E. N. Lightfoot

Separation of biomolecules using adsorptive membranes

Abstract The efficient recovery of labile biomolecules requires rapid, reliable separation processes using mild conditions. Adsorptive membranes are available in a range of chemistries and geometries which permit their application as clarification, concentration, fractionation and purification tools in a biorecovery sequence. Available devices exhibit low backpressure, short residence times and high volumetric throughputs relative to conventional chromatographic packed beds. Non-uniform flow, dead volumes and backmixing observed in some adsorptive membrane systems preclude them from achieving substantial improvements in resolution relative to conventional packed beds. Improvements in design and operation of these systems should increase their separation performance tenfold. Adsorptive separations using affinity, ion-exchange and hydrophobic membranes are reviewed.

Adsorptive membrane chromatography for purification of plasmid DNA.

Adsorptive membranes were investigated for the downstream processing of plasmid DNA by quantifying both separation efficiencies and adsorption uptake with the anion-exchange membranes. Separation efficiencies of the 10-ml Mustang-Q were measured using pulses of 6.1-kilo base pair plasmid DNA and lysozyme tracers, and comparing the responses for both conventional and reverse-flow operation. The plasmid exhibited nearly 200 plates/cm, almost as high efficiency as the protein despite the large difference in size. This behavior contrasts strongly with typical behavior for spherical porous particle packings, which predicted large decreases in efficiency with increases in tracer size. Batch adsorption isotherms for the 6.1-kilo base pair plasmid on small sheets of anion-exchange membranes at various ionic strengths showed high capacities for very large biomolecules. The maximum binding capacity for the membrane unit was calculated as 10 mg plasmid/ml, an order of magnitude greater than typical values reported for porous beads.

Protein retention in hydrophobic interaction chromatography : modeling variation with buffer ionic strength and column hydrophobicity

The variation in protein retention times with protein and surface hydrophobicity and mobile phase composition and concentration has been described with a simple thermodynamic model. Column capacity factors for two proteins have been measured as a function of mobile phase ionic strength for a series of columns with varying levels of hydrophobicity. Application of the model to these data suggests that the protein retention is dominated by the release of water molecules upon adsorption, which is consistent with the entropically driven nature of hydrophobic interactions. The calculated number of water molecules released agrees with estimates based on the reduction in hydrophobic surface area for adsorption.

Mathematical modelling of dynamics and control in metabolic networks. I. On michaelis-menten kinetics*

As a starting point for modeling of metabolic networks this paper considers the simple Michaelis-Menten reaction mechanism. After the elimination of diffusional effects a mathematically intractable mass action kinetic model is obtained. The properties of this model are explored via scaling and linearization. The scaling is carried out such that kinetic properties, concentration parameters and external influences are clearly separated. We then try to obtain reasonable estimates for values of the dimensionless groups and examine the dynamic properties of the model over this part of the parameter space. Linear analysis is found to give excellent insight into reaction dynamics and it also gives a forum for understanding and justifying the two commonly used quasi-stationary and quasi-equilibrium analyses. The first finding is that there are two separate time scales inherent in the model existing over most of the parameter space, and in particular over the regions of importance here. Full modal analysis gives a new interpretation of quasi-stationary analysis, and its extension via singular perturbation theory, and a rationalization of the quasi-equilibrium approximation. The new interpretation of the quasi-steady state assumption is that the applicability is intimately related to dynamic interactions between the concentration variables rather than the traditional notion that a quasi-stationary state is reached, after a short transient period, where the rates of formation and decomposition of the enzyme intermediate are approximately equal. The modal analysis reveals that the generally used criterion for the applicability of quasi-stationary analysis that total enzyme concentration must be much less than total substrate concentration, et much less than St, is incomplete and that the criterion et much less than Km much less than St (Km is the well known Michaelis constant) is the appropriate one. The first inequality (et much less than Km) guarantees agreement over the longer time scale leading to quasi-stationary behavior or the applicability of the zeroth order outer singular perturbation solution but the second half of the criterion (Km much less than St) justifies zeroth order inner singular perturbation solution where the substrate concentration is assumed to be invariant. Furthermore linear analysis shows that when a fast mode representing the binding of substrate to the enzyme is fast it can be relaxed leading to the quasi-equilibrium assumption. The influence of the dimensionless groups is ascertained by integrating the equations numerically, and the predictions made by the linear analysis are found to be accurate.(ABSTRACT TRUNCATED AT 400 WORDS)

