Chromatography
Unit operations of Bioseparations Unit operations of Bioseparations • Solid‐liquid separations – – – –
Centrifugation Sedimentation Filtration Microfiltration
• Solids concentration S lid t ti – crystallization, precipitation and extraction
• Concentration of soluble products Concentration of soluble products – adsorption and affinity chromatography
• Purification – chromatography
What is Chromatography? What is Chromatography? • Ability Ability to separate molecules using to separate molecules using partitioning characteristics of molecule to remain in a stationary phase versus a mobile remain in a stationary phase versus a mobile phase – Once a molecule is separated from the mixture, it Once a molecule is separated from the mixture it can be isolated and quantified
• Can chromatography identify components? Can chromatography identify components? – Not without the detector – chromatography is the process of separation! process of separation!
Chromatography: Introduction Chromatography: Introduction • Dynamic separation process based on inter‐phase y p p p mass transfer involving • Stationary phase which is generally arranged in the form of a packed bed • Mobile phase that flows through the stationary phase
• SSubstances to be separated are carried along through bstan es to be separated are arried alon thro h the packed bed by the mobile phase • These These substances selectively bind reversibly onto (or substances selectively bind reversibly onto (or partition into) the stationary phase to different extents • Based on this these substances move through the column at different velocities
Chromatographic Separation
Chromatography: Basic components Chromatography: Basic components • Major components: – Mobile phase flows through column, carries analyte – Gas = Gas Chromatography (GC) – Liquid = Liquid Chromatography (LC), Thin Layer Li id Li id Ch h (LC) Thi L Chromatography (TLC) – Supercritical fluid Supercritical fluid = Supercritical Fluid Chromatography (SFC) Supercritical Fluid Chromatography (SFC)
• Stationary phase stays in a place, does not move – GC, LC placed inside of the column , p – TLC – layer of a sorbent on the plate
• The SEPARATION is based on the partitioning between p g the mobile and stationary phase
Basic Chromatographic Terminology Basic Chromatographic Terminology • •
• • • • • • •
Chromatograph: Instrument employed for a chromatography. St ti Stationary phase: Phase that stays in place inside the column. Can h Ph th t t i l i id th l C be a particular solid or gel‐based packing (LC) or a highly viscous liquid coated on the inside of the column (GC). M bil h Mobile phase: Solvent moving through the column, either a liquid S l t i th h th l ith li id in LC or gas in GC. Eluent: Fluid entering a column. Eluate: Fluid exiting the column. Elution: The process of passing the mobile phase through the column. Chromatogram: Graph showing detector response as a function of a time. Flow rate: How much mobile phase passed / minute (ml/min). Linear velocity: Distance passed by mobile phase per 1 min in the column (cm/min).
Chromatographic separation Chromatographic separation Mobile phase t0 t1
t2
St ti Stationary phase h
t3
Chromatography equipment Chromatography equipment Sample
Column
Mobile phase reservoir
Pump
Detector
Chromatograms Mobile phase
Mobile phase
Mobile phase
Mobile phase
Mobile phase
Sample
Concentration
Migrating bands Time
Peaks
Resolution of separation p Resolution of two peaks from one another = Δtr/wav We Want Resolution > 1.5
The separation is worse with the increasing peak width
Chromatographic elution Chromatographic elution Isocratic i elution l i
Gradient elution
A B A
B
Gradients B
Step Linear
A
Non-linear
Chromatographic columns Chromatographic columns
Packed bed
Packed Open capillary tubular
Membrane
Monolith
Separation mechanisms Separation mechanisms •Adsorption Adsorption •Ion-exchange •Reverse phase •Hydrophobic H d h bi interaction i t ti •Size exclusion •Supercritical fluid •Affinity
Separation Mechanisms Separation Mechanisms • Ion exchange – Based on electrostatic interactions between the molecules and the adsorbent
• Affinity binding – Based on stereospecific Based on stereospecific recognition of target recognition of target molecules by ligands – the shape of the ligand p g is complimentary to the p y shape of the entire target molecule or at least a portion of the molecule
Separation Mechanisms Separation Mechanisms • Reversed phase Reversed phase – Partition type behaviour – Used for adsorption of non‐polar molecules Used for adsorption of non polar molecules
• Hydrophobic interaction – Based on interaction between hydrophobic patches on molecules and those on the adsorbent – Mainly used for protein separations M i l df t i ti
Separation principles in protein chromatographic purification h hi ifi i
Adsorption chromatography p g p y
Adsorption chromatography Adsorption chromatography • Biological molecules have varying tendencies to adsorb onto polar adsorbents – silica gel, alumina, diatomaceous earth, charcoal
• Performance of the adsorbent relies strongly on – the chemical composition of the surface, i.e. the types and concentrations of exposed atoms or groups concentrations of exposed atoms or groups.
