Response noise affects the graphical evaluation of response versus concentration curves

Several theories of chemoreceptor stimulation predict the samesimple relationship between response R and stimulus concentrationC: (1 + K/C),(in which R_max is maximum response and K an equilibriumconstant), also known as Beidler's taste equation. To test whetherdata points fit this equation and estimate R_max and K, severaltransformations are in use which convert the theoretical curveinto a straight line (Lineweaver-Burk, Scatchard, Eadie-Hofsteeand Beidler plots). However, even modest amounts of responsevariability may interfere badly with the evaluation of theseplots. This is not always appreciated; therefore this paperpresents an illustration of the extent of this effect, usinga realistic example. In addition, this effect may also obscurethe presence of theoretically relevant deviations from the aboveequation, caused by multiple receptor sites, or convergenceof receptors, which are expressed in a Hill coefficient n_H 1. These effects are also exemplified. The illustrations areshown graphically and by a Montre-Carlo computer simulation.The conclusion is drawn that the linearizing plots should notbe used at all for the quantitative evaluation of data. Direct,numerical iterative curve-fitting methods seem to give morereliable results.     

How the concentration of insulin affects the development of preantral follicles in goats

This study investigated the effect of adding different insulin concentrations to the culture medium for goat preantral follicle development in vitro. The ovarian fragments were immediately fixed or cultured for 7 days in MEM with insulin (0, 5, 10 ng/ml and 5 or 10 μg/ml). The results showed that, after 7 days of culture, insulin at 10 ng/ml was the best concentration to preserve follicular viability and ultrastructure, resulting in the highest rates of normal follicles. After 7 days, only treatments with 10 ng/ml and 5 μg/ml of insulin increased follicular activation when compared to other concentrations. Regarding follicular and oocyte growth, the presence of 10 ng/ml of insulin promoted a larger diameter than other treatments. In conclusion, this study shows that addition of 10 ng/ml of insulin to the culture medium improved the survival and stimulated growth of goat preantral follicles.     

Increased concentration of tracee affects estimates of muscle protein synthesis

Muscle protein synthesis was measured by infusion of L-[2H(5)]phenylalanine in two groups of anesthetized dogs, before and during infusion of insulin with euaminoacidemia, and with differing concentrations of unlabeled phenylalanine (tracee). With the infusion of insulin, muscle protein synthesis increased 39 +/- 12% based on phenylalanyl-tRNA. Calculation with plasma phenylalanine enrichment overestimated insulin stimulation by 40% (56 +/- 12 vs. 39 +/- 12%). Raising the concentration of plasma phenylalanine twofold during infusion of insulin further increased the apparent stimulation of muscle protein synthesis based on plasma relative to phenylalanyl-tRNA by 225% (65 +/- 19 vs. 20 +/- 14%, P < 0.001). In both experiments, the stimulation of synthesis rates calculated from phenylalanine enrichment within the muscle was closer to that from phenylalanyl-tRNA (48 +/- 19%, experiment 1; 30 +/- 14%, experiment 2). Results indicate that the enrichment of a labeled amino acid within plasma and tissue amino acid pools is affected by the concentration of tracee infused. Increasing the concentration of tracee overestimates the insulin-mediated stimulation of muscle protein synthesis when amino acid pools other than aminoacyl-tRNA are used as the precursor enrichment.     

Increasing temperature accelerates protein unfolding without changing the pathway of unfolding

We have traditionally relied on extremely elevated temperatures (498K, 225 degrees C) to investigate the unfolding process of proteins within the timescale available to molecular dynamics simulations with explicit solvent. However, recent advances in computer hardware have allowed us to extend our thermal denaturation studies to much lower temperatures. Here we describe the results of simulations of chymotrypsin inhibitor 2 at seven temperatures, ranging from 298K to 498K. The simulation lengths vary from 94ns to 20ns, for a total simulation time of 344ns, or 0.34 micros. At 298K, the protein is very stable over the full 50ns simulation. At 348K, corresponding to the experimentally observed melting temperature of CI2, the protein unfolds over the first 25ns, explores partially unfolded conformations for 20ns, and then refolds over the last 35ns. Above its melting temperature, complete thermal denaturation occurs in an activated process. Early unfolding is characterized by sliding or breathing motions in the protein core, leading to an unfolding transition state with a weakened core and some loss of secondary structure. After the unfolding transition, the core contacts are rapidly lost as the protein passes on to the fully denatured ensemble. While the overall character and order of events in the unfolding process are well conserved across temperatures, there are substantial differences in the timescales over which these events take place. We conclude that 498K simulations are suitable for elucidating the details of protein unfolding at a minimum of computational expense.     

