The Molecular Basis of Separation
The Molecular Basis of Separation Introduction
The separation of a mixture of peptides and proteins in interactive modes of chromatography arises from the differential adsorption of each solute according to their respective affinity for the immobilized stationary phase. Thus, when a particular molecule has a very high affinity for a specific stationary phase, i.e., when the equilibrium distribution coefficient K is high, then that solute is retained to a greater extent than another molecule with a lower affinity for the stationary phase. The degree and nature of the binding affinity is clearly dependent on the structure of the solute and the immobilized ligands. For example, in the case of RPC and HIC, binding is mediated predominantly through hydrophobic interactions between the solute and the immobilized n-alkyl ligands. In IEC, the binding is through electrostatic interactions, whereas in different modes of affinity chromatography, binding involves a mixture of hydrophobic, electrostatic, and polar forces. In the case of size exclusion chromatography, the differential movement along the column is a result of the extent to which each solute can permeate the porous structure of the stationary phase. An additional factor that influences the appearance and relative separation of a peak is the degree of band broadening of the solute band during migration through the column. Thus, as it moves down the column, the solute band broadens as a consequence of a number of factors including longitudinal diffusion, brownian motion, eddy diffusion, and mobile phase and stagnant phase mass transfer. {mosgoogle left} These effects result in band broadening that generally increases with increasing residence time in the column. The resulting degree of separation or selectivity between constituent solutes in a mixture is thus a subtle interplay between the relative affinity of the molecules for the stationary phase and the degree of diffusive processes that occur during separation. Retention and Bandwidth Relationships in Separation The time taken for a solute to pass though a chromatographic column is referred to as the retention time tr. This retention time is measured as the time taken by the solute, following injection, to emerge from the column and to be detected. In order to allow retention times to be compared to different columns or under different conditions, the retention time of a solute is normally compared with the retention time of a molecule which is not retained on the specific column of interest. This allows the unitless capacity factor k′ of a solute to be expressed in terms of the retention time tr, through the relationship k′ = (tr – to) / to (1) where to is the retention time of a non retained solute. The capacity factor k′ can also be defined as the ratio ns/nm where ns and nm are the number of moles of solute in the stationary phase and mobile phase respectively as follows: k′ = ns / nm (2) or alternatively as k′ = [X]s Vs / [X]m Vm (3) where [X]s and [X]m refer to the concentrations of the solute in the stationary and mobile phases, respectively, and Vs and Vm are the corresponding volumes of the stationary and mobile phases. Since the ratio [X]s / [X]m is the equilibrium distribution coefficient K and the ratio Vs / Vm defines the phase ratio Φ of the chromatographic system, the capacity factor can also be expressed as follows: k′ = Φ[X]s / [X]m (4) or k′ = ΦK (5) Equation 5 thus formerly describes the direct thermodynamic relationship between the retention of a peptide or protein and its affinity for the stationary phase material. The practical significance of k′ can be related to the selectivity parameter α, defined as the ratio of the capacity factors of two adjacent peaks as follows: α = k′i / k′j (6) which allows the definition of a chromatographic elution window in which retention times can be manipulated to maximise the separation of components within a mixture. Clearly, the aim is to obtain as high a value of α as possible, which reflects a high degree of separation between two peaks. The second factor involved in defining the quality of a separation is the peak width σt. The degree of peak broadening is directly related to the efficiency of the column and can be expressed in terms of the number of theoretical plates N as follows: N = (tr)2 / σ r2. (7) N can also be expressed in terms of the reduced plate height equivalent h, the column length L, and the particle diameter of the stationary phase material dp, as N = hL / dp. (8) The resolution Rs between two components of a mixture, therefore, depends on both selectivity and bandwidth according to Rs = 1 / 4 √N (α – 1)[1 / (1 + k′)]. (9) This equation describes the relationship between the quality of a separation and the relative retention, selectivity, and the bandwidth. It also provides the formal basis upon which resolution can be manipulated to achieve a particular level of separation. Thus, when faced with an unsatisfactory separation, the aim is to improve resolution by one of three possible strategies. The first is to increase α as previously and the second, but related, approach is to vary k′ within a defined range normally 1 < k′ < 10 through variation in the experimental elution conditions such as solvent strength, separation time, or nature of the immobilized ligand. Third, one can increase N, for example, by using very small particles in microbore or narrow bore columns. An appreciation of the factors that control the resolution of peptides and proteins in interactive modes of chromatography can assist in the development and manipulation of separation protocols to obtain the desired separation. The optimization of high-resolution separations of peptides and proteins involves the separation of sample components through manipulation of both retention times and solute peak shape. An enormous range of different separation techniques are available for peptide and protein analysis. The challenge facing the scientist who wishes to analyze and/or purify their peptide or protein sample is the selection of the initial separation conditions and subsequent optimisation of the appropriate experimental parameters.
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