• The order of elution of sample components depends primarily on molecule polarity primarily on molecule polarity. – Because the mobile phase is in competition with solute for adsorption sites, solvent properties are also important. – Polarity scales for solvents are available to aid mobile‐phase selection
Ion exchange Ion exchange • Ion exchange adsorbents – charged charged groups attached onto groups attached onto insoluble support material
• Examples – Cellulose, Cellulose derivatives Cellulose Cellulose derivatives – Agarose, Acrylic resins – Cross linked dextrans
Cation exchange h
• Charged groups for cationic resins Ch d f ti i i – Carboxylic, carboxymethyl, sulphopropyl
• Charged groups for anionic resins Ch d f i i i – Diethylamino ethyl (DEAE) – Quarternary aminoethyl (QAE)
Anion exchnge
Functional Groups Used in IEC Functional Groups Used in IEC
Ion exchange Ion exchange chromatography of proteins
Cation Exchange Media Exchange Media
Anion Exchange Media Anion Exchange Media
Parameters influencing ion‐exhange Parameters influencing ion exhange • pH – For binding proteins on anionic adsorbents pH is maintained above pI; on cationic adsorbents pH is kept below pI below pI
• Ionic strength – Greater the ionic strength the lesser the amount bound Greater the ionic strength the lesser the amount bound
• Buffer type – Th The charged ligands h d li d present present t t on the adsorbent th d b t are associated with mobile exchangeable counterions – Some counterions are more exchangeable and hence g their use result in higher binding of target molecules
Elution of molecules bound on ion exchange adsorbents h d b • Solution Solution containing high concentration of neutral salt containing high concentration of neutral salt e.g NaCl – At high concentration the salt shields the electrostatic interactions between the target molecules from the adsorbent resulting in desorption – The charged electrolytes also compete with the target The charged electrolytes also compete with the target molecules for binding and hence dislodge the target molecules
• Bound molecules can also be eluted by changing the solution pH
Protein
Isoelectric pH
L Lysozyme
11 0 11.0
Ovalbumin
4.6
Conalbumin
6.1
Egg white proteins
Separation of lysozyme from hen egg white using cation hi i i exchange h
Other egg white Lysozyme +NaCl proteins
+
Cation exchange adsorbent + N Cl NaCl
+ NaCl Cation exchange adsorbent + lysozyme
Cation exchange adsorbent + NaCl
Separation of human immunoglobulin G from human serum albumin using anion exchange serum albumin using anion exchange Protein
Isoelectric pH
HSA
4.9
HIgG
7.0
HSA +NaCl HI G HIgG
HAS and HIgG
+ NaCl
+
Anion exchange adsorbent
Anion exchange adsorbent + HSA
Anion exchange adsorbent + NaCl
Affinity binding
Based on stereospecific recognition of target molecules by ligands
Affi it bi di Affinity binding
Affinity ligands and purified proteins Affinity ligands and purified proteins Immobilized ligand
Purified protein
Divalent and trivalent metal Proteins with an abundance ion of His, Tryp and Cys residues id Lectins Glycoproteins, cells Carbohydrates
Lectins
Reactive dyes e.g Cibacon bl P blue, Proscion i blue bl
Most proteins, particularly nucleotide‐binding proteins l id bi di i
Nucleic acids
Exo and endonucleases, polymerases, other nucleic l th l i acid‐binding proteins
Affinity ligands and purified proteins Affinity ligands and purified proteins Immobilized ligand
Purified protein
Amino acids (e.g. Lys, Arg)
Proteases
Nucleotides, cofactors , substrates and inhibitors
Enzymes y
Proteins A and G Proteins A and G
Immunoglobulins
Hormones, drugs
Receptors
Antibodies
Antigens
Antigens
Antibodies
Support matrices for affinity adsorption
Affinity purification of a monoclonal antibody from mammalian cell culture supernatant
Impurities
Monoclonal antibody
Cell culture supernatant
+ Low pH buffer Protein A affinity Protein A affinity adsorbent
Protein A affinity adsorbent + d b Monoclonal antibody
Protein A affinity ff adsorbent
Reverse phase adsorption Reverse phase adsorption • Based on partitioning p g – Partitioning takes place into a very thin immobilised layer of hydrocarbon and not layer of hydrocarbon and not within a body of extracting solvent
•H Hydrophoic d h i low polarity substances C4 to l l it bt C4 t C18 are used for solute binding – chemically bound to solid support material such as silica
Reversed phase adsorption p p Polar media
Adsorption Immobilised hydrocarbon layer
Non‐Polar media
Desorption
Reverse phase separation of insulin Reverse phase separation of insulin Filtered fermentation media + media Acetonitrile
Impurities
Insulin
+ 80% acetonitrile + 20% IPA C 18 reverse C‐18 reverse phase adsorbent
Adsorbent + d b Insulin
C‐18 reverse phase adsorbent
Hydrophobic interaction based adsorption Hydrophobic interaction based adsorption • Based Based on the interaction between the hydrophobic on the interaction between the hydrophobic patches on molecules and on the adsorbent • Mainly used for protein separation y p p – In aqueous solutions hydrophobic aminoacids are shielded by a structured layer of water molecules – Removal of water molecules by the addition of anti‐ chaotropic agents (NH4)2SO4, Na2SO4) facilitates interaction of the exposed hydrophobic patches with interaction of the exposed hydrophobic patches with the adsorbent
• Agarose is the most widely used support material
Ligands coupled to a chromatographic matrix b l id l ether by glycidyl h Hydrophobic patches Hydrophobic patches created by grafting alkyl and aromatic hydrocarbon groups on agarose
Alkyl
Butyl
Phenyl
Octyl
Hydrophobic interaction based adsorption
Molecule
Structured water Structured water in bulk solution
Adsorption Hydrophobic layer
Low salt concentration
Desorption
Hydrophobic interaction Two aliphatic carbon chains (black circles) are immersed in water When two chains are in contact, the surface area that is covered with ordered water molecules is decreased and some water is in a state of less order in the bulk of the state of less order in the bulk of the water. The free energy of the system decreases, and thus the binding g together of the two molecules is favored.
