Protein solubility modeling.

A thermodynamic framework (UNIQUAC model with temperature dependent parameters) is applied to model the salt-induced protein crystallization equilibrium, i.e., protein solubility. The framework introduces a term for the solubility product describing protein transfer between the liquid and solid phase and a term for the solution behavior describing deviation from ideal solution. Protein solubility is modeled as a function of salt concentration and temperature for a four-component system consisting of a protein, pseudo solvent (water and buffer), cation, and anion (salt). Two different systems, lysozyme with sodium chloride and concanavalin A with ammonium sulfate, are investigated. Comparison of the modeled and experimental protein solubility data results in an average root mean square deviation of 5.8%, demonstrating that the model closely follows the experimental behavior. Model calculations and model parameters are reviewed to examine the model and protein crystallization process.     

Cloud-point temperatures for lysozyme in electrolyte solutions: effect of salt type, salt concentration and pH

Liquid-liquid phase-separation data were obtained for aqueous saline solutions of hen egg-white lysozyme at a fixed protein concentration (87 g/l). The cloud-point temperature (CPT) was measured as a function of salt type and salt concentration to 3 M, at pH 4.0 and 7.0. Salts used included those from mono and divalent cations and anions. For the monovalent cations studied, as salt concentration increases, the CPT increases. For divalent cations, as salt concentration rises, a maximum in the CPT is observed and attributed to ion binding to the protein surface and subsequent water structuring. Trends for sulfate salts were dramatically different from those for other salts because sulfate ion is strongly hydrated and excluded from the lysozyme surface. For anions at fixed salt concentration, the CPT decreases with rising anion kosmotropic character. Comparison of CPTs for pH 4.0 and 7.0 revealed two trends. At low ionic strength for a given salt, differences in CPT can be explained in terms of repulsive electrostatic interactions between protein molecules, while at higher ionic strength, differences can be attributed to hydration forces. A model is proposed for the correlation and prediction of the CPT as a function of salt type and salt concentration. NaCl was chosen as a reference salt, and CPT deviations from that of NaCl were attributed to hydration forces. The Random Phase Approximation, in conjunction with a square-well potential, was used to calculate the strength of protein-protein interactions as a function of solution conditions for all salts studied.     

Protein extraction by reverse micelles: a study of the factors affecting the forward and backward transfer of alpha-chymotrypsin and its activity

alpha-chymotrypsin is taken as a model protein to investigate three aspects of the protein extraction by reverse micelles: (1) the comparison between the two forward transfer techniques, i.e., the liquid-liquid and the solid state-liquid transfer; (2)the back-transfer, i.e., the capability of the protein to be recovered from the micellar solution; and (3) the maintainance of the enzyme activity at the end of the extraction cycle. Concerning the forward transfer from the liquid phase, we study first the effect of salt initially present in the aqueous phase on the equilibrium concentration of the extracted species; further, we study the forward protein extraction from the solid state, and the effect of pH, salt, and protein concentration on the transfer efficiency. Concerning the back transfer, we find the somewhat surprising result, that the percentage of protein back-extraction depends on the type and concentration of salt used for the forward transfer. Preliminary data concerning an alternative method for the back-transfer using silica gel to liberate the protein from the micellar environment, are presented. Finally, it is found that the enzyme activity depends again on the type and concentration of salt used for the forward transfer.     

Enhancing the production of Fc fusion protein in fed-batch fermentation of Pichia pastoris by design of experiments

This study focuses on the feasibility of producing a therapeutic Fc fusion protein in Pichia pastoris (P. pastoris) and presents an optimization design of experiment (DOE) strategy in a well-defined experimental space. The parameters examined in this study include pH, temperature, salt supplementation, and batch glycerol concentration. The effects of these process conditions were captured by statistical analysis focusing on growth rate and titer responses. Batch medium and fermentation conditions were also investigated prior to the DOE study in order to provide a favorable condition to enable the production of this Fc fusion protein. The results showed that approximately 373 mg/L of the Fc fusion protein could be produced. The pH was found to be particularly critical for the production of this Fc fusion protein. It was significantly higher than the conventional, recommended pH for P. pastoris fermentation. The development of this process shows that protein production in P. pastoris is protein specific, and there is not a set of pre-defined conditions that can work well for all types of proteins. Thorough process development would need to be performed for every type of protein in order for large-scale production in P. pastoris to be feasible.     

