Sem. II, 05/06BTE 4410: Chap. 5 continued 1 Precipitation.

Sem. II, 05/06 BTE 4410: Chap. 5 continued1

PrecipitationPrecipitation


IntroductionIntroduction widely used for the recovery of bulk proteins can be applied to fractionate proteins (separate different types) or as a volume reduction method For example: all the proteins in a stream might be precipitated and redissolved in a smaller volume or a fractional precipitation might be carried out to precipitate the protein interest and leave many of contaminating proteins in the mother liqour Precipitation is usually induced by addition of a salt or an organic solvent, or by changing the pH to alter the nature of the solution. the primary advantages: relatively inexpensive, can be carried out with simple equipment, can be done continuously and leads to a form of the protein that is often stable in long-term storage


Structure and Size In the native state, a protein in an aqueous environment assumes a structure that minimizes the contact of the hydrophobic amino acid residues with the water solvent molecules and maximizes the contact of the polar and charged residues with the water. The major forces acting to stabilize a protein in its native state are hydrogen bonding, van derWaals interactions, and solvophobic interactions (driven forces of folding protein). In aqueous solution, these forces tend to push the hydrophobic residues into the interior of the protein and the polar and charged residues on the protein’s surface.

Protein SolubilityProtein Solubility


Thus, in spite of the forces operating to force hydrophobic residues to the proteins interior, the surface of proteins usually contains a significant fraction of non polar atoms. The forces acting on a protein lead to the achievement of a minimum Gibbs free energy. For a protein in its native configuration, the net Gibbs free energy is on the order of only 10 to 20 kcal/mol. This is a relatively small net free energy, which means that the native structure is only marginally stable and can be destabilized by relatively small environmental changes Water molecules bind to the surface of the protein molecule because of association of charged and polar groups and immobilization by nonpolar

groups.



Figure 1 Schematic diagram of the limit of approach of two protein molecules to each other because of the hydration layers on each molecular surface

For example, a study of the hydration of human serum albumin found two layers of water around the protein.These hydration layers are thought to promote solubility of the protein by maintaining a distance between the surfaces of protein molecules. This phenomenon is illustrated in Figure 1.



The size of a protein becomes important with respect to solubility when the protein is excluded from part of the solvent- happen when nonionic polymers - are added to the solution result in steric exclusion of protein molecules from the volume of solution occupied by the polymer. Juckes developed a model for this phenomenon based on the protein molecule being in the form of a solid sphere and the polymer molecule in the form of a rod- gave the following equation for S, the solubility of the protein:

rs and rr= the radius of the protein solute and polymer rod, respectively, = the partial specific volume of the polymer,

cp = the polymer concentration, and β’ = a constant.

pcKS ''ln 3

'

303.2

r

rs

r

rrVK

E.1

E.2

V



Figure 2 Schematic representation of antibody—antigen

(Ab—Ag) interaction.

Based on this model- can expect the lowest protein solubility for large proteins. Molecular size - predominant factor in a type of precipitation known as affinity precipitation. When affinity groups or antibodies to a specific biomolecule (antigen) are added to a solution, the antibody—antigen interaction can form large multimolecular complexes as shown in Figure 5.2. Such complexes are usually insoluble and cause selective precipitation of the antigen.



ChargeThe net charge of a protein has a direct bearing upon the protein’s solubility. The solubility of a protein increases as its net charge increases, a result of greater interaction with dipolar water molecules. A repulsive reaction between protein molecules of like charge further increases solubility. A simple way to vary the charge on a protein is by changing the pH of the solution. The pH of the solution in which a protein has zero net charge is called the isoelectric pH or isoelectric point. The solubility of a protein - minimum at the isoelectric point. Nonuniform charge distribution, however, results in a dipole moment on the molecule, which leads to an increase in solubility and a move in the minimum solubility away from the isoelectric point.



Figure 3 The solubility (S) of insulin in 0.1 N NaCI as a function of pH. The charge Z is the average protonic charge per 12,000 g of insulin at the pH values indicated.