Hydrophobic interaction of a protein Two octyl chains are coupled to a chromatographic medium An energy gain is achieved by the interaction of the octyl chains with nonpolar moieties on a protein The carbon atoms of the hydrophobic parts of the h b f h h d h bi f h protein are indicated with black circles The oxygen atoms of the water with white circles hi i l Charged atoms or groups of the protein with white circles containing plus or minus signs. The hatched area indicates the interior part of the protein
Hydrophobic interaction: Separation of rEGF y p p Filtered Fil d fermentation media + Ammonium Ammonium sulphate
Impurities
rEGF
+
Hydrophobic interaction adsorbent
Adsorbent + d b rEGF
Ammonium sulphate free solution
Hydrophobic Hydrophobic interaction adsorbent
Partition chromatography Partition chromatography
Partition chromatography Partition chromatography • Normal‐phase chromatography Normal‐phase chromatography – When the stationary phase is more polar th th than the mobile phase, bil h
• Reverse‐phase chromatography – When non‐polar compounds are being p y separated it is usual to use a stationary phase which is less polar than the mobile p phase
Reversed‐phase Reversed phase chromatography chromatography • A A common stationary phase for reverse common stationary phase for reverse‐phase phase chromatography is hydrocarbon with 8 or 18 carbons bonded to silica gel • Solvent systems most frequently used are water‐acetonitrile and water‐methanol – Aqueous buffers are also employed to suppress ionisation of sample components.
• Elution is generally in order of increasing solute hydrophobicity.
Ion exchange chromatography g g p y
Si e exclusion chromatography Size exclusion chromatography
Affinity chromatography Affinity chromatography
Applications • • • • • • • •
Pharmaceuticals and Fine chemicals Biotechnology y Environmental analysis Foods and nutraceuticals Water treatment Analysis of chemicals g Diagnostics Process control
Chromatography: Theory of retention
Free
y Diffusion
y
Bound
y
Diffusion z
z
t
Factors influencing the transformation of shape f f h • • • • •
Interaction with the stationary phase Interaction with the stationary phase Non‐ideal inlet distribution Radial dispersion di l di i Axial dispersion Golay – Taylor dispersion
Theory of retention The association of a component with the stationary phase is quantified in terms of the capacity factor (k′):
nS k′ = nM VS c S VS k′ = =K VM c M VM ⎛1− ε ⎞ k′ = K⎜ ⎟ ⎝ ε ⎠
nS and n d M are the number of moles of a h b f l f component bound to the stationary phase and that present in the mobile phase respectively in any element of column volume any element of column volume VS and VM are the volume of stationary phase and mobile phase respectively in any element of column volume cS and cM are the corresponding values for concentration of the component in these phases respectively, and K is a distribution coefficient
ε is the voidage fraction. k' should ideally have a value between 1 and 10
Theory of Retention The retention time of the mobile phase (tM) within a column would be based purely on hydrodynamic considerations y t M
t R = (t R − t M ) '
tR
tR ' k′ = tM
tM t
⎛ 1− ε ⎞ t R = t M ⎜1 + K⎟ ε ⎝ ⎠
VC ε = Q
VC (ε + K − εK ) tR = Q Q= mobile phase flow rate Q= mobile phase flow rate K = distribution coefficient Vc = column volume
Resolution and selectivity Resolution and selectivity t R2 tR1
tM
Concentration
w1
w2
Time
Resolution
t R 2 − t R1 R= 0.5(w1 + w2 )
Selectivity parameter (α) K 2 k2′ t R 2 − tM α= = = K1 k1′ t R1 − tM
Chromatography: Plate concept •A chromatographic column is assumed to be A h t hi l i dt b made up of a large number of hypothetical plates •Each of these plates is equivalent to one •Each of these plates is equivalent to one equilibrium stage •The The plate concept is borrowed from distillation plate concept is borrowed from distillation •The greater the number of plates, the better the separation is likely to be p y •The height equivalent to a theoretical plate (HETP or simply H) should be as small as possible
H
=
l N
⎛ tR ⎞ N = 16 ⎜ ⎟ ⎝w⎠
2
Definition of Plate Height Definition of Plate Height The breadth of a Gaussian curve is related to the variance σ2. Therefore, the plate height can be d f d defined as the variance per unit h length of the column:
H = σ2/L Plate height can be defined as column length in cm which contains 34% of the solute at the end of the 34% of the solute at the end of the column (as the solute elutes) The peak width can also be represented in terms of time, τ, where:
τ = σ/v / τ = σ/(L/tR)
Band Broadening Band Broadening • Apart from specific p p characteristics of solutes that cause differential migration • Average migration rates for A i ti t f molecules of the same solute are not identical • Three main factors contribute to this behavior – Longitudinal Diffusion L it di l Diff i – Resistance to Mass Transfer – Stationary Phase Mass Transfer
Longitudinal Diffusion Longitudinal Diffusion • Molecules Molecules tend to diffuse in all directions tend to diffuse in all directions because these are always present in a concentration zone as compared to the other concentration zone as compared to the other parts of the column H = K D /V L