A model for the salt effect on adsorption equilibrium of basic protein to dye-ligand affinity adsorbent

A model describing the salt effect on adsorption equilibrium of a basic protein, lysozyme, to Cibacron Blue 3GA-modified Sepharose CL-6B (CB-Sepharose) has been developed. In this model, it is assumed that the presence of salt causes a fraction of dye-ligand molecules to lodge to the surface of the agarose gel, resulting from the induced strong hydrophobic interaction between dye ligand and agarose matrix. The salt effect on the lodging of dye-ligand is expressed by the equilibrium between salt and dye-ligand. For the interactions between protein and vacant binding sites, stoichiometric equations based either on cation exchanges or on hydrophobic interactions are proposed since the CB dye can be regarded as a cation exchanger contributed by the sulfonate groups on it. Combining with the basic concept of steric mass-action theory for ion exchange, which considers both the multipoint nature and the macromolecular steric shielding of protein adsorption, an explicit isotherm for protein adsorption equilibrium on the dye-ligand adsorbent is formulated, involving salt concentration as a variable. Analysis of the model parameters has yielded better understanding of the mechanism of salt effects on adsorption of the basic protein. Moreover, the model predictions are in good agreement with the experimental data over a wide range of salt and ligand concentrations, indicating the predictive nature of the model.     

Systematic interpolation method predicts protein chromatographic elution with salt gradients,pH gradients and combined salt/pH gradients

A methodology is presented to predict protein elution behavior from an ion exchange column using both individual or combined pH and salt gradients based on high‐throughput batch isotherm data. The buffer compositions are first optimized to generate linear pH gradients from pH 5.5 to 7 with defined concentrations of sodium chloride. Next, high‐throughput batch isotherm data are collected for a monoclonal antibody on the cation exchange resin POROS XS over a range of protein concentrations, salt concentrations, and solution pH. Finally, a previously developed empirical interpolation (EI) method is extended to describe protein binding as a function of the protein and salt concentration and solution pH without using an explicit isotherm model. The interpolated isotherm data are then used with a lumped kinetic model to predict the protein elution behavior. Experimental results obtained for laboratory scale columns show excellent agreement with the predicted elution curves for both individual or combined pH and salt gradients at protein loads up to 45 mg/mL of column. Numerical studies show that the model predictions are robust as long as the isotherm data cover the range of mobile phase compositions where the protein actually elutes from the column.     

Influence of pH and ionic strength on the steric mass-action model parameters around the isoelectric point of protein

The ion-exchange equilibrium and the dependence of the parameters in the steric mass-action (SMA) model on salt concentration and buffer pH around the isoelectric point of protein were studied. Bovine serum albumin (BSA, isoelectric point = 5.4) was used as a model protein and DEAE Sepharose FF as an ion exchanger. Finite batch adsorption experiments and isocratic elution chromatography were performed for the determination of the model parameters (i.e., characteristic charge, equilibrium constant, and steric factor). The results showed that pH had significant effects on the parameters. With an increase of pH from 4.5 to 6.5, the characteristic charge increased from 0.9 to 3.0 and leveled off as a plateau at pH above 5.5. The charge groups in the contact region of protein surface were considered to play a crucial role on the characteristic charge. The decrease of pH and increase of salt concentration lowered the absolute value of the zeta potential of the protein surface and led to a decrease of the equilibrium constant. The steric factor remained unchanged at about 31 at pH 5.5 and 6.0 and increased to 44.5 at pH 5.0 and 96.8 at pH 4.5, mainly as a result of the lower adsorption capacity of BSA at pH <5.5. Furthermore, the increase of the molecular volume of BSA at pH 4.5 would be an additional reason for the increase of the steric factor. Taking into account the effect of the pH and salt concentration on these parameters, the SMA model described the ion exchange equilibrium of protein more accurately.     

Empirical validation of a two-state kinetic model for the B-Z transition of double-stranded poly[d(G-m5C)]

5 C)] in terms of the salt concentration, the absolute temperature, and the cooperativity index. The validity of the formula was tested using circular dichroism spectroscopy after variation of the type of salt (NaCl, MgCl₂), the salt concentration, and the temperature of the polynucleotide solution. A consequence of the proposed function is that in conditions of high salt there is a predictable salt threshold which determines the particular molecular mechanism of the B-Z transition. The paper also describes the way in which this threshold level is temperature dependent. A detailed comparison of our data with the experimental data found by other authors is given. The function agrees quantitatively with the experiments and explains the contrasting results found in the literature about the influence in the B-Z transition of both the temperature and the polymer size. Received: 21 April 1999 / Accepted: 9 September 1999     

Effect of secondary structure on the potential of mean force for poly-L-lysine in the alpha-helix and beta-sheet conformations