The net charge of a protein is determined by the following factors: the total number of ionizable residues, the accessibility of the ionizable residues to the solvent, the dissociation constants (or pKa values) of the ionizable groups, and the pH of the solution Besides the chemical makeup of the ionizable groups, factors that can influence the pKa values are the chemical nature of the neighboring groups (e.g.. inductive effects), the temperature, the chemical nature of the solvent as partially reflected by its dielectric constant, and the ionic strength of the solvent.



SolventThe solvent affects the solubility of proteins primarily through two parameters, hydrophobicity and ionic strength Hydrophobicityobservations of single-phase solutions of water and monohydric alcohols - cause protein denaturation at room temperature - can be avoided at sufficiently low temperatures. Studies of monohydric alcohols have shown that denaturing efficiency is as follows:

methanol < ethanol < propanol <butanolconclusion : alcohols with longer alkyl chains - binding more effectively to apolar groups on the protein, weakening intraprotein hydrophobic interactions and thus leading to denaturation.when the temperature is low, the monohydric alcohols compete for the water of hydration on the protein and cause the protein molecules to approach more closely, so that van der Waals interactions lead to aggregation.



Ionic strength The ionic strength of the solvent can have both solubilizing and precipitating effects. The solubilizing effects - referred to as salting in, while the precipitating actions are called salting out. The addition of small quantities of neutral salts to a protein solution often increases protein solubility; the ‘salting in’ effect. However, increasing salt concentrations above an optimal level leads to destabilization of proteins in solution and eventually promotes their precipitation- known as ‘salting out’ salting-in effects by considering the solute size, solute shape, solute dipole moment, solvent dielectric constant, solution ionic strength, and temperature.



the salting-in term increases more than the salting-out term as the of dielectric constant decreases. The dielectric constant decreases as the polarity of the solvent decreases. Therefore, the salting-in effect tends to predominate in relatively nonpolar solvents, while the salting-out effect is more dominant in aqueous solvents. At high ionic strength, the salting-out effect becomes predominant and can be described empirically by the Cohn equation

Ks’ is a salting-out constant characteristic of the specific protein and salt

that is independent of temperature and pH above the isoelectric point. The constant β, the hypothetical solubility of the protein at zero ionic strength, depends only on temperature and pH for a given protein and is a minimum at the isoelectric point

IKS s'ln E7



the Kirkwood equation for the solubility of dipolar ions [E3] can be arranged to give

which is also identical in form to the Cohn equation, with

Both salting in and salting out are illustrated in Figure 4 for hemoglobin with ammonium sulfate or sodium sulfate being added.

From zero ionic strength, the solubility of the protein increases to a maximum as salt is added and then continuously decreases as even more salt is added.

IKKSS isp )(lnln 0

oSln iss KKK '

E8

E9 E10



Figure 4: The effect of (NH4) SO2 and Na2 SO4 on the solubility of hemoglobin: S0 is the solubility in pure water, and S is the solubility in the salt solution.



Salting Out of a Protein with Ammonium SulfateData were obtained on the precipitation of a protein by the addition of ammonium sulfate. The initial concentration of the protein was 30 g/liter. At ammonium sulfate concentrations of 1.0 and 2.0 M, the concentrations of the protein remaining in the mother liquor at equilibrium were 12 and 3 g/liter, respectively. From this information, estimate the ammonium sulfate concentration to give 90% recovery of the protein as precipitate.

Example 1Example 1


SolutionWe can use the Cohn equation [Equation (7)], to solve this problem if we can determine the constants in the equation. Since ionic strength is directly proportional to concentration c for a given salt [Equation (4)], we can rewrite the Cohn equation as

Substituting the experimental data into this equation gives

Example 1Example 1


Solving these equations for the constants yields

For 95% recovery, the protein solubility in the mother liquor at equilibrium is 5% of the initial protein concentration. At this solubility, from the Cohn equation


important characteristics of protein precipitation are the particle size distribution, density and mechanical strength protein precipitates that consist largely of particle sizes with small particle sizes can be difficult to filter or centrifuge low particle densities also can lead to filtration or centrifugation problems and can give excessive bulk volumes of the final dried precipitate particles with low mechanical strength can give problem with excessive attrition when the dry particles are moved low strength can also be interpreted as gel formation, which leads to major problems in filtration and centrifugation precipitates form by a series of steps that occur in sequence; initial mixing, nucleation, growth governed by diffusion and growth governed by fluid motionThe completion of the growth by fluid motion step can be followed by an “aging” step, where the particles are mixed until reaching a stable size