1 M
DM = the diffusion of solute in the mobile phase
Not very important in liquid chromatography except at low flow rates
Resistance to Mass Transfer Resistance to Mass Transfer • Stationary Phase Mass Transfer Stationary Phase Mass Transfer • Mobile Phase Mass Transfer • Multiple Path Effects li l h ff
Stationary Phase Mass Transfer Stationary Phase Mass Transfer • Not all molecules penetrate to p the same extent into the stationary phase – Some Some molecules of the same molecules of the same solute tend to stay longer in the stationary phase than other molecules
Hs = K2 ds2V/Ds ds = the thickness of stationary phase the thickness of stationary phase Ds = the diffusion coefficient of solute in the stationary phase
Mobile Phase Mass Transfer Mobile Phase Mass Transfer •
• •
•
Solute molecules which happen to pass through some stagnant mobile phase through some stagnant mobile phase regions spend longer times before they can leave Molecules which do not encounter such stagnant mobile phase regions move bl h faster Other solute molecules which are g located close to column tubing surface will also move slower than others located at the center (hydrodynamic chromatography) Some solutes which encounter a Some solutes which encounter a channel through the packing material will move much faster than others
HM = K3dp2V/D / M
Multiple Path Effects Multiple Path Effects • Multiple Multiple paths which can paths which can be followed by different molecules contribute to band broadening HE = K4dp
The overall contributions to band b d broadening • Ht = H = HL + H + HS + H + HM + H + HE + H + HV – Ht is the overall height equivalent to a theoretical plate resulting from the contributions of the plate resulting from the contributions of the different factors contributing to band broadening
• Ht = kk1dp + k + k2DM/V + K /V + K3ds2V/Ds + K + K4dp2V/DM • Ht = A + B/V + CSV + CMV
Practical Implications Practical Implications • It It turned out that resistance to mass transfer turned out that resistance to mass transfer terms (K3ds2V/Ds and K4dp2V/DM) are most important in liquid chromatography • Should be minimized by – a. Decreasing particle size gp – b. Decreasing the thickness of stationary phase – c. Working at low flow rates – d. Increase DM by using mobile phases of low viscosities
Practical Implications Practical Implications • The The longitudinal diffusion term (k longitudinal diffusion term (k2DM/V) is the /V) is the most important one in gas chromatography • Reducing this term involves: Reducing this term involves: – a. Working at higher flow rates – b. Decreasing D b D i DM by using carrier gases of higher b i i f hi h viscosities
van Deemter Equation q B H = A + + Cu u
A, B and C are system and operating condition dependent constants
u is the average velocity of mobile phase within the column column A represents eddy diffusion and is due to the variability of path length followed by f th l th f ll db fluid streams (B/u) represents axial diffusion of the component in the mobile f h i h bil phase. (Cu) represents the rate of material transfer between mobile phase and stationary phase.
H B/u opt
H min
Cu opt
u opt
u
A
van Deemter Equation The optimum flow rate can be found by taking the first derivative of equation dH /dV = O ‐ B/V2 + C V is optimum when V is optimum when dH /dV= O , therefore, C = B/V2optimum Voptimum = {B/C}0.5
Theoretically calculated velocity is always small and in practice almost twice as much as its value is used in order to save time
Problem Egg white proteins are being separated by isocratic chromatography using a 10 cm long column having 250 theoretical plates The using a 10 cm long column having 250 theoretical plates. The distribution coefficients for the proteins are as follows Protein Ovalbumin Conalbumin Lysozyme
Distribution coefficient 0 1 5
If the voidage fraction of the column is 0.45 and the mobile phase If the voidage fraction of the column is 0 45 and the mobile phase retention time is 10 minutes, predict the retention time of the three proteins. Comment on the selectivity and resolutions of separations
Solution The residence times of the three proteins can be obtained using the equation ti ⎛ 1− ε ⎞
t R ,ovalb
t R = t M ⎜1 + K⎟ ε ⎝ ⎠ ⎛ 1 − 0.45 ⎞ = 10 ⎜ 1 + × 0 ⎟ = 10 min 0.45 ⎝ ⎠
t R ,conalb
⎛ 1 − 0.45 ⎞ = 10 ⎜ 1 + × 1⎟ = 22.22 min 0.45 ⎝ ⎠
t R ,lys
⎛ 1 − 0.45 ⎞ = 10 ⎜ 1 + × 5 ⎟ = 71.11min 0.45 ⎝ ⎠
The selectivity of separation can be obtained using equation K 2 k 2′ t R 2 − t M α= = = K 1 k1′ t R1 − t M
The selectivity of the three proteins Ovalbumin
Lysozyme
Conalbumin
α conalb / ovalb
⎛1⎞ = ⎜ ⎟ = undefined ⎝0⎠
α lys / conalb
⎛5⎞ =⎜ ⎟=5 ⎝1⎠
The peak width can be determined using the equation
⎛ tR ⎞ N = 16 ⎜ ⎟ ⎝w⎠
2
wovalb
10 = = 2.52 min 250 16
wconalb
22.22 = = 5.62 min 250 16
71.11 wlys = = 2.52 2 52 min 250 16
The resolution can be determined using
t R 2 − t R1 R= 0.5(w1 + w2 )
Rconalb / ovalb
22.22 − 10 = = 2.99 2 99 0.5 ( 2.52 + 5.62 )
Rconalb / ovalb
71.11 71 11 − 22.22 22 22 = = 4.14 0.5 ( 5.62 + 17.99 )