Because poly-L-lysine (PLL) can exist in the alpha-helix or beta-sheet conformation depending on solution preparation and solution conditions, PLL is a suitable candidate to probe the dependence of protein interactions on secondary structure. The osmotic second virial coefficient and weight-average molecular weight are reported from low-angle laser-light scattering measurements for PLL as a function of NaCl concentration, pH, and alpha-helix or beta-sheet content. Interactions between PLL molecules become more attractive as salt concentration increases due to screening of PLL charge by salt ions and at low salt concentration become more attractive as pH increases due to decreased net charge on PLL. The experimental results show that interactions are stronger for the beta-sheet conformation than for the alpha-helix conformation. A spherically-symmetric model for the potential of mean force is used to account for specific interactions not described by DLVO theory and to show how differences in secondary structure affect PLL interactions.     

Effects of pH, salt, and macromolecular crowding on the stability of FK506-binding protein: an integrated experimental and theoretical study

Environmental variables can exert significant influences on the folding stability of a protein, and elucidating these influences provides insight on the determinants of protein stability. Here, experimental data on the stability of FKBP12 are reported for the effects of three environmental variables: pH, salt, and macromolecular crowding. In the pH range of 5-9, contribution to the pH dependence of the unfolding free energy from residual charge-charge interactions in the unfolded state was found to be negligible. The negligible contribution was attributed to the lack of sequentially nearest neighboring charged residues around groups that titrate in the pH range. KCl lowered the stability of FKBP12 and the E31Q/D32N double mutant at small salt concentrations but raised stability after approximately 0.5 M salt. Such a turnover behavior was accounted for by the balance of two opposing types of protein-salt interactions: the Debye-Hückel type, modeling the response of the ions to protein charges, favors the unfolded state while the Kirkwood type, accounting for the disadvantage of the ions moving toward the low-dielectric protein cavity from the bulk solvent, disfavors the unfolded state. Ficoll 70 as a crowding agent was found to have a modest effect on protein stability, in qualitative agreement with a simple model suggesting that the folded and unfolded states are nearly equally adversely affected by macromolecular crowding. For any environmental variable, it is the balance of its effects on the folded and unfolded states that determines the outcome on the folding stability.     

Seeded isothermal batch crystallization of lysozyme

The kinetics of lysozyme crystallization under seeded isothermal batch conditions was followed by measurement of the decline in solution concentration versus time. Kinetics were measured for five different values of the seed crystal mass. The data were analyzed using a recently proposed mathematical model. For each seed mass, the model fit the kinetic data well. Growth rate constants determined using the model were approximately constant over a sixfold increase in the seed crystal mass, and fell well within the range of values reported in the literature, but obtained using entirely different experimental techniques. These results confirmed the utility of the proposed model. The proposed model can be used to analyze crystallization kinetics using absorbance measurements only, without the need to characterize the crystal size, thus avoiding the need for expensive laser light scattering and digital microscopy instrumentation. Thus, the model offers a low-cost straightforward method to analyze and simulate the effects of changes in operating parameters such as the seed crystal mass, solution volume, initial protein concentration, pH, temperature, salt concentration, and time.     

Cloud-point temperatures of lysozyme in electrolyte solutions by thermooptical analysis technique

Liquid-liquid phase-separation data are obtained for aqueous solutions of lysozyme. Thermooptical analysis (TOA) technique overcomes many defects of the light scattering method, which is most commonly used for this purpose, and provides a simple, rapid and reliable experimental method to determine cloud-point temperatures (CPTs) of aqueous protein solution systems. The TOA apparatus described here needs very small amount of samples (0.02 ml), and CPT can easily be determined in a very short time. The CPTs are measured as a function of salt type and concentration at pH 4.0 and 7.0. Salts used include those from mono and divalent cations and anions, and the modified Perturbed-Hard-Sphere-Chain (PHSC) model that takes into account the shape of protein is used to interpret the effect of salts.     