Flow distribution in chromatographic columns

Abstract It becomes increasingly clear that flow non-uniformity frequently limits the performance of chromatographic columns, and that there are at least two major causes for this: non-uniform packing and inadequate header design. Static magnetic resonance imaging (MRI) of small columns in this laboratory has confirmed previous reports of packing non-uniformity and found void fractions to be smallest in the neighborhood of the wall while the central and upstream regions of the column are more loosely packed. Both static and flow MRI suggests that additional mal-distribution is introduced by non-uniform flow in headers, especially for short columns. Flow non-uniformity can reduce resolution directly, and it can also limit column capacity through perturbation-induced viscous fingering. A preliminary stress–strain analysis during column packing is reported which shows that the stress distribution depends strongly upon column aspect ratio (length/diameter) and is most favorable for low values. At the same time adequate flow distribution becomes more difficult as this ratio decreases, and this requires careful attention to the column headers. We therefore suggest a new strategy for header design and provide two specific examples which produce very nearly uniform residence time for all streamlines as well as uniform exit velocity.

Predictability of chromatographic protein separations: Study of size-exclusion media with narrow particle size distributions

Abstract It is shown that existing models of differential chromatography are capable of predicting the behavior of polydisperse packings in commercially available columns in terms of separately determined transport and equilibrium properties. Experiments conducted using proteins on size-exclusion media with a narrow particle size distribution indicate that such packings perform as well as predicted by theory of their more expensive monodisperse counterparts. These results confirm theoretical studies and previous data suggesting that a modest degree of polydispersity has no significant effect on separation efficiency, thus allowing the direct design of large columns from basic transport and equilibrium data.

A convective mass transfer model for determining intestinal wall permeabilities: laminar flow in a circular tube.

Abstract A convective mass transfer model as analyzed and developed for use in determining intestinal wall permeabilities from external perfusion experiments. Analysis of the model indicates that the ratio of the exit to inlet concentration C m C 0 is a function of only two dimensionless independent variables, the wall permeability, P w ∗ and Graetz number, Gz = πDL/2Q. The Graetz number contains the independent variables of interest, length, diflusivity, and flow rate. The radius of the intestine is included implicitly in the flow rate. Since C m C 0 and Gz are the experimental quantities, and the solution to the model system contains Pω∗ implicitly, a convenient approximate method is developed which allows a direct calculation of Pω∗. This method is in error by 10–20% in the worst cases. The approach is illustrated by application to the determination of the wall permeabilities for two non polar compounds.

Can Membrane Cascades Replace Chromatography? Adapting Binary Ideal Cascade Theory of Systems of Two Solutes in a Single Solvent

Abstract It is suggested that the adoption of efficient counterflow cascades may accelerate the continuing encroachment of membranes on chromatography for downstream processing of biologicals, and a specific numerical example is provided to demonstrate their effectiveness. Emphasis is on three‐stage ideal cascades, and it is shown that one may begin using the traditional batch operating mode. Conversion to continuous operation is then both simple and straightforward. Membrane cascades are the only means so far available for true continuous downstream processing of therapeutic proteins, which is a natural extension of the continuous upstream processes already beginning to be used for industrial production. Membranes are also attractive for larger entities such as plasmids or viruses whose low diffusivities can severely limit use of chromatographic processes.

Prediction of mass transfer rates in spatially periodic flows

Abstract The application of mass transfer boundary layer theory to spatially periodic flows is investigated. Numerical methods are used to solve the flow problems, and the solutions are used in conjunction with mass transfer boundary layer theory to predict mass transfer rates. This approach is advantageous because at large Schmidt numbers numerical solution for the concentration profiles requires very high numerical resolution in the boundary layer region. For the two prototype flows investigated, tube bank flow and Taylor–Couette flow, the predictions agree reasonably well with the experimental results. As a result, this approach should be useful for preliminary design calculations in spatially periodic systems.

Refining the scale-up of chromatographic separations.

The use of heavily loaded columns and complex processing conditions makes scale-up of chromatographic separations a non-trivial process. The wide ranges of process conditions that must be investigated demands that a large number of preliminary experiments must usually be made in small columns and laboratory-scale work stations. These preliminary data can be biased by improper column packing, poor distributors and dispersion in auxiliary apparatus, and it is important to understand these disturbing factors in detail. Moreover, it is precisely at this macroscopic level that our understanding of the chromatographic process is weakest, for large columns as well as small. This paper addresses three of these factors: Efficient elimination of peripheral effects and characterization of both header flow distribution and packing non-uniformity. This will be done using a variety of experimental and analytical approaches including nuclear magnetic resonance imaging, computational fluid dynamics and mass transfer, and careful experimentation.