Precipitate Formation PhenomenaPrecipitate Formation Phenomena


Initial Mixinginitial mixing – the mixing required to achieve homogenity after the addition of a component to cause precipitation important to bring precipitant and product molecules into collision as soon as possible important to know the mean length of eddies, also known as the “Kolmogoroff length”, le

where ρ = the liquid density, ν = the liquid kinematic viscosity and P/V = the agitator power input per unit volume of liquid

necessary to mix until all molecules have diffused across all eddies this time can be estimated from the Einstein diffusion relationship

where δ is the diffusion distance and D is the diffusion coefficient for the molecule being mixed

41

3

/

VP

vle

E11

D2

2t

E12



for spherical eddies of diameter le, this becomes

thus precipitation is initiated in a well-stirred tank for a period of time determined on the basis of isotropic turbulence (turbulence in which the products and squares of the velocity components and their derivatives are independent of direction, or, more precisely, invariant with respect to rotation and reflection of the coordinate axes in a coordinate system moving with the mean motion of the fluid.)

D8

2elt

E13



Nucleation is the generation of particles of ultramicroscopic size for particles of a given solute to form, the solution must be supersaturated with respect to the solute in a supersaturated solution the concentration of the solute in solution is greater than the normal equilibrium solubility of the solute the difference between the actual concentration in solution and the equilibrium solubility is called the degree of supersaturation or supersaturation the rate of nucleation increases exponentially up to the maximum level of supersaturation or supersaturation limit which is illustrated in Figure 5 the rate of nucleation increases to a very high value at the supersaturation limit. High supersaturations - have negative consequences in carrying out precipitation - the precipitate tends to be in the form of a colloid, a gel, or a highly solvated precipitate to obtain precipitate particles having desirable characteristics, the supersaturation should be kept relatively low



Figure 5: Nucleation rate as a function of degree of supersaturation. The normal equilibrium solubility is at A and the supersaturation limit is at B



Growth Governed By Diffusion the growth of precipitate is limited by diffusion immediately after nucleation and until the particles grow to a limiting particle size defined by the fluid motion, which generally ranges from 0.1 to 10μm for high and low shear fields respectively in a dispersion of particles of uniform size that are growing as dissolved solute diffuses to the particles, the initial rate of decrease of particle number concentration (N) can be described by a second-order rate equation that was derived by Smoluchowski:

the constant KA is determined by diffusivity D and diameter Lmol, of the molecules that are adding to the particles as follows:

2NKdt

dNA

E14

N = the number of mono-sized particles at any given time t

molA LK D8 E15



integrating eqn. (14) gives

for convenience, N0 is taken as the initial number concentration of dissolved solute moleculesThe Stokes-Einstein equation can be used to estimate the diameter of globular proteins, which can be modeled as spheres:

where k is the Boltzman constant, T is the absolute temperature and μ is the liquid viscosity eqn. (16) can be rewritten as

D3kT

Lmol

tKNN

N

A

00 1

1

E17

E18

0

11

NtKN

A E16



with M as the MW of particles at time t and M0 as the MW of the solute

so that

this equation – verified experimentally by measuring the MW of precipitating a –casein the data plotted in Figure 6 indicate good agreement with eqn. (20) after an initial lag time

N

N

M

M 0

0

)1( 00 tNKMM A

E19

E20



Figure 6: Molecular weight-time plots for the three concentrations of α3 –casein aggregating in the presence of 0.008M CaCl2. MW was determined from light-scattering and turbidity measurements



Calculation of Concentration of Nuclei in a Protein Precipitation

We wish to precipitate the protein α2 –macroglobulin contained in 100 liters of aqueous solution at 20°C in a tank at a concentration of 0.2 g/liter. α2 –Macroglobulin is a globular protein with a molecular weight of 820,000 and a diffusion coefficient of 2.41 x 10-7 cm2/s at 20°C. (Data from Handbook of Biochemistry and Molecular Biology, vol. III, G. D. Fasman, ed., CRC Press, Cleveland, 1976.) The precipitate particles have a density of 1.3 g/cm3. The solution is stirred with a 75 W (0.1 hp) motor. Calculate the concentration of nuclei at the end of the “initial mixing” period.