How bacterial protein toxins enter cells: the role of partial unfolding in membrane translocation

Bacterial protein toxins translocate across membranes by processes that are still mysterious. Studies on diphtheria toxin have shown that partial unfolding processes play a major role in toxin membrane insertion and translocation. Similar unfolding behaviour is seen with other bacterial toxins. The lessons gained from this behaviour allow us to propose novel mechanisms for toxin translocation.     

Heme orientation affects holo-myoglobin folding and unfolding kinetics

Native myoglobin (Mb) consists of two populations which differ in the orientation of the heme by 180 degrees rotation (as verified by nuclear magnetic resonance) but have identical absorption spectra and equilibrium-thermodynamic stability. Here, we report that these two fractions of native oxidized Mb (from horse) both unfold and refold (chemical denaturant, pH 7, 20 degrees C) in two parallel kinetic reactions with rate constants differing 10-fold. In accord, the oxidized heme remains coordinated to unfolded horse Mb in up to 4 M guanidine hydrochloride (pH 7, 20 degrees C).     

How life affects the atmosphere

The impact of life on the atmosphere is examined through a discussion of the budgets of important atmospheric constituents and the processes that control their concentrations. Life profoundly influences oxygen and a number of minor atmospheric constituents, but many important gases, including those with the greatest effect on global climate, appear to be little altered by biological processes, at least in the steady state.     

Topological determinants of protein unfolding rates

For proteins that fold by two-state kinetics, the folding and unfolding processes are believed to be closely related to their native structures. In particular, folding and unfolding rates are influenced by the native structures of proteins. Thus, we focus on finding important topological quantities from a protein structure that determine its unfolding rate. After constructing graphs from protein native structures, we investigate the relationships between unfolding rates and various topological quantities of the graphs. First, we find that the correlation between the unfolding rate and the contact order is not as prominent as in the case of the folding rate and the contact order. Next, we investigate the correlation between the unfolding rate and the clustering coefficient of the graph of a protein native structure, and observe no correlation between them. Finally, we find that a newly introduced quantity, the impact of edge removal per residue, has a good overall correlation with protein unfolding rates. The impact of edge removal is defined as the ratio of the change of the average path length to the edge removal probability. From these facts, we conclude that the protein unfolding process is closely related to the protein native structure.     

Machinery of protein folding and unfolding

During the past two years, a large amount of biochemical, biophysical and low- to high-resolution structural data have provided mechanistic insights into the machinery of protein folding and unfolding. It has emerged that dual functionality in terms of folding and unfolding might exist for some systems. The majority of folding/unfolding machines adopt oligomeric ring structures in a cooperative fashion and utilise the conformational changes induced by ATP binding/hydrolysis for their specific functions.     

The glycophosphatidylinositol anchor oppositely affects unfolding and refolding of alkaline phosphatase

Regarding the world wide success of artificial chaperone-assisted protein refolding technique and based on its well worked-out mechanism, it is anticipated that the lipid moieties of glycosylphosphatidylinositol (GPI) group, which is present in some membrane proteins, might interfere with the capturing step of the technique. To find an answer, we evaluated the chemical denaturation and also the refolding behavior of insoluble and soluble alkaline phosohatase (ALP), with or without GPI group, respectively. The results indicated that the presence of GPI in the enzyme increased the stability of the protein against chemical denaturation while it decreased its refolding yield by the artificial chaperone refolding technique. The lower refolding yield, compared to soluble ALP (sALP), might be due to a less efficient stripping step caused by new interactions imparted to the refolding elements of the system especially those among the hydrophobic tails of GPI and the capturing agent of the technique. These new interactions will interrupt the kinetics of detergent stripping from the captured molecules by the stripping agent (i.e., cyclodextrins). This situation will lead to higher intermolecular hydrophobic interactions among the refolding protein intermediates leading to their higher misfolding and aggregation.     

Effect of a contaminating competitive ligand on ligand-binding curves. Inverse protein concentration dependence

A theoretical binding model is considered which provides an explanation for the inverse protein concentration dependence observed for a variety of ligands. The model describes the inhibition of binding caused by a highly bound contaminant. The complete binding equation is derived and examined in terms of form, limits, and protein dependence. Furthermore, several approximate relations are derived which are useful for obtaining initial estimates of the model parameters and for a qualitative test of the applicability of the model. It is found that the binding curve may show a characteristic plateau at a saturation equal to the uncontaminated fraction of the protein and that the free ligand concentration at half saturation depends linearly on protein concentration. The practical implications of the present findings are discussed based on an analysis of simulated as well as experimental data.     