Coarse-grained strategy for modeling protein stability in concentrated solutions

We present a coarse-grained approach for modeling the thermodynamic stability of single-domain globular proteins in concentrated aqueous solutions. Our treatment derives effective protein-protein interactions from basic structural and energetic characteristics of the native and denatured states. These characteristics, along with the intrinsic (i.e., infinite dilution) thermodynamics of folding, are calculated from elementary sequence information using a heteropolymer collapse theory. We integrate this information into Reactive Canonical Monte Carlo simulations to investigate the connections between protein sequence hydrophobicity, protein-protein interactions, protein concentration, and the thermodynamic stability of the native state. The model predicts that sequence hydrophobicity can affect how protein concentration impacts native-state stability in solution. In particular, low hydrophobicity proteins are primarily stabilized by increases in protein concentration, whereas high hydrophobicity proteins exhibit richer nonmonotonic behavior. These trends appear qualitatively consistent with the available experimental data. Although factors such as pH, salt concentration, and protein charge are also important for protein stability, our analysis suggests that some of the nontrivial experimental trends may be driven by a competition between destabilizing hydrophobic protein-protein attractions and entropic crowding effects.     

On the charge regulation of proteins

It is known that the overall charge of a protein can change as the molecule approaches a charged object like another protein or a cell membrane. We have formalized this mechanism using a statistical mechanical framework and show how this rather overlooked interaction increases the attraction between protein molecules. From the theory, we can identify a unique property, the protein charge capacitance, that contains all information needed to describe the charge regulation mechanism. The capacitance can be obtained from experiment or theory and is a function of pH, salt concentration, and the number of titrating residues. For a range of different protein molecules, we calculate the capacitance and demonstrate how it can be used to quantify the charge regulation interaction. With minimal effort, the derived formulas can be used to improve existing models by including a charge regulation term. Good agreement is found between theory, simulations, and experimental data.     

Influence of the NaCl or CaCl2 concentration on the structure of heat-set bovine serum albumin gels at pH 7

The structure of heat-set systems of the globular protein bovine serum albumin (BSA) was investigated at pH 7 in different salt conditions (NaCl or CaCl(2)) using light scattering. Cross-correlation dynamic light scattering was used to correct for multiple scattering from turbid samples. After heat treatment, aggregates are formed whose size increases as the protein concentration increases. Beyond a critical concentration that decreases with increasing salt concentration, gels are formed. The heterogeneity and the reduced turbidity of the gels were found to increase with increasing salt concentration and to decrease with increasing protein concentration. The structure of the gels is determined by the strength of the repulsive electrostatic interactions between the aggregated proteins. The results obtained in NaCl are similar to those reported in previous studies for other globular proteins. CaCl(2) was found to be much more efficient in reducing electrostatic interactions than NaCl at the same ionic strength.     

Specific ion effects: why the properties of lysozyme in salt solutions follow a Hofmeister series

Protein solubility in aqueous solutions depends in a complicated and not well understood way on pH, salt type, and salt concentration. Why for instance does the use of two different monovalent salts, potassium thiocyanate and potassium chloride, produce such different results? One important and previously neglected source of ion specificity is the ionic dispersion potential that acts between each ion and the protein. This attractive potential is found to be much stronger for SCN(-) than it is for Cl(-). We present model calculations, performed within a modified ion-specific double-layer theory, that demonstrate the large effect of including these ionic dispersion potentials. The results are consistent with experiments performed on hen egg-white lysozymes and on neutral black lipid membranes. The calculated surface pH and net lysozyme charge depend strongly on the choice of anion. We demonstrate that the lysozyme net charge is larger, and the corresponding Debye length shorter, in a thiocyanate salt solution than in a chloride salt solution. Recent experiments have suggested that pK(a) values of histidines depend on salt concentration and on ionic species. We finally demonstrate that once ionic dispersion potentials are included in the theory these results can quantitatively be reinterpreted in terms of a highly specific surface pH (and a salt-independent pK(a)).     

Computer simulation of flow-dependent absorption in microperfused short Henle's loop of rats.

With computer simulation we examined the extent to which current theories and experimental data explain function of single microperfused superficial Henle's loops in rats. In the model standard phenomenological equations describe transport; two sets of transport parameters labeled rat and rabbit were taken from published experiments; Michaelis-Menten kinetics in the ascending thick limb were adjusted arbitrarily; tubular radius is either constant or depends on luminal pressure with compliance based on experimental observations; the interstitium is an infinite sink with salt and urea concentrations constant in the cortex and exponentially increasing in the outer medulla; concentrations resemble those found in hydropenic or saline diuretic rats. The following predictions were obtained. The model with rabbit parameters does not recirculate urea and will not operate with high medullary urea concentrations; with rat parameters too much urea recirculates an the results of perfusion with equilibrium solution are not reproduced. Using a compromise between rat and rabbit parameters, the model reproduces water absorption, salt reabsorption, and urea recirculation as observed in vivo in rat loops perfused at 5-40 nl/min. It also simulates perfusion with saline, equilibrium solution, saline plus furosemide, and 300 mM mannitol. When the model includes a short early distal segment, effluent salt concentration reaches a minimum at a 15 nl/min perfusion rate as observed in vivo; however, concentration at the macula densa is a monotonically increasing function of flow. When permeation rate is a function of wall surface area and thickness a better fit to experimental results is produced. However, the effect is small: water absorption alters by 4% or less and effluent salt concentration is reduced by up to 10% at low perfusion rates. Comparison of rigid and compliant loops shows no relationship between transit time per se and reabsorption.     