Example 2Example 2


SolutionDuring the initial stirring, diffusion-limited molecular collisions occur, and molecules must travel by diffusion across an eddy in order to meet. The time required for this is determined by combining the Einstein diffusion equation for spherical eddies [Equation (13)] and the equation for the Kolmogoroff eddy length le or the average diameter of an unstirred zone [Equation (11)]. Assume the properties of water since the solution is dilute, so that ρ = l.0g/cm3 and v = kinematic viscosity = 0.01 cm2/s. First, convert power per unit volume to appropriate units:

Therefore,

Example 2Example 2


Since diffusion is limiting during this 6 s period, the number concentration of nuclei N can be determined from the integrated form of the second-order rate equation for the growth of particles limited by diffusion [Equation (16)]:

where KA =8πDLmol. Since globular proteins are approximately spherical, we

Can estimate the diameter Lmol of the molecule from the Stokes—Einstein equation [Equation (17)]:

This value of Lmol allows us to calculate KA:

Example 2Example 2


N0 is the number concentration of protein molecules that are dissolved before starting precipitation, so that

Substituting into Equation (16) for N, we obtain after the initial 6 s mixing period

In this calculation we note that the term involving N0 is very small, and thus the initial number of molecules is not important to the calculation.

Example 2Example 2


Diffusion-Limited Growth of ParticlesFor the protein precipitation in example 1, calculate the time for the particles to reach a size of 1.0 μm, assuming that growth is governed by diffusion only up to this particle size. Also calculate the number concentration of the 1.0 μm particles.

Example 3Example 3


SolutionAssuming spherical particles, we can calculate the number of molecules per 1.0 imparticle from the volume per particle, the particle density, and the molecular weight of the protein. This enables us to calculate the ratio of the molecular weight of the particle to that of an individual molecule, M/Mo, and from this ratio we can calculate the time to reach this particle size by rearranging Equation (20):

Example 3Example 3


Therefore,

Substituting into the equation for time using the values of KA and

N0 calculated in Example2, we obtain

We can easily calculate N from Equation (19):

Example 3Example 3


Growth Governed By Fluid Motion growth of particles is governed by fluid motion after the particles have reached a critical size, typically 1μm in diameter in this growth regime, particles tend to grow by colliding and then sticking together. This is a flocculation process flocculation is enhanced when electrostatic repulsion between particles is reduced in comparison to the attractive van der Waals Force this can be accomplished by raising the ionic strength and lowering the temperature, to reduce the thickness of the eletrical double layer or Debye length, a round particles for particles of uniform size in a suspension, the initial rate of decrease of particle number concentration (N) due to collisions can be described by a second-order rate equation:

α = the collision effectiveness factor (fraction of collisions that result in permanent aggregates)L = the diameter of the particles and γ = the shear rate (velocity gradient)

23

3

2NL

dt

dN E21



assuming that the volume fraction of the particles (ф = πL3N/6) is constant during particle growth governed by fluid motion, eqn. (5.21) becomes;

Integrating eqn. (22) yields

Where N0 is now the particle number concentration at the time [t=0] in eqn. (23) at which particle growth starts to be governed by fluid motionfor turbulent flow, the average shear rate can be estimated by the following equation developed by Camp and Stein:

where P/V is power dissipated per unit volume and ρ and ν are the density and kinematic viscosity of the liquid, respectively

t

N

N 4exp

0

E23

21

/

VP

E24

Ndt

dN 4

E22



when precipitate particles grow large enough by colliding and sticking together, they become susceptible to breakage during collisions the rate of precipitate breakage – depend on the shear rate and particle concentration a model that has successfully described the breakup of protein precipitates is the displacement model, which depicts the rate of aggregate size change as a function of displacement from an equilibrium aggregate diameter, Le:

where the rate constant k would be expected to depend on the volume fraction of particles ф and the shear rate γ

ne LLkdt

dL E25



Figure 7: Volume mean aggregate diameter as a function of time for soy precipitate particles exposed to shear rate of 1340s-1 at different particle volume fractions (ф). Lines are drawn for the displacement model. Points are experimental data.