Global analysis of three-state protein unfolding data

A new method for analyzing three-state protein unfolding equilibria is described that overcomes the difficulties created by direct effects of denaturants on circular dichroism (CD) and fluorescence spectra of the intermediate state. The procedure begins with a singular value analysis of the data matrix to determine the number of contributing species and perturbations. This result is used to choose a fitting model and remove all spectra from the fitting equation. Because the fitting model is a product of a matrix function which is nonlinear in the thermodynamic parameters and a matrix that is linear in the parameters that specify component spectra, the problem is solved with a variable projection algorithm. Advantages of this procedure are perturbation spectra do not have to be estimated before fitting, arbitrary assumptions about magnitudes of parameters that describe the intermediate state are not required, and multiple experiments involving different spectroscopic techniques can be simultaneously analyzed. Two tests of this method were performed: First, simulated three-state data were analyzed, and the original and recovered thermodynamic parameters agreed within one standard error, whereas recovered and original component spectra agreed within 0.5%. Second, guanidine-induced unfolding titrations of the human retinoid-X-receptor ligand-binding domain were analyzed according to a three-state model. The standard unfolding free energy changes in the absence of guanidine and the guanidine concentrations at zero free-energy change for both transitions were determined from a joint analysis of fluorescence and CD spectra. Realistic spectra of the three protein states were also obtained.     

Mathematical modeling of elution curves for a protein mixture in ion exchange chromatography applied to high protein concentration

Protein elution curves in ion exchange chromatography (IEC) were simulated with a rate model. Three pure proteins and their mixture were used (α‐lactalbumin, BSA, and conalbumin) under different operational conditions. The anionic matrix Q‐Sepharose FF was used packed in a 1 mL column. A high protein concentration (37.5 mg/mL of total protein injected into the column) was used in order to extend the utility of the model. Mass transfer parameters were calculated using empiric correlations, where the axial dispersion was negligible (Pe > 300) and the mass transfer was controlled by the intraparticle diffusion (Bi > 10). The model assumes a modulator–eluite relationship were the equilibrium constant of the Langmuir isotherm was a function of salt concentration. Adsorption kinetic parameters were estimated from experimental data. The parameters for pure proteins were determined, and elution curves for changes in flow rate, ionic strength gradient, concentration, and sample size were predicted by the model. Then the kinetic parameters of the mixture were determined under the same operational conditions and some of the parameters had to be modified to take into account effects such as protein–protein interactions, competition, and displacement. Experimental elution curves obtained for changes in operational conditions such as flow rate and ionic strength gradient were simulated by the rate model for the protein mixture with a relative error in retention time of visible peaks <5%. IEC operational conditions and the peak fraction collection can be selected using a cost function of the production process which considers yield, purity, concentration, and process time that are obtained from simulations. Operational conditions that gave the minimum cost were selected. Simulations allows to diminish experimental time and cost. Biotechnol. Bioeng. 2009; 104: 572–581 © 2009 Wiley Periodicals, Inc.     

Monitoring protein unfolding transitions by NMR-spectroscopy

NMR-spectroscopy has certain unique advantages for recording unfolding transitions of proteins compared e.g. to optical methods. It enables per-residue monitoring and separate detection of the folded and unfolded state as well as possible equilibrium intermediates. This allows a detailed view on the state and cooperativity of folding of the protein of interest and the correct interpretation of subsequent experiments. Here we summarize in detail practical and theoretical aspects of such experiments. Certain pitfalls can be avoided, and meaningful simplification can be made during the analysis. Especially a good understanding of the NMR exchange regime and relaxation properties of the system of interest is beneficial. We show by a global analysis of signals of the folded and unfolded state of GB1 how accurate values of unfolding can be extracted and what limits different NMR detection and unfolding methods. E.g. commonly used exchangeable amides can lead to a systematic under determination of the thermodynamic protein stability. We give several perspectives of how to deal with more complex proteins and how the knowledge about protein stability at residue resolution helps to understand protein properties under crowding conditions, during phase separation and under high pressure.

     

The unfolding tale of the unfolded protein response.

Surface and secreted proteins are synthesized in the endoplasmic reticulum where they must fold and assemble before being transported. Changes in the ER that interfere with their proper maturation initiate the unfolded protein response pathway. New studies have filled in a missing link between the yeast and mammalian pathways.     