Feasibility: The three proteins are obtained as separate resolved peaks The three proteins are obtained as separate, resolved peaks
Problem A plasmid was found to have a retention time of 10 minutes in a chromatographic column of 0 01 m3 and a voidage fraction 0.3. chromatographic column of 0.01 m and a voidage fraction 0 3 The distribution coefficient of the plasmid is known to be equal to 2. p Calculate the mobile phase retention time and flow rate at which the above separtion was carried out we would like to use the same column mobile phase system to separate the plasmid from RNA (which has a capacity factor of 4 66) (which has a capacity factor of 4.66). Comment on the feasibility
Solution The mobile phase retention time can be calculated using the equation
⎛ 1 − 0.3 ⎞ ⇒ 10 = tM ⎜ 1 + × 2⎟ 0.3 ⎝ ⎠ ⇒ tM = 1.76 .76 min
⎛ 1− ε ⎞ t R = t M ⎜1 + K⎟ ε ⎝ ⎠
The capacity factor of plasmid can be determined using
⎛1− ε ⎞ ′ k = K⎜ ⎟ ⎝ ε ⎠
⎛ 1 − 0.3 ⎞ ′ k = 2⎜ 4 66 ⎟ = 4.66 ⎝ 0.3 ⎠
The capacity factor of RNA is 4.66 too. Therefore 4.66 =1 4.66 Therefore RNA and plasmid cannot be separated by this chromatographic separation process
α=
Problem Albumin is being separated from IgG by isocratic chromatography using a 50 cm column having a voidage fraction of 0.25 and a diameter of 10 mm at a mobile phase flow rate of 10 ml/min diameter of 10 mm at a mobile phase flow rate of 10 ml/min. The distribution coefficients for IgG and albumin are 1 and 0.1 respectively. If the albumin peak has characteristic peak width of 0.52 minutes, p p , predict the selectivity and resolution. When the mobile phase flow rate was increased to 20 ml/min the When the mobile phase flow rate was increased to 20 ml/min the HETP was found to increase by 80%. Predict the selectivity and resolution at the higher flow rate
Total column volume V = L x πd2/4 = 39.25 ~ 39 ml The mobile phase retention time cane be calculated
VC ε = Q
39 × 0.25 tM = min = 0.975 min tM 10 ⎛ 1− ε ⎞ K⎟ The retention times can be calculated using t R = t M ⎜1 + ε ⎝ ⎠ ⎛ 1 − 0.25 ⎞ t R ,alb = 0.975 ⎜ 1 + × 0.1⎟ min = 1.27 min 0.25 ⎝ ⎠ t R , IgG
⎛ 1 − 0.25 ⎞ = 0.975 ⎜ 1 + × 1⎟ min = 3.9 min 0.25 ⎝ ⎠
The number of theoretical plates in the column can be calculated from albumin retention time date using equation ⎛ tR ⎞ N = 16 ⎜ ⎟ ⎝w⎠
2
2
⎛ 1.27 ⎞ N = 16 ⎜ ⎟ = 95 ⎝ 0.52 ⎠
The peak width of IgG can be calculated using equation
⎛ tR ⎞ N = 16 ⎜ ⎟ ⎝w⎠
2
w IgG =
t R , IgG
3.9 = = 1.6 min N 95 16 16
The resolution of separation can be calculated using the equation
t R 2 − t R1 R= 0.5(w1 + w2 )
33.99 − 1.27 1 27 R= = 2.58 0.5 (1.6 + 0.52 )
The selectivity can be calculated using equation The selectivity can be calculated using equation
K2 1 α = = = 10 K1 0 .1 1 The height of a theoretical plate can be calculated using equation
l 50 H= = = 0.526cm N 95
At the higher flow rate, the height of the theoretical plate is increased by 80% . y Therefore
H = 1.8 x 0.526 cm = 0.95 cm
The number of theoretical plates will be reduced to N = 50/0.95 =
52
VC ε 39 × 0.25 tM = = min = 0.4875 min Q 20
The mobile phase retention time at higher flow rate is The mobile phase retention time at higher flow rate is
t R ,alb
⎛ 1 − 0.25 ⎞ = 0.4875 ⎜1 + × 0.1⎟ min = 0.633min 0.25 ⎝ ⎠
The new retention times are
t R , IgG
0 25 ⎞ ⎛ 1 − 0.25 = 0.4875 ⎜ 1 + × 1⎟ min = 1.95 min 0.25 ⎝ ⎠
The peak widths are
w IgG =
walb
t R , IgG
0.633 = min = 0.35 min N 52 16 16
t R ,alb
1.95 1 95 = = min = 1.08 min N 52 16 16
The selectivity is independent of the flow rate, i.e still 10 The resolution is
t R 2 − t R1 1.95 − 0.633 = = 1.84 R= 0 ( w1 + w2 ) 00.5 ( 00.35 0.5 3 + 11.08 08 ) Hence the proteins can still be separated at the higher flow rate Hence the proteins can still be separated at the higher flow rate
′ ⎞ ⎛ α − 1 ⎞⎛⎜ k ave ⎟⎟ R = 0.5 N ⎜ ⎟⎜ ′ ⎠ ⎝ α + 1 ⎠⎝ 1 + k ave
Resolution ′ = 0.5(k1′ + k 2′ ) k ave
⎛ (( t / t 0 ) − 1) 2 C = C 0 exp ⎜⎜ − 2 Shape and yield of peak 2σ ⎝ Chromatographic peak g p p
C0 = Maximum concentration M i t ti t0=Time at which maximum concentration is reached σ2= Variance of the peak = Variance of the peak
12
Concentration
10
C0
8
The total amount of a component eluted (Mtotal) component eluted (M ) from a column
6
4
∞
M Total = Q ∫ C dt
2
t0 0 0
2
4
6
8
w = 4 σ
10
Time
12
14
16
18
20
0
⎞ ⎟⎟ ⎠
The yield of a component in the effluent collected in the time The yield of a component in the effluent collected in the time period t1 to t2 % yield
⎡ ⎢ ⎢ = ⎢ ⎢ ⎢⎣
t2
∫
t1 ∞
∫ 0
⎤ C dt ⎥ ⎥ ⎥ × 100 C dt ⎥ ⎥⎦
The purity of a component A in binary separation (i.e. separation of A and B) in effluent collected in the time period t1 to t of A and B) in effluent collected in the time period t to t2 t2 ⎡ ⎤ C A dt ⎢ ⎥ ∫ t1 ⎢ ⎥ % purity A = ⎢ t2 t2 ⎥ × 100 ⎢ C A dt + C B dt ⎥ ∫t ⎢⎣ ∫t1 ⎥⎦ 1
Chromatogram for A 6 5
Conc. (g/l)
The two chromatograms were obtained for two different compounds A and B by injecting pure samples of these substances into a 30 cm long column into a 30 cm long column
4 3 2 1
We would like to separate A and B from a mixture containing the same amounts of these substances as present in the pure p p samples used for obtaining the chromatograms.