as indicated in Figure 7, protein precipitate particles reach a stable size after a certain length of time in a shear field

the time period for reaching this stable size is called the “aging” time the strength of protein particles – correlated with the product of the mean shear rate and aging time, which is known as the Camp number

as indicated in Figure 5.8, for soy protein particles, the mean particle size becomes approximately constant after reaching a Camp number of 105

aging of precipitates helps the particles withstand processing in pumps and centrifuge feed zones without further size reduction

t



Fig 8



Methods - developed to precipitate proteins are based on a knowledge of the solubility of proteins. the most obvious methods that emerge are pH adjustment to the isoelectric point of the protein (called isoelectric precipitation), addition of organic solvents, salting out, and addition of nonionic polymers.

Methods of PrecipitationMethods of Precipitation


Isoelectric precipitationis based on the fact that the solubility of a given protein is generally at a minimum at the isoelectric point (pI) of the protein (Figure 3). This is a convenient method to use when fractionating a protein mixture. For this situation the pH should be adjusted above the highest pI or below the lowest pI of all the proteins present. The pH is then changed to the nearest pI where precipitate is allowed to form and is then removed. There are two advantages of isoelectric precipitation when acids are added to cause precipitation: mineral acids are cheap, and several acids (e.g., phosphoric, hydrochloric, sulfuric) are acceptable in protein food products. This method, however, will not work for all proteins; for example, gelatin, which is a very hydrophilic protein.



Addition of organic solventSeveral organic solvents have been used to precipitate proteins, including alcohols, acetone, and ether. Alcohols - the most widely used in industry. One of the most important processes utilizing alcohol to precipitate proteins is the Cohn process to purify therapeutic proteins from human plasma. This process uses ethanol at temperatures below 0°C to minimize denaturation by the organic solvent. The variables that are manipulated in the Cohn process are pH, ionic strength, and ethanol concentration. Ionic strength is kept low, which leads to a salting-in effect This salting-in effect is enhanced when ethanol is added. Cohn’s methods for the preparation of albumin, plasminogen, prothrombin, isoagglutinins, and y-globulin starting with blood plasma



Salting outIn the salting out of proteins, salt is dissolved in the solution containing the proteins. The protein solubility decreases as the salt ionic strength rises according to the Cohn equation 5.7 most important consideration in salting out - the type of salt that is used. Salts with multiply charged anions such as sulfate, phosphate, and citrate are the most effective; while for the cation, monovalent ions should be used Following the Hofmeister or lyotropic series, the salting-out ability of the common multiply charged anions is citrate2- > phosphate3- > sulfate2- ;for the common monovalent cations the order is NH4

+ > K+ > Na+

the most desirable salt- for precipitating proteins is ammonium sulfate. Its solubility very high (approximately 4 M in pure water) and varies very little in the range of 00 to 300C. The density of its saturated solution is 1.235 gcm-3 - enough below the density of protein aggregates (approximately 1.29 gcm-3 )to allow centrifugation. protein precipitates - often very stable for years in 2 to 3 M salt



Furthermore, proteolysis and bacterial action are prevented in concentrated ammonium sulfate solutions. The only disadvantage of ammonium sulfate - cannot be used above pH 8 because of the buffering action of ammonia. Sodium citrate is very soluble and is a good alternative to ammonium sulfate when the precipitation must be performed above pH 8

Addition of nonionic polymers Several nonionic polymers have been used to precipitate proteins, including dextran, poly(vinyl pyrrolidone), poly(propylene glycol), and poly(ethylene glycol) (PEG) Of these polymers, by far the most extensively studied is PEG. Solutions of PEG up to 20% w/v can be used without viscosity becoming a problem. PEG’s with molecular weights above 4000 - found to be the most effective Protein destabilization in PEG solutions does not occur until the temperature is significantly higher than room temperature (>40 0C)


Sem. II, 05/06BTE 4410: Chap. 5 continued 1 Precipitation.

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