Diffusional barrier in the unfolding of a small protein

To determine how the dynamics of the polypeptide chain in a protein molecule are coupled to the bulk solvent viscosity, the unfolding by urea of the small protein barstar was studied in the presence of two viscogens, xylose and glycerol. Thermodynamic studies of unfolding show that both viscogens stabilize barstar by a preferential hydration mechanism, and that viscogen and urea act independently on protein stability. Kinetic studies of unfolding show that while the rate-limiting conformational change during unfolding is dependent on the bulk solvent viscosity, eta, its rate does not show an inverse dependence on eta, as expected by Kramers' theory. Instead, the rate is found to be inversely proportional to an effective viscosity, eta + xi, where xi is an adjustable parameter which needs to be included in the rate equation. xi is found to have a value of -0.7 cP in xylose and -0.5 cP in glycerol, in the case of unfolding, at constant urea concentration as well as under isostability conditions. Hence, the unfolding protein chain does not experience the bulk solvent viscosity, but instead an effective solvent viscosity, which is lower than the bulk solvent viscosity by either 0.7 cP or 0.5 cP. A second important result is the validation of the isostability assumption, commonly used in protein folding studies but hitherto untested, according to which if a certain concentration of urea can nullify the effect of a certain concentration of viscogen on stability, then the same concentrations of urea and viscogen will also not perturb the free energy of activation of the unfolding of the protein.     

Effects of hydrated water on protein unfolding

The conformational stability of a protein in aqueous solution is described in terms of the thermodynamic properties such as unfolding Gibbs free energy, which is the difference in the free energy (Gibbs function) between the native and random conformations in solution. The properties are composed of two contributions, one from enthalpy due to intramolecular interactions among constituent atoms and chain entropy of the backbone and side chains, and the other from the hydrated water around a protein molecule. The hydration free energy and enthalpy at a given temperature for a protein of known three-dimensional structure can be calculated from the accessible surface areas of constituent atoms according to a method developed recently. Since the hydration free energy and enthalpy for random conformations are computed from those for an extended conformation, the thermodynamic properties of unfolding are evaluated quantitatively. The evaluated hydration properties for proteins of known transition temperature (Tm) and unfolding enthalpy (delta Hm) show an approximately linear dependence on the number of constituent heavy atoms. Since the unfolding free energy is zero at Tm, the enthalpy originating from interatomic interactions of a polypeptide chain and the chain entropy are evaluated from an experimental value of delta Hm and computed properties due to the hydrated water around the molecule at Tm. The chain enthalpy and entropy thus estimated are largely compensated by the hydration enthalpy and entropy, respectively, making the unfolding free energy and enthalpy relatively small. The computed temperature dependences of the unfolding free energy and enthalpy for RNase A, T4 lysozyme, and myoglobin showed a good agreement with the experimental ones.(ABSTRACT TRUNCATED AT 250 WORDS)     

Thermodynamics of maltose binding protein unfolding.

The maltose binding protein (MBP or MalE) of Escherichia coli is the periplasmic component of the transport system for malto-oligosaccharides. It is used widely as a carrier protein for the production of recombinant fusion proteins. The melting of recombinant MBP was studied by differential scanning and titration calorimetry and fluorescence spectroscopy under different solvent conditions. MBP exhibits a single peak of heat absorption with a delta(Hcal)/delta(HvH) ratio in the range of 1.3-1.5, suggesting that the protein comprises two strongly interacting thermodynamic domains. Binding of maltose resulted in elevation of the Tm by 8-15 degrees C, depending of pH. The presence of ligand at neutral pH, in addition to shifting the melting process to higher temperature, caused it to become more cooperative. The delta(Hcal)/delta(HvH) ratio decreased to unity, indicating that the two domains melt together in a single two-state transition. This ligand-induced merging of the two domains appears to occur only at neutral pH, because at low pH maltose simply stabilized MBP and did not cause a decrease of the delta(Hcal)/delta(HvH) ratio. Binding of maltose to MBP is characterized by very low enthalpy changes, approximately -1 kcal/mol. The melting of MBP is accompanied by an exceptionally large change in heat capacity. 0.16 cal/K-g, which is consistent with the high amount of nonpolar surface--0.72 A2/g--that becomes accessible to solvent in the unfolded state. The high value of delta Cp determines a very steep delta G versus T profile for this protein and predicts that cold denaturation should occur above freezing temperatures. Evidence for this was provided by changes in fluorescence intensity upon cooling the protein. A sigmoidal cooperative transition with a midpoint near 5 degrees C was observed when MBP was cooled at low pH. Analysis of the melting of several fusion proteins containing MBP illustrated the feasibility of assessing the folding integrity of recombinant products prior to separating them from the MBP carrier protein.