Protein self-association in solution: the bovine beta -lactoglobulin dimer and octamer

We have used proton magnetic relaxation dispersion (MRD) to study the self-association of bovine beta-lactoglobulin variant A (BLG-A) as a function of temperature at pH 4.7 (dimer-octamer equilibrium) and as a function of NaCl concentration at pH 2.5 (monomer-dimer equilibrium). The MRD method identifies coexisting oligomers from their rotational correlation times and determines their relative populations from the associated dispersion amplitudes. From MRD-derived correlation times and hydrodynamic model calculations, we confirm that BLG-A dimers associate to octamers below room temperature. The tendency for BLG-A dimers to assemble into octamers is found to be considerably weaker than in previous light scattering studies in the presence of buffer salt. At pH 2.5, the MRD data are consistent with an essentially complete transition from monomers in the absence of salt to dimers in 1 M NaCl. Because of an interfering relaxation dispersion from nanosecond water exchange, we cannot determine the oligomer populations at intermediate salt concentrations. This nanosecond dispersion may reflect intersite exchange of water molecules trapped inside the large binding cavity of BLG-A.     

Salt effects on the denaturation of DNA. IV. A calorimetric study of the helix-coil conversion of the alternating copolymer poly[d(A-T)].

The enthalpy deltaH, entropy deltaS, and the temperature Tm of the conformational transition of poly[d (A-T)] from the ordered to the randomly oriented state have been determined at pH 6.8 with the help of an adiabatic differential scanning calorimeter in Na2SO4 solutions of increasing ionic strength. Spectrophotometric denaturation experiments supplemented the calorimetric measurements. All thermodynamic parameters were found to vary strongly with salt concentration: both deltaH and Tm increase linearly with the logarithm of the mean molal activity alpha plus or minus of Na2SO4. However, whereas the dependence of Tm on salt activity remains linear over the entire salt concentration range employed deltaH decreases abruptly in the most concentrated Na2SO4 solutions. The entropy of melting changes with salt concentration in a pattern similar to that displayed by deltaH. The data on deltaH as well as data derived from the maximum slopes of the calorimetric heat denaturation curves were used to calculate the cooperative length Lh, the stacking free energy epsilon, and the cooperativity parameter sigma of poly[d(A-T)] as a function of ionic strength. Lh decreases with increasing salt concentration whereas sigma increases. Epsilon assumes more positive values with increasing salt molality. These changes then are in agreement with the generally held belief that an increase in salt concentration leads to an increase in the "loop" content of the copolymer.     

Evaluation of differences between dual salt‐pH gradient elution and mono gradient elution using a thermodynamic model: Simultaneous separation of six monoclonal antibody charge and size variants on preparative‐scale ion exchange chromatographic resin

The efficiencies of mono gradient elution and dual salt‐pH gradient elution for separation of six mAb charge and size variants on a preparative‐scale ion exchange chromatographic resin are compared in this study. Results showed that opposite dual salt‐pH gradient elution with increasing pH gradient and simultaneously decreasing salt gradient is best suited for the separation of these mAb charge and size variants on Eshmuno^® CPX. Besides giving high binding capacity, this type of opposite dual salt‐pH gradient also provides better resolved mAb variant peaks and lower conductivity in the elution pools compared to single pH or salt gradients. To have a mechanistic understanding of the differences in mAb variants retention behaviors of mono pH gradient, parallel dual salt‐pH gradient, and opposite dual salt‐pH gradient, a linear gradient elution model was used. After determining the model parameters using the linear gradient elution model, 2D plots were used to show the pH and salt dependencies of the reciprocals of distribution coefficient, equilibrium constant, and effective ionic capacity of the mAb variants in these gradient elution systems. Comparison of the 2D plots indicated that the advantage of opposite dual salt‐pH gradient system with increasing pH gradient and simultaneously decreasing salt gradient is the noncontinuous increased acceleration of protein migration. Furthermore, the fitted model parameters can be used for the prediction and optimization of mAb variants separation in dual salt‐pH gradient and step elution. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 34:973–986, 2018