0
2
4
6
8
10
Time (min)
Chromatogram for B 12 10
Conc(g//l)
The mobile phase residence time of the column was found to be 2 minutes and the voidage d h d f fraction was determined to be 0.3.
0
8 6 4 2 0 0
2
4
6
8
10
12
Time (min)
14
16
18
20
Calculate: 1.The selectivity 2.The resolution 3 The respective capacity factors 3.The respective capacity factors 4.The plate height of the chromatographic column 5.The respective distribution coefficients If we collect the column effluent from the start until 7 minutes, calculate: 1.The purity of A in the collected material 2.The percent yield of A in the collected sample
tR1 = 5 min
Chromatogram for A
W1 = 4 min
6
Conc. (g/l) )
5 4 3 2 1 0 0
2
4
6
Time (min)
8
10
Chromatogram for B
W2 = 8 min
tR2 = 10 min 12
Conc(g/l)
10 8 6 4 2 0 0
2
4
6
8
10
12
Ti Time (min) ( i )
14
16
18
20
The selectivity (using 1 as component A and 2 as component B) From chromatograms: tR1 = 5 min and t From chromatograms: t 5 min and tR2 = 10 min; given t 10 min; given tM = 2 min 2 min Selectivity
Resolution
Capacity factors
K 2 k 2′ t R 2 − t M (10 − 2 ) min α= = = = = 2.67 (5 − 2) min K1 k1′ t R1 − t M R=
t R 2 − t R1 10 − 5 = = 0.833 0.5(w1 + w2 ) 0.5(4 + 8)
k1′ =
t R1 ' 3 min = = 1.5 tM 2 min
k 2' =
t R 2 ' 8 min = = 4 .0 tM 2 min i
The plate height of the chromatographic column 2
2 ⎛ t R1 ⎞ ⎛5⎞ ⎟⎟ = 16 ⎜ ⎟ = 25 N1 = number of plates for 1 = 16 ⎜⎜ ⎝4⎠ ⎝ w1 ⎠ 2
2 ⎛ t R2 ⎞ 10 ⎛ ⎞ ⎟⎟ = 16 ⎜ ⎟ = 25 N 2 = number of plates for 2 = 16 ⎜⎜ ⎝8⎠ ⎝ w2 ⎠
l 0 .3 m H = HETP = = = 0.012 m 25 N
Distribution coefficients
K1 =
k1'
K2 =
⎛ ε ⎜ ⎝1− ε
k 2'
⎞ ⎛ 0.3 ⎞ ⎟ = 1 .5 ⎜ ⎟ = 0.643 ⎠ ⎝ 1 − 0 .3 ⎠
⎛ ε ⎞ ⎛ 0 .3 ⎞ ⎟ = 1.71 ⎜ ⎟ = 4 .0 ⎜ ⎝1− ε ⎠ ⎝ 1 − 0.3 ⎠
The purity of A in the collected material ⎡ ⎤ C A dt ⎢ ⎥ ∫ t1 ⎢ ⎥ % purity A = ⎢ t2 t2 ⎥ × 100 ⎢ C A dt + C B dt ⎥ ∫t ⎥⎦ ⎢⎣ ∫t1 1 t2
⎛ (( t / t 0 ) − 1) 2 C = C 0 exp ⎜⎜ − 2 2 σ ⎝
⎞ ⎟⎟ ⎠
⎛ ⎛ t − 5 ⎞2 ⎞ ∫0 C0, A exp ⎜⎜ − ⎜⎝ 2σ A ⎟⎠ ⎟⎟ dt ⎝ ⎠ %A = 7 7 ⎛ ⎛ t − 5 ⎞2 ⎞ ⎛ ⎛ t − 10 ⎞ 2 ⎞ ∫0 C0, A exp ⎜⎜ − ⎜⎝ 2σ A ⎟⎠ ⎟⎟ dt + ∫0 C0, A exp ⎜⎜ − ⎜⎝ 2σ B ⎟⎠ ⎟⎟ dt ⎝ ⎠ ⎝ ⎠ 7
By solving the definite integrals in the above equation we get ⎛ ⎛ 7 − 5 ⎞⎞ ⎛ ⎛ 5 ⎞⎞ 2πσ AC0, A ⎜ Erf ⎜ ⎟ ⎟⎟ + ⎜⎜ Erf ⎜ ⎟ ⎟⎟ ⎜ 2 2 πσ πσ ⎝ ⎝ A ⎠⎠ A ⎠⎠ ⎝ ⎝ %A = ⎛ ⎛ ⎛ 7 −5 ⎞⎞ ⎛ ⎛ 5 ⎞⎞ ⎛ 7 − 10 2πσ AC0, A ⎜ Erf ⎜ + ⎜ Erf ⎜ + 2πσ B C0, B ⎜ Erf ⎜ ⎟ ⎟ ⎟ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎝ 2πσ A ⎠ ⎠ ⎝ ⎝ 2πσ A ⎠ ⎠ ⎝ 2πσ B ⎝ ⎝
w σ= 4
⎞⎞ ⎛ ⎛ 10 ⎟ ⎟⎟ + ⎜⎜ Erf ⎜ ⎠⎠ ⎝ ⎝ 2πσ B
Th f Therefore σ 1 d B = 2 2 A = 1 and σ
⎞⎞ ⎟ ⎟⎟ ⎠⎠
×100
From the chromatograms, C0,A = 5 g/l and C0,B = 10 g/l Substituting the values in the above equation we get %A = 78.5% The yield of A in sample collected from 0 to 7 minutes is given by 7
∫C % y ie ld =
0,A
0
10
∫C 0
0,A
⎛ exp ⎜ − ⎜ ⎝ ⎛ exp ⎜ − ⎜ ⎝
⎛ t − 5 ⎞ ⎞ ⎜ ⎟ ⎟ dt ⎝ 2 σ A ⎠ ⎟⎠ ×100 2 ⎛ t − 5 ⎞ ⎞ ⎜ ⎟ ⎟ dt ⎝ 2 σ A ⎠ ⎟⎠ 2
Solving the definite integrals as previously we get yield of A = 97.7%
Differential migration of two solutes A and B Differential migration of two solutes A and B
Parameters used for the characterisation of differential migration differential migration • Ve – Volume of eluting solvent required to carry the solute through the column until it emerges at its l t th h th l til it t it maximum concentration
• Capacity factor, k • Selectivity or relative retention, α • VT – Th The total volume of a gel column for gel l l f l l f l chromatography
• Gel partition coefficient, Kp • Vi
Ve= Vo+ KpVi
(Ve − Vo ) k= Vo
K 2 k2′ t R 2 − tM α= = = K1 k1′ t R1 − tM VT= Vo+ Vi+ Vs Vi = aWr
– internal volume of liquid in the pores of the particles which is difficult to measure accurately which is difficult to measure accurately Wr ρ g (VT − V0 ) – Vi is usually calculated using a is mass of dry gel (a) Vi = 1 + Wr ρ w and the water regain value (Wr)
