteins.  相似文献   

17.
Knott M  Chan HS 《Proteins》2006,65(2):373-391
Recent investigations of possible downhill folding of small proteins such as BBL have focused on the thermodynamics of non-two-state, "barrierless" folding/denaturation transitions. Downhill folding is noncooperative and thermodynamically "one-state," a phenomenon underpinned by a unimodal conformational distribution over chain properties such as enthalpy, hydrophobic exposure, and conformational dimension. In contrast, corresponding distributions for cooperative two-state folding are bimodal with well-separated population peaks. Using simplified atomic modeling of a three-helix bundle-in a scheme that accounts for hydrophobic interactions and hydrogen bonding-and coarse-grained C(alpha) models of four real proteins with various degrees of cooperativity, we evaluate the effectiveness of several observables at defining the underlying distribution. Bimodal distributions generally lead to sharper transitions, with a higher heat capacity peak at the transition midpoint, compared with unimodal distributions. However, the observation of a sigmoidal transition is not a reliable criterion for two-state behavior, and the heat capacity baselines, used to determine the van't Hoff and calorimetric enthalpies of the transition, can introduce ambiguity. Interestingly we find that, if the distribution of the single-molecule radius of gyration were available, it would permit discrimination between unimodal and bimodal underlying distributions. We investigate kinetic implications of thermodynamic noncooperativity using Langevin dynamics. Despite substantial chevron rollovers, the relaxation of the models considered is essentially single-exponential over an extended range of native stabilities. Consistent with experiments, significant deviations from single-exponential behavior occur only under strongly folding conditions.  相似文献   

18.
Using the binding of a nucleotide inhibitor (guanosine-3'-monophosphate) to a ribonuclease (ribonuclease Sa) as a model system, we show that the salt-dependence of the interaction arises due to specific ion binding at the site of nucleotide binding. The presence of specific ion-protein binding is concluded from a combination of differential scanning calorimetry and NMR data. Isothermal titration calorimetry data are then fit to determine the energetic profile (enthalpy, entropy, and heat capacity) for both the ion-protein and nucleotide-protein interactions. The results provide insight into the energetics of charge-charge interactions, and have implications for the interpretation of an observed salt-dependence. Further, the presence of specific ion-binding leads to a system behavior as a function of temperature that is drastically different from that predicted from Poisson-Boltzmann calculations.  相似文献   

19.
To obtain detailed structural information for spider dragline spidroin (MaSp1), we prepared three versions of the consensus peptide GGLGGQGAGAAAAAAGGAGQGGYGGLGSQGAGR labeled with 13C at six different sites. The 13C CP/MAS NMR spectra were observed after treating the peptides with different reagents known to alter silk protein conformations. The conformation-dependent 13C NMR chemical shifts and peak deconvolution were used to determine the local structure and the fractional compositions of the conformations, respectively. After trifluoroacetic acid (solvent)/diethyl ether (coagulant) treatment, the N-terminal region of poly-Ala (PLA) sequence, Ala8 and Ala10, adopted predominantly the alpha-helix with a substantial amount of beta-sheet. The central region, Ala15, Ala18, and Leu26, and C-terminal region, Ala31, of the peptide were dominated by either 3(1)-helix or alpha-helix. There was no indication of beta-sheet, although peak broadening indicates that the torsion angle distribution is relatively large. After 9 M LiBr/dialysis treatment, three kinds of conformation, beta-sheet, random coil, and 3(1)-helix, appeared, in almost equal amounts of beta-sheet and random coil conformations for Ala8 and Ala10 residues and distorted 3(1)-helix at the central region of the peptide. In contrast, after formic acid/methanol and 8 M urea/acetonitrile treatments, all of the local structure tends to beta-sheet, although small amounts of random coil are also observed. The peak pattern of the Ala Cbeta carbon after 8 M urea/acetonitrile treatment is similar to the corresponding patterns of silk fiber from Bombyx mori and Samia cynthia ricini. We also synthesized a longer 13C-labeled peptide containing two PLA blocks and three Gly-rich blocks. After 8 M urea/acetonitrile treatment, the conformation pattern was closely similar to that of the shorter peptide.  相似文献   

20.
The chemically-coded affinity tag (CCAT) method combines standard electrophoresis protocols with MALDI-TOF-MS analysis to identify and quantify protein abundances in complex samples in one step. This method is designed to fit into the workflow of SDS-PAGE or two-dimensional electrophoresis (2-DE) only requiring basic proteome laboratory equipment. Prior to electrophoresis two protein samples are separately labelled with a heavy or a light version of the CCAT reagent via reduced cysteines in the proteins. Equal amounts are then combined and electrophoretically separated. Proteins can then be excised from the gel to obtain their peptide mass fingerprint by mass spectrometry. This fingerprint enabled not only identification, but also quantification by comparing relative peak intensities of CCAT-labelled peptides. In this article, we display how the CCAT method can be used to analyse two protein samples in one gel and that the peak intensities of labelled peptides reflect the abundance of a protein in it.  相似文献   

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