Problem: Gel permeation chromatography A pilot‐scale gel‐chromatography column packed with Sephacryl resin is used to separate two hormones A and B. The column is 5 cm in diameter and 0.3m high; the void volume is 1 9x10‐4 m3. volume is 1.9x10 The water regain value of the gel is 3 x 10‐3 m3 kg‐ 1 dry Sephacryl; the density of wet gel is 1.25 x 103 kg m‐3. The partition coefficient for hormone A is 0.38; the partition The partition coefficient for hormone A is 0.38; the partition coefficient for hormone B is 0.15. If the eluant If th l t flow rate is 0.7 l h fl t i 0 7 l h‐11, what is the retention time h t i th t ti ti for each hormone?
The total column volume is: VT= V0 + Vi + Vs VT = π r 2 h = π (2.5 × 10-2 m) 2 (0.3m) = 5.89 × 10-4 m3
Void volume V0 = 1.9x10 ‐4 m3; ρw = 1000 kg m‐3 Internal volume Vi = a Wr
Vi =
Wr ρ g 1 + Wr ρ g
(VT − V0 )
a is mass of dry gel and Wr is the water regain value ρg is the density of wet gel and ρ is the density of wet gel and ρw is the density of water is the density of water ( ×10−3 m3 kg (3 g −1 )( )(1.25 × 103 kgm g −3 −4 3 −4 3 Vi = (5 (5.89 89 × 10 m − 1.9 1 9 × 10 m) −3 3 −1 −3 1 + (3 × 10 m kg )(1000kgm ) = 3.74 ×10−4 m3
Volume of eluting solvent Ve = Vo + KpVi KpA = 0.38 and KpB = 0.15 VeA = 1.9 x 10‐4 m3 + 0.38 (3.74 x 10‐4m3) = 3.32 x 10‐4 m3 VeB = 1.9 x 10‐4 m3 + 0.15 (3.74 x 10‐4m3) = 3.32 x 10‐4 m3 Retention time associated with these elution volumes
3 .3 2 × 1 0 − 4 m 3 tA = = 2 8 m in i 3 1m 1h o u r 0 .7 lh − 1 . 1 0 0 0 l 6 0 m in 2 .4 6 × 1 0 − 4 m 3 tB = = 2 1 m in 3 1m 1h o u r −1 0 .7 7 lh . 1 0 0 0 l 6 0 m in
Selection of the separation l f h mechanism in LC based on the p criteria of sample molecular weight, solubility and conductivity
High performance liquid chromatography (HPLC) h h ( ) • HPLC HPLC uses very high pressures (up to 4000 psi) uses very high pressures (up to 4000 psi) and very small particle size (down to 3 μm) • Four main chromatographic techniques that Four main chromatographic techniques that use a liquid mobile phase – Partition Chromatography (most widely used) P titi Ch t h ( t id l d) – Liquid‐Solid Chromatography – Ion‐Exchange Chromatography h h h – Size Exclusion (Gel Permeation) Chromatography
Factors Influencing the Column Efficiency i i id h in Liquid Chromatography h • • • • • • •
Particle size Particle size Flow rate Thickness of stationary phase Thickness of stationary phase Mobile phase viscosity Diffusion of solute in mobile and stationary phases Diffusion of solute in mobile and stationary phases How well a column is packed Sample size (μg sample/g packing) Sample size (μg sample/g packing) – In RPLC efficiency always decreases as the sample size is increased
Extra‐Column Extra Column Band Broadening Band Broadening • Extra column band broadening becomes very important for small bore columns • Major contributors – Multiple paths effects Multiple paths effects – Longitudinal diffusion – Mass transfer in stationary and mobile phases
• Other sources of band broadening unrelated to column materials and occur outside the column – – – –
Fittings dead volume Fittings dead volume Tubing length and diameter Detector volume I j ti Injection volume l
Instruments for Liquid Chromatography: Pumps h h • Reciprocating pumps – a motor driven reciprocating piston controls the flow of mobile phase with the help of two ball check valves that opens and closes with the piston movement. – The flow is thus not continuous and damping of flow is necessary. The flow is thus not continuous and damping of flow is necessary. – This is accomplished using pulse dampers which are a long coiled capillary tube
• Displacement Pumps – composed of a one directional motor driven plunger that pushes the mobile phase present in a syringe like chamber – The volume of displacement pumps is limited which lacks convenience. A constant flow rate is usually obtained with syringe like pumps constant flow rate is usually obtained with syringe like pumps
• Pneumatic pumps – simplest where a the mobile phase is pushed out of the mobile phase container by the pressure of a pressurized gas. – The flow is dependent on the back pressure of the column and usually the flow is limited to pressures below 2000 psi.
Sample Injection Valves Sample Injection Valves
Columns • Columns are almost always made from stainless steel – with most common dimensions in the range from g 25 cm long and about 4.6 mm internal diameter
• Pellicular or porous packing materials are p p g usually used – Pellicular packings are nonporous glass or polymer are nonporous glass or polymer beads ranging from 30 to 40 μm – Porous packings p g are mostly silica based with y particle diameters from 3‐10 μm
Column type Column type • Analytical Analytical 2.0 2 0 – 3 3 • Microbore 2 – 0.5 • Capillary <0.5 C ill 0
Finger‐tight end fitting column showing frit cap
Removable end fitting column
Radial compression column cartridge
PEEK column PEEK column (poly(ether ether ketone)
PEEK‐o‐bore column Integral guard column
Stand‐alone guard column
Guard columns are used to protect the Guard columns are used to protect the main analytical column
S Some commercially available bonded phases i ll il bl b d d h
Fluorescence UV‐VIS
Detectors
RI
Theoretical protein titration curves, showing how net surface charge varies with pH
Negatively charged proteins Neutral or positively charged proteins charged proteins
Typical affinity purification Affinity medium is equilibrated in binding buffer SSample is applied under conditions that favor specific l i li d d di i h f ifi binding of the target molecule(s) to a complementary binding substance (the ligand). Target substances bind specifically but reversibly to the ligand and bind specifically, but reversibly, to the ligand and unbound material washes through the column Target protein is recovered by changing conditions to Target protein is recovered by changing conditions to favor elution of the bound molecules. Elution is performed specifically, using a competitive ligand, or non‐specifically, by changing the pH, ionic strength or p y, y g g p , g polarity. Target protein is collected in a purified, concentrated form. Affinity medium is re‐equilibrated with binding buffer
Typical affinity chromatogram Typical affinity chromatogram
Common terms in affinity chromatography Matrix: for ligand attachment. Matrix should be chemically and physically inert. Spacer arm: used to improve binding between ligand and target molecule by overcoming any effects of steric hindrance. Ligand: molecule that binds reversibly to a specific target molecule or group of target molecules target molecule or group of target molecules Binding: buffer conditions are optimized to ensure that the target molecules interact buffer conditions are optimized to ensure that the target molecules interact effectively with the ligand and are retained by the affinity medium as all other molecules wash through the column.
Elution: Buffer conditions are changed to reverse (weaken) the interaction between the target molecules and the ligand so that the target molecules can be eluted from the column.
Terminology used in Affinity Chromatography h h • Wash – buffer conditions that wash unbound substances from the column without eluting the target molecules or that re‐equilibrate the column back to the starting conditions (in most cases the binding buffer is back to the starting conditions (in most cases the binding buffer is used as a wash buffer).
• Ligand coupling – covalent attachment of a ligand to a suitable pre‐activated matrix to create an affinity medium.
• Pre Pre‐activated activated matrices matrices – matrices which have been chemically modified to facilitate the coupling of specific types of ligand.
Capacity of ion exchanger Capacity of ion exchanger • Quantitative measure of its ability to take up y p exchangeable counter‐ions • The total ionic capacity – the number of charged substituent groups per gram dry ion exchanger or per ml swollen gel – Measured by titration with a strong acid or base. y g
• Available capacity for the gel – The actual amount of protein which can be bound to an i ion exchanger, under defined experimental conditions h d d fi d i l di i – dynamic capacity for the ion exchanger under defined flow rates
Schematic representation of the methodology based on average surface methodology based on average surface hydrophobicity (φ surface)
Scheme for the refolding of denatured protein with HPHIC.
A, adsorption; D d D, desorption; ti DH, dehydration; H, hydration; MP mobile phase; MP, mobile phase; ST, stationary phase.
Gas chromatography Gas chromatography Gas‐solid chromatography Gas‐liquid Gas liquid chromatography chromatography
Gas chromatography detectors: TCD FID andd ECD TCD,